Finite Group Databasebeta

← #49131178

Subgroups — #49131178

Order 36224.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31826977C211yesmaximal, characteristic
2#117×D283C211yesmaximal, characteristic, complemented
3#31826809C211yesmaximal, characteristic, complemented
4#31826808C211yesmaximal, characteristic, complemented
5#31826802C211yesmaximal, characteristic, complemented
6#31826797C211yesmaximal, characteristic, complemented
7#31826792C211yesmaximal, characteristic, complemented
8#31826791C211yesmaximal, characteristic, complemented
9#31826785C211yesmaximal, characteristic, complemented
10#31826780C211yesmaximal, characteristic, complemented
11#31826501C211yesmaximal, characteristic, complemented
12#31826462C211yesmaximal, characteristic, complemented
13#31826459C211yesmaximal, characteristic, complemented
14C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
15#427×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C22×C4×D283C2211yescharacteristic
18C22×C283⋊C8C2211yescharacteristic
19#22583594—21no—
20#22583590C2211yescharacteristic
21#22583590C2211yescharacteristic
22#22583585C2211yescharacteristic
23#22583585C2211yescharacteristic
24#22583580—21no—
25C4×D1132—21no—
26C4×D1132—21no—
27#22583569C2211yescharacteristic
28#22583568C2211yescharacteristic
29#22583568C2211yescharacteristic
30#22583567—21no—
31#22583566—21no—
32C4⋊C4×D283C2211yescharacteristic
33C4⋊C4×D283C2211yescharacteristic
34C22⋊C4×D283—21no—
35C42×D283—21no—
36#22583543C2211yescharacteristic, complemented
37#22583543C2211yescharacteristic, complemented
38#22583541C2211yescharacteristic, complemented
39#22583541C2211yescharacteristic, complemented
40#22583535C2211yescharacteristic, complemented
41#22583535C2211yescharacteristic, complemented
42#22583533C2211yescharacteristic, complemented
43#22583533C2211yescharacteristic, complemented
44#22583532C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic, complemented
46#22583530C2211yescharacteristic, complemented
47#22583530C2211yescharacteristic, complemented
48(C2×D283)⋊C8C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
52C22×C8×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#117×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic, complemented
56#107×C283C2211yescharacteristic, complemented
57#106×C283C2211yescharacteristic, complemented
58#106×C283C2211yescharacteristic, complemented
59C23×D283D411yescharacteristic
60#17985392—22no—
61#17985392—22no—
62C2×Dic566C2311yescharacteristic
63C2×D1132—21no—
64C2×D1132—21no—
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67C22×Dic283D411yescharacteristic
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—22no—
72C2×C4×D283—22no—
73C2×C4×D283D411yescharacteristic
74C2×C4×D283D411yescharacteristic
75C2×C4×D283C2311yescharacteristic
76C2×C4×D283C2311yescharacteristic
77C2×C283⋊C8—22no—
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C4⋊Dic283—21no—
81C4⋊Dic283—21no—
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C22×C4×C283C2311yescharacteristic
97C2×C8×C283—22no—
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C4⋊C4×C283C2311yescharacteristic
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C22⋊C4×C283—21no—
105C22⋊C4×C283—21no—
106C42×C283—21no—
107C42×C283—21no—
108C22×D283—22no—
109C22×D283—22no—
110C22×D283—21no—
111C22×D283—41no—
112C22×D283C2×D411yescharacteristic
113C22×D283C2×D411yescharacteristic
114Dic566—21no—
115Dic566—21no—
116D1132—21no—
117D1132—21no—
118D1132—42no—
119D1132—42no—
120C22⋊D283—42no—
121C2×Dic283—22no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—22no—
128C4×D283—22no—
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—21no—
133C4×D283—42no—
134C4×D283—42no—
135C4×D283—42no—
136C283⋊C8—21no—
137C283⋊C8—21no—
138C23×C283C2×D411yescharacteristic
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283#4112yes—
145C2×C4×C283#4112yes—
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283#12312yes—
152C22×C283C22×D411yescharacteristic
153C2×D283—21no—
154C2×D283—21no—
155C2×D283—21no—
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—44no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—41no—
162C2×D283#13512yes—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283—41no—
167C4×C283#12312yes—
168C4×C283C2×#4111yescharacteristic
169C4×C283C2×#4111yescharacteristic
170Dic283—21no—
171Dic283—21no—
172Dic283—41no—
173Dic283—41no—
174Dic283—41no—
175C2×C283—22no—
176C2×C283C2×#12311yescharacteristic
177C2×C283C2×#13511yescharacteristic
178C2×C283#57511yescharacteristic
179D283—22no—
180D283—41no—
181D283—81no—
182C283#309111yescharacteristic, complemented, Sylow
183#3091—2831nomaximal, Sylow
184#525—2831no—
185C2×#117—2831no—
186#485—2831no—
187#485—2831no—
188#484—2831no—
189#483—2831no—
190#482—2831no—
191#482—2831no—
192#481—2831no—
193#480—2831no—
194#427—2831no—
195#427D28311yescharacteristic, complemented
196#416—2831no—
197#416—2831no—
198C2×C22⋊C8—2831no—
199C2×#41—2831no—
200C23×C4—2831no—
201C22×C8—2831no—
202C22×C8C2×D28311yescharacteristic
203#123—5661no—
204C22⋊Q8—2831no—
205C22⋊Q8—2831no—
206#121—2831no—
207#121—2831no—
208#120—5661no—
209C4×D4—5661no—
210C4×D4—5661no—
211#117—2831no—
212#117—2831no—
213#117—2831no—
214#117—5661no—
215#117—5661no—
216#117C2×D28311yescharacteristic
217#117C2×D28311yescharacteristic
218C2×C4⋊C4—2831no—
219C2×C4⋊C4—2831no—
220C2×C22⋊C4—5661no—
221C2×C42—5661no—
222#107—2831no—
223#107—2831no—
224#107C2×D28311yescharacteristic, complemented
225#107C2×D28311yescharacteristic, complemented
226#106—2831no—
227#106—2831no—
228#106C2×D28311yescharacteristic, complemented
229#106C2×D28311yescharacteristic, complemented
230#103—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#102—2831no—
235#102—2831no—
236#102—2831no—
237#102—2831no—
238C22⋊C8—2831no—
239C22⋊C8—2831no—
240C22⋊C8—2831no—
241C22⋊C8—2831no—
242C24—2831no—
243#41—5662no—
244#41—5662no—
245C2×Q8—2831no—
246C2×D4—2831no—
247C2×D4—5661no—
248C2×D4—5661no—
249C2×D4—5661no—
250C22×C4—2831no—
251C22×C4—2831no—
252C22×C4—2831no—
253C22×C4—2831no—
254C22×C4—2831no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4—5662no—
258C22×C4—5662no—
259C22×C4—5661no—
260C22×C4C22×D28311yescharacteristic
261C2×C8—22no—
262C2×C8—2831no—
263C2×C8—2831no—
264C2×C8—5662no—
265C2×C8C22×D28311yescharacteristic
266C2×C8C22×D28311yescharacteristic
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4C22×D28311yescharacteristic
274C4⋊C4C22×D28311yescharacteristic
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—21no—
287C42—21no—
288C42—5661no—
289C42—5661no—
290C42—5661no—
291C23—2831no—
292C23—2831no—
293C23—5662no—
294C23—5662no—
295C23—5661no—
296C23—11321no—
297C23D4×D28311yescharacteristic
298Q8—5661no—
299Q8—5661no—
300D4—5661no—
301D4—5661no—
302D4—11322no—
303D4—11322no—
304D4—11322no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2831no—
310C2×C4—2831no—
311C2×C4—5662no—
312C2×C4—5662no—
313C2×C4—5662no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—11322no—
322C2×C4—11322no—
323C2×C4—11322no—
324C2×C4D4×D28311yescharacteristic
325C2×C4#1798539212yes—
326C2×C4#1798539312yes—
327C2×C4C23×D28311yescharacteristic
328C8—21no—
329C8—21no—
330C8—5661no—
331C8—5661no—
332C22—21no—
333C22—21no—
334C22—2832no—
335C22—5661no—
336C22—5661no—
337C22—5661no—
338C22—5661no—
339C22—5661no—
340C22—11324no—
341C22—11321no—
342C22—11321no—
343C22—11321no—
344C22#2258359512yes—
345C22C2×D4×D28311yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—5661no—
351C4—5661no—
352C4—11321no—
353C4—11321no—
354C4—11321no—
355C4#2258359512yes—
356C4C2×#1798539211yescharacteristic
357C4C2×#1798539311yescharacteristic
358C2—22no—
359C2—5662no—
360C2—11321no—
361C2—22641no—
362C2C2×#2258359511yescharacteristic
363C2#135×D28311yescharacteristic
364C2#3182726211yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#427×C283C2
socleC22×C283C22×D4
prime radical#31826977C2
hypercenter#427D283
hypocenterC283#3091
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #117×D283C2semidirect
3. #31826809C2semidirect
4. #31826808C2semidirect
5. #31826802C2semidirect
6. #31826797C2semidirect
7. #31826792C2semidirect
8. #31826791C2semidirect
9. #31826785C2semidirect
10. #31826780C2semidirect
11. #31826501C2semidirect
12. #31826462C2semidirect
13. #31826459C2semidirect
14. C2×(C2×D283)⋊C8C2semidirect
15. #427×C283C2semidirect
36. #22583543C22semidirect
37. #22583543C22semidirect
38. #22583541C22semidirect
39. #22583541C22semidirect
40. #22583535C22semidirect
41. #22583535C22semidirect
42. #22583533C22semidirect
43. #22583533C22semidirect
44. #22583532C22semidirect
45. #22583532C22semidirect
46. #22583530C22semidirect
47. #22583530C22semidirect
55. #107×C283C22semidirect
56. #107×C283C22semidirect
57. #106×C283C22semidirect
58. #106×C283C22semidirect
182. C283#3091semidirect
195. #427D283semidirect
224. #107C2×D283semidirect
225. #107C2×D283semidirect
228. #106C2×D283semidirect
229. #106C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318269772
#117×D2832
#318268092
#318268082
#318268022
#318267972
#318267922
#318267912
#318267852
#318267802
#318265012
#318264622
#318264592
C2×(C2×D283)⋊C82
#427×C2832
#3091283