Finite Group Databasebeta

← #49131085

Subgroups — #49131085

Order 36224.

398 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#31827092C211yesmaximal, characteristic, complemented
2#31826937C211yesmaximal, characteristic
3#31826768C211yesmaximal, characteristic, complemented
4#31826766C211yesmaximal, characteristic, complemented
5#31826765C211yesmaximal, characteristic, complemented
6#31826763C211yesmaximal, characteristic, complemented
7#31826753C211yesmaximal, characteristic, complemented
8#31826752C211yesmaximal, characteristic, complemented
9#31826744C211yesmaximal, characteristic, complemented
10#31826506C211yesmaximal, characteristic, complemented
11#31826502C211yesmaximal, characteristic, complemented
12#31826490C211yesmaximal, characteristic, complemented
13#31826468C211yesmaximal, characteristic
14#102×D283C211yesmaximal, characteristic
15#474×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283C2211yescharacteristic
17C2×#17985375C2211yescharacteristic
18C2×C8×D283C2211yescharacteristic
19#22583609C2211yescharacteristic, complemented
20#22583608—21no—
21#22583602C2211yescharacteristic, complemented
22#22583601C2211yescharacteristic, complemented
23#22583600—21no—
24#22583588—21no—
25#22583586—21no—
26C4×D1132C2211yescharacteristic
27D4×Dic283C2211yescharacteristic
28#22583572C2211yescharacteristic
29C4×C22⋊D283—21no—
30(C22⋊D283)⋊C4—21no—
31#22583568C2211yescharacteristic
32#22583568C2211yescharacteristic
33#22583567C2211yescharacteristic
34C4⋊C4×D283C2211yescharacteristic
35C2×(C2×D283)⋊C4—21no—
36C22⋊C4×D283—21no—
37#22583544C2211yescharacteristic, complemented
38#22583543C2211yescharacteristic, complemented
39#22583542C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41#22583541C2211yescharacteristic, complemented
42#22583541C2211yescharacteristic, complemented
43C4⋊(C283⋊C8)C2211yescharacteristic, complemented
44Dic283⋊C8C2211yescharacteristic, complemented
45Dic283⋊C8C2211yescharacteristic, complemented
46#22583532C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583531C2211yescharacteristic
50#22583530C2211yescharacteristic
51#22583530C2211yescharacteristic
52C4⋊Q8×C283C2211yescharacteristic, complemented
53C4×D4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic, complemented
55#107×C283C2211yescharacteristic, complemented
56C4⋊C8×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C23×D283—21no—
60C2×Dic566—21no—
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63D4×D283—22no—
64D4×D283Q814yescomplemented
65C22×Dic283—21no—
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283C2311yescharacteristic
70#17985375—22no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C8×D283—22no—
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4D411yescharacteristic
84Dic283⋊C4D411yescharacteristic
85C22⋊Dic283—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4D411yescharacteristic
91(C2×D283)⋊C4D411yescharacteristic
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283C2311yescharacteristic
95C2×Q8×C283—21no—
96C2×D4×C283C2311yescharacteristic
97C22×C4×C283—21no—
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C4⋊C4×C283—21no—
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C22⋊C4×C283—21no—
105C42×C283C2311yescharacteristic
106C22×D283—21no—
107C22×D283—24no—
108C22×D283—81no—
109C22×D283—81no—
110C22×D283C2×D411yescharacteristic
111Dic566—81no—
112D1132—21no—
113D1132C2×Q812yes—
114C22⋊D283—24no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—81no—
119C2×Dic283C2×D411yescharacteristic
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C4×D283—81no—
123C4×D283—81no—
124C4×D283—81no—
125C4×D283C2×Q812yes—
126C4×D283#4112yes—
127C283⋊C8—21no—
128C283⋊C8—21no—
129C23×C283—21no—
130Q8×C283—81no—
131D4×C283—21no—
132D4×C283C2×Q812yes—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—81no—
137C2×C4×C283C2×D411yescharacteristic
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2411yescharacteristic
140C8×C283—21no—
141C8×C283—21no—
142C22×C283—22no—
143C22×C283—41no—
144C22×C283—41no—
145C22×C283C22×D411yescharacteristic
146C2×D283—21no—
147C2×D283—21no—
148C2×D283—22no—
149C2×D283—41no—
150C2×D283—41no—
151C2×D283—84no—
152C2×D283C22⋊Q812yes—
153C4×C283—21no—
154C4×C283—21no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283—41no—
158C4×C283C22×Q811yescharacteristic
159C4×C283C2×#4111yescharacteristic
160Dic283—21no—
161Dic283—21no—
162Dic283—41no—
163Dic283—41no—
164Dic283—41no—
165Dic283C22⋊Q812yes—
166C2×C283—42no—
167C2×C283C2×C22⋊Q811yescharacteristic
168C2×C283#57611yescharacteristic
169C2×C283#57711yescharacteristic
170D283—22no—
171D283—42no—
172C283#308111yescharacteristic, complemented, Sylow
173#3081—2831nomaximal, Sylow
174#544—2831no—
175#518—2831no—
176#478—2831no—
177#478—2831no—
178#478—2831no—
179#478—2831no—
180#476—2831no—
181#476—2831no—
182#474—2831no—
183#474D28311yescharacteristic, complemented
184#428—2831no—
185#427—2831no—
186#424—2831no—
187#418—2831no—
188C2×#102—2831no—
189C22×D4—2831no—
190C2×M16—2831no—
191C22×C8—2831no—
192C4⋊Q8—2831no—
193C4⋊Q8—5661no—
194C4⋊Q8C2×D28311yescharacteristic, complemented
195#125—2831no—
196#125—2831no—
197#125—5661no—
198C22⋊Q8—5661no—
199C22⋊Q8—5661no—
200C4×D4—2831no—
201C4×D4—2831no—
202C4×D4—2831no—
203C4×D4—5661no—
204C4×D4—5661no—
205C4×D4C2×D28311yescharacteristic
206#117—2831no—
207#117—2831no—
208#117—2831no—
209C2×C4⋊C4—2831no—
210C2×C22⋊C4—5661no—
211C2×C22⋊C4—5661no—
212#107—2831no—
213#107—2831no—
214#107C2×D28311yescharacteristic, complemented
215#107C2×D28311yescharacteristic, complemented
216#106—2831no—
217#106—2831no—
218#106—2831no—
219#106—2831no—
220C4⋊C8—2831no—
221C4⋊C8—2831no—
222C4⋊C8—2831no—
223C4⋊C8C2×D28311yescharacteristic, complemented
224#102—2831no—
225#102—2831no—
226#102—2831no—
227#102—2831no—
228#102—2831no—
229#102—2831no—
230#102C2×D28311yescharacteristic
231#102C2×D28311yescharacteristic
232C24—5661no—
233C2×Q8—21no—
234C2×Q8—5661no—
235C2×D4—2834no—
236C2×D4—2831no—
237C2×D4—5662no—
238C2×D4—5661no—
239C2×D4C22×D28311yescharacteristic
240C22×C4—21no—
241C22×C4—2831no—
242C22×C4—5661no—
243C22×C4—5661no—
244C22×C4—5661no—
245C22×C4—5661no—
246M16—5662no—
247C2×C8—2831no—
248C2×C8—2831no—
249C2×C8—5662no—
250C2×C8C22×D28311yescharacteristic
251C2×C8C22×D28311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—2831no—
254C4⋊C4—2831no—
255C4⋊C4—2831no—
256C4⋊C4—2831no—
257C4⋊C4—2831no—
258C4⋊C4—5661no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4C22×D28311yescharacteristic
265C4⋊C4C22×D28311yescharacteristic
266C4⋊C4C22×D28311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—2831no—
269C22⋊C4—2831no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C42—2831no—
276C42—5661no—
277C42—5661no—
278C42C22×D28311yescharacteristic
279C23—21no—
280C23—2831no—
281C23—5664no—
282C23—5661no—
283C23—22641no—
284C23—22641no—
285Q8—81no—
286Q8—22641no—
287D4—21no—
288D4—2832no—
289D4—5664no—
290D4—5661no—
291D4Q8×D28312yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—2831no—
297C2×C4—2832no—
298C2×C4—2832no—
299C2×C4—2831no—
300C2×C4—2831no—
301C2×C4—5661no—
302C2×C4—5661no—
303C2×C4—5661no—
304C2×C4—22641no—
305C2×C4—22641no—
306C2×C4—22641no—
307C2×C4—22641no—
308C2×C4D4×D28311yescharacteristic
309C2×C4D4×D28311yescharacteristic
310C2×C4C23×D28311yescharacteristic
311C8—21no—
312C8—21no—
313C8—5661no—
314C8—5661no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—2832no—
319C22—5661no—
320C22—5661no—
321C22—5662no—
322C22—11321no—
323C22—11321no—
324C22—22644no—
325C22C2×D4×D28311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2832no—
332C4—5661no—
333C4—5661no—
334C4—11321no—
335C4—11321no—
336C4—11321no—
337C4C2×Q8×D28311yescharacteristic
338C4#41×D28311yescharacteristic
339C2—42no—
340C2—5662no—
341C2—11322no—
342C2C22⋊Q8×D28311yescharacteristic
343C2#3182726611yescharacteristic
344C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#474×C283C2
socleC22×C283C22×D4
prime radicalC2×D4×D283C22
hypercenter#474D283
hypocenterC283#3081
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #31827092C2semidirect
3. #31826768C2semidirect
4. #31826766C2semidirect
5. #31826765C2semidirect
6. #31826763C2semidirect
7. #31826753C2semidirect
8. #31826752C2semidirect
9. #31826744C2semidirect
10. #31826506C2semidirect
11. #31826502C2semidirect
12. #31826490C2semidirect
15. #474×C283C2semidirect
19. #22583609C22semidirect
21. #22583602C22semidirect
22. #22583601C22semidirect
37. #22583544C22semidirect
38. #22583543C22semidirect
39. #22583542C22semidirect
40. #22583541C22semidirect
41. #22583541C22semidirect
42. #22583541C22semidirect
43. C4⋊(C283⋊C8)C22semidirect
44. Dic283⋊C8C22semidirect
45. Dic283⋊C8C22semidirect
52. C4⋊Q8×C283C22semidirect
54. #107×C283C22semidirect
55. #107×C283C22semidirect
56. C4⋊C8×C283C22semidirect
64. D4×D283Q8semidirect
172. C283#3081semidirect
183. #474D283semidirect
194. C4⋊Q8C2×D283semidirect
214. #107C2×D283semidirect
215. #107C2×D283semidirect
223. C4⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270922
#318269372
#318267682
#318267662
#318267652
#318267632
#318267532
#318267522
#318267442
#318265062
#318265022
#318264902
#318264682
#102×D2832
#474×C2832
#3081283