Finite Group Databasebeta

← #34029745

Subgroups — #34029745

Order 18688.

642 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626033C211yesmaximal, characteristic, complemented
2#22626032C211yesmaximal, characteristic, complemented
3#22626031C211yesmaximal, characteristic, complemented
4#22626005C211yesmaximal, characteristic
5#22626004C211yesmaximal, characteristic
6#22626004C211yesmaximal, characteristic
7#22625991C211yesmaximal, characteristic, complemented
8#22625990C211yesmaximal, characteristic, complemented
9#22625989C211yesmaximal, characteristic, complemented
10#22625878C211yesmaximal, characteristic
11#22625878C211yesmaximal, characteristic
12#22625878C211yesmaximal, characteristic
13#22625864C211yesmaximal, characteristic, complemented
14#22625859C211yesmaximal, characteristic, complemented
15#22612485C211yesmaximal, characteristic
16C22×#11924037C2211yescharacteristic
17C2×#14556658C2211yescharacteristic
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×#14556658C2211yescharacteristic
21C2×#14556658C2211yescharacteristic
22C2×C4⋊#10596833C2211yescharacteristic
23C2×C4⋊#10596833C2211yescharacteristic
24C2×C4⋊#10596833C2211yescharacteristic
25C2×C4⋊#10596833C2211yescharacteristic
26C2×C22⋊#10596833C2211yescharacteristic
27C2×C22⋊#10596833C2211yescharacteristic
28C2×C22⋊#10596833C2211yescharacteristic
29C2×#14556646C2211yescharacteristic
30C2×#14556646C2211yescharacteristic
31C2×#14556646C2211yescharacteristic
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×#14556584C411yescharacteristic
45#17988481C411yescharacteristic
46#17988475C411yescharacteristic
47#17988471C411yescharacteristic
48#17988470C411yescharacteristic
49#17988468C411yescharacteristic
50#17988454C411yescharacteristic
51C4⋊C4×Dic73C2211yescharacteristic
52#17988438C2211yescharacteristic
53#17988438C2211yescharacteristic
54C22⋊C4×Dic73C2211yescharacteristic
55C22⋊C4×Dic73C2211yescharacteristic
56C22⋊C4×Dic73C2211yescharacteristic
57C42×Dic73C2211yescharacteristic
58#388×C73C411yescharacteristic
59C2×#11924037—41no—
60C2×#11924037—41no—
61C2×#11924037—41no—
62C22×#10596833C2311yescharacteristic
63C22×#10596833C2311yescharacteristic
64C22×#10596833C2311yescharacteristic
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69C22×#10596833C2311yescharacteristic
70#14556658—41no—
71#14556658—41no—
72#14556658—41no—
73#14556658—41no—
74#14556658—41no—
75C4⋊#10596833—41no—
76C4⋊#10596833—41no—
77C4⋊#10596833—41no—
78C4⋊#10596833—41no—
79C22⋊#10596833—41no—
80C22⋊#10596833—41no—
81C22⋊#10596833—41no—
82#14556646—41no—
83#14556646—41no—
84#14556646—41no—
85C23×Dic73C2311yescharacteristic
86#14556584—24no—
87C2×C4⋊Dic73C2×C411yescharacteristic
88C2×#11924007C2×C411yescharacteristic
89C2×#11924007C2×C411yescharacteristic
90C2×#11924007C2×C411yescharacteristic
91C2×#11924007C2×C411yescharacteristic
92C2×C22⋊Dic73C2×C411yescharacteristic
93C2×C22⋊Dic73C2×C411yescharacteristic
94C2×C22⋊Dic73C2×C411yescharacteristic
95C2×C4×Dic73C2×C411yescharacteristic
96C2×C4×Dic73C2×C411yescharacteristic
97C2×C4×Dic73C2×C411yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101C2×C4×Dic73C2311yescharacteristic
102C2×C4×Dic73C2311yescharacteristic
103C2×C4×Dic73C2311yescharacteristic
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
113#14556498C2×C411yescharacteristic
114C2×C4⋊C4×C73C2×C411yescharacteristic
115C2×C22⋊C4×C73C2×C411yescharacteristic
116C2×C22⋊C4×C73C2×C411yescharacteristic
117C2×C22⋊C4×C73C2×C411yescharacteristic
118C2×C42×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120#95×C73C2×C411yescharacteristic
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—21no—
145C2×#10596833—21no—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73C22×C411yescharacteristic
153C22×Dic73C22×C411yescharacteristic
154C22×Dic73C22×C411yescharacteristic
155C22×Dic73C22×C411yescharacteristic
156C22×Dic73C22×C411yescharacteristic
157C22×Dic73C22×C411yescharacteristic
158C22×Dic73C22×C411yescharacteristic
159C22×Dic73C2411yescharacteristic
160C4⋊Dic73—22no—
161#11924007—22no—
162#11924007—22no—
163#11924007—41no—
164#11924007—41no—
165C22⋊Dic73—22no—
166C22⋊Dic73—22no—
167C22⋊Dic73—41no—
168C4×Dic73—21no—
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—41no—
181C4×Dic73—41no—
182C4×Dic73M1614yescomplemented
183C24×C73C22×C411yescharacteristic
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C22×C411yescharacteristic
190C4⋊C4×C73—41no—
191C22⋊C4×C73—22no—
192C22⋊C4×C73—41no—
193C22⋊C4×C73—41no—
194C42×C73—41no—
195C23×C73—21no—
196C23×C73—21no—
197C23×C73—21no—
198C23×C73—21no—
199C23×C73—21no—
200C23×C73—21no—
201C23×C73—21no—
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×C73C2×M1612yes—
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73—21no—
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—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73C2×M1612yes—
245C2×Dic73C2×M1612yes—
246C2×Dic73H(5,𝔽2)11yescharacteristic
247C2×Dic73H(5,𝔽2)11yescharacteristic
248C2×Dic73H(5,𝔽2)11yescharacteristic
249C2×Dic732−1+411yescharacteristic
250C2×Dic732−1+411yescharacteristic
251C2×Dic732−1+411yescharacteristic
252#10596833—41no—
253#10596833—41no—
254#10596833—41no—
255#10596833—41no—
256#10596833—41no—
257#10596833—41no—
258#10596833—41no—
259#10596833—41no—
260C22×C73—41no—
261C22×C73—41no—
262C22×C73—41no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73#52011yescharacteristic
268C22×C73#52011yescharacteristic
269C22×C73#52011yescharacteristic
270C22×C73C22×M1611yescharacteristic
271C22×C73#56811yescharacteristic
272C22×C73#56811yescharacteristic
273C22×C73#56811yescharacteristic
274C4×C73—22no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—41no—
280Dic73—22no—
281Dic73—22no—
282Dic73—41no—
283Dic73—41no—
284Dic73—41no—
285Dic73—41no—
286Dic73—41no—
287Dic73#56011yescharacteristic
288Dic73#56311yescharacteristic
289Dic73#56311yescharacteristic
290Dic73#56311yescharacteristic
291#23378—731nomaximal, Sylow
292C2×C73—81no—
293C2×C73#238311yescharacteristic
294C2×C73#298911yescharacteristic
295C2×C73#298911yescharacteristic
296C2×C73#298911yescharacteristic
297C2×C73#299511yescharacteristic
298C2×C73#299511yescharacteristic
299C2×C73#299511yescharacteristic
300C4×#126—731no—
301#1940—731no—
302#1940—731no—
303#1940—731no—
304#1924—731no—
305#1924—731no—
306#1924—731no—
307#1917—731no—
308#1917—731no—
309#1917—731no—
310#1851—731no—
311#1851—731no—
312#1851—731no—
313#1842—731no—
314#1839—731no—
315C73#2337811yescharacteristic, complemented, Sylow
316C22×M16—731no—
317C2×#126—731no—
318C2×C4⋊C8—731no—
319C2×C4⋊C8—731no—
320C2×C4⋊C8—731no—
321C2×C4⋊C8—731no—
322C2×C4⋊C8—731no—
323C2×C4⋊C8—731no—
324C2×C4⋊C8—731no—
325C2×C4⋊C8—731no—
326C2×C4⋊C8—731no—
327C2×C22⋊C8—731no—
328C2×C22⋊C8—731no—
329C2×C22⋊C8—731no—
330C2×#97—731no—
331C2×#97—731no—
332C2×#97—731no—
333#388—731no—
334#388—731no—
335#388#6440811yescharacteristic
336#387—731no—
337#387—731no—
338#387—731no—
339#383—731no—
340C4×C4⋊C4—731no—
341C4×C4⋊C4—731no—
342C4×C4⋊C4—731no—
343C4×C22⋊C4—731no—
344C4×C22⋊C4—731no—
345C4×C22⋊C4—731no—
346C43—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—
359C23×C4—731no—
360C2×M16—2921no—
361C2×M16—2921no—
362C2×M16—2921no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—731no—
366C22×C8—731no—
367C22×C8—731no—
368C22×C8—731no—
369C22×C8—731no—
370C22×C8—731no—
371#126—1464no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4—731no—
375C2×C4⋊C4—731no—
376C2×C4⋊C4—731no—
377C2×C4⋊C4C2×#6440811yescharacteristic
378C2×C22⋊C4—731no—
379C2×C22⋊C4—731no—
380C2×C22⋊C4—731no—
381C2×C22⋊C4C2×#6440811yescharacteristic
382C2×C22⋊C4C2×#6440811yescharacteristic
383C2×C22⋊C4C2×#6440811yescharacteristic
384C2×C42—731no—
385C2×C42—731no—
386C2×C42—731no—
387C2×C42—731no—
388C2×C42—731no—
389C2×C42—731no—
390C2×C42—731no—
391C2×C42—731no—
392C2×C42—731no—
393C2×C42C2×#6440811yescharacteristic
394C4⋊C8—2921no—
395C4⋊C8—2921no—
396C4⋊C8—2921no—
397C4⋊C8—2921no—
398C4⋊C8—2921no—
399C4⋊C8—2921no—
400C4⋊C8—2921no—
401C4⋊C8—2921no—
402C4⋊C8—2921no—
403C22⋊C8—2921no—
404C22⋊C8—2921no—
405C22⋊C8—2921no—
406#97—2921no—
407#97—2921no—
408#97—2921no—
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#95C2×#6440811yescharacteristic
420#95C2×#6440811yescharacteristic
421C24C22×#6440811yescharacteristic
422C22×C4—731no—
423C22×C4—731no—
424C22×C4—731no—
425C22×C4—731no—
426C22×C4—731no—
427C22×C4—731no—
428C22×C4—731no—
429C22×C4—731no—
430C22×C4—1461no—
431C22×C4—1461no—
432C22×C4—1461no—
433C22×C4—1461no—
434C22×C4—1461no—
435C22×C4—1461no—
436C22×C4C22×#6440811yescharacteristic
437C22×C4C22×#6440811yescharacteristic
438C22×C4C22×#6440811yescharacteristic
439C22×C4C22×#6440811yescharacteristic
440C22×C4C22×#6440811yescharacteristic
441C22×C4C22×#6440811yescharacteristic
442M16—2924no—
443C2×C8—1461no—
444C2×C8—1461no—
445C2×C8—1461no—
446C2×C8—1461no—
447C2×C8—1461no—
448C2×C8—1461no—
449C2×C8—1461no—
450C2×C8—1461no—
451C2×C8—1461no—
452C2×C8—1461no—
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—
467C4⋊C4—41no—
468C4⋊C4—2921no—
469C4⋊C4—2921no—
470C4⋊C4—1462no—
471C4⋊C4—1462no—
472C4⋊C4—1462no—
473C22⋊C4—22no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—2921no—
477C22⋊C4—1462no—
478C22⋊C4—1462no—
479C42—41no—
480C42—2921no—
481C42—2921no—
482C42—734no—
483C42—1461no—
484C42—1461no—
485C42—1461no—
486C42—1461no—
487C42—1461no—
488C42—1461no—
489C42—1461no—
490C42—1461no—
491C42—1461no—
492C42—1461no—
493C42—1461no—
494C42—1461no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23C23×#6440811yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
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—2921no—
521C2×C4—2921no—
522C2×C4—2921no—
523C2×C4—2921no—
524C2×C4—731no—
525C2×C4—731no—
526C2×C4—731no—
527C2×C4—731no—
528C2×C4—731no—
529C2×C4—731no—
530C2×C4—732no—
531C2×C4—732no—
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—1461no—
550C2×C4—1461no—
551C2×C4D73⋊M1612yes—
552C8—2921no—
553C8—2921no—
554C8—2921no—
555C8—2921no—
556C8—2921no—
557C8—2921no—
558C8—2921no—
559C8—2921no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#1798965611yescharacteristic
568C22#1798965611yescharacteristic
569C22#1798965611yescharacteristic
570C22C2×D73⋊M1611yescharacteristic
571C22#1798966511yescharacteristic
572C22#1798966511yescharacteristic
573C22#1798966611yescharacteristic
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—2921no—
581C4—2921no—
582C4—2921no—
583C4—2921no—
584C4—2921no—
585C4—731no—
586C4—731no—
587C4—731no—
588C4—731no—
589C4—1462no—
590C4—1462no—
591C2—81no—
592C2#2262647811yescharacteristic
593C2#2262685111yescharacteristic
594C2#2262685311yescharacteristic
595C2#2262685411yescharacteristic
596C2#2262688411yescharacteristic
597C2#2262688511yescharacteristic
598C2#2262688711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#388×C73C4
prime radicalC24×C73C22×C4
cosocleC22×Dic73C24
hypercenter#388#64408
hypocenterC73#23378
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #22626033C2semidirect
2. #22626032C2semidirect
3. #22626031C2semidirect
7. #22625991C2semidirect
8. #22625990C2semidirect
9. #22625989C2semidirect
13. #22625864C2semidirect
14. #22625859C2semidirect
182. C4×Dic73M16semidirect
315. C73#23378semidirect

Maximal subgroups

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

subgroupindex
#226260332
#226260322
#226260312
#226260052
#226260042
#226259912
#226259902
#226259892
#226258782
#226258642
#226258592
#226124852
#2337873