Finite Group Databasebeta

← #15676728

Subgroups — #15676728

Order 2944.

864 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 185 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×#10625106C212yesmaximal, complemented
2C22×Dic23⋊C4C211yesmaximal, characteristic, complemented
3#13092336C212yesmaximal, complemented
4#13092331C212yesmaximal, complemented
5#13092297C212yesmaximal, complemented
6#13092290C214yesmaximal, complemented
7#13092280C211yesmaximal, characteristic, complemented
8C22×#41×C23C211yesmaximal, characteristic
9C2×#41×C23—28no—
10C2×#41×C23—24no—
11C22×Q8×C23C2211yescharacteristic
12C22×D4×C23C2211yescharacteristic
13C22×D4×C23C2212yes—
14C23×C4×C23C2212yes—
15C23×C4×C23C2211yescharacteristic
16C23×Dic23C2211yescharacteristic
17C23×Dic23C2211yescharacteristic
18C2×C22⋊Dic23C2212yes—
19C2×C22⋊Dic23C2214yes—
20C2×C22⋊Dic23C2214yes—
21#10625106—28no—
22C2×Dic23⋊C4—24no—
23C2×Dic23⋊C4C2212yes—
24C2×Dic23⋊C4C2212yes—
25C2×Dic23⋊C4C2214yes—
26C23⋊#95C2212yes—
27C23⋊#95C2212yes—
28C23⋊#95C2214yes—
29C24×C23C2312yes—
30C24×C23C2311yescharacteristic
31#41×C23—232no—
32C2×Q8×C23—24no—
33C2×Q8×C23—22no—
34C2×D4×C23—24no—
35C2×D4×C23—24no—
36C2×D4×C23—24no—
37C2×D4×C23—22no—
38C2×D4×C23D418yes—
39C22×C4×C23—24no—
40C22×C4×C23—24no—
41C22×C4×C23—24no—
42C22×C4×C23—24no—
43C22×C4×C23D414yes—
44C22×C4×C23C2311yescharacteristic
45C22×C4×C23C2312yes—
46C22×C4×C23C2311yescharacteristic
47C22×Dic23—22no—
48C22×Dic23—24no—
49C22×Dic23—22no—
50C22×Dic23—24no—
51C22×Dic23C2312yes—
52C22×Dic23C2314yes—
53C22×Dic23C2312yes—
54C22⋊Dic23—24no—
55C22⋊Dic23—28no—
56C22⋊Dic23—28no—
57Dic23⋊C4—24no—
58Dic23⋊C4—24no—
59Dic23⋊C4—28no—
60C23×C23—22no—
61C23×C23—22no—
62C23×C23—22no—
63C23×C23—22no—
64C23×C23—24no—
65C23×C23—24no—
66C23×C23C2×D414yes—
67C23×C23C2×D414yes—
68C23×C23C2×D412yes—
69C23×C23C2411yescharacteristic
70Q8×C23—28no—
71D4×C23—28no—
72D4×C23—216no—
73C2×C4×C23—216no—
74C2×C4×C23—28no—
75C2×C4×C23—22no—
76C2×C4×C23—22no—
77C2×C4×C23—22no—
78C2×C4×C23—22no—
79C2×C4×C23C2×D412yes—
80C2×C4×C23C2×D414yes—
81C2×C4×C23C2×D412yes—
82C2×Dic23—28no—
83C2×Dic23—22no—
84C2×Dic23—22no—
85C2×Dic23—22no—
86C2×Dic23—24no—
87C2×Dic23—24no—
88C2×Dic23—24no—
89C2×Dic23—24no—
90C2×Dic23—44no—
91C2×Dic23#4114yescomplemented
92#2406—231nomaximal, Sylow
93C22×C23—22no—
94C22×C23—22no—
95C22×C23—28no—
96C22×C23—24no—
97C22×C23—28no—
98C22×C23—42no—
99C22×C23—42no—
100C22×C23—44no—
101C22×C23#12014yes—
102C22×C23C22×D411yescharacteristic
103C22×C23C22×D412yes—
104C22×C23C2×#4112yes—
105C22×C232−1+412yes—
106C4×C23—22no—
107C4×C23—24no—
108C4×C23—22no—
109Dic23—24no—
110Dic23—42no—
111Dic23—44no—
112C22×#41D2311yescharacteristic
113C2×#123—232no—
114C22×C4⋊C4—231no—
115#395—232no—
116#394—232no—
117#386—232no—
118#385—234no—
119#381—231no—
120C2×C23—24no—
121C2×C23—44no—
122C2×C23C2×#12011yescharacteristic
123C2×C23#52511yescharacteristic
124C2×C23#53611yescharacteristic
125C2×C23#54714yes—
126C2×#41—28no—
127C2×#41—24no—
128C22×Q8C2×D2311yescharacteristic
129C22×D4C2×D2311yescharacteristic
130C22×D4C2×D2312yes—
131C23×C4—231no—
132C23×C4—231no—
133C23×C4C2×D2312yes—
134C23×C4C2×D2311yescharacteristic
135#123—468no—
136C2×C4⋊C4—232no—
137C2×C4⋊C4—232no—
138C2×C4⋊C4—234no—
139C2×C4⋊C4—464no—
140C2×C22⋊C4—232no—
141C2×C22⋊C4—234no—
142C2×C22⋊C4—234no—
143#95—232no—
144#95—232no—
145#95—234no—
146C23#240611yescharacteristic, complemented, Sylow
147C24C22×D2312yes—
148C24C22×D2311yescharacteristic
149#41—232no—
150C2×Q8—24no—
151C2×Q8—22no—
152C2×D4—24no—
153C2×D4—24no—
154C2×D4—24no—
155C2×D4—22no—
156C2×D4C22⋊D2318yes—
157C22×C4—24no—
158C22×C4—24no—
159C22×C4—24no—
160C22×C4—24no—
161C22×C4—232no—
162C22×C4—234no—
163C22×C4—232no—
164C22×C4—464no—
165C22×C4—462no—
166C22×C4—462no—
167C22×C4—464no—
168C22×C4C22⋊D2314yes—
169C22×C4C22×D2311yescharacteristic
170C22×C4C22×D2312yes—
171C22×C4C22×D2311yescharacteristic
172C4⋊C4—464no—
173C4⋊C4—464no—
174C4⋊C4—468no—
175C22⋊C4—468no—
176C22⋊C4—464no—
177C22⋊C4—468no—
178C23—22no—
179C23—22no—
180C23—24no—
181C23—24no—
182C23—22no—
183C23—22no—
184C23C2×C22⋊D2314yes—
185C23C2×C22⋊D2314yes—
186C23C2×C22⋊D2312yes—
187C23C23×D2311yescharacteristic
188Q8—28no—
189D4—28no—
190D4—216no—
191C2×C4—216no—
192C2×C4—28no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—234no—
198C2×C4—468no—
199C2×C4—462no—
200C2×C4—462no—
201C2×C4—464no—
202C2×C4—464no—
203C2×C4—464no—
204C2×C4—464no—
205C2×C4—462no—
206C2×C4—924no—
207C2×C4C2×C22⋊D2312yes—
208C2×C4C2×C22⋊D2314yes—
209C2×C4C2×C22⋊D2312yes—
210C22—22no—
211C22—22no—
212C22—28no—
213C22—24no—
214C22—28no—
215C22—42no—
216C22—42no—
217C22—44no—
218C22#1062512414yes—
219C22#41×D2312yes—
220C22#1062516112yes—
221C22C22×C22⋊D2311yescharacteristic
222C22C22×C22⋊D2312yes—
223C4—22no—
224C4—24no—
225C4—22no—
226C4—464no—
227C4—922no—
228C4—924no—
229C2—24no—
230C2—44no—
231C2C2×#1062512411yescharacteristic
232C2#1309292411yescharacteristic
233C2#1309298811yescharacteristic
234C2#1309306614yes—
subgroupG/H
center, FrattiniC23C23×D23
commutator, socle, cosocleC23×C23C24
Fitting, prime radicalC22×#41×C23C2
hypercenterC22×#41D23
hypocenterC23#2406
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10625106C2semidirect
2. C22×Dic23⋊C4C2semidirect
3. #13092336C2semidirect
4. #13092331C2semidirect
5. #13092297C2semidirect
6. #13092290C2semidirect
7. #13092280C2semidirect
91. C2×Dic23#41semidirect
146. C23#2406semidirect

Maximal subgroups

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

subgroupindex
C2×#106251062
C22×Dic23⋊C42
#130923362
#130923312
#130922972
#130922902
#130922802
C22×#41×C232
#240623