Finite Group Databasebeta

← #49131208

Subgroups — #49131208

Order 36224.

410 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D283C211yesmaximal, characteristic
2#117×D283C211yesmaximal, characteristic
3#31826807C211yesmaximal, characteristic, complemented
4#31826806C211yesmaximal, characteristic, complemented
5#31826803C211yesmaximal, characteristic, complemented
6#31826802C211yesmaximal, characteristic, complemented
7#31826799C211yesmaximal, characteristic, complemented
8#31826797C211yesmaximal, characteristic, complemented
9#31826794C211yesmaximal, characteristic, complemented
10#31826506C211yesmaximal, characteristic, complemented
11#31826504C211yesmaximal, characteristic, complemented
12#31826472C211yesmaximal, characteristic, complemented
13#31826472C211yesmaximal, characteristic, complemented
14#31826427C211yesmaximal, characteristic
15#485×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C22×C4×D283C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C2×#17985375C2211yescharacteristic
20#22583590C2211yescharacteristic
21#22583589C2211yescharacteristic
22#22583588—21no—
23#22583587—21no—
24#22583586C2211yescharacteristic
25#22583569C2211yescharacteristic
26#22583568C2211yescharacteristic
27#22583568C2211yescharacteristic
28#22583567—21no—
29#22583566—21no—
30C4⋊C4×D283—21no—
31C4⋊C4×D283C2211yescharacteristic
32C4⋊C4×D283C2211yescharacteristic
33C4⋊C4×D283C2211yescharacteristic
34C22⋊C4×D283—21no—
35C22⋊C4×D283—21no—
36C42×D283—21no—
37#22583544C2211yescharacteristic, complemented
38#22583543C2211yescharacteristic, complemented
39#22583543C2211yescharacteristic, complemented
40#22583542C2211yescharacteristic, complemented
41#22583541C2211yescharacteristic, complemented
42#22583541C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583534C2211yescharacteristic, complemented
46#22583534C2211yescharacteristic, complemented
47#22583533C2211yescharacteristic, complemented
48#22583533C2211yescharacteristic, complemented
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
52C22⋊Q8×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic, complemented
55#106×C283C2211yescharacteristic, complemented
56#103×C283C2211yescharacteristic, complemented
57#103×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic
59C23×D283D411yescharacteristic
60C2×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62Q8×D283—22no—
63Q8×D283—22no—
64C22×Dic283D411yescharacteristic
65C2×C4×D283—22no—
66C2×C4×D283—22no—
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283D411yescharacteristic
72C2×C4×D283D411yescharacteristic
73C2×C4×D283C2311yescharacteristic
74C2×C4×D283C2311yescharacteristic
75#17985375—22no—
76#17985375—22no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C4⋊Dic283—21no—
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C2×Q8×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C4⋊C4×C283—21no—
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283—21no—
108C22×D283—22no—
109C22×D283—22no—
110C22×D283—41no—
111C22×D283C2×D411yescharacteristic
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115Dic566—42no—
116C2×Dic283—22no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C4×D283—22no—
124C4×D283—21no—
125C4×D283—21no—
126C4×D283—22no—
127C4×D283—42no—
128C4×D283—42no—
129C4×D283—42no—
130C4×D283—42no—
131C4×D283#4112yes—
132C4×D283#4112yes—
133C283⋊C8—21no—
134C283⋊C8—21no—
135C23×C283C2×D411yescharacteristic
136Q8×C283—21no—
137Q8×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2411yescharacteristic
146C8×C283—21no—
147C8×C283—21no—
148C22×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283C22×D411yescharacteristic
152C2×D283—21no—
153C2×D283—21no—
154C2×D283—21no—
155C2×D283—21no—
156C2×D283—44no—
157C2×D283#12312yes—
158C2×D283#13712yes—
159C4×C283—21no—
160C4×C283—41no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283—41no—
164C4×C283C2×#4111yescharacteristic
165C4×C283C2×#4111yescharacteristic
166Dic283—21no—
167Dic283—41no—
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171Dic283#12312yes—
172C2×C283—41no—
173C2×C283C2×#12311yescharacteristic
174C2×C283C2×#13711yescharacteristic
175C2×C283#57511yescharacteristic
176D283—22no—
177D283—22no—
178C283#309511yescharacteristic, complemented, Sylow
179#3095—2831nomaximal, Sylow
180C2×C22⋊Q8—2831no—
181C2×#117—2831no—
182#485—2831no—
183#485—2831no—
184#485—2831no—
185#485D28311yescharacteristic, complemented
186#484—2831no—
187#484—2831no—
188#483—2831no—
189#483—2831no—
190#428—2831no—
191#428—2831no—
192#419—2831no—
193#419—2831no—
194#407—2831no—
195C22×Q8—2831no—
196C23×C4—2831no—
197C2×M16—2831no—
198C2×M16—2831no—
199C22⋊Q8—2831no—
200C22⋊Q8—2831no—
201C22⋊Q8—2831no—
202C22⋊Q8—5661no—
203C22⋊Q8—5661no—
204C22⋊Q8C2×D28311yescharacteristic
205#117—2831no—
206#117—2831no—
207#117—2831no—
208#117—5661no—
209#117—5661no—
210#117C2×D28311yescharacteristic
211C2×C4⋊C4—2831no—
212C2×C4⋊C4—2831no—
213C2×C4⋊C4—2831no—
214C2×C4⋊C4—5661no—
215C2×C22⋊C4—5661no—
216C2×C22⋊C4—5661no—
217C2×C42—5661no—
218#107—2831no—
219#107—2831no—
220#107—2831no—
221#107C2×D28311yescharacteristic, complemented
222#106—2831no—
223#106—2831no—
224#106—2831no—
225#106C2×D28311yescharacteristic, complemented
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103—2831no—
232#103C2×D28311yescharacteristic, complemented
233#103C2×D28311yescharacteristic, complemented
234C22⋊C8—2831no—
235C22⋊C8—2831no—
236C22⋊C8—2831no—
237C22⋊C8C2×D28311yescharacteristic
238C24—2831no—
239C2×Q8—2831no—
240C2×Q8—5661no—
241C2×Q8—5662no—
242C2×Q8—5662no—
243C2×Q8C22×D28311yescharacteristic
244C22×C4—2831no—
245C22×C4—2831no—
246C22×C4—2831no—
247C22×C4—2831no—
248C22×C4—2831no—
249C22×C4—5662no—
250C22×C4—5662no—
251C22×C4—5661no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4C22×D28311yescharacteristic
256M16—5662no—
257M16—5662no—
258C2×C8—2831no—
259C2×C8—2831no—
260C2×C8C22×D28311yescharacteristic
261C2×C8C22×D28311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—2831no—
264C4⋊C4—2831no—
265C4⋊C4—2831no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4C22×D28311yescharacteristic
273C4⋊C4C22×D28311yescharacteristic
274C4⋊C4C22×D28311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C42—21no—
284C42—5661no—
285C42—5661no—
286C42—5661no—
287C23—2831no—
288C23—2831no—
289C23—5662no—
290C23—5662no—
291C23—11321no—
292C23D4×D28311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—5661no—
296Q8—5661no—
297Q8—11322no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—2831no—
305C2×C4—2832no—
306C2×C4—2832no—
307C2×C4—2831no—
308C2×C4—5662no—
309C2×C4—5662no—
310C2×C4—5662no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—11322no—
318C2×C4—11322no—
319C2×C4—11322no—
320C2×C4—11322no—
321C2×C4D4×D28311yescharacteristic
322C2×C4C23×D28311yescharacteristic
323C8—21no—
324C8—21no—
325C8—5661no—
326C8—5661no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—2832no—
331C22—2832no—
332C22—5661no—
333C22—5661no—
334C22—5661no—
335C22—5661no—
336C22—11324no—
337C22C2×D4×D28311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2832no—
344C4—5661no—
345C4—11321no—
346C4—11321no—
347C4—11321no—
348C4—11321no—
349C4#41×D28311yescharacteristic
350C4#41×D28311yescharacteristic
351C2—41no—
352C2—5662no—
353C2—5662no—
354C2#123×D28311yescharacteristic
355C2#137×D28311yescharacteristic
356C2#3182726211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#485×C283C2
socleC22×C283C22×D4
prime radicalC23×D283D4
hypercenter#485D283
hypocenterC283#3095
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #31826807C2semidirect
4. #31826806C2semidirect
5. #31826803C2semidirect
6. #31826802C2semidirect
7. #31826799C2semidirect
8. #31826797C2semidirect
9. #31826794C2semidirect
10. #31826506C2semidirect
11. #31826504C2semidirect
12. #31826472C2semidirect
13. #31826472C2semidirect
15. #485×C283C2semidirect
37. #22583544C22semidirect
38. #22583543C22semidirect
39. #22583543C22semidirect
40. #22583542C22semidirect
41. #22583541C22semidirect
42. #22583541C22semidirect
43. #22583535C22semidirect
44. #22583535C22semidirect
45. #22583534C22semidirect
46. #22583534C22semidirect
47. #22583533C22semidirect
48. #22583533C22semidirect
54. #107×C283C22semidirect
55. #106×C283C22semidirect
56. #103×C283C22semidirect
57. #103×C283C22semidirect
178. C283#3095semidirect
185. #485D283semidirect
221. #107C2×D283semidirect
225. #106C2×D283semidirect
232. #103C2×D283semidirect
233. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D2832
#117×D2832
#318268072
#318268062
#318268032
#318268022
#318267992
#318267972
#318267942
#318265062
#318265042
#318264722
#318264272
#485×C2832
#3095283