Finite Group Databasebeta

← #34026669

Subgroups — #34026669

Order 18688.

736 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625990C211yesmaximal, characteristic, complemented
2#22625990C211yesmaximal, characteristic, complemented
3#22625985C211yesmaximal, characteristic, complemented
4#22625985C211yesmaximal, characteristic, complemented
5#22625876C211yesmaximal, characteristic
6#22625876C211yesmaximal, characteristic
7#22625860C211yesmaximal, characteristic, complemented
8#22625849C211yesmaximal, characteristic, complemented
9#22625823C211yesmaximal, characteristic
10#22625719C211yesmaximal, characteristic, complemented
11#22625669C211yesmaximal, characteristic
12#22625665C211yesmaximal, characteristic
13#22625650C211yesmaximal, characteristic, complemented
14#22625592C211yesmaximal, characteristic
15#22612328C211yesmaximal, characteristic
16C22×#11924036C2211yescharacteristic
17C22×#11924036C2211yescharacteristic
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×C4⋊#10596833C2211yescharacteristic
21C2×C4⋊#10596833C2211yescharacteristic
22C2×#14556648C2211yescharacteristic
23C2×#14556648C2211yescharacteristic
24C2×#14556646C2211yescharacteristic
25C2×#14556646C2211yescharacteristic
26C2×C4×#10596833C2211yescharacteristic
27C2×C4×#10596833C2211yescharacteristic
28#17989453C2211yescharacteristic
29#17989453C2211yescharacteristic
30#17989453C2211yescharacteristic
31#17989453C2211yescharacteristic
32#17989453C2211yescharacteristic
33#17989453C2211yescharacteristic
34#17989453C2211yescharacteristic
35#17989453C2211yescharacteristic
36#17989453C2211yescharacteristic
37#17989453C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44C2×C42×D73C2211yescharacteristic
45#17988455C411yescharacteristic
46#17988451C411yescharacteristic
47#17988451C411yescharacteristic
48#17988449C411yescharacteristic
49#17988449C411yescharacteristic
50#17988446C411yescharacteristic
51#17988446C411yescharacteristic
52#17988438C2211yescharacteristic
53#17988438C2211yescharacteristic
54#17988434C2211yescharacteristic
55#17988434C2211yescharacteristic
56#17988432C2211yescharacteristic
57#17988432C2211yescharacteristic
58#383×C73C411yescharacteristic
59C2×#11924036—22no—
60C2×#11924036—22no—
61C2×#11924036—22no—
62C2×#11924036—22no—
63C2×#11924036—41no—
64C2×#11924036—41no—
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69C22×#10596833C2311yescharacteristic
70C22×#10596833C2311yescharacteristic
71C22×#10596833C2311yescharacteristic
72C22×#10596833C2311yescharacteristic
73#14556658—22no—
74#14556658—41no—
75C4⋊#10596833—22no—
76C4⋊#10596833—41no—
77#14556648—22no—
78#14556648—22no—
79#14556646—22no—
80#14556646—41no—
81C4×#10596833—22no—
82C4×#10596833—41no—
83C22×C4×D73C2×C411yescharacteristic
84C22×C4×D73C2×C411yescharacteristic
85C22×C4×D73C2311yescharacteristic
86C2×#11924007C2×C411yescharacteristic
87C2×#11924007C2×C411yescharacteristic
88C2×#11924007C2×C411yescharacteristic
89C2×#11924007C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×#11924005C2×C411yescharacteristic
94C2×C4×Dic73C2×C411yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101C42×D73—22no—
102C42×D73—22no—
103#14556498C2×C411yescharacteristic
104#14556498C2×C411yescharacteristic
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107#14556498C2×C411yescharacteristic
108#14556498C2×C411yescharacteristic
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113C2×C42×C73C2×C411yescharacteristic
114#95×C73C2×C411yescharacteristic
115#95×C73C2×C411yescharacteristic
116#95×C73C2×C411yescharacteristic
117#95×C73C2×C411yescharacteristic
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120#11924036—44no—
121#11924036—44no—
122C2×#10596833—21no—
123C2×#10596833—21no—
124C2×#10596833—21no—
125C2×#10596833—21no—
126C2×#10596833—21no—
127C2×#10596833—21no—
128C2×#10596833—21no—
129C2×#10596833—21no—
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#4112yes—
145C2×#10596833#4112yes—
146C23×D73C22×C411yescharacteristic
147C22×Dic73C22×C411yescharacteristic
148C22×Dic73C22×C411yescharacteristic
149C22×Dic73C22×C411yescharacteristic
150C22×Dic73C22×C411yescharacteristic
151C22×Dic73C22×C411yescharacteristic
152C22×Dic73C22×C411yescharacteristic
153C22×Dic73C2411yescharacteristic
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—22no—
159C2×C4×D73—22no—
160C2×C4×D73—22no—
161C2×C4×D73—22no—
162C2×C4×D73—22no—
163C2×C4×D73—41no—
164C2×C4×D73#4112yes—
165C2×C4×D73#4112yes—
166#11924007—22no—
167#11924007—22no—
168#11924007—41no—
169#11924007—41no—
170#11924005—22no—
171#11924005—22no—
172#11924005—22no—
173#11924005—22no—
174C4×Dic73—22no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C22×C411yescharacteristic
193C22×C4×C73C22×C411yescharacteristic
194C42×C73—22no—
195C23×C73C23×C411yescharacteristic
196C22×D73—21no—
197C22×D73—21no—
198C22×D73—21no—
199C22×D73—21no—
200C22×D73#11712yes—
201C22×D73#13112yes—
202C22×D73#13112yes—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73#11712yes—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73#13112yes—
242C2×Dic73C2×#4111yescharacteristic
243C2×Dic73C2×#4111yescharacteristic
244C2×Dic73C2×#4111yescharacteristic
245C2×Dic73C2×#4111yescharacteristic
246C2×Dic73H(5,𝔽2)11yescharacteristic
247C2×Dic732−1+411yescharacteristic
248C4×D73—22no—
249C4×D73—22no—
250C4×D73—22no—
251C4×D73—22no—
252C4×D73—44no—
253C4×D73—44no—
254#10596833—22no—
255#10596833—22no—
256#10596833—41no—
257#10596833—41no—
258#10596833—41no—
259#10596833—41no—
260#10596833—41no—
261#10596833—41no—
262C22×C73C2×#11711yescharacteristic
263C22×C73C4×#4111yescharacteristic
264C22×C73#52011yescharacteristic
265C22×C73C2×#13111yescharacteristic
266C22×C73C2×#13111yescharacteristic
267C22×C73C2×#13111yescharacteristic
268C22×C73#56811yescharacteristic
269C2×D73—22no—
270C2×D73—22no—
271C2×D73—22no—
272C2×D73—22no—
273C2×D73—22no—
274C2×D73—22no—
275C2×D73#43314yes—
276C4×C73—22no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73—41no—
282C4×C73—41no—
283Dic73—22no—
284Dic73—41no—
285Dic73—41no—
286Dic73—41no—
287Dic73—41no—
288Dic73—41no—
289Dic73#55111yescharacteristic
290Dic73#55111yescharacteristic
291Dic73#55211yescharacteristic
292Dic73#55211yescharacteristic
293#22595—731nomaximal, Sylow
294C2×C73#234311yescharacteristic
295C2×C73C2×#43311yescharacteristic
296C2×C73#292411yescharacteristic
297C2×C73#296611yescharacteristic
298C2×C73#296811yescharacteristic
299C2×C73#299211yescharacteristic
300C2×C73#299411yescharacteristic
301D73—24no—
302#2283—731no—
303#1917—731no—
304#1917—731no—
305#1916—731no—
306#1916—731no—
307#1850—731no—
308#1850—731no—
309#1840—731no—
310#1832—731no—
311#1817—731no—
312#1768—731no—
313#1752—731no—
314C8×C22⋊C4—731no—
315#1746—731no—
316C2×#336—731no—
317C73#2259511yescharacteristic, complemented, Sylow
318C23×C8—731no—
319C23×C8—731no—
320C22×C42—731no—
321C2×C4⋊C8—731no—
322C2×C4⋊C8—731no—
323C2×C4⋊C8—731no—
324C2×C4⋊C8—731no—
325C2×C22⋊C8—731no—
326C2×C22⋊C8—731no—
327C2×#97—731no—
328C2×#97—731no—
329C2×C4×C8—731no—
330C2×C4×C8—731no—
331#383—731no—
332#383#6440811yescharacteristic
333#382—731no—
334#382—731no—
335#381—731no—
336#381—731no—
337#380—731no—
338#380—731no—
339C4×C4⋊C4—731no—
340C4×C4⋊C4—731no—
341C4×C22⋊C4—731no—
342C4×C22⋊C4—731no—
343#376—731no—
344#376—731no—
345#336—731no—
346#336—731no—
347#336—731no—
348#336—731no—
349#336—731no—
350#336—731no—
351#336—731no—
352#336—731no—
353#336—731no—
354#336—731no—
355#336—731no—
356#336—731no—
357#336—731no—
358#336—731no—
359#336—731no—
360#336—731no—
361C23×C4—731no—
362C23×C4—731no—
363C23×C4—731no—
364C22×C8—2921no—
365C22×C8—2921no—
366C22×C8—731no—
367C22×C8—731no—
368C22×C8—731no—
369C22×C8—731no—
370C22×C8—731no—
371C22×C8—731no—
372C22×C8—731no—
373C22×C8—731no—
374C22×C8—1462no—
375C22×C8—1462no—
376C22×C8—1462no—
377C22×C8—1462no—
378C2×C4⋊C4—731no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—731no—
381C2×C4⋊C4—731no—
382C2×C22⋊C4—731no—
383C2×C22⋊C4—731no—
384C2×C22⋊C4—731no—
385C2×C22⋊C4—731no—
386C2×C42—731no—
387C2×C42—731no—
388C2×C42—731no—
389C2×C42—731no—
390C2×C42—731no—
391C2×C42—731no—
392C2×C42—731no—
393C2×C42—1462no—
394C2×C42—1462no—
395C2×C42C2×#6440811yescharacteristic
396C4⋊C8—2921no—
397C4⋊C8—2921no—
398C4⋊C8—1462no—
399C4⋊C8—1462no—
400C22⋊C8—1462no—
401C22⋊C8—1462no—
402#97—2921no—
403#97—1462no—
404C4×C8—2921no—
405C4×C8—1462no—
406#95—731no—
407#95—731no—
408#95—731no—
409#95—731no—
410#95—731no—
411#95—731no—
412#95—731no—
413#95—731no—
414#95—731no—
415#95—731no—
416#95C2×#6440811yescharacteristic
417#95C2×#6440811yescharacteristic
418#95C2×#6440811yescharacteristic
419#95C2×#6440811yescharacteristic
420#95C2×#6440811yescharacteristic
421#95C2×#6440811yescharacteristic
422C24—731no—
423C22×C4—2921no—
424C22×C4—731no—
425C22×C4—731no—
426C22×C4—732no—
427C22×C4—732no—
428C22×C4—731no—
429C22×C4—731no—
430C22×C4—731no—
431C22×C4—731no—
432C22×C4—731no—
433C22×C4—1462no—
434C22×C4—1462no—
435C22×C4—1462no—
436C22×C4—1462no—
437C22×C4—1462no—
438C22×C4—1461no—
439C22×C4—1461no—
440C22×C4—1461no—
441C22×C4—1461no—
442C22×C4C22×#6440811yescharacteristic
443C22×C4C22×#6440811yescharacteristic
444C22×C4C22×#6440811yescharacteristic
445C22×C4C22×#6440811yescharacteristic
446C22×C4C22×#6440811yescharacteristic
447C22×C4C22×#6440811yescharacteristic
448C22×C4C22×#6440811yescharacteristic
449C2×C8—2924no—
450C2×C8—2924no—
451C2×C8—732no—
452C2×C8—732no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1461no—
475C4⋊C4—2921no—
476C4⋊C4—2921no—
477C4⋊C4—1462no—
478C4⋊C4—1462no—
479C22⋊C4—1462no—
480C22⋊C4—1462no—
481C22⋊C4—1462no—
482C22⋊C4—1462no—
483C42—22no—
484C42—1461no—
485C42—1461no—
486C42—1461no—
487C42—1461no—
488C42—1461no—
489C42—1461no—
490C42—1461no—
491C42—1461no—
492C42—1461no—
493C42—1461no—
494C42—1461no—
495C42—1461no—
496C42—1462no—
497C23—732no—
498C23—732no—
499C23—732no—
500C23—1461no—
501C23—1461no—
502C23—1461no—
503C23—1461no—
504C23C23×#6440811yescharacteristic
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—2924no—
526C2×C4—2924no—
527C2×C4—731no—
528C2×C4—731no—
529C2×C4—731no—
530C2×C4—731no—
531C2×C4—731no—
532C2×C4—731no—
533C2×C4—732no—
534C2×C4—1462no—
535C2×C4—1462no—
536C2×C4—1462no—
537C2×C4—1462no—
538C2×C4—1461no—
539C2×C4—1461no—
540C2×C4—1461no—
541C2×C4—1461no—
542C2×C4—1461no—
543C2×C4—1461no—
544C2×C4—1461no—
545C2×C4—1461no—
546C2×C4—1461no—
547C2×C4—1461no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4#1455667012yes—
556C8—2921no—
557C8—2921no—
558C8—2921no—
559C8—2921no—
560C8—2921no—
561C8—2921no—
562C8—1462no—
563C8—1462no—
564C22—734no—
565C22—1462no—
566C22—1462no—
567C22—1462no—
568C22—1462no—
569C22—1462no—
570C22—1462no—
571C22C2×#1455667011yescharacteristic
572C22#41×#6440811yescharacteristic
573C22#1798965611yescharacteristic
574C22D73⋊#13111yescharacteristic
575C22D73⋊#13111yescharacteristic
576C22D73⋊#13111yescharacteristic
577C22#1798966611yescharacteristic
578C4—22no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—2921no—
586C4—2921no—
587C4—2921no—
588C4—2921no—
589C4—2921no—
590C4—731no—
591C4—731no—
592C4—731no—
593C4—731no—
594C4—1462no—
595C2—1464no—
596C2#2262643811yescharacteristic
597C2D73⋊#43311yescharacteristic
598C2#2262662511yescharacteristic
599C2#2262674911yescharacteristic
600C2#2262676111yescharacteristic
601C2#2262686911yescharacteristic
602C2#2262688011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#383×C73C4
prime radicalC23×D73C22×C4
cosocleC22×Dic73C24
hypercenter#383#64408
hypocenterC73#22595
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
1. #22625990C2semidirect
2. #22625990C2semidirect
3. #22625985C2semidirect
4. #22625985C2semidirect
7. #22625860C2semidirect
8. #22625849C2semidirect
10. #22625719C2semidirect
13. #22625650C2semidirect
317. C73#22595semidirect

Maximal subgroups

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

subgroupindex
#226259902
#226259852
#226258762
#226258602
#226258492
#226258232
#226257192
#226256692
#226256652
#226256502
#226255922
#226123282
#2259573