Finite Group Databasebeta

← C2×#22624368 #33993595

Subgroups — C2×#22624368 #33993595

Order 18688.

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#22624368C2132yesmaximal, direct product factor
2C2×#17989339C214yesmaximal, complemented
3C2×#17989315C211yesmaximal, characteristic, complemented
4C2×#17989307C211yesmaximal, characteristic, complemented
5C2×#17989294C212yesmaximal, complemented
6C2×#17989283C212yesmaximal, complemented
7C2×Q8×D292C211yesmaximal, characteristic, complemented
8C2×#17989250C212yesmaximal, complemented
9C2×#17989243C212yesmaximal, complemented
10C2×#17989241C211yesmaximal, characteristic, complemented
11C2×#17989215C212yesmaximal, complemented
12C2×#17989208C212yesmaximal, complemented
13C2×#17989200C212yesmaximal, complemented
14C2×#17989181C214yesmaximal, complemented
15C2×#17989157C212yesmaximal, complemented
16C22×#14556591C211yesmaximal, characteristic, complemented
17C2×#17989121C211yesmaximal, characteristic, complemented
18C2×#529×C73C211yesmaximal, characteristic, complemented
19C22×#11924027C2212yes—
20C23×Dic146C2212yes—
21C22×Q8×D73C2212yes—
22#17989339C22164yescomplemented
23#17989315C22116yescomplemented
24#17989307C22116yescomplemented
25#17989294C22132yescomplemented
26#17989283C22132yescomplemented
27Q8×D292C22116yescomplemented
28#17989250C22132yescomplemented
29#17989243C22132yescomplemented
30#17989241C22116yescomplemented
31#17989215C22132yescomplemented
32#17989208C22132yescomplemented
33#17989200C22132yescomplemented
34#17989181C22164yescomplemented
35#17989157C22132yescomplemented
36C2×#14556591C2212yes—
37C2×#14556591C2211yescharacteristic
38C2×#14556591C2212yes—
39C2×#14556591C2212yes—
40C2×#14556591C2212yes—
41C2×#14556591C2211yescharacteristic
42C2×#14556591C22116yescomplemented
43C2×#14556590C2214yes—
44C2×#14556589C2212yes—
45#17989121C22116yescomplemented
46C2×#14556586C2214yes—
47C2×#14556586C2214yes—
48C2×#14556585C2212yes—
49C2×#14556584C2214yes—
50C2×#14556583C2212yes—
51C2×#14556583C2211yescharacteristic
52C2×#14556582C2214yes—
53C2×#14556582C2214yes—
54C2×#14556581C2214yes—
55C2×#14556579C2211yescharacteristic
56C2×#14556578C2212yes—
57C2×#14556577C2214yes—
58C2×#14556575C2214yes—
59C2×#14556574C2212yes—
60C2×#14556573C2214yes—
61C2×#14556573C2214yes—
62C2×#14556571C2214yes—
63C2×#14556571C2212yes—
64C2×#14556571C2212yes—
65C2×#14556570C2212yes—
66C2×#14556570C2211yescharacteristic
67C2×#14556569C2214yes—
68C2×#14556568C2214yes—
69C2×#14556568C2214yes—
70C2×#14556568C2214yes—
71C2×#14556568C2214yes—
72C2×#14556565C2212yes—
73C2×#14556565C2211yescharacteristic
74C2×#14556563C2214yes—
75C2×C4×Dic146C2212yes—
76C2×C4×Dic146C2211yescharacteristic
77C2×#14556556C2212yes—
78C2×#14556556C2212yes—
79C2×C4×D292C2212yes—
80C2×C4×D292C2211yescharacteristic
81C2×D4×Dic73C2214yes—
82C2×C4×C22⋊D73C2212yes—
83C2×#14556551C2214yes—
84C2×#14556550C2212yes—
85C2×#14556548C2212yes—
86C22×C4⋊Dic73C2212yes—
87C22×C4⋊Dic73C2212yes—
88C22×C4⋊Dic73C2212yes—
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×C73C2211yescharacteristic
98C2×C4×D4×C73C2212yes—
99C2×#117×C73C2212yes—
100C22×C42×C73C2211yescharacteristic
101C2×#11924027—48no—
102C2×#11924027C23116yes—
103C22×Dic146—48no—
104C22×Dic146C2312yes—
105C22×Dic146C2312yes—
106C22×Dic146C2311yescharacteristic
107C22×Dic146C2314yes—
108C22×Dic146C2314yes—
109C22×Dic146C23116yes—
110C2×Q8×D73—48no—
111C2×Q8×D73C23116yes—
112C22×D292C2311yescharacteristic
113C22×C22⋊D73C2312yes—
114C22×C22⋊D73C2314yes—
115C23×Dic73C2314yes—
116C23×Dic73C2314yes—
117C22×C4×D73C2312yes—
118C22×C4×D73C2314yes—
119#14556591C23116yes—
120#14556591C23116yes—
121#14556591C2318yes—
122#14556591C2318yes—
123#14556591C23116yes—
124#14556591C23116yes—
125#14556590C23132yes—
126#14556589C23116yes—
127#14556586C23132yes—
128#14556586C23132yes—
129#14556585C23116yes—
130#14556584C23132yes—
131#14556583C2318yes—
132#14556583C23116yes—
133#14556582C23132yes—
134#14556582C23132yes—
135#14556581C23132yes—
136#14556579C2318yes—
137#14556578C23116yes—
138#14556577C23132yes—
139#14556575C23132yes—
140#14556574C23116yes—
141#14556573C23132yes—
142#14556573C23132yes—
143#14556571C23132yes—
144#14556571C23116yes—
145#14556571C23116yes—
146#14556570C2318yes—
147#14556570C23116yes—
148#14556569C23132yes—
149#14556568C23132yes—
150#14556568C23132yes—
151#14556568C23132yes—
152#14556568C23132yes—
153#14556565C2318yes—
154#14556565C23116yes—
155#14556563C23132yes—
156C4×Dic146C2318yes—
157C4×Dic146C23116yes—
158#14556556C23116yes—
159#14556556C23116yes—
160C4×D292C2318yes—
161C4×D292C23116yes—
162D4×Dic73C23132yes—
163C4×C22⋊D73C23116yes—
164#14556551C23132yes—
165#14556550C23116yes—
166#14556548C23116yes—
167C2×C4⋊Dic73C2314yes—
168C2×C4⋊Dic73C2312yes—
169C2×C4⋊Dic73C2311yescharacteristic
170C2×C4⋊Dic73C2312yes—
171C2×C4⋊Dic73C2314yes—
172C2×C4⋊Dic73C2314yes—
173C2×C4⋊Dic73C2312yes—
174C2×C4⋊Dic73C2312yes—
175C2×C4⋊Dic73C2314yes—
176C2×C4⋊Dic73C23116yes—
177C2×C4⋊Dic73C23116yes—
178C2×C4⋊Dic73C23116yes—
179C2×C4⋊Dic73C2311yescharacteristic
180C2×#11924007C2314yes—
181C2×#11924007C2314yes—
182C2×#11924007C2312yes—
183C2×#11924007C2312yes—
184C2×#11924007C2312yes—
185C2×#11924007C2314yes—
186C2×#11924007C2314yes—
187C2×#11924007C2312yes—
188C2×C22⋊Dic73C2314yes—
189C2×C22⋊Dic73C2312yes—
190C2×C22⋊Dic73C2314yes—
191C2×#11924005C2312yes—
192C2×#11924005C2312yes—
193C2×#11924005C2314yes—
194C2×#11924005C2312yes—
195C2×#11924005C2314yes—
196C2×#11924005C2312yes—
197C2×C4×Dic73C2312yes—
198C2×C4×Dic73C2314yes—
199C2×C4×Dic73C2314yes—
200C22×Q8×C73C2311yescharacteristic
201C22×D4×C73C2311yescharacteristic
202C22×D4×C73C2312yes—
203C23×C4×C73C2311yescharacteristic
204C23×C4×C73C2311yescharacteristic
205C23×C4×C73C2311yescharacteristic
206C23×C4×C73C2312yes—
207#126×C73C23116yes—
208#125×C73C2318yes—
209#124×C73C2318yes—
210#123×C73C23116yes—
211C22⋊Q8×C73C2318yes—
212#121×C73C2318yes—
213C4×Q8×C73C2318yes—
214C4×D4×C73C2318yes—
215C4×D4×C73C23116yes—
216#117×C73C23116yes—
217C2×C4⋊C4×C73C2312yes—
218C2×C4⋊C4×C73C2312yes—
219C2×C4⋊C4×C73C2311yescharacteristic
220C2×C4⋊C4×C73C2312yes—
221C2×C4⋊C4×C73C2311yescharacteristic
222C2×C4⋊C4×C73C2312yes—
223C2×C22⋊C4×C73C2312yes—
224C2×C22⋊C4×C73C2312yes—
225C2×C22⋊C4×C73C2312yes—
226C2×C22⋊C4×C73C2312yes—
227C2×C22⋊C4×C73C2312yes—
228C2×C42×C73C2318yes—
229C2×C42×C73C2311yescharacteristic
230C2×C42×C73C2311yescharacteristic
231C2×C42×C73C2311yescharacteristic
232C2×C42×C73C2311yescharacteristic
233C2×C42×C73C2312yes—
234C23×D73C2412yes—
235#11924027—432no—
236C2×Dic146—28no—
237C2×Dic146—28no—
238C2×Dic146—24no—
239C2×Dic146—432no—
240C2×Dic146—48no—
241C2×Dic146—48no—
242C2×Dic146C2418yes—
243C2×Dic146C2418yes—
244C2×Dic146C2414yes—
245C2×Dic146C24116yes—
246C2×Dic146C24116yes—
247Q8×D73—432no—
248C2×D292—24no—
249C2×D292C2414yes—
250C2×C22⋊D73—28no—
251C2×C22⋊D73—48no—
252C2×C22⋊D73C2418yes—
253C2×C22⋊D73C24116yes—
254C22×Dic73—48no—
255C22×Dic73—48no—
256C22×Dic73C2412yes—
257C22×Dic73C2412yes—
258C22×Dic73C2414yes—
259C22×Dic73C2414yes—
260C22×Dic73C2412yes—
261C22×Dic73C24116yes—
262C22×Dic73C24116yes—
263C2×C4×D73—28no—
264C2×C4×D73—48no—
265C2×C4×D73C2418yes—
266C2×C4×D73C24116yes—
267C4⋊Dic73C2414yes—
268C4⋊Dic73C2418yes—
269C4⋊Dic73C2418yes—
270C4⋊Dic73C24116yes—
271C4⋊Dic73C24116yes—
272C4⋊Dic73C24116yes—
273C4⋊Dic73C2418yes—
274C4⋊Dic73C2418yes—
275C4⋊Dic73C2414yes—
276C4⋊Dic73C24116yes—
277#11924007C2418yes—
278#11924007C2418yes—
279#11924007C24116yes—
280#11924007C2418yes—
281#11924007C24116yes—
282#11924007C24116yes—
283#11924007C24116yes—
284#11924007C2418yes—
285C22⋊Dic73C24116yes—
286C22⋊Dic73C2418yes—
287C22⋊Dic73C24116yes—
288#11924005C2418yes—
289#11924005C2418yes—
290#11924005C24116yes—
291#11924005C2418yes—
292#11924005C24116yes—
293#11924005C2418yes—
294C4×Dic73C2418yes—
295C4×Dic73C24116yes—
296C4×Dic73C24116yes—
297C24×C73C2412yes—
298C24×C73C2411yescharacteristic
299C2×Q8×C73—24no—
300C2×Q8×C73C2414yes—
301C2×D4×C73—28no—
302C2×D4×C73—24no—
303C2×D4×C73C2418yes—
304C2×D4×C73C2414yes—
305C22×C4×C73—24no—
306C22×C4×C73—24no—
307C22×C4×C73—24no—
308C22×C4×C73—28no—
309C22×C4×C73C2411yescharacteristic
310C22×C4×C73C2411yescharacteristic
311C22×C4×C73C2411yescharacteristic
312C22×C4×C73C2411yescharacteristic
313C22×C4×C73C2414yes—
314C22×C4×C73C2414yes—
315C22×C4×C73C2414yes—
316C22×C4×C73C2412yes—
317C22×C4×C73C2412yes—
318C22×C4×C73C2412yes—
319C22×C4×C73C2418yes—
320C22×C4×C73C2411yescharacteristic
321C22×C4×C73C2411yescharacteristic
322C4⋊C4×C73C2418yes—
323C4⋊C4×C73C2418yes—
324C4⋊C4×C73C2414yes—
325C4⋊C4×C73C2418yes—
326C4⋊C4×C73C2414yes—
327C4⋊C4×C73C2418yes—
328C22⋊C4×C73C2418yes—
329C22⋊C4×C73C2418yes—
330C22⋊C4×C73C2418yes—
331C22⋊C4×C73C2418yes—
332C22⋊C4×C73C2418yes—
333C42×C73C2414yes—
334C42×C73C2414yes—
335C42×C73C2414yes—
336C42×C73C2414yes—
337C42×C73C2418yes—
338C23×C73—22no—
339C23×C73—22no—
340C23×C73—24no—
341C23×C73—24no—
342C23×C73—24no—
343C23×C732−1+414yes—
344C23×C73C2514yes—
345C23×C73C2512yes—
346C23×C73C2511yescharacteristic
347C22×D73—24no—
348C22×D73—24no—
349C22×D73—24no—
350C22×D73C2514yes—
351Q8×C73—28no—
352D4×C73—216no—
353D4×C73—28no—
354C2×C4×C73—22no—
355C2×C4×C73—24no—
356C2×C4×C73—28no—
357C2×C4×C73—22no—
358C2×C4×C73—22no—
359C2×C4×C73—22no—
360C2×C4×C73—24no—
361C2×C4×C73—24no—
362C2×C4×C73—28no—
363C2×C4×C73—28no—
364C2×C4×C73—216no—
365C2×C4×C73H(5,𝔽2)14yes—
366C2×C4×C732−1+414yes—
367C2×C4×C73C2512yes—
368C2×C4×C73C2512yes—
369C2×C4×C73C2512yes—
370C2×C4×C73C2512yes—
371C2×C4×C73C2514yes—
372C2×C4×C73C2514yes—
373C2×C4×C73C2514yes—
374C2×C4×C73C2512yes—
375C2×C4×C73C2512yes—
376C22⋊D73—216no—
377C22⋊D73—416no—
378C2×Dic73—24no—
379C2×Dic73—28no—
380C2×Dic73—28no—
381C2×Dic73—24no—
382C2×Dic73—24no—
383C2×Dic73—416no—
384C2×Dic73—416no—
385C2×Dic73C2514yes—
386C2×Dic73C2514yes—
387C2×Dic73C2518yes—
388C2×Dic73C2518yes—
389C2×Dic73C2514yes—
390D292—28no—
391C4×D73—216no—
392C4×D73—416no—
393Dic146—216no—
394Dic146—216no—
395Dic146—28no—
396Dic146—416no—
397Dic146—416no—
398C22×C73—22no—
399C22×C73—22no—
400C22×C73—28no—
401C22×C73—24no—
402C22×C73—24no—
403C22×C73—24no—
404C22×C73—48no—
405C22×C73C2×H(5,𝔽2)12yes—
406C22×C73C2×2−1+414yes—
407C22×C73C2×2−1+412yes—
408C22×C73C2×2−1+412yes—
409C22×C73C2611yescharacteristic
410C2×D73—24no—
411C2×D73—24no—
412C2×D73—24no—
413C2×D73—48no—
414C4×C73—22no—
415C4×C73—24no—
416C4×C73—22no—
417C4×C73—22no—
418C4×C73—22no—
419C4×C73—24no—
420C4×C73—24no—
421C4×C73C2×H(5,𝔽2)14yes—
422C4×C73C2×2−1+414yes—
423Dic73—28no—
424Dic73—28no—
425Dic73—24no—
426Dic73—24no—
427Dic73—24no—
428C2×#3552—731nomaximal, Sylow
429C2×C73—24no—
430C2×C73—44no—
431C2×C73#355214yescomplemented
432C2×C73C22×H(5,𝔽2)11yescharacteristic
433C2×C73C22×2−1+411yescharacteristic
434C2×C73C22×2−1+411yescharacteristic
435D73—44no—
436#3552—7332no—
437C2×#563—734no—
438C2×#557—731no—
439C2×#556—731no—
440C2×#554—732no—
441C2×#553—732no—
442C2×D4×Q8—732no—
443C2×D4×Q8—731no—
444C2×#548—732no—
445C2×#547—731no—
446C2×#544—732no—
447C2×#542—732no—
448C2×#541—732no—
449C2×#539—734no—
450C2×#536—732no—
451C22×C4⋊Q8—731no—
452C2×#529—731no—
453C2×#529D7311yescharacteristic, complemented
454C73C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—732no—
456C23×Q8—732no—
457C23×Q8—732no—
458#563—7364no—
459#557—7316no—
460#556—7316no—
461#554—7332no—
462#553—7332no—
463D4×Q8—7332no—
464D4×Q8—7316no—
465#548—7332no—
466#547—7316no—
467#544—7332no—
468#542—7332no—
469#541—7332no—
470#539—7364no—
471#536—7332no—
472C2×C4⋊Q8—732no—
473C2×C4⋊Q8—734no—
474C2×C4⋊Q8—732no—
475C2×C4⋊Q8—732no—
476C2×C4⋊Q8—731no—
477C2×C4⋊Q8—731no—
478C2×C4⋊Q8—732no—
479C2×C4⋊Q8—732no—
480C2×C4⋊Q8—7316no—
481#529—7316no—
482#529C2×D73116yescomplemented
483C2×#126—734no—
484C2×#126—734no—
485C2×#126—734no—
486C2×#126—732no—
487C2×#126C2×D7312yes—
488C2×#125—734no—
489C2×#125—734no—
490C2×#125—734no—
491C2×#125—731no—
492C2×#125—732no—
493C2×#125C2×D7311yescharacteristic
494C2×#124—732no—
495C2×#124—734no—
496C2×#124—731no—
497C2×#124C2×D7311yescharacteristic
498C2×#123—732no—
499C2×#123—734no—
500C2×#123—734no—
501C2×#123—734no—
502C2×#123C2×D7312yes—
503C2×C22⋊Q8—731no—
504C2×C22⋊Q8—732no—
505C2×C22⋊Q8—734no—
506C2×C22⋊Q8—732no—
507C2×C22⋊Q8—732no—
508C2×C22⋊Q8—734no—
509C2×C22⋊Q8—734no—
510C2×C22⋊Q8—734no—
511C2×C22⋊Q8—734no—
512C2×C22⋊Q8—734no—
513C2×C22⋊Q8C2×D7311yescharacteristic
514C2×#121—734no—
515C2×#121—731no—
516C2×#121—732no—
517C2×#121C2×D7311yescharacteristic
518C2×C4×Q8—732no—
519C2×C4×Q8—732no—
520C2×C4×Q8—731no—
521C2×C4×Q8—732no—
522C2×C4×Q8C2×D7311yescharacteristic
523C2×C4×D4—734no—
524C2×C4×D4—732no—
525C2×C4×D4—734no—
526C2×C4×D4—731no—
527C2×C4×D4—732no—
528C2×C4×D4C2×D7311yescharacteristic
529C2×C4×D4C2×D7312yes—
530C2×#117—732no—
531C2×#117—732no—
532C2×#117C2×D7312yes—
533C22×C4⋊C4—732no—
534C22×C4⋊C4—732no—
535C22×C4⋊C4—732no—
536C22×C42C2×D7311yescharacteristic
537C2×#41—2928no—
538C2×#41—7316no—
539C22×Q8—2928no—
540C22×Q8—2928no—
541C22×Q8—7316no—
542C22×Q8—734no—
543C22×Q8—734no—
544C22×Q8—7316no—
545C22×Q8—731no—
546C22×Q8—732no—
547C22×Q8—732no—
548C22×Q8C22×D7311yescharacteristic
549C22×D4—734no—
550C22×D4—732no—
551C22×D4—731no—
552C22×D4C22×D7312yes—
553C22×D4C22×D7311yescharacteristic
554C23×C4—734no—
555C23×C4—734no—
556C23×C4—734no—
557C23×C4—732no—
558C23×C4C22×D7311yescharacteristic
559C23×C4C22×D7311yescharacteristic
560C23×C4C22×D7312yes—
561C23×C4C22×D7311yescharacteristic
562C4⋊Q8—7316no—
563C4⋊Q8—7332no—
564C4⋊Q8—7316no—
565C4⋊Q8—7316no—
566C4⋊Q8—738no—
567C4⋊Q8—738no—
568C4⋊Q8—7316no—
569C4⋊Q8—7316no—
570#126—7332no—
571#126—7332no—
572#126—7332no—
573#126—7316no—
574#126C22×D73116yes—
575#125—7332no—
576#125—7332no—
577#125—7332no—
578#125—738no—
579#125—7316no—
580#125C22×D7318yes—
581#124—7316no—
582#124—7332no—
583#124—738no—
584#124C22×D7318yes—
585#123—7316no—
586#123—7332no—
587#123—7332no—
588#123—7332no—
589#123C22×D73116yes—
590C22⋊Q8—738no—
591C22⋊Q8—7316no—
592C22⋊Q8—7332no—
593C22⋊Q8—7316no—
594C22⋊Q8—7316no—
595C22⋊Q8—7332no—
596C22⋊Q8—7332no—
597C22⋊Q8—7332no—
598C22⋊Q8—7332no—
599C22⋊Q8—7332no—
600C22⋊Q8C22×D7318yes—
601#121—7332no—
602#121—738no—
603#121—7316no—
604#121C22×D7318yes—
605C4×Q8—7316no—
606C4×Q8—7316no—
607C4×Q8—738no—
608C4×Q8—7316no—
609C4×Q8C22×D7318yes—
610C4×D4—7332no—
611C4×D4—7316no—
612C4×D4—7332no—
613C4×D4—738no—
614C4×D4—7316no—
615C4×D4C22×D7318yes—
616C4×D4C22×D73116yes—
617#117—7316no—
618#117—7316no—
619#117C22×D73116yes—
620C2×C4⋊C4—731no—
621C2×C4⋊C4—732no—
622C2×C4⋊C4—732no—
623C2×C4⋊C4—734no—
624C2×C4⋊C4—732no—
625C2×C4⋊C4—734no—
626C2×C4⋊C4—734no—
627C2×C4⋊C4—732no—
628C2×C4⋊C4—7316no—
629C2×C4⋊C4—7316no—
630C2×C4⋊C4—7316no—
631C2×C4⋊C4—731no—
632C2×C4⋊C4—732no—
633C2×C4⋊C4—732no—
634C2×C4⋊C4—734no—
635C2×C4⋊C4—732no—
636C2×C4⋊C4—734no—
637C2×C4⋊C4—734no—
638C2×C4⋊C4—734no—
639C2×C4⋊C4—734no—
640C2×C4⋊C4—732no—
641C2×C4⋊C4C22×D7312yes—
642C2×C4⋊C4C22×D7312yes—
643C2×C4⋊C4C22×D7311yescharacteristic
644C2×C4⋊C4C22×D7312yes—
645C2×C4⋊C4C22×D7311yescharacteristic
646C2×C4⋊C4C22×D7312yes—
647C2×C22⋊C4—734no—
648C2×C22⋊C4—732no—
649C2×C22⋊C4—734no—
650C2×C22⋊C4—732no—
651C2×C22⋊C4—732no—
652C2×C22⋊C4—734no—
653C2×C22⋊C4—734no—
654C2×C22⋊C4—732no—
655C2×C22⋊C4—732no—
656C2×C22⋊C4C22×D7312yes—
657C2×C22⋊C4C22×D7312yes—
658C2×C22⋊C4C22×D7312yes—
659C2×C22⋊C4C22×D7312yes—
660C2×C22⋊C4C22×D7312yes—
661C2×C42—732no—
662C2×C42—734no—
663C2×C42—734no—
664C2×C42C22×D7311yescharacteristic
665C2×C42C22×D7311yescharacteristic
666C2×C42C22×D7312yes—
667C2×C42C22×D7311yescharacteristic
668C2×C42C22×D7311yescharacteristic
669C2×C42C22×D7318yes—
670C24—732no—
671C24C23×D7312yes—
672C24C23×D7311yescharacteristic
673#41—29232no—
674C2×Q8—24no—
675C2×Q8—29232no—
676C2×Q8—2928no—
677C2×Q8—2928no—
678C2×Q8—29232no—
679C2×Q8—7316no—
680C2×Q8—7316no—
681C2×Q8—734no—
682C2×Q8—738no—
683C2×Q8—738no—
684C2×Q8—1468no—
685C2×Q8—1468no—
686C2×Q8—1464no—
687C2×Q8C23×D7314yes—
688C2×D4—28no—
689C2×D4—24no—
690C2×D4—2928no—
691C2×D4—7316no—
692C2×D4—738no—
693C2×D4—734no—
694C2×D4—1468no—
695C2×D4—1464no—
696C2×D4C23×D7318yes—
697C2×D4C23×D7314yes—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—28no—
702C22×C4—2928no—
703C22×C4—2928no—
704C22×C4—2928no—
705C22×C4—7316no—
706C22×C4—7316no—
707C22×C4—7316no—
708C22×C4—732no—
709C22×C4—732no—
710C22×C4—734no—
711C22×C4—734no—
712C22×C4—732no—
713C22×C4—738no—
714C22×C4—1468no—
715C22×C4C23×D7314yes—
716C22×C4C23×D7314yes—
717C22×C4C23×D7314yes—
718C22×C4C23×D7318yes—
719C22×C4C23×D7312yes—
720C22×C4C23×D7312yes—
721C22×C4C23×D7311yescharacteristic
722C22×C4C23×D7311yescharacteristic
723C22×C4C23×D7311yescharacteristic
724C22×C4C23×D7311yescharacteristic
725C22×C4C23×D7312yes—
726C22×C4C23×D7311yescharacteristic
727C22×C4C23×D7311yescharacteristic
728C4⋊C4—738no—
729C4⋊C4—738no—
730C4⋊C4—738no—
731C4⋊C4—7316no—
732C4⋊C4—7316no—
733C4⋊C4—7316no—
734C4⋊C4—7316no—
735C4⋊C4—738no—
736C4⋊C4—734no—
737C4⋊C4—738no—
738C4⋊C4—738no—
739C4⋊C4—7316no—
740C4⋊C4—738no—
741C4⋊C4—7316no—
742C4⋊C4—7316no—
743C4⋊C4—738no—
744C4⋊C4—734no—
745C4⋊C4—7316no—
746C4⋊C4C23×D7318yes—
747C4⋊C4C23×D7318yes—
748C4⋊C4C23×D7314yes—
749C4⋊C4C23×D7318yes—
750C4⋊C4C23×D7314yes—
751C4⋊C4C23×D7318yes—
752C22⋊C4—7316no—
753C22⋊C4—738no—
754C22⋊C4—7316no—
755C22⋊C4—738no—
756C22⋊C4—738no—
757C22⋊C4—7316no—
758C22⋊C4—7316no—
759C22⋊C4—738no—
760C22⋊C4—738no—
761C22⋊C4C23×D7318yes—
762C22⋊C4C23×D7318yes—
763C22⋊C4C23×D7318yes—
764C22⋊C4C23×D7318yes—
765C22⋊C4C23×D7318yes—
766C42—738no—
767C42—7316no—
768C42—7316no—
769C42C23×D7314yes—
770C42C23×D7314yes—
771C42C23×D7314yes—
772C42C23×D7314yes—
773C42C23×D7318yes—
774C23—22no—
775C23—22no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—734no—
780C23—1464no—
781C23—1464no—
782C23—1464no—
783C23#1455663814yes—
784C23C24×D7314yes—
785C23C24×D7312yes—
786C23C24×D7311yescharacteristic
787Q8—28no—
788Q8—29216no—
789Q8—29216no—
790Q8—14616no—
791Q8—14616no—
792Q8—1468no—
793D4—216no—
794D4—28no—
795D4—29216no—
796D4—14616no—
797D4—1468no—
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—29216no—
810C2×C4—29216no—
811C2×C4—29216no—
812C2×C4—734no—
813C2×C4—734no—
814C2×C4—738no—
815C2×C4—738no—
816C2×C4—734no—
817C2×C4—1464no—
818C2×C4—1468no—
819C2×C4—1468no—
820C2×C4—1464no—
821C2×C4—1464no—
822C2×C4—14616no—
823C2×C4#1455663714yes—
824C2×C4#1455663814yes—
825C2×C4C24×D7314yes—
826C2×C4C24×D7314yes—
827C2×C4C24×D7312yes—
828C2×C4C24×D7312yes—
829C2×C4C24×D7312yes—
830C2×C4C24×D7312yes—
831C2×C4C24×D7314yes—
832C2×C4C24×D7312yes—
833C2×C4C24×D7312yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—48no—
841C22—2928no—
842C22—1464no—
843C22—1464no—
844C22—1464no—
845C22C2×#1455663712yes—
846C22C2×#1455663814yes—
847C22C2×#1455663812yes—
848C22C2×#1455663812yes—
849C22C25×D7311yescharacteristic
850C4—22no—
851C4—24no—
852C4—22no—
853C4—22no—
854C4—24no—
855C4—22no—
856C4—24no—
857C4—1464no—
858C4—1468no—
859C4—1468no—
860C4—1464no—
861C4—1464no—
862C4C2×#1455663714yes—
863C4C2×#1455663814yes—
864C2—24no—
865C2—44no—
866C2—2924no—
867C2#2262436814yesdirect product factor
868C2C22×#1455663711yescharacteristic
869C2C22×#1455663811yescharacteristic
870C2C22×#1455663811yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#529×C73C2
socleC23×C73C25
hypercenterC2×#529D73
hypocenterC73C2×#3552
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22624368C2direct (N × H)
2. C2×#17989339C2semidirect
3. C2×#17989315C2semidirect
4. C2×#17989307C2semidirect
5. C2×#17989294C2semidirect
6. C2×#17989283C2semidirect
7. C2×Q8×D292C2semidirect
8. C2×#17989250C2semidirect
9. C2×#17989243C2semidirect
10. C2×#17989241C2semidirect
11. C2×#17989215C2semidirect
12. C2×#17989208C2semidirect
13. C2×#17989200C2semidirect
14. C2×#17989181C2semidirect
15. C2×#17989157C2semidirect
16. C22×#14556591C2semidirect
17. C2×#17989121C2semidirect
18. C2×#529×C73C2semidirect
22. #17989339C22semidirect
23. #17989315C22semidirect
24. #17989307C22semidirect
25. #17989294C22semidirect
26. #17989283C22semidirect
27. Q8×D292C22semidirect
28. #17989250C22semidirect
29. #17989243C22semidirect
30. #17989241C22semidirect
31. #17989215C22semidirect
32. #17989208C22semidirect
33. #17989200C22semidirect
34. #17989181C22semidirect
35. #17989157C22semidirect
42. C2×#14556591C22semidirect
45. #17989121C22semidirect
89. #529×C73C22semidirect
431. C2×C73#3552semidirect
453. C2×#529D73semidirect
454. C73C2×#3552semidirect
482. #529C2×D73semidirect
867. C2#22624368direct (N × H)

Maximal subgroups

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

subgroupindex
#226243682
C2×#179893392
C2×#179893152
C2×#179893072
C2×#179892942
C2×#179892832
C2×Q8×D2922
C2×#179892502
C2×#179892432
C2×#179892412
C2×#179892152
C2×#179892082
C2×#179892002
C2×#179891812
C2×#179891572
C22×#145565912
C2×#179891212
C2×#529×C732
C2×#355273