Finite Group Databasebeta

← C2×#22624419 #33993704

Subgroups — C2×#22624419 #33993704

Order 18688.

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#22624419C2132yesmaximal, direct product factor
2C2×#17989338C214yesmaximal, complemented
3C2×Q8×Dic146C211yesmaximal, characteristic, complemented
4C2×#17989316C211yesmaximal, characteristic, complemented
5C2×#17989315C212yesmaximal, complemented
6C2×#17989310C212yesmaximal, complemented
7C2×#17989310C211yesmaximal, characteristic, complemented
8C2×#17989308C212yesmaximal, complemented
9C2×#17989297C211yesmaximal, characteristic, complemented
10C2×#17989271C212yesmaximal, complemented
11C2×#17989214C212yesmaximal, complemented
12C2×#17989208C212yesmaximal
13C2×#17989199C212yesmaximal, complemented
14C2×#17989198C212yesmaximal, complemented
15C2×#17989196C214yesmaximal, complemented
16C2×#17989144C211yesmaximal, characteristic, complemented
17C2×#17989121C211yesmaximal, characteristic
18C2×#533×C73C211yesmaximal, characteristic, complemented
19#17989338C22164yescomplemented
20Q8×Dic146C22116yescomplemented
21#17989316C22116yescomplemented
22#17989315C22132yescomplemented
23#17989310C22132yescomplemented
24#17989310C22116yescomplemented
25#17989308C22132yescomplemented
26#17989297C22116yescomplemented
27#17989271C22132yescomplemented
28#17989214C22132yescomplemented
29#17989208C22132yes—
30#17989199C22132yescomplemented
31#17989198C22132yescomplemented
32#17989196C22164yescomplemented
33#17989144C22116yescomplemented
34C2×#14556591C2212yes—
35C2×#14556591C2212yes—
36C2×#14556591C2211yescharacteristic
37C2×#14556591C2211yescharacteristic
38C2×#14556590C2214yes—
39C2×#14556590C2212yes—
40C2×#14556589C2214yes—
41#17989121C22116yes—
42C2×#14556586C2214yes—
43C2×#14556586C2214yes—
44C2×#14556586C2214yes—
45C2×#14556586C2214yes—
46C2×#14556585C2212yes—
47C2×#14556584C2214yes—
48C2×#14556584C2214yes—
49C2×#14556583C2211yescharacteristic
50C2×#14556583C2212yes—
51C2×#14556583C2212yes—
52C2×#14556582C2214yes—
53C2×#14556582C2212yes—
54C2×#14556581C2214yes—
55C2×#14556581C2214yes—
56C2×#14556581C2214yes—
57C2×#14556581C2214yes—
58C2×#14556579C2212yes—
59C2×#14556579C2211yescharacteristic
60C2×#14556577C2214yes—
61C2×#14556574C2212yes—
62C2×#14556573C2214yes—
63C2×#14556570C2212yes—
64C2×#14556570C2211yescharacteristic
65C2×#14556570C2212yes—
66C2×#14556569C2214yes—
67C2×#14556569C2214yes—
68C2×#14556567C2214yes—
69C2×#14556567C2212yes—
70C2×#14556567C2212yes—
71C2×#14556565C2211yescharacteristic
72C2×Q8×Dic73C2212yes—
73C2×Q8×Dic73C2212yes—
74C2×C4×Dic146C2212yes—
75C2×C4×Dic146C2212yes—
76C2×C4×Dic146C2212yes—
77C2×C4×Dic146C2211yescharacteristic
78C2×C4×Dic146C2212yes—
79C2×C4×Dic146C2212yes—
80C2×#14556556C2214yes—
81C2×C4×D292C2212yes—
82C2×C4×D292C2211yescharacteristic
83C2×C4×C22⋊D73C2212yes—
84C2×#14556550C2212yes—
85C2×#14556549C2214yes—
86C2×#14556549C2212yes—
87C2×#14556548C2212yes—
88C2×C4⋊C4×D73C2212yes—
89#533×C73C22116yescomplemented
90C2×C4⋊Q8×C73C2211yescharacteristic
91C2×C4⋊Q8×C73C2211yescharacteristic
92C2×#125×C73C2212yes—
93C2×C22⋊Q8×C73C2212yes—
94C2×C22⋊Q8×C73C2211yescharacteristic
95C2×C22⋊Q8×C73C2211yescharacteristic
96C2×C4×Q8×C73C2212yes—
97C2×C4×Q8×C73C2211yescharacteristic
98C2×C4×Q8×C73C2211yescharacteristic
99C2×#117×C73C2212yes—
100C22×C42×C73C2211yescharacteristic
101C22×Dic146C2311yescharacteristic
102C22×Dic146C2312yes—
103C22×Dic146C2314yes—
104C22×Dic146C2312yes—
105C22×D292C2311yescharacteristic
106C22×C22⋊D73C2312yes—
107C22×C4×D73C2312yes—
108C22×C4×D73C2314yes—
109#14556591C2318yes—
110#14556591C2318yes—
111#14556591C23116yes—
112#14556591C23116yes—
113#14556590C23132yes—
114#14556590C23116yes—
115#14556589C23132yes—
116#14556586C23132yes—
117#14556586C23132yes—
118#14556586C23132yes—
119#14556586C23132yes—
120#14556585C23116yes—
121#14556584C23132yes—
122#14556584C23132yes—
123#14556583C2318yes—
124#14556583C23116yes—
125#14556583C23116yes—
126#14556582C23132yes—
127#14556582C23116yes—
128#14556581C23132yes—
129#14556581C23132yes—
130#14556581C23132yes—
131#14556581C23132yes—
132#14556579C2318yes—
133#14556579C23116yes—
134#14556577C23132yes—
135#14556574C23116yes—
136#14556573C23132yes—
137#14556570C2318yes—
138#14556570C23116yes—
139#14556570C23116yes—
140#14556569C23132yes—
141#14556569C23132yes—
142#14556567C23116yes—
143#14556567C23116yes—
144#14556567C23132yes—
145#14556565C2318yes—
146Q8×Dic73C23116yes—
147Q8×Dic73C23116yes—
148C4×Dic146C2318yes—
149C4×Dic146C23116yes—
150C4×Dic146C23116yes—
151C4×Dic146C23116yes—
152C4×Dic146C23116yes—
153C4×Dic146C23116yes—
154#14556556C23132yes—
155C4×D292C2318yes—
156C4×D292C23116yes—
157C4×C22⋊D73C23116yes—
158#14556550C23116yes—
159#14556549C23132yes—
160#14556549C23116yes—
161#14556548C23116yes—
162C2×C4⋊Dic73C2312yes—
163C2×C4⋊Dic73C2314yes—
164C2×C4⋊Dic73C2312yes—
165C2×C4⋊Dic73C2311yescharacteristic
166C2×C4⋊Dic73C2312yes—
167C2×C4⋊Dic73C2314yes—
168C2×C4⋊Dic73C2312yes—
169C2×C4⋊Dic73C2314yes—
170C2×C4⋊Dic73C2311yescharacteristic
171C2×#11924007C2312yes—
172C2×#11924007C2314yes—
173C2×#11924007C2314yes—
174C2×#11924007C2314yes—
175C2×#11924007C2314yes—
176C2×#11924007C2312yes—
177C2×#11924007C2312yes—
178C2×#11924007C2312yes—
179C2×#11924007C2314yes—
180C2×#11924007C2314yes—
181C2×#11924007C2314yes—
182C4⋊C4×D73C23116yes—
183C2×C22⋊Dic73C2314yes—
184C2×C22⋊Dic73C2312yes—
185C2×#11924005C2312yes—
186C2×#11924005C2312yes—
187C2×#11924005C2312yes—
188C2×#11924005C2314yes—
189C2×#11924005C2314yes—
190C2×#11924005C2314yes—
191C2×#11924005C2312yes—
192C2×C4×Dic73C2314yes—
193C2×C4×Dic73C2312yes—
194C2×C4×Dic73C2314yes—
195C2×C4×Dic73C2314yes—
196C2×C4×Dic73C2314yes—
197C22×Q8×C73C2311yescharacteristic
198C22×Q8×C73C2311yescharacteristic
199C22×Q8×C73C2312yes—
200C23×C4×C73C2311yescharacteristic
201C23×C4×C73C2311yescharacteristic
202C23×C4×C73C2311yescharacteristic
203C4⋊Q8×C73C2318yes—
204C4⋊Q8×C73C2318yes—
205#125×C73C23116yes—
206C22⋊Q8×C73C2318yes—
207C22⋊Q8×C73C2318yes—
208C22⋊Q8×C73C23116yes—
209C4×Q8×C73C2318yes—
210C4×Q8×C73C23116yes—
211C4×Q8×C73C2318yes—
212#117×C73C23116yes—
213C2×C4⋊C4×C73C2312yes—
214C2×C4⋊C4×C73C2311yescharacteristic
215C2×C4⋊C4×C73C2312yes—
216C2×C4⋊C4×C73C2312yes—
217C2×C4⋊C4×C73C2312yes—
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×C42×C73C2318yes—
225C2×C42×C73C2311yescharacteristic
226C2×C42×C73C2312yes—
227C2×C42×C73C2312yes—
228C2×C42×C73C2311yescharacteristic
229C2×C42×C73C2311yescharacteristic
230C2×C42×C73C2311yescharacteristic
231C23×D73C2412yes—
232C2×Dic146—24no—
233C2×Dic146—28no—
234C2×Dic146—44no—
235C2×Dic146—48no—
236C2×Dic146C2414yes—
237C2×Dic146C2418yes—
238C2×Dic146C24116yes—
239C2×Dic146C2418yes—
240C2×D292—24no—
241C2×D292C2414yes—
242C2×C22⋊D73—44no—
243C2×C22⋊D73C2418yes—
244C22×Dic73C2414yes—
245C22×Dic73C2412yes—
246C22×Dic73C2412yes—
247C22×Dic73C2412yes—
248C22×Dic73C2414yes—
249C2×C4×D73—28no—
250C2×C4×D73—48no—
251C2×C4×D73C2418yes—
252C2×C4×D73C24116yes—
253C4⋊Dic73C2418yes—
254C4⋊Dic73C2418yes—
255C4⋊Dic73C24116yes—
256C4⋊Dic73C2414yes—
257C4⋊Dic73C2418yes—
258C4⋊Dic73C2414yes—
259C4⋊Dic73C2418yes—
260C4⋊Dic73C24116yes—
261C4⋊Dic73C24116yes—
262#11924007C24116yes—
263#11924007C2418yes—
264#11924007C2418yes—
265#11924007C2418yes—
266#11924007C24116yes—
267#11924007C24116yes—
268#11924007C24116yes—
269#11924007C24116yes—
270#11924007C24116yes—
271#11924007C24116yes—
272#11924007C2418yes—
273C22⋊Dic73C24116yes—
274C22⋊Dic73C2418yes—
275#11924005C2418yes—
276#11924005C2418yes—
277#11924005C2418yes—
278#11924005C24116yes—
279#11924005C24116yes—
280#11924005C24116yes—
281#11924005C2418yes—
282C4×Dic73C2418yes—
283C4×Dic73C24116yes—
284C4×Dic73C24116yes—
285C4×Dic73C24116yes—
286C4×Dic73C24116yes—
287C24×C73C2411yescharacteristic
288C2×Q8×C73—24no—
289C2×Q8×C73—24no—
290C2×Q8×C73—44no—
291C2×Q8×C73C2414yes—
292C2×Q8×C73C2414yes—
293C2×Q8×C73C2418yes—
294C22×C4×C73—24no—
295C22×C4×C73—24no—
296C22×C4×C73—42no—
297C22×C4×C73C2411yescharacteristic
298C22×C4×C73C2411yescharacteristic
299C22×C4×C73C2411yescharacteristic
300C22×C4×C73C2411yescharacteristic
301C22×C4×C73C2414yes—
302C22×C4×C73C2414yes—
303C22×C4×C73C2412yes—
304C22×C4×C73C2412yes—
305C22×C4×C73C2412yes—
306C22×C4×C73C2412yes—
307C22×C4×C73C2414yes—
308C22×C4×C73C2411yescharacteristic
309C22×C4×C73C2411yescharacteristic
310C4⋊C4×C73C2418yes—
311C4⋊C4×C73C2418yes—
312C4⋊C4×C73C2418yes—
313C4⋊C4×C73C2418yes—
314C4⋊C4×C73C2418yes—
315C4⋊C4×C73C2418yes—
316C4⋊C4×C73C2414yes—
317C4⋊C4×C73C2414yes—
318C4⋊C4×C73C2418yes—
319C22⋊C4×C73C2418yes—
320C22⋊C4×C73C2418yes—
321C42×C73C2414yes—
322C42×C73C2414yes—
323C42×C73C2414yes—
324C42×C73C2414yes—
325C42×C73C2418yes—
326C42×C73C2418yes—
327C23×C73—22no—
328C23×C73—22no—
329C23×C73—22no—
330C23×C73C2512yes—
331C23×C73C2511yescharacteristic
332C22×D73—24no—
333C22×D73—24no—
334C22×D73—24no—
335C22×D73C2514yes—
336Q8×C73—28no—
337Q8×C73—28no—
338Q8×C73—48no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—24no—
342C2×C4×C73—24no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—24no—
346C2×C4×C73—24no—
347C2×C4×C73—28no—
348C2×C4×C73—28no—
349C2×C4×C73—44no—
350C2×C4×C732−1+414yes—
351C2×C4×C732−1+414yes—
352C2×C4×C73C2512yes—
353C2×C4×C73C2512yes—
354C2×C4×C73C2512yes—
355C2×C4×C73C2512yes—
356C2×C4×C73C2514yes—
357C2×C4×C73C2514yes—
358C2×C4×C73C2514yes—
359C2×C4×C73C2514yes—
360C2×C4×C73C2512yes—
361C2×C4×C73C2512yes—
362C22⋊D73—48no—
363C2×Dic73—24no—
364C2×Dic73—28no—
365C2×Dic73—24no—
366C2×Dic73—28no—
367C2×Dic73—24no—
368C2×Dic73C2514yes—
369C2×Dic73C2518yes—
370C2×Dic73C2514yes—
371C2×Dic73C2514yes—
372C2×Dic73C2518yes—
373D292—28no—
374C4×D73—216no—
375C4×D73—416no—
376Dic146—28no—
377Dic146—216no—
378Dic146—48no—
379Dic146—416no—
380C22×C73—22no—
381C22×C73—22no—
382C22×C73—22no—
383C22×C73—44no—
384C22×C73C2×2−1+412yes—
385C22×C73C2×2−1+412yes—
386C22×C73#58512yes—
387C22×C73C2611yescharacteristic
388C2×D73—24no—
389C2×D73—24no—
390C2×D73—24no—
391C2×D73—48no—
392C4×C73—22no—
393C4×C73—22no—
394C4×C73—24no—
395C4×C73—24no—
396C4×C73—22no—
397C4×C73—24no—
398C4×C73—24no—
399C4×C73—22no—
400C4×C73C2×2−1+414yes—
401C4×C73C2×2−1+414yes—
402Dic73—24no—
403Dic73—28no—
404Dic73—24no—
405Dic73—28no—
406Dic73—24no—
407C2×#3555—731nomaximal, Sylow
408C2×C73—42no—
409C2×C73#355514yescomplemented
410C2×C73C22×2−1+411yescharacteristic
411C2×C73C22×2−1+411yescharacteristic
412C2×C73C2×#58511yescharacteristic
413D73—44no—
414#3555—7332no—
415C2×#563—734no—
416C2×Q82—731no—
417C2×#557—732no—
418C2×#557—731no—
419C2×#556—732no—
420C2×#556—732no—
421C2×#556—731no—
422C2×#554—731no—
423C2×#552—732no—
424C2×#544—732no—
425C2×#542—732no—
426C2×#541—732no—
427C2×#541—734no—
428C2×#541—732no—
429C2×#533—731no—
430C2×#533D7311yescharacteristic, complemented
431C2×#529—731no—
432C73C2×#355511yescharacteristic, complemented, Sylow
433#563—7364no—
434Q82—7316no—
435#557—7332no—
436#557—7316no—
437#556—7332no—
438#556—7332no—
439#556—7316no—
440#554—7316no—
441#552—7332no—
442#544—7332no—
443#542—7332no—
444#541—7332no—
445#541—7364no—
446#541—7332no—
447#533—7316no—
448#533C2×D73116yescomplemented
449C2×C4⋊Q8—734no—
450C2×C4⋊Q8—734no—
451C2×C4⋊Q8—732no—
452C2×C4⋊Q8—731no—
453C2×C4⋊Q8—731no—
454C2×C4⋊Q8—732no—
455C2×C4⋊Q8—732no—
456C2×C4⋊Q8C2×D7311yescharacteristic
457C2×C4⋊Q8C2×D7311yescharacteristic
458#529—7316no—
459C2×#126—734no—
460C2×#126—734no—
461C2×#126—734no—
462C2×#126—734no—
463C2×#126—734no—
464C2×#126—734no—
465C2×#126—732no—
466C2×#125—734no—
467C2×#125—734no—
468C2×#125—734no—
469C2×#125—734no—
470C2×#125—734no—
471C2×#125—732no—
472C2×#125—731no—
473C2×#125—732no—
474C2×#125—732no—
475C2×#125C2×D7312yes—
476C2×#124—734no—
477C2×#124—731no—
478C2×#124—732no—
479C2×#123—732no—
480C2×#123—734no—
481C2×C22⋊Q8—732no—
482C2×C22⋊Q8—732no—
483C2×C22⋊Q8—734no—
484C2×C22⋊Q8—731no—
485C2×C22⋊Q8—732no—
486C2×C22⋊Q8—732no—
487C2×C22⋊Q8—734no—
488C2×C22⋊Q8—734no—
489C2×C22⋊Q8C2×D7311yescharacteristic
490C2×C22⋊Q8C2×D7311yescharacteristic
491C2×C22⋊Q8C2×D7312yes—
492C2×#121—731no—
493C2×C4×Q8—732no—
494C2×C4×Q8—732no—
495C2×C4×Q8—734no—
496C2×C4×Q8—731no—
497C2×C4×Q8—732no—
498C2×C4×Q8—732no—
499C2×C4×Q8—732no—
500C2×C4×Q8—732no—
501C2×C4×Q8—732no—
502C2×C4×Q8C2×D7311yescharacteristic
503C2×C4×Q8C2×D7312yes—
504C2×C4×Q8C2×D7311yescharacteristic
505C2×C4×D4—732no—
506C2×C4×D4—731no—
507C2×C4×D4—732no—
508C2×#117—732no—
509C2×#117—734no—
510C2×#117—732no—
511C2×#117—732no—
512C2×#117C2×D7312yes—
513C22×C4⋊C4—732no—
514C22×C42C2×D7311yescharacteristic
515C22×Q8—732no—
516C22×Q8—734no—
517C22×Q8—731no—
518C22×Q8—732no—
519C22×Q8C22×D7311yescharacteristic
520C22×Q8C22×D7311yescharacteristic
521C22×Q8C22×D7312yes—
522C22×D4—732no—
523C22×D4—731no—
524C23×C4—734no—
525C23×C4—732no—
526C23×C4C22×D7311yescharacteristic
527C23×C4C22×D7311yescharacteristic
528C23×C4C22×D7311yescharacteristic
529C4⋊Q8—7332no—
530C4⋊Q8—7332no—
531C4⋊Q8—7316no—
532C4⋊Q8—738no—
533C4⋊Q8—738no—
534C4⋊Q8—7316no—
535C4⋊Q8—7316no—
536C4⋊Q8C22×D7318yes—
537C4⋊Q8C22×D7318yes—
538#126—7332no—
539#126—7332no—
540#126—7332no—
541#126—7332no—
542#126—7332no—
543#126—7332no—
544#126—7316no—
545#125—7332no—
546#125—7332no—
547#125—7332no—
548#125—7332no—
549#125—7332no—
550#125—7316no—
551#125—738no—
552#125—7316no—
553#125—7316no—
554#125C22×D73116yes—
555#124—7332no—
556#124—738no—
557#124—7316no—
558#123—7316no—
559#123—7332no—
560C22⋊Q8—7316no—
561C22⋊Q8—7316no—
562C22⋊Q8—7332no—
563C22⋊Q8—738no—
564C22⋊Q8—7316no—
565C22⋊Q8—7316no—
566C22⋊Q8—7332no—
567C22⋊Q8—7332no—
568C22⋊Q8C22×D7318yes—
569C22⋊Q8C22×D7318yes—
570C22⋊Q8C22×D73116yes—
571#121—738no—
572C4×Q8—7316no—
573C4×Q8—7316no—
574C4×Q8—7332no—
575C4×Q8—738no—
576C4×Q8—7316no—
577C4×Q8—7316no—
578C4×Q8—7316no—
579C4×Q8—7316no—
580C4×Q8—7316no—
581C4×Q8C22×D7318yes—
582C4×Q8C22×D73116yes—
583C4×Q8C22×D7318yes—
584C4×D4—7316no—
585C4×D4—738no—
586C4×D4—7316no—
587#117—7316no—
588#117—7332no—
589#117—7316no—
590#117—7316no—
591#117C22×D73116yes—
592C2×C4⋊C4—732no—
593C2×C4⋊C4—734no—
594C2×C4⋊C4—732no—
595C2×C4⋊C4—732no—
596C2×C4⋊C4—734no—
597C2×C4⋊C4—732no—
598C2×C4⋊C4—731no—
599C2×C4⋊C4—732no—
600C2×C4⋊C4—732no—
601C2×C4⋊C4—731no—
602C2×C4⋊C4—734no—
603C2×C4⋊C4—734no—
604C2×C4⋊C4—734no—
605C2×C4⋊C4—734no—
606C2×C4⋊C4—734no—
607C2×C4⋊C4—732no—
608C2×C4⋊C4—734no—
609C2×C4⋊C4—732no—
610C2×C4⋊C4—734no—
611C2×C4⋊C4—734no—
612C2×C4⋊C4—7316no—
613C2×C4⋊C4C22×D7311yescharacteristic
614C2×C4⋊C4C22×D7312yes—
615C2×C4⋊C4C22×D7311yescharacteristic
616C2×C4⋊C4C22×D7312yes—
617C2×C4⋊C4C22×D7312yes—
618C2×C4⋊C4C22×D7312yes—
619C2×C4⋊C4C22×D7312yes—
620C2×C4⋊C4C22×D7312yes—
621C2×C4⋊C4C22×D7312yes—
622C2×C22⋊C4—734no—
623C2×C22⋊C4—732no—
624C2×C22⋊C4—732no—
625C2×C22⋊C4—732no—
626C2×C22⋊C4—732no—
627C2×C22⋊C4—734no—
628C2×C22⋊C4—734no—
629C2×C22⋊C4—732no—
630C2×C22⋊C4—734no—
631C2×C22⋊C4C22×D7312yes—
632C2×C22⋊C4C22×D7312yes—
633C2×C42—734no—
634C2×C42—732no—
635C2×C42—734no—
636C2×C42—734no—
637C2×C42—734no—
638C2×C42C22×D7311yescharacteristic
639C2×C42C22×D7312yes—
640C2×C42C22×D7312yes—
641C2×C42C22×D7311yescharacteristic
642C2×C42C22×D7311yescharacteristic
643C2×C42C22×D7311yescharacteristic
644C2×C42C22×D7318yes—
645C24—732no—
646C24C23×D7311yescharacteristic
647C2×Q8—24no—
648C2×Q8—24no—
649C2×Q8—44no—
650C2×Q8—2924no—
651C2×Q8—2928no—
652C2×Q8—738no—
653C2×Q8—7316no—
654C2×Q8—734no—
655C2×Q8—738no—
656C2×Q8—1464no—
657C2×Q8—1468no—
658C2×Q8C23×D7314yes—
659C2×Q8C23×D7314yes—
660C2×Q8C23×D7318yes—
661C2×D4—2924no—
662C2×D4—738no—
663C2×D4—734no—
664C2×D4—1464no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—42no—
668C22×C4—2928no—
669C22×C4—7316no—
670C22×C4—734no—
671C22×C4—732no—
672C22×C4—732no—
673C22×C4—732no—
674C22×C4—734no—
675C22×C4—738no—
676C22×C4—1468no—
677C22×C4C23×D7314yes—
678C22×C4C23×D7314yes—
679C22×C4C23×D7311yescharacteristic
680C22×C4C23×D7312yes—
681C22×C4C23×D7312yes—
682C22×C4C23×D7312yes—
683C22×C4C23×D7311yescharacteristic
684C22×C4C23×D7311yescharacteristic
685C22×C4C23×D7311yescharacteristic
686C22×C4C23×D7312yes—
687C22×C4C23×D7314yes—
688C22×C4C23×D7311yescharacteristic
689C22×C4C23×D7311yescharacteristic
690C4⋊C4—7316no—
691C4⋊C4—738no—
692C4⋊C4—738no—
693C4⋊C4—738no—
694C4⋊C4—7316no—
695C4⋊C4—7316no—
696C4⋊C4—7316no—
697C4⋊C4—7316no—
698C4⋊C4—7316no—
699C4⋊C4—7316no—
700C4⋊C4—738no—
701C4⋊C4—738no—
702C4⋊C4—738no—
703C4⋊C4—7316no—
704C4⋊C4—734no—
705C4⋊C4—738no—
706C4⋊C4—734no—
707C4⋊C4—738no—
708C4⋊C4—7316no—
709C4⋊C4—7316no—
710C4⋊C4C23×D7314yes—
711C4⋊C4C23×D7318yes—
712C4⋊C4C23×D7314yes—
713C4⋊C4C23×D7318yes—
714C4⋊C4C23×D7318yes—
715C4⋊C4C23×D7318yes—
716C4⋊C4C23×D7318yes—
717C4⋊C4C23×D7318yes—
718C4⋊C4C23×D7318yes—
719C22⋊C4—7316no—
720C22⋊C4—738no—
721C22⋊C4—738no—
722C22⋊C4—738no—
723C22⋊C4—738no—
724C22⋊C4—7316no—
725C22⋊C4—7316no—
726C22⋊C4—738no—
727C22⋊C4—7316no—
728C22⋊C4C23×D7318yes—
729C22⋊C4C23×D7318yes—
730C42—7316no—
731C42—738no—
732C42—7316no—
733C42—7316no—
734C42—7316no—
735C42C23×D7314yes—
736C42C23×D7314yes—
737C42C23×D7314yes—
738C42C23×D7314yes—
739C42C23×D7318yes—
740C42C23×D7318yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—734no—
745C23—1464no—
746C23—1464no—
747C23—1464no—
748C23C24×D7312yes—
749C23C24×D7311yescharacteristic
750Q8—28no—
751Q8—28no—
752Q8—48no—
753Q8—2928no—
754Q8—29216no—
755Q8—1468no—
756Q8—14616no—
757D4—2928no—
758D4—1468no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—44no—
770C2×C4—29216no—
771C2×C4—738no—
772C2×C4—734no—
773C2×C4—734no—
774C2×C4—734no—
775C2×C4—738no—
776C2×C4—1464no—
777C2×C4—1468no—
778C2×C4—1464no—
779C2×C4—1468no—
780C2×C4—1464no—
781C2×C4—14616no—
782C2×C4#1455663814yes—
783C2×C4#1455663914yes—
784C2×C4C24×D7312yes—
785C2×C4C24×D7314yes—
786C2×C4C24×D7314yes—
787C2×C4C24×D7314yes—
788C2×C4C24×D7312yes—
789C2×C4C24×D7312yes—
790C2×C4C24×D7312yes—
791C2×C4C24×D7314yes—
792C2×C4C24×D7312yes—
793C2×C4C24×D7312yes—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—2928no—
799C22—1464no—
800C22—1464no—
801C22—1464no—
802C22C2×#1455663812yes—
803C22C2×#1455663912yes—
804C22#1798942312yes—
805C22C25×D7311yescharacteristic
806C4—22no—
807C4—24no—
808C4—24no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—24no—
814C4—1464no—
815C4—1468no—
816C4—1464no—
817C4—1468no—
818C4—1464no—
819C4C2×#1455663814yes—
820C4C2×#1455663914yes—
821C2—42no—
822C2—2924no—
823C2#2262441914yesdirect product factor
824C2C22×#1455663811yescharacteristic
825C2C22×#1455663911yescharacteristic
826C2C2×#1798942311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#533×C73C2
socleC23×C73C25
prime radicalC2×#14556565C22
hypercenterC2×#533D73
hypocenterC73C2×#3555
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #22624419C2direct (N × H)
2. C2×#17989338C2semidirect
3. C2×Q8×Dic146C2semidirect
4. C2×#17989316C2semidirect
5. C2×#17989315C2semidirect
6. C2×#17989310C2semidirect
7. C2×#17989310C2semidirect
8. C2×#17989308C2semidirect
9. C2×#17989297C2semidirect
10. C2×#17989271C2semidirect
11. C2×#17989214C2semidirect
13. C2×#17989199C2semidirect
14. C2×#17989198C2semidirect
15. C2×#17989196C2semidirect
16. C2×#17989144C2semidirect
18. C2×#533×C73C2semidirect
19. #17989338C22semidirect
20. Q8×Dic146C22semidirect
21. #17989316C22semidirect
22. #17989315C22semidirect
23. #17989310C22semidirect
24. #17989310C22semidirect
25. #17989308C22semidirect
26. #17989297C22semidirect
27. #17989271C22semidirect
28. #17989214C22semidirect
30. #17989199C22semidirect
31. #17989198C22semidirect
32. #17989196C22semidirect
33. #17989144C22semidirect
89. #533×C73C22semidirect
409. C2×C73#3555semidirect
430. C2×#533D73semidirect
432. C73C2×#3555semidirect
448. #533C2×D73semidirect
823. C2#22624419direct (N × H)

Maximal subgroups

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

subgroupindex
#226244192
C2×#179893382
C2×Q8×Dic1462
C2×#179893162
C2×#179893152
C2×#179893102
C2×#179893082
C2×#179892972
C2×#179892712
C2×#179892142
C2×#179892082
C2×#179891992
C2×#179891982
C2×#179891962
C2×#179891442
C2×#179891212
C2×#533×C732
C2×#355573