Finite Group Databasebeta

← C2×#24921900 #36312015

Subgroups — C2×#24921900 #36312015

Order 21248.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921900C2132yesmaximal, direct product factor
2C2×#19128453C214yesmaximal, complemented
3C2×#19128429C211yesmaximal, characteristic, complemented
4C2×#19128421C211yesmaximal, characteristic, complemented
5C2×#19128408C212yesmaximal, complemented
6C2×#19128397C212yesmaximal, complemented
7C2×Q8×D332C211yesmaximal, characteristic, complemented
8C2×#19128364C212yesmaximal, complemented
9C2×#19128357C212yesmaximal, complemented
10C2×#19128355C211yesmaximal, characteristic, complemented
11C2×#19128329C212yesmaximal, complemented
12C2×#19128322C212yesmaximal, complemented
13C2×#19128314C212yesmaximal, complemented
14C2×#19128295C214yesmaximal, complemented
15C2×#19128271C212yesmaximal, complemented
16C22×#14581792C211yesmaximal, characteristic, complemented
17C2×#19128235C211yesmaximal, characteristic, complemented
18C2×#529×C83C211yesmaximal, characteristic, complemented
19C22×#13050589C2212yes—
20C23×Dic166C2212yes—
21C22×Q8×D83C2212yes—
22#19128453C22164yescomplemented
23#19128429C22116yescomplemented
24#19128421C22116yescomplemented
25#19128408C22132yescomplemented
26#19128397C22132yescomplemented
27Q8×D332C22116yescomplemented
28#19128364C22132yescomplemented
29#19128357C22132yescomplemented
30#19128355C22116yescomplemented
31#19128329C22132yescomplemented
32#19128322C22132yescomplemented
33#19128314C22132yescomplemented
34#19128295C22164yescomplemented
35#19128271C22132yescomplemented
36C2×#14581792C2212yes—
37C2×#14581792C2212yes—
38C2×#14581792C2212yes—
39C2×#14581792C2211yescharacteristic
40C2×#14581792C2211yescharacteristic
41C2×#14581792C2212yes—
42C2×#14581792C22116yescomplemented
43C2×#14581791C2214yes—
44C2×#14581790C2212yes—
45#19128235C22116yescomplemented
46C2×#14581787C2214yes—
47C2×#14581787C2214yes—
48C2×#14581786C2212yes—
49C2×#14581785C2214yes—
50C2×#14581784C2211yescharacteristic
51C2×#14581784C2212yes—
52C2×#14581783C2214yes—
53C2×#14581783C2214yes—
54C2×#14581782C2214yes—
55C2×#14581780C2211yescharacteristic
56C2×#14581779C2212yes—
57C2×#14581778C2214yes—
58C2×#14581776C2214yes—
59C2×#14581775C2212yes—
60C2×#14581774C2214yes—
61C2×#14581774C2214yes—
62C2×#14581772C2212yes—
63C2×#14581772C2212yes—
64C2×#14581772C2214yes—
65C2×#14581771C2212yes—
66C2×#14581771C2211yescharacteristic
67C2×#14581770C2214yes—
68C2×#14581769C2214yes—
69C2×#14581769C2214yes—
70C2×#14581769C2214yes—
71C2×#14581769C2214yes—
72C2×#14581766C2212yes—
73C2×#14581766C2211yescharacteristic
74C2×#14581764C2214yes—
75C2×C4×Dic166C2212yes—
76C2×C4×Dic166C2211yescharacteristic
77C2×#14581757C2212yes—
78C2×#14581757C2212yes—
79C2×C4×D332C2212yes—
80C2×C4×D332C2211yescharacteristic
81C2×D4×Dic83C2214yes—
82C2×C4×C22⋊D83C2212yes—
83C2×(C22⋊D83)⋊C4C2214yes—
84C2×#14581751C2212yes—
85C2×#14581749C2212yes—
86C22×C4⋊Dic83C2212yes—
87C22×C4⋊Dic83C2212yes—
88C22×C4⋊Dic83C2212yes—
89#529×C83C22116yescomplemented
90C2×#126×C83C2212yes—
91C2×#125×C83C2211yescharacteristic
92C2×#124×C83C2211yescharacteristic
93C2×#123×C83C2212yes—
94C2×C22⋊Q8×C83C2211yescharacteristic
95C2×#121×C83C2211yescharacteristic
96C2×C4×Q8×C83C2211yescharacteristic
97C2×C4×D4×C83C2211yescharacteristic
98C2×C4×D4×C83C2212yes—
99C2×#117×C83C2212yes—
100C22×C42×C83C2211yescharacteristic
101C2×#13050589—48no—
102C2×#13050589C23116yes—
103C22×Dic166—48no—
104C22×Dic166C2312yes—
105C22×Dic166C2312yes—
106C22×Dic166C2311yescharacteristic
107C22×Dic166C23116yes—
108C22×Dic166C2314yes—
109C22×Dic166C2314yes—
110C2×Q8×D83—48no—
111C2×Q8×D83C23116yes—
112C22×D332C2311yescharacteristic
113C22×C22⋊D83C2312yes—
114C22×C22⋊D83C2314yes—
115C23×Dic83C2314yes—
116C23×Dic83C2314yes—
117C22×C4×D83C2312yes—
118C22×C4×D83C2314yes—
119#14581792C23116yes—
120#14581792C23116yes—
121#14581792C2318yes—
122#14581792C2318yes—
123#14581792C23116yes—
124#14581792C23116yes—
125#14581791C23132yes—
126#14581790C23116yes—
127#14581787C23132yes—
128#14581787C23132yes—
129#14581786C23116yes—
130#14581785C23132yes—
131#14581784C2318yes—
132#14581784C23116yes—
133#14581783C23132yes—
134#14581783C23132yes—
135#14581782C23132yes—
136#14581780C2318yes—
137#14581779C23116yes—
138#14581778C23132yes—
139#14581776C23132yes—
140#14581775C23116yes—
141#14581774C23132yes—
142#14581774C23132yes—
143#14581772C23116yes—
144#14581772C23116yes—
145#14581772C23132yes—
146#14581771C23116yes—
147#14581771C2318yes—
148#14581770C23132yes—
149#14581769C23132yes—
150#14581769C23132yes—
151#14581769C23132yes—
152#14581769C23132yes—
153#14581766C23116yes—
154#14581766C2318yes—
155#14581764C23132yes—
156C4×Dic166C23116yes—
157C4×Dic166C2318yes—
158#14581757C23116yes—
159#14581757C23116yes—
160C4×D332C23116yes—
161C4×D332C2318yes—
162D4×Dic83C23132yes—
163C4×C22⋊D83C23116yes—
164(C22⋊D83)⋊C4C23132yes—
165#14581751C23116yes—
166#14581749C23116yes—
167C2×C4⋊Dic83C23116yes—
168C2×C4⋊Dic83C23116yes—
169C2×C4⋊Dic83C2311yescharacteristic
170C2×C4⋊Dic83C2312yes—
171C2×C4⋊Dic83C2312yes—
172C2×C4⋊Dic83C2314yes—
173C2×C4⋊Dic83C2314yes—
174C2×C4⋊Dic83C2314yes—
175C2×C4⋊Dic83C2312yes—
176C2×C4⋊Dic83C2312yes—
177C2×C4⋊Dic83C23116yes—
178C2×C4⋊Dic83C2311yescharacteristic
179C2×C4⋊Dic83C2314yes—
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2312yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2314yes—
185C2×Dic83⋊C4C2314yes—
186C2×Dic83⋊C4C2314yes—
187C2×Dic83⋊C4C2312yes—
188C2×C22⋊Dic83C2314yes—
189C2×C22⋊Dic83C2312yes—
190C2×C22⋊Dic83C2314yes—
191C2×(C2×D83)⋊C4C2312yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2314yes—
194C2×(C2×D83)⋊C4C2312yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2312yes—
197C2×C4×Dic83C2312yes—
198C2×C4×Dic83C2314yes—
199C2×C4×Dic83C2314yes—
200C22×Q8×C83C2311yescharacteristic
201C22×D4×C83C2312yes—
202C22×D4×C83C2311yescharacteristic
203C23×C4×C83C2311yescharacteristic
204C23×C4×C83C2311yescharacteristic
205C23×C4×C83C2311yescharacteristic
206C23×C4×C83C2312yes—
207#126×C83C23116yes—
208#125×C83C2318yes—
209#124×C83C2318yes—
210#123×C83C23116yes—
211C22⋊Q8×C83C2318yes—
212#121×C83C2318yes—
213C4×Q8×C83C2318yes—
214C4×D4×C83C2318yes—
215C4×D4×C83C23116yes—
216#117×C83C23116yes—
217C2×C4⋊C4×C83C2312yes—
218C2×C4⋊C4×C83C2312yes—
219C2×C4⋊C4×C83C2311yescharacteristic
220C2×C4⋊C4×C83C2312yes—
221C2×C4⋊C4×C83C2311yescharacteristic
222C2×C4⋊C4×C83C2312yes—
223C2×C22⋊C4×C83C2312yes—
224C2×C22⋊C4×C83C2312yes—
225C2×C22⋊C4×C83C2312yes—
226C2×C22⋊C4×C83C2312yes—
227C2×C22⋊C4×C83C2312yes—
228C2×C42×C83C2311yescharacteristic
229C2×C42×C83C2311yescharacteristic
230C2×C42×C83C2311yescharacteristic
231C2×C42×C83C2311yescharacteristic
232C2×C42×C83C2318yes—
233C2×C42×C83C2312yes—
234C23×D83C2412yes—
235#13050589—432no—
236C2×Dic166—28no—
237C2×Dic166—28no—
238C2×Dic166—24no—
239C2×Dic166—432no—
240C2×Dic166—48no—
241C2×Dic166—48no—
242C2×Dic166C2414yes—
243C2×Dic166C2418yes—
244C2×Dic166C2418yes—
245C2×Dic166C24116yes—
246C2×Dic166C24116yes—
247Q8×D83—432no—
248C2×D332—24no—
249C2×D332C2414yes—
250C2×C22⋊D83—28no—
251C2×C22⋊D83—48no—
252C2×C22⋊D83C2418yes—
253C2×C22⋊D83C24116yes—
254C22×Dic83—48no—
255C22×Dic83—48no—
256C22×Dic83C2412yes—
257C22×Dic83C2414yes—
258C22×Dic83C2414yes—
259C22×Dic83C2412yes—
260C22×Dic83C2412yes—
261C22×Dic83C24116yes—
262C22×Dic83C24116yes—
263C2×C4×D83—28no—
264C2×C4×D83—48no—
265C2×C4×D83C2418yes—
266C2×C4×D83C24116yes—
267C4⋊Dic83C2414yes—
268C4⋊Dic83C2418yes—
269C4⋊Dic83C24116yes—
270C4⋊Dic83C24116yes—
271C4⋊Dic83C24116yes—
272C4⋊Dic83C24116yes—
273C4⋊Dic83C2414yes—
274C4⋊Dic83C2418yes—
275C4⋊Dic83C2418yes—
276C4⋊Dic83C2418yes—
277Dic83⋊C4C24116yes—
278Dic83⋊C4C24116yes—
279Dic83⋊C4C2418yes—
280Dic83⋊C4C2418yes—
281Dic83⋊C4C2418yes—
282Dic83⋊C4C24116yes—
283Dic83⋊C4C24116yes—
284Dic83⋊C4C2418yes—
285C22⋊Dic83C24116yes—
286C22⋊Dic83C2418yes—
287C22⋊Dic83C24116yes—
288(C2×D83)⋊C4C24116yes—
289(C2×D83)⋊C4C24116yes—
290(C2×D83)⋊C4C2418yes—
291(C2×D83)⋊C4C2418yes—
292(C2×D83)⋊C4C2418yes—
293(C2×D83)⋊C4C2418yes—
294C4×Dic83C24116yes—
295C4×Dic83C2418yes—
296C4×Dic83C24116yes—
297C24×C83C2412yes—
298C24×C83C2411yescharacteristic
299C2×Q8×C83—24no—
300C2×Q8×C83C2414yes—
301C2×D4×C83—28no—
302C2×D4×C83—24no—
303C2×D4×C83C2418yes—
304C2×D4×C83C2414yes—
305C22×C4×C83—24no—
306C22×C4×C83—24no—
307C22×C4×C83—24no—
308C22×C4×C83—28no—
309C22×C4×C83C2414yes—
310C22×C4×C83C2418yes—
311C22×C4×C83C2414yes—
312C22×C4×C83C2412yes—
313C22×C4×C83C2411yescharacteristic
314C22×C4×C83C2414yes—
315C22×C4×C83C2411yescharacteristic
316C22×C4×C83C2411yescharacteristic
317C22×C4×C83C2411yescharacteristic
318C22×C4×C83C2412yes—
319C22×C4×C83C2412yes—
320C22×C4×C83C2411yescharacteristic
321C22×C4×C83C2411yescharacteristic
322C4⋊C4×C83C2418yes—
323C4⋊C4×C83C2418yes—
324C4⋊C4×C83C2414yes—
325C4⋊C4×C83C2414yes—
326C4⋊C4×C83C2418yes—
327C4⋊C4×C83C2418yes—
328C22⋊C4×C83C2418yes—
329C22⋊C4×C83C2418yes—
330C22⋊C4×C83C2418yes—
331C22⋊C4×C83C2418yes—
332C22⋊C4×C83C2418yes—
333C42×C83C2414yes—
334C42×C83C2418yes—
335C42×C83C2414yes—
336C42×C83C2414yes—
337C42×C83C2414yes—
338C23×C83—22no—
339C23×C83—22no—
340C23×C83—24no—
341C23×C83—24no—
342C23×C83—24no—
343C23×C832−1+414yes—
344C23×C83C2514yes—
345C23×C83C2512yes—
346C23×C83C2511yescharacteristic
347C22×D83—24no—
348C22×D83—24no—
349C22×D83—24no—
350C22×D83C2514yes—
351Q8×C83—28no—
352D4×C83—216no—
353D4×C83—28no—
354C2×C4×C83—22no—
355C2×C4×C83—24no—
356C2×C4×C83—28no—
357C2×C4×C83—22no—
358C2×C4×C83—22no—
359C2×C4×C83—22no—
360C2×C4×C83—24no—
361C2×C4×C83—24no—
362C2×C4×C83—28no—
363C2×C4×C83—28no—
364C2×C4×C83—216no—
365C2×C4×C83H(5,𝔽2)14yes—
366C2×C4×C832−1+414yes—
367C2×C4×C83C2512yes—
368C2×C4×C83C2512yes—
369C2×C4×C83C2512yes—
370C2×C4×C83C2512yes—
371C2×C4×C83C2514yes—
372C2×C4×C83C2514yes—
373C2×C4×C83C2514yes—
374C2×C4×C83C2512yes—
375C2×C4×C83C2512yes—
376C22⋊D83—216no—
377C22⋊D83—416no—
378C2×Dic83—24no—
379C2×Dic83—28no—
380C2×Dic83—28no—
381C2×Dic83—24no—
382C2×Dic83—24no—
383C2×Dic83—416no—
384C2×Dic83—416no—
385C2×Dic83C2514yes—
386C2×Dic83C2514yes—
387C2×Dic83C2518yes—
388C2×Dic83C2518yes—
389C2×Dic83C2514yes—
390D332—28no—
391C4×D83—216no—
392C4×D83—416no—
393Dic166—216no—
394Dic166—216no—
395Dic166—28no—
396Dic166—416no—
397Dic166—416no—
398C22×C83—22no—
399C22×C83—22no—
400C22×C83—28no—
401C22×C83—24no—
402C22×C83—24no—
403C22×C83—24no—
404C22×C83—48no—
405C22×C83C2×H(5,𝔽2)12yes—
406C22×C83C2×2−1+414yes—
407C22×C83C2×2−1+412yes—
408C22×C83C2×2−1+412yes—
409C22×C83C2611yescharacteristic
410C2×D83—24no—
411C2×D83—24no—
412C2×D83—24no—
413C2×D83—48no—
414C4×C83—22no—
415C4×C83—24no—
416C4×C83—22no—
417C4×C83—22no—
418C4×C83—22no—
419C4×C83—24no—
420C4×C83—24no—
421C4×C83C2×H(5,𝔽2)14yes—
422C4×C83C2×2−1+414yes—
423Dic83—28no—
424Dic83—28no—
425Dic83—24no—
426Dic83—24no—
427Dic83—24no—
428C2×#3552—831nomaximal, Sylow
429C2×C83—24no—
430C2×C83—44no—
431C2×C83#355214yescomplemented
432C2×C83C22×H(5,𝔽2)11yescharacteristic
433C2×C83C22×2−1+411yescharacteristic
434C2×C83C22×2−1+411yescharacteristic
435D83—44no—
436#3552—8332no—
437C2×#563—834no—
438C2×#557—831no—
439C2×#556—831no—
440C2×#554—832no—
441C2×#553—832no—
442C2×D4×Q8—832no—
443C2×D4×Q8—831no—
444C2×#548—832no—
445C2×#547—831no—
446C2×#544—832no—
447C2×#542—832no—
448C2×#541—832no—
449C2×#539—834no—
450C2×#536—832no—
451C22×C4⋊Q8—831no—
452C2×#529—831no—
453C2×#529D8311yescharacteristic, complemented
454C83C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—832no—
456C23×Q8—832no—
457C23×Q8—832no—
458#563—8364no—
459#557—8316no—
460#556—8316no—
461#554—8332no—
462#553—8332no—
463D4×Q8—8332no—
464D4×Q8—8316no—
465#548—8332no—
466#547—8316no—
467#544—8332no—
468#542—8332no—
469#541—8332no—
470#539—8364no—
471#536—8332no—
472C2×C4⋊Q8—832no—
473C2×C4⋊Q8—834no—
474C2×C4⋊Q8—832no—
475C2×C4⋊Q8—832no—
476C2×C4⋊Q8—831no—
477C2×C4⋊Q8—831no—
478C2×C4⋊Q8—832no—
479C2×C4⋊Q8—8316no—
480C2×C4⋊Q8—832no—
481#529—8316no—
482#529C2×D83116yescomplemented
483C2×#126—834no—
484C2×#126—834no—
485C2×#126—834no—
486C2×#126—832no—
487C2×#126C2×D8312yes—
488C2×#125—834no—
489C2×#125—834no—
490C2×#125—834no—
491C2×#125—831no—
492C2×#125—832no—
493C2×#125C2×D8311yescharacteristic
494C2×#124—832no—
495C2×#124—834no—
496C2×#124—831no—
497C2×#124C2×D8311yescharacteristic
498C2×#123—832no—
499C2×#123—834no—
500C2×#123—834no—
501C2×#123—834no—
502C2×#123C2×D8312yes—
503C2×C22⋊Q8—831no—
504C2×C22⋊Q8—832no—
505C2×C22⋊Q8—834no—
506C2×C22⋊Q8—832no—
507C2×C22⋊Q8—832no—
508C2×C22⋊Q8—834no—
509C2×C22⋊Q8—834no—
510C2×C22⋊Q8—834no—
511C2×C22⋊Q8—834no—
512C2×C22⋊Q8—834no—
513C2×C22⋊Q8C2×D8311yescharacteristic
514C2×#121—834no—
515C2×#121—831no—
516C2×#121—832no—
517C2×#121C2×D8311yescharacteristic
518C2×C4×Q8—832no—
519C2×C4×Q8—832no—
520C2×C4×Q8—831no—
521C2×C4×Q8—832no—
522C2×C4×Q8C2×D8311yescharacteristic
523C2×C4×D4—834no—
524C2×C4×D4—832no—
525C2×C4×D4—834no—
526C2×C4×D4—831no—
527C2×C4×D4—832no—
528C2×C4×D4C2×D8311yescharacteristic
529C2×C4×D4C2×D8312yes—
530C2×#117—832no—
531C2×#117—832no—
532C2×#117C2×D8312yes—
533C22×C4⋊C4—832no—
534C22×C4⋊C4—832no—
535C22×C4⋊C4—832no—
536C22×C42C2×D8311yescharacteristic
537C2×#41—3328no—
538C2×#41—8316no—
539C22×Q8—3328no—
540C22×Q8—3328no—
541C22×Q8—8316no—
542C22×Q8—834no—
543C22×Q8—834no—
544C22×Q8—8316no—
545C22×Q8—831no—
546C22×Q8—832no—
547C22×Q8—832no—
548C22×Q8C22×D8311yescharacteristic
549C22×D4—834no—
550C22×D4—832no—
551C22×D4—831no—
552C22×D4C22×D8312yes—
553C22×D4C22×D8311yescharacteristic
554C23×C4—834no—
555C23×C4—834no—
556C23×C4—834no—
557C23×C4—832no—
558C23×C4C22×D8311yescharacteristic
559C23×C4C22×D8311yescharacteristic
560C23×C4C22×D8312yes—
561C23×C4C22×D8311yescharacteristic
562C4⋊Q8—8316no—
563C4⋊Q8—8332no—
564C4⋊Q8—8316no—
565C4⋊Q8—8316no—
566C4⋊Q8—838no—
567C4⋊Q8—838no—
568C4⋊Q8—8316no—
569C4⋊Q8—8316no—
570#126—8332no—
571#126—8332no—
572#126—8332no—
573#126—8316no—
574#126C22×D83116yes—
575#125—8332no—
576#125—8332no—
577#125—8332no—
578#125—838no—
579#125—8316no—
580#125C22×D8318yes—
581#124—8316no—
582#124—8332no—
583#124—838no—
584#124C22×D8318yes—
585#123—8316no—
586#123—8332no—
587#123—8332no—
588#123—8332no—
589#123C22×D83116yes—
590C22⋊Q8—838no—
591C22⋊Q8—8316no—
592C22⋊Q8—8332no—
593C22⋊Q8—8332no—
594C22⋊Q8—8316no—
595C22⋊Q8—8316no—
596C22⋊Q8—8332no—
597C22⋊Q8—8332no—
598C22⋊Q8—8332no—
599C22⋊Q8—8332no—
600C22⋊Q8C22×D8318yes—
601#121—8332no—
602#121—838no—
603#121—8316no—
604#121C22×D8318yes—
605C4×Q8—8316no—
606C4×Q8—8316no—
607C4×Q8—838no—
608C4×Q8—8316no—
609C4×Q8C22×D8318yes—
610C4×D4—8332no—
611C4×D4—8316no—
612C4×D4—8332no—
613C4×D4—838no—
614C4×D4—8316no—
615C4×D4C22×D8318yes—
616C4×D4C22×D83116yes—
617#117—8316no—
618#117—8316no—
619#117C22×D83116yes—
620C2×C4⋊C4—831no—
621C2×C4⋊C4—832no—
622C2×C4⋊C4—832no—
623C2×C4⋊C4—834no—
624C2×C4⋊C4—832no—
625C2×C4⋊C4—834no—
626C2×C4⋊C4—834no—
627C2×C4⋊C4—832no—
628C2×C4⋊C4—8316no—
629C2×C4⋊C4—8316no—
630C2×C4⋊C4—8316no—
631C2×C4⋊C4—831no—
632C2×C4⋊C4—832no—
633C2×C4⋊C4—832no—
634C2×C4⋊C4—834no—
635C2×C4⋊C4—832no—
636C2×C4⋊C4—834no—
637C2×C4⋊C4—834no—
638C2×C4⋊C4—834no—
639C2×C4⋊C4—834no—
640C2×C4⋊C4—832no—
641C2×C4⋊C4C22×D8312yes—
642C2×C4⋊C4C22×D8312yes—
643C2×C4⋊C4C22×D8311yescharacteristic
644C2×C4⋊C4C22×D8312yes—
645C2×C4⋊C4C22×D8311yescharacteristic
646C2×C4⋊C4C22×D8312yes—
647C2×C22⋊C4—834no—
648C2×C22⋊C4—832no—
649C2×C22⋊C4—834no—
650C2×C22⋊C4—832no—
651C2×C22⋊C4—832no—
652C2×C22⋊C4—834no—
653C2×C22⋊C4—834no—
654C2×C22⋊C4—832no—
655C2×C22⋊C4—832no—
656C2×C22⋊C4C22×D8312yes—
657C2×C22⋊C4C22×D8312yes—
658C2×C22⋊C4C22×D8312yes—
659C2×C22⋊C4C22×D8312yes—
660C2×C22⋊C4C22×D8312yes—
661C2×C42—832no—
662C2×C42—834no—
663C2×C42—834no—
664C2×C42C22×D8311yescharacteristic
665C2×C42C22×D8311yescharacteristic
666C2×C42C22×D8312yes—
667C2×C42C22×D8311yescharacteristic
668C2×C42C22×D8311yescharacteristic
669C2×C42C22×D8318yes—
670C24—832no—
671C24C23×D8312yes—
672C24C23×D8311yescharacteristic
673#41—33232no—
674C2×Q8—24no—
675C2×Q8—33232no—
676C2×Q8—3328no—
677C2×Q8—3328no—
678C2×Q8—33232no—
679C2×Q8—8316no—
680C2×Q8—8316no—
681C2×Q8—834no—
682C2×Q8—838no—
683C2×Q8—838no—
684C2×Q8—1668no—
685C2×Q8—1668no—
686C2×Q8—1664no—
687C2×Q8C23×D8314yes—
688C2×D4—28no—
689C2×D4—24no—
690C2×D4—3328no—
691C2×D4—8316no—
692C2×D4—838no—
693C2×D4—834no—
694C2×D4—1668no—
695C2×D4—1664no—
696C2×D4C23×D8318yes—
697C2×D4C23×D8314yes—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—28no—
702C22×C4—3328no—
703C22×C4—3328no—
704C22×C4—3328no—
705C22×C4—8316no—
706C22×C4—8316no—
707C22×C4—8316no—
708C22×C4—832no—
709C22×C4—832no—
710C22×C4—834no—
711C22×C4—834no—
712C22×C4—832no—
713C22×C4—838no—
714C22×C4—1668no—
715C22×C4C23×D8314yes—
716C22×C4C23×D8314yes—
717C22×C4C23×D8314yes—
718C22×C4C23×D8318yes—
719C22×C4C23×D8312yes—
720C22×C4C23×D8312yes—
721C22×C4C23×D8311yescharacteristic
722C22×C4C23×D8311yescharacteristic
723C22×C4C23×D8311yescharacteristic
724C22×C4C23×D8311yescharacteristic
725C22×C4C23×D8312yes—
726C22×C4C23×D8311yescharacteristic
727C22×C4C23×D8311yescharacteristic
728C4⋊C4—834no—
729C4⋊C4—838no—
730C4⋊C4—838no—
731C4⋊C4—8316no—
732C4⋊C4—838no—
733C4⋊C4—8316no—
734C4⋊C4—8316no—
735C4⋊C4—838no—
736C4⋊C4—834no—
737C4⋊C4—838no—
738C4⋊C4—838no—
739C4⋊C4—8316no—
740C4⋊C4—838no—
741C4⋊C4—8316no—
742C4⋊C4—8316no—
743C4⋊C4—8316no—
744C4⋊C4—8316no—
745C4⋊C4—838no—
746C4⋊C4C23×D8318yes—
747C4⋊C4C23×D8318yes—
748C4⋊C4C23×D8314yes—
749C4⋊C4C23×D8318yes—
750C4⋊C4C23×D8314yes—
751C4⋊C4C23×D8318yes—
752C22⋊C4—8316no—
753C22⋊C4—838no—
754C22⋊C4—8316no—
755C22⋊C4—838no—
756C22⋊C4—838no—
757C22⋊C4—8316no—
758C22⋊C4—8316no—
759C22⋊C4—838no—
760C22⋊C4—838no—
761C22⋊C4C23×D8318yes—
762C22⋊C4C23×D8318yes—
763C22⋊C4C23×D8318yes—
764C22⋊C4C23×D8318yes—
765C22⋊C4C23×D8318yes—
766C42—838no—
767C42—8316no—
768C42—8316no—
769C42C23×D8314yes—
770C42C23×D8314yes—
771C42C23×D8314yes—
772C42C23×D8314yes—
773C42C23×D8318yes—
774C23—22no—
775C23—22no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—834no—
780C23—1664no—
781C23—1664no—
782C23—1664no—
783C23#1458183914yes—
784C23C24×D8314yes—
785C23C24×D8312yes—
786C23C24×D8311yescharacteristic
787Q8—28no—
788Q8—33216no—
789Q8—33216no—
790Q8—16616no—
791Q8—16616no—
792Q8—1668no—
793D4—216no—
794D4—28no—
795D4—33216no—
796D4—16616no—
797D4—1668no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—216no—
809C2×C4—33216no—
810C2×C4—33216no—
811C2×C4—33216no—
812C2×C4—834no—
813C2×C4—834no—
814C2×C4—838no—
815C2×C4—838no—
816C2×C4—834no—
817C2×C4—1664no—
818C2×C4—1668no—
819C2×C4—1668no—
820C2×C4—1664no—
821C2×C4—1664no—
822C2×C4—16616no—
823C2×C4#1458183814yes—
824C2×C4#1458183914yes—
825C2×C4C24×D8314yes—
826C2×C4C24×D8314yes—
827C2×C4C24×D8312yes—
828C2×C4C24×D8312yes—
829C2×C4C24×D8312yes—
830C2×C4C24×D8312yes—
831C2×C4C24×D8314yes—
832C2×C4C24×D8312yes—
833C2×C4C24×D8312yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—48no—
841C22—3328no—
842C22—1664no—
843C22—1664no—
844C22—1664no—
845C22C2×#1458183812yes—
846C22C2×#1458183914yes—
847C22C2×#1458183912yes—
848C22C2×#1458183912yes—
849C22C25×D8311yescharacteristic
850C4—22no—
851C4—24no—
852C4—22no—
853C4—22no—
854C4—24no—
855C4—22no—
856C4—24no—
857C4—1664no—
858C4—1668no—
859C4—1668no—
860C4—1664no—
861C4—1664no—
862C4C2×#1458183814yes—
863C4C2×#1458183914yes—
864C2—24no—
865C2—44no—
866C2—3324no—
867C2#2492190014yesdirect product factor
868C2C22×#1458183811yescharacteristic
869C2C22×#1458183911yescharacteristic
870C2C22×#1458183911yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#529×C83C2
socleC23×C83C25
hypercenterC2×#529D83
hypocenterC83C2×#3552
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #24921900C2direct (N × H)
2. C2×#19128453C2semidirect
3. C2×#19128429C2semidirect
4. C2×#19128421C2semidirect
5. C2×#19128408C2semidirect
6. C2×#19128397C2semidirect
7. C2×Q8×D332C2semidirect
8. C2×#19128364C2semidirect
9. C2×#19128357C2semidirect
10. C2×#19128355C2semidirect
11. C2×#19128329C2semidirect
12. C2×#19128322C2semidirect
13. C2×#19128314C2semidirect
14. C2×#19128295C2semidirect
15. C2×#19128271C2semidirect
16. C22×#14581792C2semidirect
17. C2×#19128235C2semidirect
18. C2×#529×C83C2semidirect
22. #19128453C22semidirect
23. #19128429C22semidirect
24. #19128421C22semidirect
25. #19128408C22semidirect
26. #19128397C22semidirect
27. Q8×D332C22semidirect
28. #19128364C22semidirect
29. #19128357C22semidirect
30. #19128355C22semidirect
31. #19128329C22semidirect
32. #19128322C22semidirect
33. #19128314C22semidirect
34. #19128295C22semidirect
35. #19128271C22semidirect
42. C2×#14581792C22semidirect
45. #19128235C22semidirect
89. #529×C83C22semidirect
431. C2×C83#3552semidirect
453. C2×#529D83semidirect
454. C83C2×#3552semidirect
482. #529C2×D83semidirect
867. C2#24921900direct (N × H)

Maximal subgroups

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

subgroupindex
#249219002
C2×#191284532
C2×#191284292
C2×#191284212
C2×#191284082
C2×#191283972
C2×Q8×D3322
C2×#191283642
C2×#191283572
C2×#191283552
C2×#191283292
C2×#191283222
C2×#191283142
C2×#191282952
C2×#191282712
C22×#145817922
C2×#191282352
C2×#529×C832
C2×#355283