Finite Group Databasebeta

← C2×#22624271 #33993666

Subgroups — C2×#22624271 #33993666

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#22624271C2132yesmaximal, direct product factor
2C2×#17989339C214yesmaximal, complemented
3C2×Q8×Dic146C211yesmaximal, characteristic, complemented
4C2×#17989302C211yesmaximal, characteristic, complemented
5C2×#17989297C211yesmaximal, characteristic, complemented
6C2×#17989294C211yesmaximal, characteristic, complemented
7C2×#17989279C212yesmaximal, complemented
8C2×#17989277C212yesmaximal, complemented
9C2×#17989241C212yesmaximal, complemented
10C2×#17989237C212yesmaximal, complemented
11C2×#17989217C212yesmaximal, complemented
12C2×#17989215C212yesmaximal, complemented
13C2×#17989208C212yesmaximal, complemented
14C2×#17989206C212yesmaximal, complemented
15C2×#17989159C214yesmaximal, complemented
16C22×#14556591C211yesmaximal, characteristic, complemented
17C2×#17989121C211yesmaximal, characteristic, complemented
18C2×#529×C73C211yesmaximal, characteristic, complemented
19C22×#11924027C2214yes—
20C23×Dic146C2212yes—
21#17989339C22164yescomplemented
22Q8×Dic146C22116yescomplemented
23#17989302C22116yescomplemented
24#17989297C22116yescomplemented
25#17989294C22116yescomplemented
26#17989279C22132yescomplemented
27#17989277C22132yescomplemented
28#17989241C22132yescomplemented
29#17989237C22132yescomplemented
30#17989217C22132yescomplemented
31#17989215C22132yescomplemented
32#17989208C22132yescomplemented
33#17989206C22132yescomplemented
34#17989159C22164yescomplemented
35C2×#14556591C2212yes—
36C2×#14556591C2211yescharacteristic
37C2×#14556591C2212yes—
38C2×#14556591C2212yes—
39C2×#14556591C2212yes—
40C2×#14556591C2211yescharacteristic
41C2×#14556591C22116yescomplemented
42C2×#14556590C2214yes—
43C2×#14556590C2214yes—
44C2×#14556590C2212yes—
45#17989121C22116yescomplemented
46C2×#14556586C2214yes—
47C2×#14556585C2212yes—
48C2×#14556584C2214yes—
49C2×#14556583C2211yescharacteristic
50C2×#14556583C2212yes—
51C2×#14556582C2214yes—
52C2×#14556582C2212yes—
53C2×#14556581C2214yes—
54C2×#14556579C2211yescharacteristic
55C2×#14556577C2214yes—
56C2×#14556577C2214yes—
57C2×#14556575C2214yes—
58C2×#14556575C2214yes—
59C2×#14556574C2212yes—
60C2×#14556573C2214yes—
61C2×#14556572C2214yes—
62C2×#14556571C2214yes—
63C2×#14556570C2212yes—
64C2×#14556570C2211yescharacteristic
65C2×#14556569C2214yes—
66C2×#14556569C2214yes—
67C2×#14556568C2214yes—
68C2×#14556568C2214yes—
69C2×#14556568C2214yes—
70C2×#14556567C2212yes—
71C2×#14556565C2212yes—
72C2×#14556565C2211yescharacteristic
73C2×#14556562C2212yes—
74C2×Q8×Dic73C2212yes—
75C2×C4×Dic146C2212yes—
76C2×C4×Dic146C2211yescharacteristic
77C2×C4×D292C2212yes—
78C2×C4×D292C2211yescharacteristic
79C2×D4×Dic73C2212yes—
80C2×C4×C22⋊D73C2212yes—
81C2×#14556550C2212yes—
82C2×#14556549C2212yes—
83C2×#14556548C2212yes—
84C2×#14556547C2214yes—
85C22×C4⋊Dic73C2212yes—
86C22×C4⋊Dic73C2212yes—
87C22×C4⋊Dic73C2212yes—
88C2×C4⋊C4×D73C2212yes—
89#529×C73C22116yescomplemented
90C2×#126×C73C2212yes—
91C2×#125×C73C2211yescharacteristic
92C2×#124×C73C2211yescharacteristic
93C2×#123×C73C2212yes—
94C2×C22⋊Q8×C73C2211yescharacteristic
95C2×#121×C73C2211yescharacteristic
96C2×C4×Q8×C73C2211yescharacteristic
97C2×C4×D4×C73C2212yes—
98C2×C4×D4×C73C2211yescharacteristic
99C2×#117×C73C2212yes—
100C22×C42×C73C2211yescharacteristic
101C2×#11924027—416no—
102C2×#11924027C23132yes—
103C22×Dic146—48no—
104C22×Dic146C2311yescharacteristic
105C22×Dic146C2314yes—
106C22×Dic146C2312yes—
107C22×Dic146C2314yes—
108C22×Dic146C2312yes—
109C22×Dic146C23116yes—
110C22×D292C2311yescharacteristic
111C22×C22⋊D73C2312yes—
112C22×C22⋊D73C2314yes—
113C23×Dic73C2314yes—
114C23×Dic73C2314yes—
115C22×C4×D73C2312yes—
116C22×C4×D73C2314yes—
117#14556591C23116yes—
118#14556591C23116yes—
119#14556591C2318yes—
120#14556591C2318yes—
121#14556591C23116yes—
122#14556591C23116yes—
123#14556590C23132yes—
124#14556590C23132yes—
125#14556590C23116yes—
126#14556586C23132yes—
127#14556585C23116yes—
128#14556584C23132yes—
129#14556583C2318yes—
130#14556583C23116yes—
131#14556582C23132yes—
132#14556582C23116yes—
133#14556581C23132yes—
134#14556579C2318yes—
135#14556577C23132yes—
136#14556577C23132yes—
137#14556575C23132yes—
138#14556575C23132yes—
139#14556574C23116yes—
140#14556573C23132yes—
141#14556572C23132yes—
142#14556571C23132yes—
143#14556570C2318yes—
144#14556570C23116yes—
145#14556569C23132yes—
146#14556569C23132yes—
147#14556568C23132yes—
148#14556568C23132yes—
149#14556568C23132yes—
150#14556567C23116yes—
151#14556565C2318yes—
152#14556565C23116yes—
153#14556562C23116yes—
154Q8×Dic73C23116yes—
155C4×Dic146C2318yes—
156C4×Dic146C23116yes—
157C4×D292C2318yes—
158C4×D292C23116yes—
159D4×Dic73C23116yes—
160C4×C22⋊D73C23116yes—
161#14556550C23116yes—
162#14556549C23116yes—
163#14556548C23116yes—
164#14556547C23132yes—
165C2×C4⋊Dic73C2312yes—
166C2×C4⋊Dic73C2314yes—
167C2×C4⋊Dic73C2314yes—
168C2×C4⋊Dic73C2312yes—
169C2×C4⋊Dic73C2312yes—
170C2×C4⋊Dic73C2312yes—
171C2×C4⋊Dic73C2311yescharacteristic
172C2×C4⋊Dic73C2314yes—
173C2×C4⋊Dic73C2314yes—
174C2×C4⋊Dic73C23116yes—
175C2×C4⋊Dic73C23116yes—
176C2×C4⋊Dic73C23116yes—
177C2×C4⋊Dic73C2311yescharacteristic
178C2×#11924007C2312yes—
179C2×#11924007C2312yes—
180C2×#11924007C2314yes—
181C2×#11924007C2314yes—
182C2×#11924007C2314yes—
183C2×#11924007C2314yes—
184C2×#11924007C2312yes—
185C2×#11924007C2312yes—
186C4⋊C4×D73C23116yes—
187C2×C22⋊Dic73C2312yes—
188C2×C22⋊Dic73C2314yes—
189C2×C22⋊Dic73C2314yes—
190C2×#11924005C2312yes—
191C2×#11924005C2312yes—
192C2×#11924005C2314yes—
193C2×#11924005C2312yes—
194C2×#11924005C2314yes—
195C2×#11924005C2312yes—
196C2×C4×Dic73C2314yes—
197C2×C4×Dic73C2314yes—
198C2×C4×Dic73C2312yes—
199C22×Q8×C73C2311yescharacteristic
200C22×D4×C73C2312yes—
201C22×D4×C73C2311yescharacteristic
202C23×C4×C73C2311yescharacteristic
203C23×C4×C73C2311yescharacteristic
204C23×C4×C73C2311yescharacteristic
205C23×C4×C73C2312yes—
206#126×C73C23116yes—
207#125×C73C2318yes—
208#124×C73C2318yes—
209#123×C73C23116yes—
210C22⋊Q8×C73C2318yes—
211#121×C73C2318yes—
212C4×Q8×C73C2318yes—
213C4×D4×C73C23116yes—
214C4×D4×C73C2318yes—
215#117×C73C23116yes—
216C2×C4⋊C4×C73C2312yes—
217C2×C4⋊C4×C73C2311yescharacteristic
218C2×C4⋊C4×C73C2312yes—
219C2×C4⋊C4×C73C2312yes—
220C2×C4⋊C4×C73C2311yescharacteristic
221C2×C4⋊C4×C73C2312yes—
222C2×C22⋊C4×C73C2312yes—
223C2×C22⋊C4×C73C2312yes—
224C2×C22⋊C4×C73C2312yes—
225C2×C22⋊C4×C73C2312yes—
226C2×C22⋊C4×C73C2312yes—
227C2×C42×C73C2318yes—
228C2×C42×C73C2311yescharacteristic
229C2×C42×C73C2311yescharacteristic
230C2×C42×C73C2311yescharacteristic
231C2×C42×C73C2311yescharacteristic
232C2×C42×C73C2312yes—
233C23×D73C2412yes—
234#11924027—464no—
235C2×Dic146—24no—
236C2×Dic146—44no—
237C2×Dic146—48no—
238C2×Dic146—44no—
239C2×Dic146—432no—
240C2×Dic146—48no—
241C2×Dic146C2414yes—
242C2×Dic146C2418yes—
243C2×Dic146C24116yes—
244C2×Dic146C24116yes—
245C2×Dic146C2418yes—
246C2×D292—24no—
247C2×D292C2414yes—
248C2×C22⋊D73—28no—
249C2×C22⋊D73—48no—
250C2×C22⋊D73C2418yes—
251C2×C22⋊D73C24116yes—
252C22×Dic73—216no—
253C22×Dic73—48no—
254C22×Dic73C2412yes—
255C22×Dic73C2412yes—
256C22×Dic73C2414yes—
257C22×Dic73C2412yes—
258C22×Dic73C2414yes—
259C22×Dic73C24116yes—
260C22×Dic73C24116yes—
261C2×C4×D73—28no—
262C2×C4×D73—48no—
263C2×C4×D73C2418yes—
264C2×C4×D73C24116yes—
265C4⋊Dic73C2418yes—
266C4⋊Dic73C2418yes—
267C4⋊Dic73C2414yes—
268C4⋊Dic73C2418yes—
269C4⋊Dic73C2418yes—
270C4⋊Dic73C24116yes—
271C4⋊Dic73C24116yes—
272C4⋊Dic73C24116yes—
273C4⋊Dic73C2414yes—
274C4⋊Dic73C24116yes—
275#11924007C24116yes—
276#11924007C24116yes—
277#11924007C24116yes—
278#11924007C2418yes—
279#11924007C2418yes—
280#11924007C2418yes—
281#11924007C2418yes—
282#11924007C24116yes—
283C22⋊Dic73C2418yes—
284C22⋊Dic73C24116yes—
285C22⋊Dic73C24116yes—
286#11924005C2418yes—
287#11924005C2418yes—
288#11924005C24116yes—
289#11924005C2418yes—
290#11924005C24116yes—
291#11924005C2418yes—
292C4×Dic73C24116yes—
293C4×Dic73C24116yes—
294C4×Dic73C2418yes—
295C24×C73C2412yes—
296C24×C73C2411yescharacteristic
297C2×Q8×C73—24no—
298C2×Q8×C73C2414yes—
299C2×D4×C73—28no—
300C2×D4×C73—24no—
301C2×D4×C73C2418yes—
302C2×D4×C73C2414yes—
303C22×C4×C73—24no—
304C22×C4×C73—24no—
305C22×C4×C73—28no—
306C22×C4×C73—24no—
307C22×C4×C73C2411yescharacteristic
308C22×C4×C73C2411yescharacteristic
309C22×C4×C73C2411yescharacteristic
310C22×C4×C73C2411yescharacteristic
311C22×C4×C73C2414yes—
312C22×C4×C73C2414yes—
313C22×C4×C73C2414yes—
314C22×C4×C73C2412yes—
315C22×C4×C73C2412yes—
316C22×C4×C73C2412yes—
317C22×C4×C73C2418yes—
318C22×C4×C73C2411yescharacteristic
319C22×C4×C73C2411yescharacteristic
320C4⋊C4×C73C2418yes—
321C4⋊C4×C73C2418yes—
322C4⋊C4×C73C2414yes—
323C4⋊C4×C73C2418yes—
324C4⋊C4×C73C2414yes—
325C4⋊C4×C73C2418yes—
326C22⋊C4×C73C2418yes—
327C22⋊C4×C73C2418yes—
328C22⋊C4×C73C2418yes—
329C22⋊C4×C73C2418yes—
330C22⋊C4×C73C2418yes—
331C42×C73C2414yes—
332C42×C73C2414yes—
333C42×C73C2414yes—
334C42×C73C2414yes—
335C42×C73C2418yes—
336C23×C73—22no—
337C23×C73—22no—
338C23×C73—24no—
339C23×C73—24no—
340C23×C73—24no—
341C23×C73H(5,𝔽2)14yes—
342C23×C73C2514yes—
343C23×C73C2512yes—
344C23×C73C2511yescharacteristic
345C22×D73—24no—
346C22×D73—24no—
347C22×D73—24no—
348C22×D73C2514yes—
349Q8×C73—28no—
350D4×C73—216no—
351D4×C73—28no—
352C2×C4×C73—28no—
353C2×C4×C73—22no—
354C2×C4×C73—22no—
355C2×C4×C73—24no—
356C2×C4×C73—22no—
357C2×C4×C73—22no—
358C2×C4×C73—24no—
359C2×C4×C73—24no—
360C2×C4×C73—28no—
361C2×C4×C73—216no—
362C2×C4×C73—28no—
363C2×C4×C732−1+414yes—
364C2×C4×C732−1+414yes—
365C2×C4×C73C2512yes—
366C2×C4×C73C2512yes—
367C2×C4×C73C2512yes—
368C2×C4×C73C2512yes—
369C2×C4×C73C2514yes—
370C2×C4×C73C2514yes—
371C2×C4×C73C2514yes—
372C2×C4×C73C2512yes—
373C2×C4×C73C2512yes—
374C22⋊D73—216no—
375C22⋊D73—416no—
376C2×Dic73—28no—
377C2×Dic73—28no—
378C2×Dic73—232no—
379C2×Dic73—24no—
380C2×Dic73—24no—
381C2×Dic73—24no—
382C2×Dic73—416no—
383C2×Dic73C2514yes—
384C2×Dic73C2514yes—
385C2×Dic73C2518yes—
386C2×Dic73C2514yes—
387C2×Dic73C2518yes—
388D292—28no—
389C4×D73—216no—
390C4×D73—416no—
391Dic146—28no—
392Dic146—48no—
393Dic146—416no—
394Dic146—48no—
395Dic146—416no—
396C22×C73—22no—
397C22×C73—22no—
398C22×C73—28no—
399C22×C73—24no—
400C22×C73—24no—
401C22×C73—24no—
402C22×C73—48no—
403C22×C73C2×H(5,𝔽2)14yes—
404C22×C73C2×H(5,𝔽2)12yes—
405C22×C73C2×2−1+412yes—
406C22×C73C2×2−1+412yes—
407C22×C73C2611yescharacteristic
408C2×D73—24no—
409C2×D73—24no—
410C2×D73—24no—
411C2×D73—48no—
412C4×C73—22no—
413C4×C73—22no—
414C4×C73—24no—
415C4×C73—22no—
416C4×C73—22no—
417C4×C73—24no—
418C4×C73—24no—
419C4×C73C2×2−1+414yes—
420C4×C73C2×2−1+414yes—
421Dic73—28no—
422Dic73—28no—
423Dic73—24no—
424Dic73—24no—
425Dic73—24no—
426C2×#3544—731nomaximal, Sylow
427C2×C73—24no—
428C2×C73—44no—
429C2×C73#354414yescomplemented
430C2×C73C22×H(5,𝔽2)11yescharacteristic
431C2×C73C22×2−1+411yescharacteristic
432C2×C73C22×2−1+411yescharacteristic
433D73—44no—
434#3544—7332no—
435C2×#563—734no—
436C2×Q82—731no—
437C2×#555—731no—
438C2×#554—731no—
439C2×#554—731no—
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×#529D7311yescharacteristic, complemented
452C73C2×#354411yescharacteristic, complemented, Sylow
453C22×#41—734no—
454C23×Q8—732no—
455#563—7364no—
456Q82—7316no—
457#555—7316no—
458#554—7316no—
459#554—7316no—
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—734no—
470C2×C4⋊Q8—734no—
471C2×C4⋊Q8—732no—
472C2×C4⋊Q8—732no—
473C2×C4⋊Q8—732no—
474C2×C4⋊Q8—731no—
475C2×C4⋊Q8—731no—
476C2×C4⋊Q8—732no—
477C2×C4⋊Q8—732no—
478C2×C4⋊Q8—7316no—
479#529—7316no—
480#529C2×D73116yescomplemented
481C2×#126—734no—
482C2×#126—734no—
483C2×#126—732no—
484C2×#126C2×D7312yes—
485C2×#125—732no—
486C2×#125—734no—
487C2×#125—734no—
488C2×#125—731no—
489C2×#125—732no—
490C2×#125C2×D7311yescharacteristic
491C2×#124—734no—
492C2×#124—734no—
493C2×#124—731no—
494C2×#124C2×D7311yescharacteristic
495C2×#123—734no—
496C2×#123—732no—
497C2×#123—734no—
498C2×#123—734no—
499C2×#123—734no—
500C2×#123C2×D7312yes—
501C2×C22⋊Q8—732no—
502C2×C22⋊Q8—731no—
503C2×C22⋊Q8—732no—
504C2×C22⋊Q8—734no—
505C2×C22⋊Q8—734no—
506C2×C22⋊Q8—734no—
507C2×C22⋊Q8—734no—
508C2×C22⋊Q8—734no—
509C2×C22⋊Q8—734no—
510C2×C22⋊Q8C2×D7311yescharacteristic
511C2×#121—732no—
512C2×#121—731no—
513C2×#121—732no—
514C2×#121C2×D7311yescharacteristic
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—731no—
522C2×C4×D4—732no—
523C2×C4×D4C2×D7312yes—
524C2×C4×D4C2×D7311yescharacteristic
525C2×#117—732no—
526C2×#117—732no—
527C2×#117—734no—
528C2×#117—732no—
529C2×#117C2×D7312yes—
530C22×C4⋊C4—732no—
531C22×C4⋊C4—732no—
532C22×C4⋊C4—732no—
533C22×C4⋊C4—732no—
534C22×C42C2×D7311yescharacteristic
535C2×#41—29216no—
536C2×#41—7332no—
537C22×Q8—2928no—
538C22×Q8—732no—
539C22×Q8—734no—
540C22×Q8—734no—
541C22×Q8—732no—
542C22×Q8—7316no—
543C22×Q8—731no—
544C22×Q8C22×D7311yescharacteristic
545C22×D4—734no—
546C22×D4—732no—
547C22×D4—731no—
548C22×D4C22×D7311yescharacteristic
549C22×D4C22×D7312yes—
550C23×C4—734no—
551C23×C4—734no—
552C23×C4—734no—
553C23×C4—732no—
554C23×C4C22×D7311yescharacteristic
555C23×C4C22×D7311yescharacteristic
556C23×C4C22×D7312yes—
557C23×C4C22×D7311yescharacteristic
558C4⋊Q8—7332no—
559C4⋊Q8—7332no—
560C4⋊Q8—7316no—
561C4⋊Q8—7316no—
562C4⋊Q8—7316no—
563C4⋊Q8—738no—
564C4⋊Q8—738no—
565C4⋊Q8—7316no—
566C4⋊Q8—7316no—
567#126—7332no—
568#126—7332no—
569#126—7316no—
570#126C22×D73116yes—
571#125—7316no—
572#125—7332no—
573#125—7332no—
574#125—738no—
575#125—7316no—
576#125C22×D7318yes—
577#124—7332no—
578#124—7332no—
579#124—738no—
580#124C22×D7318yes—
581#123—7332no—
582#123—7316no—
583#123—7332no—
584#123—7332no—
585#123—7332no—
586#123C22×D73116yes—
587C22⋊Q8—7316no—
588C22⋊Q8—738no—
589C22⋊Q8—7316no—
590C22⋊Q8—7332no—
591C22⋊Q8—7332no—
592C22⋊Q8—7332no—
593C22⋊Q8—7332no—
594C22⋊Q8—7332no—
595C22⋊Q8—7332no—
596C22⋊Q8C22×D7318yes—
597#121—7316no—
598#121—738no—
599#121—7316no—
600#121C22×D7318yes—
601C4×Q8—7316no—
602C4×Q8—738no—
603C4×Q8—7316no—
604C4×Q8C22×D7318yes—
605C4×D4—7316no—
606C4×D4—7316no—
607C4×D4—738no—
608C4×D4—7316no—
609C4×D4C22×D73116yes—
610C4×D4C22×D7318yes—
611#117—7316no—
612#117—7316no—
613#117—7332no—
614#117—7316no—
615#117C22×D73116yes—
616C2×C4⋊C4—732no—
617C2×C4⋊C4—732no—
618C2×C4⋊C4—731no—
619C2×C4⋊C4—732no—
620C2×C4⋊C4—732no—
621C2×C4⋊C4—734no—
622C2×C4⋊C4—734no—
623C2×C4⋊C4—734no—
624C2×C4⋊C4—734no—
625C2×C4⋊C4—7316no—
626C2×C4⋊C4—7316no—
627C2×C4⋊C4—7316no—
628C2×C4⋊C4—731no—
629C2×C4⋊C4—734no—
630C2×C4⋊C4—734no—
631C2×C4⋊C4—732no—
632C2×C4⋊C4—732no—
633C2×C4⋊C4—732no—
634C2×C4⋊C4—732no—
635C2×C4⋊C4—734no—
636C2×C4⋊C4—734no—
637C2×C4⋊C4—7316no—
638C2×C4⋊C4C22×D7311yescharacteristic
639C2×C4⋊C4C22×D7311yescharacteristic
640C2×C4⋊C4C22×D7312yes—
641C2×C4⋊C4C22×D7312yes—
642C2×C4⋊C4C22×D7312yes—
643C2×C4⋊C4C22×D7312yes—
644C2×C22⋊C4—732no—
645C2×C22⋊C4—734no—
646C2×C22⋊C4—734no—
647C2×C22⋊C4—732no—
648C2×C22⋊C4—734no—
649C2×C22⋊C4—732no—
650C2×C22⋊C4—734no—
651C2×C22⋊C4—732no—
652C2×C22⋊C4—732no—
653C2×C22⋊C4C22×D7312yes—
654C2×C22⋊C4C22×D7312yes—
655C2×C22⋊C4C22×D7312yes—
656C2×C22⋊C4C22×D7312yes—
657C2×C22⋊C4C22×D7312yes—
658C2×C42—734no—
659C2×C42—732no—
660C2×C42—734no—
661C2×C42C22×D7311yescharacteristic
662C2×C42C22×D7311yescharacteristic
663C2×C42C22×D7312yes—
664C2×C42C22×D7311yescharacteristic
665C2×C42C22×D7311yescharacteristic
666C2×C42C22×D7318yes—
667C24—732no—
668C24C23×D7312yes—
669C24C23×D7311yescharacteristic
670#41—29264no—
671C2×Q8—24no—
672C2×Q8—2924no—
673C2×Q8—2928no—
674C2×Q8—2924no—
675C2×Q8—29232no—
676C2×Q8—2928no—
677C2×Q8—738no—
678C2×Q8—7316no—
679C2×Q8—7316no—
680C2×Q8—738no—
681C2×Q8—734no—
682C2×Q8—1464no—
683C2×Q8C23×D7314yes—
684C2×D4—28no—
685C2×D4—24no—
686C2×D4—2928no—
687C2×D4—7316no—
688C2×D4—738no—
689C2×D4—734no—
690C2×D4—1468no—
691C2×D4—1464no—
692C2×D4C23×D7314yes—
693C2×D4C23×D7318yes—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—28no—
697C22×C4—24no—
698C22×C4—2928no—
699C22×C4—2928no—
700C22×C4—7316no—
701C22×C4—7316no—
702C22×C4—7316no—
703C22×C4—732no—
704C22×C4—732no—
705C22×C4—734no—
706C22×C4—732no—
707C22×C4—734no—
708C22×C4—738no—
709C22×C4—14616no—
710C22×C4—1468no—
711C22×C4C23×D7314yes—
712C22×C4C23×D7314yes—
713C22×C4C23×D7314yes—
714C22×C4C23×D7318yes—
715C22×C4C23×D7312yes—
716C22×C4C23×D7312yes—
717C22×C4C23×D7311yescharacteristic
718C22×C4C23×D7311yescharacteristic
719C22×C4C23×D7311yescharacteristic
720C22×C4C23×D7311yescharacteristic
721C22×C4C23×D7312yes—
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—738no—
733C4⋊C4—738no—
734C4⋊C4—734no—
735C4⋊C4—738no—
736C4⋊C4—738no—
737C4⋊C4—7316no—
738C4⋊C4—7316no—
739C4⋊C4—7316no—
740C4⋊C4—734no—
741C4⋊C4—7316no—
742C4⋊C4C23×D7314yes—
743C4⋊C4C23×D7314yes—
744C4⋊C4C23×D7318yes—
745C4⋊C4C23×D7318yes—
746C4⋊C4C23×D7318yes—
747C4⋊C4C23×D7318yes—
748C22⋊C4—738no—
749C22⋊C4—7316no—
750C22⋊C4—7316no—
751C22⋊C4—738no—
752C22⋊C4—7316no—
753C22⋊C4—738no—
754C22⋊C4—7316no—
755C22⋊C4—738no—
756C22⋊C4—738no—
757C22⋊C4C23×D7318yes—
758C22⋊C4C23×D7318yes—
759C22⋊C4C23×D7318yes—
760C22⋊C4C23×D7318yes—
761C22⋊C4C23×D7318yes—
762C42—7316no—
763C42—738no—
764C42—7316no—
765C42C23×D7314yes—
766C42C23×D7314yes—
767C42C23×D7314yes—
768C42C23×D7314yes—
769C42C23×D7318yes—
770C23—22no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—734no—
776C23—1464no—
777C23—1464no—
778C23—1464no—
779C23#1455663714yes—
780C23C24×D7314yes—
781C23C24×D7312yes—
782C23C24×D7311yescharacteristic
783Q8—28no—
784Q8—2928no—
785Q8—29216no—
786Q8—2928no—
787Q8—29216no—
788Q8—1468no—
789D4—216no—
790D4—28no—
791D4—29216no—
792D4—14616no—
793D4—1468no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—216no—
804C2×C4—28no—
805C2×C4—29216no—
806C2×C4—29216no—
807C2×C4—734no—
808C2×C4—734no—
809C2×C4—738no—
810C2×C4—734no—
811C2×C4—738no—
812C2×C4—1468no—
813C2×C4—1464no—
814C2×C4—1468no—
815C2×C4—14632no—
816C2×C4—1464no—
817C2×C4—1464no—
818C2×C4—14616no—
819C2×C4#1455663814yes—
820C2×C4#1455663814yes—
821C2×C4C24×D7314yes—
822C2×C4C24×D7314yes—
823C2×C4C24×D7312yes—
824C2×C4C24×D7312yes—
825C2×C4C24×D7312yes—
826C2×C4C24×D7312yes—
827C2×C4C24×D7314yes—
828C2×C4C24×D7312yes—
829C2×C4C24×D7312yes—
830C22—28no—
831C22—22no—
832C22—22no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—48no—
837C22—2928no—
838C22—1464no—
839C22—1464no—
840C22—1464no—
841C22C2×#1455663714yes—
842C22C2×#1455663712yes—
843C22C2×#1455663812yes—
844C22C2×#1455663812yes—
845C22C25×D7311yescharacteristic
846C4—22no—
847C4—22no—
848C4—24no—
849C4—24no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—1468no—
854C4—1464no—
855C4—1468no—
856C4—1464no—
857C4—1464no—
858C4C2×#1455663814yes—
859C4C2×#1455663814yes—
860C2—24no—
861C2—44no—
862C2—2924no—
863C2#2262427114yesdirect product factor
864C2C22×#1455663711yescharacteristic
865C2C22×#1455663811yescharacteristic
866C2C22×#1455663811yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#529×C73C2
socleC23×C73C25
hypercenterC2×#529D73
hypocenterC73C2×#3544
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22624271C2direct (N × H)
2. C2×#17989339C2semidirect
3. C2×Q8×Dic146C2semidirect
4. C2×#17989302C2semidirect
5. C2×#17989297C2semidirect
6. C2×#17989294C2semidirect
7. C2×#17989279C2semidirect
8. C2×#17989277C2semidirect
9. C2×#17989241C2semidirect
10. C2×#17989237C2semidirect
11. C2×#17989217C2semidirect
12. C2×#17989215C2semidirect
13. C2×#17989208C2semidirect
14. C2×#17989206C2semidirect
15. C2×#17989159C2semidirect
16. C22×#14556591C2semidirect
17. C2×#17989121C2semidirect
18. C2×#529×C73C2semidirect
21. #17989339C22semidirect
22. Q8×Dic146C22semidirect
23. #17989302C22semidirect
24. #17989297C22semidirect
25. #17989294C22semidirect
26. #17989279C22semidirect
27. #17989277C22semidirect
28. #17989241C22semidirect
29. #17989237C22semidirect
30. #17989217C22semidirect
31. #17989215C22semidirect
32. #17989208C22semidirect
33. #17989206C22semidirect
34. #17989159C22semidirect
41. C2×#14556591C22semidirect
45. #17989121C22semidirect
89. #529×C73C22semidirect
429. C2×C73#3544semidirect
451. C2×#529D73semidirect
452. C73C2×#3544semidirect
480. #529C2×D73semidirect
863. C2#22624271direct (N × H)

Maximal subgroups

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

subgroupindex
#226242712
C2×#179893392
C2×Q8×Dic1462
C2×#179893022
C2×#179892972
C2×#179892942
C2×#179892792
C2×#179892772
C2×#179892412
C2×#179892372
C2×#179892172
C2×#179892152
C2×#179892082
C2×#179892062
C2×#179891592
C22×#145565912
C2×#179891212
C2×#529×C732
C2×#354473