Finite Group Databasebeta

← #15674556

Subgroups — #15674556

Order 2944.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#13093045C211yesmaximal, characteristic
2#13092426C211yesmaximal, characteristic
3#13092324C211yesmaximal, characteristic
4#13092185C211yesmaximal, characteristic
5#13092178C211yesmaximal, characteristic
6#13092176C211yesmaximal, characteristic
7C23×#419C211yesmaximal, characteristic
8C22×Q8×C23C2211yescharacteristic
9C2×M16×C23C2211yescharacteristic
10C23×#117C2211yescharacteristic
11#10625097C2211yescharacteristic
12C2×C4⋊Dic23C2211yescharacteristic
13C2×C4×Dic23C2211yescharacteristic
14C2×#67267C2211yescharacteristic
15#10625061—21no—
16#10625059—21no—
17#10625049—22no—
18#10625041—21no—
19#10625040—21no—
20C23×#103—21no—
21C23×#103—21no—
22#10625017—21no—
23#10625017—21no—
24C23⋊#95—22no—
25C2×Q8×C23—21no—
26C2×Q8×C23—21no—
27C2×Q8×C23—21no—
28C2×Q8×C23—21no—
29C2×Q8×C23—21no—
30C2×Q8×C23Q812yescomplemented
31C22×C4×C23—21no—
32C22×C4×C23C2311yescharacteristic
33C22×Dic23—21no—
34C22×Dic23D412yes—
35C2×Dic46—22no—
36M16×C23—21no—
37M16×C23—21no—
38C2×C8×C23—21no—
39C4⋊C4×C23D411yescharacteristic
40C4⋊C4×C23D411yescharacteristic
41C22⋊C4×C23—21no—
42C42×C23—21no—
43C22⋊Dic23—21no—
44C4⋊Dic23—22no—
45C4⋊Dic23—21no—
46C4⋊Dic23—21no—
47C4⋊Dic23D411yescharacteristic
48C4⋊Dic23D411yescharacteristic
49Dic23⋊C4—22no—
50Dic23⋊C4—22no—
51C4×Dic23—21no—
52C4×Dic23—21no—
53C4×Dic23—21no—
54#67267—21no—
55#67267—21no—
56C2×C23⋊C8—21no—
57C23×C23C2×D411yescharacteristic
58Q8×C23—22no—
59Q8×C23—22no—
60Q8×C23—41no—
61Q8×C23—41no—
62C2×C4×C23—21no—
63C2×C4×C23—21no—
64C2×C4×C23—22no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23C2×D411yescharacteristic
69C2×C4×C23C2×Q811yescharacteristic
70C2×C4×C23#4111yescharacteristic
71C2×C4×C23#4111yescharacteristic
72C2×C4×C23#4111yescharacteristic
73C2×Dic23—22no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—22no—
77C2×Dic23—41no—
78C2×Dic23—41no—
79C2×Dic23—42no—
80Dic46—82no—
81C8×C23—41no—
82C23⋊C8—41no—
83#2028—231nomaximal, Sylow
84C22×C23—21no—
85C22×C23—21no—
86C22×C23#12011yescharacteristic
87C22×C23C22⋊Q811yescharacteristic
88C22×C23#12411yescharacteristic
89C4×C23—42no—
90C4×C23—41no—
91C4×C23—41no—
92C4×C23C22⋊Q811yescharacteristic
93C4×C23C22⋊Q811yescharacteristic
94C4×C23#12411yescharacteristic
95C4×C23#12411yescharacteristic
96Dic23—42no—
97Dic23—41no—
98Dic23—42no—
99Dic23—41no—
100#544—231no—
101#419—231no—
102#419D2311yescharacteristic
103#391—231no—
104#343—231no—
105#339—231no—
106#339—231no—
107C2×C23—21no—
108C2×C23—21no—
109C2×C23#39311yescharacteristic
110C2×C23#45511yescharacteristic
111C2×C23#45611yescharacteristic
112C22×Q8C2×D2311yescharacteristic
113C2×M16—231no—
114C2×M16C2×D2311yescharacteristic
115C4⋊Q8—461no—
116C4⋊Q8—461no—
117#125—461no—
118#125—461no—
119C22⋊Q8—462no—
120#117—231no—
121#117C2×D2311yescharacteristic
122C2×C4⋊C4—231no—
123C2×C42—231no—
124#103—21no—
125#103—21no—
126#103—461no—
127#103—461no—
128#95—462no—
129C23#202811yescharacteristic, complemented, Sylow
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—462no—
136C2×Q8Dic4612yescomplemented
137C22×C4—21no—
138C22×C4—232no—
139C22×C4—461no—
140C22×C4C22×D2311yescharacteristic
141M16—21no—
142M16—21no—
143M16—461no—
144M16—461no—
145C2×C8—21no—
146C2×C8—461no—
147C4⋊C4—231no—
148C4⋊C4—231no—
149C4⋊C4—462no—
150C4⋊C4—462no—
151C4⋊C4—462no—
152C4⋊C4—461no—
153C4⋊C4—461no—
154C4⋊C4C22⋊D2311yescharacteristic
155C4⋊C4C22⋊D2311yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—461no—
158C42—21no—
159C42—461no—
160C42—461no—
161C42—461no—
162C23D4×D2311yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—1842no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—462no—
174C2×C4—461no—
175C2×C4—461no—
176C2×C4—462no—
177C2×C4—921no—
178C2×C4—921no—
179C2×C4—922no—
180C2×C4C2×Dic4611yescharacteristic
181C2×C4#6728811yescharacteristic
182C2×C4D4×D2311yescharacteristic
183C2×C4#6729011yescharacteristic
184C2×C4#6729011yescharacteristic
185C2×C4C2×C22⋊D2311yescharacteristic
186C8—41no—
187C8—921no—
188C22—21no—
189C22—21no—
190C22#1062504911yescharacteristic
191C22#1062505611yescharacteristic
192C22#1062510811yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—922no—
197C4—922no—
198C4—921no—
199C4—921no—
200C4#1062504911yescharacteristic
201C4#1062505611yescharacteristic
202C4#1062509511yescharacteristic
203C4#1062510711yescharacteristic
204C2—21no—
205C2—21no—
206C2#1309232911yescharacteristic
207C2#1309259311yescharacteristic
208C2#1309259811yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#419C2
socleC22×C23#120
prime radicalC23×C23C2×D4
hypercenter#419D23
hypocenterC23#2028
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C23Q8semidirect
129. C23#2028semidirect
136. C2×Q8Dic46semidirect

Maximal subgroups

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

subgroupindex
#130930452
#130924262
#130923242
#130921852
#130921782
#130921762
C23×#4192
#202823