Finite Group Databasebeta

← #15673416

Subgroups — #15673416

Order 2944.

312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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#13092885C211yesmaximal, characteristic
2#13092440C211yesmaximal, characteristic, complemented
3C2×#10624987C211yesmaximal, characteristic
4C2×#10625007C211yesmaximal, characteristic
5C4×Dic23⋊C4C211yesmaximal, characteristic, complemented
6#13092176C211yesmaximal, characteristic, complemented
7C23×#339C211yesmaximal, characteristic, complemented
8C2×#67288C2211yescharacteristic
9C2×M16×C23C2211yescharacteristic
10C23×#117C2211yescharacteristic
11C2×C42×C23C2211yescharacteristic
12C2×Dic23⋊C4—21no—
13C2×C4×Dic23C2211yescharacteristic
14C2×C4×Dic23C2211yescharacteristic
15C2×#67267C2211yescharacteristic
16#10625064C411yescharacteristic, complemented
17#10625064C411yescharacteristic, complemented
18#10625058C411yescharacteristic, complemented
19#10625058C411yescharacteristic, complemented
20(C22⋊D23)⋊C4—21no—
21(C22⋊D23)⋊C4—21no—
22#10625043—21no—
23C42×D23—21no—
24C23⋊#95—21no—
25#10625007—22no—
26Dic23⋊C8—21no—
27Dic23⋊C8—21no—
28#10624987—22no—
29C22×C4×C23—21no—
30C22×C4×C23C2311yescharacteristic
31C2×C22⋊D23—21no—
32C22×Dic23—21no—
33C22×Dic23D411yescharacteristic
34C22×Dic23D411yescharacteristic
35#67288—21no—
36#67288—21no—
37#67288D412yes—
38#67288Q812yes—
39C2×D92C2×C411yescharacteristic
40C2×C4×D23—21no—
41C2×C4×D23—21no—
42C2×C4×D23—21no—
43C2×Dic46C2×C411yescharacteristic
44M16×C23—21no—
45M16×C23—21no—
46C2×C8×C23—21no—
47C4⋊C4×C23C2×C411yescharacteristic
48C4⋊C4×C23C2×C411yescharacteristic
49C22⋊C4×C23—21no—
50C42×C23—21no—
51C42×C23—21no—
52C42×C23—21no—
53(C2×D23)⋊C4—21no—
54(C2×D23)⋊C4—21no—
55Dic23⋊C4—24no—
56Dic23⋊C4—21no—
57Dic23⋊C4—21no—
58C4×Dic23—21no—
59C4×Dic23—21no—
60C4×Dic23—21no—
61C4×Dic23—21no—
62C4×Dic23C2×C411yescharacteristic
63C4×Dic23C2×C411yescharacteristic
64C4×Dic23D411yescharacteristic
65C4×Dic23D411yescharacteristic
66#67267—21no—
67#67267—21no—
68C2×C23⋊C8—21no—
69C23×C23C2×D411yescharacteristic
70C22×D23—21no—
71C2×C4×C23—22no—
72C2×C4×C23—21no—
73C2×C4×C23—21no—
74C2×C4×C23—41no—
75C2×C4×C23—41no—
76C2×C4×C23C22×C411yescharacteristic
77C2×C4×C23C2×D411yescharacteristic
78C2×C4×C23C2×D411yescharacteristic
79C2×C4×C23C2×Q811yescharacteristic
80C2×C4×C23#4111yescharacteristic
81C2×C4×C23#4111yescharacteristic
82C22⋊D23—22no—
83C22⋊D23—22no—
84C2×Dic23—21no—
85C2×Dic23—22no—
86C2×Dic23—22no—
87C2×Dic23—41no—
88C2×Dic23—41no—
89C2×Dic23—41no—
90C2×Dic23C22⋊C411yescharacteristic
91C2×Dic23C22⋊C411yescharacteristic
92C2×Dic23C22⋊C411yescharacteristic
93C2×Dic23C22⋊C411yescharacteristic
94D92—21no—
95D92C4⋊C412yescomplemented
96C4×D23—22no—
97C4×D23—22no—
98C4×D23—42no—
99C4×D23—42no—
100Dic46—21no—
101Dic46C4⋊C412yescomplemented
102C8×C23—41no—
103C23⋊C8—41no—
104#1806—231nomaximal, Sylow
105C22×C23—21no—
106C22×C23—21no—
107C22×C23C2×C22⋊C411yescharacteristic
108C22×C23#12111yescharacteristic
109C22×C23C22⋊Q811yescharacteristic
110C2×D23—22no—
111C2×D23—41no—
112C2×D23—41no—
113C4×C23—42no—
114C4×C23—41no—
115C4×C23—41no—
116C4×C23C2×C4⋊C411yescharacteristic
117C4×C23#11711yescharacteristic
118C4×C23#12111yescharacteristic
119C4×C23C22⋊Q811yescharacteristic
120Dic23—22no—
121Dic23—21no—
122Dic23—21no—
123Dic23—21no—
124Dic23—42no—
125Dic23#10412yescomplemented
126C4×#41—231no—
127#423—231no—
128C2×#104—231no—
129C2×#104—231no—
130C4×C4⋊C4—231no—
131#339—231no—
132#339D2311yescharacteristic, complemented
133C2×C23—21no—
134C2×C23—21no—
135C2×C23#38011yescharacteristic
136C2×C23C2×#10411yescharacteristic
137C2×C23#42111yescharacteristic
138D23—42no—
139C2×#41—231no—
140C2×M16—231no—
141C2×M16C2×D2311yescharacteristic
142C4×Q8—231no—
143C4×Q8—231no—
144C4×D4—231no—
145C4×D4—231no—
146C4×D4—461no—
147C4×D4—461no—
148#117—461no—
149#117C2×D2311yescharacteristic
150C2×C4⋊C4—461no—
151C2×C42—231no—
152C2×C42—231no—
153C2×C42—461no—
154C2×C42C2×D2311yescharacteristic
155C4⋊C8—461no—
156C4⋊C8—461no—
157#104—462no—
158#104—462no—
159#95—461no—
160C23#180611yescharacteristic, complemented, Sylow
161#41—232no—
162#41—232no—
163#41—461no—
164#41—461no—
165C2×Q8—231no—
166C2×D4—231no—
167C2×D4—461no—
168C22×C4—21no—
169C22×C4—231no—
170C22×C4—231no—
171C22×C4—461no—
172C22×C4—461no—
173C22×C4—461no—
174C22×C4—461no—
175C22×C4C22×D2311yescharacteristic
176M16—21no—
177M16—21no—
178M16—461no—
179M16—461no—
180C2×C8—21no—
181C2×C8—461no—
182C4⋊C4—461no—
183C4⋊C4—461no—
184C4⋊C4—464no—
185C4⋊C4C4×D2311yescharacteristic
186C4⋊C4C4×D2311yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—461no—
189C22⋊C4—461no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—231no—
194C42—231no—
195C42—231no—
196C42—231no—
197C42—461no—
198C42—461no—
199C42—461no—
200C42—461no—
201C23—461no—
202C23D4×D2311yescharacteristic
203Q8—232no—
204Q8—461no—
205D4—232no—
206D4—462no—
207D4—462no—
208D4—461no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—231no—
215C2×C4—231no—
216C2×C4—231no—
217C2×C4—231no—
218C2×C4—462no—
219C2×C4—461no—
220C2×C4—462no—
221C2×C4—462no—
222C2×C4—462no—
223C2×C4—922no—
224C2×C4—922no—
225C2×C4—921no—
226C2×C4—921no—
227C2×C4—921no—
228C2×C4C2×C4×D2311yescharacteristic
229C2×C4#6728811yescharacteristic
230C2×C4#6728811yescharacteristic
231C2×C4D4×D2311yescharacteristic
232C2×C4D4×D2311yescharacteristic
233C2×C4Q8×D2311yescharacteristic
234C8—41no—
235C8—921no—
236C22—21no—
237C22—21no—
238C22—462no—
239C22—921no—
240C22—921no—
241C22C22⋊C4×D2311yescharacteristic
242C22#1062505511yescharacteristic
243C22#1062506711yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—232no—
248C4—461no—
249C4—461no—
250C4—461no—
251C4—462no—
252C4—922no—
253C4#1062504311yescharacteristic
254C4#1062505511yescharacteristic
255C4C4⋊C4×D2311yescharacteristic
256C4#1062506711yescharacteristic
257C2—21no—
258C2—21no—
259C2—922no—
260C2#1309227611yescharacteristic
261C2#104×D2311yescharacteristic
262C2#1309243211yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#339C2
socleC22×C23C2×C22⋊C4
prime radicalC2×#67288C22
cosocleC22×C4×C23C23
hypercenter#339D23
hypocenterC23#1806
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #13092440C2semidirect
5. C4×Dic23⋊C4C2semidirect
6. #13092176C2semidirect
7. C23×#339C2semidirect
16. #10625064C4semidirect
17. #10625064C4semidirect
18. #10625058C4semidirect
19. #10625058C4semidirect
95. D92C4⋊C4semidirect
101. Dic46C4⋊C4semidirect
125. Dic23#104semidirect
132. #339D23semidirect
160. C23#1806semidirect

Maximal subgroups

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

subgroupindex
#130928852
#130924402
C2×#106249872
C2×#106250072
C4×Dic23⋊C42
#130921762
C23×#3392
#180623