Finite Group Databasebeta

← #33101479

Subgroups — #33101479

Order 18688.

1478 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988659C211yesmaximal, characteristic, complemented
2C2×#17988588C211yesmaximal, characteristic, complemented
3C2×#17988583C211yesmaximal, characteristic, complemented
4#22612860C211yesmaximal, characteristic, complemented
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#22609941C211yesmaximal, characteristic, complemented
12#22609871C211yesmaximal, characteristic, complemented
13#22609871C211yesmaximal, characteristic, complemented
14#22609756C211yesmaximal, characteristic, complemented
15C2×#547×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×#14556550C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20#17988659—24no—
21C2×C4⋊#10596831C2211yescharacteristic
22#17988588—24no—
23#17988583—24no—
24C2×#14556515C2211yescharacteristic
25C2×#14556515C2211yescharacteristic
26C2×#14556515C2211yescharacteristic
27C2×#14556515C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556515C2211yescharacteristic
30C2×#14556515C2211yescharacteristic
31C2×#14556515C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×#14556512C2211yescharacteristic
34C2×#14556512C2211yescharacteristic
35C2×#14556512C2211yescharacteristic
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
51C22×#41×C73C2211yescharacteristic
52C22×#41×C73C2211yescharacteristic
53#547×C73—24no—
54#547×C73C418yescomplemented
55C2×C4⋊Q8×C73C2211yescharacteristic
56C2×#123×C73—21no—
57C2×#123×C73—21no—
58C2×C22⋊Q8×C73C2211yescharacteristic
59C2×C22⋊Q8×C73C2211yescharacteristic
60C2×#121×C73—21no—
61C2×C4×D4×C73C2211yescharacteristic
62C2×C4×D4×C73C2211yescharacteristic
63C22×C4⋊C4×C73—21no—
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—41no—
95#14556515—41no—
96#14556515—41no—
97#14556515—41no—
98#14556512—22no—
99#14556512—22no—
100#14556512—22no—
101#14556512D414yescomplemented
102C22⋊#10596831—22no—
103C22⋊#10596831—22no—
104#14556502—22no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110C2×#41×C73—22no—
111C2×#41×C73—22no—
112C2×#41×C73—22no—
113C2×#41×C73—22no—
114C2×#41×C73—22no—
115C2×#41×C73—22no—
116C2×#41×C73—41no—
117C2×#41×C73—41no—
118C2×#41×C73—41no—
119C2×#41×C73—41no—
120C2×#41×C73C2×C414yes—
121C2×#41×C73C2×C414yescomplemented
122C22×Q8×C73C2311yescharacteristic
123C22×Q8×C73C2311yescharacteristic
124C22×D4×C73—21no—
125C22×D4×C73—21no—
126C22×D4×C73D411yescharacteristic
127C22×D4×C73C2311yescharacteristic
128C23×C4×C73—21no—
129C23×C4×C73—21no—
130C23×C4×C73—21no—
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C4⋊Q8×C73—22no—
134C4⋊Q8×C73C2×C414yescomplemented
135#123×C73—28no—
136#123×C73—28no—
137C22⋊Q8×C73—22no—
138C22⋊Q8×C73—22no—
139C22⋊Q8×C73C2×C414yes—
140C22⋊Q8×C73C2×C414yescomplemented
141#121×C73—28no—
142C4×D4×C73—22no—
143C4×D4×C73C2×C414yes—
144C4×D4×C73C2×C414yescomplemented
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—28no—
151C2×C4⋊C4×C73D411yescharacteristic
152C2×C4⋊C4×C73C2311yescharacteristic
153C2×C22⋊C4×C73—21no—
154C2×C22⋊C4×C73—21no—
155C2×C22⋊C4×C73—21no—
156C2×C22⋊C4×C73D411yescharacteristic
157C2×C22⋊C4×C73D411yescharacteristic
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×C73—21no—
195C24×C73C2×D411yescharacteristic
196C24×C73C2×D411yescharacteristic
197#41×C73—28no—
198#41×C73—28no—
199#41×C73—44no—
200#41×C73—44no—
201#41×C73—44no—
202#41×C73—44no—
203#41×C73—44no—
204#41×C73—44no—
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—21no—
214C2×Q8×C73—21no—
215C2×Q8×C73C22×C412yes—
216C2×Q8×C73C22×C412yes—
217C2×D4×C73—24no—
218C2×D4×C73—24no—
219C2×D4×C73—21no—
220C2×D4×C73—21no—
221C2×D4×C73—21no—
222C2×D4×C73—41no—
223C2×D4×C73—41no—
224C2×D4×C73—42no—
225C2×D4×C73—42no—
226C2×D4×C73—42no—
227C2×D4×C73—42no—
228C2×D4×C73C22⋊C414yes—
229C2×D4×C73C22×C412yes—
230C2×D4×C73C2×D412yes—
231C2×D4×C73#4112yes—
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—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—24no—
244C22×C4×C73—24no—
245C22×C4×C73—24no—
246C22×C4×C73—42no—
247C22×C4×C73—42no—
248C22×C4×C73—42no—
249C22×C4×C73—42no—
250C22×C4×C73—42no—
251C22×C4×C73—42no—
252C22×C4×C73C22×C412yes—
253C22×C4×C73C22×C412yes—
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2×D411yescharacteristic
256C22×C4×C73C2×D411yescharacteristic
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D412yes—
259C22×C4×C73C2×D412yes—
260C22×C4×C73C2411yescharacteristic
261C4⋊C4×C73—24no—
262C4⋊C4×C73—24no—
263C4⋊C4×C73—24no—
264C4⋊C4×C73—24no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73C22⋊C414yes—
267C4⋊C4×C73C22×C412yes—
268C22⋊C4×C73—24no—
269C22⋊C4×C73—24no—
270C22⋊C4×C73—24no—
271C22⋊C4×C73C22⋊C414yes—
272C22⋊C4×C73C22⋊C414yes—
273C42×C73C22×C412yes—
274C42×C73C2×D412yes—
275C23×C73—22no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—22no—
279C23×C73—21no—
280C23×C73—21no—
281C23×C73—22no—
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—21no—
285C23×C73—21no—
286C23×C73—21no—
287C23×C73—21no—
288C23×C73—21no—
289C23×C73—21no—
290C23×C73—41no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73C2×C22⋊C412yes—
295C23×C73C2×C22⋊C412yes—
296C23×C73C22×D411yescharacteristic
297Q8×C73—22no—
298Q8×C73—22no—
299Q8×C73—22no—
300Q8×C73—22no—
301Q8×C73—41no—
302Q8×C73—41no—
303Q8×C73—41no—
304Q8×C73—41no—
305D4×C73—22no—
306D4×C73—22no—
307D4×C73—22no—
308D4×C73—44no—
309D4×C73—48no—
310D4×C73—48no—
311D4×C73C4×D414yes—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—48no—
332C2×C4×C73—48no—
333C2×C4×C73—48no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73C2×C22⋊C412yes—
341C2×C4×C73C2×C22⋊C412yes—
342C2×C4×C73C2×C22⋊C412yes—
343C2×C4×C73C2×C22⋊C412yes—
344C2×C4×C73C23×C411yescharacteristic
345C2×C4×C73C22×D411yescharacteristic
346C2×C4×C73C22×D411yescharacteristic
347C2×C4×C73C2×#4111yescharacteristic
348C2×C4×C73H(5,𝔽2)11yescharacteristic
349C2×C4×C73H(5,𝔽2)11yescharacteristic
350C2×Dic73—22no—
351C2×Dic73—41no—
352C2×Dic73—41no—
353C2×Dic73—41no—
354C2×Dic73—41no—
355C2×Dic73—41no—
356C2×Dic73—41no—
357C2×Dic73—41no—
358C2×Dic73—41no—
359C2×Dic73—41no—
360C2×Dic73—41no—
361C2×Dic73—41no—
362C2×Dic73—84no—
363#10596831—22no—
364#10596831—41no—
365#10596831—41no—
366#10596831—41no—
367C22×C73—22no—
368C22×C73—22no—
369C22×C73—24no—
370C22×C73—22no—
371C22×C73—22no—
372C22×C73—22no—
373C22×C73—22no—
374C22×C73—42no—
375C22×C73—42no—
376C22×C73—41no—
377C22×C73—41no—
378C22×C73—42no—
379C22×C73—41no—
380C22×C73—41no—
381C22×C73—42no—
382C22×C73—41no—
383C22×C73—41no—
384C22×C73—42no—
385C22×C73—41no—
386C22×C73—41no—
387C22×C73—42no—
388C22×C73C22×C22⋊C411yescharacteristic
389C22×C73D4211yescharacteristic
390C22×C73#54611yescharacteristic
391C22×C73#57511yescharacteristic
392C22×C73#57511yescharacteristic
393C22×C73#57711yescharacteristic
394C22×C73#57811yescharacteristic
395C4×C73—22no—
396C4×C73—22no—
397C4×C73—22no—
398C4×C73—22no—
399C4×C73—42no—
400C4×C73—42no—
401C4×C73—42no—
402C4×C73C2×C4×D411yescharacteristic
403C4×C73#51811yescharacteristic
404C4×C73D4211yescharacteristic
405C4×C73#54611yescharacteristic
406Dic73—42no—
407Dic73—81no—
408Dic73—81no—
409Dic73—81no—
410#22420—731nomaximal, Sylow
411C2×C73—42no—
412C2×C73—42no—
413C2×C73—44no—
414C2×C73D4×C22⋊C411yescharacteristic
415C2×C73#289611yescharacteristic
416C2×C73#289811yescharacteristic
417C2×C73#326711yescharacteristic
418C2×C73#326911yescharacteristic
419C2×C73#330711yescharacteristic
420C2×C73#331511yescharacteristic
421C2×#547D7311yescharacteristic
422C2×#435—731no—
423C2×#417—731no—
424C2×#416—731no—
425#2352—731no—
426#1981—731no—
427#1960—731no—
428#1894—731no—
429#1892—731no—
430#1873—731no—
431#1872—731no—
432#1804—731no—
433#1788—731no—
434#1788—731no—
435#1762—731no—
436C73#2242011yescharacteristic, complemented, Sylow
437C22×#41C2×D7311yescharacteristic
438C22×#41C2×D7311yescharacteristic
439C22×M16—731no—
440C23×C8—731no—
441#547—24no—
442#547Dic7318yescomplemented
443C2×C4⋊Q8C2×D7311yescharacteristic
444C2×#123—21no—
445C2×#123—21no—
446C2×C22⋊Q8C2×D7311yescharacteristic
447C2×C22⋊Q8C2×D7311yescharacteristic
448C2×#121—21no—
449C2×C4×D4C2×D7311yescharacteristic
450C2×C4×D4C2×D7311yescharacteristic
451C2×#117—731no—
452C22×C4⋊C4—21no—
453C22×C4⋊C4—731no—
454#435—1464no—
455C2×C4⋊C8—731no—
456#417—1464no—
457#416—1464no—
458C2×#103—731no—
459C2×#103—731no—
460C2×#103—731no—
461C2×#103—731no—
462C2×#103—731no—
463C2×#103—731no—
464C2×#103—731no—
465C2×#103—731no—
466C2×#102—731no—
467C2×#102—731no—
468C2×#102—731no—
469C2×#102—731no—
470C2×C22⋊C8—731no—
471C2×C22⋊C8—731no—
472C2×#97—731no—
473#388—1461no—
474#387—1461no—
475#386—1461no—
476#382—731no—
477#380—731no—
478#380—731no—
479C4×C4⋊C4—731no—
480C4×C22⋊C4—1461no—
481#340—731no—
482#340—731no—
483#340—731no—
484#340—731no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41C2×Dic7314yes—
496C2×#41C2×Dic7314yescomplemented
497C22×Q8C22×D7311yescharacteristic
498C22×Q8C22×D7311yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C22⋊D7311yescharacteristic
502C22×D4C22×D7311yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—1461no—
507C23×C4C22×D7311yescharacteristic
508C23×C4C22×D7311yescharacteristic
509C2×M16—2921no—
510C2×M16—1462no—
511C2×M16—1462no—
512C22×C8—2921no—
513C22×C8—731no—
514C22×C8—731no—
515C22×C8—731no—
516C22×C8—731no—
517C22×C8—1462no—
518C22×C8—1462no—
519C4⋊Q8—22no—
520C4⋊Q8C2×Dic7314yescomplemented
521#123—28no—
522#123—28no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8C2×Dic7314yes—
526C22⋊Q8C2×Dic7314yescomplemented
527#121—28no—
528C4×D4—22no—
529C4×D4C2×Dic7314yes—
530C4×D4C2×Dic7314yescomplemented
531C4×D4C22⋊D7314yes—
532#117—2921no—
533#117—1462no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—28no—
539C2×C4⋊C4—2921no—
540C2×C4⋊C4—731no—
541C2×C4⋊C4—731no—
542C2×C4⋊C4—731no—
543C2×C4⋊C4—731no—
544C2×C4⋊C4—1461no—
545C2×C4⋊C4—1462no—
546C2×C4⋊C4C22⋊D7311yescharacteristic
547C2×C4⋊C4C22×D7311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1461no—
552C2×C22⋊C4—1461no—
553C2×C22⋊C4—1461no—
554C2×C22⋊C4C22⋊D7311yescharacteristic
555C2×C22⋊C4C22⋊D7311yescharacteristic
556C2×C42—1461no—
557C2×C42—1461no—
558C2×C42C22×D7311yescharacteristic
559C4⋊C8—1462no—
560#103—2921no—
561#103—2921no—
562#103—2921no—
563#103—2921no—
564#103—1462no—
565#103—1462no—
566#103—1462no—
567#103—1462no—
568#102—734no—
569#102—1462no—
570#102—1462no—
571#102—1462no—
572C22⋊C8—1462no—
573C22⋊C8—1462no—
574#97—1462no—
575#95—1461no—
576#95—1461no—
577#95—1461no—
578#95—1461no—
579#95—1461no—
580C24—21no—
581C24C2×C22⋊D7311yescharacteristic
582C24C2×C22⋊D7311yescharacteristic
583#41—28no—
584#41—28no—
585#41—44no—
586#41—44no—
587#41—44no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C22×Dic7312yes—
602C2×Q8C22×Dic7312yes—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4C22⋊Dic7314yes—
615C2×D4C22×Dic7312yes—
616C2×D4D4×D7312yes—
617C2×D4#1192402712yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—2922no—
639C22×C4—2922no—
640C22×C4—5841no—
641C22×C4—1461no—
642C22×C4—1461no—
643C22×C4—1461no—
644C22×C4—1461no—
645C22×C4C22×Dic7312yes—
646C22×C4C22×Dic7312yes—
647C22×C4C2×C22⋊D7311yescharacteristic
648C22×C4C2×C22⋊D7311yescharacteristic
649C22×C4C2×C22⋊D7311yescharacteristic
650C22×C4C2×C22⋊D7311yescharacteristic
651C22×C4C2×C22⋊D7312yes—
652C22×C4C2×C22⋊D7312yes—
653C22×C4C23×D7311yescharacteristic
654M16—2924no—
655C2×C8—2924no—
656C2×C8—732no—
657C2×C8—1461no—
658C2×C8—1461no—
659C2×C8—1461no—
660C2×C8—1461no—
661C2×C8—1461no—
662C2×C8—1461no—
663C2×C8—1461no—
664C2×C8—1461no—
665C2×C8—1461no—
666C2×C8—1461no—
667C2×C8—1461no—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—2922no—
674C4⋊C4—732no—
675C4⋊C4—1461no—
676C4⋊C4—1461no—
677C4⋊C4—1461no—
678C4⋊C4—1461no—
679C4⋊C4—1461no—
680C4⋊C4—1461no—
681C4⋊C4—1461no—
682C4⋊C4C22⋊Dic7314yes—
683C4⋊C4C22×Dic7312yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—2922no—
688C22⋊C4—2922no—
689C22⋊C4—5841no—
690C22⋊C4C22⋊Dic7314yes—
691C22⋊C4C22⋊Dic7314yes—
692C42—2922no—
693C42—5841no—
694C42C22×Dic7312yes—
695C42C2×C22⋊D7312yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C2×C22⋊Dic7312yes—
716C23C2×C22⋊Dic7312yes—
717C23C22×C22⋊D7311yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—44no—
730D4—48no—
731D4—48no—
732D4D4×Dic7314yes—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—48no—
754C2×C4—48no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—2921no—
762C2×C4—2921no—
763C2×C4—2921no—
764C2×C4—2921no—
765C2×C4—2921no—
766C2×C4—2921no—
767C2×C4—2921no—
768C2×C4—2921no—
769C2×C4—2921no—
770C2×C4—2921no—
771C2×C4—2921no—
772C2×C4—5844no—
773C2×C4—1462no—
774C2×C4C2×C22⋊Dic7312yes—
775C2×C4C2×C22⋊Dic7312yes—
776C2×C4C2×C22⋊Dic7312yes—
777C2×C4C2×C22⋊Dic7312yes—
778C2×C4C23×Dic7311yescharacteristic
779C2×C4C2×D4×D7311yescharacteristic
780C2×C4C22×C22⋊D7311yescharacteristic
781C2×C4C2×#1192402711yescharacteristic
782C2×C4#1455663611yescharacteristic
783C2×C4#1455663611yescharacteristic
784C8—2921no—
785C8—2921no—
786C8—2921no—
787C8—1462no—
788C22—22no—
789C22—22no—
790C22—24no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—41no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22C22×C22⋊Dic7311yescharacteristic
810C22D4×C22⋊D7311yescharacteristic
811C22#1798923111yescharacteristic
812C22#1798938511yescharacteristic
813C22#1798938511yescharacteristic
814C22#1798939511yescharacteristic
815C22#1798940211yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—2922no—
824C4—5841no—
825C4—5841no—
826C4—5841no—
827C4C2×D4×Dic7311yescharacteristic
828C4#1798906211yescharacteristic
829C4D4×C22⋊D7311yescharacteristic
830C4#1798923111yescharacteristic
831C2—42no—
832C2—42no—
833C2—44no—
834C2D4×C22⋊Dic7311yescharacteristic
835C2#2261845011yescharacteristic
836C2#2261846411yescharacteristic
837C2#2262145711yescharacteristic
838C2#2262148211yescharacteristic
839C2#2262190711yescharacteristic
840C2#2262202711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
Fitting, prime radicalC2×#547×C73C2
socleC23×C73C22×D4
cosocleC22×C4×C73C24
hypercenterC2×#547D73
hypocenterC73#22420
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#17988659C2semidirect
2. C2×#17988588C2semidirect
3. C2×#17988583C2semidirect
4. #22612860C2semidirect
5. #22610855C2semidirect
6. #22610752C2semidirect
7. #22610365C2semidirect
8. #22610355C2semidirect
9. #22610244C2semidirect
10. #22610239C2semidirect
11. #22609941C2semidirect
12. #22609871C2semidirect
13. #22609871C2semidirect
14. #22609756C2semidirect
54. #547×C73C4semidirect
101. #14556512D4semidirect
121. C2×#41×C73C2×C4semidirect
134. C4⋊Q8×C73C2×C4semidirect
140. C22⋊Q8×C73C2×C4semidirect
144. C4×D4×C73C2×C4semidirect
436. C73#22420semidirect
442. #547Dic73semidirect
496. C2×#41C2×Dic73semidirect
520. C4⋊Q8C2×Dic73semidirect
526. C22⋊Q8C2×Dic73semidirect
530. C4×D4C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886592
C2×#179885882
C2×#179885832
#226128602
#226108552
#226107522
#226103652
#226103552
#226102442
#226102392
#226099412
#226098712
#226097562
C2×#547×C732
#2242073