Finite Group Databasebeta

← C2×#22623909 #33994098

Subgroups — C2×#22623909 #33994098

Order 18688.

7142 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#22623909C2132yesmaximal, direct product factor
2C2×#17989315C211yesmaximal, characteristic, complemented
3C2×#17989297C211yesmaximal, characteristic, complemented
4C2×#17989294C211yesmaximal, characteristic, complemented
5C2×#17989283C212yesmaximal, complemented
6C2×#17989277C212yesmaximal, complemented
7C2×#17989276C212yesmaximal, complemented
8C2×#17989270C214yesmaximal, complemented
9C2×#17989241C211yesmaximal, characteristic, complemented
10C2×#17989236C212yesmaximal, complemented
11C2×#17989195C212yesmaximal, complemented
12C2×#17989179C214yesmaximal, complemented
13C2×#17989144C211yesmaximal, characteristic, complemented
14C2×#17989121C212yesmaximal, complemented
15C2×#17989121C211yesmaximal, characteristic, complemented
16C22×#14556583C212yesmaximal, complemented
17C2×#17989066C212yesmaximal, complemented
18C2×C4×#41×C73C211yesmaximal, characteristic, complemented
19C22×#11924027C2212yes—
20#17989315C22116yescomplemented
21#17989297C22116yescomplemented
22#17989294C22116yescomplemented
23#17989283C22132yescomplemented
24#17989277C22132yescomplemented
25#17989276C22132yescomplemented
26#17989270C22164yescomplemented
27#17989241C22116yescomplemented
28#17989236C22132yescomplemented
29#17989195C22132yescomplemented
30#17989179C22164yescomplemented
31#17989144C22116yescomplemented
32C2×#14556591C2211yescharacteristic
33C2×#14556591C2211yescharacteristic
34C2×#14556589C2212yes—
35#17989121C22116yescomplemented
36#17989121C22132yescomplemented
37C2×#14556586C2214yes—
38C2×#14556585C2214yes—
39C2×#14556585C2212yes—
40C2×#14556584C2214yes—
41C2×#14556583C2212yes—
42C2×#14556583C2214yes—
43C2×#14556583C2214yes—
44C2×#14556583C2211yescharacteristic
45C2×#14556583C2212yes—
46C2×#14556583C2212yes—
47C2×#14556583C22132yescomplemented
48C2×#14556582C2212yes—
49C2×#14556581C2214yes—
50C2×#14556581C2214yes—
51C2×#14556579C2211yescharacteristic
52C2×#14556575C2214yes—
53C2×#14556574C2212yes—
54C2×#14556574C2214yes—
55C2×#14556573C2214yes—
56C2×#14556572C2214yes—
57C2×#14556571C2212yes—
58C2×#14556570C2212yes—
59C2×#14556570C2212yes—
60C2×#14556570C2211yescharacteristic
61C2×#14556570C2212yes—
62C2×#14556569C2214yes—
63C2×#14556568C2214yes—
64C2×#14556567C2212yes—
65C2×#14556565C2212yes—
66C2×#14556565C2211yescharacteristic
67C2×#14556563C2214yes—
68#17989066C22132yescomplemented
69C2×C4×Dic146C2212yes—
70C2×C4×Dic146C2211yescharacteristic
71C2×C4×Dic146C2212yes—
72C2×C4×Dic146C2212yes—
73C2×#14556556C2212yes—
74C2×C4×D292C2211yescharacteristic
75C2×C4×D292C2212yes—
76C2×D4×Dic73C2212yes—
77C2×C4×C22⋊D73C2214yes—
78C2×C4×C22⋊D73C2212yes—
79C2×#14556551C2214yes—
80C2×#14556550C2212yes—
81C2×#14556548C2212yes—
82C2×#14556548C2214yes—
83C2×#14556547C2214yes—
84C22×C4⋊Dic73C2212yes—
85C22×C4⋊Dic73C2212yes—
86C22×#11924007C2214yes—
87C22×#11924007C2214yes—
88C2×C4⋊C4×D73C2212yes—
89C22×#41×C73C2211yescharacteristic
90C4×#41×C73C22116yescomplemented
91C2×C4×Q8×C73C2211yescharacteristic
92C2×C4×Q8×C73C2211yescharacteristic
93C2×C4×D4×C73C2212yes—
94C2×C4×D4×C73C2211yescharacteristic
95C2×C4×D4×C73C2211yescharacteristic
96C2×C4×D4×C73C2212yes—
97C2×#117×C73C2212yes—
98C2×#117×C73C2211yescharacteristic
99C22×C42×C73C2212yes—
100C22×C42×C73C2211yescharacteristic
101C2×#11924027—216no—
102C2×#11924027C23116yes—
103C22×Dic146C2312yes—
104C22×Dic146C2311yescharacteristic
105C22×Dic146C2312yes—
106C22×D292C2311yescharacteristic
107C22×C22⋊D73C2314yes—
108C22×C22⋊D73C2312yes—
109C23×Dic73C2314yes—
110C23×Dic73C2314yes—
111C22×C4×D73C2312yes—
112C22×C4×D73C2314yes—
113#14556591C2318yes—
114#14556591C2318yes—
115#14556589C23116yes—
116#14556586C23132yes—
117#14556585C23132yes—
118#14556585C23116yes—
119#14556584C23132yes—
120#14556583C23116yes—
121#14556583C2318yes—
122#14556583C23132yes—
123#14556583C23132yes—
124#14556583C23116yes—
125#14556583C23116yes—
126#14556582C23116yes—
127#14556581C23132yes—
128#14556581C23132yes—
129#14556579C2318yes—
130#14556575C23132yes—
131#14556574C23116yes—
132#14556574C23132yes—
133#14556573C23132yes—
134#14556572C23132yes—
135#14556571C23116yes—
136#14556570C2318yes—
137#14556570C23116yes—
138#14556570C23116yes—
139#14556570C23116yes—
140#14556569C23132yes—
141#14556568C23132yes—
142#14556567C23116yes—
143#14556565C23116yes—
144#14556565C2318yes—
145#14556563C23132yes—
146C4×Dic146C23116yes—
147C4×Dic146C2318yes—
148C4×Dic146C23116yes—
149C4×Dic146C23116yes—
150#14556556C23116yes—
151C4×D292C2318yes—
152C4×D292C23116yes—
153D4×Dic73C23116yes—
154C4×C22⋊D73C23132yes—
155C4×C22⋊D73C23116yes—
156#14556551C23132yes—
157#14556550C23116yes—
158#14556548C23116yes—
159#14556548C23132yes—
160#14556547C23132yes—
161C2×C4⋊Dic73C2312yes—
162C2×C4⋊Dic73C2312yes—
163C2×C4⋊Dic73C2312yes—
164C2×C4⋊Dic73C2312yes—
165C2×C4⋊Dic73C23116yes—
166C2×C4⋊Dic73C23116yes—
167C2×C4⋊Dic73C2311yescharacteristic
168C2×C4⋊Dic73C2311yescharacteristic
169C2×C4⋊Dic73C2314yes—
170C2×C4⋊Dic73C2314yes—
171C2×#11924007C2314yes—
172C2×#11924007C2314yes—
173C2×#11924007C23132yes—
174C2×#11924007C23132yes—
175C2×#11924007C2314yes—
176C2×#11924007C2312yes—
177C2×#11924007C2312yes—
178C2×#11924007C2314yes—
179C2×#11924007C2314yes—
180C2×#11924007C2314yes—
181C2×#11924007C2314yes—
182C2×#11924007C2312yes—
183C2×#11924007C2314yes—
184C2×#11924007C2312yes—
185C4⋊C4×D73C23116yes—
186C2×C22⋊Dic73C2314yes—
187C2×C22⋊Dic73C2314yes—
188C2×C22⋊Dic73C2312yes—
189C2×#11924005C2312yes—
190C2×#11924005C2312yes—
191C2×#11924005C2312yes—
192C2×#11924005C2314yes—
193C2×#11924005C2314yes—
194C2×#11924005C2312yes—
195C2×C4×Dic73C2312yes—
196C2×C4×Dic73C2314yes—
197C2×C4×Dic73C2314yes—
198C2×#41×C73—28no—
199C2×#41×C73C2318yes—
200C22×Q8×C73C2311yescharacteristic
201C22×D4×C73C2312yes—
202C22×D4×C73C2311yescharacteristic
203C23×C4×C73C2312yes—
204C23×C4×C73C2311yescharacteristic
205C23×C4×C73C2312yes—
206C23×C4×C73C2311yescharacteristic
207C23×C4×C73C2312yes—
208C23×C4×C73C2311yescharacteristic
209C4×Q8×C73C2318yes—
210C4×Q8×C73C2318yes—
211C4×D4×C73C23116yes—
212C4×D4×C73C2318yes—
213C4×D4×C73C23116yes—
214C4×D4×C73C2318yes—
215#117×C73C23116yes—
216#117×C73C2318yes—
217C2×C4⋊C4×C73C2311yescharacteristic
218C2×C4⋊C4×C73C2312yes—
219C2×C4⋊C4×C73C2311yescharacteristic
220C2×C4⋊C4×C73C2312yes—
221C2×C22⋊C4×C73C2312yes—
222C2×C22⋊C4×C73C2312yes—
223C2×C22⋊C4×C73C2312yes—
224C2×C42×C73C2318yes—
225C2×C42×C73C23116yes—
226C2×C42×C73C2311yescharacteristic
227C2×C42×C73C2311yescharacteristic
228C2×C42×C73C2312yes—
229C2×C42×C73C2311yescharacteristic
230C2×C42×C73C2311yescharacteristic
231C2×C42×C73C2312yes—
232C2×C42×C73C2312yes—
233C23×D73C2412yes—
234#11924027—264no—
235C2×Dic146—28no—
236C2×Dic146—24no—
237C2×Dic146—44no—
238C2×Dic146C2418yes—
239C2×Dic146C2414yes—
240C2×Dic146C2418yes—
241C2×D292—24no—
242C2×D292C2414yes—
243C2×C22⋊D73—216no—
244C2×C22⋊D73—44no—
245C2×C22⋊D73C24116yes—
246C2×C22⋊D73C2418yes—
247C22×Dic73—216no—
248C22×Dic73—48no—
249C22×Dic73C2412yes—
250C22×Dic73C2414yes—
251C22×Dic73C2414yes—
252C22×Dic73C2412yes—
253C22×Dic73C2412yes—
254C22×Dic73C24116yes—
255C22×Dic73C24116yes—
256C2×C4×D73—28no—
257C2×C4×D73—48no—
258C2×C4×D73C2418yes—
259C2×C4×D73C24116yes—
260C4⋊Dic73C2418yes—
261C4⋊Dic73C2414yes—
262C4⋊Dic73C2414yes—
263C4⋊Dic73C2418yes—
264C4⋊Dic73C2418yes—
265C4⋊Dic73C24116yes—
266C4⋊Dic73C24116yes—
267C4⋊Dic73C2418yes—
268#11924007C24116yes—
269#11924007C2418yes—
270#11924007C2418yes—
271#11924007C24116yes—
272#11924007C24116yes—
273#11924007C24116yes—
274#11924007C24116yes—
275#11924007C24116yes—
276#11924007C2418yes—
277#11924007C24116yes—
278#11924007C2418yes—
279#11924007C24116yes—
280C22⋊Dic73C24116yes—
281C22⋊Dic73C24116yes—
282C22⋊Dic73C2418yes—
283#11924005C2418yes—
284#11924005C2418yes—
285#11924005C2418yes—
286#11924005C24116yes—
287#11924005C24116yes—
288#11924005C2418yes—
289C4×Dic73C24116yes—
290C4×Dic73C24116yes—
291C4×Dic73C2418yes—
292C24×C73C2411yescharacteristic
293C24×C73C2412yes—
294#41×C73—232no—
295C2×Q8×C73—24no—
296C2×Q8×C73C2414yes—
297C2×D4×C73—28no—
298C2×D4×C73#4118yes—
299C2×D4×C73C2418yes—
300C2×D4×C73C2414yes—
301C22×C4×C73—28no—
302C22×C4×C73—24no—
303C22×C4×C73—28no—
304C22×C4×C73—24no—
305C22×C4×C73—44no—
306C22×C4×C73—42no—
307C22×C4×C73C2411yescharacteristic
308C22×C4×C73C2411yescharacteristic
309C22×C4×C73C2411yescharacteristic
310C22×C4×C73C2412yes—
311C22×C4×C73C2412yes—
312C22×C4×C73C2411yescharacteristic
313C22×C4×C73C2412yes—
314C22×C4×C73C2418yes—
315C22×C4×C73C2414yes—
316C22×C4×C73C2418yes—
317C22×C4×C73C2414yes—
318C22×C4×C73C2418yes—
319C22×C4×C73C2414yes—
320C22×C4×C73C2411yescharacteristic
321C22×C4×C73C2411yescharacteristic
322C4⋊C4×C73C2414yes—
323C4⋊C4×C73C2418yes—
324C4⋊C4×C73C2414yes—
325C4⋊C4×C73C2418yes—
326C22⋊C4×C73C2418yes—
327C22⋊C4×C73C2418yes—
328C22⋊C4×C73C2418yes—
329C42×C73C2414yes—
330C42×C73C2418yes—
331C42×C73C2414yes—
332C42×C73C2414yes—
333C42×C73C2418yes—
334C42×C73C2414yes—
335C42×C73C2418yes—
336C23×C73—24no—
337C23×C73—24no—
338C23×C73—22no—
339C23×C73—22no—
340C23×C73—22no—
341C23×C73C2×#4118yes—
342C23×C73C2512yes—
343C23×C73C2514yes—
344C23×C73C2511yescharacteristic
345C22×D73—24no—
346C22×D73—24no—
347C22×D73—24no—
348C22×D73C2514yes—
349Q8×C73—28no—
350D4×C73—216no—
351D4×C73C2×#41116yes—
352C2×C4×C73—22no—
353C2×C4×C73—24no—
354C2×C4×C73—216no—
355C2×C4×C73—22no—
356C2×C4×C73—24no—
357C2×C4×C73—22no—
358C2×C4×C73—24no—
359C2×C4×C73—22no—
360C2×C4×C73—28no—
361C2×C4×C73—216no—
362C2×C4×C73—28no—
363C2×C4×C73—44no—
364C2×C4×C73—48no—
365C2×C4×C73C2×#4114yes—
366C2×C4×C732−1+414yes—
367C2×C4×C73C2512yes—
368C2×C4×C73C2512yes—
369C2×C4×C73C2512yes—
370C2×C4×C73C2514yes—
371C2×C4×C73C2514yes—
372C2×C4×C73C2512yes—
373C2×C4×C73C2514yes—
374C2×C4×C73C2512yes—
375C2×C4×C73C2512yes—
376C22⋊D73—232no—
377C22⋊D73—48no—
378C2×Dic73—24no—
379C2×Dic73—28no—
380C2×Dic73—232no—
381C2×Dic73—24no—
382C2×Dic73—28no—
383C2×Dic73—24no—
384C2×Dic73—416no—
385C2×Dic73C2514yes—
386C2×Dic73C2518yes—
387C2×Dic73C2518yes—
388C2×Dic73C2514yes—
389C2×Dic73C2514yes—
390D292—28no—
391C4×D73—216no—
392C4×D73—416no—
393Dic146—216no—
394Dic146—28no—
395Dic146—48no—
396C22×C73—24no—
397C22×C73—24no—
398C22×C73—216no—
399C22×C73—22no—
400C22×C73—22no—
401C22×C73—22no—
402C22×C73—44no—
403C22×C73C22×#4118yes—
404C22×C73C22×#4112yes—
405C22×C73C2×2−1+412yes—
406C22×C73#58512yes—
407C22×C73C2611yescharacteristic
408C2×D73—24no—
409C2×D73—24no—
410C2×D73—24no—
411C2×D73—48no—
412C4×C73—22no—
413C4×C73—24no—
414C4×C73—22no—
415C4×C73—24no—
416C4×C73—22no—
417C4×C73—24no—
418C4×C73—22no—
419C4×C73C22×#4114yes—
420C4×C73C2×2−1+414yes—
421Dic73—28no—
422Dic73—24no—
423Dic73—24no—
424Dic73—28no—
425Dic73—24no—
426C2×#3515—731nomaximal, Sylow
427C2×C73—28no—
428C2×C73—42no—
429C2×C73#351514yescomplemented
430C2×C73C23×#4111yescharacteristic
431C2×C73C22×2−1+411yescharacteristic
432C2×C73C2×#58511yescharacteristic
433D73—44no—
434#3515—7332no—
435C2×#557—731no—
436C2×#554—731no—
437C2×#554—731no—
438C2×#553—732no—
439C2×#552—732no—
440C2×#552—734no—
441C2×#552—732no—
442C2×#547—732no—
443C2×#547—731no—
444C2×#541—732no—
445C2×#539—734no—
446C2×#533—731no—
447C2×#529—731no—
448C2×#529—732no—
449C22×#125—732no—
450C2×#520—732no—
451C2×C4×#41D7311yescharacteristic, complemented
452C73C2×#351511yescharacteristic, complemented, Sylow
453C22×#41—732no—
454C22×#41C2×D7311yescharacteristic
455#557—7316no—
456#554—7316no—
457#554—7316no—
458#553—7332no—
459#552—7332no—
460#552—7364no—
461#552—7332no—
462#547—7332no—
463#547—7316no—
464#541—7332no—
465#539—7364no—
466#533—7316no—
467C2×C4⋊Q8—732no—
468C2×C4⋊Q8—731no—
469C2×C4⋊Q8—731no—
470#529—7332no—
471#529—7316no—
472C2×#126—734no—
473C2×#126—734no—
474C2×#126—734no—
475C2×#126—732no—
476C2×#125—734no—
477C2×#125—734no—
478C2×#125—732no—
479C2×#125—731no—
480C2×#125—732no—
481C2×#125—734no—
482C2×#125—734no—
483C2×#125—732no—
484C2×#125—732no—
485C2×#125—7332no—
486C2×#124—731no—
487C2×#123—734no—
488C2×#123—732no—
489C2×#123—734no—
490C2×#123—734no—
491C2×#123—734no—
492C2×C22⋊Q8—732no—
493C2×C22⋊Q8—731no—
494C2×C22⋊Q8—732no—
495C2×C22⋊Q8—732no—
496C2×C22⋊Q8—732no—
497C2×C22⋊Q8—734no—
498C2×C22⋊Q8—732no—
499C2×C22⋊Q8—734no—
500C2×#121—734no—
501C2×#121—732no—
502C2×#121—731no—
503#520—7332no—
504C4×#41C2×D73116yescomplemented
505C2×C4×Q8—732no—
506C2×C4×Q8—732no—
507C2×C4×Q8—732no—
508C2×C4×Q8—731no—
509C2×C4×Q8—732no—
510C2×C4×Q8C2×D7311yescharacteristic
511C2×C4×Q8C2×D7311yescharacteristic
512C2×C4×D4—732no—
513C2×C4×D4—734no—
514C2×C4×D4—732no—
515C2×C4×D4—734no—
516C2×C4×D4—731no—
517C2×C4×D4—732no—
518C2×C4×D4C2×D7311yescharacteristic
519C2×C4×D4C2×D7312yes—
520C2×C4×D4C2×D7311yescharacteristic
521C2×C4×D4C2×D7312yes—
522C2×#117—732no—
523C2×#117—734no—
524C2×#117—732no—
525C2×#117—734no—
526C2×#117C2×D7311yescharacteristic
527C2×#117C2×D7312yes—
528C22×C4⋊C4—734no—
529C22×C4⋊C4—734no—
530C22×C4⋊C4—732no—
531C22×C4⋊C4—732no—
532C22×C4⋊C4—732no—
533C22×C42C2×D7312yes—
534C22×C42C2×D7311yescharacteristic
535C2×#41—28no—
536C2×#41—7316no—
537C2×#41—14616no—
538C2×#41C22×D7318yes—
539C22×Q8—732no—
540C22×Q8—731no—
541C22×Q8—732no—
542C22×Q8C22×D7311yescharacteristic
543C22×D4—732no—
544C22×D4—734no—
545C22×D4—731no—
546C22×D4C22×D7312yes—
547C22×D4C22×D7311yescharacteristic
548C23×C4—734no—
549C23×C4—734no—
550C23×C4—734no—
551C23×C4—732no—
552C23×C4C22×D7312yes—
553C23×C4C22×D7312yes—
554C23×C4C22×D7311yescharacteristic
555C23×C4C22×D7311yescharacteristic
556C23×C4C22×D7312yes—
557C23×C4C22×D7311yescharacteristic
558C4⋊Q8—7316no—
559C4⋊Q8—738no—
560C4⋊Q8—738no—
561#126—7332no—
562#126—7332no—
563#126—7332no—
564#126—7316no—
565#125—7332no—
566#125—7332no—
567#125—7316no—
568#125—738no—
569#125—7316no—
570#125—7332no—
571#125—7332no—
572#125—7316no—
573#125—7316no—
574#124—738no—
575#123—7332no—
576#123—7316no—
577#123—7332no—
578#123—7332no—
579#123—7332no—
580C22⋊Q8—7316no—
581C22⋊Q8—738no—
582C22⋊Q8—7316no—
583C22⋊Q8—7316no—
584C22⋊Q8—7316no—
585C22⋊Q8—7332no—
586C22⋊Q8—7316no—
587C22⋊Q8—7332no—
588#121—7332no—
589#121—7316no—
590#121—738no—
591C4×Q8—7316no—
592C4×Q8—7316no—
593C4×Q8—7316no—
594C4×Q8—738no—
595C4×Q8—7316no—
596C4×Q8C22×D7318yes—
597C4×Q8C22×D7318yes—
598C4×D4—7316no—
599C4×D4—7332no—
600C4×D4—7316no—
601C4×D4—7332no—
602C4×D4—738no—
603C4×D4—7316no—
604C4×D4C22×D7318yes—
605C4×D4C22×D73116yes—
606C4×D4C22×D7318yes—
607C4×D4C22×D73116yes—
608#117—7316no—
609#117—7332no—
610#117—7316no—
611#117—7332no—
612#117C22×D7318yes—
613#117C22×D73116yes—
614C2×C4⋊C4—734no—
615C2×C4⋊C4—732no—
616C2×C4⋊C4—731no—
617C2×C4⋊C4—732no—
618C2×C4⋊C4—731no—
619C2×C4⋊C4—732no—
620C2×C4⋊C4—732no—
621C2×C4⋊C4—734no—
622C2×C4⋊C4—732no—
623C2×C4⋊C4—734no—
624C2×C4⋊C4—734no—
625C2×C4⋊C4—7332no—
626C2×C4⋊C4—734no—
627C2×C4⋊C4—734no—
628C2×C4⋊C4—734no—
629C2×C4⋊C4—734no—
630C2×C4⋊C4—7332no—
631C2×C4⋊C4—7316no—
632C2×C4⋊C4—7316no—
633C2×C4⋊C4—732no—
634C2×C4⋊C4—734no—
635C2×C4⋊C4—732no—
636C2×C4⋊C4—732no—
637C2×C4⋊C4—734no—
638C2×C4⋊C4—7316no—
639C2×C4⋊C4C22×D7311yescharacteristic
640C2×C4⋊C4C22×D7312yes—
641C2×C4⋊C4C22×D7311yescharacteristic
642C2×C4⋊C4C22×D7312yes—
643C2×C22⋊C4—734no—
644C2×C22⋊C4—734no—
645C2×C22⋊C4—732no—
646C2×C22⋊C4—732no—
647C2×C22⋊C4—732no—
648C2×C22⋊C4—732no—
649C2×C22⋊C4—734no—
650C2×C22⋊C4—734no—
651C2×C22⋊C4—732no—
652C2×C22⋊C4C22×D7312yes—
653C2×C22⋊C4C22×D7312yes—
654C2×C22⋊C4C22×D7312yes—
655C2×C42—734no—
656C2×C42—734no—
657C2×C42—732no—
658C2×C42C22×D7312yes—
659C2×C42C22×D7311yescharacteristic
660C2×C42C22×D7311yescharacteristic
661C2×C42C22×D7312yes—
662C2×C42C22×D7311yescharacteristic
663C2×C42C22×D7312yes—
664C2×C42C22×D73116yes—
665C2×C42C22×D7318yes—
666C2×C42C22×D7311yescharacteristic
667C24—732no—
668C24C23×D7311yescharacteristic
669C24C23×D7312yes—
670#41—232no—
671#41—14664no—
672C2×Q8—24no—
673C2×Q8—2924no—
674C2×Q8—738no—
675C2×Q8—734no—
676C2×Q8—738no—
677C2×Q8—1468no—
678C2×Q8—1464no—
679C2×Q8C23×D7314yes—
680C2×D4—28no—
681C2×D4—2924no—
682C2×D4—738no—
683C2×D4—7316no—
684C2×D4—734no—
685C2×D4—14616no—
686C2×D4—1464no—
687C2×D4#1192402818yes—
688C2×D4C23×D7318yes—
689C2×D4C23×D7314yes—
690C22×C4—28no—
691C22×C4—24no—
692C22×C4—28no—
693C22×C4—24no—
694C22×C4—44no—
695C22×C4—42no—
696C22×C4—2928no—
697C22×C4—2928no—
698C22×C4—7316no—
699C22×C4—7316no—
700C22×C4—7316no—
701C22×C4—732no—
702C22×C4—734no—
703C22×C4—734no—
704C22×C4—732no—
705C22×C4—732no—
706C22×C4—738no—
707C22×C4—14616no—
708C22×C4—1468no—
709C22×C4C23×D7318yes—
710C22×C4C23×D7318yes—
711C22×C4C23×D7314yes—
712C22×C4C23×D7314yes—
713C22×C4C23×D7311yescharacteristic
714C22×C4C23×D7312yes—
715C22×C4C23×D7311yescharacteristic
716C22×C4C23×D7311yescharacteristic
717C22×C4C23×D7312yes—
718C22×C4C23×D7311yescharacteristic
719C22×C4C23×D7312yes—
720C22×C4C23×D7318yes—
721C22×C4C23×D7314yes—
722C22×C4C23×D7311yescharacteristic
723C22×C4C23×D7311yescharacteristic
724C4⋊C4—7316no—
725C4⋊C4—738no—
726C4⋊C4—738no—
727C4⋊C4—7316no—
728C4⋊C4—7316no—
729C4⋊C4—7316no—
730C4⋊C4—7316no—
731C4⋊C4—7316no—
732C4⋊C4—738no—
733C4⋊C4—7316no—
734C4⋊C4—738no—
735C4⋊C4—7316no—
736C4⋊C4—734no—
737C4⋊C4—734no—
738C4⋊C4—738no—
739C4⋊C4—738no—
740C4⋊C4—738no—
741C4⋊C4—7316no—
742C4⋊C4—7316no—
743C4⋊C4—738no—
744C4⋊C4C23×D7314yes—
745C4⋊C4C23×D7318yes—
746C4⋊C4C23×D7314yes—
747C4⋊C4C23×D7318yes—
748C22⋊C4—7316no—
749C22⋊C4—7316no—
750C22⋊C4—738no—
751C22⋊C4—738no—
752C22⋊C4—738no—
753C22⋊C4—738no—
754C22⋊C4—7316no—
755C22⋊C4—7316no—
756C22⋊C4—738no—
757C22⋊C4C23×D7318yes—
758C22⋊C4C23×D7318yes—
759C22⋊C4C23×D7318yes—
760C42—7316no—
761C42—7316no—
762C42—738no—
763C42C23×D7314yes—
764C42C23×D7318yes—
765C42C23×D7314yes—
766C42C23×D7314yes—
767C42C23×D7318yes—
768C42C23×D7314yes—
769C42C23×D7318yes—
770C23—24no—
771C23—24no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—734no—
776C23—1464no—
777C23—1464no—
778C23—1464no—
779C23C2×#1192402818yes—
780C23C24×D7312yes—
781C23C24×D7314yes—
782C23C24×D7311yescharacteristic
783Q8—28no—
784Q8—2928no—
785Q8—14616no—
786Q8—1468no—
787D4—216no—
788D4—2928no—
789D4—14632no—
790D4—1468no—
791D4C2×#11924028116yes—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—216no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—28no—
801C2×C4—216no—
802C2×C4—28no—
803C2×C4—48no—
804C2×C4—44no—
805C2×C4—29216no—
806C2×C4—29216no—
807C2×C4—734no—
808C2×C4—738no—
809C2×C4—738no—
810C2×C4—734no—
811C2×C4—734no—
812C2×C4—1464no—
813C2×C4—1468no—
814C2×C4—14632no—
815C2×C4—1464no—
816C2×C4—1464no—
817C2×C4—1468no—
818C2×C4—14616no—
819C2×C4C2×#1192402814yes—
820C2×C4#1455663814yes—
821C2×C4C24×D7312yes—
822C2×C4C24×D7314yes—
823C2×C4C24×D7312yes—
824C2×C4C24×D7312yes—
825C2×C4C24×D7314yes—
826C2×C4C24×D7312yes—
827C2×C4C24×D7314yes—
828C2×C4C24×D7312yes—
829C2×C4C24×D7312yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—2928no—
838C22—1464no—
839C22—1464no—
840C22—1464no—
841C22C22×#1192402818yes—
842C22C22×#1192402812yes—
843C22C2×#1455663812yes—
844C22#1798942312yes—
845C22C25×D7311yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—24no—
852C4—22no—
853C4—1464no—
854C4—1468no—
855C4—1464no—
856C4—1464no—
857C4—1468no—
858C4C22×#1192402814yes—
859C4C2×#1455663814yes—
860C2—28no—
861C2—42no—
862C2—2924no—
863C2#2262390914yesdirect product factor
864C2C23×#1192402811yescharacteristic
865C2C22×#1455663811yescharacteristic
866C2C2×#1798942311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×C4×#41×C73C2
socleC23×C73C25
hypercenterC2×C4×#41D73
hypocenterC73C2×#3515
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #22623909C2direct (N × H)
2. C2×#17989315C2semidirect
3. C2×#17989297C2semidirect
4. C2×#17989294C2semidirect
5. C2×#17989283C2semidirect
6. C2×#17989277C2semidirect
7. C2×#17989276C2semidirect
8. C2×#17989270C2semidirect
9. C2×#17989241C2semidirect
10. C2×#17989236C2semidirect
11. C2×#17989195C2semidirect
12. C2×#17989179C2semidirect
13. C2×#17989144C2semidirect
14. C2×#17989121C2semidirect
15. C2×#17989121C2semidirect
16. C22×#14556583C2semidirect
17. C2×#17989066C2semidirect
18. C2×C4×#41×C73C2semidirect
20. #17989315C22semidirect
21. #17989297C22semidirect
22. #17989294C22semidirect
23. #17989283C22semidirect
24. #17989277C22semidirect
25. #17989276C22semidirect
26. #17989270C22semidirect
27. #17989241C22semidirect
28. #17989236C22semidirect
29. #17989195C22semidirect
30. #17989179C22semidirect
31. #17989144C22semidirect
35. #17989121C22semidirect
36. #17989121C22semidirect
47. C2×#14556583C22semidirect
68. #17989066C22semidirect
90. C4×#41×C73C22semidirect
429. C2×C73#3515semidirect
451. C2×C4×#41D73semidirect
452. C73C2×#3515semidirect
504. C4×#41C2×D73semidirect
863. C2#22623909direct (N × H)

Maximal subgroups

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

subgroupindex
#226239092
C2×#179893152
C2×#179892972
C2×#179892942
C2×#179892832
C2×#179892772
C2×#179892762
C2×#179892702
C2×#179892412
C2×#179892362
C2×#179891952
C2×#179891792
C2×#179891442
C2×#179891212
C22×#145565832
C2×#179890662
C2×C4×#41×C732
C2×#351573