Finite Group Databasebeta

← C2×#24921952 #36312123

Subgroups — C2×#24921952 #36312123

Order 21248.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921952C2132yesmaximal, direct product factor
2C2×#19128450C214yesmaximal, complemented
3C2×#19128429C211yesmaximal, characteristic, complemented
4C2×#19128426C212yesmaximal, complemented
5C2×#19128425C212yesmaximal, complemented
6C2×#19128424C211yesmaximal, characteristic, complemented
7C2×#19128423C212yesmaximal, complemented
8C2×#19128412C211yesmaximal, characteristic, complemented
9C2×#19128392C212yesmaximal, complemented
10C2×#19128328C212yesmaximal, complemented
11C2×#19128325C212yesmaximal
12C2×#19128312C214yesmaximal, complemented
13C2×#19128309C212yesmaximal, complemented
14C2×#19128309C212yesmaximal, complemented
15C2×#19128256C211yesmaximal, characteristic, complemented
16C2×#19128255C211yesmaximal, characteristic, complemented
17C2×#19128238C211yesmaximal, characteristic
18C2×Q82×C83C211yesmaximal, characteristic, complemented
19#19128450C22164yescomplemented
20#19128429C22116yescomplemented
21#19128426C22132yescomplemented
22#19128425C22132yescomplemented
23#19128424C22116yescomplemented
24#19128423C22132yescomplemented
25#19128412C22116yescomplemented
26#19128392C22132yescomplemented
27#19128328C22132yescomplemented
28#19128325C22132yes—
29#19128312C22164yescomplemented
30#19128309C22132yescomplemented
31#19128309C22132yescomplemented
32#19128256C22116yescomplemented
33#19128255C22116yescomplemented
34C2×#14581792C2211yescharacteristic
35C2×#14581791C2211yescharacteristic
36C2×#14581790C2214yes—
37C2×#14581790C2211yescharacteristic
38C2×#14581790C2212yes—
39#19128238C22116yes—
40C2×#14581787C2214yes—
41C2×#14581787C2212yes—
42C2×#14581787C2214yes—
43C2×#14581787C2214yes—
44C2×#14581787C2214yes—
45C2×#14581786C2214yes—
46C2×#14581786C2214yes—
47C2×#14581784C2212yes—
48C2×#14581784C2214yes—
49C2×#14581783C2212yes—
50C2×#14581783C2211yescharacteristic
51C2×#14581783C2212yes—
52C2×#14581782C2214yes—
53C2×#14581782C2214yes—
54C2×#14581782C2212yes—
55C2×#14581782C2214yes—
56C2×#14581782C2214yes—
57C2×#14581781C2214yes—
58C2×#14581781C2211yescharacteristic
59C2×#14581780C2212yes—
60C2×#14581777C2214yes—
61C2×#14581777C2212yes—
62C2×#14581772C2212yes—
63C2×#14581772C2212yes—
64C2×#14581772C2211yescharacteristic
65C2×#14581770C2214yes—
66C2×#14581770C2212yes—
67C2×#14581768C2214yes—
68C2×#14581768C2211yescharacteristic
69C2×#14581768C2212yes—
70C2×#14581768C2211yescharacteristic
71C2×#14581768C2214yes—
72C2×#14581768C2212yes—
73C2×#14581767C2211yescharacteristic
74C2×Q8×Dic83C2212yes—
75C2×Q8×Dic83C2214yes—
76C2×C4×Dic166C2211yescharacteristic
77C2×C4×Dic166C2212yes—
78C2×C4×Dic166C2212yes—
79C2×C4×Dic166C2212yes—
80C2×#14581757C2212yes—
81C2×#14581757C2212yes—
82C2×C4×D332C2212yes—
83C2×C4×D332C2211yescharacteristic
84C2×#14581754C2212yes—
85C2×#14581750C2212yes—
86C2×#14581750C2212yes—
87C2×#14581749C2212yes—
88C2×#14581749C2212yes—
89C2×#14581749C2214yes—
90C2×C4⋊C4×D83C2212yes—
91C2×C42×D83C2211yescharacteristic
92Q82×C83C22116yescomplemented
93C2×C4⋊Q8×C83C2212yes—
94C2×C4⋊Q8×C83C2212yes—
95C2×C4⋊Q8×C83C2211yescharacteristic
96C2×C4⋊Q8×C83C2214yes—
97C2×C4×Q8×C83C2212yes—
98C2×C4×Q8×C83C2211yescharacteristic
99C2×C4×Q8×C83C2211yescharacteristic
100C2×C4×Q8×C83C2212yes—
101C22×Dic166C2312yes—
102C22×Dic166C2311yescharacteristic
103C22×Dic166C2312yes—
104C22×D332C2311yescharacteristic
105C22×D332C2312yes—
106C22×C4×D83C2311yescharacteristic
107C22×C4×D83C2311yescharacteristic
108C22×C4×D83C2312yes—
109C22×C4×D83C2311yescharacteristic
110C22×C4×D83C2314yes—
111#14581792C2318yes—
112#14581791C2318yes—
113#14581790C23132yes—
114#14581790C23116yes—
115#14581790C2318yes—
116#14581787C23132yes—
117#14581787C23132yes—
118#14581787C23132yes—
119#14581787C23132yes—
120#14581787C23116yes—
121#14581786C23132yes—
122#14581786C23132yes—
123#14581784C23116yes—
124#14581784C23132yes—
125#14581783C23116yes—
126#14581783C23116yes—
127#14581783C2318yes—
128#14581782C23132yes—
129#14581782C23132yes—
130#14581782C23132yes—
131#14581782C23132yes—
132#14581782C23116yes—
133#14581781C23132yes—
134#14581781C2318yes—
135#14581780C23116yes—
136#14581777C23132yes—
137#14581777C23116yes—
138#14581772C23116yes—
139#14581772C23116yes—
140#14581772C2318yes—
141#14581770C23132yes—
142#14581770C23116yes—
143#14581768C23132yes—
144#14581768C2318yes—
145#14581768C23116yes—
146#14581768C23132yes—
147#14581768C23116yes—
148#14581768C2318yes—
149#14581767C2318yes—
150Q8×Dic83C23132yes—
151Q8×Dic83C23116yes—
152C4×Dic166C2318yes—
153C4×Dic166C23116yes—
154C4×Dic166C23116yes—
155C4×Dic166C23116yes—
156#14581757C23116yes—
157#14581757C23116yes—
158C4×D332C23116yes—
159C4×D332C2318yes—
160#14581754C23116yes—
161#14581750C23116yes—
162#14581750C23116yes—
163#14581749C23116yes—
164#14581749C23116yes—
165#14581749C23132yes—
166C2×C4⋊Dic83C2311yescharacteristic
167C2×C4⋊Dic83C2312yes—
168C2×C4⋊Dic83C2311yescharacteristic
169C2×C4⋊Dic83C2312yes—
170C2×C4⋊Dic83C2312yes—
171C2×C4⋊Dic83C2314yes—
172C2×C4⋊Dic83C2314yes—
173C2×C4⋊Dic83C2312yes—
174C2×Dic83⋊C4C2314yes—
175C2×Dic83⋊C4C2312yes—
176C2×Dic83⋊C4C2312yes—
177C2×Dic83⋊C4C2312yes—
178C2×Dic83⋊C4C2314yes—
179C2×Dic83⋊C4C2312yes—
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2314yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2314yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2314yes—
187C4⋊C4×D83C23116yes—
188C2×(C2×D83)⋊C4C2312yes—
189C2×(C2×D83)⋊C4C2312yes—
190C2×(C2×D83)⋊C4C2312yes—
191C2×(C2×D83)⋊C4C2314yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2312yes—
194C2×(C2×D83)⋊C4C2314yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2312yes—
199C2×C4×Dic83C2311yescharacteristic
200C2×C4×Dic83C2311yescharacteristic
201C2×C4×Dic83C2311yescharacteristic
202C2×C4×Dic83C2314yes—
203C2×C4×Dic83C2312yes—
204C2×C4×Dic83C2314yes—
205C2×C4×Dic83C2314yes—
206C42×D83C2318yes—
207C22×Q8×C83C2311yescharacteristic
208C22×Q8×C83C2311yescharacteristic
209C22×Q8×C83C2312yes—
210C22×Q8×C83C2314yes—
211C4⋊Q8×C83C23116yes—
212C4⋊Q8×C83C23116yes—
213C4⋊Q8×C83C2318yes—
214C4⋊Q8×C83C23132yes—
215C4×Q8×C83C23116yes—
216C4×Q8×C83C23116yes—
217C4×Q8×C83C2318yes—
218C4×Q8×C83C2318yes—
219C2×C4⋊C4×C83C2312yes—
220C2×C4⋊C4×C83C2311yescharacteristic
221C2×C4⋊C4×C83C2312yes—
222C2×C4⋊C4×C83C2311yescharacteristic
223C2×C4⋊C4×C83C2312yes—
224C2×C4⋊C4×C83C2314yes—
225C2×C4⋊C4×C83C2314yes—
226C2×C4⋊C4×C83C2312yes—
227C2×C42×C83C2311yescharacteristic
228C2×C42×C83C2312yes—
229C2×C42×C83C2312yes—
230C2×C42×C83C2314yes—
231C23×D83C2411yescharacteristic
232C23×D83C2412yes—
233C2×Dic166—24no—
234C2×Dic166—28no—
235C2×Dic166—44no—
236C2×Dic166C2414yes—
237C2×Dic166C2418yes—
238C2×Dic166C2418yes—
239C2×D332—24no—
240C2×D332—44no—
241C2×D332C2414yes—
242C2×D332C2418yes—
243C22×Dic83C2412yes—
244C22×Dic83C2411yescharacteristic
245C22×Dic83C2411yescharacteristic
246C22×Dic83C2411yescharacteristic
247C22×Dic83C2412yes—
248C22×Dic83C2414yes—
249C22×Dic83C2412yes—
250C2×C4×D83—24no—
251C2×C4×D83—28no—
252C2×C4×D83—24no—
253C2×C4×D83—48no—
254C2×C4×D83—42no—
255C2×C4×D83C2414yes—
256C2×C4×D83C2414yes—
257C2×C4×D83C2418yes—
258C2×C4×D83C2414yes—
259C2×C4×D83C24116yes—
260C4⋊Dic83C24116yes—
261C4⋊Dic83C24116yes—
262C4⋊Dic83C2418yes—
263C4⋊Dic83C2414yes—
264C4⋊Dic83C2418yes—
265C4⋊Dic83C2414yes—
266C4⋊Dic83C2418yes—
267C4⋊Dic83C2418yes—
268Dic83⋊C4C2418yes—
269Dic83⋊C4C2418yes—
270Dic83⋊C4C24116yes—
271Dic83⋊C4C24116yes—
272Dic83⋊C4C2418yes—
273Dic83⋊C4C24116yes—
274Dic83⋊C4C2418yes—
275Dic83⋊C4C24116yes—
276Dic83⋊C4C24116yes—
277Dic83⋊C4C2418yes—
278Dic83⋊C4C2418yes—
279Dic83⋊C4C2418yes—
280Dic83⋊C4C24116yes—
281(C2×D83)⋊C4C2418yes—
282(C2×D83)⋊C4C2418yes—
283(C2×D83)⋊C4C2418yes—
284(C2×D83)⋊C4C24116yes—
285(C2×D83)⋊C4C24116yes—
286(C2×D83)⋊C4C24116yes—
287(C2×D83)⋊C4C24116yes—
288(C2×D83)⋊C4C2418yes—
289(C2×D83)⋊C4C2418yes—
290(C2×D83)⋊C4C2418yes—
291(C2×D83)⋊C4C2418yes—
292C4×Dic83C24116yes—
293C4×Dic83C2414yes—
294C4×Dic83C2414yes—
295C4×Dic83C24116yes—
296C4×Dic83C24116yes—
297C4×Dic83C2414yes—
298C4×Dic83C2418yes—
299C2×Q8×C83—24no—
300C2×Q8×C83—24no—
301C2×Q8×C83—44no—
302C2×Q8×C83—48no—
303C2×Q8×C83C2414yes—
304C2×Q8×C83C2414yes—
305C2×Q8×C83C2418yes—
306C2×Q8×C83C24116yes—
307C22×C4×C83C2411yescharacteristic
308C22×C4×C83C2414yes—
309C22×C4×C83C2412yes—
310C22×C4×C83C2412yes—
311C22×C4×C83C2412yes—
312C22×C4×C83C2412yes—
313C22×C4×C83C2411yescharacteristic
314C22×C4×C83C2411yescharacteristic
315C4⋊C4×C83C2414yes—
316C4⋊C4×C83C24116yes—
317C4⋊C4×C83C2418yes—
318C4⋊C4×C83C2418yes—
319C4⋊C4×C83C2418yes—
320C4⋊C4×C83C2414yes—
321C4⋊C4×C83C24116yes—
322C4⋊C4×C83C2418yes—
323C42×C83C2418yes—
324C42×C83C24116yes—
325C42×C83C2418yes—
326C42×C83C2414yes—
327C23×C83C2511yescharacteristic
328C22×D83—22no—
329C22×D83—22no—
330C22×D83—24no—
331C22×D83—24no—
332C22×D83—24no—
333C22×D83—22no—
334C22×D83C2512yes—
335C22×D83C2514yes—
336Q8×C83—28no—
337Q8×C83—28no—
338Q8×C83—416no—
339Q8×C83—48no—
340C2×C4×C83—24no—
341C2×C4×C83—24no—
342C2×C4×C83—22no—
343C2×C4×C83—28no—
344C2×C4×C83—24no—
345C2×C4×C83—24no—
346C2×C4×C832−1+414yes—
347C2×C4×C832−1+414yes—
348C2×C4×C83C2514yes—
349C2×C4×C83C2514yes—
350C2×C4×C83C2514yes—
351C2×C4×C83C2514yes—
352C2×C4×C83C2518yes—
353C2×C4×C83C2512yes—
354C2×C4×C83C2512yes—
355C2×C4×C83C2512yes—
356C2×Dic83—22no—
357C2×Dic83—24no—
358C2×Dic83—22no—
359C2×Dic83—24no—
360C2×Dic83—28no—
361C2×Dic83—24no—
362C2×Dic83—22no—
363C2×Dic83C2512yes—
364C2×Dic83C2514yes—
365C2×Dic83C2518yes—
366C2×Dic83C2512yes—
367C2×Dic83C2512yes—
368C2×Dic83C2514yes—
369C2×Dic83C2514yes—
370D332—28no—
371D332—48no—
372C4×D83—28no—
373C4×D83—28no—
374C4×D83—216no—
375C4×D83—44no—
376C4×D83—416no—
377Dic166—216no—
378Dic166—28no—
379Dic166—48no—
380C22×C83C2×2−1+412yes—
381C22×C83C2×2−1+412yes—
382C22×C83#58512yes—
383C22×C83C2611yescharacteristic
384C2×D83—22no—
385C2×D83—22no—
386C2×D83—24no—
387C2×D83—24no—
388C2×D83—24no—
389C2×D83—22no—
390C2×D83—44no—
391C2×D83—48no—
392C4×C83—24no—
393C4×C83—24no—
394C4×C83—24no—
395C4×C83—22no—
396C4×C83—28no—
397C4×C83—24no—
398C4×C83C2×2−1+414yes—
399C4×C83C2×2−1+414yes—
400Dic83—28no—
401Dic83—24no—
402Dic83—22no—
403Dic83—22no—
404Dic83—24no—
405Dic83—22no—
406Dic83—24no—
407C2×#3555—831nomaximal, Sylow
408C2×C83#355514yescomplemented
409C2×C83C22×2−1+411yescharacteristic
410C2×C83C22×2−1+411yescharacteristic
411C2×C83C2×#58511yescharacteristic
412D83—42no—
413D83—44no—
414#3555—8332no—
415C2×#563—834no—
416C2×Q82D8311yescharacteristic, complemented
417C2×#557—832no—
418C2×#557—831no—
419C2×#556—832no—
420C2×#556—832no—
421C2×#556—831no—
422C2×#554—831no—
423C2×#552—832no—
424C2×#544—832no—
425C2×#542—832no—
426C2×#541—834no—
427C2×#541—832no—
428C2×#541—832no—
429C2×#533—831no—
430C2×#533—831no—
431C2×#529—831no—
432C83C2×#355511yescharacteristic, complemented, Sylow
433#563—8364no—
434Q82C2×D83116yescomplemented
435#557—8332no—
436#557—8316no—
437#556—8332no—
438#556—8332no—
439#556—8316no—
440#554—8316no—
441#552—8332no—
442#544—8332no—
443#542—8332no—
444#541—8364no—
445#541—8332no—
446#541—8332no—
447#533—8316no—
448#533—8316no—
449C2×C4⋊Q8—831no—
450C2×C4⋊Q8—832no—
451C2×C4⋊Q8—834no—
452C2×C4⋊Q8—831no—
453C2×C4⋊Q8—831no—
454C2×C4⋊Q8C2×D8311yescharacteristic
455C2×C4⋊Q8C2×D8314yes—
456C2×C4⋊Q8C2×D8312yes—
457C2×C4⋊Q8C2×D8312yes—
458#529—8316no—
459C2×#126—832no—
460C2×#126—834no—
461C2×#126—834no—
462C2×#126—834no—
463C2×#126—834no—
464C2×#126—834no—
465C2×#126—834no—
466C2×#125—831no—
467C2×#125—832no—
468C2×#125—832no—
469C2×#125—834no—
470C2×#125—834no—
471C2×#125—832no—
472C2×#125—834no—
473C2×#125—834no—
474C2×#125—834no—
475C2×#125—832no—
476C2×#124—831no—
477C2×#124—834no—
478C2×#124—832no—
479C2×#123—832no—
480C2×#123—834no—
481C2×C22⋊Q8—831no—
482C2×C22⋊Q8—831no—
483C2×C22⋊Q8—832no—
484C2×C22⋊Q8—834no—
485C2×C22⋊Q8—832no—
486C2×C22⋊Q8—834no—
487C2×C22⋊Q8—832no—
488C2×C22⋊Q8—832no—
489C2×C22⋊Q8—831no—
490C2×C22⋊Q8—832no—
491C2×C22⋊Q8—834no—
492C2×#121—831no—
493C2×C4×Q8—832no—
494C2×C4×Q8—834no—
495C2×C4×Q8—832no—
496C2×C4×Q8—832no—
497C2×C4×Q8—831no—
498C2×C4×Q8—832no—
499C2×C4×Q8—832no—
500C2×C4×Q8—832no—
501C2×C4×Q8C2×D8311yescharacteristic
502C2×C4×Q8C2×D8311yescharacteristic
503C2×C4×Q8C2×D8312yes—
504C2×C4×Q8C2×D8312yes—
505C2×C4×D4—832no—
506C2×C4×D4—832no—
507C2×C4×D4—831no—
508C2×#117—832no—
509C2×#117—832no—
510C2×#117—832no—
511C2×#117—832no—
512C2×#117—834no—
513C22×C4⋊C4—832no—
514C22×C42—831no—
515C22×Q8—832no—
516C22×Q8—831no—
517C22×Q8—832no—
518C22×Q8C22×D8311yescharacteristic
519C22×Q8C22×D8311yescharacteristic
520C22×Q8C22×D8312yes—
521C22×Q8C22×D8314yes—
522C22×D4—832no—
523C22×D4—831no—
524C23×C4—834no—
525C23×C4—831no—
526C23×C4—832no—
527C23×C4—831no—
528C23×C4—831no—
529C4⋊Q8—838no—
530C4⋊Q8—8316no—
531C4⋊Q8—8332no—
532C4⋊Q8—838no—
533C4⋊Q8—838no—
534C4⋊Q8C22×D8318yes—
535C4⋊Q8C22×D83132yes—
536C4⋊Q8C22×D83116yes—
537C4⋊Q8C22×D83116yes—
538#126—8316no—
539#126—8332no—
540#126—8332no—
541#126—8332no—
542#126—8332no—
543#126—8332no—
544#126—8332no—
545#125—838no—
546#125—8316no—
547#125—8316no—
548#125—8332no—
549#125—8332no—
550#125—8332no—
551#125—8332no—
552#125—8316no—
553#125—8332no—
554#125—8316no—
555#124—838no—
556#124—8332no—
557#124—8316no—
558#123—8316no—
559#123—8332no—
560C22⋊Q8—838no—
561C22⋊Q8—838no—
562C22⋊Q8—8316no—
563C22⋊Q8—8332no—
564C22⋊Q8—8316no—
565C22⋊Q8—8332no—
566C22⋊Q8—8316no—
567C22⋊Q8—8332no—
568C22⋊Q8—8316no—
569C22⋊Q8—838no—
570C22⋊Q8—8316no—
571#121—838no—
572C4×Q8—8316no—
573C4×Q8—8332no—
574C4×Q8—8316no—
575C4×Q8—8316no—
576C4×Q8—838no—
577C4×Q8—8316no—
578C4×Q8—8316no—
579C4×Q8—8316no—
580C4×Q8C22×D8318yes—
581C4×Q8C22×D8318yes—
582C4×Q8C22×D83116yes—
583C4×Q8C22×D83116yes—
584C4×D4—8316no—
585C4×D4—8316no—
586C4×D4—838no—
587#117—8316no—
588#117—8316no—
589#117—8316no—
590#117—8316no—
591#117—8332no—
592C2×C4⋊C4—831no—
593C2×C4⋊C4—834no—
594C2×C4⋊C4—832no—
595C2×C4⋊C4—832no—
596C2×C4⋊C4—832no—
597C2×C4⋊C4—832no—
598C2×C4⋊C4—834no—
599C2×C4⋊C4—832no—
600C2×C4⋊C4—832no—
601C2×C4⋊C4—831no—
602C2×C4⋊C4—832no—
603C2×C4⋊C4—832no—
604C2×C4⋊C4—832no—
605C2×C4⋊C4—834no—
606C2×C4⋊C4—834no—
607C2×C4⋊C4—834no—
608C2×C4⋊C4—834no—
609C2×C4⋊C4—834no—
610C2×C4⋊C4—832no—
611C2×C4⋊C4—832no—
612C2×C4⋊C4—834no—
613C2×C4⋊C4—8316no—
614C2×C4⋊C4C22×D8312yes—
615C2×C4⋊C4C22×D8311yescharacteristic
616C2×C4⋊C4C22×D8312yes—
617C2×C4⋊C4C22×D8311yescharacteristic
618C2×C4⋊C4C22×D8312yes—
619C2×C4⋊C4C22×D8314yes—
620C2×C4⋊C4C22×D8312yes—
621C2×C4⋊C4C22×D8314yes—
622C2×C22⋊C4—832no—
623C2×C22⋊C4—832no—
624C2×C22⋊C4—832no—
625C2×C22⋊C4—834no—
626C2×C22⋊C4—832no—
627C2×C22⋊C4—834no—
628C2×C22⋊C4—832no—
629C2×C22⋊C4—834no—
630C2×C22⋊C4—832no—
631C2×C22⋊C4—834no—
632C2×C22⋊C4—832no—
633C2×C42—834no—
634C2×C42—831no—
635C2×C42—832no—
636C2×C42—834no—
637C2×C42—831no—
638C2×C42—834no—
639C2×C42—831no—
640C2×C42—838no—
641C2×C42C22×D8312yes—
642C2×C42C22×D8312yes—
643C2×C42C22×D8314yes—
644C2×C42C22×D8311yescharacteristic
645C24—831no—
646C24—832no—
647C2×Q8—24no—
648C2×Q8—24no—
649C2×Q8—44no—
650C2×Q8—48no—
651C2×Q8—3324no—
652C2×Q8—838no—
653C2×Q8—834no—
654C2×Q8—838no—
655C2×Q8—1664no—
656C2×Q8—1668no—
657C2×Q8C23×D8314yes—
658C2×Q8C23×D8314yes—
659C2×Q8C23×D8318yes—
660C2×Q8C23×D83116yes—
661C2×D4—3324no—
662C2×D4—838no—
663C2×D4—834no—
664C2×D4—1664no—
665C22×C4—3328no—
666C22×C4—3322no—
667C22×C4—834no—
668C22×C4—8316no—
669C22×C4—831no—
670C22×C4—834no—
671C22×C4—832no—
672C22×C4—831no—
673C22×C4—832no—
674C22×C4—831no—
675C22×C4—832no—
676C22×C4—834no—
677C22×C4—834no—
678C22×C4—838no—
679C22×C4—1668no—
680C22×C4—1664no—
681C22×C4—1664no—
682C22×C4C23×D8312yes—
683C22×C4C23×D8312yes—
684C22×C4C23×D8314yes—
685C22×C4C23×D8311yescharacteristic
686C22×C4C23×D8312yes—
687C22×C4C23×D8312yes—
688C22×C4C23×D8311yescharacteristic
689C22×C4C23×D8311yescharacteristic
690C4⋊C4—834no—
691C4⋊C4—8316no—
692C4⋊C4—838no—
693C4⋊C4—838no—
694C4⋊C4—838no—
695C4⋊C4—838no—
696C4⋊C4—8316no—
697C4⋊C4—838no—
698C4⋊C4—838no—
699C4⋊C4—834no—
700C4⋊C4—838no—
701C4⋊C4—838no—
702C4⋊C4—838no—
703C4⋊C4—8316no—
704C4⋊C4—8316no—
705C4⋊C4—8316no—
706C4⋊C4—8316no—
707C4⋊C4—8316no—
708C4⋊C4—838no—
709C4⋊C4—838no—
710C4⋊C4—8316no—
711C4⋊C4C23×D8318yes—
712C4⋊C4C23×D8314yes—
713C4⋊C4C23×D8318yes—
714C4⋊C4C23×D8314yes—
715C4⋊C4C23×D8318yes—
716C4⋊C4C23×D83116yes—
717C4⋊C4C23×D8318yes—
718C4⋊C4C23×D83116yes—
719C22⋊C4—838no—
720C22⋊C4—838no—
721C22⋊C4—838no—
722C22⋊C4—8316no—
723C22⋊C4—838no—
724C22⋊C4—8316no—
725C22⋊C4—838no—
726C22⋊C4—8316no—
727C22⋊C4—838no—
728C22⋊C4—8316no—
729C22⋊C4—838no—
730C42—834no—
731C42—834no—
732C42—834no—
733C42—8316no—
734C42—838no—
735C42—8316no—
736C42—8316no—
737C42C23×D8314yes—
738C42C23×D8318yes—
739C42C23×D8318yes—
740C42C23×D83116yes—
741C23—832no—
742C23—834no—
743C23—1662no—
744C23—1662no—
745C23—1664no—
746C23—1664no—
747C23—1664no—
748C23—1662no—
749C23C24×D8311yescharacteristic
750Q8—28no—
751Q8—28no—
752Q8—48no—
753Q8—416no—
754Q8—3328no—
755Q8—1668no—
756Q8—16616no—
757D4—3328no—
758D4—1668no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—33216no—
766C2×C4—3324no—
767C2×C4—832no—
768C2×C4—838no—
769C2×C4—834no—
770C2×C4—832no—
771C2×C4—834no—
772C2×C4—832no—
773C2×C4—834no—
774C2×C4—1662no—
775C2×C4—1664no—
776C2×C4—1662no—
777C2×C4—1664no—
778C2×C4—1668no—
779C2×C4—1664no—
780C2×C4—1662no—
781C2×C4—1668no—
782C2×C4—16616no—
783C2×C4—1668no—
784C2×C4#1458184014yes—
785C2×C4#1458184014yes—
786C2×C4C24×D8314yes—
787C2×C4C24×D8314yes—
788C2×C4C24×D8312yes—
789C2×C4C24×D8318yes—
790C2×C4C24×D8314yes—
791C2×C4C24×D8314yes—
792C2×C4C24×D8312yes—
793C2×C4C24×D8312yes—
794C22—3324no—
795C22—3328no—
796C22—1662no—
797C22—1662no—
798C22—1664no—
799C22—1664no—
800C22—1664no—
801C22—1662no—
802C22C2×#1458184012yes—
803C22C2×#1458184012yes—
804C22#1912853612yes—
805C22C25×D8311yescharacteristic
806C4—24no—
807C4—24no—
808C4—28no—
809C4—22no—
810C4—24no—
811C4—24no—
812C4—1662no—
813C4—1664no—
814C4—1662no—
815C4—1664no—
816C4—1668no—
817C4—1664no—
818C4—1662no—
819C4C2×#1458184014yes—
820C4C2×#1458184014yes—
821C2—3322no—
822C2—3324no—
823C2#2492195214yesdirect product factor
824C2C22×#1458184011yescharacteristic
825C2C22×#1458184011yescharacteristic
826C2C2×#1912853611yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×Q82×C83C2
socleC23×C83C25
prime radicalC2×#14581767C22
hypercenterC2×Q82D83
hypocenterC83C2×#3555
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
1. #24921952C2direct (N × H)
2. C2×#19128450C2semidirect
3. C2×#19128429C2semidirect
4. C2×#19128426C2semidirect
5. C2×#19128425C2semidirect
6. C2×#19128424C2semidirect
7. C2×#19128423C2semidirect
8. C2×#19128412C2semidirect
9. C2×#19128392C2semidirect
10. C2×#19128328C2semidirect
12. C2×#19128312C2semidirect
13. C2×#19128309C2semidirect
14. C2×#19128309C2semidirect
15. C2×#19128256C2semidirect
16. C2×#19128255C2semidirect
18. C2×Q82×C83C2semidirect
19. #19128450C22semidirect
20. #19128429C22semidirect
21. #19128426C22semidirect
22. #19128425C22semidirect
23. #19128424C22semidirect
24. #19128423C22semidirect
25. #19128412C22semidirect
26. #19128392C22semidirect
27. #19128328C22semidirect
29. #19128312C22semidirect
30. #19128309C22semidirect
31. #19128309C22semidirect
32. #19128256C22semidirect
33. #19128255C22semidirect
92. Q82×C83C22semidirect
408. C2×C83#3555semidirect
416. C2×Q82D83semidirect
432. C83C2×#3555semidirect
434. Q82C2×D83semidirect
823. C2#24921952direct (N × H)

Maximal subgroups

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

subgroupindex
#249219522
C2×#191284502
C2×#191284292
C2×#191284262
C2×#191284252
C2×#191284242
C2×#191284232
C2×#191284122
C2×#191283922
C2×#191283282
C2×#191283252
C2×#191283122
C2×#191283092
C2×#191282562
C2×#191282552
C2×#191282382
C2×Q82×C832
C2×#355583