Finite Group Databasebeta

← C2×#22624407 #33993699

Subgroups — C2×#22624407 #33993699

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#22624407C2132yesmaximal, direct product factor
2C2×#17989339C214yesmaximal, complemented
3C2×Q8×Dic146C211yesmaximal, characteristic, complemented
4C2×#17989316C212yesmaximal, complemented
5C2×#17989312C211yesmaximal, characteristic, complemented
6C2×#17989306C212yesmaximal, complemented
7C2×#17989305C212yesmaximal, complemented
8C2×#17989294C211yesmaximal, characteristic, complemented
9C2×#17989279C212yesmaximal, complemented
10C2×#17989215C212yesmaximal, complemented
11C2×#17989206C212yesmaximal
12C2×#17989197C212yesmaximal, complemented
13C2×#17989195C212yesmaximal, complemented
14C2×#17989194C214yesmaximal, complemented
15C2×#17989142C211yesmaximal, characteristic, complemented
16C2×#17989141C211yesmaximal, characteristic, complemented
17C2×#17989119C211yesmaximal, characteristic
18C2×#556×C73C211yesmaximal, characteristic, complemented
19#17989339C22164yescomplemented
20Q8×Dic146C22116yescomplemented
21#17989316C22132yescomplemented
22#17989312C22116yescomplemented
23#17989306C22132yescomplemented
24#17989305C22132yescomplemented
25#17989294C22116yescomplemented
26#17989279C22132yescomplemented
27#17989215C22132yescomplemented
28#17989206C22132yes—
29#17989197C22132yescomplemented
30#17989195C22132yescomplemented
31#17989194C22164yescomplemented
32#17989142C22116yescomplemented
33#17989141C22116yescomplemented
34C2×#14556591C2212yes—
35C2×#14556591C2214yes—
36C2×#14556591C2211yescharacteristic
37C2×#14556590C2214yes—
38C2×#14556590C2212yes—
39C2×#14556590C2211yescharacteristic
40C2×#14556589C2212yes—
41C2×#14556589C2211yescharacteristic
42#17989119C22116yes—
43C2×#14556586C2214yes—
44C2×#14556585C2214yes—
45C2×#14556584C2212yes—
46C2×#14556584C2214yes—
47C2×#14556584C2214yes—
48C2×#14556584C2214yes—
49C2×#14556583C2214yes—
50C2×#14556582C2212yes—
51C2×#14556582C2211yescharacteristic
52C2×#14556582C2214yes—
53C2×#14556582C2212yes—
54C2×#14556582C2214yes—
55C2×#14556582C2212yes—
56C2×#14556581C2214yes—
57C2×#14556581C2212yes—
58C2×#14556581C2214yes—
59C2×#14556578C2211yescharacteristic
60C2×#14556577C2214yes—
61C2×#14556575C2214yes—
62C2×#14556573C2212yes—
63C2×#14556571C2211yescharacteristic
64C2×#14556571C2212yes—
65C2×#14556571C2211yescharacteristic
66C2×#14556570C2212yes—
67C2×#14556569C2212yes—
68C2×#14556568C2214yes—
69C2×#14556568C2214yes—
70C2×#14556568C2214yes—
71C2×#14556567C2212yes—
72C2×#14556567C2211yescharacteristic
73C2×#14556562C2211yescharacteristic
74C2×Q8×Dic73C2212yes—
75C2×Q8×Dic73C2212yes—
76C2×Q8×Dic73C2212yes—
77C2×C4×Dic146C2211yescharacteristic
78C2×C4×Dic146C2211yescharacteristic
79C2×C4×Dic146C2214yes—
80C2×C4×Dic146C2212yes—
81C2×C4×Dic146C2212yes—
82C2×#14556556C2212yes—
83C2×#14556556C2212yes—
84C2×D4×Dic73C2212yes—
85C2×C4×C22⋊D73C2212yes—
86C2×#14556550C2212yes—
87C2×#14556549C2212yes—
88C2×#14556548C2212yes—
89C2×#14556547C2214yes—
90C22×C4⋊Dic73C2212yes—
91C2×C42×D73C2211yescharacteristic
92#556×C73C22116yescomplemented
93C2×C4⋊Q8×C73C2211yescharacteristic
94C2×#126×C73C2214yes—
95C2×#124×C73C2212yes—
96C2×C22⋊Q8×C73C2212yes—
97C2×C4×Q8×C73C2212yes—
98C2×C4×Q8×C73C2211yescharacteristic
99C2×C4×D4×C73C2211yescharacteristic
100C2×#117×C73C2212yes—
101C22×Dic146C2311yescharacteristic
102C22×Dic146C2311yescharacteristic
103C22×Dic146C2314yes—
104C22×Dic146C2312yes—
105C22×Dic146C2312yes—
106C22×C22⋊D73C2312yes—
107C23×Dic73C2314yes—
108C22×C4×D73C2311yescharacteristic
109C22×C4×D73C2311yescharacteristic
110C22×C4×D73C2311yescharacteristic
111#14556591C2318yes—
112#14556591C23116yes—
113#14556591C23132yes—
114#14556590C2318yes—
115#14556590C23132yes—
116#14556590C23116yes—
117#14556589C2318yes—
118#14556589C23116yes—
119#14556586C23132yes—
120#14556585C23132yes—
121#14556584C23116yes—
122#14556584C23132yes—
123#14556584C23132yes—
124#14556584C23132yes—
125#14556583C23132yes—
126#14556582C23116yes—
127#14556582C23132yes—
128#14556582C23116yes—
129#14556582C23132yes—
130#14556582C23116yes—
131#14556582C2318yes—
132#14556581C23116yes—
133#14556581C23132yes—
134#14556581C23132yes—
135#14556578C2318yes—
136#14556577C23132yes—
137#14556575C23132yes—
138#14556573C23116yes—
139#14556571C2318yes—
140#14556571C23116yes—
141#14556571C2318yes—
142#14556570C23116yes—
143#14556569C23116yes—
144#14556568C23132yes—
145#14556568C23132yes—
146#14556568C23132yes—
147#14556567C2318yes—
148#14556567C23116yes—
149#14556562C2318yes—
150Q8×Dic73C23116yes—
151Q8×Dic73C23116yes—
152Q8×Dic73C23116yes—
153C4×Dic146C2318yes—
154C4×Dic146C23116yes—
155C4×Dic146C23132yes—
156C4×Dic146C23116yes—
157C4×Dic146C2318yes—
158#14556556C23116yes—
159#14556556C23116yes—
160D4×Dic73C23116yes—
161C4×C22⋊D73C23116yes—
162#14556550C23116yes—
163#14556549C23116yes—
164#14556548C23116yes—
165#14556547C23132yes—
166C2×C4⋊Dic73C2312yes—
167C2×C4⋊Dic73C2314yes—
168C2×C4⋊Dic73C2311yescharacteristic
169C2×C4⋊Dic73C2312yes—
170C2×C4⋊Dic73C2312yes—
171C2×C4⋊Dic73C2311yescharacteristic
172C2×C4⋊Dic73C2314yes—
173C2×C4⋊Dic73C2314yes—
174C2×C4⋊Dic73C2314yes—
175C2×C4⋊Dic73C23116yes—
176C2×C4⋊Dic73C2312yes—
177C2×C4⋊Dic73C2312yes—
178C2×#11924007C2314yes—
179C2×#11924007C2312yes—
180C2×#11924007C2314yes—
181C2×#11924007C2312yes—
182C2×#11924007C2314yes—
183C2×#11924007C2312yes—
184C2×#11924007C2312yes—
185C2×#11924007C2312yes—
186C2×#11924007C2312yes—
187C2×#11924007C2314yes—
188C2×#11924007C2312yes—
189C2×#11924007C2314yes—
190C2×C22⋊Dic73C2312yes—
191C2×C22⋊Dic73C2312yes—
192C2×C22⋊Dic73C2312yes—
193C2×C22⋊Dic73C2314yes—
194C2×#11924005C2312yes—
195C2×#11924005C2312yes—
196C2×#11924005C2314yes—
197C2×#11924005C2312yes—
198C2×C4×Dic73C2311yescharacteristic
199C2×C4×Dic73C2312yes—
200C2×C4×Dic73C2314yes—
201C2×C4×Dic73C2312yes—
202C2×C4×Dic73C2311yescharacteristic
203C2×C4×Dic73C2311yescharacteristic
204C2×C4×Dic73C2314yes—
205C2×C4×Dic73C2314yes—
206C42×D73C2318yes—
207C22×Q8×C73C2311yescharacteristic
208C22×Q8×C73C2312yes—
209C22×D4×C73C2311yescharacteristic
210C23×C4×C73C2312yes—
211C4⋊Q8×C73C2318yes—
212#126×C73C23132yes—
213#124×C73C23116yes—
214C22⋊Q8×C73C23116yes—
215C4×Q8×C73C2318yes—
216C4×Q8×C73C23116yes—
217C4×D4×C73C2318yes—
218#117×C73C23116yes—
219C2×C4⋊C4×C73C2311yescharacteristic
220C2×C4⋊C4×C73C2312yes—
221C2×C4⋊C4×C73C2312yes—
222C2×C4⋊C4×C73C2311yescharacteristic
223C2×C4⋊C4×C73C2314yes—
224C2×C4⋊C4×C73C2312yes—
225C2×C22⋊C4×C73C2314yes—
226C2×C22⋊C4×C73C2312yes—
227C2×C22⋊C4×C73C2314yes—
228C2×C42×C73C2314yes—
229C2×C42×C73C2311yescharacteristic
230C2×C42×C73C2312yes—
231C23×D73C2411yescharacteristic
232C2×Dic146—24no—
233C2×Dic146—24no—
234C2×Dic146—44no—
235C2×Dic146—44no—
236C2×Dic146—48no—
237C2×Dic146C2414yes—
238C2×Dic146C2414yes—
239C2×Dic146C2418yes—
240C2×Dic146C2418yes—
241C2×Dic146C24116yes—
242C2×C22⋊D73—44no—
243C2×C22⋊D73C2418yes—
244C22×Dic73—48no—
245C22×Dic73C2411yescharacteristic
246C22×Dic73C2412yes—
247C22×Dic73C2412yes—
248C22×Dic73C2412yes—
249C22×Dic73C2414yes—
250C22×Dic73C2411yescharacteristic
251C22×Dic73C2411yescharacteristic
252C22×Dic73C2412yes—
253C22×Dic73C24116yes—
254C2×C4×D73—24no—
255C2×C4×D73—24no—
256C2×C4×D73—42no—
257C2×C4×D73C2414yes—
258C2×C4×D73C2414yes—
259C2×C4×D73C2414yes—
260C4⋊Dic73C2414yes—
261C4⋊Dic73C2418yes—
262C4⋊Dic73C24116yes—
263C4⋊Dic73C2418yes—
264C4⋊Dic73C2418yes—
265C4⋊Dic73C2418yes—
266C4⋊Dic73C2418yes—
267C4⋊Dic73C2414yes—
268C4⋊Dic73C24116yes—
269C4⋊Dic73C24116yes—
270C4⋊Dic73C24116yes—
271#11924007C2418yes—
272#11924007C24116yes—
273#11924007C2418yes—
274#11924007C2418yes—
275#11924007C2418yes—
276#11924007C24116yes—
277#11924007C24116yes—
278#11924007C2418yes—
279#11924007C24116yes—
280#11924007C24116yes—
281#11924007C2418yes—
282#11924007C2418yes—
283C22⋊Dic73C2418yes—
284C22⋊Dic73C2418yes—
285C22⋊Dic73C2418yes—
286C22⋊Dic73C24116yes—
287#11924005C2418yes—
288#11924005C2418yes—
289#11924005C24116yes—
290#11924005C2418yes—
291C4×Dic73C2414yes—
292C4×Dic73C2414yes—
293C4×Dic73C2414yes—
294C4×Dic73C24116yes—
295C4×Dic73C24116yes—
296C4×Dic73C2418yes—
297C4×Dic73C2418yes—
298C4×Dic73C24116yes—
299C24×C73C2412yes—
300C2×Q8×C73—24no—
301C2×Q8×C73—28no—
302C2×Q8×C73C2414yes—
303C2×Q8×C73C2418yes—
304C2×D4×C73—24no—
305C2×D4×C73C2414yes—
306C22×C4×C73—28no—
307C22×C4×C73C2412yes—
308C22×C4×C73C2412yes—
309C22×C4×C73C2411yescharacteristic
310C22×C4×C73C2414yes—
311C22×C4×C73C2412yes—
312C22×C4×C73C2418yes—
313C22×C4×C73C2411yescharacteristic
314C22×C4×C73C2411yescharacteristic
315C4⋊C4×C73C2414yes—
316C4⋊C4×C73C2418yes—
317C4⋊C4×C73C2414yes—
318C4⋊C4×C73C24116yes—
319C4⋊C4×C73C2418yes—
320C4⋊C4×C73C2418yes—
321C22⋊C4×C73C24116yes—
322C22⋊C4×C73C2418yes—
323C22⋊C4×C73C24116yes—
324C42×C73C24116yes—
325C42×C73C2414yes—
326C42×C73C2418yes—
327C23×C73—24no—
328C23×C73—24no—
329C23×C73—24no—
330C23×C73C2514yes—
331C23×C73C2511yescharacteristic
332C22×D73—22no—
333C22×D73—22no—
334C22×D73—22no—
335C22×D73C2512yes—
336Q8×C73—28no—
337Q8×C73—216no—
338D4×C73—28no—
339C2×C4×C73—24no—
340C2×C4×C73—24no—
341C2×C4×C73—28no—
342C2×C4×C73—22no—
343C2×C4×C73—24no—
344C2×C4×C73—216no—
345C2×C4×C732−1+414yes—
346C2×C4×C732−1+414yes—
347C2×C4×C73C2514yes—
348C2×C4×C73C2514yes—
349C2×C4×C73C2512yes—
350C2×C4×C73C2518yes—
351C2×C4×C73C2514yes—
352C2×C4×C73C2512yes—
353C2×C4×C73C2512yes—
354C22⋊D73—48no—
355C2×Dic73—22no—
356C2×Dic73—22no—
357C2×Dic73—24no—
358C2×Dic73—24no—
359C2×Dic73—22no—
360C2×Dic73—24no—
361C2×Dic73—28no—
362C2×Dic73—24no—
363C2×Dic73—416no—
364C2×Dic73C2512yes—
365C2×Dic73C2514yes—
366C2×Dic73C2514yes—
367C2×Dic73C2514yes—
368C2×Dic73C2518yes—
369C2×Dic73C2512yes—
370C2×Dic73C2512yes—
371C2×Dic73C2514yes—
372C4×D73—28no—
373C4×D73—28no—
374C4×D73—44no—
375Dic146—28no—
376Dic146—28no—
377Dic146—48no—
378Dic146—48no—
379Dic146—416no—
380C22×C73—24no—
381C22×C73—24no—
382C22×C73—24no—
383C22×C73—48no—
384C22×C73C2×2−1+412yes—
385C22×C73C2×2−1+412yes—
386C22×C73#58512yes—
387C22×C73C2611yescharacteristic
388C2×D73—22no—
389C2×D73—22no—
390C2×D73—22no—
391C2×D73—44no—
392C4×C73—24no—
393C4×C73—24no—
394C4×C73—28no—
395C4×C73—24no—
396C4×C73—22no—
397C4×C73C2×2−1+414yes—
398C4×C73C2×2−1+414yes—
399Dic73—24no—
400Dic73—24no—
401Dic73—22no—
402Dic73—22no—
403Dic73—22no—
404Dic73—28no—
405Dic73—24no—
406Dic73—24no—
407C2×#3555—731nomaximal, Sylow
408C2×C73—44no—
409C2×C73#355514yescomplemented
410C2×C73C22×2−1+411yescharacteristic
411C2×C73C22×2−1+411yescharacteristic
412C2×C73C2×#58511yescharacteristic
413D73—42no—
414#3555—7332no—
415C2×#563—734no—
416C2×Q82—731no—
417C2×#557—731no—
418C2×#557—732no—
419C2×#556—732no—
420C2×#556—732no—
421C2×#556D7311yescharacteristic, complemented
422C2×#554—731no—
423C2×#552—732no—
424C2×#544—732no—
425C2×#542—732no—
426C2×#541—734no—
427C2×#541—732no—
428C2×#541—732no—
429C2×#533—731no—
430C2×#533—731no—
431C2×#529—731no—
432C73C2×#355511yescharacteristic, complemented, Sylow
433#563—7364no—
434Q82—7316no—
435#557—7316no—
436#557—7332no—
437#556—7332no—
438#556—7332no—
439#556C2×D73116yescomplemented
440#554—7316no—
441#552—7332no—
442#544—7332no—
443#542—7332no—
444#541—7364no—
445#541—7332no—
446#541—7332no—
447#533—7316no—
448#533—7316no—
449C2×C4⋊Q8—731no—
450C2×C4⋊Q8—732no—
451C2×C4⋊Q8—731no—
452C2×C4⋊Q8—734no—
453C2×C4⋊Q8—732no—
454C2×C4⋊Q8—731no—
455C2×C4⋊Q8—732no—
456C2×C4⋊Q8—734no—
457C2×C4⋊Q8C2×D7311yescharacteristic
458#529—7316no—
459C2×#126—734no—
460C2×#126—732no—
461C2×#126—734no—
462C2×#126—734no—
463C2×#126—734no—
464C2×#126—734no—
465C2×#126C2×D7314yes—
466C2×#125—731no—
467C2×#125—732no—
468C2×#125—732no—
469C2×#125—734no—
470C2×#125—734no—
471C2×#125—732no—
472C2×#125—734no—
473C2×#125—734no—
474C2×#125—732no—
475C2×#125—734no—
476C2×#124—731no—
477C2×#124—734no—
478C2×#124C2×D7312yes—
479C2×#123—732no—
480C2×#123—734no—
481C2×C22⋊Q8—732no—
482C2×C22⋊Q8—731no—
483C2×C22⋊Q8—732no—
484C2×C22⋊Q8—731no—
485C2×C22⋊Q8—731no—
486C2×C22⋊Q8—732no—
487C2×C22⋊Q8—732no—
488C2×C22⋊Q8—734no—
489C2×C22⋊Q8—734no—
490C2×C22⋊Q8—734no—
491C2×C22⋊Q8C2×D7312yes—
492C2×#121—731no—
493C2×C4×Q8—732no—
494C2×C4×Q8—732no—
495C2×C4×Q8—732no—
496C2×C4×Q8—732no—
497C2×C4×Q8—732no—
498C2×C4×Q8—731no—
499C2×C4×Q8—731no—
500C2×C4×Q8—732no—
501C2×C4×Q8—734no—
502C2×C4×Q8—732no—
503C2×C4×Q8C2×D7311yescharacteristic
504C2×C4×Q8C2×D7312yes—
505C2×C4×D4—732no—
506C2×C4×D4—732no—
507C2×C4×D4C2×D7311yescharacteristic
508C2×#117—732no—
509C2×#117—732no—
510C2×#117—734no—
511C2×#117—732no—
512C2×#117C2×D7312yes—
513C22×C4⋊C4—732no—
514C22×C42—731no—
515C22×Q8—732no—
516C22×Q8—732no—
517C22×Q8—734no—
518C22×Q8—731no—
519C22×Q8—731no—
520C22×Q8C22×D7311yescharacteristic
521C22×Q8C22×D7312yes—
522C22×D4—732no—
523C22×D4C22×D7311yescharacteristic
524C23×C4—734no—
525C23×C4—731no—
526C23×C4—731no—
527C23×C4—731no—
528C23×C4C22×D7312yes—
529C4⋊Q8—738no—
530C4⋊Q8—7316no—
531C4⋊Q8—738no—
532C4⋊Q8—7332no—
533C4⋊Q8—7316no—
534C4⋊Q8—738no—
535C4⋊Q8—7316no—
536C4⋊Q8—7332no—
537C4⋊Q8C22×D7318yes—
538#126—7332no—
539#126—7316no—
540#126—7332no—
541#126—7332no—
542#126—7332no—
543#126—7332no—
544#126C22×D73132yes—
545#125—738no—
546#125—7316no—
547#125—7316no—
548#125—7332no—
549#125—7332no—
550#125—7316no—
551#125—7332no—
552#125—7332no—
553#125—7316no—
554#125—7332no—
555#124—738no—
556#124—7332no—
557#124C22×D73116yes—
558#123—7316no—
559#123—7332no—
560C22⋊Q8—7316no—
561C22⋊Q8—738no—
562C22⋊Q8—7316no—
563C22⋊Q8—738no—
564C22⋊Q8—738no—
565C22⋊Q8—7316no—
566C22⋊Q8—7316no—
567C22⋊Q8—7332no—
568C22⋊Q8—7332no—
569C22⋊Q8—7332no—
570C22⋊Q8C22×D73116yes—
571#121—738no—
572C4×Q8—7316no—
573C4×Q8—7316no—
574C4×Q8—7316no—
575C4×Q8—7316no—
576C4×Q8—7316no—
577C4×Q8—738no—
578C4×Q8—738no—
579C4×Q8—7316no—
580C4×Q8—7332no—
581C4×Q8—7316no—
582C4×Q8C22×D7318yes—
583C4×Q8C22×D73116yes—
584C4×D4—7316no—
585C4×D4—7316no—
586C4×D4C22×D7318yes—
587#117—7316no—
588#117—7316no—
589#117—7332no—
590#117—7316no—
591#117C22×D73116yes—
592C2×C4⋊C4—731no—
593C2×C4⋊C4—732no—
594C2×C4⋊C4—734no—
595C2×C4⋊C4—7316no—
596C2×C4⋊C4—732no—
597C2×C4⋊C4—732no—
598C2×C4⋊C4—732no—
599C2×C4⋊C4—734no—
600C2×C4⋊C4—732no—
601C2×C4⋊C4—732no—
602C2×C4⋊C4—732no—
603C2×C4⋊C4—732no—
604C2×C4⋊C4—731no—
605C2×C4⋊C4—732no—
606C2×C4⋊C4—732no—
607C2×C4⋊C4—734no—
608C2×C4⋊C4—734no—
609C2×C4⋊C4—734no—
610C2×C4⋊C4—734no—
611C2×C4⋊C4—732no—
612C2×C4⋊C4—734no—
613C2×C4⋊C4—732no—
614C2×C4⋊C4—734no—
615C2×C4⋊C4—734no—
616C2×C4⋊C4C22×D7312yes—
617C2×C4⋊C4C22×D7311yescharacteristic
618C2×C4⋊C4C22×D7311yescharacteristic
619C2×C4⋊C4C22×D7312yes—
620C2×C4⋊C4C22×D7312yes—
621C2×C4⋊C4C22×D7314yes—
622C2×C22⋊C4—732no—
623C2×C22⋊C4—732no—
624C2×C22⋊C4—732no—
625C2×C22⋊C4—734no—
626C2×C22⋊C4—732no—
627C2×C22⋊C4—734no—
628C2×C22⋊C4—732no—
629C2×C22⋊C4—732no—
630C2×C22⋊C4C22×D7314yes—
631C2×C22⋊C4C22×D7314yes—
632C2×C22⋊C4C22×D7312yes—
633C2×C42—734no—
634C2×C42—731no—
635C2×C42—732no—
636C2×C42—732no—
637C2×C42—734no—
638C2×C42—731no—
639C2×C42—734no—
640C2×C42—731no—
641C2×C42—738no—
642C2×C42C22×D7312yes—
643C2×C42C22×D7314yes—
644C2×C42C22×D7311yescharacteristic
645C24—731no—
646C24C23×D7312yes—
647C2×Q8—24no—
648C2×Q8—28no—
649C2×Q8—2924no—
650C2×Q8—2924no—
651C2×Q8—2928no—
652C2×Q8—738no—
653C2×Q8—738no—
654C2×Q8—7316no—
655C2×Q8—734no—
656C2×Q8—734no—
657C2×Q8—1464no—
658C2×Q8—1464no—
659C2×Q8C23×D7314yes—
660C2×Q8C23×D7318yes—
661C2×D4—24no—
662C2×D4—2924no—
663C2×D4—738no—
664C2×D4C23×D7314yes—
665C22×C4—28no—
666C22×C4—2922no—
667C22×C4—2928no—
668C22×C4—7316no—
669C22×C4—734no—
670C22×C4—731no—
671C22×C4—732no—
672C22×C4—732no—
673C22×C4—732no—
674C22×C4—731no—
675C22×C4—734no—
676C22×C4—731no—
677C22×C4—732no—
678C22×C4—734no—
679C22×C4—734no—
680C22×C4—1464no—
681C22×C4—1464no—
682C22×C4C23×D7318yes—
683C22×C4C23×D7314yes—
684C22×C4C23×D7312yes—
685C22×C4C23×D7311yescharacteristic
686C22×C4C23×D7312yes—
687C22×C4C23×D7312yes—
688C22×C4C23×D7311yescharacteristic
689C22×C4C23×D7311yescharacteristic
690C4⋊C4—738no—
691C4⋊C4—738no—
692C4⋊C4—7316no—
693C4⋊C4—738no—
694C4⋊C4—738no—
695C4⋊C4—738no—
696C4⋊C4—7316no—
697C4⋊C4—7316no—
698C4⋊C4—738no—
699C4⋊C4—7316no—
700C4⋊C4—738no—
701C4⋊C4—7316no—
702C4⋊C4—734no—
703C4⋊C4—738no—
704C4⋊C4—7316no—
705C4⋊C4—738no—
706C4⋊C4—738no—
707C4⋊C4—738no—
708C4⋊C4—734no—
709C4⋊C4—738no—
710C4⋊C4—7316no—
711C4⋊C4—7316no—
712C4⋊C4—7316no—
713C4⋊C4C23×D7318yes—
714C4⋊C4C23×D7314yes—
715C4⋊C4C23×D7314yes—
716C4⋊C4C23×D7318yes—
717C4⋊C4C23×D7318yes—
718C4⋊C4C23×D73116yes—
719C22⋊C4—738no—
720C22⋊C4—738no—
721C22⋊C4—738no—
722C22⋊C4—7316no—
723C22⋊C4—738no—
724C22⋊C4—7316no—
725C22⋊C4—738no—
726C22⋊C4—738no—
727C22⋊C4C23×D73116yes—
728C22⋊C4C23×D73116yes—
729C22⋊C4C23×D7318yes—
730C42—734no—
731C42—734no—
732C42—734no—
733C42—7316no—
734C42—738no—
735C42—738no—
736C42—7316no—
737C42—7316no—
738C42C23×D7314yes—
739C42C23×D7318yes—
740C42C23×D73116yes—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—732no—
745C23—1462no—
746C23—1462no—
747C23—1462no—
748C23C24×D7314yes—
749C23C24×D7311yescharacteristic
750Q8—28no—
751Q8—216no—
752Q8—2928no—
753Q8—2928no—
754Q8—29216no—
755Q8—1468no—
756Q8—1468no—
757D4—28no—
758D4—2928no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—216no—
765C2×C4—2924no—
766C2×C4—29216no—
767C2×C4—732no—
768C2×C4—734no—
769C2×C4—734no—
770C2×C4—734no—
771C2×C4—732no—
772C2×C4—732no—
773C2×C4—738no—
774C2×C4—734no—
775C2×C4—1462no—
776C2×C4—1462no—
777C2×C4—1464no—
778C2×C4—1464no—
779C2×C4—1464no—
780C2×C4—1462no—
781C2×C4—1468no—
782C2×C4—1464no—
783C2×C4—1468no—
784C2×C4—1468no—
785C2×C4#1455663814yes—
786C2×C4#1455663814yes—
787C2×C4C24×D7318yes—
788C2×C4C24×D7314yes—
789C2×C4C24×D7312yes—
790C2×C4C24×D7314yes—
791C2×C4C24×D7314yes—
792C2×C4C24×D7312yes—
793C2×C4C24×D7312yes—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—48no—
798C22—2924no—
799C22—1462no—
800C22—1462no—
801C22—1462no—
802C22C2×#1455663812yes—
803C22C2×#1455663812yes—
804C22#1798942412yes—
805C22C25×D7311yescharacteristic
806C4—24no—
807C4—24no—
808C4—28no—
809C4—22no—
810C4—24no—
811C4—1462no—
812C4—1462no—
813C4—1464no—
814C4—1464no—
815C4—1464no—
816C4—1462no—
817C4—1468no—
818C4—1464no—
819C4C2×#1455663814yes—
820C4C2×#1455663814yes—
821C2—44no—
822C2—2922no—
823C2#2262440714yesdirect product factor
824C2C22×#1455663811yescharacteristic
825C2C22×#1455663811yescharacteristic
826C2C2×#1798942411yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#556×C73C2
socleC23×C73C25
prime radicalC2×#14556562C22
hypercenterC2×#556D73
hypocenterC73C2×#3555
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #22624407C2direct (N × H)
2. C2×#17989339C2semidirect
3. C2×Q8×Dic146C2semidirect
4. C2×#17989316C2semidirect
5. C2×#17989312C2semidirect
6. C2×#17989306C2semidirect
7. C2×#17989305C2semidirect
8. C2×#17989294C2semidirect
9. C2×#17989279C2semidirect
10. C2×#17989215C2semidirect
12. C2×#17989197C2semidirect
13. C2×#17989195C2semidirect
14. C2×#17989194C2semidirect
15. C2×#17989142C2semidirect
16. C2×#17989141C2semidirect
18. C2×#556×C73C2semidirect
19. #17989339C22semidirect
20. Q8×Dic146C22semidirect
21. #17989316C22semidirect
22. #17989312C22semidirect
23. #17989306C22semidirect
24. #17989305C22semidirect
25. #17989294C22semidirect
26. #17989279C22semidirect
27. #17989215C22semidirect
29. #17989197C22semidirect
30. #17989195C22semidirect
31. #17989194C22semidirect
32. #17989142C22semidirect
33. #17989141C22semidirect
92. #556×C73C22semidirect
409. C2×C73#3555semidirect
421. C2×#556D73semidirect
432. C73C2×#3555semidirect
439. #556C2×D73semidirect
823. C2#22624407direct (N × H)

Maximal subgroups

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

subgroupindex
#226244072
C2×#179893392
C2×Q8×Dic1462
C2×#179893162
C2×#179893122
C2×#179893062
C2×#179893052
C2×#179892942
C2×#179892792
C2×#179892152
C2×#179892062
C2×#179891972
C2×#179891952
C2×#179891942
C2×#179891422
C2×#179891412
C2×#179891192
C2×#556×C732
C2×#355573