Finite Group Databasebeta

← C2×#22623745 #33994313

Subgroups — C2×#22623745 #33994313

Order 18688.

7478 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623745C2132yesmaximal, direct product factor
2C2×Q8×Dic146C211yesmaximal, characteristic, complemented
3C2×#17989317C211yesmaximal, characteristic, complemented
4C2×#17989314C212yesmaximal, complemented
5C2×#17989295C212yesmaximal, complemented
6C2×#17989294C211yesmaximal, characteristic, complemented
7C2×#17989292C212yesmaximal, complemented
8C2×D4×Dic146C212yesmaximal, complemented
9C2×#17989250C214yesmaximal, complemented
10C2×#17989217C212yesmaximal, complemented
11C2×#17989216C214yesmaximal, complemented
12C2×#17989141C211yesmaximal, characteristic, complemented
13C2×#17989139C212yesmaximal, complemented
14C22×#14556590C212yesmaximal, complemented
15C2×C4⋊Q8×D73C211yesmaximal, characteristic, complemented
16C2×#17989066C212yesmaximal
17C2×C4×#11924027C211yesmaximal, characteristic
18C2×#554×C73C211yesmaximal, characteristic, complemented
19C22×#11924027C2211yescharacteristic
20C23×Dic146C2214yes—
21C22×Q8×D73C2212yes—
22Q8×Dic146C22116yescomplemented
23#17989317C22116yescomplemented
24#17989314C22132yescomplemented
25#17989295C22132yescomplemented
26#17989294C22116yescomplemented
27#17989292C22132yescomplemented
28D4×Dic146C22132yescomplemented
29#17989250C22164yescomplemented
30#17989217C22132yescomplemented
31#17989216C22164yescomplemented
32#17989141C22116yescomplemented
33#17989139C22132yescomplemented
34C2×#14556591C2212yes—
35C2×#14556591C2211yescharacteristic
36C2×#14556590C2214yes—
37C2×#14556590C2212yes—
38C2×#14556590C2212yes—
39C2×#14556590C2212yes—
40C2×#14556590C2214yes—
41C2×#14556590C2212yes—
42C2×#14556590C2214yes—
43C2×#14556590C2212yes—
44C2×#14556590C2211yescharacteristic
45C2×#14556590C22132yescomplemented
46C2×#14556589C2214yes—
47C2×#14556589C2212yes—
48C2×#14556589C2211yescharacteristic
49C4⋊Q8×D73C22116yescomplemented
50C2×#14556582C2212yes—
51C2×#14556581C2214yes—
52C2×#14556581C2214yes—
53C2×#14556581C2212yes—
54C2×#14556581C2214yes—
55C2×#14556571C2214yes—
56C2×#14556571C2211yescharacteristic
57C2×#14556570C2214yes—
58C2×#14556570C2212yes—
59C2×#14556569C2214yes—
60C2×#14556569C2212yes—
61C2×#14556568C2214yes—
62C2×#14556568C2214yes—
63C2×#14556568C2214yes—
64C2×#14556567C2211yescharacteristic
65#17989066C22132yes—
66C4×#11924027C22116yes—
67C2×Q8×Dic73C2212yes—
68C2×C4×Dic146C2212yes—
69C2×C4×Dic146C2212yes—
70C2×C4×Dic146C2211yescharacteristic
71C2×C4×Dic146C2211yescharacteristic
72C2×#14556556C2211yescharacteristic
73C2×#14556556C2212yes—
74C2×#14556556C2214yes—
75C2×#14556556C2212yes—
76C2×D4×Dic73C2211yescharacteristic
77C2×D4×Dic73C2212yes—
78C2×C4×C22⋊D73C2212yes—
79C2×C4×C22⋊D73C2214yes—
80C2×#14556551C2212yes—
81C2×#14556551C2214yes—
82C2×#14556549C2211yescharacteristic
83C2×#14556548C2212yes—
84C2×#14556547C2212yes—
85C2×#14556547C2214yes—
86C22×C4⋊Dic73C2212yes—
87C22×#11924007C2214yes—
88C2×C4⋊C4×D73C2212yes—
89C2×C4⋊C4×D73C2212yes—
90C22×C4×Dic73C2212yes—
91C2×C42×D73C2211yescharacteristic
92#554×C73C22116yescomplemented
93C2×C4⋊Q8×C73C2211yescharacteristic
94C2×#125×C73C2212yes—
95C2×C22⋊Q8×C73C2214yes—
96C2×C22⋊Q8×C73C2212yes—
97C2×C4×Q8×C73C2211yescharacteristic
98C2×C4×D4×C73C2211yescharacteristic
99C2×C4×D4×C73C2212yes—
100C22×C4⋊C4×C73C2212yes—
101C2×#11924027Q8116yescomplemented
102C2×#11924027C2318yes—
103C22×Dic146—416no—
104C22×Dic146C2311yescharacteristic
105C22×Dic146C2314yes—
106C22×Dic146C2312yes—
107C22×Dic146C2314yes—
108C22×Dic146C2312yes—
109C22×Dic146C2314yes—
110C22×Dic146C23132yes—
111C22×Dic146C2311yescharacteristic
112C2×Q8×D73—48no—
113C2×Q8×D73C23116yes—
114C22×C22⋊D73C2312yes—
115C23×Dic73C2312yes—
116C23×Dic73C2314yes—
117C23×Dic73C2312yes—
118C22×C4×D73C2311yescharacteristic
119C22×C4×D73C2311yescharacteristic
120C22×C4×D73C2314yes—
121C22×C4×D73C2311yescharacteristic
122#14556591C2318yes—
123#14556591C23116yes—
124#14556590C23116yes—
125#14556590C23116yes—
126#14556590C2318yes—
127#14556590C23132yes—
128#14556590C23132yes—
129#14556590C23116yes—
130#14556590C23116yes—
131#14556590C23132yes—
132#14556590C23116yes—
133#14556589C23116yes—
134#14556589C2318yes—
135#14556589C23132yes—
136#14556582C23116yes—
137#14556581C23132yes—
138#14556581C23116yes—
139#14556581C23132yes—
140#14556581C23132yes—
141#14556571C2318yes—
142#14556571C23132yes—
143#14556570C23116yes—
144#14556570C23132yes—
145#14556569C23116yes—
146#14556569C23132yes—
147#14556568C23132yes—
148#14556568C23132yes—
149#14556568C23132yes—
150#14556567C2318yes—
151Q8×Dic73C23116yes—
152C4×Dic146C23116yes—
153C4×Dic146C2318yes—
154C4×Dic146C2318yes—
155C4×Dic146C23116yes—
156#14556556C23132yes—
157#14556556C23116yes—
158#14556556C2318yes—
159#14556556C23116yes—
160D4×Dic73C2318yes—
161D4×Dic73C23116yes—
162C4×C22⋊D73C23132yes—
163C4×C22⋊D73C23116yes—
164#14556551C23116yes—
165#14556551C23132yes—
166#14556549C2318yes—
167#14556548C23116yes—
168#14556547C23132yes—
169#14556547C23116yes—
170C2×C4⋊Dic73C2311yescharacteristic
171C2×C4⋊Dic73C2311yescharacteristic
172C2×C4⋊Dic73C2312yes—
173C2×C4⋊Dic73C2314yes—
174C2×C4⋊Dic73C2312yes—
175C2×C4⋊Dic73C2314yes—
176C2×C4⋊Dic73C23116yes—
177C2×C4⋊Dic73C2312yes—
178C2×#11924007C2312yes—
179C2×#11924007C2312yes—
180C2×#11924007C2314yes—
181C2×#11924007C2314yes—
182C2×#11924007C2314yes—
183C2×#11924007C2314yes—
184C2×#11924007C2312yes—
185C2×#11924007C2312yes—
186C2×#11924007C2312yes—
187C2×#11924007C2314yes—
188C2×#11924007C23132yes—
189C2×#11924007C2312yes—
190C2×#11924007C2314yes—
191C2×#11924007C2312yes—
192C4⋊C4×D73C23116yes—
193C4⋊C4×D73C23116yes—
194C2×C22⋊Dic73C2314yes—
195C2×C22⋊Dic73C2312yes—
196C2×#11924005C2312yes—
197C2×#11924005C2312yes—
198C2×#11924005C2312yes—
199C2×C4×Dic73C2311yescharacteristic
200C2×C4×Dic73C2311yescharacteristic
201C2×C4×Dic73C2314yes—
202C2×C4×Dic73C2311yescharacteristic
203C2×C4×Dic73C2312yes—
204C2×C4×Dic73C2312yes—
205C2×C4×Dic73C2312yes—
206C2×C4×Dic73C2314yes—
207C2×C4×Dic73C2312yes—
208C2×C4×Dic73C23116yes—
209C42×D73C2318yes—
210C22×Q8×C73C2311yescharacteristic
211C22×Q8×C73C2312yes—
212C22×D4×C73C2311yescharacteristic
213C23×C4×C73C2312yes—
214C23×C4×C73C2314yes—
215C4⋊Q8×C73C2318yes—
216#125×C73C23116yes—
217C22⋊Q8×C73C23116yes—
218C22⋊Q8×C73C23132yes—
219C4×Q8×C73C2318yes—
220C4×D4×C73C23116yes—
221C4×D4×C73C2318yes—
222C2×C4⋊C4×C73C2311yescharacteristic
223C2×C4⋊C4×C73C2314yes—
224C2×C4⋊C4×C73C2312yes—
225C2×C4⋊C4×C73C2312yes—
226C2×C4⋊C4×C73C2312yes—
227C2×C4⋊C4×C73C23116yes—
228C2×C4⋊C4×C73C2311yescharacteristic
229C2×C4⋊C4×C73C2314yes—
230C2×C22⋊C4×C73C2314yes—
231C2×C22⋊C4×C73C2312yes—
232C2×C42×C73C2312yes—
233C2×C42×C73C2311yescharacteristic
234C23×D73C2411yescharacteristic
235#11924027C2×Q8164yescomplemented
236C2×Dic146—24no—
237C2×Dic146—216no—
238C2×Dic146—28no—
239C2×Dic146—464no—
240C2×Dic146—44no—
241C2×Dic146—48no—
242C2×Dic146—48no—
243C2×Dic146C2×Q818yescomplemented
244C2×Dic146C2414yes—
245C2×Dic146C24116yes—
246C2×Dic146C2418yes—
247C2×Dic146C2418yes—
248C2×Dic146C24116yes—
249C2×Dic146C24116yes—
250C2×Dic146C2414yes—
251Q8×D73—432no—
252C2×C22⋊D73C2×Q8116yescomplemented
253C2×C22⋊D73C2418yes—
254C22×Dic73—28no—
255C22×Dic73—48no—
256C22×Dic73C2×Q8116yescomplemented
257C22×Dic73C2412yes—
258C22×Dic73C2412yes—
259C22×Dic73C2411yescharacteristic
260C22×Dic73C2418yes—
261C22×Dic73C2412yes—
262C22×Dic73C2414yes—
263C22×Dic73C24116yes—
264C22×Dic73C2412yes—
265C22×Dic73C2411yescharacteristic
266C22×Dic73C2418yes—
267C22×Dic73C2411yescharacteristic
268C2×C4×D73—24no—
269C2×C4×D73—24no—
270C2×C4×D73—48no—
271C2×C4×D73C2×Q818yescomplemented
272C2×C4×D73C2414yes—
273C2×C4×D73C2414yes—
274C2×C4×D73C24116yes—
275C2×C4×D73C2414yes—
276C4⋊Dic73C2418yes—
277C4⋊Dic73C2418yes—
278C4⋊Dic73C2414yes—
279C4⋊Dic73C24116yes—
280C4⋊Dic73C2414yes—
281C4⋊Dic73C2418yes—
282C4⋊Dic73C24116yes—
283#11924007C24116yes—
284#11924007C24116yes—
285#11924007C2418yes—
286#11924007C24116yes—
287#11924007C24116yes—
288#11924007C2418yes—
289#11924007C2418yes—
290#11924007C2418yes—
291#11924007C2418yes—
292#11924007C24116yes—
293#11924007C24116yes—
294#11924007C2418yes—
295#11924007C2418yes—
296C22⋊Dic73C24116yes—
297C22⋊Dic73C2418yes—
298#11924005C2418yes—
299#11924005C2418yes—
300#11924005C2418yes—
301C4×Dic73C2414yes—
302C4×Dic73C2414yes—
303C4×Dic73C2414yes—
304C4×Dic73C2418yes—
305C4×Dic73C2418yes—
306C4×Dic73C2418yes—
307C4×Dic73C24116yes—
308C4×Dic73C24116yes—
309C4×Dic73C2418yes—
310C24×C73C2412yes—
311C2×Q8×C73—24no—
312C2×Q8×C73—44no—
313C2×Q8×C73C2414yes—
314C2×Q8×C73C2418yes—
315C2×D4×C73C2×Q818yescomplemented
316C2×D4×C73C2414yes—
317C22×C4×C73—28no—
318C22×C4×C73—48no—
319C22×C4×C73C2412yes—
320C22×C4×C73C2411yescharacteristic
321C22×C4×C73C2412yes—
322C22×C4×C73C2412yes—
323C22×C4×C73C2414yes—
324C22×C4×C73C2418yes—
325C22×C4×C73C24116yes—
326C22×C4×C73C2411yescharacteristic
327C22×C4×C73C2411yescharacteristic
328C4⋊C4×C73C2414yes—
329C4⋊C4×C73C24116yes—
330C4⋊C4×C73C2418yes—
331C4⋊C4×C73C2414yes—
332C4⋊C4×C73C2418yes—
333C4⋊C4×C73C2418yes—
334C4⋊C4×C73C24116yes—
335C22⋊C4×C73C24116yes—
336C22⋊C4×C73C2418yes—
337C42×C73C2418yes—
338C42×C73C2414yes—
339C23×C73—24no—
340C23×C73—24no—
341C23×C73C22×Q818yes—
342C23×C73C2514yes—
343C23×C73C2511yescharacteristic
344C22×D73—22no—
345C22×D73—22no—
346C22×D73C22×Q814yes—
347C22×D73C2512yes—
348Q8×C73—28no—
349Q8×C73—48no—
350D4×C73C22×Q8116yescomplemented
351C2×C4×C73—24no—
352C2×C4×C73—28no—
353C2×C4×C73—22no—
354C2×C4×C73—24no—
355C2×C4×C73—24no—
356C2×C4×C73—216no—
357C2×C4×C73—416no—
358C2×C4×C73C22×Q814yes—
359C2×C4×C732−1+414yes—
360C2×C4×C73C2514yes—
361C2×C4×C73C2512yes—
362C2×C4×C73C2514yes—
363C2×C4×C73C2514yes—
364C2×C4×C73C2518yes—
365C2×C4×C73C2512yes—
366C2×C4×C73C2512yes—
367C22⋊D73C22×Q8132yescomplemented
368C2×Dic73—28no—
369C2×Dic73—24no—
370C2×Dic73—24no—
371C2×Dic73—22no—
372C2×Dic73—24no—
373C2×Dic73—216no—
374C2×Dic73—416no—
375C2×Dic73C22×Q814yes—
376C2×Dic73C22×Q818yes—
377C2×Dic73C22×Q8132yescomplemented
378C2×Dic73H(5,𝔽2)14yes—
379C2×Dic73C2514yes—
380C2×Dic73C2514yes—
381C2×Dic73C2512yes—
382C2×Dic73C2514yes—
383C2×Dic73C2518yes—
384C2×Dic73C2514yes—
385C2×Dic73C2512yes—
386C2×Dic73C2512yes—
387C4×D73—28no—
388C4×D73—28no—
389C4×D73—416no—
390C4×D73C22×Q8116yescomplemented
391Dic146—28no—
392Dic146—232no—
393Dic146—216no—
394Dic146—48no—
395Dic146—416no—
396Dic146—416no—
397Dic146C22×Q8116yescomplemented
398C22×C73—24no—
399C22×C73—24no—
400C22×C73—216no—
401C22×C73C23×Q818yes—
402C22×C73C23×Q812yes—
403C22×C73C2×H(5,𝔽2)12yes—
404C22×C73C2×2−1+412yes—
405C22×C73C2611yescharacteristic
406C2×D73—22no—
407C2×D73—22no—
408C2×D73—28no—
409C2×D73C23×Q814yes—
410C4×C73—24no—
411C4×C73—28no—
412C4×C73—22no—
413C4×C73—24no—
414C4×C73—24no—
415C4×C73C23×Q814yes—
416C4×C73C2×2−1+414yes—
417Dic73—28no—
418Dic73—24no—
419Dic73—24no—
420Dic73—24no—
421Dic73—22no—
422Dic73C23×Q818yes—
423Dic73C23×Q814yes—
424Dic73C2×H(5,𝔽2)14yes—
425C2×#3503—731nomaximal, Sylow
426C2×C73—28no—
427C2×C73#350314yescomplemented
428C2×C73C24×Q811yescharacteristic
429C2×C73C22×H(5,𝔽2)11yescharacteristic
430C2×C73C22×2−1+411yescharacteristic
431D73—24no—
432#3503—7332no—
433C2×Q82—731no—
434C2×Q82—731no—
435C2×#557—732no—
436C2×#554—732no—
437C2×#554—731no—
438C2×#554—732no—
439C2×#554D7311yescharacteristic, complemented
440C2×D4×Q8—734no—
441C2×D4×Q8—732no—
442C2×#544—732no—
443C2×#544—734no—
444C2×#533—732no—
445C2×#533—731no—
446C22×C4⋊Q8—731no—
447C22×C4⋊Q8—732no—
448C2×#520—732no—
449C2×C4×#41—731no—
450C73C2×#350311yescharacteristic, complemented, Sylow
451C22×#41—731no—
452C23×Q8—732no—
453C23×Q8—734no—
454Q82—7316no—
455Q82—7316no—
456#557—7332no—
457#554—7332no—
458#554—7316no—
459#554—7332no—
460#554C2×D73116yescomplemented
461D4×Q8—7364no—
462D4×Q8—7332no—
463#544—7332no—
464#544—7364no—
465#533—7332no—
466#533—7316no—
467C2×C4⋊Q8—732no—
468C2×C4⋊Q8—731no—
469C2×C4⋊Q8—734no—
470C2×C4⋊Q8—7316no—
471C2×C4⋊Q8—732no—
472C2×C4⋊Q8—731no—
473C2×C4⋊Q8—734no—
474C2×C4⋊Q8—734no—
475C2×C4⋊Q8—732no—
476C2×C4⋊Q8—732no—
477C2×C4⋊Q8—732no—
478C2×C4⋊Q8—734no—
479C2×C4⋊Q8—732no—
480C2×C4⋊Q8—7332no—
481C2×C4⋊Q8—731no—
482C2×C4⋊Q8—732no—
483C2×C4⋊Q8C2×D7311yescharacteristic
484C2×#125—732no—
485C2×#125—734no—
486C2×#125—734no—
487C2×#125—734no—
488C2×#125—732no—
489C2×#125C2×D7312yes—
490C2×C22⋊Q8—731no—
491C2×C22⋊Q8—732no—
492C2×C22⋊Q8—734no—
493C2×C22⋊Q8—732no—
494C2×C22⋊Q8—731no—
495C2×C22⋊Q8—734no—
496C2×C22⋊Q8—734no—
497C2×C22⋊Q8—734no—
498C2×C22⋊Q8—734no—
499C2×C22⋊Q8—734no—
500C2×C22⋊Q8C2×D7312yes—
501C2×C22⋊Q8C2×D7314yes—
502#520—7332no—
503C4×#41—7316no—
504C2×C4×Q8—732no—
505C2×C4×Q8—731no—
506C2×C4×Q8—732no—
507C2×C4×Q8—734no—
508C2×C4×Q8—732no—
509C2×C4×Q8—731no—
510C2×C4×Q8—732no—
511C2×C4×Q8—732no—
512C2×C4×Q8—731no—
513C2×C4×Q8C2×D7311yescharacteristic
514C2×C4×D4—731no—
515C2×C4×D4—732no—
516C2×C4×D4—732no—
517C2×C4×D4—734no—
518C2×C4×D4—732no—
519C2×C4×D4—734no—
520C2×C4×D4C2×D7311yescharacteristic
521C2×C4×D4C2×D7312yes—
522C2×#117—731no—
523C2×#117—732no—
524C2×#117—734no—
525C2×#117—732no—
526C22×C4⋊C4—734no—
527C22×C4⋊C4—732no—
528C22×C4⋊C4—732no—
529C22×C4⋊C4—732no—
530C22×C4⋊C4C2×D7312yes—
531C22×C42—732no—
532C22×C42—731no—
533C2×#41—7316no—
534C2×#41—738no—
535C22×Q8—29216no—
536C22×Q8—2928no—
537C22×Q8—7316no—
538C22×Q8—734no—
539C22×Q8—734no—
540C22×Q8—732no—
541C22×Q8—7332no—
542C22×Q8—731no—
543C22×Q8—731no—
544C22×Q8—734no—
545C22×Q8—732no—
546C22×Q8C22×D7311yescharacteristic
547C22×Q8C22×D7312yes—
548C22×D4—732no—
549C22×D4C22×D7311yescharacteristic
550C23×C4—734no—
551C23×C4—734no—
552C23×C4—732no—
553C23×C4—731no—
554C23×C4—732no—
555C23×C4—731no—
556C23×C4—731no—
557C23×C4C22×D7312yes—
558C23×C4C22×D7314yes—
559C4⋊Q8—7316no—
560C4⋊Q8—738no—
561C4⋊Q8—7332no—
562C4⋊Q8—7316no—
563C4⋊Q8—738no—
564C4⋊Q8—7332no—
565C4⋊Q8—7332no—
566C4⋊Q8—7316no—
567C4⋊Q8—7316no—
568C4⋊Q8—7316no—
569C4⋊Q8—7332no—
570C4⋊Q8—7316no—
571C4⋊Q8—738no—
572C4⋊Q8—7316no—
573C4⋊Q8C22×D7318yes—
574#125—7316no—
575#125—7332no—
576#125—7332no—
577#125—7332no—
578#125—7316no—
579#125C22×D73116yes—
580C22⋊Q8—738no—
581C22⋊Q8—7316no—
582C22⋊Q8—7332no—
583C22⋊Q8—7316no—
584C22⋊Q8—738no—
585C22⋊Q8—7332no—
586C22⋊Q8—7332no—
587C22⋊Q8—7332no—
588C22⋊Q8—7332no—
589C22⋊Q8—7332no—
590C22⋊Q8C22×D73116yes—
591C22⋊Q8C22×D73132yes—
592C4×Q8—7316no—
593C4×Q8—738no—
594C4×Q8—7316no—
595C4×Q8—7332no—
596C4×Q8—7316no—
597C4×Q8—738no—
598C4×Q8—7316no—
599C4×Q8—7316no—
600C4×Q8—738no—
601C4×Q8C22×D7318yes—
602C4×D4—738no—
603C4×D4—7316no—
604C4×D4—7316no—
605C4×D4—7332no—
606C4×D4—7316no—
607C4×D4—7332no—
608C4×D4C22×D7318yes—
609C4×D4C22×D73116yes—
610#117—738no—
611#117—7316no—
612#117—7332no—
613#117—7316no—
614C2×C4⋊C4—734no—
615C2×C4⋊C4—732no—
616C2×C4⋊C4—731no—
617C2×C4⋊C4—732no—
618C2×C4⋊C4—734no—
619C2×C4⋊C4—734no—
620C2×C4⋊C4—732no—
621C2×C4⋊C4—7332no—
622C2×C4⋊C4—734no—
623C2×C4⋊C4—734no—
624C2×C4⋊C4—7316no—
625C2×C4⋊C4—732no—
626C2×C4⋊C4—732no—
627C2×C4⋊C4—732no—
628C2×C4⋊C4—731no—
629C2×C4⋊C4—732no—
630C2×C4⋊C4—734no—
631C2×C4⋊C4—732no—
632C2×C4⋊C4—732no—
633C2×C4⋊C4—734no—
634C2×C4⋊C4—732no—
635C2×C4⋊C4—734no—
636C2×C4⋊C4—7316no—
637C2×C4⋊C4—7316no—
638C2×C4⋊C4C22×D7312yes—
639C2×C4⋊C4C22×D7312yes—
640C2×C4⋊C4C22×D7311yescharacteristic
641C2×C4⋊C4C22×D7314yes—
642C2×C4⋊C4C22×D73116yes—
643C2×C4⋊C4C22×D7311yescharacteristic
644C2×C4⋊C4C22×D7314yes—
645C2×C4⋊C4C22×D7312yes—
646C2×C22⋊C4—734no—
647C2×C22⋊C4—732no—
648C2×C22⋊C4—732no—
649C2×C22⋊C4—732no—
650C2×C22⋊C4—732no—
651C2×C22⋊C4C22×D7314yes—
652C2×C22⋊C4C22×D7312yes—
653C2×C42—731no—
654C2×C42—732no—
655C2×C42—734no—
656C2×C42—734no—
657C2×C42—732no—
658C2×C42—732no—
659C2×C42—732no—
660C2×C42—731no—
661C2×C42—7316no—
662C2×C42—731no—
663C2×C42—738no—
664C2×C42C22×D7312yes—
665C2×C42C22×D7311yescharacteristic
666C24—731no—
667C24C23×D7312yes—
668#41—7364no—
669C2×Q8—24no—
670C2×Q8—44no—
671C2×Q8—2928no—
672C2×Q8—2928no—
673C2×Q8—2924no—
674C2×Q8—29264no—
675C2×Q8—29232no—
676C2×Q8—738no—
677C2×Q8—7316no—
678C2×Q8—7316no—
679C2×Q8—738no—
680C2×Q8—734no—
681C2×Q8—734no—
682C2×Q8—7316no—
683C2×Q8—738no—
684C2×Q8—1468no—
685C2×Q8—14616no—
686C2×Q8—1464no—
687C2×Q8C23×D7314yes—
688C2×Q8C23×D7318yes—
689C2×D4—7316no—
690C2×D4—738no—
691C2×D4Q8×D7318yescomplemented
692C2×D4C23×D7314yes—
693C22×C4—28no—
694C22×C4—48no—
695C22×C4—2928no—
696C22×C4—2928no—
697C22×C4—7316no—
698C22×C4—7316no—
699C22×C4—7316no—
700C22×C4—738no—
701C22×C4—732no—
702C22×C4—731no—
703C22×C4—731no—
704C22×C4—738no—
705C22×C4—734no—
706C22×C4—738no—
707C22×C4—732no—
708C22×C4—731no—
709C22×C4—732no—
710C22×C4—732no—
711C22×C4—734no—
712C22×C4—734no—
713C22×C4—734no—
714C22×C4—1464no—
715C22×C4—1468no—
716C22×C4—1464no—
717C22×C4C23×D7318yes—
718C22×C4C23×D7312yes—
719C22×C4C23×D7312yes—
720C22×C4C23×D7311yescharacteristic
721C22×C4C23×D7314yes—
722C22×C4C23×D7312yes—
723C22×C4C23×D73116yes—
724C22×C4C23×D7311yescharacteristic
725C22×C4C23×D7311yescharacteristic
726C4⋊C4—7316no—
727C4⋊C4—738no—
728C4⋊C4—7316no—
729C4⋊C4—7316no—
730C4⋊C4—7316no—
731C4⋊C4—738no—
732C4⋊C4—738no—
733C4⋊C4—738no—
734C4⋊C4—738no—
735C4⋊C4—7316no—
736C4⋊C4—738no—
737C4⋊C4—7316no—
738C4⋊C4—738no—
739C4⋊C4—738no—
740C4⋊C4—734no—
741C4⋊C4—738no—
742C4⋊C4—7316no—
743C4⋊C4—734no—
744C4⋊C4—738no—
745C4⋊C4—7316no—
746C4⋊C4C23×D7318yes—
747C4⋊C4C23×D7318yes—
748C4⋊C4C23×D7314yes—
749C4⋊C4C23×D73116yes—
750C4⋊C4C23×D7314yes—
751C4⋊C4C23×D73116yes—
752C4⋊C4C23×D7318yes—
753C22⋊C4—7316no—
754C22⋊C4—738no—
755C22⋊C4—738no—
756C22⋊C4—738no—
757C22⋊C4—738no—
758C22⋊C4C23×D73116yes—
759C22⋊C4C23×D7318yes—
760C42—734no—
761C42—734no—
762C42—738no—
763C42—738no—
764C42—738no—
765C42—734no—
766C42—7316no—
767C42—7316no—
768C42—738no—
769C42C23×D7314yes—
770C42C23×D7318yes—
771C23—24no—
772C23—24no—
773C23—734no—
774C23—732no—
775C23—1462no—
776C23—1462no—
777C23C2×Q8×D7318yes—
778C23C24×D7314yes—
779C23C24×D7311yescharacteristic
780Q8—28no—
781Q8—48no—
782Q8—29216no—
783Q8—29216no—
784Q8—2928no—
785Q8—7316no—
786Q8—14616no—
787Q8—14632no—
788Q8—1468no—
789D4—7332no—
790D4C2×Q8×D73116yescomplemented
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—216no—
797C2×C4—416no—
798C2×C4—29216no—
799C2×C4—29216no—
800C2×C4—734no—
801C2×C4—738no—
802C2×C4—7332no—
803C2×C4—734no—
804C2×C4—734no—
805C2×C4—732no—
806C2×C4—732no—
807C2×C4—7316no—
808C2×C4—734no—
809C2×C4—732no—
810C2×C4—734no—
811C2×C4—738no—
812C2×C4—734no—
813C2×C4—1468no—
814C2×C4—14616no—
815C2×C4—1468no—
816C2×C4—1464no—
817C2×C4—1464no—
818C2×C4—1462no—
819C2×C4—1464no—
820C2×C4—1468no—
821C2×C4C2×Q8×D7314yes—
822C2×C4#1455663814yes—
823C2×C4C24×D7314yes—
824C2×C4C24×D7314yes—
825C2×C4C24×D7312yes—
826C2×C4C24×D7318yes—
827C2×C4C24×D7314yes—
828C2×C4C24×D7312yes—
829C2×C4C24×D7312yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—734no—
834C22—1468no—
835C22—1462no—
836C22—1462no—
837C22C22×Q8×D7318yes—
838C22C22×Q8×D7312yes—
839C22H(5,𝔽2)×D7312yes—
840C22C2×#1455663812yes—
841C22C25×D7311yescharacteristic
842C4—24no—
843C4—28no—
844C4—22no—
845C4—24no—
846C4—24no—
847C4—734no—
848C4—738no—
849C4—734no—
850C4—1468no—
851C4—1464no—
852C4—1464no—
853C4—1462no—
854C4—1464no—
855C4C22×Q8×D7314yes—
856C4C2×#1455663814yes—
857C2—28no—
858C2—1464no—
859C2#2262374514yesdirect product factor
860C2C23×Q8×D7311yescharacteristic
861C2C2×H(5,𝔽2)×D7311yescharacteristic
862C2C22×#1455663811yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#554×C73C2
socleC23×C73C25
prime radicalC22×#11924027C22
hypercenterC2×#554D73
hypocenterC73C2×#3503
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #22623745C2direct (N × H)
2. C2×Q8×Dic146C2semidirect
3. C2×#17989317C2semidirect
4. C2×#17989314C2semidirect
5. C2×#17989295C2semidirect
6. C2×#17989294C2semidirect
7. C2×#17989292C2semidirect
8. C2×D4×Dic146C2semidirect
9. C2×#17989250C2semidirect
10. C2×#17989217C2semidirect
11. C2×#17989216C2semidirect
12. C2×#17989141C2semidirect
13. C2×#17989139C2semidirect
14. C22×#14556590C2semidirect
15. C2×C4⋊Q8×D73C2semidirect
18. C2×#554×C73C2semidirect
22. Q8×Dic146C22semidirect
23. #17989317C22semidirect
24. #17989314C22semidirect
25. #17989295C22semidirect
26. #17989294C22semidirect
27. #17989292C22semidirect
28. D4×Dic146C22semidirect
29. #17989250C22semidirect
30. #17989217C22semidirect
31. #17989216C22semidirect
32. #17989141C22semidirect
33. #17989139C22semidirect
45. C2×#14556590C22semidirect
49. C4⋊Q8×D73C22semidirect
92. #554×C73C22semidirect
101. C2×#11924027Q8semidirect
235. #11924027C2×Q8semidirect
243. C2×Dic146C2×Q8semidirect
252. C2×C22⋊D73C2×Q8semidirect
256. C22×Dic73C2×Q8semidirect
271. C2×C4×D73C2×Q8semidirect
315. C2×D4×C73C2×Q8semidirect
350. D4×C73C22×Q8semidirect
367. C22⋊D73C22×Q8semidirect
377. C2×Dic73C22×Q8semidirect
390. C4×D73C22×Q8semidirect
397. Dic146C22×Q8semidirect
427. C2×C73#3503semidirect
439. C2×#554D73semidirect
450. C73C2×#3503semidirect
460. #554C2×D73semidirect
691. C2×D4Q8×D73semidirect
790. D4C2×Q8×D73semidirect
859. C2#22623745direct (N × H)

Maximal subgroups

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

subgroupindex
#226237452
C2×Q8×Dic1462
C2×#179893172
C2×#179893142
C2×#179892952
C2×#179892942
C2×#179892922
C2×D4×Dic1462
C2×#179892502
C2×#179892172
C2×#179892162
C2×#179891412
C2×#179891392
C22×#145565902
C2×C4⋊Q8×D732
C2×#179890662
C2×C4×#119240272
C2×#554×C732
C2×#350373