Finite Group Databasebeta

← #22621775

Subgroups — #22621775

Order 9344.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989233C211yesmaximal, characteristic, complemented
2#17988944C211yesmaximal, characteristic, complemented
3#17988922C211yesmaximal, characteristic, complemented
4#17988911C211yesmaximal, characteristic, complemented
5#17988884C211yesmaximal, characteristic, complemented
6#17988821C211yesmaximal, characteristic, complemented
7#17988814C211yesmaximal, characteristic, complemented
8#17988802C211yesmaximal, characteristic, complemented
9#17988730C211yesmaximal, characteristic, complemented
10#17988720C211yesmaximal, characteristic, complemented
11C4×#11924013C211yesmaximal, characteristic, complemented
12D4×#10596831C211yesmaximal, characteristic, complemented
13#17988581C211yesmaximal, characteristic, complemented
14C2×#14556511C211yesmaximal, characteristic, complemented
15#553×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C2×#11924016C2211yescharacteristic, complemented
19C2×#11924013C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21C22×#10596831C2211yescharacteristic
22C22×#10596831C2211yescharacteristic, complemented
23#14556579C2211yescharacteristic
24#14556576—21no—
25#14556570C2211yescharacteristic
26#14556565C2211yescharacteristic
27#14556564—21no—
28#14556559—21no—
29C4×D292C2211yescharacteristic
30C22⋊C4×D73—21no—
31#14556524C2211yescharacteristic, complemented
32#14556524C2211yescharacteristic, complemented
33#14556522C2211yescharacteristic, complemented
34C4⋊#10596831C2211yescharacteristic, complemented
35#14556514C2211yescharacteristic, complemented
36#14556514C2211yescharacteristic, complemented
37#14556514C2211yescharacteristic, complemented
38#14556512C2211yescharacteristic, complemented
39#14556511C2211yescharacteristic
40#14556511C2211yescharacteristic
41#14556511C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44#14556511C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic, complemented
47C4×#10596831C2211yescharacteristic, complemented
48#126×C73—21no—
49#125×C73C2211yescharacteristic, complemented
50#123×C73—21no—
51#121×C73—21no—
52#121×C73C2211yescharacteristic
53#121×C73C2211yescharacteristic, complemented
54C4×D4×C73—21no—
55C4×D4×C73C2211yescharacteristic
56C4×D4×C73C2211yescharacteristic, complemented
57#117×C73C2211yescharacteristic, complemented
58C2×C4⋊C4×C73C2211yescharacteristic
59C23×D73—21no—
60#11924028—22no—
61#11924028—41no—
62C2×Dic146C2311yescharacteristic
63C2×D292—22no—
64C2×D292—21no—
65C2×D292—41no—
66C2×D292C2311yescharacteristic
67C2×D292C2311yescharacteristic
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72#11924016—41no—
73#11924013—22no—
74#11924013—41no—
75C2×#10596831—41no—
76C2×#10596831—41no—
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C2×#10596831C2311yescharacteristic
80C2×#10596831C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83C22⋊Dic73—21no—
84#11924005—21no—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88C2×D4×C73—21no—
89C2×D4×C73—21no—
90C2×D4×C73D411yescharacteristic
91C2×D4×C73C2311yescharacteristic
92C22×C4×C73—21no—
93C22×C4×C73—21no—
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C4⋊C4×C73—21no—
97C4⋊C4×C73—21no—
98C4⋊C4×C73—21no—
99C4⋊C4×C73D411yescharacteristic
100C4⋊C4×C73C2311yescharacteristic
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C22⋊C4×C73—21no—
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C22⋊C4×C73D411yescharacteristic
108C22⋊C4×C73D411yescharacteristic
109C42×C73—21no—
110C42×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C23×C73C2×D411yescharacteristic
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—42no—
117C22×D73—42no—
118C22×D73—81no—
119D4×C73—22no—
120D4×C73—21no—
121D4×C73—21no—
122D4×C73—42no—
123D4×C73—81no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—81no—
132C2×C4×C73—81no—
133C2×C4×C73C2×D411yescharacteristic
134C2×C4×C73C2×D411yescharacteristic
135C2×C4×C73C2×D411yescharacteristic
136C2×C4×C73C2×D411yescharacteristic
137C2×C4×C73C2411yescharacteristic
138C22⋊D73—42no—
139C22⋊D73—81no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142D292—21no—
143D292—21no—
144D292—21no—
145D292—42no—
146D292#4112yes—
147C4×D73—42no—
148C4×D73—81no—
149Dic146—21no—
150Dic146—21no—
151#10596831—21no—
152#10596831—21no—
153#10596831—21no—
154#10596831—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73#13512yes—
164C22×C73C22×D411yescharacteristic
165C2×D73—22no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—84no—
172C4×C73—21no—
173C4×C73—21no—
174C4×C73—21no—
175C4×C73—21no—
176C4×C73—41no—
177C4×C73—41no—
178C4×C73—41no—
179C4×C73C2×#4111yescharacteristic
180C4×C73H(5,𝔽2)11yescharacteristic
181Dic73—41no—
182Dic73—41no—
183C2×C73—22no—
184C2×C73—41no—
185C2×C73—81no—
186C2×C73#54611yescharacteristic
187C2×C73C2×#13511yescharacteristic
188C2×C73#57611yescharacteristic
189D73—42no—
190D73—81no—
191#3297—731nomaximal, Sylow
192C73#329711yescharacteristic, complemented, Sylow
193#553D7311yescharacteristic, complemented
194#546—731no—
195#488—731no—
196#484—731no—
197#482—731no—
198#478—731no—
199#466—731no—
200#465—731no—
201#463—731no—
202#449—731no—
203#447—731no—
204C4×D8—731no—
205C8×D4—731no—
206#416—731no—
207C2×#102—731no—
208C2×#41—731no—
209C22×D4—731no—
210C2×SD16—731no—
211C2×D8—731no—
212C2×D8—731no—
213C22×C8—731no—
214C22×C8—731no—
215#126—21no—
216#125C2×D7311yescharacteristic, complemented
217#124—731no—
218#123—21no—
219#123—1461no—
220C22⋊Q8—731no—
221#121—21no—
222#121—731no—
223#121—1461no—
224#121C2×D7311yescharacteristic
225#121C2×D7311yescharacteristic, complemented
226#120—1461no—
227C4×D4—21no—
228C4×D4—731no—
229C4×D4C2×D7311yescharacteristic
230C4×D4C2×D7311yescharacteristic, complemented
231#117C2×D7311yescharacteristic, complemented
232C2×C4⋊C4C2×D7311yescharacteristic
233C2×C22⋊C4—1461no—
234#107—731no—
235#107—731no—
236#106—731no—
237C4⋊C8—731no—
238#103—731no—
239#103—731no—
240#103—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247#102—731no—
248C22⋊C8—731no—
249C22⋊C8—731no—
250C4×C8—731no—
251C24—1461no—
252#41—2921no—
253#41—1462no—
254C2×Q8—731no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—2921no—
258C2×D4—731no—
259C2×D4—731no—
260C2×D4—1462no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4C22⋊D7311yescharacteristic
265C2×D4C22×D7311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—1461no—
269C22×C4—1461no—
270C22×C4C22×D7311yescharacteristic
271C22×C4C22×D7311yescharacteristic
272SD16—2921no—
273D8—2921no—
274D8—1462no—
275C2×C8—2921no—
276C2×C8—2921no—
277C2×C8—731no—
278C2×C8—731no—
279C2×C8—731no—
280C2×C8—731no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—731no—
285C4⋊C4—1461no—
286C4⋊C4C22⋊D7311yescharacteristic
287C4⋊C4C22×D7311yescharacteristic
288C4⋊C4C22×D7311yescharacteristic
289C4⋊C4C22×D7311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C22⋊C4—1461no—
299C22⋊C4C22⋊D7311yescharacteristic
300C22⋊C4C22⋊D7311yescharacteristic
301C42—21no—
302C42C22×D7311yescharacteristic
303C23—21no—
304C23—2922no—
305C23—2922no—
306C23—5841no—
307C23—1461no—
308C23—1461no—
309C23C2×C22⋊D7311yescharacteristic
310C23C2×C22⋊D7311yescharacteristic
311Q8—1461no—
312Q8—1461no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—2922no—
319D4—2922no—
320D4—5841no—
321D4—732no—
322D4—1461no—
323D4—1461no—
324D4—1461no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—2922no—
335C2×C4—5841no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4C2×C22⋊D7311yescharacteristic
339C2×C4C2×C22⋊D7311yescharacteristic
340C2×C4C2×C22⋊D7311yescharacteristic
341C2×C4C2×C22⋊D7311yescharacteristic
342C2×C4C23×D7311yescharacteristic
343C8—1461no—
344C8—1461no—
345C8—1461no—
346C8—1461no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—2921no—
356C22—2921no—
357C22—2921no—
358C22—2921no—
359C22—2921no—
360C22—5844no—
361C22—1462no—
362C22#1455661112yes—
363C22C22×C22⋊D7311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—2921no—
372C4—2921no—
373C4#41×D7311yescharacteristic
374C4#1455663711yescharacteristic
375C2—22no—
376C2—41no—
377C2—81no—
378C2—2922no—
379C2—5841no—
380C2#1798922511yescharacteristic
381C2C2×#1455661111yescharacteristic
382C2#1798939011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#553×C73C2
socleC22×C73C22×D4
hypercenter#553D73
hypocenterC73#3297
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #17989233C2semidirect
2. #17988944C2semidirect
3. #17988922C2semidirect
4. #17988911C2semidirect
5. #17988884C2semidirect
6. #17988821C2semidirect
7. #17988814C2semidirect
8. #17988802C2semidirect
9. #17988730C2semidirect
10. #17988720C2semidirect
11. C4×#11924013C2semidirect
12. D4×#10596831C2semidirect
13. #17988581C2semidirect
14. C2×#14556511C2semidirect
15. #553×C73C2semidirect
18. C2×#11924016C22semidirect
22. C22×#10596831C22semidirect
31. #14556524C22semidirect
32. #14556524C22semidirect
33. #14556522C22semidirect
34. C4⋊#10596831C22semidirect
35. #14556514C22semidirect
36. #14556514C22semidirect
37. #14556514C22semidirect
38. #14556512C22semidirect
46. C22⋊#10596831C22semidirect
47. C4×#10596831C22semidirect
49. #125×C73C22semidirect
53. #121×C73C22semidirect
56. C4×D4×C73C22semidirect
57. #117×C73C22semidirect
192. C73#3297semidirect
193. #553D73semidirect
216. #125C2×D73semidirect
225. #121C2×D73semidirect
230. C4×D4C2×D73semidirect
231. #117C2×D73semidirect