Finite Group Databasebeta

← #49131047

Subgroups — #49131047

Order 36224.

388 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827018C211yesmaximal, characteristic, complemented
2#31826933C211yesmaximal, characteristic
3#31826775C211yesmaximal, characteristic, complemented
4#31826771C211yesmaximal, characteristic, complemented
5#31826768C211yesmaximal, characteristic, complemented
6#31826764C211yesmaximal, characteristic, complemented
7#31826759C211yesmaximal, characteristic, complemented
8#31826754C211yesmaximal, characteristic, complemented
9#31826749C211yesmaximal, characteristic, complemented
10#31826744C211yesmaximal, characteristic, complemented
11#31826501C211yesmaximal, characteristic, complemented
12C2×Dic283⋊C8C211yesmaximal, characteristic, complemented
13#31826462C211yesmaximal, characteristic
14#31826459C211yesmaximal, characteristic
15#427×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C22×C283⋊C8C2211yescharacteristic
18#22583609C2211yescharacteristic
19#22583609C2211yescharacteristic
20#22583601C2211yescharacteristic
21#22583601C2211yescharacteristic
22#22583587—21no—
23#22583587—21no—
24C4×Dic566—21no—
25C4×Dic566—21no—
26#22583575C2211yescharacteristic
27#22583575C2211yescharacteristic
28#22583572C2211yescharacteristic
29#22583572C2211yescharacteristic
30(C22⋊D283)⋊C4—21no—
31(C22⋊D283)⋊C4—21no—
32#22583569C2211yescharacteristic
33#22583567—21no—
34C2×C4×Dic283C2211yescharacteristic
35C42×D283—21no—
36#22583543C2211yescharacteristic
37#22583543C2211yescharacteristic
38#22583541C2211yescharacteristic
39#22583541C2211yescharacteristic
40Dic283⋊C8C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583530C2211yescharacteristic
51#22583530C2211yescharacteristic
52C22×C8×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#117×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic
57#106×C283C2211yescharacteristic
58#106×C283C2211yescharacteristic
59#17985392—22no—
60#17985392Q814yescomplemented
61C2×Dic566—21no—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64C2×D1132C2311yescharacteristic
65C2×C22⋊D283—21no—
66C22×Dic283D411yescharacteristic
67C22×Dic283D411yescharacteristic
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C283⋊C8—22no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C4⋊Dic283—21no—
75C4⋊Dic283—21no—
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84C22⋊Dic283—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87C4×Dic283—21no—
88C4×Dic283—21no—
89C4×Dic283—21no—
90C4×Dic283D411yescharacteristic
91C4×Dic283D411yescharacteristic
92C4×Dic283C2311yescharacteristic
93C4×Dic283C2311yescharacteristic
94C22×C4×C283C2311yescharacteristic
95C2×C8×C283—22no—
96C2×C8×C283C2311yescharacteristic
97C2×C8×C283C2311yescharacteristic
98C4⋊C4×C283C2311yescharacteristic
99C4⋊C4×C283C2311yescharacteristic
100C4⋊C4×C283C2311yescharacteristic
101C4⋊C4×C283C2311yescharacteristic
102C22⋊C4×C283—21no—
103C22⋊C4×C283—21no—
104C42×C283—21no—
105C42×C283—21no—
106C22×D283—21no—
107Dic566—21no—
108Dic566—42no—
109Dic566—42no—
110Dic566C2×Q812yes—
111D1132—21no—
112D1132C2×Q812yes—
113C22⋊D283—24no—
114C2×Dic283—21no—
115C2×Dic283—22no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—41no—
119C2×Dic283C2×D411yescharacteristic
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C4×D283—24no—
124C4×D283—42no—
125C4×D283—42no—
126C283⋊C8—21no—
127C283⋊C8—21no—
128C23×C283C2×D411yescharacteristic
129C2×C4×C283—21no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283C2×D411yescharacteristic
134C2×C4×C283C2×Q812yes—
135C2×C4×C283#4112yes—
136C2×C4×C283C2411yescharacteristic
137C8×C283—21no—
138C8×C283—21no—
139C22×C283—21no—
140C22×C283—21no—
141C22×C283C22⋊Q812yes—
142C22×C283C22×D411yescharacteristic
143C2×D283—22no—
144C2×D283—41no—
145C2×D283—41no—
146C4×C283—41no—
147C4×C283—41no—
148C4×C283—41no—
149C4×C283—41no—
150C4×C283C22⋊Q812yes—
151C4×C283C22×Q811yescharacteristic
152C4×C283C2×#4111yescharacteristic
153Dic283—22no—
154Dic283—21no—
155Dic283—21no—
156Dic283—21no—
157Dic283—41no—
158Dic283—41no—
159Dic283#13512yes—
160C2×C283—22no—
161C2×C283C2×C22⋊Q811yescharacteristic
162C2×C283C2×#13511yescharacteristic
163C2×C283#57511yescharacteristic
164D283—42no—
165C283#307611yescharacteristic, complemented, Sylow
166#3076—2831nomaximal, Sylow
167#533—2831no—
168C4×#41—2831no—
169#479—2831no—
170#479—2831no—
171#478—2831no—
172#478—2831no—
173#477—2831no—
174#476—2831no—
175#475—2831no—
176#474—2831no—
177#427—2831no—
178#427D28311yescharacteristic, complemented
179C2×C4⋊C8—2831no—
180#416—2831no—
181#416—2831no—
182C2×#41—2831no—
183C22×C8—2831no—
184C22×C8C2×D28311yescharacteristic
185C4⋊Q8—2831no—
186C4⋊Q8—2831no—
187#125—2831no—
188#125—2831no—
189C22⋊Q8—5661no—
190C22⋊Q8—5661no—
191C4×Q8—2831no—
192C4×Q8—2831no—
193C4×Q8—5661no—
194C4×Q8—5661no—
195C4×D4—2831no—
196C4×D4—2831no—
197C4×D4—5661no—
198C4×D4—5661no—
199#117—2831no—
200#117—5661no—
201#117C2×D28311yescharacteristic
202#117C2×D28311yescharacteristic
203C2×C42—2831no—
204C2×C42—5661no—
205#107—2831no—
206#107—2831no—
207#107C2×D28311yescharacteristic
208#107C2×D28311yescharacteristic
209#106—2831no—
210#106—2831no—
211#106C2×D28311yescharacteristic
212#106C2×D28311yescharacteristic
213C4⋊C8—2831no—
214C4⋊C8—2831no—
215C4⋊C8—2831no—
216C4⋊C8—2831no—
217#103—2831no—
218#103—2831no—
219#103—2831no—
220#103—2831no—
221#102—2831no—
222#102—2831no—
223#102—2831no—
224#102—2831no—
225#41—2834no—
226#41—5662no—
227C2×Q8—2831no—
228C2×Q8—5661no—
229C2×Q8—5661no—
230C2×D4—2831no—
231C2×D4—5661no—
232C22×C4—2831no—
233C22×C4—2831no—
234C22×C4—5661no—
235C22×C4—5661no—
236C22×C4—5661no—
237C22×C4C22×D28311yescharacteristic
238C2×C8—22no—
239C2×C8—2831no—
240C2×C8—2831no—
241C2×C8—5662no—
242C2×C8C22×D28311yescharacteristic
243C2×C8C22×D28311yescharacteristic
244C4⋊C4—2831no—
245C4⋊C4—2831no—
246C4⋊C4—5661no—
247C4⋊C4—5661no—
248C4⋊C4—5661no—
249C4⋊C4—5661no—
250C4⋊C4—5661no—
251C4⋊C4—5661no—
252C4⋊C4—5661no—
253C4⋊C4—5661no—
254C4⋊C4C22×D28311yescharacteristic
255C4⋊C4C22×D28311yescharacteristic
256C4⋊C4C22×D28311yescharacteristic
257C4⋊C4C22×D28311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—5661no—
261C22⋊C4—5661no—
262C22⋊C4—5661no—
263C42—21no—
264C42—21no—
265C42—2831no—
266C42—2831no—
267C42—2831no—
268C42—2831no—
269C42—5661no—
270C42—5661no—
271C42—5661no—
272C23—5661no—
273C23D4×D28311yescharacteristic
274Q8—2832no—
275Q8—5661no—
276Q8—11322no—
277Q8—11322no—
278D4—2832no—
279D4—5664no—
280D4—5661no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—2831no—
286C2×C4—2831no—
287C2×C4—2831no—
288C2×C4—2831no—
289C2×C4—5662no—
290C2×C4—5661no—
291C2×C4—5664no—
292C2×C4—5661no—
293C2×C4—5661no—
294C2×C4—11322no—
295C2×C4—11322no—
296C2×C4—11321no—
297C2×C4D4×D28311yescharacteristic
298C2×C4Q8×D28312yes—
299C2×C4#1798539212yes—
300C2×C4C23×D28311yescharacteristic
301C8—21no—
302C8—21no—
303C8—5661no—
304C8—5661no—
305C22—21no—
306C22—21no—
307C22—5662no—
308C22—11321no—
309C22—11321no—
310C22#2258358812yes—
311C22C2×D4×D28311yescharacteristic
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—2832no—
317C4—5662no—
318C4—5661no—
319C4—5661no—
320C4—5661no—
321C4—11321no—
322C4—11321no—
323C4#2258358812yes—
324C4C2×Q8×D28311yescharacteristic
325C4C2×#1798539211yescharacteristic
326C2—22no—
327C2—11322no—
328C2C2×#2258358811yescharacteristic
329C2#135×D28311yescharacteristic
330C2#3182726211yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#427×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985392C22
hypercenter#427D283
hypocenterC283#3076
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
1. #31827018C2semidirect
3. #31826775C2semidirect
4. #31826771C2semidirect
5. #31826768C2semidirect
6. #31826764C2semidirect
7. #31826759C2semidirect
8. #31826754C2semidirect
9. #31826749C2semidirect
10. #31826744C2semidirect
11. #31826501C2semidirect
12. C2×Dic283⋊C8C2semidirect
15. #427×C283C2semidirect
60. #17985392Q8semidirect
165. C283#3076semidirect
178. #427D283semidirect

Maximal subgroups

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

subgroupindex
#318270182
#318269332
#318267752
#318267712
#318267682
#318267642
#318267592
#318267542
#318267492
#318267442
#318265012
C2×Dic283⋊C82
#318264622
#318264592
#427×C2832
#3076283