Finite Group Databasebeta

← C2×#22624272 #33993667

Subgroups — C2×#22624272 #33993667

Order 18688.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624272C2132yesmaximal, direct product factor
2C2×#17989338C214yesmaximal, complemented
3C2×Q8×Dic146C211yesmaximal, characteristic, complemented
4C2×#17989302C211yesmaximal, characteristic, complemented
5C2×#17989298C211yesmaximal, characteristic, complemented
6C2×#17989275C212yesmaximal, complemented
7C2×#17989271C212yesmaximal, complemented
8C2×#17989242C212yesmaximal, complemented
9C2×#17989238C212yesmaximal, complemented
10C2×#17989218C212yesmaximal, complemented
11C2×#17989217C212yesmaximal, complemented
12C2×#17989210C212yesmaximal, complemented
13C2×#17989202C212yesmaximal, complemented
14C2×#17989160C214yesmaximal, complemented
15C2×C4⋊Q8×D73C211yesmaximal, characteristic, complemented
16C2×#17989124C211yesmaximal, characteristic, complemented
17C2×#17989119C211yesmaximal, characteristic, complemented
18C2×#554×C73C211yesmaximal, characteristic, complemented
19C22×#11924028C2214yes—
20C22×Q8×D73C2212yes—
21#17989338C22164yescomplemented
22Q8×Dic146C22116yescomplemented
23#17989302C22116yescomplemented
24#17989298C22116yescomplemented
25#17989275C22132yescomplemented
26#17989271C22132yescomplemented
27#17989242C22132yescomplemented
28#17989238C22132yescomplemented
29#17989218C22132yescomplemented
30#17989217C22132yescomplemented
31#17989210C22132yescomplemented
32#17989202C22132yescomplemented
33#17989160C22164yescomplemented
34C2×#14556591C2212yes—
35C2×#14556591C2211yescharacteristic
36C2×#14556590C2214yes—
37C2×#14556590C2214yes—
38C2×#14556590C2212yes—
39C2×#14556590C2212yes—
40C2×#14556590C2212yes—
41C2×#14556589C2212yes—
42C4⋊Q8×D73C22116yescomplemented
43#17989124C22116yescomplemented
44#17989119C22116yescomplemented
45C2×#14556586C2212yes—
46C2×#14556586C2214yes—
47C2×#14556584C2212yes—
48C2×#14556584C2214yes—
49C2×#14556582C2214yes—
50C2×#14556582C2211yescharacteristic
51C2×#14556582C2211yescharacteristic
52C2×#14556582C2212yes—
53C2×#14556581C2214yes—
54C2×#14556580C2211yescharacteristic
55C2×#14556578C2211yescharacteristic
56C2×#14556577C2214yes—
57C2×#14556577C2214yes—
58C2×#14556576C2212yes—
59C2×#14556576C2214yes—
60C2×#14556574C2214yes—
61C2×#14556573C2212yes—
62C2×#14556573C2214yes—
63C2×#14556573C2214yes—
64C2×#14556571C2214yes—
65C2×#14556571C2212yes—
66C2×#14556571C2211yescharacteristic
67C2×#14556570C2214yes—
68C2×#14556570C2214yes—
69C2×#14556569C2214yes—
70C2×#14556567C2214yes—
71C2×#14556567C2211yescharacteristic
72C2×#14556566C2211yescharacteristic
73C2×#14556565C2212yes—
74C2×#14556562C2212yes—
75C2×#14556562C2211yescharacteristic
76C2×Q8×Dic73C2212yes—
77C2×C4×Dic146C2212yes—
78C2×C4×Dic146C2211yescharacteristic
79C2×C4×D292C2212yes—
80C2×C4×D292C2211yescharacteristic
81C2×#14556553C2212yes—
82C2×C4×C22⋊D73C2212yes—
83C2×#14556550C2212yes—
84C2×#14556550C2212yes—
85C2×#14556549C2214yes—
86C2×#14556549C2212yes—
87C2×#14556548C2212yes—
88C2×C4⋊C4×D73C2212yes—
89C2×C4⋊C4×D73C2212yes—
90C2×C4⋊C4×D73C2212yes—
91C2×C42×D73C2211yescharacteristic
92#554×C73C22116yescomplemented
93C2×C4⋊Q8×C73C2211yescharacteristic
94C2×#125×C73C2212yes—
95C2×C22⋊Q8×C73C2214yes—
96C2×C22⋊Q8×C73C2212yes—
97C2×C4×Q8×C73C2211yescharacteristic
98C2×C4×D4×C73C2212yes—
99C2×C4×D4×C73C2211yescharacteristic
100C22×C4⋊C4×C73C2212yes—
101C2×#11924028—416no—
102C2×#11924028C23132yes—
103C22×Dic146C2311yescharacteristic
104C22×Dic146C2312yes—
105C22×Dic146C2314yes—
106C22×Dic146C2314yes—
107C2×Q8×D73—48no—
108C2×Q8×D73C23116yes—
109C22×D292C2312yes—
110C22×D292C2311yescharacteristic
111C22×C22⋊D73C2312yes—
112C22×C22⋊D73C2314yes—
113C22×C4×D73C2311yescharacteristic
114C22×C4×D73C2314yes—
115C22×C4×D73C2311yescharacteristic
116C22×C4×D73C2311yescharacteristic
117C22×C4×D73C2312yes—
118C22×C4×D73C2314yes—
119#14556591C2318yes—
120#14556591C23116yes—
121#14556590C23116yes—
122#14556590C23116yes—
123#14556590C23132yes—
124#14556590C23132yes—
125#14556590C23116yes—
126#14556589C23116yes—
127#14556586C23116yes—
128#14556586C23132yes—
129#14556584C23132yes—
130#14556584C23116yes—
131#14556582C2318yes—
132#14556582C2318yes—
133#14556582C23116yes—
134#14556582C23132yes—
135#14556581C23132yes—
136#14556580C2318yes—
137#14556578C2318yes—
138#14556577C23132yes—
139#14556577C23132yes—
140#14556576C23116yes—
141#14556576C23132yes—
142#14556574C23132yes—
143#14556573C23116yes—
144#14556573C23132yes—
145#14556573C23132yes—
146#14556571C23132yes—
147#14556571C23116yes—
148#14556571C2318yes—
149#14556570C23132yes—
150#14556570C23132yes—
151#14556569C23132yes—
152#14556567C2318yes—
153#14556567C23132yes—
154#14556566C2318yes—
155#14556565C23116yes—
156#14556562C23116yes—
157#14556562C2318yes—
158Q8×Dic73C23116yes—
159C4×Dic146C23116yes—
160C4×Dic146C2318yes—
161C4×D292C23116yes—
162C4×D292C2318yes—
163#14556553C23116yes—
164C4×C22⋊D73C23116yes—
165#14556550C23116yes—
166#14556550C23116yes—
167#14556549C23132yes—
168#14556549C23116yes—
169#14556548C23116yes—
170C2×C4⋊Dic73C2312yes—
171C2×C4⋊Dic73C2312yes—
172C2×C4⋊Dic73C2312yes—
173C2×C4⋊Dic73C2314yes—
174C2×C4⋊Dic73C2311yescharacteristic
175C2×C4⋊Dic73C2314yes—
176C2×C4⋊Dic73C2311yescharacteristic
177C2×C4⋊Dic73C2312yes—
178C2×C4⋊Dic73C2312yes—
179C2×#11924007C2314yes—
180C2×#11924007C2314yes—
181C2×#11924007C2312yes—
182C2×#11924007C2312yes—
183C2×#11924007C2314yes—
184C2×#11924007C2314yes—
185C2×#11924007C2312yes—
186C2×#11924007C2312yes—
187C4⋊C4×D73C23116yes—
188C4⋊C4×D73C23116yes—
189C4⋊C4×D73C23116yes—
190C2×C22⋊Dic73C2312yes—
191C2×C22⋊Dic73C2314yes—
192C2×C22⋊Dic73C2312yes—
193C2×C22⋊Dic73C2312yes—
194C2×#11924005C2312yes—
195C2×#11924005C2312yes—
196C2×#11924005C2312yes—
197C2×#11924005C2312yes—
198C2×#11924005C2314yes—
199C2×#11924005C2314yes—
200C2×#11924005C2312yes—
201C2×#11924005C2312yes—
202C2×C4×Dic73C2311yescharacteristic
203C2×C4×Dic73C2311yescharacteristic
204C2×C4×Dic73C2311yescharacteristic
205C2×C4×Dic73C2314yes—
206C2×C4×Dic73C2314yes—
207C2×C4×Dic73C2312yes—
208C42×D73C2318yes—
209C22×Q8×C73C2311yescharacteristic
210C22×Q8×C73C2312yes—
211C22×D4×C73C2311yescharacteristic
212C23×C4×C73C2312yes—
213C23×C4×C73C2314yes—
214C4⋊Q8×C73C2318yes—
215#125×C73C23116yes—
216C22⋊Q8×C73C23132yes—
217C22⋊Q8×C73C23116yes—
218C4×Q8×C73C2318yes—
219C4×D4×C73C23116yes—
220C4×D4×C73C2318yes—
221C2×C4⋊C4×C73C2311yescharacteristic
222C2×C4⋊C4×C73C2312yes—
223C2×C4⋊C4×C73C2314yes—
224C2×C4⋊C4×C73C2312yes—
225C2×C4⋊C4×C73C2312yes—
226C2×C4⋊C4×C73C23116yes—
227C2×C4⋊C4×C73C2311yescharacteristic
228C2×C4⋊C4×C73C2314yes—
229C2×C22⋊C4×C73C2314yes—
230C2×C22⋊C4×C73C2312yes—
231C2×C42×C73C2312yes—
232C2×C42×C73C2311yescharacteristic
233C23×D73C2412yes—
234C23×D73C2411yescharacteristic
235#11924028—464no—
236C2×Dic146—24no—
237C2×Dic146—44no—
238C2×Dic146—48no—
239C2×Dic146—48no—
240C2×Dic146C2414yes—
241C2×Dic146C24116yes—
242C2×Dic146C24116yes—
243C2×Dic146C2418yes—
244Q8×D73—432no—
245C2×D292—28no—
246C2×D292—24no—
247C2×D292C2414yes—
248C2×D292C2418yes—
249C2×C22⋊D73—28no—
250C2×C22⋊D73—48no—
251C2×C22⋊D73C2418yes—
252C2×C22⋊D73C24116yes—
253C22×Dic73C2412yes—
254C22×Dic73C2411yescharacteristic
255C22×Dic73C2411yescharacteristic
256C22×Dic73C2412yes—
257C22×Dic73C2411yescharacteristic
258C22×Dic73C2414yes—
259C22×Dic73C2412yes—
260C2×C4×D73—24no—
261C2×C4×D73—216no—
262C2×C4×D73—24no—
263C2×C4×D73—24no—
264C2×C4×D73—28no—
265C2×C4×D73—48no—
266C2×C4×D73C2414yes—
267C2×C4×D73C2414yes—
268C2×C4×D73C2414yes—
269C2×C4×D73C24116yes—
270C2×C4×D73C2418yes—
271C2×C4×D73C24116yes—
272C4⋊Dic73C2414yes—
273C4⋊Dic73C2418yes—
274C4⋊Dic73C2418yes—
275C4⋊Dic73C24116yes—
276C4⋊Dic73C2414yes—
277C4⋊Dic73C2418yes—
278C4⋊Dic73C2418yes—
279C4⋊Dic73C2418yes—
280C4⋊Dic73C24116yes—
281#11924007C24116yes—
282#11924007C24116yes—
283#11924007C24116yes—
284#11924007C2418yes—
285#11924007C2418yes—
286#11924007C2418yes—
287#11924007C2418yes—
288#11924007C24116yes—
289C22⋊Dic73C2418yes—
290C22⋊Dic73C24116yes—
291C22⋊Dic73C2418yes—
292C22⋊Dic73C2418yes—
293#11924005C2418yes—
294#11924005C2418yes—
295#11924005C2418yes—
296#11924005C2418yes—
297#11924005C24116yes—
298#11924005C24116yes—
299#11924005C2418yes—
300#11924005C2418yes—
301C4×Dic73C2414yes—
302C4×Dic73C2414yes—
303C4×Dic73C2414yes—
304C4×Dic73C24116yes—
305C4×Dic73C24116yes—
306C4×Dic73C2418yes—
307C24×C73C2412yes—
308C2×Q8×C73—24no—
309C2×Q8×C73—44no—
310C2×Q8×C73C2414yes—
311C2×Q8×C73C2418yes—
312C2×D4×C73—24no—
313C2×D4×C73C2414yes—
314C22×C4×C73—28no—
315C22×C4×C73—48no—
316C22×C4×C73C2412yes—
317C22×C4×C73C2411yescharacteristic
318C22×C4×C73C2412yes—
319C22×C4×C73C2412yes—
320C22×C4×C73C2414yes—
321C22×C4×C73C2418yes—
322C22×C4×C73C24116yes—
323C22×C4×C73C2411yescharacteristic
324C22×C4×C73C2411yescharacteristic
325C4⋊C4×C73C2414yes—
326C4⋊C4×C73C24116yes—
327C4⋊C4×C73C2418yes—
328C4⋊C4×C73C2414yes—
329C4⋊C4×C73C2418yes—
330C4⋊C4×C73C2418yes—
331C4⋊C4×C73C24116yes—
332C22⋊C4×C73C24116yes—
333C22⋊C4×C73C2418yes—
334C42×C73C2418yes—
335C42×C73C2414yes—
336C23×C73—24no—
337C23×C73—24no—
338C23×C73—24no—
339C23×C73C2514yes—
340C23×C73C2511yescharacteristic
341C22×D73—22no—
342C22×D73—22no—
343C22×D73—24no—
344C22×D73—24no—
345C22×D73—24no—
346C22×D73H(5,𝔽2)14yes—
347C22×D73C2514yes—
348C22×D73C2512yes—
349Q8×C73—28no—
350Q8×C73—48no—
351D4×C73—28no—
352C2×C4×C73—24no—
353C2×C4×C73—28no—
354C2×C4×C73—22no—
355C2×C4×C73—24no—
356C2×C4×C73—24no—
357C2×C4×C73—216no—
358C2×C4×C73—416no—
359C2×C4×C732−1+414yes—
360C2×C4×C732−1+414yes—
361C2×C4×C73C2514yes—
362C2×C4×C73C2512yes—
363C2×C4×C73C2514yes—
364C2×C4×C73C2514yes—
365C2×C4×C73C2518yes—
366C2×C4×C73C2512yes—
367C2×C4×C73C2512yes—
368C22⋊D73—216no—
369C22⋊D73—416no—
370C2×Dic73—28no—
371C2×Dic73—22no—
372C2×Dic73—24no—
373C2×Dic73—22no—
374C2×Dic73—22no—
375C2×Dic73—24no—
376C2×Dic73—24no—
377C2×Dic73C2514yes—
378C2×Dic73C2512yes—
379C2×Dic73C2512yes—
380C2×Dic73C2514yes—
381C2×Dic73C2512yes—
382C2×Dic73C2518yes—
383C2×Dic73C2514yes—
384D292—216no—
385D292—28no—
386C4×D73—28no—
387C4×D73—232no—
388C4×D73—28no—
389C4×D73—28no—
390C4×D73—216no—
391C4×D73—416no—
392Dic146—28no—
393Dic146—416no—
394Dic146—48no—
395Dic146—416no—
396C22×C73—24no—
397C22×C73—24no—
398C22×C73—24no—
399C22×C73—48no—
400C22×C73C2×H(5,𝔽2)12yes—
401C22×C73C2×2−1+412yes—
402C22×C73C2×2−1+412yes—
403C22×C73C2611yescharacteristic
404C2×D73—22no—
405C2×D73—22no—
406C2×D73—28no—
407C2×D73—24no—
408C2×D73—24no—
409C2×D73—24no—
410C2×D73—48no—
411C2×D73C2×H(5,𝔽2)14yes—
412C4×C73—22no—
413C4×C73—24no—
414C4×C73—28no—
415C4×C73—24no—
416C4×C73—24no—
417C4×C73C2×2−1+414yes—
418C4×C73C2×2−1+414yes—
419Dic73—22no—
420Dic73—28no—
421Dic73—24no—
422Dic73—24no—
423Dic73—22no—
424Dic73—22no—
425Dic73—24no—
426C2×#3544—731nomaximal, Sylow
427C2×C73—44no—
428C2×C73#354414yescomplemented
429C2×C73C22×H(5,𝔽2)11yescharacteristic
430C2×C73C22×2−1+411yescharacteristic
431C2×C73C22×2−1+411yescharacteristic
432D73—24no—
433D73—44no—
434#3544—7332no—
435C2×#563—734no—
436C2×Q82—731no—
437C2×#555—731no—
438C2×#554—731no—
439C2×#554D7311yescharacteristic, complemented
440C2×#552—732no—
441C2×#552—732no—
442C2×#547—732no—
443C2×#547—732no—
444C2×#544—732no—
445C2×#544—732no—
446C2×#542—732no—
447C2×#542—732no—
448C2×#536—734no—
449C22×C4⋊Q8—731no—
450C2×#529—731no—
451C2×#529—731no—
452C73C2×#354411yescharacteristic, complemented, Sylow
453C22×#41—734no—
454C23×Q8—732no—
455#563—7364no—
456Q82—7316no—
457#555—7316no—
458#554—7316no—
459#554C2×D73116yescomplemented
460#552—7332no—
461#552—7332no—
462#547—7332no—
463#547—7332no—
464#544—7332no—
465#544—7332no—
466#542—7332no—
467#542—7332no—
468#536—7364no—
469C2×C4⋊Q8—732no—
470C2×C4⋊Q8—7316no—
471C2×C4⋊Q8—732no—
472C2×C4⋊Q8—732no—
473C2×C4⋊Q8—734no—
474C2×C4⋊Q8—734no—
475C2×C4⋊Q8—732no—
476C2×C4⋊Q8—731no—
477C2×C4⋊Q8—732no—
478C2×C4⋊Q8C2×D7311yescharacteristic
479#529—7316no—
480#529—7316no—
481C2×#126—732no—
482C2×#126—734no—
483C2×#126—732no—
484C2×#126—734no—
485C2×#125—731no—
486C2×#125—731no—
487C2×#125—732no—
488C2×#125—734no—
489C2×#125—734no—
490C2×#125C2×D7312yes—
491C2×#124—731no—
492C2×#124—731no—
493C2×#124—734no—
494C2×#124—734no—
495C2×#123—734no—
496C2×#123—732no—
497C2×#123—734no—
498C2×#123—732no—
499C2×#123—734no—
500C2×#123—734no—
501C2×C22⋊Q8—731no—
502C2×C22⋊Q8—734no—
503C2×C22⋊Q8—734no—
504C2×C22⋊Q8—734no—
505C2×C22⋊Q8—731no—
506C2×C22⋊Q8—734no—
507C2×C22⋊Q8—732no—
508C2×C22⋊Q8—734no—
509C2×C22⋊Q8C2×D7314yes—
510C2×C22⋊Q8C2×D7312yes—
511C2×#121—731no—
512C2×#121—732no—
513C2×#121—732no—
514C2×#121—731no—
515C2×C4×Q8—732no—
516C2×C4×Q8—731no—
517C2×C4×Q8—732no—
518C2×C4×Q8C2×D7311yescharacteristic
519C2×C4×D4—732no—
520C2×C4×D4—732no—
521C2×C4×D4—732no—
522C2×C4×D4—731no—
523C2×C4×D4C2×D7311yescharacteristic
524C2×C4×D4C2×D7312yes—
525C2×#117—732no—
526C2×#117—732no—
527C2×#117—734no—
528C2×#117—732no—
529C2×#117—732no—
530C22×C4⋊C4—732no—
531C22×C4⋊C4—732no—
532C22×C4⋊C4—732no—
533C22×C4⋊C4C2×D7312yes—
534C22×C42—731no—
535C2×#41—29216no—
536C2×#41—7332no—
537C22×Q8—2928no—
538C22×Q8—7316no—
539C22×Q8—734no—
540C22×Q8—734no—
541C22×Q8—732no—
542C22×Q8—731no—
543C22×Q8C22×D7311yescharacteristic
544C22×Q8C22×D7312yes—
545C22×D4—734no—
546C22×D4—732no—
547C22×D4—731no—
548C22×D4—732no—
549C22×D4C22×D7311yescharacteristic
550C23×C4—734no—
551C23×C4—734no—
552C23×C4—731no—
553C23×C4—731no—
554C23×C4—732no—
555C23×C4—731no—
556C23×C4C22×D7312yes—
557C23×C4C22×D7314yes—
558C4⋊Q8—7316no—
559C4⋊Q8—7316no—
560C4⋊Q8—7316no—
561C4⋊Q8—7332no—
562C4⋊Q8—7332no—
563C4⋊Q8—7316no—
564C4⋊Q8—738no—
565C4⋊Q8—7316no—
566C4⋊Q8C22×D7318yes—
567#126—7316no—
568#126—7332no—
569#126—7316no—
570#126—7332no—
571#125—738no—
572#125—738no—
573#125—7316no—
574#125—7332no—
575#125—7332no—
576#125C22×D73116yes—
577#124—738no—
578#124—738no—
579#124—7332no—
580#124—7332no—
581#123—7332no—
582#123—7316no—
583#123—7332no—
584#123—7316no—
585#123—7332no—
586#123—7332no—
587C22⋊Q8—738no—
588C22⋊Q8—7332no—
589C22⋊Q8—7332no—
590C22⋊Q8—7332no—
591C22⋊Q8—738no—
592C22⋊Q8—7332no—
593C22⋊Q8—7316no—
594C22⋊Q8—7332no—
595C22⋊Q8C22×D73132yes—
596C22⋊Q8C22×D73116yes—
597#121—738no—
598#121—7316no—
599#121—7316no—
600#121—738no—
601C4×Q8—7316no—
602C4×Q8—738no—
603C4×Q8—7316no—
604C4×Q8C22×D7318yes—
605C4×D4—7316no—
606C4×D4—7316no—
607C4×D4—7316no—
608C4×D4—738no—
609C4×D4C22×D7318yes—
610C4×D4C22×D73116yes—
611#117—7316no—
612#117—7316no—
613#117—7332no—
614#117—7316no—
615#117—7316no—
616C2×C4⋊C4—731no—
617C2×C4⋊C4—732no—
618C2×C4⋊C4—732no—
619C2×C4⋊C4—734no—
620C2×C4⋊C4—734no—
621C2×C4⋊C4—734no—
622C2×C4⋊C4—731no—
623C2×C4⋊C4—734no—
624C2×C4⋊C4—732no—
625C2×C4⋊C4—732no—
626C2×C4⋊C4—732no—
627C2×C4⋊C4—732no—
628C2×C4⋊C4—732no—
629C2×C4⋊C4—732no—
630C2×C4⋊C4—732no—
631C2×C4⋊C4—734no—
632C2×C4⋊C4—734no—
633C2×C4⋊C4—7316no—
634C2×C4⋊C4—7316no—
635C2×C4⋊C4—7316no—
636C2×C4⋊C4C22×D7312yes—
637C2×C4⋊C4C22×D7312yes—
638C2×C4⋊C4C22×D7311yescharacteristic
639C2×C4⋊C4C22×D7314yes—
640C2×C4⋊C4C22×D73116yes—
641C2×C4⋊C4C22×D7311yescharacteristic
642C2×C4⋊C4C22×D7314yes—
643C2×C4⋊C4C22×D7312yes—
644C2×C22⋊C4—732no—
645C2×C22⋊C4—734no—
646C2×C22⋊C4—732no—
647C2×C22⋊C4—732no—
648C2×C22⋊C4—732no—
649C2×C22⋊C4—732no—
650C2×C22⋊C4—732no—
651C2×C22⋊C4—734no—
652C2×C22⋊C4—732no—
653C2×C22⋊C4—734no—
654C2×C22⋊C4—732no—
655C2×C22⋊C4—732no—
656C2×C22⋊C4C22×D7314yes—
657C2×C22⋊C4C22×D7312yes—
658C2×C42—734no—
659C2×C42—731no—
660C2×C42—731no—
661C2×C42—732no—
662C2×C42—734no—
663C2×C42—731no—
664C2×C42—738no—
665C2×C42C22×D7312yes—
666C2×C42C22×D7311yescharacteristic
667C24—731no—
668C24—732no—
669C24C23×D7312yes—
670#41—29264no—
671C2×Q8—24no—
672C2×Q8—44no—
673C2×Q8—2928no—
674C2×Q8—2924no—
675C2×Q8—2928no—
676C2×Q8—29232no—
677C2×Q8—7316no—
678C2×Q8—7316no—
679C2×Q8—738no—
680C2×Q8—734no—
681C2×Q8—1464no—
682C2×Q8C23×D7314yes—
683C2×Q8C23×D7318yes—
684C2×D4—24no—
685C2×D4—2928no—
686C2×D4—7316no—
687C2×D4—738no—
688C2×D4—734no—
689C2×D4—738no—
690C2×D4—1468no—
691C2×D4—1468no—
692C2×D4—1464no—
693C2×D4C23×D7314yes—
694C22×C4—28no—
695C22×C4—48no—
696C22×C4—2928no—
697C22×C4—7316no—
698C22×C4—732no—
699C22×C4—731no—
700C22×C4—732no—
701C22×C4—731no—
702C22×C4—731no—
703C22×C4—734no—
704C22×C4—732no—
705C22×C4—734no—
706C22×C4—734no—
707C22×C4—734no—
708C22×C4—7316no—
709C22×C4—738no—
710C22×C4—1464no—
711C22×C4—14616no—
712C22×C4—1464no—
713C22×C4—1468no—
714C22×C4—1464no—
715C22×C4C23×D7318yes—
716C22×C4C23×D7312yes—
717C22×C4C23×D7312yes—
718C22×C4C23×D7311yescharacteristic
719C22×C4C23×D7312yes—
720C22×C4C23×D7314yes—
721C22×C4C23×D73116yes—
722C22×C4C23×D7311yescharacteristic
723C22×C4C23×D7311yescharacteristic
724C4⋊C4—7316no—
725C4⋊C4—7316no—
726C4⋊C4—7316no—
727C4⋊C4—738no—
728C4⋊C4—738no—
729C4⋊C4—738no—
730C4⋊C4—738no—
731C4⋊C4—7316no—
732C4⋊C4—734no—
733C4⋊C4—738no—
734C4⋊C4—738no—
735C4⋊C4—734no—
736C4⋊C4—7316no—
737C4⋊C4—738no—
738C4⋊C4—738no—
739C4⋊C4—738no—
740C4⋊C4—7316no—
741C4⋊C4C23×D7318yes—
742C4⋊C4C23×D7318yes—
743C4⋊C4C23×D7314yes—
744C4⋊C4C23×D73116yes—
745C4⋊C4C23×D7314yes—
746C4⋊C4C23×D73116yes—
747C4⋊C4C23×D7318yes—
748C22⋊C4—738no—
749C22⋊C4—7316no—
750C22⋊C4—738no—
751C22⋊C4—738no—
752C22⋊C4—738no—
753C22⋊C4—738no—
754C22⋊C4—738no—
755C22⋊C4—7316no—
756C22⋊C4—738no—
757C22⋊C4—7316no—
758C22⋊C4—738no—
759C22⋊C4—738no—
760C22⋊C4C23×D73116yes—
761C22⋊C4C23×D7318yes—
762C42—734no—
763C42—734no—
764C42—734no—
765C42—7316no—
766C42—738no—
767C42—7316no—
768C42C23×D7314yes—
769C42C23×D7318yes—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—734no—
774C23—732no—
775C23—734no—
776C23—1464no—
777C23—1464no—
778C23—1464no—
779C23—1462no—
780C23—1462no—
781C23C24×D7314yes—
782C23C24×D7311yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—29216no—
786Q8—2928no—
787Q8—29216no—
788Q8—1468no—
789D4—28no—
790D4—29216no—
791D4—14616no—
792D4—14616no—
793D4—1468no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—216no—
800C2×C4—416no—
801C2×C4—29216no—
802C2×C4—734no—
803C2×C4—732no—
804C2×C4—732no—
805C2×C4—734no—
806C2×C4—732no—
807C2×C4—738no—
808C2×C4—734no—
809C2×C4—1468no—
810C2×C4—14632no—
811C2×C4—1464no—
812C2×C4—1468no—
813C2×C4—1462no—
814C2×C4—1462no—
815C2×C4—1464no—
816C2×C4—1462no—
817C2×C4—1464no—
818C2×C4—1468no—
819C2×C4—14616no—
820C2×C4—1468no—
821C2×C4#1455663814yes—
822C2×C4#1455663914yes—
823C2×C4C24×D7314yes—
824C2×C4C24×D7314yes—
825C2×C4C24×D7312yes—
826C2×C4C24×D7314yes—
827C2×C4C24×D7318yes—
828C2×C4C24×D7312yes—
829C2×C4C24×D7312yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—2928no—
835C22—734no—
836C22—1464no—
837C22—1464no—
838C22—1464no—
839C22—1468no—
840C22—1462no—
841C22—1462no—
842C22H(5,𝔽2)×D7312yes—
843C22C2×#1455663812yes—
844C22C2×#1455663912yes—
845C22C25×D7311yescharacteristic
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—24no—
851C4—1464no—
852C4—1468no—
853C4—1462no—
854C4—1462no—
855C4—1462no—
856C4—1464no—
857C4—1464no—
858C4C2×#1455663814yes—
859C4C2×#1455663914yes—
860C2—44no—
861C2—2924no—
862C2—1464no—
863C2#2262427214yesdirect product factor
864C2C2×H(5,𝔽2)×D7311yescharacteristic
865C2C22×#1455663811yescharacteristic
866C2C22×#1455663911yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#554×C73C2
socleC23×C73C25
hypercenterC2×#554D73
hypocenterC73C2×#3544
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #22624272C2direct (N × H)
2. C2×#17989338C2semidirect
3. C2×Q8×Dic146C2semidirect
4. C2×#17989302C2semidirect
5. C2×#17989298C2semidirect
6. C2×#17989275C2semidirect
7. C2×#17989271C2semidirect
8. C2×#17989242C2semidirect
9. C2×#17989238C2semidirect
10. C2×#17989218C2semidirect
11. C2×#17989217C2semidirect
12. C2×#17989210C2semidirect
13. C2×#17989202C2semidirect
14. C2×#17989160C2semidirect
15. C2×C4⋊Q8×D73C2semidirect
16. C2×#17989124C2semidirect
17. C2×#17989119C2semidirect
18. C2×#554×C73C2semidirect
21. #17989338C22semidirect
22. Q8×Dic146C22semidirect
23. #17989302C22semidirect
24. #17989298C22semidirect
25. #17989275C22semidirect
26. #17989271C22semidirect
27. #17989242C22semidirect
28. #17989238C22semidirect
29. #17989218C22semidirect
30. #17989217C22semidirect
31. #17989210C22semidirect
32. #17989202C22semidirect
33. #17989160C22semidirect
42. C4⋊Q8×D73C22semidirect
43. #17989124C22semidirect
44. #17989119C22semidirect
92. #554×C73C22semidirect
428. C2×C73#3544semidirect
439. C2×#554D73semidirect
452. C73C2×#3544semidirect
459. #554C2×D73semidirect
863. C2#22624272direct (N × H)

Maximal subgroups

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

subgroupindex
#226242722
C2×#179893382
C2×Q8×Dic1462
C2×#179893022
C2×#179892982
C2×#179892752
C2×#179892712
C2×#179892422
C2×#179892382
C2×#179892182
C2×#179892172
C2×#179892102
C2×#179892022
C2×#179891602
C2×C4⋊Q8×D732
C2×#179891242
C2×#179891192
C2×#554×C732
C2×#354473