Finite Group Databasebeta

← #44483161

Subgroups — #44483161

Order 30592.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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
1#29505328C211yesmaximal, characteristic
2#29504827C211yesmaximal, characteristic
3#97×D239C211yesmaximal, characteristic
4#29504514C211yesmaximal, characteristic, complemented
5#29504513C211yesmaximal, characteristic, complemented
6#29504513C211yesmaximal, characteristic, complemented
7#330×C239C211yesmaximal, characteristic, complemented
8C2×C8×D239—21no—
9#21439959C411yescharacteristic
10#21439959C411yescharacteristic
11#21439952C2211yescharacteristic
12#21439938—21no—
13#21439938—21no—
14#21439925—21no—
15#21439925—21no—
16#21439918C411yescharacteristic
17#21439918C411yescharacteristic
18C42×D239C2211yescharacteristic
19Dic239⋊C8—21no—
20(C2×D239)⋊C8—21no—
21#21439871C2211yescharacteristic
22#21439871C2211yescharacteristic
23#21439870—21no—
24#125×C239C2211yescharacteristic
25#97×C239C2211yescharacteristic
26#97×C239C2211yescharacteristic
27C2×Dic478—21no—
28C2×Dic478—21no—
29C2×C4×D239C2×C411yescharacteristic
30C2×C4×D239D411yescharacteristic
31C2×C4×D239D411yescharacteristic
32C2×C239⋊C8—21no—
33C2×C239⋊C8—21no—
34C8×D239—24no—
35C4⋊Dic239C2×C411yescharacteristic
36C4⋊Dic239C2×C411yescharacteristic
37Dic239⋊C4—21no—
38Dic239⋊C4—21no—
39Dic239⋊C4—21no—
40Dic239⋊C4—21no—
41(C2×D239)⋊C4—21no—
42(C2×D239)⋊C4—21no—
43C4×Dic239—21no—
44C4×Dic239—21no—
45C4×Dic239C2×C411yescharacteristic
46C4×Dic239D411yescharacteristic
47C4×Dic239D411yescharacteristic
48C2×C8×C239—21no—
49C2×C8×C239—21no—
50C4⋊C4×C239—21no—
51C4⋊C4×C239—21no—
52C4⋊C4×C239C2×C411yescharacteristic
53C4⋊C4×C239C2×C411yescharacteristic
54C42×C239C2311yescharacteristic
55C22×D239C22⋊C411yescharacteristic
56Dic478—42no—
57Dic478—42no—
58C2×Dic239—21no—
59C2×Dic239—21no—
60C2×Dic239C22⋊C411yescharacteristic
61C2×Dic239C22⋊C411yescharacteristic
62C2×Dic239C22⋊C411yescharacteristic
63C4×D239—22no—
64C4×D239—22no—
65C4×D239—41no—
66C239⋊C8—22no—
67C239⋊C8—41no—
68C2×C4×C239—21no—
69C2×C4×C239—21no—
70C2×C4×C239C22×C411yescharacteristic
71C2×C4×C239C2×D411yescharacteristic
72C2×C4×C239C2×D411yescharacteristic
73C8×C239—22no—
74C8×C239—41no—
75C22×C239C2×C22⋊C411yescharacteristic
76C2×D239—21no—
77C2×D239—21no—
78C2×D239#10112yes—
79C4×C239—21no—
80C4×C239—21no—
81C4×C239—21no—
82C4×C239—41no—
83C4×C239—41no—
84Dic239—21no—
85Dic239—21no—
86Dic239—41no—
87Dic239—41no—
88Dic239#10412yes—
89C2×C239C2×#10111yescharacteristic
90C2×C239C2×#10411yescharacteristic
91C2×C239#42111yescharacteristic
92D239—22no—
93C239#153111yescharacteristic, complemented, Sylow
94#1531—2391nomaximal, Sylow
95#533—2391no—
96#432—2391no—
97C2×#97—2391no—
98#330—2391no—
99#330—2391no—
100#330—2391no—
101#330D23911yescharacteristic, complemented
102C22×C8—4781no—
103C4⋊Q8—2391no—
104C4⋊Q8—2391no—
105#125—2391no—
106#125C2×D23911yescharacteristic
107C22⋊Q8—4781no—
108C22⋊Q8—4781no—
109C4×Q8—4781no—
110C4×Q8—4781no—
111#117—2391no—
112#117—2391no—
113C2×C42—2391no—
114C4⋊C8—4781no—
115C22⋊C8—4781no—
116#97—4781no—
117#97—2391no—
118#97—2391no—
119#97C2×D23911yescharacteristic
120#97C2×D23911yescharacteristic
121C2×Q8—4781no—
122C2×Q8—4781no—
123C22×C4—2391no—
124C22×C4—2391no—
125C22×C4—2391no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—4784no—
129C2×C8—4781no—
130C2×C8—4781no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—4781no—
134C4⋊C4—4781no—
135C4⋊C4—4781no—
136C4⋊C4—4781no—
137C4⋊C4—2391no—
138C4⋊C4—2391no—
139C4⋊C4C4×D23911yescharacteristic
140C4⋊C4C4×D23911yescharacteristic
141C22⋊C4—4781no—
142C22⋊C4—4781no—
143C42—4781no—
144C42—4781no—
145C42—2391no—
146C42—2391no—
147C42—2391no—
148C42C22×D23911yescharacteristic
149C23—2391no—
150Q8—9562no—
151Q8—9562no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—9561no—
155C2×C4—4782no—
156C2×C4—4782no—
157C2×C4—4781no—
158C2×C4—4781no—
159C2×C4—2391no—
160C2×C4—2391no—
161C2×C4—2391no—
162C2×C4C2×C4×D23911yescharacteristic
163C2×C4D4×D23911yescharacteristic
164C2×C4D4×D23911yescharacteristic
165C8—22no—
166C8—41no—
167C8—9561no—
168C8—4782no—
169C22—4781no—
170C22—4781no—
171C22—2392no—
172C22C22⋊C4×D23911yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—9561no—
179C4—9561no—
180C4—4781no—
181C4—4781no—
182C4—2392no—
183C2—4782no—
184C2#101×D23911yescharacteristic
185C2#104×D23911yescharacteristic
186C2#2950478711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D239
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
Fitting#330×C239C2
socleC22×C239C2×C22⋊C4
prime radicalC22×D239C22⋊C4
cosocleC42×C239C23
hypercenter#330D239
hypocenterC239#1531
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #29504514C2semidirect
5. #29504513C2semidirect
6. #29504513C2semidirect
7. #330×C239C2semidirect
93. C239#1531semidirect
101. #330D239semidirect

Maximal subgroups

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

subgroupindex
#295053282
#295048272
#97×D2392
#295045142
#295045132
#330×C2392
#1531239