Finite Group Databasebeta

← C2×#24921249 #36312869

Subgroups — C2×#24921249 #36312869

Order 21248.

11534 conjugacy classes of subgroups.

The subgroup lattice has 1528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581839C211yesmaximal, characteristic, complemented
2C22×#14581837C211yesmaximal, characteristic, complemented
3#24921249C2132yesmaximal, direct product factor
4C2×#19128361C211yesmaximal, characteristic, complemented
5C2×#19128360C211yesmaximal, characteristic, complemented
6C2×#19128359C211yesmaximal, characteristic, complemented
7C2×#19128357C211yesmaximal, characteristic, complemented
8C2×#19128346C211yesmaximal, characteristic, complemented
9C2×#19128345C211yesmaximal, characteristic, complemented
10C2×#19128343C212yesmaximal, complemented
11C2×#19128341C212yesmaximal, complemented
12C2×#19128340C212yesmaximal, complemented
13C2×#19128339C211yesmaximal, characteristic, complemented
14C2×#19128338C212yesmaximal, complemented
15C2×#19128274C211yesmaximal, characteristic, complemented
16C2×#19128273C212yesmaximal, complemented
17C2×#19128267C211yesmaximal, characteristic, complemented
18C2×#19128266C212yesmaximal, complemented
19C2×#19128248C211yesmaximal, characteristic, complemented
20C2×#19128246C212yesmaximal, complemented
21C22×#14581778C212yesmaximal, complemented
22C2×#124×D83C211yesmaximal, characteristic, complemented
23C2×C4×#13050589C211yesmaximal, characteristic, complemented
24C2×#546×C83C211yesmaximal, characteristic, complemented
25C2×#14581839—216no—
26C2×#14581839C22116yescomplemented
27C2×#14581837—216no—
28C2×#14581837C22116yescomplemented
29C22×#13050590C2211yescharacteristic
30C22×#13050590C2211yescharacteristic
31C22×#13050590C2212yescomplemented
32C22×#13050590C2211yescharacteristic, complemented
33C22×#13050589C2211yescharacteristic
34C22×#13050589C2212yes—
35C22×#13050589C2211yescharacteristic
36C22×#13050589C2212yescomplemented
37C22×#13050589C2211yescharacteristic, complemented
38C22×#13050589C2212yescomplemented
39C23×Dic166C2211yescharacteristic, complemented
40C23×Dic166C2212yescomplemented
41C22×Q8×D83C2211yescharacteristic, complemented
42C22×Q8×D83C2211yescharacteristic, complemented
43C23×C22⋊D83C2212yes—
44C23×C22⋊D83C2212yes—
45C22×D4×D83C2211yescharacteristic
46C22×D4×D83C2212yes—
47C22×D4×D83C2211yescharacteristic
48#19128361C22116yescomplemented
49#19128360C22116yescomplemented
50#19128359C22116yescomplemented
51#19128357C22116yescomplemented
52#19128346C22116yescomplemented
53#19128345C22116yescomplemented
54#19128343C22132yescomplemented
55#19128341C22132yescomplemented
56#19128340C22132yescomplemented
57#19128339C22116yescomplemented
58#19128338C22132yescomplemented
59#19128274C22116yescomplemented
60#19128273C22132yescomplemented
61#19128267C22116yescomplemented
62#19128266C22132yescomplemented
63#19128248C22116yescomplemented
64#19128246C22132yescomplemented
65C2×#14581791C2212yescomplemented
66C2×#14581791C2211yescharacteristic, complemented
67C2×#14581788C2212yescomplemented
68C2×#14581788C2211yescharacteristic, complemented
69C2×#14581781C2211yescharacteristic, complemented
70C2×#14581780C2211yescharacteristic, complemented
71C2×#14581779C2211yescharacteristic, complemented
72C2×#14581778C2212yescomplemented
73C2×#14581778C2212yescomplemented
74C2×#14581778C2212yescomplemented
75C2×#14581778C2212yescomplemented
76C2×#14581778C2212yescomplemented
77C2×#14581778C2212yescomplemented
78C2×#14581778C2211yescharacteristic, complemented
79C2×#14581778C2212yescomplemented
80C2×#14581778C2212yescomplemented
81C2×#14581778C2211yescharacteristic, complemented
82C2×#14581778C22132yescomplemented
83#124×D83C22116yescomplemented
84C2×#14581777C2212yescomplemented
85C2×#14581776C2212yescomplemented
86C2×#14581775C2212yescomplemented
87C2×#14581774C2212yescomplemented
88C2×#14581773C2212yescomplemented
89C2×#14581772C2211yescharacteristic, complemented
90C2×#14581771C2211yescharacteristic, complemented
91C2×#14581770C2212yescomplemented
92C2×#14581770C2212yescomplemented
93C2×#14581769C2212yescomplemented
94C2×#14581769C2212yescomplemented
95C2×#14581768C2211yescharacteristic, complemented
96C2×#14581767C2211yescharacteristic, complemented
97C2×#14581767C2211yescharacteristic, complemented
98C2×#14581766C2211yescharacteristic, complemented
99C2×#14581766C2212yescomplemented
100C2×#14581765C2211yescharacteristic, complemented
101C2×#14581765C2211yescharacteristic, complemented
102C2×#14581765C2212yescomplemented
103C2×#14581765C2212yescomplemented
104C2×#14581764C2212yescomplemented
105C2×#14581764C2212yescomplemented
106C2×#14581764C2212yescomplemented
107C2×#14581764C2212yescomplemented
108C2×#14581763C2211yescharacteristic, complemented
109C2×#14581763C2211yescharacteristic, complemented
110C2×#14581762C2212yescomplemented
111C2×#14581762C2212yescomplemented
112C2×#14581761C2212yescomplemented
113C2×#14581760C2212yescomplemented
114C2×#14581760C2212yescomplemented
115C4×#13050589C22116yescomplemented
116C2×C4×Dic166C2211yescharacteristic, complemented
117C2×#14581757C2211yescharacteristic, complemented
118C2×C4×D332C2211yescharacteristic, complemented
119C2×D4×Dic83C2211yescharacteristic, complemented
120C2×D4×Dic83C2212yescomplemented
121C2×#14581754C2212yescomplemented
122C2×C4×C22⋊D83C2212yescomplemented
123C2×C4×C22⋊D83C2211yescharacteristic, complemented
124C2×C4×C22⋊D83C2211yescharacteristic, complemented
125C2×(C22⋊D83)⋊C4C2212yescomplemented
126C2×(C22⋊D83)⋊C4C2212yescomplemented
127C2×(C22⋊D83)⋊C4C2212yescomplemented
128C2×#14581750C2211yescharacteristic, complemented
129C2×#14581748C2212yescomplemented
130C22×C22⋊Dic83C2212yescomplemented
131C22×(C2×D83)⋊C4C2212yescomplemented
132C22×(C2×D83)⋊C4C2212yescomplemented
133C2×C22⋊C4×D83C2212yescomplemented
134C2×C22⋊C4×D83C2212yescomplemented
135C22×C4×Dic83C2212yescomplemented
136C2×C42×D83C2211yescharacteristic, complemented
137C22×#41×C83C2211yescharacteristic, complemented
138C23×D4×C83C2211yescharacteristic
139#546×C83C22116yescomplemented
140C2×#124×C83C2211yescharacteristic, complemented
141C2×#123×C83C2212yescomplemented
142C2×C22⋊Q8×C83C2211yescharacteristic, complemented
143C2×#121×C83C2212yescomplemented
144C2×#121×C83C2211yescharacteristic, complemented
145C2×#120×C83C2212yescomplemented
146C2×C4×D4×C83C2211yescharacteristic, complemented
147C2×C4×D4×C83C2211yescharacteristic, complemented
148C22×C22⋊C4×C83C2212yescomplemented
149C24×D83C2312yes—
150C24×D83C2312yes—
151#14581839—2128no—
152#14581837—2128no—
153C2×#13050590—28no—
154C2×#13050590—216no—
155C2×#13050590—28no—
156C2×#13050590—28no—
157C2×#13050590C2318yes—
158C2×#13050590C2318yes—
159C2×#13050590C23116yescomplemented
160C2×#13050590C2318yescomplemented
161C2×#13050589—28no—
162C2×#13050589—216no—
163C2×#13050589—216no—
164C2×#13050589—216no—
165C2×#13050589—28no—
166C2×#13050589D4116yescomplemented
167C2×#13050589C2318yes—
168C2×#13050589C23116yes—
169C2×#13050589C2318yes—
170C2×#13050589C23116yescomplemented
171C2×#13050589C2318yescomplemented
172C2×#13050589C23116yescomplemented
173C22×Dic166—28no—
174C22×Dic166—216no—
175C22×Dic166C2312yes—
176C22×Dic166C2312yes—
177C22×Dic166C2311yescharacteristic
178C22×Dic166C2312yes—
179C22×Dic166C2311yescharacteristic
180C22×Dic166C2311yescharacteristic
181C22×Dic166C2311yescharacteristic
182C22×Dic166C2318yescomplemented
183C22×Dic166C23116yescomplemented
184C2×Q8×D83—28no—
185C2×Q8×D83—28no—
186C2×Q8×D83C2318yescomplemented
187C2×Q8×D83C2318yescomplemented
188C22×D332C2311yescharacteristic
189C22×D332C2311yescharacteristic
190C22×D332C2311yescharacteristic
191C22×D332C2312yes—
192C22×D332C2311yescharacteristic
193C22×C22⋊D83—216no—
194C22×C22⋊D83—216no—
195C22×C22⋊D83C23116yes—
196C22×C22⋊D83C2311yescharacteristic
197C22×C22⋊D83C2312yes—
198C22×C22⋊D83C2311yescharacteristic
199C22×C22⋊D83C2312yes—
200C22×C22⋊D83C2312yes—
201C22×C22⋊D83C2312yes—
202C22×C22⋊D83C2312yes—
203C22×C22⋊D83C2311yescharacteristic
204C22×C22⋊D83C23116yes—
205C22×C22⋊D83C2311yescharacteristic
206C22×C22⋊D83C2312yes—
207C22×C22⋊D83C2312yes—
208C22×C22⋊D83C2311yescharacteristic
209C22×C22⋊D83C2311yescharacteristic
210C22×C22⋊D83C2312yes—
211C2×D4×D83—216no—
212C2×D4×D83—28no—
213C2×D4×D83—28no—
214C2×D4×D83C2318yes—
215C2×D4×D83C23116yes—
216C2×D4×D83C2318yes—
217C23×Dic83C2312yes—
218C23×Dic83C2312yes—
219C23×Dic83C2312yes—
220C23×Dic83C2312yes—
221C23×Dic83C2312yes—
222C22×C4×D83C2312yes—
223C22×C4×D83C2312yes—
224C22×C4×D83C2312yes—
225C22×C4×D83C2311yescharacteristic
226C22×C4×D83C2311yescharacteristic
227C22×C4×D83C2311yescharacteristic
228C22×C4×D83C2311yescharacteristic
229C22×C4×D83C2311yescharacteristic
230#14581791C23116yescomplemented
231#14581791C2318yescomplemented
232#14581788C23116yescomplemented
233#14581788C2318yescomplemented
234#14581781C2318yescomplemented
235#14581780C2318yescomplemented
236#14581779C2318yescomplemented
237#14581778C23116yescomplemented
238#14581778C23116yescomplemented
239#14581778C23116yescomplemented
240#14581778C23116yescomplemented
241#14581778C23116yescomplemented
242#14581778C23116yescomplemented
243#14581778C2318yescomplemented
244#14581778C23116yescomplemented
245#14581778C23116yescomplemented
246#14581778C2318yescomplemented
247#14581777C23116yescomplemented
248#14581776C23116yescomplemented
249#14581775C23116yescomplemented
250#14581774C23116yescomplemented
251#14581773C23116yescomplemented
252#14581772C2318yescomplemented
253#14581771C2318yescomplemented
254#14581770C23116yescomplemented
255#14581770C23116yescomplemented
256#14581769C23116yescomplemented
257#14581769C23116yescomplemented
258#14581768C2318yescomplemented
259#14581767C2318yescomplemented
260#14581767C2318yescomplemented
261#14581766C2318yescomplemented
262#14581766C23116yescomplemented
263#14581765C2318yescomplemented
264#14581765C2318yescomplemented
265#14581765C23116yescomplemented
266#14581765C23116yescomplemented
267#14581764C23116yescomplemented
268#14581764C23116yescomplemented
269#14581764C23116yescomplemented
270#14581764C23116yescomplemented
271#14581763C2318yescomplemented
272#14581763C2318yescomplemented
273#14581762C23116yescomplemented
274#14581762C23116yescomplemented
275#14581761C23116yescomplemented
276#14581760C23116yescomplemented
277#14581760C23116yescomplemented
278C4×Dic166C2318yescomplemented
279#14581757C2318yescomplemented
280C4×D332C2318yescomplemented
281D4×Dic83C23116yescomplemented
282D4×Dic83C2318yescomplemented
283#14581754C23116yescomplemented
284C4×C22⋊D83C2318yescomplemented
285C4×C22⋊D83C23116yescomplemented
286C4×C22⋊D83C2318yescomplemented
287(C22⋊D83)⋊C4C23116yescomplemented
288(C22⋊D83)⋊C4C23116yescomplemented
289(C22⋊D83)⋊C4C23116yescomplemented
290#14581750C2318yescomplemented
291#14581748C23116yescomplemented
292C2×C4⋊Dic83C2311yescharacteristic
293C2×C4⋊Dic83C2312yes—
294C2×C4⋊Dic83C2311yescharacteristic
295C2×Dic83⋊C4C2312yes—
296C2×Dic83⋊C4C2312yes—
297C2×Dic83⋊C4C2312yes—
298C2×Dic83⋊C4C2312yes—
299C2×Dic83⋊C4C2311yescharacteristic
300C2×Dic83⋊C4C2311yescharacteristic
301C2×C22⋊Dic83C2312yes—
302C2×C22⋊Dic83C2312yes—
303C2×C22⋊Dic83C2311yescharacteristic
304C2×C22⋊Dic83C2312yes—
305C2×C22⋊Dic83C2312yes—
306C2×C22⋊Dic83C2312yes—
307C2×C22⋊Dic83C2311yescharacteristic
308C2×C22⋊Dic83C23116yescomplemented
309C2×(C2×D83)⋊C4C2312yes—
310C2×(C2×D83)⋊C4C2312yes—
311C2×(C2×D83)⋊C4C2312yes—
312C2×(C2×D83)⋊C4C2312yes—
313C2×(C2×D83)⋊C4C2311yescharacteristic
314C2×(C2×D83)⋊C4C2311yescharacteristic
315C2×(C2×D83)⋊C4C2312yes—
316C2×(C2×D83)⋊C4C2312yes—
317C2×(C2×D83)⋊C4C2312yes—
318C2×(C2×D83)⋊C4C2312yes—
319C2×(C2×D83)⋊C4C2312yes—
320C2×(C2×D83)⋊C4C2311yescharacteristic
321C2×(C2×D83)⋊C4C2311yescharacteristic
322C2×(C2×D83)⋊C4C23116yescomplemented
323C2×(C2×D83)⋊C4C23116yescomplemented
324C22⋊C4×D83C23116yescomplemented
325C22⋊C4×D83C23116yescomplemented
326C2×C4×Dic83C2311yescharacteristic
327C2×C4×Dic83C2311yescharacteristic
328C2×C4×Dic83C2311yescharacteristic
329C2×C4×Dic83C2312yes—
330C2×C4×Dic83C2312yes—
331C2×C4×Dic83C2312yes—
332C2×C4×Dic83C23116yescomplemented
333C42×D83C2318yescomplemented
334C25×C83C2312yes—
335C2×#41×C83—28no—
336C2×#41×C83C2318yescomplemented
337C22×Q8×C83C2311yescharacteristic
338C22×D4×C83—28no—
339C22×D4×C83C2318yes—
340C22×D4×C83C2312yes—
341C22×D4×C83C2312yes—
342C22×D4×C83C2311yescharacteristic
343C22×D4×C83C2311yescharacteristic
344C22×D4×C83C2312yes—
345C22×D4×C83C2311yescharacteristic
346C23×C4×C83C2312yes—
347C23×C4×C83C2311yescharacteristic
348C23×C4×C83C2311yescharacteristic
349C23×C4×C83C2312yes—
350#124×C83C2318yescomplemented
351#123×C83C23116yescomplemented
352C22⋊Q8×C83C2318yescomplemented
353#121×C83C23116yescomplemented
354#121×C83C2318yescomplemented
355#120×C83C23116yescomplemented
356C4×D4×C83C2318yescomplemented
357C4×D4×C83C2318yescomplemented
358C2×C4⋊C4×C83C2311yescharacteristic
359C2×C4⋊C4×C83C2311yescharacteristic
360C2×C4⋊C4×C83C2312yes—
361C2×C22⋊C4×C83C2311yescharacteristic
362C2×C22⋊C4×C83C2312yes—
363C2×C22⋊C4×C83C2312yes—
364C2×C22⋊C4×C83C2312yes—
365C2×C22⋊C4×C83C2312yes—
366C2×C22⋊C4×C83C2311yescharacteristic
367C2×C22⋊C4×C83C2312yes—
368C2×C22⋊C4×C83C23116yescomplemented
369C2×C42×C83C2311yescharacteristic
370C23×D83—28no—
371C23×D83—28no—
372C23×D83—44no—
373C23×D83—44no—
374C23×D83—44no—
375C23×D83—44no—
376C23×D83C2411yescharacteristic
377C23×D83C2412yes—
378C23×D83C2411yescharacteristic
379C23×D83C2411yescharacteristic
380C23×D83C2418yes—
381C23×D83C2418yes—
382#13050590—264no—
383#13050590—232no—
384#13050590—232no—
385#13050590—232no—
386#13050589—232no—
387#13050589—264no—
388#13050589—264no—
389#13050589—264no—
390#13050589—232no—
391#13050589C2×D4164yescomplemented
392C2×Dic166—24no—
393C2×Dic166—28no—
394C2×Dic166—28no—
395C2×Dic166—28no—
396C2×Dic166—24no—
397C2×Dic166—264no—
398C2×Dic166—24no—
399C2×Dic166—232no—
400C2×Dic166C2×D418yes—
401C2×Dic166C2418yes—
402C2×Dic166C2418yes—
403C2×Dic166C2414yes—
404C2×Dic166C2418yes—
405C2×Dic166C2414yes—
406C2×Dic166C2414yes—
407C2×Dic166C2414yes—
408Q8×D83—232no—
409Q8×D83—232no—
410C2×D332—24no—
411C2×D332—24no—
412C2×D332—24no—
413C2×D332—44no—
414C2×D332—42no—
415C2×D332C2414yes—
416C2×D332C2414yes—
417C2×D332C2414yes—
418C2×D332C2414yes—
419C2×D332C2418yes—
420C2×C22⋊D83—28no—
421C2×C22⋊D83—28no—
422C2×C22⋊D83—24no—
423C2×C22⋊D83—24no—
424C2×C22⋊D83—264no—
425C2×C22⋊D83—28no—
426C2×C22⋊D83—28no—
427C2×C22⋊D83—28no—
428C2×C22⋊D83—24no—
429C2×C22⋊D83—264no—
430C2×C22⋊D83—24no—
431C2×C22⋊D83—42no—
432C2×C22⋊D83—42no—
433C2×C22⋊D83—44no—
434C2×C22⋊D83—44no—
435C2×C22⋊D83C2×D4116yes—
436C2×C22⋊D83C2414yes—
437C2×C22⋊D83C2418yes—
438C2×C22⋊D83C2414yes—
439C2×C22⋊D83C2418yes—
440C2×C22⋊D83C2418yes—
441C2×C22⋊D83C2418yes—
442C2×C22⋊D83C2418yes—
443C2×C22⋊D83C2414yes—
444C2×C22⋊D83C2414yes—
445C2×C22⋊D83C2414yes—
446C2×C22⋊D83C2418yes—
447C2×C22⋊D83C2414yes—
448C2×C22⋊D83C2418yes—
449C2×C22⋊D83C2418yes—
450D4×D83—232no—
451D4×D83—264no—
452D4×D83—232no—
453C22×Dic83—28no—
454C22×Dic83—28no—
455C22×Dic83—28no—
456C22×Dic83—44no—
457C22×Dic83C2×D4116yes—
458C22×Dic83C2418yes—
459C22×Dic83C2418yes—
460C22×Dic83C2418yes—
461C22×Dic83C2411yescharacteristic
462C22×Dic83C2412yes—
463C22×Dic83C2411yescharacteristic
464C22×Dic83C2411yescharacteristic
465C22×Dic83C2411yescharacteristic
466C22×Dic83C2412yes—
467C22×Dic83C2418yes—
468C22×Dic83C2412yes—
469C22×Dic83C2411yescharacteristic
470C22×Dic83C2418yes—
471C2×C4×D83—28no—
472C2×C4×D83—24no—
473C2×C4×D83—24no—
474C2×C4×D83—28no—
475C2×C4×D83—28no—
476C2×C4×D83—42no—
477C2×C4×D83—42no—
478C2×C4×D83C2×D418yes—
479C2×C4×D83C2414yes—
480C2×C4×D83C2418yes—
481C2×C4×D83C2414yes—
482C2×C4×D83C2418yes—
483C2×C4×D83C2418yes—
484C2×C4×D83C2414yes—
485C2×C4×D83C2414yes—
486C2×C4×D83C2414yes—
487C4⋊Dic83C2414yes—
488C4⋊Dic83C2414yes—
489C4⋊Dic83C2418yes—
490Dic83⋊C4C2418yes—
491Dic83⋊C4C2418yes—
492Dic83⋊C4C2418yes—
493Dic83⋊C4C2418yes—
494Dic83⋊C4C2414yes—
495Dic83⋊C4C2414yes—
496C22⋊Dic83C2418yes—
497C22⋊Dic83C2418yes—
498C22⋊Dic83C2418yes—
499C22⋊Dic83C2418yes—
500C22⋊Dic83C2414yes—
501C22⋊Dic83C2414yes—
502C22⋊Dic83C2418yes—
503(C2×D83)⋊C4C2418yes—
504(C2×D83)⋊C4C2418yes—
505(C2×D83)⋊C4C2418yes—
506(C2×D83)⋊C4C2418yes—
507(C2×D83)⋊C4C2418yes—
508(C2×D83)⋊C4C2418yes—
509(C2×D83)⋊C4C2418yes—
510(C2×D83)⋊C4C2414yes—
511(C2×D83)⋊C4C2418yes—
512(C2×D83)⋊C4C2414yes—
513(C2×D83)⋊C4C2414yes—
514(C2×D83)⋊C4C2418yes—
515(C2×D83)⋊C4C2414yes—
516C4×Dic83C2414yes—
517C4×Dic83C2414yes—
518C4×Dic83C2418yes—
519C4×Dic83C2418yes—
520C4×Dic83C2418yes—
521C4×Dic83C2414yes—
522C24×C83—28no—
523C24×C83—44no—
524C24×C83—44no—
525C24×C83C2411yescharacteristic
526C24×C83C2412yes—
527C24×C83C2411yescharacteristic
528C24×C83C2412yes—
529C24×C83C2418yes—
530#41×C83—232no—
531C2×Q8×C83—24no—
532C2×Q8×C83C2414yes—
533C2×D4×C83—28no—
534C2×D4×C83—28no—
535C2×D4×C83—232no—
536C2×D4×C83—24no—
537C2×D4×C83—44no—
538C2×D4×C83—42no—
539C2×D4×C83C2×D418yes—
540C2×D4×C83C2418yes—
541C2×D4×C83C2414yes—
542C2×D4×C83C2418yes—
543C2×D4×C83C2418yes—
544C2×D4×C83C2414yes—
545C2×D4×C83C2414yes—
546C22×C4×C83—28no—
547C22×C4×C83—24no—
548C22×C4×C83—24no—
549C22×C4×C83—44no—
550C22×C4×C83C2414yes—
551C22×C4×C83C2414yes—
552C22×C4×C83C2418yes—
553C22×C4×C83C2411yescharacteristic
554C22×C4×C83C2412yes—
555C22×C4×C83C2411yescharacteristic
556C22×C4×C83C2411yescharacteristic
557C22×C4×C83C2411yescharacteristic
558C22×C4×C83C2412yes—
559C22×C4×C83C2418yes—
560C22×C4×C83C2411yescharacteristic
561C4⋊C4×C83C2414yes—
562C4⋊C4×C83C2414yes—
563C4⋊C4×C83C2418yes—
564C22⋊C4×C83C2418yes—
565C22⋊C4×C83C2418yes—
566C22⋊C4×C83C2418yes—
567C22⋊C4×C83C2418yes—
568C22⋊C4×C83C2414yes—
569C22⋊C4×C83C2414yes—
570C22⋊C4×C83C2418yes—
571C42×C83C2414yes—
572C23×C83—24no—
573C23×C83—24no—
574C23×C83—22no—
575C23×C83—22no—
576C23×C83—24no—
577C23×C83—22no—
578C23×C83—22no—
579C23×C83—24no—
580C23×C83—22no—
581C23×C83—22no—
582C23×C83—24no—
583C23×C83—216no—
584C23×C83—48no—
585C23×C83—48no—
586C23×C83—816no—
587C23×C83C22×D418yes—
588C23×C83C2512yes—
589C23×C83C2514yes—
590C23×C83C2512yes—
591C23×C83C2514yes—
592C23×C83C2511yescharacteristic
593C22×D83—22no—
594C22×D83—22no—
595C22×D83—22no—
596C22×D83—22no—
597C22×D83—24no—
598C22×D83—22no—
599C22×D83—22no—
600C22×D83—22no—
601C22×D83—24no—
602C22×D83—24no—
603C22×D83—22no—
604C22×D83—216no—
605C22×D83—216no—
606C22×D83—48no—
607C22×D83—48no—
608C22×D83—48no—
609C22×D83—48no—
610C22×D83—816no—
611C22×D83—816no—
612C22×D83C22×D414yes—
613C22×D83C2512yes—
614C22×D83C2514yes—
615C22×D83C2512yes—
616C22×D83C2512yes—
617Q8×C83—28no—
618D4×C83—216no—
619D4×C83—216no—
620D4×C83—28no—
621D4×C83—44no—
622D4×C83—48no—
623D4×C83C22×D4116yes—
624C2×C4×C83—22no—
625C2×C4×C83—22no—
626C2×C4×C83—24no—
627C2×C4×C83—216no—
628C2×C4×C83—22no—
629C2×C4×C83—24no—
630C2×C4×C83—22no—
631C2×C4×C83—28no—
632C2×C4×C83—28no—
633C2×C4×C83—48no—
634C2×C4×C83C22×D414yes—
635C2×C4×C83C2512yes—
636C2×C4×C83C2512yes—
637C2×C4×C83C2514yes—
638C2×C4×C83C2512yes—
639C2×C4×C83C2514yes—
640C2×C4×C83C2512yes—
641C2×C4×C83C2512yes—
642C22⋊D83—216no—
643C22⋊D83—216no—
644C22⋊D83—28no—
645C22⋊D83—28no—
646C22⋊D83—216no—
647C22⋊D83—216no—
648C22⋊D83—28no—
649C22⋊D83—216no—
650C22⋊D83—28no—
651C22⋊D83—44no—
652C22⋊D83—44no—
653C22⋊D83—48no—
654C22⋊D83—48no—
655C22⋊D83C22×D4132yes—
656C2×Dic83—22no—
657C2×Dic83—24no—
658C2×Dic83—22no—
659C2×Dic83—216no—
660C2×Dic83—22no—
661C2×Dic83—22no—
662C2×Dic83—24no—
663C2×Dic83—216no—
664C2×Dic83—216no—
665C2×Dic83—48no—
666C2×Dic83C22×D418yes—
667C2×Dic83C22×D414yes—
668C2×Dic83C22×D4132yes—
669C2×Dic83C2512yes—
670C2×Dic83C2514yes—
671C2×Dic83C2512yes—
672C2×Dic83C2512yes—
673C2×Dic83C2514yes—
674C2×Dic83C2512yes—
675C2×Dic83C2512yes—
676C2×Dic83C2514yes—
677D332—28no—
678D332—28no—
679D332—28no—
680D332—44no—
681D332—48no—
682C4×D83—216no—
683C4×D83—28no—
684C4×D83—28no—
685C4×D83—216no—
686C4×D83—216no—
687C4×D83—44no—
688C4×D83—44no—
689C4×D83C22×D4116yes—
690Dic166—28no—
691Dic166—216no—
692Dic166—216no—
693Dic166—28no—
694Dic166—216no—
695Dic166—28no—
696Dic166C22×D4116yes—
697C22×C83—24no—
698C22×C83—24no—
699C22×C83—216no—
700C22×C83—22no—
701C22×C83—24no—
702C22×C83—22no—
703C22×C83—22no—
704C22×C83—22no—
705C22×C83—24no—
706C22×C83—22no—
707C22×C83—24no—
708C22×C83—22no—
709C22×C83—48no—
710C22×C83—44no—
711C22×C83—44no—
712C22×C83—816no—
713C22×C83C23×D418yes—
714C22×C83C23×D412yes—
715C22×C83#58512yes—
716C22×C83#58512yes—
717C22×C83C2611yescharacteristic
718C2×D83—22no—
719C2×D83—22no—
720C2×D83—28no—
721C2×D83—22no—
722C2×D83—22no—
723C2×D83—24no—
724C2×D83—22no—
725C2×D83—22no—
726C2×D83—24no—
727C2×D83—22no—
728C2×D83—22no—
729C2×D83—24no—
730C2×D83—44no—
731C2×D83—48no—
732C2×D83—44no—
733C2×D83—816no—
734C2×D83—816no—
735C2×D83C23×D414yes—
736C4×C83—22no—
737C4×C83—24no—
738C4×C83—22no—
739C4×C83—22no—
740C4×C83—22no—
741C4×C83—24no—
742C4×C83C23×D414yes—
743Dic83—24no—
744Dic83—22no—
745Dic83—22no—
746Dic83—22no—
747Dic83—22no—
748Dic83—24no—
749Dic83C23×D414yes—
750Dic83C23×D418yes—
751C2×#3500—831nomaximal, Sylow
752C2×C83—28no—
753C2×C83—44no—
754C2×C83—42no—
755C2×C83—42no—
756C2×C83#350014yescomplemented
757C2×C83C24×D411yescharacteristic
758C2×C83C2×#58511yescharacteristic
759C2×C83C2×#58511yescharacteristic
760D83—24no—
761D83—42no—
762D83—44no—
763D83—42no—
764C22×2−1+4—831no—
765C22×H(5,𝔽2)—831no—
766#3500—8332no—
767C2×#548—831no—
768C2×#548—831no—
769C2×#548—831no—
770C2×#548—831no—
771C2×#546—831no—
772C2×#546—831no—
773C2×#546—832no—
774C2×#546—832no—
775C2×#546—832no—
776C2×#546—831no—
777C2×#546—832no—
778C2×#546D8311yescharacteristic, complemented
779C2×#536—832no—
780C2×#536—831no—
781C2×#535—831no—
782C2×#535—832no—
783C2×#532—832no—
784C2×#532—831no—
785C22×#124—831no—
786C22×#124—832no—
787C2×C4×#41—831no—
788C83C2×#350011yescharacteristic, complemented, Sylow
789C2×2−1+4—8316no—
790C2×2−1+4—16616no—
791C2×H(5,𝔽2)—8316no—
792C2×H(5,𝔽2)—16616no—
793C22×#41—831no—
794C22×#41—832no—
795C22×#41—831no—
796C22×#41—832no—
797C22×#41—831no—
798C22×#41—832no—
799C22×#41—831no—
800C22×#41—831no—
801C22×#41—831no—
802C22×#41—832no—
803C22×#41C2×D8311yescharacteristic, complemented
804C23×Q8—831no—
805C23×Q8—831no—
806C23×Q8—832no—
807C23×Q8—831no—
808C23×D4—832no—
809C23×D4—832no—
810C23×D4—831no—
811C23×D4—832no—
812C23×D4—831no—
813C23×D4C2×D8311yescharacteristic
814#548—8316no—
815#548—8316no—
816#548—8316no—
817#548—8316no—
818#546—8316no—
819#546—8316no—
820#546—8332no—
821#546—8332no—
822#546—8332no—
823#546—8316no—
824#546—8332no—
825#546C2×D83116yescomplemented
826#536—8332no—
827#536—8316no—
828#535—8316no—
829#535—8332no—
830#532—8332no—
831#532—8316no—
832C2×C4⋊Q8—832no—
833C2×C4⋊Q8—831no—
834C2×#127—832no—
835C2×#127—831no—
836C2×#124—831no—
837C2×#124—831no—
838C2×#124—8316no—
839C2×#124—832no—
840C2×#124—831no—
841C2×#124—832no—
842C2×#124—832no—
843C2×#124—832no—
844C2×#124—832no—
845C2×#124—832no—
846C2×#124—832no—
847C2×#124—832no—
848C2×#124—831no—
849C2×#124—8332no—
850C2×#124—831no—
851C2×#124C2×D8311yescharacteristic, complemented
852C2×#123—832no—
853C2×#123—832no—
854C2×#123—832no—
855C2×#123—832no—
856C2×#123—832no—
857C2×#123C2×D8312yescomplemented
858C2×C22⋊Q8—831no—
859C2×C22⋊Q8—831no—
860C2×C22⋊Q8—832no—
861C2×C22⋊Q8—832no—
862C2×C22⋊Q8—831no—
863C2×C22⋊Q8—832no—
864C2×C22⋊Q8—832no—
865C2×C22⋊Q8C2×D8311yescharacteristic, complemented
866C2×#121—831no—
867C2×#121—832no—
868C2×#121—832no—
869C2×#121—831no—
870C2×#121—832no—
871C2×#121—832no—
872C2×#121—832no—
873C2×#121—831no—
874C2×#121—831no—
875C2×#121—831no—
876C2×#121—831no—
877C2×#121—831no—
878C2×#121—832no—
879C2×#121—832no—
880C2×#121C2×D8312yescomplemented
881C2×#121C2×D8311yescharacteristic, complemented
882C2×#120—832no—
883C2×#120—832no—
884C2×#120—832no—
885C2×#120—832no—
886C2×#120—832no—
887C2×#120C2×D8312yescomplemented
888C4×#41—8316no—
889C2×C4×Q8—831no—
890C2×C4×Q8—831no—
891C2×C4×D4—831no—
892C2×C4×D4—832no—
893C2×C4×D4—832no—
894C2×C4×D4—831no—
895C2×C4×D4—831no—
896C2×C4×D4—832no—
897C2×C4×D4—832no—
898C2×C4×D4—832no—
899C2×C4×D4—832no—
900C2×C4×D4—831no—
901C2×C4×D4C2×D8311yescharacteristic, complemented
902C2×C4×D4C2×D8311yescharacteristic, complemented
903C2×#117—831no—
904C2×#117—832no—
905C22×C22⋊C4—832no—
906C22×C22⋊C4—832no—
907C22×C22⋊C4—832no—
908C22×C22⋊C4—832no—
909C22×C22⋊C4—832no—
910C22×C22⋊C4C2×D8312yescomplemented
911C22×C42—832no—
912C22×C42—831no—
913C25—832no—
914C25—832no—
915C25C22×D8312yes—
9162−1+4—166128no—
917H(5,𝔽2)—166128no—
918C2×#41—28no—
919C2×#41—8316no—
920C2×#41—838no—
921C2×#41—8316no—
922C2×#41—8316no—
923C2×#41—838no—
924C2×#41—8316no—
925C2×#41—838no—
926C2×#41—838no—
927C2×#41—838no—
928C2×#41—8316no—
929C2×#41—838no—
930C2×#41—1668no—
931C2×#41—1668no—
932C2×#41—16616no—
933C2×#41—1668no—
934C2×#41—16616no—
935C2×#41—16616no—
936C2×#41—16616no—
937C2×#41—1668no—
938C2×#41—1668no—
939C2×#41C22×D8318yescomplemented
940C22×Q8—838no—
941C22×Q8—838no—
942C22×Q8—831no—
943C22×Q8—832no—
944C22×Q8—832no—
945C22×Q8—831no—
946C22×Q8—832no—
947C22×Q8—831no—
948C22×Q8—8316no—
949C22×Q8—831no—
950C22×Q8—838no—
951C22×Q8—16616no—
952C22×Q8—1668no—
953C22×Q8—1668no—
954C22×Q8—1668no—
955C22×Q8C22×D8311yescharacteristic
956C22×D4—28no—
957C22×D4—831no—
958C22×D4—832no—
959C22×D4—832no—
960C22×D4—831no—
961C22×D4—832no—
962C22×D4—831no—
963C22×D4—832no—
964C22×D4—831no—
965C22×D4—832no—
966C22×D4—832no—
967C22×D4—832no—
968C22×D4—832no—
969C22×D4—831no—
970C22×D4—8316no—
971C22×D4—831no—
972C22×D4—8316no—
973C22×D4—838no—
974C22×D4—8316no—
975C22×D4—838no—
976C22×D4—832no—
977C22×D4—831no—
978C22×D4—831no—
979C22×D4—831no—
980C22×D4—831no—
981C22×D4—1668no—
982C22×D4—16616no—
983C22×D4—16616no—
984C22×D4—16616no—
985C22×D4—1668no—
986C22×D4C22×D8312yes—
987C22×D4C22×D8312yes—
988C22×D4C22×D8311yescharacteristic
989C22×D4C22×D8318yes—
990C22×D4C22×D8312yes—
991C22×D4C22×D8311yescharacteristic
992C22×D4C22×D8311yescharacteristic
993C23×C4—832no—
994C23×C4—831no—
995C23×C4—831no—
996C23×C4—832no—
997C23×C4—831no—
998C23×C4—832no—
999C23×C4—832no—
1000C23×C4—832no—
1001C23×C4—832no—
1002C23×C4—832no—
1003C23×C4—831no—
1004C23×C4—832no—
1005C23×C4—831no—
1006C23×C4C22×D8312yes—
1007C23×C4C22×D8311yescharacteristic
1008C23×C4C22×D8311yescharacteristic
1009C23×C4C22×D8312yes—
1010C4⋊Q8—8316no—
1011C4⋊Q8—838no—
1012#127—8316no—
1013#127—838no—
1014#124—838no—
1015#124—838no—
1016#124—8316no—
1017#124—838no—
1018#124—8316no—
1019#124—8316no—
1020#124—8316no—
1021#124—8316no—
1022#124—8316no—
1023#124—8316no—
1024#124—8316no—
1025#124—838no—
1026#124—838no—
1027#124C22×D8318yescomplemented
1028#123—8316no—
1029#123—8316no—
1030#123—8316no—
1031#123—8316no—
1032#123—8316no—
1033#123C22×D83116yescomplemented
1034C22⋊Q8—838no—
1035C22⋊Q8—838no—
1036C22⋊Q8—8316no—
1037C22⋊Q8—8316no—
1038C22⋊Q8—838no—
1039C22⋊Q8—8316no—
1040C22⋊Q8—8316no—
1041C22⋊Q8C22×D8318yescomplemented
1042#121—838no—
1043#121—838no—
1044#121—8316no—
1045#121—8316no—
1046#121—8316no—
1047#121—8316no—
1048#121—8316no—
1049#121—838no—
1050#121—838no—
1051#121—838no—
1052#121—838no—
1053#121—838no—
1054#121—8316no—
1055#121—8316no—
1056#121C22×D83116yescomplemented
1057#121C22×D8318yescomplemented
1058#120—8316no—
1059#120—8316no—
1060#120—8316no—
1061#120—8316no—
1062#120—8316no—
1063#120C22×D83116yescomplemented
1064C4×Q8—838no—
1065C4×Q8—838no—
1066C4×D4—838no—
1067C4×D4—8316no—
1068C4×D4—8316no—
1069C4×D4—838no—
1070C4×D4—838no—
1071C4×D4—8316no—
1072C4×D4—8316no—
1073C4×D4—8316no—
1074C4×D4—8316no—
1075C4×D4—838no—
1076C4×D4C22×D8318yescomplemented
1077C4×D4C22×D8318yescomplemented
1078#117—838no—
1079#117—8316no—
1080C2×C4⋊C4—832no—
1081C2×C4⋊C4—832no—
1082C2×C4⋊C4—831no—
1083C2×C4⋊C4—831no—
1084C2×C4⋊C4—832no—
1085C2×C4⋊C4—832no—
1086C2×C4⋊C4—831no—
1087C2×C4⋊C4—832no—
1088C2×C4⋊C4—831no—
1089C2×C4⋊C4C22×D8311yescharacteristic
1090C2×C4⋊C4C22×D8312yes—
1091C2×C4⋊C4C22×D8311yescharacteristic
1092C2×C22⋊C4—832no—
1093C2×C22⋊C4—831no—
1094C2×C22⋊C4—832no—
1095C2×C22⋊C4—832no—
1096C2×C22⋊C4—832no—
1097C2×C22⋊C4—8316no—
1098C2×C22⋊C4—832no—
1099C2×C22⋊C4—831no—
1100C2×C22⋊C4—832no—
1101C2×C22⋊C4—831no—
1102C2×C22⋊C4—831no—
1103C2×C22⋊C4—832no—
1104C2×C22⋊C4—832no—
1105C2×C22⋊C4—832no—
1106C2×C22⋊C4—832no—
1107C2×C22⋊C4—832no—
1108C2×C22⋊C4—832no—
1109C2×C22⋊C4—832no—
1110C2×C22⋊C4—8316no—
1111C2×C22⋊C4—8316no—
1112C2×C22⋊C4—832no—
1113C2×C22⋊C4—831no—
1114C2×C22⋊C4—831no—
1115C2×C22⋊C4—8316no—
1116C2×C22⋊C4—8316no—
1117C2×C22⋊C4C22×D8312yes—
1118C2×C22⋊C4C22×D8312yes—
1119C2×C22⋊C4C22×D8311yescharacteristic
1120C2×C22⋊C4C22×D8312yes—
1121C2×C22⋊C4C22×D8312yes—
1122C2×C22⋊C4C22×D8312yes—
1123C2×C22⋊C4C22×D8311yescharacteristic
1124C2×C22⋊C4C22×D83116yescomplemented
1125C2×C42—832no—
1126C2×C42—831no—
1127C2×C42—832no—
1128C2×C42—832no—
1129C2×C42—831no—
1130C2×C42—8316no—
1131C2×C42—831no—
1132C2×C42—838no—
1133C2×C42C22×D8311yescharacteristic
1134C24—28no—
1135C24—44no—
1136C24—44no—
1137C24—3324no—
1138C24—3324no—
1139C24—3324no—
1140C24—3324no—
1141C24—838no—
1142C24—838no—
1143C24—831no—
1144C24—832no—
1145C24—831no—
1146C24—831no—
1147C24—1668no—
1148C24—1668no—
1149C24C23×D8312yes—
1150C24C23×D8311yescharacteristic
1151C24C23×D8311yescharacteristic
1152C24C23×D8312yes—
1153C24C23×D8318yes—
1154#41—232no—
1155#41—8364no—
1156#41—16632no—
1157#41—16632no—
1158#41—16664no—
1159#41—16632no—
1160#41—16664no—
1161#41—16664no—
1162#41—16664no—
1163#41—16632no—
1164#41—16632no—
1165C2×Q8—24no—
1166C2×Q8—838no—
1167C2×Q8—834no—
1168C2×Q8—838no—
1169C2×Q8—838no—
1170C2×Q8—834no—
1171C2×Q8—838no—
1172C2×Q8—834no—
1173C2×Q8—834no—
1174C2×Q8—1664no—
1175C2×Q8—1668no—
1176C2×Q8—1668no—
1177C2×Q8—1668no—
1178C2×Q8—16664no—
1179C2×Q8—1664no—
1180C2×Q8—16632no—
1181C2×Q8—16632no—
1182C2×Q8—16632no—
1183C2×Q8—1664no—
1184C2×Q8C23×D8314yes—
1185C2×D4—28no—
1186C2×D4—28no—
1187C2×D4—232no—
1188C2×D4—24no—
1189C2×D4—44no—
1190C2×D4—42no—
1191C2×D4—3324no—
1192C2×D4—3322no—
1193C2×D4—3322no—
1194C2×D4—3322no—
1195C2×D4—3324no—
1196C2×D4—3324no—
1197C2×D4—834no—
1198C2×D4—838no—
1199C2×D4—838no—
1200C2×D4—834no—
1201C2×D4—8316no—
1202C2×D4—838no—
1203C2×D4—834no—
1204C2×D4—838no—
1205C2×D4—834no—
1206C2×D4—838no—
1207C2×D4—838no—
1208C2×D4—838no—
1209C2×D4—838no—
1210C2×D4—834no—
1211C2×D4—834no—
1212C2×D4—838no—
1213C2×D4—834no—
1214C2×D4—834no—
1215C2×D4—834no—
1216C2×D4—834no—
1217C2×D4—1664no—
1218C2×D4—1664no—
1219C2×D4—16632no—
1220C2×D4—1664no—
1221C2×D4—1668no—
1222C2×D4—1668no—
1223C2×D4—1668no—
1224C2×D4—16664no—
1225C2×D4—1664no—
1226C2×D4—16664no—
1227C2×D4—16664no—
1228C2×D4—1664no—
1229C2×D4—1664no—
1230C2×D4—1668no—
1231C2×D4—1668no—
1232C2×D4—16632no—
1233C2×D4—1664no—
1234C2×D4D4×D8318yes—
1235C2×D4C23×D8318yes—
1236C2×D4C23×D8318yes—
1237C2×D4C23×D8314yes—
1238C2×D4C23×D8318yes—
1239C2×D4C23×D8314yes—
1240C2×D4C23×D8314yes—
1241C22×C4—28no—
1242C22×C4—24no—
1243C22×C4—24no—
1244C22×C4—44no—
1245C22×C4—3322no—
1246C22×C4—3322no—
1247C22×C4—3324no—
1248C22×C4—838no—
1249C22×C4—834no—
1250C22×C4—834no—
1251C22×C4—8316no—
1252C22×C4—838no—
1253C22×C4—831no—
1254C22×C4—832no—
1255C22×C4—838no—
1256C22×C4—834no—
1257C22×C4—838no—
1258C22×C4—838no—
1259C22×C4—838no—
1260C22×C4—831no—
1261C22×C4—831no—
1262C22×C4—832no—
1263C22×C4—831no—
1264C22×C4—832no—
1265C22×C4—831no—
1266C22×C4—838no—
1267C22×C4—838no—
1268C22×C4—834no—
1269C22×C4—838no—
1270C22×C4—834no—
1271C22×C4—1668no—
1272C22×C4—1668no—
1273C22×C4—1668no—
1274C22×C4—1668no—
1275C22×C4—1668no—
1276C22×C4—1668no—
1277C22×C4—1664no—
1278C22×C4—1664no—
1279C22×C4C23×D8318yes—
1280C22×C4C23×D8314yes—
1281C22×C4C23×D8314yes—
1282C22×C4C23×D8311yescharacteristic
1283C22×C4C23×D8312yes—
1284C22×C4C23×D8311yescharacteristic
1285C22×C4C23×D8312yes—
1286C22×C4C23×D8311yescharacteristic
1287C22×C4C23×D8311yescharacteristic
1288C22×C4C23×D8318yes—
1289C22×C4C23×D8311yescharacteristic
1290C4⋊C4—838no—
1291C4⋊C4—838no—
1292C4⋊C4—834no—
1293C4⋊C4—834no—
1294C4⋊C4—838no—
1295C4⋊C4—838no—
1296C4⋊C4—834no—
1297C4⋊C4—838no—
1298C4⋊C4—834no—
1299C4⋊C4C23×D8314yes—
1300C4⋊C4C23×D8318yes—
1301C4⋊C4C23×D8314yes—
1302C22⋊C4—838no—
1303C22⋊C4—834no—
1304C22⋊C4—838no—
1305C22⋊C4—838no—
1306C22⋊C4—838no—
1307C22⋊C4—838no—
1308C22⋊C4—834no—
1309C22⋊C4—838no—
1310C22⋊C4—834no—
1311C22⋊C4—834no—
1312C22⋊C4—838no—
1313C22⋊C4—838no—
1314C22⋊C4—838no—
1315C22⋊C4—838no—
1316C22⋊C4—838no—
1317C22⋊C4—838no—
1318C22⋊C4—838no—
1319C22⋊C4—838no—
1320C22⋊C4—834no—
1321C22⋊C4—834no—
1322C22⋊C4C23×D8318yes—
1323C22⋊C4C23×D8318yes—
1324C22⋊C4C23×D8314yes—
1325C22⋊C4C23×D8318yes—
1326C22⋊C4C23×D8318yes—
1327C22⋊C4C23×D8318yes—
1328C22⋊C4C23×D8314yes—
1329C42—834no—
1330C42—838no—
1331C42—834no—
1332C42—838no—
1333C42—838no—
1334C42—834no—
1335C42C23×D8314yes—
1336C23—24no—
1337C23—24no—
1338C23—22no—
1339C23—22no—
1340C23—24no—
1341C23—22no—
1342C23—24no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23—24no—
1347C23—216no—
1348C23—48no—
1349C23—48no—
1350C23—816no—
1351C23—3328no—
1352C23—3328no—
1353C23—3328no—
1354C23—3328no—
1355C23—834no—
1356C23—832no—
1357C23—834no—
1358C23—832no—
1359C23—832no—
1360C23—66416no—
1361C23—66416no—
1362C23—16616no—
1363C23—1662no—
1364C23—1664no—
1365C23—1662no—
1366C23—1662no—
1367C23—1664no—
1368C23—1662no—
1369C23—1662no—
1370C23—1662no—
1371C23—1664no—
1372C23—16616no—
1373C23—1662no—
1374C23—1662no—
1375C23C2×D4×D8318yes—
1376C23C24×D8314yes—
1377C23C24×D8312yes—
1378C23C24×D8312yes—
1379C23C24×D8314yes—
1380C23C24×D8311yescharacteristic
1381Q8—28no—
1382Q8—8316no—
1383Q8—1668no—
1384Q8—16616no—
1385Q8—16616no—
1386Q8—16616no—
1387Q8—1668no—
1388Q8—1668no—
1389D4—216no—
1390D4—216no—
1391D4—28no—
1392D4—48no—
1393D4—44no—
1394D4—3328no—
1395D4—3324no—
1396D4—3324no—
1397D4—3324no—
1398D4—3328no—
1399D4—3328no—
1400D4—8332no—
1401D4—1668no—
1402D4—1668no—
1403D4—1668no—
1404D4—16616no—
1405D4—16616no—
1406D4—16616no—
1407D4—1668no—
1408D4—1668no—
1409D4—1668no—
1410D4—16616no—
1411D4—16616no—
1412D4—1668no—
1413D4C2×D4×D83116yes—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—216no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—22no—
1421C2×C4—28no—
1422C2×C4—28no—
1423C2×C4—48no—
1424C2×C4—3324no—
1425C2×C4—3324no—
1426C2×C4—3328no—
1427C2×C4—834no—
1428C2×C4—838no—
1429C2×C4—8332no—
1430C2×C4—832no—
1431C2×C4—834no—
1432C2×C4—8316no—
1433C2×C4—832no—
1434C2×C4—832no—
1435C2×C4—834no—
1436C2×C4—832no—
1437C2×C4—834no—
1438C2×C4—832no—
1439C2×C4—16616no—
1440C2×C4—16616no—
1441C2×C4—16616no—
1442C2×C4—16616no—
1443C2×C4—16616no—
1444C2×C4—1662no—
1445C2×C4—1664no—
1446C2×C4—1662no—
1447C2×C4—16616no—
1448C2×C4—1662no—
1449C2×C4—1662no—
1450C2×C4—1664no—
1451C2×C4—1668no—
1452C2×C4—1668no—
1453C2×C4C2×D4×D8314yes—
1454C2×C4C24×D8312yes—
1455C2×C4C24×D8314yes—
1456C2×C4C24×D8312yes—
1457C2×C4C24×D8314yes—
1458C2×C4C24×D8312yes—
1459C2×C4C24×D8312yes—
1460C2×C4C24×D8312yes—
1461C22—24no—
1462C22—24no—
1463C22—216no—
1464C22—22no—
1465C22—22no—
1466C22—24no—
1467C22—22no—
1468C22—24no—
1469C22—22no—
1470C22—22no—
1471C22—22no—
1472C22—24no—
1473C22—44no—
1474C22—48no—
1475C22—44no—
1476C22—816no—
1477C22—3324no—
1478C22—3328no—
1479C22—3324no—
1480C22—834no—
1481C22—66416no—
1482C22—66416no—
1483C22—1662no—
1484C22—1664no—
1485C22—1662no—
1486C22—1662no—
1487C22—1664no—
1488C22—1662no—
1489C22—1662no—
1490C22—1662no—
1491C22—1664no—
1492C22—1662no—
1493C22—1662no—
1494C22—1668no—
1495C22C22×D4×D8318yes—
1496C22C22×D4×D8312yes—
1497C22#1912853612yes—
1498C22#1912853712yes—
1499C22C25×D8311yescharacteristic
1500C4—22no—
1501C4—22no—
1502C4—24no—
1503C4—22no—
1504C4—24no—
1505C4—22no—
1506C4—834no—
1507C4—838no—
1508C4—1662no—
1509C4—1664no—
1510C4—1662no—
1511C4—1662no—
1512C4—1662no—
1513C4—1664no—
1514C4C22×D4×D8314yes—
1515C2—28no—
1516C2—42no—
1517C2—44no—
1518C2—42no—
1519C2—3322no—
1520C2—3324no—
1521C2—3322no—
1522C2—1664no—
1523C2#2492124914yesdirect product factor
1524C2C23×D4×D8311yescharacteristic
1525C2C2×#1912853611yescharacteristic
1526C2C2×#1912853711yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#546×C83C2
socleC23×C83C25
hypercenterC2×#546D83
hypocenterC83C2×#3500
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#14581839C2semidirect
2. C22×#14581837C2semidirect
3. #24921249C2direct (N × H)
4. C2×#19128361C2semidirect
5. C2×#19128360C2semidirect
6. C2×#19128359C2semidirect
7. C2×#19128357C2semidirect
8. C2×#19128346C2semidirect
9. C2×#19128345C2semidirect
10. C2×#19128343C2semidirect
11. C2×#19128341C2semidirect
12. C2×#19128340C2semidirect
13. C2×#19128339C2semidirect
14. C2×#19128338C2semidirect
15. C2×#19128274C2semidirect
16. C2×#19128273C2semidirect
17. C2×#19128267C2semidirect
18. C2×#19128266C2semidirect
19. C2×#19128248C2semidirect
20. C2×#19128246C2semidirect
21. C22×#14581778C2semidirect
22. C2×#124×D83C2semidirect
23. C2×C4×#13050589C2semidirect
24. C2×#546×C83C2semidirect
26. C2×#14581839C22semidirect
28. C2×#14581837C22semidirect
31. C22×#13050590C22semidirect
32. C22×#13050590C22semidirect
36. C22×#13050589C22semidirect
37. C22×#13050589C22semidirect
38. C22×#13050589C22semidirect
39. C23×Dic166C22semidirect
40. C23×Dic166C22semidirect
41. C22×Q8×D83C22semidirect
42. C22×Q8×D83C22semidirect
48. #19128361C22semidirect
49. #19128360C22semidirect
50. #19128359C22semidirect
51. #19128357C22semidirect
52. #19128346C22semidirect
53. #19128345C22semidirect
54. #19128343C22semidirect
55. #19128341C22semidirect
56. #19128340C22semidirect
57. #19128339C22semidirect
58. #19128338C22semidirect
59. #19128274C22semidirect
60. #19128273C22semidirect
61. #19128267C22semidirect
62. #19128266C22semidirect
63. #19128248C22semidirect
64. #19128246C22semidirect
65. C2×#14581791C22semidirect
66. C2×#14581791C22semidirect
67. C2×#14581788C22semidirect
68. C2×#14581788C22semidirect
69. C2×#14581781C22semidirect
70. C2×#14581780C22semidirect
71. C2×#14581779C22semidirect
72. C2×#14581778C22semidirect
73. C2×#14581778C22semidirect
74. C2×#14581778C22semidirect
75. C2×#14581778C22semidirect
76. C2×#14581778C22semidirect
77. C2×#14581778C22semidirect
78. C2×#14581778C22semidirect
79. C2×#14581778C22semidirect
80. C2×#14581778C22semidirect
81. C2×#14581778C22semidirect
82. C2×#14581778C22semidirect
83. #124×D83C22semidirect
84. C2×#14581777C22semidirect
85. C2×#14581776C22semidirect
86. C2×#14581775C22semidirect
87. C2×#14581774C22semidirect
88. C2×#14581773C22semidirect
89. C2×#14581772C22semidirect
90. C2×#14581771C22semidirect
91. C2×#14581770C22semidirect
92. C2×#14581770C22semidirect
93. C2×#14581769C22semidirect
94. C2×#14581769C22semidirect
95. C2×#14581768C22semidirect
96. C2×#14581767C22semidirect
97. C2×#14581767C22semidirect
98. C2×#14581766C22semidirect
99. C2×#14581766C22semidirect
100. C2×#14581765C22semidirect
101. C2×#14581765C22semidirect
102. C2×#14581765C22semidirect
103. C2×#14581765C22semidirect
104. C2×#14581764C22semidirect
105. C2×#14581764C22semidirect
106. C2×#14581764C22semidirect
107. C2×#14581764C22semidirect
108. C2×#14581763C22semidirect
109. C2×#14581763C22semidirect
110. C2×#14581762C22semidirect
111. C2×#14581762C22semidirect
112. C2×#14581761C22semidirect
113. C2×#14581760C22semidirect
114. C2×#14581760C22semidirect
115. C4×#13050589C22semidirect
116. C2×C4×Dic166C22semidirect
117. C2×#14581757C22semidirect
118. C2×C4×D332C22semidirect
119. C2×D4×Dic83C22semidirect
120. C2×D4×Dic83C22semidirect
121. C2×#14581754C22semidirect
122. C2×C4×C22⋊D83C22semidirect
123. C2×C4×C22⋊D83C22semidirect
124. C2×C4×C22⋊D83C22semidirect
125. C2×(C22⋊D83)⋊C4C22semidirect
126. C2×(C22⋊D83)⋊C4C22semidirect
127. C2×(C22⋊D83)⋊C4C22semidirect
128. C2×#14581750C22semidirect
129. C2×#14581748C22semidirect
130. C22×C22⋊Dic83C22semidirect
131. C22×(C2×D83)⋊C4C22semidirect
132. C22×(C2×D83)⋊C4C22semidirect
133. C2×C22⋊C4×D83C22semidirect
134. C2×C22⋊C4×D83C22semidirect
135. C22×C4×Dic83C22semidirect
136. C2×C42×D83C22semidirect
137. C22×#41×C83C22semidirect
139. #546×C83C22semidirect
140. C2×#124×C83C22semidirect
141. C2×#123×C83C22semidirect
142. C2×C22⋊Q8×C83C22semidirect
143. C2×#121×C83C22semidirect
144. C2×#121×C83C22semidirect
145. C2×#120×C83C22semidirect
146. C2×C4×D4×C83C22semidirect
147. C2×C4×D4×C83C22semidirect
148. C22×C22⋊C4×C83C22semidirect
159. C2×#13050590C23semidirect
160. C2×#13050590C23semidirect
166. C2×#13050589D4semidirect
170. C2×#13050589C23semidirect
171. C2×#13050589C23semidirect
172. C2×#13050589C23semidirect
182. C22×Dic166C23semidirect
183. C22×Dic166C23semidirect
186. C2×Q8×D83C23semidirect
187. C2×Q8×D83C23semidirect
230. #14581791C23semidirect
231. #14581791C23semidirect
232. #14581788C23semidirect
233. #14581788C23semidirect
234. #14581781C23semidirect
235. #14581780C23semidirect
236. #14581779C23semidirect
237. #14581778C23semidirect
238. #14581778C23semidirect
239. #14581778C23semidirect
240. #14581778C23semidirect
241. #14581778C23semidirect
242. #14581778C23semidirect
243. #14581778C23semidirect
244. #14581778C23semidirect
245. #14581778C23semidirect
246. #14581778C23semidirect
247. #14581777C23semidirect
248. #14581776C23semidirect
249. #14581775C23semidirect
250. #14581774C23semidirect
251. #14581773C23semidirect
252. #14581772C23semidirect
253. #14581771C23semidirect
254. #14581770C23semidirect
255. #14581770C23semidirect
256. #14581769C23semidirect
257. #14581769C23semidirect
258. #14581768C23semidirect
259. #14581767C23semidirect
260. #14581767C23semidirect
261. #14581766C23semidirect
262. #14581766C23semidirect
263. #14581765C23semidirect
264. #14581765C23semidirect
265. #14581765C23semidirect
266. #14581765C23semidirect
267. #14581764C23semidirect
268. #14581764C23semidirect
269. #14581764C23semidirect
270. #14581764C23semidirect
271. #14581763C23semidirect
272. #14581763C23semidirect
273. #14581762C23semidirect
274. #14581762C23semidirect
275. #14581761C23semidirect
276. #14581760C23semidirect
277. #14581760C23semidirect
278. C4×Dic166C23semidirect
279. #14581757C23semidirect
280. C4×D332C23semidirect
281. D4×Dic83C23semidirect
282. D4×Dic83C23semidirect
283. #14581754C23semidirect
284. C4×C22⋊D83C23semidirect
285. C4×C22⋊D83C23semidirect
286. C4×C22⋊D83C23semidirect
287. (C22⋊D83)⋊C4C23semidirect
288. (C22⋊D83)⋊C4C23semidirect
289. (C22⋊D83)⋊C4C23semidirect
290. #14581750C23semidirect
291. #14581748C23semidirect
308. C2×C22⋊Dic83C23semidirect
322. C2×(C2×D83)⋊C4C23semidirect
323. C2×(C2×D83)⋊C4C23semidirect
324. C22⋊C4×D83C23semidirect
325. C22⋊C4×D83C23semidirect
332. C2×C4×Dic83C23semidirect
333. C42×D83C23semidirect
336. C2×#41×C83C23semidirect
350. #124×C83C23semidirect
351. #123×C83C23semidirect
352. C22⋊Q8×C83C23semidirect
353. #121×C83C23semidirect
354. #121×C83C23semidirect
355. #120×C83C23semidirect
356. C4×D4×C83C23semidirect
357. C4×D4×C83C23semidirect
368. C2×C22⋊C4×C83C23semidirect
391. #13050589C2×D4semidirect
756. C2×C83#3500semidirect
778. C2×#546D83semidirect
788. C83C2×#3500semidirect
803. C22×#41C2×D83semidirect
825. #546C2×D83semidirect
851. C2×#124C2×D83semidirect
857. C2×#123C2×D83semidirect
865. C2×C22⋊Q8C2×D83semidirect
880. C2×#121C2×D83semidirect
881. C2×#121C2×D83semidirect
887. C2×#120C2×D83semidirect
901. C2×C4×D4C2×D83semidirect
902. C2×C4×D4C2×D83semidirect
910. C22×C22⋊C4C2×D83semidirect
939. C2×#41C22×D83semidirect
1027. #124C22×D83semidirect
1033. #123C22×D83semidirect
1041. C22⋊Q8C22×D83semidirect
1056. #121C22×D83semidirect
1057. #121C22×D83semidirect
1063. #120C22×D83semidirect
1076. C4×D4C22×D83semidirect
1077. C4×D4C22×D83semidirect
1124. C2×C22⋊C4C22×D83semidirect
1523. C2#24921249direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145818392
C22×#145818372
#249212492
C2×#191283612
C2×#191283602
C2×#191283592
C2×#191283572
C2×#191283462
C2×#191283452
C2×#191283432
C2×#191283412
C2×#191283402
C2×#191283392
C2×#191283382
C2×#191282742
C2×#191282732
C2×#191282672
C2×#191282662
C2×#191282482
C2×#191282462
C22×#145817782
C2×#124×D832
C2×C4×#130505892
C2×#546×C832
C2×#350083