Finite Group Databasebeta

← #44483178

Subgroups — #44483178

Order 30592.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#29505307C211yesmaximal, characteristic
2#29504827C211yesmaximal, characteristic, complemented
3#29504827C211yesmaximal, characteristic, complemented
4#29504514C211yesmaximal, characteristic, complemented
5#29504511C211yesmaximal, characteristic, complemented
6#29504511C211yesmaximal, characteristic, complemented
7#330×C239C211yesmaximal, characteristic, complemented
8#21439955—21no—
9#21439948C2211yescharacteristic
10#21439945—21no—
11#21439940C411yescharacteristic
12#21439935C411yescharacteristic
13#21439925C411yescharacteristic
14#21439922—21no—
15#21439922C411yescharacteristic
16#21439918—21no—
17C42×D239C2211yescharacteristic
18Dic239⋊C8—21no—
19Dic239⋊C8—21no—
20(C2×D239)⋊C8—21no—
21(C2×D239)⋊C8—21no—
22#21439871C2211yescharacteristic
23#21439871C2211yescharacteristic
24#125×C239C2211yescharacteristic
25#97×C239C2211yescharacteristic
26#97×C239C2211yescharacteristic
27C2×Dic478C2×C411yescharacteristic
28C2×D956—21no—
29C2×D956C2×C411yescharacteristic
30C2×C4×D239—21no—
31C2×C4×D239C2×C411yescharacteristic
32C2×C4×D239D411yescharacteristic
33C2×C4×D239D411yescharacteristic
34C2×C239⋊C8—21no—
35C2×C239⋊C8—21no—
36C4⋊Dic239—21no—
37Dic239⋊C4—21no—
38(C2×D239)⋊C4—21no—
39(C2×D239)⋊C4—21no—
40(C2×D239)⋊C4—21no—
41(C2×D239)⋊C4—21no—
42(C2×D239)⋊C4—21no—
43C4×Dic239—21no—
44C4×Dic239C2×C411yescharacteristic
45C4×Dic239D411yescharacteristic
46C4×Dic239D411yescharacteristic
47C2×C8×C239—21no—
48C2×C8×C239—21no—
49C4⋊C4×C239—21no—
50C4⋊C4×C239—21no—
51C4⋊C4×C239C2×C411yescharacteristic
52C4⋊C4×C239C2×C411yescharacteristic
53C42×C239C2311yescharacteristic
54C22×D239—21no—
55C22×D239C22⋊C411yescharacteristic
56Dic478—41no—
57D956—41no—
58D956—42no—
59C2×Dic239—21no—
60C2×Dic239C22⋊C411yescharacteristic
61C2×Dic239C22⋊C411yescharacteristic
62C2×Dic239C22⋊C411yescharacteristic
63C4×D239—41no—
64C4×D239—41no—
65C4×D239—41no—
66C4×D239—42no—
67C239⋊C8—41no—
68C239⋊C8—41no—
69C2×C4×C239—21no—
70C2×C4×C239—21no—
71C2×C4×C239C22×C411yescharacteristic
72C2×C4×C239C2×D411yescharacteristic
73C2×C4×C239C2×D411yescharacteristic
74C8×C239—41no—
75C8×C239—41no—
76C22×C239C2×C22⋊C411yescharacteristic
77C2×D239—21no—
78C2×D239—21no—
79C2×D239—21no—
80C2×D239—41no—
81C2×D239—41no—
82C2×D239—41no—
83C4×C239—21no—
84C4×C239—21no—
85C4×C239—21no—
86C4×C239—41no—
87C4×C239—41no—
88Dic239—21no—
89Dic239—21no—
90Dic239—21no—
91Dic239—41no—
92C2×C239#41311yescharacteristic
93C2×C239#42111yescharacteristic
94C2×C239#42111yescharacteristic
95D239—41no—
96D239—81no—
97C239#153511yescharacteristic, complemented, Sylow
98#1535—2391nomaximal, Sylow
99#529—2391no—
100#432—2391no—
101#432—2391no—
102#330—2391no—
103#330D23911yescharacteristic, complemented
104#329—2391no—
105#329—2391no—
106#126—4781no—
107#125C2×D23911yescharacteristic
108#124—2391no—
109#123—4781no—
110C22⋊Q8—2391no—
111#121—2391no—
112C4×Q8—2391no—
113C4×D4—4781no—
114C4×D4—2391no—
115#117—4781no—
116C2×C42—2391no—
117C4⋊C8—4781no—
118C4⋊C8—4781no—
119C22⋊C8—4781no—
120C22⋊C8—4781no—
121#97—2391no—
122#97—2391no—
123#97C2×D23911yescharacteristic
124#97C2×D23911yescharacteristic
125C2×Q8—2391no—
126C2×D4—4781no—
127C2×D4—2391no—
128C22×C4—4781no—
129C22×C4—2391no—
130C22×C4—2391no—
131C22×C4—2391no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—4781no—
135C2×C8—4781no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—4781no—
139C4⋊C4—4781no—
140C4⋊C4C4×D23911yescharacteristic
141C4⋊C4C4×D23911yescharacteristic
142C22⋊C4—4781no—
143C22⋊C4—4781no—
144C22⋊C4—4781no—
145C22⋊C4—4781no—
146C22⋊C4—4781no—
147C42—4781no—
148C42—2391no—
149C42—2391no—
150C42—2391no—
151C42C22×D23911yescharacteristic
152C23—4781no—
153C23—2391no—
154Q8—9561no—
155D4—9561no—
156D4—9562no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—9561no—
160C2×C4—9561no—
161C2×C4—9561no—
162C2×C4—9562no—
163C2×C4—4781no—
164C2×C4—2391no—
165C2×C4—2391no—
166C2×C4—2391no—
167C2×C4C2×C4×D23911yescharacteristic
168C2×C4D4×D23911yescharacteristic
169C2×C4D4×D23911yescharacteristic
170C8—41no—
171C8—41no—
172C8—9561no—
173C8—9561no—
174C22—9561no—
175C22—9561no—
176C22—9561no—
177C22—4781no—
178C22—4781no—
179C22—4781no—
180C22C22⋊C4×D23911yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—9561no—
187C4—4781no—
188C4—4781no—
189C4—4781no—
190C2—19121no—
191C2—9561no—
192C2#2950475511yescharacteristic
193C2#2950478711yescharacteristic
194C2#2950478711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D239
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
Fitting#330×C239C2
socleC22×C239C2×C22⋊C4
prime radical#21439935C4
cosocleC42×C239C23
hypercenter#330D239
hypocenterC239#1535
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
2. #29504827C2semidirect
3. #29504827C2semidirect
4. #29504514C2semidirect
5. #29504511C2semidirect
6. #29504511C2semidirect
7. #330×C239C2semidirect
97. C239#1535semidirect
103. #330D239semidirect

Maximal subgroups

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

subgroupindex
#295053072
#295048272
#295045142
#295045112
#330×C2392
#1535239