Finite Group Databasebeta

← #46830684

Subgroups — #46830684

Order 34624.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#22575836C211yesmaximal, characteristic, complemented
2C22×C4×D541C211yesmaximal, characteristic, complemented
3#31772613C211yesmaximal, characteristic, complemented
4#31772610C211yesmaximal, characteristic, complemented
5#31772606C211yesmaximal, characteristic, complemented
6#31772605C211yesmaximal, characteristic, complemented
7#31772601C211yesmaximal, characteristic, complemented
8#31772600C211yesmaximal, characteristic, complemented
9#31772598C211yesmaximal, characteristic, complemented
10#31772596C211yesmaximal, characteristic, complemented
11C4×D2164C211yesmaximal, characteristic, complemented
12C4×C22⋊D541C211yesmaximal, characteristic, complemented
13C4×C22⋊D541C211yesmaximal, characteristic, complemented
14#31772585C211yesmaximal, characteristic, complemented
15C4×D4×C541C211yesmaximal, characteristic, complemented
16C23×D541C2211yescharacteristic
17#22575836—24no—
18C2×Dic1082C2211yescharacteristic, complemented
19C2×D2164C2211yescharacteristic
20C2×D2164C2211yescharacteristic
21C2×C22⋊D541C2211yescharacteristic
22C2×C22⋊D541C2211yescharacteristic
23C2×C22⋊D541C2211yescharacteristic
24C2×C22⋊D541C2211yescharacteristic, complemented
25C22×Dic541C2211yescharacteristic
26C2×C4×D541—24no—
27C2×C4×D541C2211yescharacteristic
28C2×C4×D541C2211yescharacteristic
29C2×C4×D541C2211yescharacteristic
30C2×C4×D541C2211yescharacteristic
31C2×C4×D541C2211yescharacteristic, complemented
32C4⋊Dic541C2211yescharacteristic, complemented
33#22575815C2211yescharacteristic, complemented
34#22575815C2211yescharacteristic, complemented
35#22575815C2211yescharacteristic, complemented
36#22575815C2211yescharacteristic, complemented
37C22⋊Dic541C2211yescharacteristic
38C22⋊Dic541C2211yescharacteristic, complemented
39#22575813C2211yescharacteristic
40#22575813C2211yescharacteristic
41#22575813C2211yescharacteristic
42#22575813C2211yescharacteristic
43#22575813C2211yescharacteristic, complemented
44#22575813C2211yescharacteristic, complemented
45C4×Dic541C2211yescharacteristic, complemented
46C2×D4×C541C2211yescharacteristic
47C22×C4×C541C2211yescharacteristic
48C22×C4×C541C2211yescharacteristic, complemented
49C4⋊C4×C541C2211yescharacteristic, complemented
50C22⋊C4×C541C2211yescharacteristic
51C22⋊C4×C541C2211yescharacteristic, complemented
52C42×C541C2211yescharacteristic, complemented
53C22×D541—22no—
54C22×D541—22no—
55C22×D541—22no—
56C22×D541C2311yescharacteristic
57C22×D541C2311yescharacteristic
58C22×D541C2311yescharacteristic
59Dic1082—22no—
60D2164—22no—
61D2164—22no—
62C22⋊D541—22no—
63C22⋊D541—22no—
64C22⋊D541—22no—
65C22⋊D541—22no—
66C2×Dic541—22no—
67C2×Dic541C2311yescharacteristic
68C2×Dic541C2311yescharacteristic
69C2×Dic541C2311yescharacteristic
70C2×Dic541C2311yescharacteristic
71C2×Dic541C2311yescharacteristic
72C4×D541—22no—
73C4×D541—22no—
74C4×D541—22no—
75C4×D541—22no—
76C4×D541D414yescomplemented
77C23×C541C2311yescharacteristic
78C23×C541C2311yescharacteristic
79D4×C541—22no—
80C2×C4×C541—22no—
81C2×C4×C541—22no—
82C2×C4×C541C2311yescharacteristic
83C2×C4×C541C2311yescharacteristic
84C2×C4×C541C2311yescharacteristic
85C2×C4×C541C2311yescharacteristic
86C2×C4×C541C2311yescharacteristic
87C22×C541—21no—
88C22×C541—21no—
89C22×C541—21no—
90C22×C541—21no—
91C22×C541—21no—
92C22×C541#4112yescomplemented
93C22×C541C2411yescharacteristic
94C2×D541—28no—
95C2×D541—21no—
96C2×D541—21no—
97C2×D541—21no—
98C2×D541—21no—
99C2×D541—21no—
100C2×D541—21no—
101C2×D541—21no—
102C2×D541C2×D412yes—
103C2×D541#4112yescomplemented
104C4×C541—21no—
105C4×C541—21no—
106C4×C541—21no—
107C4×C541—21no—
108C4×C541C2×D412yes—
109Dic541—21no—
110Dic541—21no—
111Dic541—21no—
112Dic541—21no—
113Dic541C2×D412yes—
114C2×C541—22no—
115C2×C541—41no—
116C2×C541C22×D411yescharacteristic
117C2×C541C2×#4111yescharacteristic
118C2×C541C2×#4111yescharacteristic
119D541—22no—
120D541—22no—
121D541—41no—
122C541#52511yescharacteristic, complemented, Sylow
123#525—5411nomaximal, Sylow
124C2×#41—5411no—
125C23×C4—5411no—
126#123—5411no—
127#123—5411no—
128C22⋊Q8—5411no—
129C22⋊Q8—5411no—
130#121—5411no—
131#121—5411no—
132#120—5411no—
133#120—5411no—
134C4×D4—5411no—
135C4×D4—5411no—
136C4×D4—5411no—
137C4×D4D54111yescharacteristic, complemented
138#117—5411no—
139C24—5411no—
140#41—10824no—
141C2×Q8—5411no—
142C2×D4—5411no—
143C2×D4—5411no—
144C2×D4—5411no—
145C2×D4—5411no—
146C2×D4—5411no—
147C2×D4—5411no—
148C2×D4C2×D54111yescharacteristic
149C22×C4—5411no—
150C22×C4—5411no—
151C22×C4—5411no—
152C22×C4—5411no—
153C22×C4—5411no—
154C22×C4—5411no—
155C22×C4—10824no—
156C22×C4C2×D54111yescharacteristic
157C22×C4C2×D54111yescharacteristic, complemented
158C4⋊C4—5411no—
159C4⋊C4—5411no—
160C4⋊C4—5411no—
161C4⋊C4—5411no—
162C4⋊C4—5411no—
163C4⋊C4C2×D54111yescharacteristic, complemented
164C22⋊C4—5411no—
165C22⋊C4—5411no—
166C22⋊C4—5411no—
167C22⋊C4—5411no—
168C22⋊C4—5411no—
169C22⋊C4—5411no—
170C22⋊C4—5411no—
171C22⋊C4—5411no—
172C22⋊C4C2×D54111yescharacteristic
173C22⋊C4C2×D54111yescharacteristic, complemented
174C42—5411no—
175C42C2×D54111yescharacteristic, complemented
176C23—5411no—
177C23—5411no—
178C23—5411no—
179C23—10822no—
180C23—10822no—
181C23—10822no—
182C23C22×D54111yescharacteristic
183C23C22×D54111yescharacteristic
184Q8—10822no—
185D4—22no—
186D4—10822no—
187D4—10822no—
188D4—10822no—
189D4—10822no—
190D4—10822no—
191D4—10822no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—5411no—
195C2×C4—5414no—
196C2×C4—5411no—
197C2×C4—5411no—
198C2×C4—5411no—
199C2×C4—5411no—
200C2×C4—10822no—
201C2×C4—10822no—
202C2×C4—10822no—
203C2×C4—10822no—
204C2×C4—10822no—
205C2×C4C22×D54111yescharacteristic
206C2×C4C22×D54111yescharacteristic
207C2×C4C22×D54111yescharacteristic
208C2×C4C22×D54111yescharacteristic
209C2×C4C22×D54111yescharacteristic
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—5412no—
216C22—5412no—
217C22—10828no—
218C22—10821no—
219C22—10821no—
220C22—10821no—
221C22—10821no—
222C22—10821no—
223C22—10821no—
224C22—10821no—
225C22#2257583612yescomplemented
226C22C23×D54111yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—5412no—
232C4—10821no—
233C4—10821no—
234C4—10821no—
235C4—10821no—
236C4D4×D54112yes—
237C2—22no—
238C2—41no—
239C2—10822no—
240C2—10822no—
241C2—21641no—
242C2C2×D4×D54111yescharacteristic
243C2#41×D54111yescharacteristic
244C2C2×#2257583611yescharacteristic
subgroupG/H
centerC2×C4C22×D541
commutator, socle, cosocleC22×C541C24
FrattiniC22C23×D541
FittingC4×D4×C541C2
hypercenterC4×D4D541
hypocenterC541#525
LCSG ▷ C22×C541 ▷ C541
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#22575836C2semidirect
2. C22×C4×D541C2semidirect
3. #31772613C2semidirect
4. #31772610C2semidirect
5. #31772606C2semidirect
6. #31772605C2semidirect
7. #31772601C2semidirect
8. #31772600C2semidirect
9. #31772598C2semidirect
10. #31772596C2semidirect
11. C4×D2164C2semidirect
12. C4×C22⋊D541C2semidirect
13. C4×C22⋊D541C2semidirect
14. #31772585C2semidirect
15. C4×D4×C541C2semidirect
18. C2×Dic1082C22semidirect
24. C2×C22⋊D541C22semidirect
31. C2×C4×D541C22semidirect
32. C4⋊Dic541C22semidirect
33. #22575815C22semidirect
34. #22575815C22semidirect
35. #22575815C22semidirect
36. #22575815C22semidirect
38. C22⋊Dic541C22semidirect
43. #22575813C22semidirect
44. #22575813C22semidirect
45. C4×Dic541C22semidirect
48. C22×C4×C541C22semidirect
49. C4⋊C4×C541C22semidirect
51. C22⋊C4×C541C22semidirect
52. C42×C541C22semidirect
76. C4×D541D4semidirect
92. C22×C541#41semidirect
103. C2×D541#41semidirect
122. C541#525semidirect
137. C4×D4D541semidirect
157. C22×C4C2×D541semidirect
163. C4⋊C4C2×D541semidirect
173. C22⋊C4C2×D541semidirect
175. C42C2×D541semidirect
225. C22#22575836semidirect

Maximal subgroups

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

subgroupindex
C2×#225758362
C22×C4×D5412
#317726132
#317726102
#317726062
#317726052
#317726012
#317726002
#317725982
#317725962
C4×D21642
C4×C22⋊D5412
#317725852
C4×D4×C5412
#525541