Finite Group Databasebeta

← #49131211

Subgroups — #49131211

Order 36224.

410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583590C211yesmaximal, characteristic
2#117×D283C211yesmaximal, characteristic
3#31826809C212yesmaximal, complemented
4#31826808C212yesmaximal, complemented
5#31826802C212yesmaximal, complemented
6#31826797C212yesmaximal, complemented
7#31826505C211yesmaximal, characteristic, complemented
8#31826475C211yesmaximal, characteristic, complemented
9#31826473C211yesmaximal, characteristic, complemented
10#31826428C211yesmaximal, characteristic
11#428×C283C211yesmaximal, characteristic, complemented
12C22×Dic566C2211yescharacteristic
13C22×C4×D283C2211yescharacteristic
14C2×#17985376C2211yescharacteristic
15#22583590—21no—
16#22583590—21no—
17#22583590C2212yes—
18#22583590C2212yes—
19#22583569C2211yescharacteristic
20#22583568C2211yescharacteristic
21#22583568C2211yescharacteristic
22#22583567—21no—
23#22583566—21no—
24C2×C4⋊Dic283—21no—
25C4⋊C4×D283C2211yescharacteristic
26C4⋊C4×D283C2211yescharacteristic
27C2×(C2×D283)⋊C4—21no—
28C22⋊C4×D283—21no—
29C42×D283—21no—
30#22583543C2212yescomplemented
31#22583541C2212yescomplemented
32#22583535C2212yescomplemented
33#22583535C2212yescomplemented
34#22583533C2212yescomplemented
35#22583533C2212yescomplemented
36(C2×D283)⋊C8C2212yes—
37(C2×D283)⋊C8C2212yes—
38C2×M16×C283C2211yescharacteristic
39#117×C283C2211yescharacteristic
40C2×C4⋊C4×C283C2211yescharacteristic
41#107×C283C2212yescomplemented
42#106×C283C2212yescomplemented
43C23×D283D411yescharacteristic
44C2×Dic566—21no—
45C2×Dic566—22no—
46C2×Dic566—22no—
47C2×Dic566C2312yes—
48C22×Dic283—21no—
49C22×Dic283D411yescharacteristic
50C2×C4×D283—21no—
51C2×C4×D283—21no—
52C2×C4×D283—22no—
53C2×C4×D283—22no—
54C2×C4×D283D411yescharacteristic
55C2×C4×D283D411yescharacteristic
56C2×C4×D283C2311yescharacteristic
57C2×C4×D283C2311yescharacteristic
58#17985376—22no—
59C2×C283⋊C8C2312yes—
60C4⋊Dic283—22no—
61C4⋊Dic283—22no—
62C4⋊Dic283C2311yescharacteristic
63C4⋊Dic283C2311yescharacteristic
64Dic283⋊C4—21no—
65Dic283⋊C4—21no—
66C22⋊Dic283—21no—
67(C2×D283)⋊C4—21no—
68(C2×D283)⋊C4—21no—
69(C2×D283)⋊C4—22no—
70(C2×D283)⋊C4—22no—
71C4×Dic283—21no—
72C4×Dic283—21no—
73C4×Dic283—21no—
74C22×C4×C283—21no—
75C22×C4×C283C2311yescharacteristic
76M16×C283—22no—
77C2×C8×C283C2312yes—
78C4⋊C4×C283—21no—
79C4⋊C4×C283C2311yescharacteristic
80C4⋊C4×C283C2311yescharacteristic
81C4⋊C4×C283C2312yes—
82C22⋊C4×C283—21no—
83C42×C283—21no—
84C22×D283—22no—
85C22×D283—22no—
86C22×D283—41no—
87C22×D283C2×D411yescharacteristic
88C22×D283C2×D411yescharacteristic
89Dic566—22no—
90Dic566—22no—
91Dic566—42no—
92C2×Dic283—22no—
93C2×Dic283—21no—
94C2×Dic283—21no—
95C2×Dic283—22no—
96C2×Dic283—42no—
97C2×Dic283C2×D411yescharacteristic
98C2×Dic283C2×D411yescharacteristic
99C4×D283—22no—
100C4×D283—22no—
101C4×D283—21no—
102C4×D283—21no—
103C4×D283—21no—
104C4×D283—21no—
105C4×D283—42no—
106C4×D283—42no—
107C283⋊C8—22no—
108C23×C283C2×D411yescharacteristic
109C2×C4×C283—21no—
110C2×C4×C283—21no—
111C2×C4×C283—22no—
112C2×C4×C283—42no—
113C2×C4×C283C2×D411yescharacteristic
114C2×C4×C283#4112yes—
115C2×C4×C283#4112yes—
116C2×C4×C283C2411yescharacteristic
117C8×C283—22no—
118C22×C283—21no—
119C22×C283—21no—
120C22×C283#12312yes—
121C22×C283C22×D411yescharacteristic
122C2×D283—21no—
123C2×D283—21no—
124C2×D283—21no—
125C2×D283—21no—
126C2×D283—21no—
127C2×D283—44no—
128C2×D283#13712yes—
129C4×C283—41no—
130C4×C283—42no—
131C4×C283—41no—
132C4×C283#12312yes—
133C4×C283C2×#4111yescharacteristic
134C4×C283C2×#4111yescharacteristic
135Dic283—21no—
136Dic283—21no—
137Dic283—42no—
138Dic283—41no—
139Dic283—41no—
140C2×C283—22no—
141C2×C283C2×#12311yescharacteristic
142C2×C283C2×#13711yescharacteristic
143C2×C283#57511yescharacteristic
144D283—22no—
145D283—41no—
146C283#309511yescharacteristic, complemented, Sylow
147#3095—2831nomaximal, Sylow
148C2×C22⋊Q8—2831no—
149C2×#117—2831no—
150#485—2832no—
151#485—2832no—
152#484—2832no—
153#483—2832no—
154#428—2831no—
155#428D28311yescharacteristic, complemented
156#419—2831no—
157#419—2831no—
158#407—2831no—
159C22×Q8—2831no—
160C23×C4—2831no—
161C2×M16—2831no—
162C2×M16C2×D28311yescharacteristic
163C22⋊Q8—2832no—
164C22⋊Q8—2832no—
165C22⋊Q8—5661no—
166C22⋊Q8—5661no—
167#117—2831no—
168#117—2831no—
169#117—2831no—
170#117—5661no—
171#117—5661no—
172#117C2×D28311yescharacteristic
173C2×C4⋊C4—2831no—
174C2×C4⋊C4—2831no—
175C2×C4⋊C4—5661no—
176C2×C4⋊C4C2×D28311yescharacteristic
177C2×C22⋊C4—5661no—
178C2×C22⋊C4—5661no—
179C2×C42—5661no—
180#107—2832no—
181#107C2×D28312yescomplemented
182#106—2832no—
183#106C2×D28312yescomplemented
184#103—2832no—
185#103—2832no—
186#103—2832no—
187#103—2832no—
188C22⋊C8—2832no—
189C22⋊C8—2832no—
190C24—2831no—
191C2×Q8—2832no—
192C2×Q8—5661no—
193C2×Q8—5662no—
194C2×Q8—5662no—
195C22×C4—21no—
196C22×C4—2831no—
197C22×C4—2831no—
198C22×C4—2831no—
199C22×C4—2831no—
200C22×C4—2831no—
201C22×C4—5661no—
202C22×C4—5661no—
203C22×C4—5662no—
204C22×C4—5662no—
205C22×C4—5661no—
206C22×C4C22×D28311yescharacteristic
207M16—22no—
208M16—5662no—
209C2×C8—2832no—
210C2×C8C22×D28312yes—
211C4⋊C4—21no—
212C4⋊C4—2831no—
213C4⋊C4—2831no—
214C4⋊C4—5661no—
215C4⋊C4—5661no—
216C4⋊C4—5662no—
217C4⋊C4—5662no—
218C4⋊C4C22×D28311yescharacteristic
219C4⋊C4C22×D28311yescharacteristic
220C4⋊C4C22×D28312yes—
221C22⋊C4—21no—
222C22⋊C4—5661no—
223C22⋊C4—5661no—
224C22⋊C4—5662no—
225C22⋊C4—5662no—
226C22⋊C4—5661no—
227C42—21no—
228C42—5661no—
229C42—5661no—
230C42—5661no—
231C23—2831no—
232C23—2831no—
233C23—5662no—
234C23—5662no—
235C23—11321no—
236C23D4×D28311yescharacteristic
237Q8—5662no—
238Q8—5662no—
239Q8—11322no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—2831no—
245C2×C4—2831no—
246C2×C4—5662no—
247C2×C4—5662no—
248C2×C4—5662no—
249C2×C4—5661no—
250C2×C4—5661no—
251C2×C4—5661no—
252C2×C4—5661no—
253C2×C4—5661no—
254C2×C4—5661no—
255C2×C4—5662no—
256C2×C4—11322no—
257C2×C4—11322no—
258C2×C4—11322no—
259C2×C4D4×D28311yescharacteristic
260C2×C4#1798539212yes—
261C2×C4#1798539312yes—
262C2×C4C23×D28311yescharacteristic
263C8—22no—
264C8—5662no—
265C22—21no—
266C22—21no—
267C22—2832no—
268C22—5661no—
269C22—5661no—
270C22—5661no—
271C22—5661no—
272C22—5661no—
273C22—11324no—
274C22#2258359512yes—
275C22C2×D4×D28311yescharacteristic
276C4—41no—
277C4—42no—
278C4—41no—
279C4—5661no—
280C4—5661no—
281C4—11322no—
282C4—11321no—
283C4—11321no—
284C4#2258359512yes—
285C4C2×#1798539211yescharacteristic
286C4C2×#1798539311yescharacteristic
287C2—22no—
288C2—5662no—
289C2—11321no—
290C2C2×#2258359511yescharacteristic
291C2#137×D28311yescharacteristic
292C2#3182726111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#428×C283C2
socleC22×C283C22×D4
prime radicalC23×D283D4
hypercenter#428D283
hypocenterC283#3095
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #31826809C2semidirect
4. #31826808C2semidirect
5. #31826802C2semidirect
6. #31826797C2semidirect
7. #31826505C2semidirect
8. #31826475C2semidirect
9. #31826473C2semidirect
11. #428×C283C2semidirect
30. #22583543C22semidirect
31. #22583541C22semidirect
32. #22583535C22semidirect
33. #22583535C22semidirect
34. #22583533C22semidirect
35. #22583533C22semidirect
41. #107×C283C22semidirect
42. #106×C283C22semidirect
146. C283#3095semidirect
155. #428D283semidirect
181. #107C2×D283semidirect
183. #106C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835902
#117×D2832
#318268092
#318268082
#318268022
#318267972
#318265052
#318264752
#318264732
#318264282
#428×C2832
#3095283