Finite Group Databasebeta

← #49130430

Subgroups — #49130430

Order 36224.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827002C211yesmaximal, characteristic
2#31826596C211yesmaximal, characteristic, complemented
3#31826544C211yesmaximal, characteristic, complemented
4#31826542C211yesmaximal, characteristic, complemented
5#31826538C211yesmaximal, characteristic, complemented
6#31826538C211yesmaximal, characteristic, complemented
7#31826535C211yesmaximal, characteristic, complemented
8#31826535C211yesmaximal, characteristic, complemented
9#31826527C211yesmaximal, characteristic, complemented
10#31826524C211yesmaximal, characteristic, complemented
11#31826520C211yesmaximal, characteristic, complemented
12#31826490C211yesmaximal, characteristic, complemented
13#31826490C211yesmaximal, characteristic, complemented
14#31826487C211yesmaximal, characteristic, complemented
15#446×C283C211yesmaximal, characteristic, complemented
16C2×#17985375C2211yescharacteristic
17C2×#17985375C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C2×#17985375C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic
21C2×C8×D283C2211yescharacteristic
22#22583605C411yescharacteristic
23#22583605C411yescharacteristic
24#22583601C411yescharacteristic
25#22583599C411yescharacteristic
26#22583595C411yescharacteristic
27#22583595C411yescharacteristic
28#22583586C411yescharacteristic
29#22583585C411yescharacteristic
30C4×D1132C2211yescharacteristic
31C4×D1132C2211yescharacteristic
32C4×D1132C2211yescharacteristic
33#22583567C2211yescharacteristic
34#22583567C2211yescharacteristic
35C42×D283C2211yescharacteristic
36C4⋊(C283⋊C8)C2211yescharacteristic
37C4⋊(C283⋊C8)C2211yescharacteristic
38C4⋊(C283⋊C8)C2211yescharacteristic
39Dic283⋊C8C2211yescharacteristic
40Dic283⋊C8C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43(C2×D283)⋊C8C2211yescharacteristic
44(C2×D283)⋊C8C2211yescharacteristic
45(C2×D283)⋊C8C2211yescharacteristic
46(C2×D283)⋊C8C2211yescharacteristic
47(C2×D283)⋊C8C2211yescharacteristic
48(C2×D283)⋊C8C2211yescharacteristic
49#22583521C2211yescharacteristic
50#22583521C2211yescharacteristic
51C4×C283⋊C8C2211yescharacteristic
52C4×Q8×C283C2211yescharacteristic
53C4⋊C8×C283C2211yescharacteristic
54C4⋊C8×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic
56#97×C283C2211yescharacteristic
57#97×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59C2×D1132C2×C411yescharacteristic
60C2×D1132C2×C411yescharacteristic
61C2×D1132C2×C411yescharacteristic
62C2×C4×D283C2×C411yescharacteristic
63C2×C4×D283C2×C411yescharacteristic
64C2×C4×D283C2311yescharacteristic
65C2×C4×D283C2311yescharacteristic
66C2×C4×D283C2311yescharacteristic
67#17985375—41no—
68#17985375—41no—
69#17985375—41no—
70#17985375—41no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C8×D283—41no—
76C8×D283—41no—
77C4⋊Dic283C2×C411yescharacteristic
78C4⋊Dic283C2×C411yescharacteristic
79C4⋊Dic283C2×C411yescharacteristic
80Dic283⋊C4C2×C411yescharacteristic
81Dic283⋊C4C2×C411yescharacteristic
82Dic283⋊C4C2×C411yescharacteristic
83Dic283⋊C4C2×C411yescharacteristic
84(C2×D283)⋊C4C2×C411yescharacteristic
85(C2×D283)⋊C4C2×C411yescharacteristic
86(C2×D283)⋊C4C2×C411yescharacteristic
87(C2×D283)⋊C4C2×C411yescharacteristic
88(C2×D283)⋊C4C2×C411yescharacteristic
89(C2×D283)⋊C4C2×C411yescharacteristic
90(C2×D283)⋊C4C2×C411yescharacteristic
91(C2×D283)⋊C4C2×C411yescharacteristic
92(C2×D283)⋊C4C2×C411yescharacteristic
93(C2×D283)⋊C4C2×C411yescharacteristic
94C4×Dic283C2×C411yescharacteristic
95C4×Dic283C2×C411yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×Q8×C283C2×C411yescharacteristic
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283C2×C411yescharacteristic
103C4⋊C4×C283C2×C411yescharacteristic
104C4⋊C4×C283C2×C411yescharacteristic
105C42×C283C2311yescharacteristic
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283C22×C411yescharacteristic
109C22×D283C22×C411yescharacteristic
110C22×D283C22×C411yescharacteristic
111D1132—41no—
112D1132—41no—
113D1132—41no—
114C2×Dic283C22×C411yescharacteristic
115C2×Dic283C22×C411yescharacteristic
116C2×Dic283C22×C411yescharacteristic
117C2×Dic283C22×C411yescharacteristic
118C2×Dic283C22×C411yescharacteristic
119C4×D283—21no—
120C4×D283—21no—
121C4×D283—21no—
122C4×D283—21no—
123C4×D283—21no—
124C4×D283—21no—
125C4×D283—41no—
126C4×D283—41no—
127C283⋊C8—21no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130C283⋊C8—21no—
131Q8×C283—41no—
132C2×C4×C283C22×C411yescharacteristic
133C2×C4×C283C22×C411yescharacteristic
134C2×C4×C283C22×C411yescharacteristic
135C2×C4×C283C22×C411yescharacteristic
136C2×C4×C283C22×C411yescharacteristic
137C2×C4×C283C22×C411yescharacteristic
138C2×C4×C283C2411yescharacteristic
139C8×C283—21no—
140C8×C283—21no—
141C8×C283—21no—
142C8×C283—21no—
143C22×C283C23×C411yescharacteristic
144C2×D283—21no—
145C2×D283—21no—
146C2×D283—21no—
147C2×D283—21no—
148C2×D283—21no—
149C2×D283—21no—
150C2×D283—21no—
151C2×D283—21no—
152C2×D283—21no—
153C4×C283—21no—
154C4×C283—21no—
155C4×C283—21no—
156C4×C283—21no—
157C4×C283—21no—
158C4×C283—21no—
159C4×C283H(5,𝔽2)11yescharacteristic
160C4×C2832−1+411yescharacteristic
161Dic283—21no—
162Dic283—21no—
163Dic283—21no—
164Dic283—21no—
165Dic283—21no—
166C2×C283#52011yescharacteristic
167C2×C283#56811yescharacteristic
168C2×C283#56811yescharacteristic
169D283—41no—
170D283—41no—
171D283—41no—
172C283#299511yescharacteristic, complemented, Sylow
173#2995—2831nomaximal, Sylow
174#529—2831no—
175#446—2831no—
176#446D28311yescharacteristic, complemented
177#436—2831no—
178#436—2831no—
179#435—2831no—
180#435—2831no—
181#435—2831no—
182#435—2831no—
183#433—2831no—
184#433—2831no—
185#432—2831no—
186#424—2831no—
187#424—2831no—
188#423—2831no—
189C2×M16—2831no—
190C2×M16—2831no—
191C2×M16—2831no—
192C2×M16—2831no—
193C22×C8—2831no—
194C22×C8—2831no—
195#126—2831no—
196#126—2831no—
197#125—2831no—
198#124—2831no—
199#123—2831no—
200#123—2831no—
201C22⋊Q8—2831no—
202#121—2831no—
203C4×Q8C2×D28311yescharacteristic
204C4×D4—2831no—
205C4×D4—2831no—
206C4×D4—2831no—
207#117—2831no—
208#117—2831no—
209C2×C42—2831no—
210C4⋊C8—2831no—
211C4⋊C8—2831no—
212C4⋊C8—2831no—
213C4⋊C8—2831no—
214C4⋊C8—2831no—
215C4⋊C8—2831no—
216C4⋊C8—2831no—
217C4⋊C8C2×D28311yescharacteristic
218C4⋊C8C2×D28311yescharacteristic
219C4⋊C8C2×D28311yescharacteristic
220C22⋊C8—2831no—
221C22⋊C8—2831no—
222C22⋊C8—2831no—
223C22⋊C8—2831no—
224C22⋊C8—2831no—
225C22⋊C8—2831no—
226#97—2831no—
227#97—2831no—
228#97C2×D28311yescharacteristic
229#97C2×D28311yescharacteristic
230C4×C8—2831no—
231C4×C8C2×D28311yescharacteristic
232C2×Q8C4×D28311yescharacteristic
233C2×D4—2831no—
234C2×D4—2831no—
235C2×D4—2831no—
236C22×C4—2831no—
237C22×C4—2831no—
238C22×C4—2831no—
239C22×C4—2831no—
240C22×C4—2831no—
241M16—11321no—
242M16—11321no—
243M16—11321no—
244M16—11321no—
245C2×C8—2831no—
246C2×C8—2831no—
247C2×C8—2831no—
248C2×C8—2831no—
249C2×C8—11321no—
250C2×C8—11321no—
251C2×C8C22×D28311yescharacteristic
252C2×C8C22×D28311yescharacteristic
253C2×C8C22×D28311yescharacteristic
254C2×C8C22×D28311yescharacteristic
255C4⋊C4—2831no—
256C4⋊C4—2831no—
257C4⋊C4—2831no—
258C4⋊C4—2831no—
259C4⋊C4—2831no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4C4×D28311yescharacteristic
263C4⋊C4C4×D28311yescharacteristic
264C4⋊C4C4×D28311yescharacteristic
265C22⋊C4—2831no—
266C22⋊C4—2831no—
267C22⋊C4—2831no—
268C22⋊C4—2831no—
269C22⋊C4—2831no—
270C22⋊C4—2831no—
271C22⋊C4—2831no—
272C22⋊C4—2831no—
273C22⋊C4—2831no—
274C22⋊C4—2831no—
275C42—2831no—
276C42—2831no—
277C42—2831no—
278C42C22×D28311yescharacteristic
279C42C22×D28311yescharacteristic
280C42C22×D28311yescharacteristic
281C23—2831no—
282C23—2831no—
283C23—2831no—
284Q8—41no—
285D4—11321no—
286D4—11321no—
287D4—11321no—
288C2×C4—2831no—
289C2×C4—2831no—
290C2×C4—2831no—
291C2×C4—2831no—
292C2×C4—2831no—
293C2×C4—5661no—
294C2×C4—5661no—
295C2×C4—5661no—
296C2×C4—5661no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—11321no—
300C2×C4—11321no—
301C2×C4C2×C4×D28311yescharacteristic
302C2×C4C2×C4×D28311yescharacteristic
303C2×C4C2×C4×D28311yescharacteristic
304C2×C4C2×C4×D28311yescharacteristic
305C2×C4C2×C4×D28311yescharacteristic
306C2×C4C2×C4×D28311yescharacteristic
307C2×C4C23×D28311yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C8—5661no—
313C8—5661no—
314C8—5661no—
315C8—5661no—
316C22—5661no—
317C22—5661no—
318C22—5661no—
319C22—5661no—
320C22—5661no—
321C22—5661no—
322C22—5661no—
323C22—5661no—
324C22—5661no—
325C22C22×C4×D28311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—5661no—
333C4—5661no—
334C4—5661no—
335C4—5661no—
336C4—5661no—
337C4#2258365611yescharacteristic
338C4#2258365811yescharacteristic
339C2—11321no—
340C2—11321no—
341C2—11321no—
342C2#3182694711yescharacteristic
343C2#3182723011yescharacteristic
344C2#3182723111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D283
commutator, socleC22×C283C23×C4
Fitting#446×C283C2
prime radical#22583585C4
cosocleC2×C4×C283C24
hypercenter#446D283
hypocenterC283#2995
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #31826596C2semidirect
3. #31826544C2semidirect
4. #31826542C2semidirect
5. #31826538C2semidirect
6. #31826538C2semidirect
7. #31826535C2semidirect
8. #31826535C2semidirect
9. #31826527C2semidirect
10. #31826524C2semidirect
11. #31826520C2semidirect
12. #31826490C2semidirect
13. #31826490C2semidirect
14. #31826487C2semidirect
15. #446×C283C2semidirect
172. C283#2995semidirect
176. #446D283semidirect

Maximal subgroups

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

subgroupindex
#318270022
#318265962
#318265442
#318265422
#318265382
#318265352
#318265272
#318265242
#318265202
#318264902
#318264872
#446×C2832
#2995283