Finite Group Databasebeta

← #15674524

Subgroups — #15674524

Order 2944.

638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 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#13092979C211yesmaximal, characteristic, complemented
2C2×#10625053C212yesmaximal, complemented
3C2×#10624988C212yesmaximal, complemented
4#13092272C211yesmaximal, characteristic, complemented
5C23×#342C211yesmaximal, characteristic, complemented
6C24×D23C2211yescharacteristic
7C22×C22⋊D23C2212yes—
8C22×D92—22no—
9C2×C22⋊C4×C23C2211yescharacteristic
10C2×C22⋊C4×C23C2212yes—
11C2×C22⋊Dic23C2211yescharacteristic
12#10625101—22no—
13C2×(C2×D23)⋊C4—22no—
14C2×(C2×D23)⋊C4—22no—
15#10625057—22no—
16#10625053—24no—
17#10625053—22no—
18#10625053—24no—
19#10624988—24no—
20C24×C23C2311yescharacteristic
21C23×D23—21no—
22C23×D23—22no—
23C23×D23—22no—
24C23×D23—21no—
25C23×D23—44no—
26C23×D23D412yescomplemented
27C23×D23D412yescomplemented
28C22×C4×C23—22no—
29C22×C4×C23D412yescomplemented
30C2×C22⋊D23—22no—
31C2×C22⋊D23—22no—
32C2×C22⋊D23—22no—
33C2×C22⋊D23—22no—
34C2×C22⋊D23—22no—
35C2×C22⋊D23—22no—
36C22×Dic23—21no—
37C22×Dic23D412yescomplemented
38C2×D92—28no—
39C2×D92—22no—
40C2×D92—48no—
41C22⋊C4×C23—22no—
42C22⋊C4×C23—22no—
43C22⋊C4×C23D414yescomplemented
44C22⋊Dic23—22no—
45(C2×D23)⋊C4—28no—
46(C2×D23)⋊C4—24no—
47(C2×D23)⋊C4—44no—
48C4⋊Dic23—22no—
49C23×C23—42no—
50C23×C23C2×D411yescharacteristic
51C23×C23C2×D412yes—
52C23×C23C2×D412yes—
53C23×C23C2×D411yescharacteristic
54C23×C23#4111yescharacteristic
55C22×D23—24no—
56C22×D23—28no—
57C22×D23—24no—
58C22×D23—22no—
59C22×D23—22no—
60C22×D23—22no—
61C22×D23—22no—
62C22×D23—44no—
63C22×D23—48no—
64C22×D23—44no—
65C22×D23—42no—
66C22×D23—44no—
67C22×D23—41no—
68C22×D23—42no—
69C22×D23—41no—
70C22×D23—44no—
71C2×C4×C23—22no—
72C2×C4×C23—24no—
73C2×C4×C23—44no—
74C2×C4×C23—42no—
75C22⋊D23—42no—
76C22⋊D23—42no—
77C22⋊D23—42no—
78C22⋊D23—42no—
79C2×Dic23—22no—
80C2×Dic23—22no—
81C2×Dic23—22no—
82C2×Dic23—42no—
83C2×Dic23—41no—
84D92—416no—
85D92—82no—
86#2021—231nomaximal, Sylow
87C22×C23—22no—
88C22×C23—24no—
89C22×C23—42no—
90C22×C23—41no—
91C22×C23—41no—
92C22×C23#12012yes—
93C22×C23#12011yescharacteristic
94C22×C23#12112yes—
95C22×C23#12111yescharacteristic
96C22×C23#12711yescharacteristic
97C2×D23—28no—
98C2×D23—24no—
99C2×D23—44no—
100C2×D23—44no—
101C2×D23—42no—
102C2×D23—48no—
103C2×D23—42no—
104C2×D23—44no—
105C2×D23—44no—
106C2×D23—42no—
107C2×D23—44no—
108C2×D23—82no—
109C4×C23—44no—
110C4×C23—42no—
111Dic23—42no—
112Dic23—81no—
113#534—231no—
114C2×#120—232no—
115C2×#99—232no—
116#379—231no—
117#342D2311yescharacteristic, complemented
118C2×C23—21no—
119C2×C23—22no—
120C2×C23—21no—
121C2×C23—22no—
122C2×C23#39211yescharacteristic
123C2×C23B(4,𝔽2)12yes—
124D23—44no—
125D23—82no—
126C25—231no—
127C22×D4—232no—
128C22×D4—462no—
129#123—462no—
130#121—462no—
131#120—464no—
132#120—462no—
133#120—464no—
134C2×C22⋊C4—231no—
135C2×C22⋊C4—462no—
136C2×C22⋊C4—462no—
137C2×C22⋊C4C2×D2311yescharacteristic
138C2×C22⋊C4C2×D2312yes—
139#99—464no—
140C23#202111yescharacteristic, complemented, Sylow
141C24—232no—
142C24—232no—
143C24—461no—
144C24—462no—
145C24—462no—
146C24—461no—
147C24—924no—
148C24C22×D2311yescharacteristic
149C2×D4—468no—
150C2×D4—462no—
151C2×D4—462no—
152C2×D4—462no—
153C2×D4—462no—
154C2×D4—462no—
155C2×D4—462no—
156C2×D4—462no—
157C2×D4—928no—
158C22×C4—22no—
159C22×C4—232no—
160C22×C4—461no—
161C22×C4D9212yescomplemented
162C4⋊C4—462no—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—468no—
166C22⋊C4—464no—
167C22⋊C4—462no—
168C22⋊C4—924no—
169C22⋊C4D9214yescomplemented
170C23—42no—
171C23—464no—
172C23—468no—
173C23—464no—
174C23—462no—
175C23—462no—
176C23—462no—
177C23—462no—
178C23—922no—
179C23—924no—
180C23—924no—
181C23—924no—
182C23—928no—
183C23—924no—
184C23—921no—
185C23—921no—
186C23—922no—
187C23C2×D9211yescharacteristic
188C23C2×D9212yes—
189C23D4×D2312yes—
190C23D4×D2311yescharacteristic
191C23#6729211yescharacteristic
192D4—9216no—
193D4—922no—
194D4—922no—
195D4—922no—
196D4—922no—
197D4—1842no—
198C2×C4—24no—
199C2×C4—22no—
200C2×C4—44no—
201C2×C4—42no—
202C2×C4—462no—
203C2×C4—462no—
204C2×C4—462no—
205C2×C4—922no—
206C2×C4—921no—
207C22—22no—
208C22—24no—
209C22—42no—
210C22—41no—
211C22—41no—
212C22—468no—
213C22—464no—
214C22—924no—
215C22—924no—
216C22—922no—
217C22—928no—
218C22—924no—
219C22—922no—
220C22—924no—
221C22—922no—
222C22—924no—
223C22—1842no—
224C22#1062504511yescharacteristic
225C22#1062505312yes—
226C22#1062505311yescharacteristic
227C22#1062506612yes—
228C22#1062506611yescharacteristic
229C4—44no—
230C4—42no—
231C4—922no—
232C4—1841no—
233C2—22no—
234C2—21no—
235C2—21no—
236C2—22no—
237C2—924no—
238C2—1842no—
239C2#1309232711yescharacteristic
240C2#1309260512yes—
subgroupG/H
centerC22#10625053
commutator, cosocleC24×C23C23
FrattiniC24C22×D23
FittingC23×#342C2
socleC22×C23#120
hypercenter#342D23
hypocenterC23#2021
LCSG ▷ C24×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #13092979C2semidirect
2. C2×#10625053C2semidirect
3. C2×#10624988C2semidirect
4. #13092272C2semidirect
5. C23×#342C2semidirect
26. C23×D23D4semidirect
27. C23×D23D4semidirect
29. C22×C4×C23D4semidirect
37. C22×Dic23D4semidirect
43. C22⋊C4×C23D4semidirect
117. #342D23semidirect
140. C23#2021semidirect
161. C22×C4D92semidirect
169. C22⋊C4D92semidirect

Maximal subgroups

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

subgroupindex
#130929792
C2×#106250532
C2×#106249882
#130922722
C23×#3422
#202123