Finite Group Databasebeta

← #33101554

Subgroups — #33101554

Order 18688.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988659C211yesmaximal, characteristic
2C2×#17988596C211yesmaximal, characteristic, complemented
3C22×#14556515C211yesmaximal, characteristic, complemented
4#22612860C211yesmaximal, characteristic
5#22610855C211yesmaximal, characteristic, complemented
6#22610752C211yesmaximal, characteristic, complemented
7#22610365C211yesmaximal, characteristic, complemented
8#22610355C211yesmaximal, characteristic, complemented
9#22610244C211yesmaximal, characteristic, complemented
10#22610239C211yesmaximal, characteristic, complemented
11#22609946C211yesmaximal, characteristic, complemented
12#22609866C211yesmaximal, characteristic, complemented
13#22609866C211yesmaximal, characteristic, complemented
14#22609761C211yesmaximal, characteristic, complemented
15C2×D4×Q8×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×#14556550C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20#17988659—24no—
21C2×C4⋊#10596831C2211yescharacteristic
22#17988596—24no—
23C2×#14556515—24no—
24C2×#14556515C2211yescharacteristic
25C2×#14556515C2211yescharacteristic
26C2×#14556515C2211yescharacteristic
27C2×#14556515C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556515C2211yescharacteristic
30C2×#14556515C2211yescharacteristic
31C2×#14556515C2211yescharacteristic
32C2×#14556515C2211yescharacteristic
33C2×#14556515C2211yescharacteristic
34C2×#14556515C2211yescharacteristic
35C2×#14556515C2211yescharacteristic
36C2×C22⋊#10596831C2211yescharacteristic
37C2×C22⋊#10596831C2211yescharacteristic
38C2×#14556502C2211yescharacteristic
39#17988480—21no—
40#17988473—21no—
41#17988467—21no—
42#17988453C2211yescharacteristic
43#17988447C2211yescharacteristic
44#17988447C2211yescharacteristic
45C4×C4⋊Dic73C2211yescharacteristic
46C22⋊C4×Dic73—21no—
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51C23×Q8×C73C2211yescharacteristic
52C23×Q8×C73C2211yescharacteristic
53D4×Q8×C73—24no—
54D4×Q8×C73C418yescomplemented
55C2×C4⋊Q8×C73—21no—
56C2×C4⋊Q8×C73C2211yescharacteristic
57C2×C22⋊Q8×C73—21no—
58C2×C22⋊Q8×C73—21no—
59C2×C22⋊Q8×C73C2211yescharacteristic
60C2×C22⋊Q8×C73C2211yescharacteristic
61C2×C4×Q8×C73C2211yescharacteristic
62C2×C4×D4×C73—21no—
63C2×C4×D4×C73C2211yescharacteristic
64C23×Dic73—21no—
65C2×#11924012—22no—
66C2×#11924012—22no—
67C2×#11924012—41no—
68C22×#10596831—22no—
69C22×#10596831—22no—
70C22×#10596831—41no—
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75#14556550—22no—
76#14556550—41no—
77C2×C4⋊Dic73—22no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73—41no—
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C22⋊Dic73—21no—
85C2×C22⋊Dic73—21no—
86C2×C22⋊Dic73—21no—
87C2×C4×Dic73—21no—
88C2×C4×Dic73—21no—
89C4⋊#10596831—22no—
90#14556515—22no—
91#14556515—22no—
92#14556515—22no—
93#14556515—22no—
94#14556515—22no—
95#14556515—22no—
96#14556515—22no—
97#14556515—41no—
98#14556515—41no—
99#14556515—41no—
100#14556515—41no—
101#14556515D414yescomplemented
102C22⋊#10596831—22no—
103C22⋊#10596831—22no—
104#14556502—22no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110C22×Q8×C73—21no—
111C22×Q8×C73—21no—
112C22×Q8×C73—22no—
113C22×Q8×C73—22no—
114C22×Q8×C73—22no—
115C22×Q8×C73—22no—
116C22×Q8×C73—22no—
117C22×Q8×C73—22no—
118C22×Q8×C73—41no—
119C22×Q8×C73—41no—
120C22×Q8×C73—41no—
121C22×Q8×C73—41no—
122C22×Q8×C73C2×C414yes—
123C22×Q8×C73C2×C414yescomplemented
124C22×Q8×C73C2311yescharacteristic
125C22×Q8×C73C2311yescharacteristic
126C22×Q8×C73C2311yescharacteristic
127C22×D4×C73D411yescharacteristic
128C23×C4×C73—21no—
129C23×C4×C73—21no—
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C4⋊Q8×C73—28no—
133C4⋊Q8×C73—22no—
134C4⋊Q8×C73C2×C414yescomplemented
135C22⋊Q8×C73—22no—
136C22⋊Q8×C73—22no—
137C22⋊Q8×C73—28no—
138C22⋊Q8×C73—28no—
139C22⋊Q8×C73C2×C414yes—
140C22⋊Q8×C73C2×C414yescomplemented
141C4×Q8×C73—22no—
142C4×Q8×C73C2×C414yescomplemented
143C4×D4×C73—28no—
144C4×D4×C73C2×C414yes—
145C4×D4×C73D414yes—
146C2×C4⋊C4×C73—21no—
147C2×C4⋊C4×C73—21no—
148C2×C4⋊C4×C73—21no—
149C2×C4⋊C4×C73—21no—
150C2×C4⋊C4×C73—21no—
151C2×C4⋊C4×C73D411yescharacteristic
152C2×C4⋊C4×C73C2311yescharacteristic
153C2×C22⋊C4×C73—21no—
154C2×C22⋊C4×C73—21no—
155C2×C22⋊C4×C73D411yescharacteristic
156C2×C22⋊C4×C73D411yescharacteristic
157C2×C42×C73—21no—
158C2×C42×C73C2311yescharacteristic
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C22×Dic73—42no—
164C22×Dic73—42no—
165C22×Dic73—81no—
166#11924012—44no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—44no—
179C2×#10596831C2×D412yes—
180C4⋊Dic73—21no—
181C4⋊Dic73—21no—
182C4⋊Dic73—21no—
183C4⋊Dic73—21no—
184C4⋊Dic73—21no—
185C4⋊Dic73—21no—
186C4⋊Dic73—21no—
187C4⋊Dic73—42no—
188C4⋊Dic73C2×D412yes—
189C22⋊Dic73—42no—
190C22⋊Dic73—42no—
191C22⋊Dic73—81no—
192C4×Dic73—42no—
193C4×Dic73—81no—
194C24×C73C2×D411yescharacteristic
195C24×C73C2×D411yescharacteristic
196C2×Q8×C73—24no—
197C2×Q8×C73—24no—
198C2×Q8×C73—21no—
199C2×Q8×C73—21no—
200C2×Q8×C73—21no—
201C2×Q8×C73—21no—
202C2×Q8×C73—21no—
203C2×Q8×C73—28no—
204C2×Q8×C73—28no—
205C2×Q8×C73—21no—
206C2×Q8×C73—21no—
207C2×Q8×C73—21no—
208C2×Q8×C73—21no—
209C2×Q8×C73—21no—
210C2×Q8×C73—21no—
211C2×Q8×C73—21no—
212C2×Q8×C73—21no—
213C2×Q8×C73—42no—
214C2×Q8×C73—42no—
215C2×Q8×C73—42no—
216C2×Q8×C73—42no—
217C2×Q8×C73—44no—
218C2×Q8×C73—44no—
219C2×Q8×C73—44no—
220C2×Q8×C73—44no—
221C2×Q8×C73—44no—
222C2×Q8×C73—44no—
223C2×Q8×C73C22×C412yes—
224C2×Q8×C73C22×C412yes—
225C2×Q8×C73C22×C412yes—
226C2×Q8×C73C2×D412yes—
227C2×Q8×C73#4112yes—
228C2×D4×C73—22no—
229C2×D4×C73—22no—
230C2×D4×C73C22⋊C414yes—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—24no—
241C22×C4×C73—24no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—42no—
246C22×C4×C73—42no—
247C22×C4×C73—42no—
248C22×C4×C73—42no—
249C22×C4×C73C22×C412yes—
250C22×C4×C73C22×C412yes—
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2×D411yescharacteristic
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2×D412yes—
256C22×C4×C73C2×D412yes—
257C22×C4×C73C2411yescharacteristic
258C4⋊C4×C73—24no—
259C4⋊C4×C73—24no—
260C4⋊C4×C73—24no—
261C4⋊C4×C73—24no—
262C4⋊C4×C73—24no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73C22⋊C414yes—
265C4⋊C4×C73C22×C412yes—
266C22⋊C4×C73—24no—
267C22⋊C4×C73—24no—
268C22⋊C4×C73C22⋊C414yes—
269C22⋊C4×C73C22⋊C414yes—
270C42×C73—24no—
271C42×C73C22×C412yes—
272C42×C73C2×D412yes—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—21no—
281C23×C73—21no—
282C23×C73—21no—
283C23×C73C2×C22⋊C412yes—
284C23×C73C2×C22⋊C412yes—
285C23×C73#13712yes—
286C23×C73#13712yes—
287C23×C73C22×D411yescharacteristic
288Q8×C73—22no—
289Q8×C73—22no—
290Q8×C73—22no—
291Q8×C73—22no—
292Q8×C73—22no—
293Q8×C73—22no—
294Q8×C73—22no—
295Q8×C73—48no—
296Q8×C73—48no—
297Q8×C73—41no—
298Q8×C73—41no—
299Q8×C73—41no—
300Q8×C73—41no—
301Q8×C73C4×D414yes—
302D4×C73—28no—
303C2×C4×C73—22no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—22no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—22no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—48no—
326C2×C4×C73—48no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73C2×C22⋊C412yes—
334C2×C4×C73C2×C22⋊C412yes—
335C2×C4×C73C2×C22⋊C412yes—
336C2×C4×C73C2×C22⋊C412yes—
337C2×C4×C73C23×C411yescharacteristic
338C2×C4×C73C22×D411yescharacteristic
339C2×C4×C73C22×D411yescharacteristic
340C2×C4×C73C2×#4111yescharacteristic
341C2×C4×C73H(5,𝔽2)11yescharacteristic
342C2×C4×C73H(5,𝔽2)11yescharacteristic
343C2×Dic73—22no—
344C2×Dic73—41no—
345C2×Dic73—41no—
346C2×Dic73—41no—
347C2×Dic73—41no—
348C2×Dic73—41no—
349C2×Dic73—41no—
350C2×Dic73—41no—
351C2×Dic73—41no—
352C2×Dic73—41no—
353C2×Dic73—41no—
354C2×Dic73—41no—
355C2×Dic73—84no—
356#10596831—22no—
357#10596831—41no—
358#10596831—41no—
359#10596831—41no—
360C22×C73—22no—
361C22×C73—22no—
362C22×C73—22no—
363C22×C73—22no—
364C22×C73—22no—
365C22×C73—22no—
366C22×C73—22no—
367C22×C73—22no—
368C22×C73—22no—
369C22×C73—41no—
370C22×C73—41no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73#41914yescomplemented
374C22×C73C22×C22⋊C411yescharacteristic
375C22×C73D4211yescharacteristic
376C22×C73#54611yescharacteristic
377C22×C73C2×#13711yescharacteristic
378C22×C73C2×#13711yescharacteristic
379C22×C73#57711yescharacteristic
380C22×C73#57811yescharacteristic
381C4×C73—22no—
382C4×C73—22no—
383C4×C73—24no—
384C4×C73—22no—
385C4×C73—22no—
386C4×C73—42no—
387C4×C73—42no—
388C4×C73—42no—
389C4×C73C2×C4×D411yescharacteristic
390C4×C73#51811yescharacteristic
391C4×C73D4211yescharacteristic
392C4×C73#54611yescharacteristic
393Dic73—42no—
394Dic73—81no—
395Dic73—81no—
396Dic73—81no—
397#22425—731nomaximal, Sylow
398C2×C73—24no—
399C2×C73—42no—
400C2×C73D4×C22⋊C411yescharacteristic
401C2×C73C2×#41911yescharacteristic
402C2×C73#289811yescharacteristic
403C2×C73#326611yescharacteristic
404C2×C73#327011yescharacteristic
405C2×C73#331211yescharacteristic
406C2×C73#332011yescharacteristic
407C2×D4×Q8D7311yescharacteristic
408C2×#435—731no—
409C2×#419—731no—
410C22×#103—731no—
411#2352—731no—
412#1981—731no—
413#1960—731no—
414#1894—731no—
415#1892—731no—
416#1873—731no—
417#1872—731no—
418#1805—731no—
419#1787—731no—
420#1787—731no—
421#1763—731no—
422C73#2242511yescharacteristic, complemented, Sylow
423C23×Q8C2×D7311yescharacteristic
424C23×Q8C2×D7311yescharacteristic
425C22×M16—731no—
426C23×C8—731no—
427D4×Q8—24no—
428D4×Q8Dic7318yescomplemented
429C2×C4⋊Q8—21no—
430C2×C4⋊Q8C2×D7311yescharacteristic
431C2×C22⋊Q8—21no—
432C2×C22⋊Q8—21no—
433C2×C22⋊Q8C2×D7311yescharacteristic
434C2×C22⋊Q8C2×D7311yescharacteristic
435C2×C4×Q8C2×D7311yescharacteristic
436C2×C4×D4—21no—
437C2×C4×D4C2×D7311yescharacteristic
438C2×#117—731no—
439C22×C4⋊C4—731no—
440#435—1464no—
441C2×C4⋊C8—731no—
442#419—1464no—
443C2×#103—731no—
444C2×#103—731no—
445C2×#103—731no—
446C2×#103—731no—
447C2×#103—731no—
448C2×#103—731no—
449C2×#103—731no—
450C2×#103—731no—
451C2×#103—731no—
452C2×#103—731no—
453C2×#103—731no—
454C2×#103—731no—
455C2×#103—1464no—
456C2×C22⋊C8—731no—
457C2×C22⋊C8—731no—
458C2×#97—731no—
459#388—1461no—
460#387—1461no—
461#386—1461no—
462#382—731no—
463#380—731no—
464#380—731no—
465C4×C4⋊C4—731no—
466C4×C22⋊C4—1461no—
467#340—731no—
468#340—731no—
469#340—731no—
470#340—731no—
471C22×Q8—21no—
472C22×Q8—21no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8—22no—
477C22×Q8—22no—
478C22×Q8—22no—
479C22×Q8—41no—
480C22×Q8—41no—
481C22×Q8—41no—
482C22×Q8—41no—
483C22×Q8C2×Dic7314yes—
484C22×Q8C2×Dic7314yescomplemented
485C22×Q8C22×D7311yescharacteristic
486C22×Q8C22×D7311yescharacteristic
487C22×Q8C22×D7311yescharacteristic
488C22×D4C22⋊D7311yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—1461no—
492C23×C4C22×D7311yescharacteristic
493C23×C4C22×D7311yescharacteristic
494C2×M16—2921no—
495C2×M16—1462no—
496C2×M16—1462no—
497C22×C8—2921no—
498C22×C8—731no—
499C22×C8—731no—
500C22×C8—731no—
501C22×C8—731no—
502C22×C8—1462no—
503C22×C8—1462no—
504C4⋊Q8—28no—
505C4⋊Q8—22no—
506C4⋊Q8C2×Dic7314yescomplemented
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—28no—
510C22⋊Q8—28no—
511C22⋊Q8C2×Dic7314yes—
512C22⋊Q8C2×Dic7314yescomplemented
513C4×Q8—22no—
514C4×Q8C2×Dic7314yescomplemented
515C4×D4—28no—
516C4×D4C2×Dic7314yes—
517C4×D4C22⋊D7314yes—
518#117—2921no—
519#117—1462no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—2921no—
526C2×C4⋊C4—731no—
527C2×C4⋊C4—731no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
530C2×C4⋊C4—1461no—
531C2×C4⋊C4—1462no—
532C2×C4⋊C4C22⋊D7311yescharacteristic
533C2×C4⋊C4C22×D7311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—1461no—
537C2×C22⋊C4—1461no—
538C2×C22⋊C4—1461no—
539C2×C22⋊C4C22⋊D7311yescharacteristic
540C2×C22⋊C4C22⋊D7311yescharacteristic
541C2×C42—21no—
542C2×C42—1461no—
543C2×C42—1461no—
544C2×C42C22×D7311yescharacteristic
545C4⋊C8—1462no—
546#103—2921no—
547#103—2921no—
548#103—2921no—
549#103—2921no—
550#103—734no—
551#103—1462no—
552#103—1462no—
553#103—1462no—
554#103—1462no—
555#103—1462no—
556#103—1462no—
557#103—1462no—
558C22⋊C8—1462no—
559C22⋊C8—1462no—
560#97—1462no—
561#95—1461no—
562#95—1461no—
563#95—1461no—
564#95—1461no—
565#95—1461no—
566C24C2×C22⋊D7311yescharacteristic
567C24C2×C22⋊D7311yescharacteristic
568C2×Q8—24no—
569C2×Q8—24no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—28no—
576C2×Q8—28no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—42no—
586C2×Q8—42no—
587C2×Q8—42no—
588C2×Q8—42no—
589C2×Q8—44no—
590C2×Q8—44no—
591C2×Q8—44no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—44no—
595C2×Q8C22×Dic7312yes—
596C2×Q8C22×Dic7312yes—
597C2×Q8C22×Dic7312yes—
598C2×Q8D4×D7312yes—
599C2×Q8#1192402712yes—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4C22⋊Dic7314yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—2922no—
622C22×C4—2922no—
623C22×C4—5841no—
624C22×C4—1461no—
625C22×C4—1461no—
626C22×C4—1461no—
627C22×C4—1461no—
628C22×C4C22×Dic7312yes—
629C22×C4C22×Dic7312yes—
630C22×C4C2×C22⋊D7311yescharacteristic
631C22×C4C2×C22⋊D7311yescharacteristic
632C22×C4C2×C22⋊D7311yescharacteristic
633C22×C4C2×C22⋊D7311yescharacteristic
634C22×C4C2×C22⋊D7312yes—
635C22×C4C2×C22⋊D7312yes—
636C22×C4C23×D7311yescharacteristic
637M16—2924no—
638C2×C8—2924no—
639C2×C8—732no—
640C2×C8—1461no—
641C2×C8—1461no—
642C2×C8—1461no—
643C2×C8—1461no—
644C2×C8—1461no—
645C2×C8—1461no—
646C2×C8—1461no—
647C2×C8—1461no—
648C2×C8—1461no—
649C2×C8—1461no—
650C2×C8—1461no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—21no—
657C4⋊C4—2922no—
658C4⋊C4—732no—
659C4⋊C4—1461no—
660C4⋊C4—1461no—
661C4⋊C4—1461no—
662C4⋊C4—1461no—
663C4⋊C4—1461no—
664C4⋊C4—1461no—
665C4⋊C4—1461no—
666C4⋊C4C22⋊Dic7314yes—
667C4⋊C4C22×Dic7312yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—2922no—
671C22⋊C4—2922no—
672C22⋊C4—5841no—
673C22⋊C4C22⋊Dic7314yes—
674C22⋊C4C22⋊Dic7314yes—
675C42—24no—
676C42—2922no—
677C42—5841no—
678C42C22×Dic7312yes—
679C42C2×C22⋊D7312yes—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23C2×C22⋊Dic7312yes—
691C23C2×C22⋊Dic7312yes—
692C23#1455662212yes—
693C23#1455662212yes—
694C23C22×C22⋊D7311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—22no—
701Q8—22no—
702Q8—48no—
703Q8—48no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8D4×Dic7314yes—
709D4—28no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—2921no—
741C2×C4—2921no—
742C2×C4—2921no—
743C2×C4—2921no—
744C2×C4—2921no—
745C2×C4—2921no—
746C2×C4—2921no—
747C2×C4—2921no—
748C2×C4—2921no—
749C2×C4—2921no—
750C2×C4—2921no—
751C2×C4—5844no—
752C2×C4—1462no—
753C2×C4C2×C22⋊Dic7312yes—
754C2×C4C2×C22⋊Dic7312yes—
755C2×C4C2×C22⋊Dic7312yes—
756C2×C4C2×C22⋊Dic7312yes—
757C2×C4C23×Dic7311yescharacteristic
758C2×C4C2×D4×D7311yescharacteristic
759C2×C4C22×C22⋊D7311yescharacteristic
760C2×C4C2×#1192402711yescharacteristic
761C2×C4#1455663611yescharacteristic
762C2×C4#1455663611yescharacteristic
763C8—2921no—
764C8—2921no—
765C8—2921no—
766C8—1462no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22#1798859614yescomplemented
781C22C22×C22⋊Dic7311yescharacteristic
782C22D4×C22⋊D7311yescharacteristic
783C22#1798923111yescharacteristic
784C22C2×#1455662211yescharacteristic
785C22C2×#1455662211yescharacteristic
786C22#1798939511yescharacteristic
787C22#1798940211yescharacteristic
788C4—22no—
789C4—22no—
790C4—24no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—2922no—
797C4—5841no—
798C4—5841no—
799C4—5841no—
800C4C2×D4×Dic7311yescharacteristic
801C4#1798906211yescharacteristic
802C4D4×C22⋊D7311yescharacteristic
803C4#1798923111yescharacteristic
804C2—24no—
805C2—42no—
806C2D4×C22⋊Dic7311yescharacteristic
807C2C2×#1798859611yescharacteristic
808C2#2261846411yescharacteristic
809C2#2262144211yescharacteristic
810C2#2262150211yescharacteristic
811C2#2262198211yescharacteristic
812C2#2262210211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×D4×Q8×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73D4
cosocleC22×C4×C73C24
hypercenterC2×D4×Q8D73
hypocenterC73#22425
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#17988596C2semidirect
3. C22×#14556515C2semidirect
5. #22610855C2semidirect
6. #22610752C2semidirect
7. #22610365C2semidirect
8. #22610355C2semidirect
9. #22610244C2semidirect
10. #22610239C2semidirect
11. #22609946C2semidirect
12. #22609866C2semidirect
13. #22609866C2semidirect
14. #22609761C2semidirect
54. D4×Q8×C73C4semidirect
101. #14556515D4semidirect
123. C22×Q8×C73C2×C4semidirect
134. C4⋊Q8×C73C2×C4semidirect
140. C22⋊Q8×C73C2×C4semidirect
142. C4×Q8×C73C2×C4semidirect
373. C22×C73#419semidirect
422. C73#22425semidirect
428. D4×Q8Dic73semidirect
484. C22×Q8C2×Dic73semidirect
506. C4⋊Q8C2×Dic73semidirect
512. C22⋊Q8C2×Dic73semidirect
514. C4×Q8C2×Dic73semidirect
780. C22#17988596semidirect

Maximal subgroups

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

subgroupindex
C2×#179886592
C2×#179885962
C22×#145565152
#226128602
#226108552
#226107522
#226103652
#226103552
#226102442
#226102392
#226099462
#226098662
#226097612
C2×D4×Q8×C732
#2242573