Finite Group Databasebeta

← C2×#24921619 #36311528

Subgroups — C2×#24921619 #36311528

Order 21248.

9542 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921619C2132yesmaximal, direct product factor
2C2×#19128443C211yesmaximal, characteristic, complemented
3C2×#19128442C212yesmaximal, complemented
4C2×#19128441C211yesmaximal, characteristic, complemented
5C2×#19128375C212yesmaximal, complemented
6C2×#19128343C212yesmaximal, complemented
7C2×#19128342C212yesmaximal, complemented
8C2×#19128341C212yesmaximal, complemented
9C2×D4×D332C212yesmaximal, complemented
10C2×#19128333C211yesmaximal, characteristic, complemented
11C2×#19128291C212yesmaximal, complemented
12C2×#19128290C212yesmaximal, complemented
13C2×#19128284C212yesmaximal, complemented
14C2×#19128270C212yesmaximal, complemented
15C2×#19128269C211yesmaximal, characteristic, complemented
16C2×#19128262C211yesmaximal, characteristic, complemented
17C2×#19128262C212yesmaximal, complemented
18C22×#14581762C212yesmaximal, complemented
19C2×#120×D83C211yesmaximal, characteristic, complemented
20C2×#551×C83C211yesmaximal, characteristic, complemented
21C25×D83C2211yescharacteristic, complemented
22C22×#13050591C2211yescharacteristic, complemented
23C22×#13050590C2212yescomplemented
24C23×D332C2212yescomplemented
25C23×D332C2212yescomplemented
26C23×D332C2211yescharacteristic, complemented
27C23×C22⋊D83C2212yescomplemented
28C22×D4×D83C2212yescomplemented
29C22×D4×D83C2211yescharacteristic, complemented
30C22×D4×D83C2212yescomplemented
31#19128443C22116yescomplemented
32#19128442C22132yescomplemented
33#19128441C22116yescomplemented
34#19128375C22132yescomplemented
35#19128343C22132yescomplemented
36#19128342C22132yescomplemented
37#19128341C22132yescomplemented
38D4×D332C22132yescomplemented
39#19128333C22116yescomplemented
40#19128291C22132yescomplemented
41#19128290C22132yescomplemented
42#19128284C22132yescomplemented
43#19128270C22132yescomplemented
44#19128269C22116yescomplemented
45#19128262C22132yescomplemented
46#19128262C22116yescomplemented
47C2×#14581789C2212yescomplemented
48C2×#14581789C2211yescharacteristic, complemented
49C2×#14581788C2211yescharacteristic, complemented
50C2×#14581787C2212yescomplemented
51C2×#14581787C2212yescomplemented
52C2×#14581786C2212yescomplemented
53C2×#14581781C2212yescomplemented
54C2×#14581781C2211yescharacteristic, complemented
55C2×#14581780C2212yescomplemented
56C2×#14581780C2212yescomplemented
57C2×#14581778C2212yescomplemented
58C2×#14581778C2212yescomplemented
59C2×#14581777C2212yescomplemented
60C2×#14581777C2212yescomplemented
61C2×#14581777C2212yescomplemented
62C2×#14581777C2212yescomplemented
63C2×#14581777C2212yescomplemented
64C2×#14581775C2212yescomplemented
65C2×#14581775C2211yescharacteristic, complemented
66C2×#14581774C2212yescomplemented
67C2×#14581770C2212yescomplemented
68C2×#14581769C2212yescomplemented
69C2×#14581767C2212yescomplemented
70C2×#14581767C2212yescomplemented
71C2×#14581767C2212yescomplemented
72C2×#14581767C2212yescomplemented
73C2×#14581767C2212yescomplemented
74C2×#14581767C2212yescomplemented
75C2×#14581767C2212yescomplemented
76C2×#14581766C2212yescomplemented
77C2×#14581766C2212yescomplemented
78C2×#14581765C2212yescomplemented
79C2×#14581765C2212yescomplemented
80C2×#14581765C2212yescomplemented
81C2×#14581765C2212yescomplemented
82C2×#14581765C2212yescomplemented
83C2×#14581764C2212yescomplemented
84C2×#14581762C2212yes—
85C2×#14581762C22132yescomplemented
86C2×#14581762C2212yescomplemented
87C2×#14581762C2212yescomplemented
88C2×#14581762C2211yescharacteristic, complemented
89C2×#14581762C2212yescomplemented
90C2×#14581762C2212yescomplemented
91C2×#14581762C2212yescomplemented
92C2×#14581762C2212yescomplemented
93C2×#14581762C2212yescomplemented
94C2×#14581762C2212yescomplemented
95C2×#14581762C2212yescomplemented
96C2×#14581762C2211yescharacteristic, complemented
97C2×#14581762C2212yescomplemented
98C2×#14581762C2212yescomplemented
99C2×#14581762C2212yescomplemented
100C2×#14581761C2211yescharacteristic, complemented
101C2×#14581760C2212yescomplemented
102C2×#14581760C2211yescharacteristic, complemented
103C2×#14581760C2211yescharacteristic, complemented
104#120×D83C22116yescomplemented
105C2×C4×D332C2212yescomplemented
106C2×#14581754C2212yescomplemented
107C2×C4×C22⋊D83C2212yescomplemented
108C2×(C22⋊D83)⋊C4C2212yescomplemented
109C2×(C22⋊D83)⋊C4C2212yescomplemented
110C2×#14581749C2211yescharacteristic, complemented
111C22×(C2×D83)⋊C4C2212yescomplemented
112C22×(C2×D83)⋊C4C2212yescomplemented
113C2×C22⋊C4×D83C2212yescomplemented
114C2×C22⋊C4×D83C2211yescharacteristic, complemented
115C2×C22⋊C4×D83C2212yescomplemented
116C2×C22⋊C4×D83C2211yescharacteristic, complemented
117#551×C83C22116yescomplemented
118C2×#126×C83C2212yescomplemented
119C2×#124×C83C2211yescharacteristic, complemented
120C2×#123×C83C2211yescharacteristic, complemented
121C2×#123×C83C2212yescomplemented
122C2×C22⋊Q8×C83C2212yescomplemented
123C2×#120×C83C2211yescharacteristic
124C2×C4×D4×C83C2212yescomplemented
125C2×#117×C83C2212yescomplemented
126C22×C22⋊C4×C83C2212yescomplemented
127C24×D83—48no—
128C24×D83—44no—
129C24×D83C2312yes—
130C24×D83C2311yescharacteristic
131C24×D83C2311yescharacteristic
132C24×D83C2312yes—
133C24×D83C2312yes—
134C24×D83C2311yescharacteristic
135C24×D83C2318yescomplemented
136C24×D83C2311yescharacteristic, complemented
137C2×#13050591—44no—
138C2×#13050591C2318yescomplemented
139C2×#13050590—48no—
140C2×#13050590C23116yescomplemented
141C22×Dic166C2312yescomplemented
142C22×D332—48no—
143C22×D332—48no—
144C22×D332—44no—
145C22×D332C2312yes—
146C22×D332C2312yes—
147C22×D332C2312yes—
148C22×D332C2312yes—
149C22×D332C2312yes—
150C22×D332C2312yes—
151C22×D332C2312yes—
152C22×D332C2312yes—
153C22×D332C2312yes—
154C22×D332C2311yescharacteristic
155C22×D332C23116yescomplemented
156C22×D332C23116yescomplemented
157C22×D332C2312yescomplemented
158C22×D332C2311yescharacteristic, complemented
159C22×D332C2312yescomplemented
160C22×D332C2312yescomplemented
161C22×D332C2318yescomplemented
162C22×C22⋊D83—48no—
163C22×C22⋊D83C2312yes—
164C22×C22⋊D83C2312yes—
165C22×C22⋊D83C2312yes—
166C22×C22⋊D83C2311yescharacteristic
167C22×C22⋊D83C2312yes—
168C22×C22⋊D83C2312yes—
169C22×C22⋊D83C2311yescharacteristic
170C22×C22⋊D83C2312yes—
171C22×C22⋊D83C23116yescomplemented
172C22×C22⋊D83C2312yescomplemented
173C2×D4×D83—48no—
174C2×D4×D83—48no—
175C2×D4×D83—44no—
176C2×D4×D83C23116yescomplemented
177C2×D4×D83C2318yescomplemented
178C2×D4×D83C23116yescomplemented
179C23×Dic83C2312yes—
180C22×C4×D83C2311yescharacteristic
181C22×C4×D83C2312yes—
182C22×C4×D83C2312yescomplemented
183C22×C4×D83C2312yescomplemented
184C22×C4×D83C2312yescomplemented
185C22×C4×D83C2312yescomplemented
186#14581789C23116yescomplemented
187#14581789C2318yescomplemented
188#14581788C2318yescomplemented
189#14581787C23116yescomplemented
190#14581787C23116yescomplemented
191#14581786C23116yescomplemented
192#14581781C23116yescomplemented
193#14581781C2318yescomplemented
194#14581780C23116yescomplemented
195#14581780C23116yescomplemented
196#14581778C23116yescomplemented
197#14581778C23116yescomplemented
198#14581777C23116yescomplemented
199#14581777C23116yescomplemented
200#14581777C23116yescomplemented
201#14581777C23116yescomplemented
202#14581777C23116yescomplemented
203#14581775C23116yescomplemented
204#14581775C2318yescomplemented
205#14581774C23116yescomplemented
206#14581770C23116yescomplemented
207#14581769C23116yescomplemented
208#14581767C23116yescomplemented
209#14581767C23116yescomplemented
210#14581767C23116yescomplemented
211#14581767C23116yescomplemented
212#14581767C23116yescomplemented
213#14581767C23116yescomplemented
214#14581767C23116yescomplemented
215#14581766C23116yescomplemented
216#14581766C23116yescomplemented
217#14581765C23116yescomplemented
218#14581765C23116yescomplemented
219#14581765C23116yescomplemented
220#14581765C23116yescomplemented
221#14581765C23116yescomplemented
222#14581764C23116yescomplemented
223#14581762C23116yes—
224#14581762C23116yescomplemented
225#14581762C2318yescomplemented
226#14581762C23116yescomplemented
227#14581762C23116yescomplemented
228#14581762C23116yescomplemented
229#14581762C23116yescomplemented
230#14581762C23116yescomplemented
231#14581762C23116yescomplemented
232#14581762C23116yescomplemented
233#14581762C23116yescomplemented
234#14581762C23116yescomplemented
235#14581762C23116yescomplemented
236#14581762C23116yescomplemented
237#14581762C2318yescomplemented
238#14581761C2318yescomplemented
239#14581760C2318yescomplemented
240#14581760C23116yescomplemented
241#14581760C2318yescomplemented
242C4×D332C23116yescomplemented
243#14581754C23116yescomplemented
244C4×C22⋊D83C23116yescomplemented
245(C22⋊D83)⋊C4C23116yescomplemented
246(C22⋊D83)⋊C4C23116yescomplemented
247#14581749C2318yescomplemented
248C2×C4⋊Dic83C2312yescomplemented
249C2×Dic83⋊C4C2312yescomplemented
250C2×Dic83⋊C4C2312yescomplemented
251C2×Dic83⋊C4C2312yescomplemented
252C2×Dic83⋊C4C2312yescomplemented
253C2×C22⋊Dic83C2312yes—
254C2×C22⋊Dic83C2311yescharacteristic
255C2×C22⋊Dic83C2311yescharacteristic, complemented
256C2×(C2×D83)⋊C4C2312yes—
257C2×(C2×D83)⋊C4C2312yes—
258C2×(C2×D83)⋊C4C2312yes—
259C2×(C2×D83)⋊C4C2312yes—
260C2×(C2×D83)⋊C4C2312yes—
261C2×(C2×D83)⋊C4C2312yes—
262C2×(C2×D83)⋊C4C2312yes—
263C2×(C2×D83)⋊C4C2312yes—
264C2×(C2×D83)⋊C4C2312yes—
265C2×(C2×D83)⋊C4C2312yes—
266C2×(C2×D83)⋊C4C2312yes—
267C2×(C2×D83)⋊C4C23116yescomplemented
268C2×(C2×D83)⋊C4C23116yescomplemented
269C2×(C2×D83)⋊C4C2312yescomplemented
270C2×(C2×D83)⋊C4C2312yescomplemented
271C2×(C2×D83)⋊C4C2312yescomplemented
272C2×(C2×D83)⋊C4C2312yescomplemented
273C2×(C2×D83)⋊C4C2312yescomplemented
274C2×(C2×D83)⋊C4C2312yescomplemented
275C2×(C2×D83)⋊C4C2312yescomplemented
276C22⋊C4×D83C23116yescomplemented
277C22⋊C4×D83C2318yescomplemented
278C22⋊C4×D83C23116yescomplemented
279C22⋊C4×D83C2318yescomplemented
280C2×C4×Dic83C2311yescharacteristic, complemented
281C2×C4×Dic83C2312yescomplemented
282C25×C83C2311yescharacteristic
283C22×Q8×C83C2311yescharacteristic, complemented
284C22×D4×C83C2312yes—
285C22×D4×C83C2311yescharacteristic
286C23×C4×C83C2312yes—
287C23×C4×C83C2312yes—
288C23×C4×C83C2311yescharacteristic, complemented
289#126×C83C23116yescomplemented
290#124×C83C2318yescomplemented
291#123×C83C2318yescomplemented
292#123×C83C23116yescomplemented
293C22⋊Q8×C83C23116yescomplemented
294#120×C83C2318yes—
295C4×D4×C83C23116yescomplemented
296#117×C83C23116yescomplemented
297C2×C4⋊C4×C83C2312yescomplemented
298C2×C4⋊C4×C83C2312yescomplemented
299C2×C4⋊C4×C83C2312yescomplemented
300C2×C4⋊C4×C83C2312yescomplemented
301C2×C22⋊C4×C83C2312yes—
302C2×C22⋊C4×C83C2312yes—
303C2×C22⋊C4×C83C2312yes—
304C2×C22⋊C4×C83C2312yes—
305C2×C22⋊C4×C83C2312yes—
306C2×C22⋊C4×C83C2311yescharacteristic
307C2×C22⋊C4×C83C23116yescomplemented
308C2×C22⋊C4×C83C2312yescomplemented
309C2×C22⋊C4×C83C2311yescharacteristic, complemented
310C2×C42×C83C2311yescharacteristic, complemented
311C2×C42×C83C2312yescomplemented
312C23×D83—28no—
313C23×D83—28no—
314C23×D83—28no—
315C23×D83—24no—
316C23×D83—28no—
317C23×D83—24no—
318C23×D83—416no—
319C23×D83—44no—
320C23×D83—44no—
321C23×D83—44no—
322C23×D83—44no—
323C23×D83—44no—
324C23×D83—42no—
325C23×D83—432no—
326C23×D83—44no—
327C23×D83—44no—
328C23×D83—44no—
329C23×D83—44no—
330C23×D83—42no—
331C23×D83—464no—
332C23×D83C2411yescharacteristic
333C23×D83C2412yes—
334C23×D83C2412yes—
335C23×D83C2411yescharacteristic
336C23×D83C2412yes—
337C23×D83C2418yes—
338C23×D83C2411yescharacteristic
339C23×D83C2418yes—
340C23×D83C2414yes—
341C23×D83C2414yes—
342C23×D83C2418yes—
343C23×D83C2414yes—
344C23×D83C2414yescomplemented
345#13050591—416no—
346#13050590—432no—
347C2×Dic166—44no—
348C2×Dic166C2418yescomplemented
349C2×D332—28no—
350C2×D332—28no—
351C2×D332—416no—
352C2×D332—432no—
353C2×D332—44no—
354C2×D332—42no—
355C2×D332—44no—
356C2×D332—44no—
357C2×D332—44no—
358C2×D332—44no—
359C2×D332—44no—
360C2×D332—44no—
361C2×D332—44no—
362C2×D332—432no—
363C2×D332—44no—
364C2×D332—44no—
365C2×D332—42no—
366C2×D332C2418yes—
367C2×D332C2418yes—
368C2×D332C2418yes—
369C2×D332C2418yes—
370C2×D332C2418yes—
371C2×D332C2418yes—
372C2×D332C2418yes—
373C2×D332C2418yes—
374C2×D332C2418yes—
375C2×D332C2414yes—
376C2×D332C2418yescomplemented
377C2×D332C2414yescomplemented
378C2×D332C2418yescomplemented
379C2×D332C2418yescomplemented
380C2×C22⋊D83—28no—
381C2×C22⋊D83—28no—
382C2×C22⋊D83—28no—
383C2×C22⋊D83—42no—
384C2×C22⋊D83—42no—
385C2×C22⋊D83—44no—
386C2×C22⋊D83—44no—
387C2×C22⋊D83—44no—
388C2×C22⋊D83—44no—
389C2×C22⋊D83—432no—
390C2×C22⋊D83C2418yes—
391C2×C22⋊D83C2418yes—
392C2×C22⋊D83C2418yes—
393C2×C22⋊D83C2414yes—
394C2×C22⋊D83C2418yes—
395C2×C22⋊D83C2418yes—
396C2×C22⋊D83C2414yes—
397C2×C22⋊D83C2418yes—
398C2×C22⋊D83C2418yescomplemented
399D4×D83—416no—
400D4×D83—432no—
401D4×D83—432no—
402C22×Dic83—44no—
403C22×Dic83C2411yescharacteristic
404C22×Dic83C2412yes—
405C22×Dic83C2412yes—
406C22×Dic83C2412yes—
407C22×Dic83C2418yes—
408C2×C4×D83—24no—
409C2×C4×D83—44no—
410C2×C4×D83—44no—
411C2×C4×D83—44no—
412C2×C4×D83—44no—
413C2×C4×D83—44no—
414C2×C4×D83C2414yes—
415C2×C4×D83C2418yes—
416C2×C4×D83C2418yescomplemented
417C2×C4×D83C2418yescomplemented
418C2×C4×D83C2418yescomplemented
419C2×C4×D83C2418yescomplemented
420C4⋊Dic83C2418yescomplemented
421Dic83⋊C4C2418yescomplemented
422Dic83⋊C4C2418yescomplemented
423Dic83⋊C4C2418yescomplemented
424Dic83⋊C4C2418yescomplemented
425C22⋊Dic83C2418yes—
426C22⋊Dic83C2414yes—
427C22⋊Dic83C2414yescomplemented
428(C2×D83)⋊C4C2418yes—
429(C2×D83)⋊C4C2418yes—
430(C2×D83)⋊C4C2418yes—
431(C2×D83)⋊C4C2418yes—
432(C2×D83)⋊C4C2418yes—
433(C2×D83)⋊C4C2418yes—
434(C2×D83)⋊C4C2418yes—
435(C2×D83)⋊C4C2418yes—
436(C2×D83)⋊C4C2418yes—
437(C2×D83)⋊C4C2418yes—
438(C2×D83)⋊C4C2418yes—
439(C2×D83)⋊C4C2418yescomplemented
440(C2×D83)⋊C4C2418yescomplemented
441(C2×D83)⋊C4C2418yescomplemented
442(C2×D83)⋊C4C2418yescomplemented
443(C2×D83)⋊C4C2418yescomplemented
444(C2×D83)⋊C4C2418yescomplemented
445(C2×D83)⋊C4C2418yescomplemented
446C4×Dic83C2418yescomplemented
447C4×Dic83C2414yescomplemented
448C24×C83—28no—
449C24×C83—42no—
450C24×C83C2411yescharacteristic
451C24×C83C2411yescharacteristic
452C24×C83C2414yes—
453C24×C83C2412yes—
454C2×Q8×C83—42no—
455C2×Q8×C83C2414yescomplemented
456C2×D4×C83—28no—
457C2×D4×C83—42no—
458C2×D4×C83C2418yes—
459C2×D4×C83C2414yes—
460C22×C4×C83—28no—
461C22×C4×C83—44no—
462C22×C4×C83—42no—
463C22×C4×C83C2418yes—
464C22×C4×C83C2412yes—
465C22×C4×C83C2411yescharacteristic
466C22×C4×C83C2412yes—
467C22×C4×C83C2412yes—
468C22×C4×C83C2412yes—
469C22×C4×C83C2412yes—
470C22×C4×C83C2418yes—
471C22×C4×C83C2414yescomplemented
472C4⋊C4×C83C2418yescomplemented
473C4⋊C4×C83C2418yescomplemented
474C4⋊C4×C83C2418yescomplemented
475C4⋊C4×C83C2418yescomplemented
476C22⋊C4×C83C2418yes—
477C22⋊C4×C83C2418yes—
478C22⋊C4×C83C2418yes—
479C22⋊C4×C83C2418yes—
480C22⋊C4×C83C2418yes—
481C22⋊C4×C83C2414yes—
482C22⋊C4×C83C2418yescomplemented
483C22⋊C4×C83C2414yescomplemented
484C42×C83C2414yescomplemented
485C42×C83C2418yescomplemented
486C23×C83—24no—
487C23×C83—24no—
488C23×C83—22no—
489C23×C83—24no—
490C23×C83—22no—
491C23×C83—216no—
492C23×C83—24no—
493C23×C83—44no—
494C23×C83—416no—
495C23×C83H(5,𝔽2)18yes—
496C23×C83C2512yes—
497C23×C83C2512yes—
498C23×C83C2514yes—
499C23×C83C2511yescharacteristic
500C22×D83—24no—
501C22×D83—24no—
502C22×D83—24no—
503C22×D83—24no—
504C22×D83—24no—
505C22×D83—216no—
506C22×D83—24no—
507C22×D83—22no—
508C22×D83—24no—
509C22×D83—22no—
510C22×D83—24no—
511C22×D83—24no—
512C22×D83—24no—
513C22×D83—216no—
514C22×D83—24no—
515C22×D83—24no—
516C22×D83—216no—
517C22×D83—28no—
518C22×D83—216no—
519C22×D83—28no—
520C22×D83—48no—
521C22×D83—48no—
522C22×D83—44no—
523C22×D83—48no—
524C22×D83—48no—
525C22×D83—48no—
526C22×D83—48no—
527C22×D83—48no—
528C22×D83—48no—
529C22×D83—48no—
530C22×D83—44no—
531C22×D83—432no—
532C22×D83—416no—
533C22×D83—432no—
534C22×D83—4128no—
535C22×D83—416no—
536C22×D83—88no—
537C22×D83—816no—
538C22×D83—88no—
539C22×D83H(5,𝔽2)14yes—
540C22×D83C2514yes—
541C22×D83C2512yes—
542C22×D83C2514yes—
543C22×D83C2512yes—
544C22×D83C2514yes—
545C22×D83C2512yes—
546Q8×C83—44no—
547D4×C83—216no—
548D4×C83—44no—
549C2×C4×C83—24no—
550C2×C4×C83—24no—
551C2×C4×C83—216no—
552C2×C4×C83—24no—
553C2×C4×C83—24no—
554C2×C4×C83—24no—
555C2×C4×C83—22no—
556C2×C4×C83—48no—
557C2×C4×C83—44no—
558C2×C4×C83C2514yes—
559C2×C4×C83C2514yes—
560C2×C4×C83C2514yes—
561C2×C4×C83C2512yes—
562C2×C4×C83C2514yes—
563C2×C4×C83C2514yes—
564C22⋊D83—216no—
565C22⋊D83—216no—
566C22⋊D83—216no—
567C22⋊D83—48no—
568C22⋊D83—44no—
569C22⋊D83—44no—
570C22⋊D83—48no—
571C22⋊D83—48no—
572C22⋊D83—48no—
573C2×Dic83—22no—
574C2×Dic83—24no—
575C2×Dic83—24no—
576C2×Dic83—24no—
577C2×Dic83—48no—
578C2×Dic83C2514yes—
579C2×Dic83C2514yes—
580C2×Dic83C2514yes—
581C2×Dic83C2512yes—
582D332—216no—
583D332—216no—
584D332—44no—
585D332—48no—
586D332—48no—
587D332—48no—
588D332—48no—
589D332—48no—
590D332—48no—
591D332—48no—
592D332—48no—
593D332—48no—
594D332—48no—
595D332—44no—
596C4×D83—28no—
597C4×D83—48no—
598C4×D83—48no—
599C4×D83—48no—
600C4×D83—48no—
601C4×D83—48no—
602Dic166—48no—
603C22×C83—24no—
604C22×C83—24no—
605C22×C83—216no—
606C22×C83—24no—
607C22×C83—24no—
608C22×C83—22no—
609C22×C83—22no—
610C22×C83—416no—
611C22×C83—44no—
612C22×C83—44no—
613C22×C83C2×H(5,𝔽2)12yes—
614C22×C83C2×H(5,𝔽2)18yes—
615C22×C83C2×H(5,𝔽2)14yes—
616C22×C83C2611yescharacteristic
617C2×D83—24no—
618C2×D83—28no—
619C2×D83—24no—
620C2×D83—24no—
621C2×D83—24no—
622C2×D83—24no—
623C2×D83—24no—
624C2×D83—22no—
625C2×D83—24no—
626C2×D83—24no—
627C2×D83—24no—
628C2×D83—24no—
629C2×D83—24no—
630C2×D83—22no—
631C2×D83—24no—
632C2×D83—432no—
633C2×D83—416no—
634C2×D83—432no—
635C2×D83—416no—
636C2×D83—48no—
637C2×D83—44no—
638C2×D83—48no—
639C2×D83—44no—
640C2×D83—48no—
641C2×D83—88no—
642C2×D83—816no—
643C2×D83—88no—
644C2×D83C2×H(5,𝔽2)14yes—
645C4×C83—24no—
646C4×C83—22no—
647C4×C83—24no—
648C4×C83—24no—
649C4×C83—24no—
650C4×C83—24no—
651Dic83—24no—
652Dic83—24no—
653Dic83—22no—
654Dic83—24no—
655C2×#3532—831nomaximal, Sylow
656C2×C83—28no—
657C2×C83—42no—
658C2×C83—42no—
659C2×C83#353214yescomplemented
660C2×C83C22×H(5,𝔽2)11yescharacteristic
661C2×C83C22×H(5,𝔽2)12yes—
662D83—24no—
663D83—44no—
664D83—42no—
665D83—44no—
666D83—42no—
667D83—44no—
668#3532—8332no—
669C2×H(3,𝔽4)—831no—
670C2×#560—832no—
671C2×#560—831no—
672C2×#551—832no—
673C2×#551D8311yescharacteristic, complemented
674C2×#546—832no—
675C2×#546—832no—
676C2×#546—832no—
677C2×D42—831no—
678C2×D42—832no—
679C2×#538—832no—
680C2×#538—832no—
681C2×#538—832no—
682C2×#535—831no—
683C2×#535—832no—
684C2×#534—832no—
685C2×#534—831no—
686C22×#120—831no—
687C22×#120—832no—
688C83C2×#353211yescharacteristic, complemented, Sylow
689C26—831no—
690C22×#41—831no—
691C22×#41—832no—
692C23×D4—832no—
693C23×D4—831no—
694C23×D4—832no—
695C23×D4—832no—
696C23×D4—832no—
697C23×D4—832no—
698C23×D4—831no—
699H(3,𝔽4)—8316no—
700#560—8332no—
701#560—8316no—
702#551—8332no—
703#551C2×D83116yescomplemented
704#546—8332no—
705#546—8332no—
706#546—8332no—
707D42—8316no—
708D42—8332no—
709#538—8332no—
710#538—8332no—
711#538—8332no—
712#535—8316no—
713#535—8332no—
714#534—8332no—
715#534—8316no—
716C2×#127—831no—
717C2×#127—831no—
718C2×#127—832no—
719C2×#126—832no—
720C2×#126—832no—
721C2×#126—832no—
722C2×#126C2×D8312yescomplemented
723C2×#124—831no—
724C2×#124—832no—
725C2×#124—832no—
726C2×#124—832no—
727C2×#124—832no—
728C2×#124—832no—
729C2×#124C2×D8311yescharacteristic, complemented
730C2×#123—832no—
731C2×#123—831no—
732C2×#123—832no—
733C2×#123—832no—
734C2×#123—832no—
735C2×#123—832no—
736C2×#123—832no—
737C2×#123—832no—
738C2×#123C2×D8311yescharacteristic, complemented
739C2×#123C2×D8312yescomplemented
740C2×C22⋊Q8—832no—
741C2×C22⋊Q8—832no—
742C2×C22⋊Q8C2×D8312yescomplemented
743C2×#121—832no—
744C2×#121—832no—
745C2×#121—832no—
746C2×#121—832no—
747C2×#121—832no—
748C2×#121—832no—
749C2×#121—832no—
750C2×#121—832no—
751C2×#121—832no—
752C2×#121—832no—
753C2×#121—832no—
754C2×#121—832no—
755C2×#121—832no—
756C2×#121—832no—
757C2×#121—832no—
758C2×#120—831no—
759C2×#120—832no—
760C2×#120—831no—
761C2×#120—831no—
762C2×#120—8316no—
763C2×#120—832no—
764C2×#120—832no—
765C2×#120—832no—
766C2×#120—832no—
767C2×#120—832no—
768C2×#120—832no—
769C2×#120—832no—
770C2×#120—832no—
771C2×#120—831no—
772C2×#120—832no—
773C2×#120—832no—
774C2×#120—832no—
775C2×#120—8332no—
776C2×#120—831no—
777C2×#120—832no—
778C2×#120—832no—
779C2×#120C2×D8311yescharacteristic
780C2×C4×D4—832no—
781C2×C4×D4—832no—
782C2×C4×D4—832no—
783C2×C4×D4—832no—
784C2×C4×D4—832no—
785C2×C4×D4C2×D8312yescomplemented
786C2×#117—831no—
787C2×#117C2×D8312yescomplemented
788C22×C22⋊C4—832no—
789C22×C22⋊C4—832no—
790C22×C22⋊C4—831no—
791C22×C22⋊C4—832no—
792C22×C22⋊C4—832no—
793C22×C22⋊C4—831no—
794C22×C22⋊C4C2×D8312yescomplemented
795C25—3328no—
796C25—3324no—
797C25—831no—
798C25—838no—
799C25—831no—
800C25—831no—
801C25—832no—
802C25—831no—
803C25—832no—
804C25—832no—
805C25C22×D8311yescharacteristic
806C2×#41—3328no—
807C2×#41—3324no—
808C2×#41—838no—
809C2×#41—8316no—
810C22×Q8—832no—
811C22×Q8C22×D8311yescharacteristic, complemented
812C22×D4—3328no—
813C22×D4—3328no—
814C22×D4—3324no—
815C22×D4—3328no—
816C22×D4—3328no—
817C22×D4—3328no—
818C22×D4—3324no—
819C22×D4—831no—
820C22×D4—832no—
821C22×D4—832no—
822C22×D4—831no—
823C22×D4—832no—
824C22×D4—8316no—
825C22×D4—832no—
826C22×D4—838no—
827C22×D4—8316no—
828C22×D4—8316no—
829C22×D4—832no—
830C22×D4—832no—
831C22×D4—832no—
832C22×D4—832no—
833C22×D4—832no—
834C22×D4—832no—
835C22×D4—832no—
836C22×D4—832no—
837C22×D4—832no—
838C22×D4—831no—
839C22×D4—832no—
840C22×D4—831no—
841C22×D4—832no—
842C22×D4—8316no—
843C22×D4—8316no—
844C22×D4—832no—
845C22×D4—832no—
846C22×D4—832no—
847C22×D4—832no—
848C22×D4—838no—
849C22×D4C22×D8312yes—
850C22×D4C22×D8311yescharacteristic
851C23×C4—832no—
852C23×C4—832no—
853C23×C4—832no—
854C23×C4—832no—
855C23×C4—832no—
856C23×C4—832no—
857C23×C4—831no—
858C23×C4C22×D8312yes—
859C23×C4C22×D8312yes—
860C23×C4C22×D8311yescharacteristic, complemented
861#127—838no—
862#127—838no—
863#127—8316no—
864#126—8316no—
865#126—8316no—
866#126—8316no—
867#126C22×D83116yescomplemented
868#124—838no—
869#124—8316no—
870#124—8316no—
871#124—8316no—
872#124—8316no—
873#124—8316no—
874#124C22×D8318yescomplemented
875#123—8316no—
876#123—838no—
877#123—8316no—
878#123—8316no—
879#123—8316no—
880#123—8316no—
881#123—8316no—
882#123—8316no—
883#123C22×D8318yescomplemented
884#123C22×D83116yescomplemented
885C22⋊Q8—8316no—
886C22⋊Q8—8316no—
887C22⋊Q8C22×D83116yescomplemented
888#121—8316no—
889#121—8316no—
890#121—8316no—
891#121—8316no—
892#121—8316no—
893#121—8316no—
894#121—8316no—
895#121—8316no—
896#121—8316no—
897#121—8316no—
898#121—8316no—
899#121—8316no—
900#121—8316no—
901#121—8316no—
902#121—8316no—
903#120—838no—
904#120—8316no—
905#120—838no—
906#120—838no—
907#120—8316no—
908#120—8316no—
909#120—8316no—
910#120—8316no—
911#120—8316no—
912#120—8316no—
913#120—8316no—
914#120—8316no—
915#120—838no—
916#120—8316no—
917#120—8316no—
918#120—8316no—
919#120—838no—
920#120—8316no—
921#120—8316no—
922#120C22×D8318yes—
923C4×D4—8316no—
924C4×D4—8316no—
925C4×D4—8316no—
926C4×D4—8316no—
927C4×D4—8316no—
928C4×D4C22×D83116yescomplemented
929#117—838no—
930#117C22×D83116yescomplemented
931C2×C4⋊C4—832no—
932C2×C4⋊C4—832no—
933C2×C4⋊C4—832no—
934C2×C4⋊C4—832no—
935C2×C4⋊C4—832no—
936C2×C4⋊C4C22×D8312yescomplemented
937C2×C4⋊C4C22×D8312yescomplemented
938C2×C4⋊C4C22×D8312yescomplemented
939C2×C4⋊C4C22×D8312yescomplemented
940C2×C22⋊C4—832no—
941C2×C22⋊C4—831no—
942C2×C22⋊C4—831no—
943C2×C22⋊C4—832no—
944C2×C22⋊C4—832no—
945C2×C22⋊C4—832no—
946C2×C22⋊C4—832no—
947C2×C22⋊C4—832no—
948C2×C22⋊C4—832no—
949C2×C22⋊C4—832no—
950C2×C22⋊C4—832no—
951C2×C22⋊C4—832no—
952C2×C22⋊C4—832no—
953C2×C22⋊C4—832no—
954C2×C22⋊C4—8316no—
955C2×C22⋊C4—8316no—
956C2×C22⋊C4—832no—
957C2×C22⋊C4—832no—
958C2×C22⋊C4—832no—
959C2×C22⋊C4—832no—
960C2×C22⋊C4—832no—
961C2×C22⋊C4—832no—
962C2×C22⋊C4—832no—
963C2×C22⋊C4—838no—
964C2×C22⋊C4—8316no—
965C2×C22⋊C4—8316no—
966C2×C22⋊C4—838no—
967C2×C22⋊C4C22×D8312yes—
968C2×C22⋊C4C22×D8312yes—
969C2×C22⋊C4C22×D8311yescharacteristic
970C2×C22⋊C4C22×D8312yes—
971C2×C22⋊C4C22×D8312yes—
972C2×C22⋊C4C22×D8312yes—
973C2×C22⋊C4C22×D83116yescomplemented
974C2×C22⋊C4C22×D8311yescharacteristic, complemented
975C2×C22⋊C4C22×D8312yescomplemented
976C2×C42—831no—
977C2×C42—832no—
978C2×C42C22×D8311yescharacteristic, complemented
979C2×C42C22×D8312yescomplemented
980C24—28no—
981C24—42no—
982C24—3324no—
983C24—3324no—
984C24—3324no—
985C24—3322no—
986C24—3324no—
987C24—33232no—
988C24—3324no—
989C24—3324no—
990C24—3324no—
991C24—3322no—
992C24—3324no—
993C24—3324no—
994C24—33264no—
995C24—33216no—
996C24—834no—
997C24—834no—
998C24—834no—
999C24—838no—
1000C24—834no—
1001C24—838no—
1002C24—838no—
1003C24—831no—
1004C24—832no—
1005C24—831no—
1006C24—832no—
1007C24—832no—
1008C24—831no—
1009C24—1668no—
1010C24—1664no—
1011C24—1664no—
1012C24—1668no—
1013C24—1668no—
1014C24—1668no—
1015C24C23×D8311yescharacteristic
1016C24C23×D8311yescharacteristic
1017C24C23×D8314yes—
1018C24C23×D8312yes—
1019#41—33232no—
1020#41—33216no—
1021C2×Q8—42no—
1022C2×Q8—3324no—
1023C2×Q8—838no—
1024C2×Q8C23×D8314yescomplemented
1025C2×D4—28no—
1026C2×D4—42no—
1027C2×D4—3324no—
1028C2×D4—3324no—
1029C2×D4—3324no—
1030C2×D4—3322no—
1031C2×D4—3324no—
1032C2×D4—3324no—
1033C2×D4—3324no—
1034C2×D4—3324no—
1035C2×D4—33232no—
1036C2×D4—3324no—
1037C2×D4—3324no—
1038C2×D4—3322no—
1039C2×D4—3324no—
1040C2×D4—33232no—
1041C2×D4—33216no—
1042C2×D4—33232no—
1043C2×D4—33232no—
1044C2×D4—33232no—
1045C2×D4—33216no—
1046C2×D4—3322no—
1047C2×D4—3322no—
1048C2×D4—3324no—
1049C2×D4—3324no—
1050C2×D4—3324no—
1051C2×D4—3324no—
1052C2×D4—834no—
1053C2×D4—838no—
1054C2×D4—838no—
1055C2×D4—834no—
1056C2×D4—838no—
1057C2×D4—838no—
1058C2×D4—838no—
1059C2×D4—838no—
1060C2×D4—838no—
1061C2×D4—838no—
1062C2×D4—838no—
1063C2×D4—838no—
1064C2×D4—838no—
1065C2×D4—838no—
1066C2×D4—838no—
1067C2×D4—834no—
1068C2×D4—838no—
1069C2×D4—834no—
1070C2×D4—838no—
1071C2×D4—838no—
1072C2×D4—838no—
1073C2×D4—838no—
1074C2×D4—838no—
1075C2×D4—1668no—
1076C2×D4—1668no—
1077C2×D4—1668no—
1078C2×D4—1668no—
1079C2×D4—1668no—
1080C2×D4C23×D8318yes—
1081C2×D4C23×D8314yes—
1082C22×C4—28no—
1083C22×C4—44no—
1084C22×C4—42no—
1085C22×C4—3324no—
1086C22×C4—3324no—
1087C22×C4—3324no—
1088C22×C4—3324no—
1089C22×C4—3324no—
1090C22×C4—3324no—
1091C22×C4—838no—
1092C22×C4—838no—
1093C22×C4—838no—
1094C22×C4—838no—
1095C22×C4—838no—
1096C22×C4—838no—
1097C22×C4—832no—
1098C22×C4—832no—
1099C22×C4—832no—
1100C22×C4—831no—
1101C22×C4—834no—
1102C22×C4—1664no—
1103C22×C4C23×D8318yes—
1104C22×C4C23×D8311yescharacteristic
1105C22×C4C23×D8312yes—
1106C22×C4C23×D8312yes—
1107C22×C4C23×D8312yes—
1108C22×C4C23×D8312yes—
1109C22×C4C23×D8312yes—
1110C22×C4C23×D8318yes—
1111C22×C4C23×D8314yescomplemented
1112C4⋊C4—838no—
1113C4⋊C4—838no—
1114C4⋊C4—838no—
1115C4⋊C4—838no—
1116C4⋊C4—838no—
1117C4⋊C4C23×D8318yescomplemented
1118C4⋊C4C23×D8318yescomplemented
1119C4⋊C4C23×D8318yescomplemented
1120C4⋊C4C23×D8318yescomplemented
1121C22⋊C4—838no—
1122C22⋊C4—834no—
1123C22⋊C4—834no—
1124C22⋊C4—838no—
1125C22⋊C4—838no—
1126C22⋊C4—838no—
1127C22⋊C4—838no—
1128C22⋊C4—838no—
1129C22⋊C4—838no—
1130C22⋊C4—838no—
1131C22⋊C4—838no—
1132C22⋊C4—838no—
1133C22⋊C4—838no—
1134C22⋊C4—838no—
1135C22⋊C4—838no—
1136C22⋊C4—838no—
1137C22⋊C4—838no—
1138C22⋊C4—838no—
1139C22⋊C4—838no—
1140C22⋊C4—838no—
1141C22⋊C4—838no—
1142C22⋊C4C23×D8318yes—
1143C22⋊C4C23×D8318yes—
1144C22⋊C4C23×D8314yes—
1145C22⋊C4C23×D8318yes—
1146C22⋊C4C23×D8318yes—
1147C22⋊C4C23×D8318yes—
1148C22⋊C4C23×D8314yescomplemented
1149C22⋊C4C23×D8318yescomplemented
1150C42—834no—
1151C42—838no—
1152C42C23×D8314yescomplemented
1153C42C23×D8318yescomplemented
1154C23—24no—
1155C23—24no—
1156C23—22no—
1157C23—22no—
1158C23—24no—
1159C23—216no—
1160C23—24no—
1161C23—44no—
1162C23—416no—
1163C23—33232no—
1164C23—33232no—
1165C23—3328no—
1166C23—3328no—
1167C23—3328no—
1168C23—3324no—
1169C23—3328no—
1170C23—3328no—
1171C23—3328no—
1172C23—3328no—
1173C23—3324no—
1174C23—3328no—
1175C23—3328no—
1176C23—332128no—
1177C23—33216no—
1178C23—33216no—
1179C23—834no—
1180C23—832no—
1181C23—834no—
1182C23—832no—
1183C23—834no—
1184C23—834no—
1185C23—832no—
1186C23—66416no—
1187C23—6648no—
1188C23—6648no—
1189C23—16616no—
1190C23—1668no—
1191C23—1668no—
1192C23—1664no—
1193C23—1662no—
1194C23—1664no—
1195C23—1664no—
1196C23—1662no—
1197C23—1664no—
1198C23—1664no—
1199C23—1664no—
1200C23—1664no—
1201C23—1664no—
1202C23—16616no—
1203C23—16616no—
1204C23—1664no—
1205C23—1664no—
1206C23—1664no—
1207C23—16616no—
1208C23—1664no—
1209C23#1458183818yes—
1210C23C24×D8312yes—
1211C23C24×D8312yes—
1212C23C24×D8314yes—
1213C23C24×D8311yescharacteristic
1214Q8—44no—
1215Q8—3328no—
1216D4—216no—
1217D4—44no—
1218D4—3328no—
1219D4—3328no—
1220D4—3328no—
1221D4—3324no—
1222D4—3328no—
1223D4—3328no—
1224D4—3328no—
1225D4—3328no—
1226D4—3328no—
1227D4—3328no—
1228D4—3324no—
1229D4—3328no—
1230D4—3324no—
1231D4—3324no—
1232D4—3328no—
1233D4—3328no—
1234D4—3328no—
1235D4—3328no—
1236D4—16616no—
1237D4—16616no—
1238D4—16616no—
1239D4—16616no—
1240D4—16616no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—216no—
1247C2×C4—24no—
1248C2×C4—48no—
1249C2×C4—44no—
1250C2×C4—3328no—
1251C2×C4—3328no—
1252C2×C4—3328no—
1253C2×C4—3328no—
1254C2×C4—3328no—
1255C2×C4—3328no—
1256C2×C4—834no—
1257C2×C4—834no—
1258C2×C4—834no—
1259C2×C4—832no—
1260C2×C4—1668no—
1261C2×C4—1662no—
1262C2×C4—1664no—
1263C2×C4—1664no—
1264C2×C4—1664no—
1265C2×C4C24×D8312yes—
1266C2×C4C24×D8314yes—
1267C2×C4C24×D8314yes—
1268C2×C4C24×D8314yes—
1269C2×C4C24×D8314yes—
1270C2×C4C24×D8314yes—
1271C22—216no—
1272C22—24no—
1273C22—24no—
1274C22—22no—
1275C22—22no—
1276C22—24no—
1277C22—24no—
1278C22—416no—
1279C22—44no—
1280C22—44no—
1281C22—33232no—
1282C22—33232no—
1283C22—33216no—
1284C22—33216no—
1285C22—3324no—
1286C22—3328no—
1287C22—3328no—
1288C22—3328no—
1289C22—3324no—
1290C22—834no—
1291C22—66416no—
1292C22—6648no—
1293C22—6648no—
1294C22—1664no—
1295C22—1662no—
1296C22—1664no—
1297C22—1664no—
1298C22—1662no—
1299C22—1664no—
1300C22—1664no—
1301C22—1664no—
1302C22—1664no—
1303C22—1664no—
1304C22—1664no—
1305C22—1664no—
1306C22—1664no—
1307C22—1668no—
1308C22—1664no—
1309C22H(5,𝔽2)×D8312yes—
1310C22C2×#1458183818yes—
1311C22C2×#1458183814yes—
1312C22C25×D8311yescharacteristic
1313C4—24no—
1314C4—24no—
1315C4—22no—
1316C4—24no—
1317C4—24no—
1318C4—24no—
1319C4—1662no—
1320C4—1664no—
1321C4—1664no—
1322C4—1664no—
1323C2—28no—
1324C2—42no—
1325C2—42no—
1326C2—3322no—
1327C2—3324no—
1328C2—3324no—
1329C2—3324no—
1330C2—3322no—
1331C2—1664no—
1332C2#2492161914yesdirect product factor
1333C2C2×H(5,𝔽2)×D8311yescharacteristic
1334C2C22×#1458183812yes—
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#551×C83C2
socleC23×C83C25
hypercenterC2×#551D83
hypocenterC83C2×#3532
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. #24921619C2direct (N × H)
2. C2×#19128443C2semidirect
3. C2×#19128442C2semidirect
4. C2×#19128441C2semidirect
5. C2×#19128375C2semidirect
6. C2×#19128343C2semidirect
7. C2×#19128342C2semidirect
8. C2×#19128341C2semidirect
9. C2×D4×D332C2semidirect
10. C2×#19128333C2semidirect
11. C2×#19128291C2semidirect
12. C2×#19128290C2semidirect
13. C2×#19128284C2semidirect
14. C2×#19128270C2semidirect
15. C2×#19128269C2semidirect
16. C2×#19128262C2semidirect
17. C2×#19128262C2semidirect
18. C22×#14581762C2semidirect
19. C2×#120×D83C2semidirect
20. C2×#551×C83C2semidirect
21. C25×D83C22semidirect
22. C22×#13050591C22semidirect
23. C22×#13050590C22semidirect
24. C23×D332C22semidirect
25. C23×D332C22semidirect
26. C23×D332C22semidirect
27. C23×C22⋊D83C22semidirect
28. C22×D4×D83C22semidirect
29. C22×D4×D83C22semidirect
30. C22×D4×D83C22semidirect
31. #19128443C22semidirect
32. #19128442C22semidirect
33. #19128441C22semidirect
34. #19128375C22semidirect
35. #19128343C22semidirect
36. #19128342C22semidirect
37. #19128341C22semidirect
38. D4×D332C22semidirect
39. #19128333C22semidirect
40. #19128291C22semidirect
41. #19128290C22semidirect
42. #19128284C22semidirect
43. #19128270C22semidirect
44. #19128269C22semidirect
45. #19128262C22semidirect
46. #19128262C22semidirect
47. C2×#14581789C22semidirect
48. C2×#14581789C22semidirect
49. C2×#14581788C22semidirect
50. C2×#14581787C22semidirect
51. C2×#14581787C22semidirect
52. C2×#14581786C22semidirect
53. C2×#14581781C22semidirect
54. C2×#14581781C22semidirect
55. C2×#14581780C22semidirect
56. C2×#14581780C22semidirect
57. C2×#14581778C22semidirect
58. C2×#14581778C22semidirect
59. C2×#14581777C22semidirect
60. C2×#14581777C22semidirect
61. C2×#14581777C22semidirect
62. C2×#14581777C22semidirect
63. C2×#14581777C22semidirect
64. C2×#14581775C22semidirect
65. C2×#14581775C22semidirect
66. C2×#14581774C22semidirect
67. C2×#14581770C22semidirect
68. C2×#14581769C22semidirect
69. C2×#14581767C22semidirect
70. C2×#14581767C22semidirect
71. C2×#14581767C22semidirect
72. C2×#14581767C22semidirect
73. C2×#14581767C22semidirect
74. C2×#14581767C22semidirect
75. C2×#14581767C22semidirect
76. C2×#14581766C22semidirect
77. C2×#14581766C22semidirect
78. C2×#14581765C22semidirect
79. C2×#14581765C22semidirect
80. C2×#14581765C22semidirect
81. C2×#14581765C22semidirect
82. C2×#14581765C22semidirect
83. C2×#14581764C22semidirect
85. C2×#14581762C22semidirect
86. C2×#14581762C22semidirect
87. C2×#14581762C22semidirect
88. C2×#14581762C22semidirect
89. C2×#14581762C22semidirect
90. C2×#14581762C22semidirect
91. C2×#14581762C22semidirect
92. C2×#14581762C22semidirect
93. C2×#14581762C22semidirect
94. C2×#14581762C22semidirect
95. C2×#14581762C22semidirect
96. C2×#14581762C22semidirect
97. C2×#14581762C22semidirect
98. C2×#14581762C22semidirect
99. C2×#14581762C22semidirect
100. C2×#14581761C22semidirect
101. C2×#14581760C22semidirect
102. C2×#14581760C22semidirect
103. C2×#14581760C22semidirect
104. #120×D83C22semidirect
105. C2×C4×D332C22semidirect
106. C2×#14581754C22semidirect
107. C2×C4×C22⋊D83C22semidirect
108. C2×(C22⋊D83)⋊C4C22semidirect
109. C2×(C22⋊D83)⋊C4C22semidirect
110. C2×#14581749C22semidirect
111. C22×(C2×D83)⋊C4C22semidirect
112. C22×(C2×D83)⋊C4C22semidirect
113. C2×C22⋊C4×D83C22semidirect
114. C2×C22⋊C4×D83C22semidirect
115. C2×C22⋊C4×D83C22semidirect
116. C2×C22⋊C4×D83C22semidirect
117. #551×C83C22semidirect
118. C2×#126×C83C22semidirect
119. C2×#124×C83C22semidirect
120. C2×#123×C83C22semidirect
121. C2×#123×C83C22semidirect
122. C2×C22⋊Q8×C83C22semidirect
124. C2×C4×D4×C83C22semidirect
125. C2×#117×C83C22semidirect
126. C22×C22⋊C4×C83C22semidirect
135. C24×D83C23semidirect
136. C24×D83C23semidirect
138. C2×#13050591C23semidirect
140. C2×#13050590C23semidirect
141. C22×Dic166C23semidirect
155. C22×D332C23semidirect
156. C22×D332C23semidirect
157. C22×D332C23semidirect
158. C22×D332C23semidirect
159. C22×D332C23semidirect
160. C22×D332C23semidirect
161. C22×D332C23semidirect
171. C22×C22⋊D83C23semidirect
172. C22×C22⋊D83C23semidirect
176. C2×D4×D83C23semidirect
177. C2×D4×D83C23semidirect
178. C2×D4×D83C23semidirect
182. C22×C4×D83C23semidirect
183. C22×C4×D83C23semidirect
184. C22×C4×D83C23semidirect
185. C22×C4×D83C23semidirect
186. #14581789C23semidirect
187. #14581789C23semidirect
188. #14581788C23semidirect
189. #14581787C23semidirect
190. #14581787C23semidirect
191. #14581786C23semidirect
192. #14581781C23semidirect
193. #14581781C23semidirect
194. #14581780C23semidirect
195. #14581780C23semidirect
196. #14581778C23semidirect
197. #14581778C23semidirect
198. #14581777C23semidirect
199. #14581777C23semidirect
200. #14581777C23semidirect
201. #14581777C23semidirect
202. #14581777C23semidirect
203. #14581775C23semidirect
204. #14581775C23semidirect
205. #14581774C23semidirect
206. #14581770C23semidirect
207. #14581769C23semidirect
208. #14581767C23semidirect
209. #14581767C23semidirect
210. #14581767C23semidirect
211. #14581767C23semidirect
212. #14581767C23semidirect
213. #14581767C23semidirect
214. #14581767C23semidirect
215. #14581766C23semidirect
216. #14581766C23semidirect
217. #14581765C23semidirect
218. #14581765C23semidirect
219. #14581765C23semidirect
220. #14581765C23semidirect
221. #14581765C23semidirect
222. #14581764C23semidirect
224. #14581762C23semidirect
225. #14581762C23semidirect
226. #14581762C23semidirect
227. #14581762C23semidirect
228. #14581762C23semidirect
229. #14581762C23semidirect
230. #14581762C23semidirect
231. #14581762C23semidirect
232. #14581762C23semidirect
233. #14581762C23semidirect
234. #14581762C23semidirect
235. #14581762C23semidirect
236. #14581762C23semidirect
237. #14581762C23semidirect
238. #14581761C23semidirect
239. #14581760C23semidirect
240. #14581760C23semidirect
241. #14581760C23semidirect
242. C4×D332C23semidirect
243. #14581754C23semidirect
244. C4×C22⋊D83C23semidirect
245. (C22⋊D83)⋊C4C23semidirect
246. (C22⋊D83)⋊C4C23semidirect
247. #14581749C23semidirect
248. C2×C4⋊Dic83C23semidirect
249. C2×Dic83⋊C4C23semidirect
250. C2×Dic83⋊C4C23semidirect
251. C2×Dic83⋊C4C23semidirect
252. C2×Dic83⋊C4C23semidirect
255. C2×C22⋊Dic83C23semidirect
267. C2×(C2×D83)⋊C4C23semidirect
268. C2×(C2×D83)⋊C4C23semidirect
269. C2×(C2×D83)⋊C4C23semidirect
270. C2×(C2×D83)⋊C4C23semidirect
271. C2×(C2×D83)⋊C4C23semidirect
272. C2×(C2×D83)⋊C4C23semidirect
273. C2×(C2×D83)⋊C4C23semidirect
274. C2×(C2×D83)⋊C4C23semidirect
275. C2×(C2×D83)⋊C4C23semidirect
276. C22⋊C4×D83C23semidirect
277. C22⋊C4×D83C23semidirect
278. C22⋊C4×D83C23semidirect
279. C22⋊C4×D83C23semidirect
280. C2×C4×Dic83C23semidirect
281. C2×C4×Dic83C23semidirect
283. C22×Q8×C83C23semidirect
288. C23×C4×C83C23semidirect
289. #126×C83C23semidirect
290. #124×C83C23semidirect
291. #123×C83C23semidirect
292. #123×C83C23semidirect
293. C22⋊Q8×C83C23semidirect
295. C4×D4×C83C23semidirect
296. #117×C83C23semidirect
297. C2×C4⋊C4×C83C23semidirect
298. C2×C4⋊C4×C83C23semidirect
299. C2×C4⋊C4×C83C23semidirect
300. C2×C4⋊C4×C83C23semidirect
307. C2×C22⋊C4×C83C23semidirect
308. C2×C22⋊C4×C83C23semidirect
309. C2×C22⋊C4×C83C23semidirect
310. C2×C42×C83C23semidirect
311. C2×C42×C83C23semidirect
344. C23×D83C24semidirect
348. C2×Dic166C24semidirect
376. C2×D332C24semidirect
377. C2×D332C24semidirect
378. C2×D332C24semidirect
379. C2×D332C24semidirect
398. C2×C22⋊D83C24semidirect
416. C2×C4×D83C24semidirect
417. C2×C4×D83C24semidirect
418. C2×C4×D83C24semidirect
419. C2×C4×D83C24semidirect
420. C4⋊Dic83C24semidirect
421. Dic83⋊C4C24semidirect
422. Dic83⋊C4C24semidirect
423. Dic83⋊C4C24semidirect
424. Dic83⋊C4C24semidirect
427. C22⋊Dic83C24semidirect
439. (C2×D83)⋊C4C24semidirect
440. (C2×D83)⋊C4C24semidirect
441. (C2×D83)⋊C4C24semidirect
442. (C2×D83)⋊C4C24semidirect
443. (C2×D83)⋊C4C24semidirect
444. (C2×D83)⋊C4C24semidirect
445. (C2×D83)⋊C4C24semidirect
446. C4×Dic83C24semidirect
447. C4×Dic83C24semidirect
455. C2×Q8×C83C24semidirect
471. C22×C4×C83C24semidirect
472. C4⋊C4×C83C24semidirect
473. C4⋊C4×C83C24semidirect
474. C4⋊C4×C83C24semidirect
475. C4⋊C4×C83C24semidirect
482. C22⋊C4×C83C24semidirect
483. C22⋊C4×C83C24semidirect
484. C42×C83C24semidirect
485. C42×C83C24semidirect
659. C2×C83#3532semidirect
673. C2×#551D83semidirect
688. C83C2×#3532semidirect
703. #551C2×D83semidirect
722. C2×#126C2×D83semidirect
729. C2×#124C2×D83semidirect
738. C2×#123C2×D83semidirect
739. C2×#123C2×D83semidirect
742. C2×C22⋊Q8C2×D83semidirect
785. C2×C4×D4C2×D83semidirect
787. C2×#117C2×D83semidirect
794. C22×C22⋊C4C2×D83semidirect
811. C22×Q8C22×D83semidirect
860. C23×C4C22×D83semidirect
867. #126C22×D83semidirect
874. #124C22×D83semidirect
883. #123C22×D83semidirect
884. #123C22×D83semidirect
887. C22⋊Q8C22×D83semidirect
928. C4×D4C22×D83semidirect
930. #117C22×D83semidirect
936. C2×C4⋊C4C22×D83semidirect
937. C2×C4⋊C4C22×D83semidirect
938. C2×C4⋊C4C22×D83semidirect
939. C2×C4⋊C4C22×D83semidirect
973. C2×C22⋊C4C22×D83semidirect
974. C2×C22⋊C4C22×D83semidirect
975. C2×C22⋊C4C22×D83semidirect
978. C2×C42C22×D83semidirect
979. C2×C42C22×D83semidirect
1024. C2×Q8C23×D83semidirect
1111. C22×C4C23×D83semidirect
1117. C4⋊C4C23×D83semidirect
1118. C4⋊C4C23×D83semidirect
1119. C4⋊C4C23×D83semidirect
1120. C4⋊C4C23×D83semidirect
1148. C22⋊C4C23×D83semidirect
1149. C22⋊C4C23×D83semidirect
1152. C42C23×D83semidirect
1153. C42C23×D83semidirect
1332. C2#24921619direct (N × H)

Maximal subgroups

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

subgroupindex
#249216192
C2×#191284432
C2×#191284422
C2×#191284412
C2×#191283752
C2×#191283432
C2×#191283422
C2×#191283412
C2×D4×D3322
C2×#191283332
C2×#191282912
C2×#191282902
C2×#191282842
C2×#191282702
C2×#191282692
C2×#191282622
C22×#145817622
C2×#120×D832
C2×#551×C832
C2×#353283