Finite Group Databasebeta

← #34020624

Subgroups — #34020624

Order 18688.

886 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989611C211yesmaximal, characteristic
2C2×#17989611C211yesmaximal, characteristic
3#22625731C211yesmaximal, characteristic, complemented
4#22625731C211yesmaximal, characteristic, complemented
5#22625730C211yesmaximal, characteristic, complemented
6#22625730C211yesmaximal, characteristic, complemented
7#22625727C211yesmaximal, characteristic, complemented
8#22625726C211yesmaximal, characteristic, complemented
9#22625723C211yesmaximal, characteristic, complemented
10C4⋊C4×#10596833C211yesmaximal, characteristic, complemented
11#22625661C211yesmaximal, characteristic
12#22625661C211yesmaximal, characteristic
13#22625657C211yesmaximal, characteristic
14C4×C22⋊#10596833C211yesmaximal, characteristic
15#22612410C211yesmaximal, characteristic
16#17989611C418yescomplemented
17#17989611C418yescomplemented
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×C4⋊#10596833C2211yescharacteristic
21C2×C4⋊#10596833C2211yescharacteristic
22C2×C22⋊#10596833C2211yescharacteristic
23C2×C22⋊#10596833C2211yescharacteristic
24C2×C22⋊#10596833C2211yescharacteristic
25C2×C22⋊#10596833C2211yescharacteristic
26C2×#14556646C2211yescharacteristic
27C2×#14556646C2211yescharacteristic
28C2×#14556646C2211yescharacteristic
29C2×#14556646C2211yescharacteristic
30C2×#14556646C2211yescharacteristic
31C2×#14556646C2211yescharacteristic
32C2×C4×#10596833C2211yescharacteristic
33C2×C4×#10596833C2211yescharacteristic
34C2×C4×#10596833C2211yescharacteristic
35C2×C4×#10596833C2211yescharacteristic
36C2×C4×#10596833C2211yescharacteristic
37C2×C4×#10596833C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44#17989453C2211yescharacteristic
45#17989453C2211yescharacteristic
46C2×#14556547C2211yescharacteristic
47C2×#14556547C2211yescharacteristic
48C22×C4×Dic73C2211yescharacteristic
49#17988484C411yescharacteristic
50#17988484C411yescharacteristic
51#17988482C411yescharacteristic
52#17988482C411yescharacteristic
53#17988462C411yescharacteristic
54#17988460C411yescharacteristic
55#17988459C411yescharacteristic
56C4⋊C4×Dic73C2211yescharacteristic
57C4⋊C4×Dic73C2211yescharacteristic
58#17988438C2211yescharacteristic
59#17988438C2211yescharacteristic
60#385×C73C411yescharacteristic
61C22×#10596833C2311yescharacteristic
62C22×#10596833C2311yescharacteristic
63C22×#10596833C2311yescharacteristic
64C22×#10596833C2311yescharacteristic
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69#14556658C2×C414yescomplemented
70#14556658C2×C414yescomplemented
71C4⋊#10596833C2×C414yescomplemented
72C4⋊#10596833C2×C414yescomplemented
73C22⋊#10596833C2×C414yes—
74C22⋊#10596833C2×C414yes—
75C22⋊#10596833C2×C414yes—
76C22⋊#10596833C2×C414yes—
77#14556646—41no—
78#14556646—41no—
79#14556646—41no—
80#14556646—41no—
81#14556646C2×C414yescomplemented
82#14556646C2×C414yescomplemented
83C4×#10596833—41no—
84C4×#10596833—41no—
85C4×#10596833—41no—
86C4×#10596833—41no—
87C4×#10596833C2×C414yescomplemented
88C4×#10596833C2×C414yescomplemented
89C23×Dic73C2×C411yescharacteristic
90C23×Dic73C2311yescharacteristic
91#14556547—41no—
92#14556547—41no—
93#14556547C2×C414yes—
94#14556547C2×C414yes—
95C2×C4⋊Dic73C2×C411yescharacteristic
96C2×C4⋊Dic73C2×C411yescharacteristic
97C2×#11924007C2×C411yescharacteristic
98C2×#11924007C2×C411yescharacteristic
99C2×#11924007C2×C411yescharacteristic
100C2×#11924007C2×C411yescharacteristic
101C2×#11924007C2×C411yescharacteristic
102C2×#11924007C2×C411yescharacteristic
103C2×#11924007C2×C411yescharacteristic
104C2×#11924007C2×C411yescharacteristic
105C2×C22⋊Dic73C2×C411yescharacteristic
106C2×C22⋊Dic73C2×C411yescharacteristic
107C2×C4×Dic73—41no—
108C2×C4×Dic73—41no—
109C2×C4×Dic73C2×C411yescharacteristic
110C2×C4×Dic73C2×C411yescharacteristic
111C2×C4×Dic73C2311yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C2×C4×Dic73C2311yescharacteristic
114C2×C4×Dic73C2311yescharacteristic
115C2×C4×Dic73C2311yescharacteristic
116C2×C4×Dic73C2311yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122#14556498C2×C411yescharacteristic
123C23×C4×C73C2×C411yescharacteristic
124C2×C4⋊C4×C73C2×C411yescharacteristic
125C2×C4⋊C4×C73C2×C411yescharacteristic
126C2×C22⋊C4×C73C2×C411yescharacteristic
127C2×C22⋊C4×C73C2×C411yescharacteristic
128#95×C73C2×C411yescharacteristic
129#95×C73C2×C411yescharacteristic
130C2×#10596833—21no—
131C2×#10596833—21no—
132C2×#10596833—21no—
133C2×#10596833—21no—
134C2×#10596833—21no—
135C2×#10596833—21no—
136C2×#10596833—21no—
137C2×#10596833—21no—
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—21no—
145C2×#10596833—21no—
146C2×#10596833C22×C412yes—
147C2×#10596833C22×C412yes—
148C2×#10596833C22×C412yes—
149C2×#10596833C22×C412yes—
150C2×#10596833C22×C412yes—
151C2×#10596833C22×C412yes—
152C2×#10596833C22×C412yes—
153C2×#10596833C22×C412yes—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73—22no—
159C22×Dic73—41no—
160C22×Dic73—41no—
161C22×Dic73C22×C411yescharacteristic
162C22×Dic73C22×C411yescharacteristic
163C22×Dic73C22×C411yescharacteristic
164C22×Dic73C22×C411yescharacteristic
165C22×Dic73C22×C411yescharacteristic
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C412yes—
168C22×Dic73C22×C412yes—
169C22×Dic73C22×C411yescharacteristic
170C22×Dic73C2411yescharacteristic
171C4⋊Dic73—22no—
172C4⋊Dic73—41no—
173#11924007—22no—
174#11924007—22no—
175#11924007—41no—
176#11924007—41no—
177#11924007—41no—
178#11924007—41no—
179#11924007C4214yes—
180#11924007C4214yes—
181C22⋊Dic73—41no—
182C22⋊Dic73C4214yes—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—41no—
192C4×Dic73—41no—
193C4×Dic73C22×C412yes—
194C4×Dic73C22×C412yes—
195C4×Dic73C22×C412yes—
196C4×Dic73C22×C412yes—
197C24×C73C22×C411yescharacteristic
198C22×C4×C73—22no—
199C22×C4×C73—41no—
200C22×C4×C73—41no—
201C22×C4×C73C22×C411yescharacteristic
202C22×C4×C73C22×C411yescharacteristic
203C22×C4×C73C22×C411yescharacteristic
204C22×C4×C73C22×C411yescharacteristic
205C22×C4×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207C4⋊C4×C73—22no—
208C4⋊C4×C73—41no—
209C22⋊C4×C73—41no—
210C22⋊C4×C73C4214yes—
211C23×C73—21no—
212C23×C73—21no—
213C23×C73—21no—
214C23×C73—21no—
215C23×C73—21no—
216C23×C73—21no—
217C23×C73C2×C4212yes—
218C23×C73C23×C411yescharacteristic
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—44no—
235C2×C4×C73C2×C4212yes—
236C2×C4×C73C2×C4212yes—
237C2×C4×C73#13112yes—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—22no—
247C2×Dic73—22no—
248C2×Dic73—22no—
249C2×Dic73—22no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—44no—
260C2×Dic73C2×C4212yes—
261C2×Dic73C2×C4212yes—
262C2×Dic73C2×C4212yes—
263C2×Dic73#13112yes—
264C2×Dic73C23×C411yescharacteristic
265C2×Dic73C23×C411yescharacteristic
266C2×Dic73H(5,𝔽2)11yescharacteristic
267C2×Dic73H(5,𝔽2)11yescharacteristic
268C2×Dic732−1+411yescharacteristic
269C2×Dic732−1+411yescharacteristic
270#10596833—22no—
271#10596833—22no—
272#10596833—22no—
273#10596833—22no—
274#10596833—22no—
275#10596833—22no—
276#10596833—22no—
277#10596833—22no—
278C22×C73—22no—
279C22×C73—22no—
280C22×C73—22no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73—41no—
285C22×C73C22×C4211yescharacteristic
286C22×C73#51811yescharacteristic
287C22×C73#51911yescharacteristic
288C22×C73C2×#13111yescharacteristic
289C22×C73C2×#13111yescharacteristic
290C22×C73#56811yescharacteristic
291C22×C73#56811yescharacteristic
292C4×C73—22no—
293C4×C73—22no—
294C4×C73—22no—
295C4×C73—41no—
296C4×C73—41no—
297C4×C73—41no—
298Dic73—22no—
299Dic73—22no—
300Dic73—22no—
301Dic73—22no—
302Dic73—41no—
303Dic73—41no—
304Dic73—41no—
305Dic73#52011yescharacteristic
306Dic73#52011yescharacteristic
307Dic73#52011yescharacteristic
308Dic73#52011yescharacteristic
309#20541—731nomaximal, Sylow
310C2×C73—42no—
311C2×C73#227411yescharacteristic
312C2×C73C4×#13111yescharacteristic
313C2×C73#287511yescharacteristic
314C2×C73#297611yescharacteristic
315C2×C73#297611yescharacteristic
316C2×C73#298511yescharacteristic
317C2×C73#298511yescharacteristic
318C2×#433—731no—
319C2×#433—731no—
320#2296—731no—
321#1771—731no—
322#1771—731no—
323#1771—731no—
324#1771—731no—
325#1770—731no—
326#1770—731no—
327C8×C4⋊C4—731no—
328C8×C4⋊C4—731no—
329#1750—731no—
330#1750—731no—
331#1749—731no—
332C4×C22⋊C8—731no—
333C73#2054111yescharacteristic, complemented, Sylow
334C2×#117—731no—
335C2×#117—731no—
336C22×C42—731no—
337#433—738no—
338#433—738no—
339C2×C4⋊C8—731no—
340C2×C4⋊C8—731no—
341C2×C4⋊C8—731no—
342C2×C4⋊C8—731no—
343C2×C22⋊C8—731no—
344C2×C22⋊C8—731no—
345C2×C22⋊C8—731no—
346C2×C22⋊C8—731no—
347C2×#97—731no—
348C2×#97—731no—
349C2×#97—731no—
350C2×#97—731no—
351C2×#97—731no—
352C2×#97—731no—
353C2×C4×C8—731no—
354C2×C4×C8—731no—
355C2×C4×C8—731no—
356C2×C4×C8—731no—
357C2×C4×C8—731no—
358C2×C4×C8—731no—
359#389—731no—
360#389—731no—
361#389—731no—
362#389—731no—
363#385—731no—
364#385—731no—
365#385—731no—
366#385#6440811yescharacteristic
367C4×C4⋊C4—731no—
368C4×C4⋊C4—731no—
369C4×C4⋊C4—731no—
370C4×C4⋊C4—731no—
371#336—731no—
372#336—731no—
373#336—731no—
374#336—731no—
375#336—731no—
376#336—731no—
377#336—731no—
378#336—731no—
379C23×C4—731no—
380C23×C4—731no—
381C23×C4C2×#6440811yescharacteristic
382C22×C8—731no—
383C22×C8—731no—
384C22×C8—731no—
385C22×C8—731no—
386C22×C8—731no—
387C22×C8—731no—
388C22×C8—731no—
389C22×C8—731no—
390#117—2921no—
391#117—2921no—
392#117—734no—
393#117—734no—
394C2×C4⋊C4—731no—
395C2×C4⋊C4—731no—
396C2×C4⋊C4—731no—
397C2×C4⋊C4—731no—
398C2×C4⋊C4—731no—
399C2×C4⋊C4—731no—
400C2×C4⋊C4—731no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—731no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4C2×#6440811yescharacteristic
405C2×C4⋊C4C2×#6440811yescharacteristic
406C2×C22⋊C4—731no—
407C2×C22⋊C4—731no—
408C2×C22⋊C4C2×#6440811yescharacteristic
409C2×C22⋊C4C2×#6440811yescharacteristic
410C2×C42—2921no—
411C2×C42—2921no—
412C2×C42—731no—
413C2×C42—731no—
414C2×C42—731no—
415C2×C42—731no—
416C2×C42—731no—
417C2×C42—731no—
418C2×C42—731no—
419C2×C42—731no—
420C4⋊C8—734no—
421C4⋊C8—734no—
422C4⋊C8—734no—
423C4⋊C8—734no—
424C22⋊C8—734no—
425C22⋊C8—734no—
426C22⋊C8—734no—
427C22⋊C8—734no—
428#97—2921no—
429#97—2921no—
430#97—2921no—
431#97—2921no—
432#97—734no—
433#97—734no—
434C4×C8—2921no—
435C4×C8—2921no—
436C4×C8—2921no—
437C4×C8—2921no—
438C4×C8—734no—
439C4×C8—734no—
440#95—731no—
441#95—731no—
442#95—731no—
443#95—731no—
444#95—731no—
445#95—731no—
446#95C2×#6440811yescharacteristic
447#95C2×#6440811yescharacteristic
448C24C22×#6440811yescharacteristic
449C22×C4—22no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—2921no—
453C22×C4—2921no—
454C22×C4—731no—
455C22×C4—731no—
456C22×C4—731no—
457C22×C4—731no—
458C22×C4—731no—
459C22×C4—732no—
460C22×C4—732no—
461C22×C4—731no—
462C22×C4—731no—
463C22×C4—731no—
464C22×C4—1462no—
465C22×C4—1461no—
466C22×C4—1461no—
467C22×C4—1461no—
468C22×C4—1461no—
469C22×C4C22×#6440811yescharacteristic
470C22×C4C22×#6440811yescharacteristic
471C22×C4C22×#6440811yescharacteristic
472C22×C4C22×#6440811yescharacteristic
473C22×C4C22×#6440811yescharacteristic
474C22×C4C22×#6440811yescharacteristic
475C2×C8—732no—
476C2×C8—732no—
477C2×C8—732no—
478C2×C8—732no—
479C2×C8—732no—
480C2×C8—732no—
481C2×C8—732no—
482C2×C8—732no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8—1461no—
494C2×C8—1461no—
495C2×C8—1461no—
496C2×C8—1461no—
497C2×C8—1461no—
498C2×C8—1461no—
499C4⋊C4—22no—
500C4⋊C4—41no—
501C4⋊C4—2921no—
502C4⋊C4—2921no—
503C4⋊C4—2921no—
504C4⋊C4—2921no—
505C4⋊C4—2921no—
506C4⋊C4—734no—
507C4⋊C4—734no—
508C4⋊C4—1462no—
509C4⋊C4—1462no—
510C4⋊C4—1462no—
511C22⋊C4—41no—
512C22⋊C4—2921no—
513C22⋊C4—734no—
514C22⋊C4C4×#6440814yes—
515C42—2921no—
516C42—2921no—
517C42—732no—
518C42—732no—
519C42—732no—
520C42—732no—
521C42—1461no—
522C42—1461no—
523C42—1461no—
524C42—1461no—
525C42—1461no—
526C42—1461no—
527C42—1461no—
528C42—1461no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23C2×C4×#6440812yes—
536C23C23×#6440811yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—44no—
553C2×C4—2924no—
554C2×C4—731no—
555C2×C4—731no—
556C2×C4—731no—
557C2×C4—731no—
558C2×C4—731no—
559C2×C4—731no—
560C2×C4—732no—
561C2×C4—732no—
562C2×C4—732no—
563C2×C4—732no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4—1461no—
573C2×C4—1462no—
574C2×C4—1462no—
575C2×C4—1462no—
576C2×C4—1462no—
577C2×C4—1461no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4—1461no—
581C2×C4—1461no—
582C2×C4—1461no—
583C2×C4—1461no—
584C2×C4—1461no—
585C2×C4C2×C4×#6440812yes—
586C2×C4C2×C4×#6440812yes—
587C2×C4#1455667812yes—
588C8—1462no—
589C8—1462no—
590C8—1462no—
591C8—1462no—
592C8—1462no—
593C8—1462no—
594C8—1462no—
595C8—1462no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22C22×C4×#6440811yescharacteristic
604C22#1798965411yescharacteristic
605C22#1798965511yescharacteristic
606C22C2×#1455667811yescharacteristic
607C22D73⋊#13111yescharacteristic
608C22#1798966511yescharacteristic
609C22#1798966611yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—2921no—
617C4—2921no—
618C4—2921no—
619C4—731no—
620C4—731no—
621C4—731no—
622C4—731no—
623C4—1462no—
624C4—1462no—
625C4—1462no—
626C4—1462no—
627C2—42no—
628C2#2262636911yescharacteristic
629C2C4×#1455667811yescharacteristic
630C2#2262650211yescharacteristic
631C2#2262679711yescharacteristic
632C2#2262679911yescharacteristic
633C2#2262683511yescharacteristic
634C2#2262683711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutatorC22×C73C22×C42
Fitting#385×C73C4
socleC23×C73C23×C4
prime radicalC24×C73C22×C4
cosocleC22×Dic73C24
hypercenter#385#64408
hypocenterC73#20541
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #22625731C2semidirect
4. #22625731C2semidirect
5. #22625730C2semidirect
6. #22625730C2semidirect
7. #22625727C2semidirect
8. #22625726C2semidirect
9. #22625723C2semidirect
10. C4⋊C4×#10596833C2semidirect
16. #17989611C4semidirect
17. #17989611C4semidirect
69. #14556658C2×C4semidirect
70. #14556658C2×C4semidirect
71. C4⋊#10596833C2×C4semidirect
72. C4⋊#10596833C2×C4semidirect
81. #14556646C2×C4semidirect
82. #14556646C2×C4semidirect
87. C4×#10596833C2×C4semidirect
88. C4×#10596833C2×C4semidirect
333. C73#20541semidirect

Maximal subgroups

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

subgroupindex
C2×#179896112
#226257312
#226257302
#226257272
#226257262
#226257232
C4⋊C4×#105968332
#226256612
#226256572
C4×C22⋊#105968332
#226124102
#2054173