Finite Group Databasebeta

← C2×#22623814 #33994423

Subgroups — C2×#22623814 #33994423

Order 18688.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623814C2132yesmaximal, direct product factor
2C2×#17989315C211yesmaximal, characteristic, complemented
3C2×#17989312C212yesmaximal, complemented
4C2×#17989311C211yesmaximal, characteristic, complemented
5C2×#17989310C211yesmaximal, characteristic, complemented
6C2×#17989309C212yesmaximal, complemented
7C2×#17989278C212yesmaximal, complemented
8C2×#17989275C212yesmaximal, complemented
9C2×#17989269C214yesmaximal, complemented
10C2×#17989196C214yesmaximal, complemented
11C2×#17989162C212yesmaximal
12C2×#17989143C212yesmaximal, complemented
13C2×#17989141C212yesmaximal, complemented
14C2×#17989141C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D73C211yesmaximal, characteristic, complemented
16C2×#17989063C212yesmaximal, complemented
17C2×C4×#11924029C211yesmaximal, characteristic
18C2×#557×C73C211yesmaximal, characteristic, complemented
19C22×#11924029C2211yescharacteristic
20C22×Q8×D73C2212yes—
21#17989315C22116yescomplemented
22#17989312C22132yescomplemented
23#17989311C22116yescomplemented
24#17989310C22116yescomplemented
25#17989309C22132yescomplemented
26#17989278C22132yescomplemented
27#17989275C22132yescomplemented
28#17989269C22164yescomplemented
29#17989196C22164yescomplemented
30#17989162C22132yes—
31#17989143C22132yescomplemented
32#17989141C22132yescomplemented
33#17989141C22116yescomplemented
34C2×#14556591C2211yescharacteristic
35C2×#14556590C2212yes—
36C2×#14556590C2212yes—
37C2×#14556590C2211yescharacteristic
38C2×#14556589C2212yes—
39C2×#14556589C2212yes—
40C2×#14556589C2211yescharacteristic
41C4⋊Q8×D73C22116yescomplemented
42C2×#14556586C2214yes—
43C2×#14556586C2214yes—
44C2×#14556586C2214yes—
45C2×#14556585C2214yes—
46C2×#14556583C2212yes—
47C2×#14556582C2214yes—
48C2×#14556581C2214yes—
49C2×#14556581C2214yes—
50C2×#14556581C2214yes—
51C2×#14556581C2212yes—
52C2×#14556580C2212yes—
53C2×#14556579C2212yes—
54C2×#14556576C2214yes—
55C2×#14556576C2214yes—
56C2×#14556571C2211yescharacteristic
57C2×#14556571C2212yes—
58C2×#14556569C2214yes—
59C2×#14556569C2214yes—
60C2×#14556569C2212yes—
61C2×#14556569C2214yes—
62C2×#14556567C2211yescharacteristic
63C2×#14556567C2212yes—
64#17989063C22132yescomplemented
65C4×#11924029C22116yes—
66C2×Q8×Dic73C2211yescharacteristic
67C2×Q8×Dic73C2212yes—
68C2×C4×Dic146C2212yes—
69C2×C4×Dic146C2212yes—
70C2×C4×Dic146C2212yes—
71C2×C4×Dic146C2211yescharacteristic
72C2×C4×Dic146C2214yes—
73C2×#14556556C2214yes—
74C2×#14556556C2212yes—
75C2×#14556556C2214yes—
76C2×C4×D292C2212yes—
77C2×C4×D292C2211yescharacteristic
78C2×#14556553C2212yes—
79C2×#14556553C2211yescharacteristic
80C2×#14556549C2212yes—
81C2×#14556549C2211yescharacteristic
82C2×#14556549C2214yes—
83C2×#14556549C2212yes—
84C2×#14556549C2212yes—
85C2×#14556548C2212yes—
86C2×#14556548C2214yes—
87C2×#14556548C2214yes—
88C2×C4⋊C4×D73C2212yes—
89C2×C4⋊C4×D73C2212yes—
90C2×C42×D73C2211yescharacteristic
91C2×C42×D73C2212yes—
92#557×C73C22116yescomplemented
93C2×C4⋊Q8×C73C2212yes—
94C2×C4⋊Q8×C73C2211yescharacteristic
95C2×#125×C73C2214yes—
96C2×#125×C73C2212yes—
97C2×C4×Q8×C73C2211yescharacteristic
98C2×C4×Q8×C73C2212yes—
99C2×C4×Q8×C73C2212yes—
100C2×C4×Q8×C73C2211yescharacteristic
101C2×#11924029—28no—
102C2×#11924029C2318yes—
103C22×Dic146C2312yes—
104C22×Dic146C2311yescharacteristic
105C22×Dic146C2314yes—
106C22×Dic146C2312yes—
107C2×Q8×D73—216no—
108C2×Q8×D73C23116yes—
109C22×D292C2312yes—
110C22×D292C2311yescharacteristic
111C22×C4×D73C2314yes—
112C22×C4×D73C2312yes—
113C22×C4×D73C2311yescharacteristic
114C22×C4×D73C2311yescharacteristic
115C22×C4×D73C2312yes—
116C22×C4×D73C2312yes—
117C22×C4×D73C2311yescharacteristic
118#14556591C2318yes—
119#14556590C23116yes—
120#14556590C23116yes—
121#14556590C2318yes—
122#14556589C23116yes—
123#14556589C2318yes—
124#14556589C23116yes—
125#14556586C23132yes—
126#14556586C23132yes—
127#14556586C23132yes—
128#14556585C23132yes—
129#14556583C23116yes—
130#14556582C23132yes—
131#14556581C23116yes—
132#14556581C23132yes—
133#14556581C23132yes—
134#14556581C23132yes—
135#14556580C23116yes—
136#14556579C23116yes—
137#14556576C23132yes—
138#14556576C23132yes—
139#14556571C2318yes—
140#14556571C23116yes—
141#14556569C23132yes—
142#14556569C23116yes—
143#14556569C23132yes—
144#14556569C23132yes—
145#14556567C2318yes—
146#14556567C23116yes—
147Q8×Dic73C23116yes—
148Q8×Dic73C2318yes—
149C4×Dic146C23132yes—
150C4×Dic146C23116yes—
151C4×Dic146C23116yes—
152C4×Dic146C2318yes—
153C4×Dic146C23116yes—
154#14556556C23132yes—
155#14556556C23132yes—
156#14556556C23116yes—
157C4×D292C23116yes—
158C4×D292C2318yes—
159#14556553C23116yes—
160#14556553C2318yes—
161#14556549C23116yes—
162#14556549C23116yes—
163#14556549C23116yes—
164#14556549C23132yes—
165#14556549C2318yes—
166#14556548C23116yes—
167#14556548C23132yes—
168#14556548C23132yes—
169C2×C4⋊Dic73C2312yes—
170C2×C4⋊Dic73C2312yes—
171C2×C4⋊Dic73C2311yescharacteristic
172C2×C4⋊Dic73C2311yescharacteristic
173C2×C4⋊Dic73C2312yes—
174C2×C4⋊Dic73C2314yes—
175C2×C4⋊Dic73C2312yes—
176C2×#11924007C2314yes—
177C2×#11924007C2314yes—
178C2×#11924007C2312yes—
179C2×#11924007C2312yes—
180C2×#11924007C2314yes—
181C2×#11924007C2314yes—
182C2×#11924007C2312yes—
183C2×#11924007C2314yes—
184C2×#11924007C2314yes—
185C2×#11924007C2312yes—
186C2×#11924007C2312yes—
187C4⋊C4×D73C23116yes—
188C4⋊C4×D73C23116yes—
189C2×#11924005C2312yes—
190C2×#11924005C2312yes—
191C2×#11924005C2312yes—
192C2×#11924005C2314yes—
193C2×#11924005C2314yes—
194C2×#11924005C2312yes—
195C2×#11924005C2312yes—
196C2×#11924005C2314yes—
197C2×#11924005C2314yes—
198C2×C4×Dic73C2311yescharacteristic
199C2×C4×Dic73C2311yescharacteristic
200C2×C4×Dic73C2312yes—
201C2×C4×Dic73C2311yescharacteristic
202C2×C4×Dic73C2312yes—
203C2×C4×Dic73C2312yes—
204C2×C4×Dic73C2314yes—
205C2×C4×Dic73C2314yes—
206C2×C4×Dic73C2314yes—
207C42×D73C2318yes—
208C42×D73C23116yes—
209C22×Q8×C73C2311yescharacteristic
210C22×Q8×C73C2312yes—
211C22×Q8×C73C2311yescharacteristic
212C4⋊Q8×C73C2318yes—
213C4⋊Q8×C73C23116yes—
214#125×C73C23116yes—
215#125×C73C23132yes—
216C4×Q8×C73C23116yes—
217C4×Q8×C73C2318yes—
218C4×Q8×C73C23116yes—
219C4×Q8×C73C2318yes—
220C2×C4⋊C4×C73C2311yescharacteristic
221C2×C4⋊C4×C73C2312yes—
222C2×C4⋊C4×C73C2312yes—
223C2×C4⋊C4×C73C2311yescharacteristic
224C2×C4⋊C4×C73C2312yes—
225C2×C4⋊C4×C73C2314yes—
226C2×C4⋊C4×C73C2312yes—
227C2×C4⋊C4×C73C2314yes—
228C2×C4⋊C4×C73C2314yes—
229C2×C42×C73C2311yescharacteristic
230C2×C42×C73C2312yes—
231C2×C42×C73C2314yes—
232C2×C42×C73C2312yes—
233C23×D73C2412yes—
234C23×D73C2411yescharacteristic
235#11924029—232no—
236C2×Dic146—28no—
237C2×Dic146—24no—
238C2×Dic146—216no—
239C2×Dic146—28no—
240C2×Dic146C2418yes—
241C2×Dic146C24116yes—
242C2×Dic146C2418yes—
243C2×Dic146C2414yes—
244Q8×D73—264no—
245C2×D292—28no—
246C2×D292—24no—
247C2×D292C2418yes—
248C2×D292C2414yes—
249C22×Dic73C2412yes—
250C22×Dic73C2412yes—
251C22×Dic73C2412yes—
252C22×Dic73C2411yescharacteristic
253C22×Dic73C2414yes—
254C22×Dic73C2411yescharacteristic
255C22×Dic73C2411yescharacteristic
256C2×C4×D73—216no—
257C2×C4×D73—24no—
258C2×C4×D73—28no—
259C2×C4×D73—28no—
260C2×C4×D73—24no—
261C2×C4×D73—28no—
262C2×C4×D73#4118yes—
263C2×C4×D73C2414yes—
264C2×C4×D73C2414yes—
265C2×C4×D73C2418yes—
266C2×C4×D73C2418yes—
267C2×C4×D73C2418yes—
268C2×C4×D73C24116yes—
269C2×C4×D73C2414yes—
270C4⋊Dic73C2418yes—
271C4⋊Dic73C2418yes—
272C4⋊Dic73C2414yes—
273C4⋊Dic73C2414yes—
274C4⋊Dic73C2418yes—
275C4⋊Dic73C24116yes—
276C4⋊Dic73C2418yes—
277#11924007C24116yes—
278#11924007C24116yes—
279#11924007C2418yes—
280#11924007C2418yes—
281#11924007C24116yes—
282#11924007C24116yes—
283#11924007C2418yes—
284#11924007C24116yes—
285#11924007C2418yes—
286#11924007C24116yes—
287#11924007C2418yes—
288#11924005C2418yes—
289#11924005C2418yes—
290#11924005C2418yes—
291#11924005C24116yes—
292#11924005C24116yes—
293#11924005C2418yes—
294#11924005C2418yes—
295#11924005C24116yes—
296#11924005C24116yes—
297C4×Dic73C2414yes—
298C4×Dic73C2418yes—
299C4×Dic73C2414yes—
300C4×Dic73C2418yes—
301C4×Dic73C2414yes—
302C4×Dic73C24116yes—
303C4×Dic73C24116yes—
304C4×Dic73C2418yes—
305C4×Dic73C24116yes—
306C2×Q8×C73—28no—
307C2×Q8×C73—24no—
308C2×Q8×C73—24no—
309C2×Q8×C73C2414yes—
310C2×Q8×C73C2418yes—
311C2×Q8×C73C2414yes—
312C22×C4×C73C2412yes—
313C22×C4×C73C2412yes—
314C22×C4×C73C2412yes—
315C22×C4×C73C2411yescharacteristic
316C22×C4×C73C2414yes—
317C22×C4×C73C2412yes—
318C22×C4×C73C2411yescharacteristic
319C22×C4×C73C2411yescharacteristic
320C4⋊C4×C73C2414yes—
321C4⋊C4×C73C2414yes—
322C4⋊C4×C73C2418yes—
323C4⋊C4×C73C24116yes—
324C4⋊C4×C73C2418yes—
325C4⋊C4×C73C2418yes—
326C4⋊C4×C73C24116yes—
327C4⋊C4×C73C2418yes—
328C4⋊C4×C73C24116yes—
329C42×C73C2418yes—
330C42×C73C24116yes—
331C42×C73C2414yes—
332C42×C73C2418yes—
333C23×C73C2511yescharacteristic
334C22×D73—22no—
335C22×D73—22no—
336C22×D73—24no—
337C22×D73—24no—
338C22×D73—24no—
339C22×D73C2×#4114yes—
340C22×D73C2514yes—
341C22×D73C2512yes—
342Q8×C73—216no—
343Q8×C73—28no—
344Q8×C73—28no—
345C2×C4×C73—24no—
346C2×C4×C73—28no—
347C2×C4×C73—24no—
348C2×C4×C73—24no—
349C2×C4×C73—22no—
350C2×C4×C73—24no—
351C2×C4×C73C2×#4114yes—
352C2×C4×C732−1+414yes—
353C2×C4×C73C2514yes—
354C2×C4×C73C2514yes—
355C2×C4×C73C2514yes—
356C2×C4×C73C2512yes—
357C2×C4×C73C2518yes—
358C2×C4×C73C2514yes—
359C2×C4×C73C2512yes—
360C2×C4×C73C2512yes—
361C2×Dic73—28no—
362C2×Dic73—24no—
363C2×Dic73—22no—
364C2×Dic73—24no—
365C2×Dic73—24no—
366C2×Dic73C2×#4114yes—
367C2×Dic732−1+414yes—
368C2×Dic73C2514yes—
369C2×Dic73C2514yes—
370C2×Dic73C2514yes—
371C2×Dic73C2512yes—
372C2×Dic73C2518yes—
373C2×Dic73C2512yes—
374C2×Dic73C2512yes—
375D292—216no—
376D292—28no—
377C4×D73—232no—
378C4×D73—28no—
379C4×D73—216no—
380C4×D73—216no—
381C4×D73—28no—
382C4×D73—216no—
383C4×D73C2×#41116yes—
384Dic146—216no—
385Dic146—28no—
386Dic146—232no—
387Dic146—216no—
388C22×C73C22×#4112yes—
389C22×C73C2×2−1+412yes—
390C22×C73C2×2−1+412yes—
391C22×C73C2611yescharacteristic
392C2×D73—22no—
393C2×D73—22no—
394C2×D73—28no—
395C2×D73—24no—
396C2×D73—24no—
397C2×D73—24no—
398C2×D73—48no—
399C2×D73C22×#4114yes—
400C4×C73—28no—
401C4×C73—24no—
402C4×C73—24no—
403C4×C73—24no—
404C4×C73—22no—
405C4×C73—24no—
406C4×C73C22×#4114yes—
407C4×C73C2×2−1+414yes—
408Dic73—28no—
409Dic73—24no—
410Dic73—24no—
411Dic73—24no—
412Dic73—22no—
413Dic73C22×#4114yes—
414Dic73C2×2−1+414yes—
415C2×#3509—731nomaximal, Sylow
416C2×C73#350914yescomplemented
417C2×C73C23×#4111yescharacteristic
418C2×C73C22×2−1+411yescharacteristic
419C2×C73C22×2−1+411yescharacteristic
420D73—24no—
421D73—44no—
422#3509—7332no—
423C2×#557—732no—
424C2×#557—731no—
425C2×#557D7311yescharacteristic, complemented
426C2×#556—731no—
427C2×#556—732no—
428C2×#556—731no—
429C2×#552—734no—
430C2×#552—732no—
431C2×#552—732no—
432C2×#541—734no—
433C2×#536—732no—
434C2×#533—732no—
435C2×#533—731no—
436C2×#533—732no—
437C22×C4⋊Q8—731no—
438C2×#519—732no—
439C2×C4×#41—731no—
440C73C2×#350911yescharacteristic, complemented, Sylow
441C22×#41—731no—
442C23×Q8—732no—
443#557—7332no—
444#557—7316no—
445#557C2×D73116yescomplemented
446#556—7316no—
447#556—7332no—
448#556—7316no—
449#552—7364no—
450#552—7332no—
451#552—7332no—
452#541—7364no—
453#536—7332no—
454#533—7332no—
455#533—7316no—
456#533—7332no—
457C2×C4⋊Q8—732no—
458C2×C4⋊Q8—731no—
459C2×C4⋊Q8—732no—
460C2×C4⋊Q8—7316no—
461C2×C4⋊Q8—732no—
462C2×C4⋊Q8—732no—
463C2×C4⋊Q8—731no—
464C2×C4⋊Q8—731no—
465C2×C4⋊Q8C2×D7311yescharacteristic
466C2×C4⋊Q8C2×D7312yes—
467C2×#126—734no—
468C2×#126—734no—
469C2×#126—734no—
470C2×#126—734no—
471C2×#125—732no—
472C2×#125—734no—
473C2×#125—734no—
474C2×#125—734no—
475C2×#125—734no—
476C2×#125—732no—
477C2×#125C2×D7312yes—
478C2×#125C2×D7314yes—
479C2×#124—732no—
480C2×#124—732no—
481C2×#123—734no—
482C2×#123—734no—
483C2×C22⋊Q8—731no—
484C2×C22⋊Q8—732no—
485C2×C22⋊Q8—734no—
486C2×C22⋊Q8—734no—
487C2×C22⋊Q8—732no—
488C2×C22⋊Q8—731no—
489C2×C22⋊Q8—734no—
490C2×C22⋊Q8—732no—
491#519—7332no—
492C4×#41—7316no—
493C2×C4×Q8—731no—
494C2×C4×Q8—732no—
495C2×C4×Q8—734no—
496C2×C4×Q8—732no—
497C2×C4×Q8—734no—
498C2×C4×Q8—734no—
499C2×C4×Q8—732no—
500C2×C4×Q8—732no—
501C2×C4×Q8—731no—
502C2×C4×Q8—732no—
503C2×C4×Q8C2×D7311yescharacteristic
504C2×C4×Q8C2×D7312yes—
505C2×C4×Q8C2×D7312yes—
506C2×C4×Q8C2×D7311yescharacteristic
507C2×C4×D4—732no—
508C2×C4×D4—731no—
509C2×C4×D4—732no—
510C2×C4×D4—731no—
511C2×#117—731no—
512C2×#117—732no—
513C2×#117—734no—
514C2×#117—732no—
515C2×#117—732no—
516C2×#117—732no—
517C2×#117—734no—
518C2×#117—734no—
519C22×C4⋊C4—732no—
520C22×C4⋊C4—732no—
521C22×C42—731no—
522C22×C42—732no—
523C2×#41—738no—
524C2×#41—1468no—
525C22×Q8—7316no—
526C22×Q8—732no—
527C22×Q8—731no—
528C22×Q8—734no—
529C22×Q8—732no—
530C22×Q8—14616no—
531C22×Q8C22×D7312yes—
532C22×Q8C22×D7311yescharacteristic
533C22×Q8C22×D7311yescharacteristic
534C22×D4—732no—
535C22×D4—731no—
536C23×C4—731no—
537C23×C4—734no—
538C23×C4—731no—
539C23×C4—731no—
540C23×C4—732no—
541C23×C4—732no—
542C23×C4—732no—
543C4⋊Q8—7316no—
544C4⋊Q8—738no—
545C4⋊Q8—7316no—
546C4⋊Q8—7316no—
547C4⋊Q8—7316no—
548C4⋊Q8—738no—
549C4⋊Q8—738no—
550C4⋊Q8C22×D7318yes—
551C4⋊Q8C22×D73116yes—
552#126—7332no—
553#126—7332no—
554#126—7332no—
555#126—7332no—
556#125—7316no—
557#125—7332no—
558#125—7332no—
559#125—7332no—
560#125—7332no—
561#125—7316no—
562#125C22×D73116yes—
563#125C22×D73132yes—
564#124—7316no—
565#124—7316no—
566#123—7332no—
567#123—7332no—
568C22⋊Q8—738no—
569C22⋊Q8—7316no—
570C22⋊Q8—7332no—
571C22⋊Q8—7332no—
572C22⋊Q8—7316no—
573C22⋊Q8—738no—
574C22⋊Q8—7332no—
575C22⋊Q8—7316no—
576C4×Q8—738no—
577C4×Q8—7316no—
578C4×Q8—7332no—
579C4×Q8—7316no—
580C4×Q8—7332no—
581C4×Q8—7332no—
582C4×Q8—7316no—
583C4×Q8—7316no—
584C4×Q8—7316no—
585C4×Q8—738no—
586C4×Q8C22×D7318yes—
587C4×Q8C22×D73116yes—
588C4×Q8C22×D73116yes—
589C4×Q8C22×D7318yes—
590C4×D4—7316no—
591C4×D4—738no—
592C4×D4—7316no—
593C4×D4—738no—
594#117—738no—
595#117—7316no—
596#117—7332no—
597#117—7316no—
598#117—7316no—
599#117—7316no—
600#117—7332no—
601#117—7332no—
602C2×C4⋊C4—734no—
603C2×C4⋊C4—732no—
604C2×C4⋊C4—734no—
605C2×C4⋊C4—732no—
606C2×C4⋊C4—732no—
607C2×C4⋊C4—731no—
608C2×C4⋊C4—731no—
609C2×C4⋊C4—732no—
610C2×C4⋊C4—732no—
611C2×C4⋊C4—732no—
612C2×C4⋊C4—734no—
613C2×C4⋊C4—734no—
614C2×C4⋊C4—734no—
615C2×C4⋊C4—734no—
616C2×C4⋊C4—734no—
617C2×C4⋊C4—732no—
618C2×C4⋊C4—732no—
619C2×C4⋊C4—732no—
620C2×C4⋊C4—7316no—
621C2×C4⋊C4—7316no—
622C2×C4⋊C4C22×D7312yes—
623C2×C4⋊C4C22×D7312yes—
624C2×C4⋊C4C22×D7311yescharacteristic
625C2×C4⋊C4C22×D7311yescharacteristic
626C2×C4⋊C4C22×D7312yes—
627C2×C4⋊C4C22×D7314yes—
628C2×C4⋊C4C22×D7314yes—
629C2×C4⋊C4C22×D7314yes—
630C2×C4⋊C4C22×D7312yes—
631C2×C22⋊C4—732no—
632C2×C22⋊C4—732no—
633C2×C22⋊C4—732no—
634C2×C22⋊C4—732no—
635C2×C22⋊C4—732no—
636C2×C22⋊C4—734no—
637C2×C22⋊C4—734no—
638C2×C22⋊C4—734no—
639C2×C22⋊C4—734no—
640C2×C42—732no—
641C2×C42—734no—
642C2×C42—734no—
643C2×C42—734no—
644C2×C42—731no—
645C2×C42—732no—
646C2×C42—732no—
647C2×C42—731no—
648C2×C42—731no—
649C2×C42—738no—
650C2×C42—7316no—
651C2×C42C22×D7314yes—
652C2×C42C22×D7312yes—
653C2×C42C22×D7312yes—
654C2×C42C22×D7311yescharacteristic
655C24—731no—
656C24—732no—
657#41—14632no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—738no—
662C2×Q8—734no—
663C2×Q8—7316no—
664C2×Q8—738no—
665C2×Q8—1468no—
666C2×Q8—14616no—
667C2×Q8—14664no—
668C2×Q8—1468no—
669C2×Q8—1464no—
670C2×Q8C23×D7318yes—
671C2×Q8C23×D7314yes—
672C2×Q8C23×D7314yes—
673C2×D4—738no—
674C2×D4—734no—
675C2×D4—1468no—
676C2×D4—1464no—
677C22×C4—731no—
678C22×C4—731no—
679C22×C4—738no—
680C22×C4—734no—
681C22×C4—732no—
682C22×C4—732no—
683C22×C4—732no—
684C22×C4—731no—
685C22×C4—734no—
686C22×C4—734no—
687C22×C4—734no—
688C22×C4—738no—
689C22×C4—738no—
690C22×C4—738no—
691C22×C4—7316no—
692C22×C4—1468no—
693C22×C4—1464no—
694C22×C4—1468no—
695C22×C4—14616no—
696C22×C4—1468no—
697C22×C4—1464no—
698C22×C4C23×D7312yes—
699C22×C4C23×D7312yes—
700C22×C4C23×D7311yescharacteristic
701C22×C4C23×D7314yes—
702C22×C4C23×D7312yes—
703C22×C4C23×D7312yes—
704C22×C4C23×D7311yescharacteristic
705C22×C4C23×D7311yescharacteristic
706C4⋊C4—7316no—
707C4⋊C4—7316no—
708C4⋊C4—738no—
709C4⋊C4—738no—
710C4⋊C4—738no—
711C4⋊C4—7316no—
712C4⋊C4—7316no—
713C4⋊C4—7316no—
714C4⋊C4—7316no—
715C4⋊C4—738no—
716C4⋊C4—738no—
717C4⋊C4—738no—
718C4⋊C4—738no—
719C4⋊C4—734no—
720C4⋊C4—734no—
721C4⋊C4—738no—
722C4⋊C4—7316no—
723C4⋊C4—738no—
724C4⋊C4C23×D7318yes—
725C4⋊C4C23×D7318yes—
726C4⋊C4C23×D7314yes—
727C4⋊C4C23×D7314yes—
728C4⋊C4C23×D7318yes—
729C4⋊C4C23×D73116yes—
730C4⋊C4C23×D73116yes—
731C4⋊C4C23×D73116yes—
732C4⋊C4C23×D7318yes—
733C22⋊C4—738no—
734C22⋊C4—738no—
735C22⋊C4—738no—
736C22⋊C4—738no—
737C22⋊C4—738no—
738C22⋊C4—7316no—
739C22⋊C4—7316no—
740C22⋊C4—7316no—
741C22⋊C4—7316no—
742C42—734no—
743C42—738no—
744C42—734no—
745C42—738no—
746C42—734no—
747C42—7316no—
748C42—7316no—
749C42—7316no—
750C42—738no—
751C42C23×D7318yes—
752C42C23×D7314yes—
753C42C23×D73116yes—
754C42C23×D7318yes—
755C23—734no—
756C23—732no—
757C23—734no—
758C23—1464no—
759C23—1464no—
760C23—1464no—
761C23—1462no—
762C23—1462no—
763C23C24×D7311yescharacteristic
764Q8—216no—
765Q8—28no—
766Q8—28no—
767Q8—14632no—
768Q8—14616no—
769Q8—14616no—
770Q8—1468no—
771D4—14616no—
772D4—1468no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—734no—
780C2×C4—734no—
781C2×C4—732no—
782C2×C4—732no—
783C2×C4—7316no—
784C2×C4—734no—
785C2×C4—734no—
786C2×C4—734no—
787C2×C4—732no—
788C2×C4—738no—
789C2×C4—14616no—
790C2×C4—14616no—
791C2×C4—1468no—
792C2×C4—14632no—
793C2×C4—1468no—
794C2×C4—1464no—
795C2×C4—1464no—
796C2×C4—1462no—
797C2×C4—1464no—
798C2×C4—14616no—
799C2×C4—1468no—
800C2×C4#41×D7314yes—
801C2×C4#1455663914yes—
802C2×C4C24×D7314yes—
803C2×C4C24×D7314yes—
804C2×C4C24×D7312yes—
805C2×C4C24×D7318yes—
806C2×C4C24×D7314yes—
807C2×C4C24×D7314yes—
808C2×C4C24×D7312yes—
809C2×C4C24×D7312yes—
810C22—2928no—
811C22—734no—
812C22—1464no—
813C22—1464no—
814C22—1464no—
815C22—1468no—
816C22—1462no—
817C22—1462no—
818C22C2×#41×D7312yes—
819C222−1+4×D7312yes—
820C22C2×#1455663912yes—
821C22C25×D7311yescharacteristic
822C4—24no—
823C4—28no—
824C4—24no—
825C4—22no—
826C4—24no—
827C4—24no—
828C4—734no—
829C4—734no—
830C4—1468no—
831C4—1464no—
832C4—1464no—
833C4—1462no—
834C4—1464no—
835C4C2×#41×D7314yes—
836C4C2×#1455663914yes—
837C2—2924no—
838C2—1464no—
839C2#2262381414yesdirect product factor
840C2C22×#41×D7311yescharacteristic
841C2C2×2−1+4×D7311yescharacteristic
842C2C22×#1455663911yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#557×C73C2
socleC23×C73C25
prime radicalC22×#11924029C22
hypercenterC2×#557D73
hypocenterC73C2×#3509
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22623814C2direct (N × H)
2. C2×#17989315C2semidirect
3. C2×#17989312C2semidirect
4. C2×#17989311C2semidirect
5. C2×#17989310C2semidirect
6. C2×#17989309C2semidirect
7. C2×#17989278C2semidirect
8. C2×#17989275C2semidirect
9. C2×#17989269C2semidirect
10. C2×#17989196C2semidirect
12. C2×#17989143C2semidirect
13. C2×#17989141C2semidirect
14. C2×#17989141C2semidirect
15. C2×C4⋊Q8×D73C2semidirect
16. C2×#17989063C2semidirect
18. C2×#557×C73C2semidirect
21. #17989315C22semidirect
22. #17989312C22semidirect
23. #17989311C22semidirect
24. #17989310C22semidirect
25. #17989309C22semidirect
26. #17989278C22semidirect
27. #17989275C22semidirect
28. #17989269C22semidirect
29. #17989196C22semidirect
31. #17989143C22semidirect
32. #17989141C22semidirect
33. #17989141C22semidirect
41. C4⋊Q8×D73C22semidirect
64. #17989063C22semidirect
92. #557×C73C22semidirect
416. C2×C73#3509semidirect
425. C2×#557D73semidirect
440. C73C2×#3509semidirect
445. #557C2×D73semidirect
839. C2#22623814direct (N × H)

Maximal subgroups

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

subgroupindex
#226238142
C2×#179893152
C2×#179893122
C2×#179893112
C2×#179893102
C2×#179893092
C2×#179892782
C2×#179892752
C2×#179892692
C2×#179891962
C2×#179891622
C2×#179891432
C2×#179891412
C2×C4⋊Q8×D732
C2×#179890632
C2×C4×#119240292
C2×#557×C732
C2×#350973