Finite Group Databasebeta

← #34026676

Subgroups — #34026676

Order 18688.

704 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#22625991C211yesmaximal, characteristic, complemented
2#22625988C211yesmaximal, characteristic, complemented
3#22625987C211yesmaximal, characteristic, complemented
4#22625984C211yesmaximal, characteristic, complemented
5#22625878C211yesmaximal, characteristic
6#22625878C211yesmaximal, characteristic
7#22625860C211yesmaximal, characteristic, complemented
8#22625849C211yesmaximal, characteristic, complemented
9#22625821C211yesmaximal, characteristic
10#22625719C211yesmaximal, characteristic, complemented
11#22625673C211yesmaximal, characteristic
12#22625673C211yesmaximal, characteristic
13#22625650C211yesmaximal, characteristic, complemented
14#22625594C211yesmaximal, characteristic
15#22612326C211yesmaximal, characteristic
16C22×#11924037C2211yescharacteristic
17C22×#11924037C2211yescharacteristic
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×C4⋊#10596833C2211yescharacteristic
21C2×C4⋊#10596833C2211yescharacteristic
22C2×C22⋊#10596833C2211yescharacteristic
23C2×C22⋊#10596833C2211yescharacteristic
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
44C22×C4×Dic73C2211yescharacteristic
45#17988454C411yescharacteristic
46#17988454C411yescharacteristic
47#17988452C411yescharacteristic
48#17988452C411yescharacteristic
49#17988448C411yescharacteristic
50#17988448C411yescharacteristic
51#17988447C411yescharacteristic
52C4⋊C4×Dic73C2211yescharacteristic
53C4⋊C4×Dic73C2211yescharacteristic
54C22⋊C4×Dic73C2211yescharacteristic
55C22⋊C4×Dic73C2211yescharacteristic
56#17988432C2211yescharacteristic
57#17988432C2211yescharacteristic
58#380×C73C411yescharacteristic
59C2×#11924037—22no—
60C2×#11924037—22no—
61C2×#11924037—22no—
62C2×#11924037—22no—
63C2×#11924037—41no—
64C2×#11924037—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—
77C22⋊#10596833—22no—
78C22⋊#10596833—22no—
79#14556646—22no—
80#14556646—41no—
81C4×#10596833—22no—
82C4×#10596833—41no—
83C23×Dic73C2×C411yescharacteristic
84C23×Dic73C2311yescharacteristic
85C2×C4⋊Dic73C2×C411yescharacteristic
86C2×C4⋊Dic73C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×C22⋊Dic73C2×C411yescharacteristic
89C2×C4×Dic73—22no—
90C2×C4×Dic73—22no—
91C2×C4×Dic73C2×C411yescharacteristic
92C2×C4×Dic73C2×C411yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99#14556498C2×C411yescharacteristic
100#14556498C2×C411yescharacteristic
101#14556498C2×C411yescharacteristic
102#14556498C2×C411yescharacteristic
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
113C23×C4×C73C2×C411yescharacteristic
114C2×C4⋊C4×C73C2×C411yescharacteristic
115C2×C4⋊C4×C73C2×C411yescharacteristic
116C2×C22⋊C4×C73C2×C411yescharacteristic
117C2×C22⋊C4×C73C2×C411yescharacteristic
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120#11924037—44no—
121#11924037—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—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73—22no—
151C22×Dic73—41no—
152C22×Dic73—41no—
153C22×Dic73C22×C411yescharacteristic
154C22×Dic73C22×C411yescharacteristic
155C22×Dic73C22×C411yescharacteristic
156C22×Dic73C22×C411yescharacteristic
157C22×Dic73C22×C411yescharacteristic
158C22×Dic73C22×C411yescharacteristic
159C22×Dic73C22×C411yescharacteristic
160C22×Dic73#4112yes—
161C22×Dic73#4112yes—
162C22×Dic73C2411yescharacteristic
163C4⋊Dic73—22no—
164C4⋊Dic73—41no—
165C22⋊Dic73—41no—
166C22⋊Dic73—41no—
167C4×Dic73—22no—
168C4×Dic73—22no—
169C4×Dic73—21no—
170C4×Dic73—21no—
171C4×Dic73—21no—
172C4×Dic73—21no—
173C4×Dic73—21no—
174C4×Dic73—21no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C24×C73C22×C411yescharacteristic
182C22×C4×C73—22no—
183C22×C4×C73—22no—
184C22×C4×C73—41no—
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C22×C411yescharacteristic
191C4⋊C4×C73—22no—
192C4⋊C4×C73—41no—
193C22⋊C4×C73—41no—
194C22⋊C4×C73—41no—
195C23×C73—21no—
196C23×C73—21no—
197C23×C73—21no—
198C23×C73—21no—
199C23×C73—21no—
200C23×C73—21no—
201C23×C73#11712yes—
202C23×C73C23×C411yescharacteristic
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—44no—
221C2×C4×C73#13112yes—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—22no—
225C2×Dic73—22no—
226C2×Dic73—22no—
227C2×Dic73—22no—
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—21no—
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—44no—
247C2×Dic73#11712yes—
248C2×Dic73C2×#4111yescharacteristic
249C2×Dic73C2×#4111yescharacteristic
250C2×Dic73C2×#4111yescharacteristic
251C2×Dic73C2×#4111yescharacteristic
252C2×Dic73H(5,𝔽2)11yescharacteristic
253C2×Dic732−1+411yescharacteristic
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×C73—22no—
263C22×C73—22no—
264C22×C73—22no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73—41no—
268C22×C73—41no—
269C22×C73C2×#11711yescharacteristic
270C22×C73C4×#4111yescharacteristic
271C22×C73#52011yescharacteristic
272C22×C73C2×#13111yescharacteristic
273C22×C73#56811yescharacteristic
274C22×C73#56811yescharacteristic
275C22×C73#56811yescharacteristic
276C4×C73—22no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73—41no—
282Dic73—22no—
283Dic73—41no—
284Dic73—41no—
285Dic73—41no—
286Dic73—41no—
287Dic73—41no—
288Dic73—41no—
289Dic73#55111yescharacteristic
290Dic73#55111yescharacteristic
291Dic73#55211yescharacteristic
292Dic73#55211yescharacteristic
293#22596—731nomaximal, Sylow
294C2×C73—42no—
295C2×C73#234311yescharacteristic
296C2×C73#292111yescharacteristic
297C2×C73#292411yescharacteristic
298C2×C73#296711yescharacteristic
299C2×C73#296911yescharacteristic
300C2×C73#299311yescharacteristic
301C2×C73#299511yescharacteristic
302#2283—731no—
303#1917—731no—
304#1917—731no—
305#1916—731no—
306#1916—731no—
307#1851—731no—
308#1851—731no—
309#1840—731no—
310#1832—731no—
311#1817—731no—
312#1768—731no—
313#1753—731no—
314#1753—731no—
315#1746—731no—
316#1728—731no—
317C73#2259611yescharacteristic, complemented, Sylow
318C22×M16—731no—
319C22×M16—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—731no—
333#382—731no—
334#382—731no—
335#381—731no—
336#381—731no—
337#380—731no—
338#380#6440811yescharacteristic
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×C4C2×#6440811yescharacteristic
364C2×M16—2921no—
365C2×M16—2921no—
366C2×M16—1462no—
367C2×M16—1462no—
368C2×M16—1462no—
369C2×M16—1462no—
370C22×C8—731no—
371C22×C8—731no—
372C22×C8—731no—
373C22×C8—731no—
374C22×C8—731no—
375C22×C8—731no—
376C22×C8—731no—
377C22×C8—731no—
378C2×C4⋊C4—731no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4C2×#6440811yescharacteristic
381C2×C4⋊C4C2×#6440811yescharacteristic
382C2×C22⋊C4—731no—
383C2×C22⋊C4—731no—
384C2×C22⋊C4C2×#6440811yescharacteristic
385C2×C22⋊C4C2×#6440811yescharacteristic
386C2×C42—731no—
387C2×C42—731no—
388C2×C42—731no—
389C2×C42—731no—
390C2×C42—731no—
391C2×C42—731no—
392C2×C42—731no—
393C2×C42—731no—
394C2×C42—1462no—
395C2×C42—1462no—
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#95—731no—
417#95—731no—
418#95—731no—
419#95—731no—
420#95C2×#6440811yescharacteristic
421#95C2×#6440811yescharacteristic
422C24C22×#6440811yescharacteristic
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—41no—
426C22×C4—2921no—
427C22×C4—2921no—
428C22×C4—731no—
429C22×C4—731no—
430C22×C4—732no—
431C22×C4—732no—
432C22×C4—731no—
433C22×C4—731no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—1462no—
439C22×C4—1461no—
440C22×C4—1461no—
441C22×C4—1461no—
442C22×C4—1461no—
443C22×C4C22×#6440811yescharacteristic
444C22×C4C22×#6440811yescharacteristic
445C22×C4C22×#6440811yescharacteristic
446C22×C4C22×#6440811yescharacteristic
447C22×C4C22×#6440811yescharacteristic
448C22×C4C22×#6440811yescharacteristic
449M16—2924no—
450M16—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—22no—
476C4⋊C4—41no—
477C4⋊C4—2921no—
478C4⋊C4—1462no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—2921no—
482C22⋊C4—2921no—
483C42—1461no—
484C42—1461no—
485C42—1461no—
486C42—1461no—
487C42—1461no—
488C42—1461no—
489C42—1461no—
490C42—1461no—
491C42—1461no—
492C42—1461no—
493C42—1462no—
494C42—1461no—
495C42—1461no—
496C42—1462no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23#1455667012yes—
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—44no—
523C2×C4—2924no—
524C2×C4—731no—
525C2×C4—731no—
526C2×C4—731no—
527C2×C4—731no—
528C2×C4—731no—
529C2×C4—731no—
530C2×C4—732no—
531C2×C4—1461no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4—1461no—
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—1462no—
550C2×C4—1462no—
551C2×C4—1462no—
552C2×C4—1462no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4#1455667812yes—
556C8—2921no—
557C8—2921no—
558C8—2921no—
559C8—2921no—
560C8—2921no—
561C8—2921no—
562C8—1462no—
563C8—1462no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22C2×#1455667011yescharacteristic
572C22#41×#6440811yescharacteristic
573C22#1798965611yescharacteristic
574C22C2×#1455667811yescharacteristic
575C22#1798966511yescharacteristic
576C22#1798966511yescharacteristic
577C22#1798966711yescharacteristic
578C4—22no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—2921no—
585C4—2921no—
586C4—2921no—
587C4—2921no—
588C4—2921no—
589C4—2921no—
590C4—731no—
591C4—731no—
592C4—731no—
593C4—731no—
594C4—1462no—
595C2—42no—
596C2#2262643811yescharacteristic
597C2#2262661311yescharacteristic
598C2#2262662011yescharacteristic
599C2#2262675211yescharacteristic
600C2#2262676211yescharacteristic
601C2#2262687611yescharacteristic
602C2#2262688411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#380×C73C4
prime radicalC24×C73C22×C4
cosocleC22×Dic73C24
hypercenter#380#64408
hypocenterC73#22596
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. #22625991C2semidirect
2. #22625988C2semidirect
3. #22625987C2semidirect
4. #22625984C2semidirect
7. #22625860C2semidirect
8. #22625849C2semidirect
10. #22625719C2semidirect
13. #22625650C2semidirect
317. C73#22596semidirect

Maximal subgroups

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

subgroupindex
#226259912
#226259882
#226259872
#226259842
#226258782
#226258602
#226258492
#226258212
#226257192
#226256732
#226256502
#226255942
#226123262
#2259673