Finite Group Databasebeta

← #15673839

Subgroups — #15673839

Order 2944.

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

normal subgroups only

This group has 442 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#13092929C211yesmaximal, characteristic
2C2×C42×D23C211yesmaximal, characteristic, complemented
3C2×#10624987C211yesmaximal, characteristic, complemented
4C2×#10625007C211yesmaximal, characteristic, complemented
5#13092380C211yesmaximal, characteristic, complemented
6#13092176C211yesmaximal, characteristic, complemented
7C23×#339C211yesmaximal, characteristic, complemented
8C2×#67288C2211yescharacteristic
9C22×C4×D23—21no—
10C22×C4×D23C2211yescharacteristic
11C2×M16×C23C2211yescharacteristic
12C23×#117C2211yescharacteristic
13C2×C42×C23C2211yescharacteristic
14C2×C4×Dic23—21no—
15C2×C4×Dic23C2211yescharacteristic
16C2×#67267C2211yescharacteristic
17#10625068C412yescomplemented
18#10625066C412yescomplemented
19#10625057—21no—
20#10625053—21no—
21C4×D92—22no—
22C42×D23—22no—
23C42×D23—22no—
24#10625007—22no—
25(C2×D23)⋊C8—22no—
26#10624987—22no—
27C23×D23D411yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C2×C22⋊D23—21no—
31C22×Dic23—21no—
32C22×Dic23D411yescharacteristic
33#67288—21no—
34#67288—21no—
35#67288—21no—
36#67288—21no—
37C2×D92—22no—
38C2×D92C2×C411yescharacteristic, complemented
39C2×C4×D23—24no—
40C2×C4×D23—28no—
41C2×C4×D23—21no—
42C2×C4×D23—21no—
43C2×C4×D23—21no—
44C2×C4×D23—21no—
45C2×C4×D23—21no—
46C2×C4×D23C2×C412yes—
47C2×C4×D23D412yes—
48C2×Dic46C2×C411yescharacteristic, complemented
49M16×C23—21no—
50M16×C23—21no—
51C2×C8×C23—21no—
52C4⋊C4×C23C2×C412yescomplemented
53C22⋊C4×C23—21no—
54C42×C23—21no—
55C42×C23—21no—
56C42×C23D412yescomplemented
57(C2×D23)⋊C4—22no—
58(C2×D23)⋊C4—22no—
59C4⋊Dic23—22no—
60C4×Dic23—24no—
61C4×Dic23—21no—
62C4×Dic23D412yescomplemented
63#67267—21no—
64#67267—21no—
65C2×C23⋊C8—21no—
66C23×C23C2×D411yescharacteristic
67C22×D23—21no—
68C22×D23—21no—
69C22×D23—24no—
70C22×D23—21no—
71C22×D23C22⋊C412yes—
72C2×C4×C23—24no—
73C2×C4×C23—22no—
74C2×C4×C23—22no—
75C2×C4×C23C22×C411yescharacteristic
76C2×C4×C23C2×D411yescharacteristic
77C2×C4×C23C2×D411yescharacteristic
78C2×C4×C23C2×D411yescharacteristic
79C2×C4×C23#4111yescharacteristic
80C2×C4×C23#4111yescharacteristic
81C22⋊D23—41no—
82C22⋊D23—41no—
83C2×Dic23—24no—
84C2×Dic23—21no—
85C2×Dic23—22no—
86C2×Dic23—21no—
87C2×Dic23—21no—
88C2×Dic23C22⋊C412yes—
89D92—21no—
90D92—21no—
91D92—44no—
92C4×D23—216no—
93C4×D23—22no—
94C4×D23—22no—
95C4×D23—22no—
96C4×D23—22no—
97C4×D23—41no—
98C4×D23—41no—
99Dic46—21no—
100Dic46—21no—
101C8×C23—41no—
102C23⋊C8—41no—
103#1896—231nomaximal, Sylow
104C22×C23—22no—
105C22×C23C2×C22⋊C411yescharacteristic
106C22×C23#12011yescharacteristic
107C22×C23#12311yescharacteristic
108C2×D23—24no—
109C2×D23—24no—
110C2×D23—22no—
111C2×D23—22no—
112C2×D23—41no—
113C2×D23—42no—
114C2×D23#10414yescomplemented
115C4×C23—24no—
116C4×C23—42no—
117C4×C23C4×D411yescharacteristic
118C4×C23C4×D411yescharacteristic
119C4×C23#12111yescharacteristic
120C4×C23#12111yescharacteristic
121Dic23—24no—
122Dic23—22no—
123Dic23—41no—
124#525—231no—
125C22×C42—231no—
126C2×#104—231no—
127C2×#104—231no—
128#407—231no—
129#339—231no—
130#339D2311yescharacteristic, complemented
131C2×C23—21no—
132C2×C23—21no—
133C2×C23#38611yescharacteristic
134C2×C23C2×#10412yes—
135D23—24no—
136D23—81no—
137C2×#41—231no—
138C23×C4—231no—
139C23×C4—461no—
140C2×M16—231no—
141C2×M16C2×D2311yescharacteristic
142#123—461no—
143C22⋊Q8—232no—
144#121—232no—
145#120—461no—
146C4×D4—462no—
147#117C2×D2311yescharacteristic
148C2×C42—231no—
149C2×C42—462no—
150C2×C42—461no—
151C2×C42—462no—
152C2×C42C2×D2311yescharacteristic
153#104—462no—
154#104—462no—
155C22⋊C8—462no—
156C23#189611yescharacteristic, complemented, Sylow
157C24—231no—
158#41—461no—
159#41—461no—
160#41—461no—
161#41—461no—
162C2×Q8—231no—
163C2×D4—231no—
164C2×D4—462no—
165C2×D4—461no—
166C22×C4—21no—
167C22×C4—231no—
168C22×C4—232no—
169C22×C4—232no—
170C22×C4—464no—
171C22×C4—468no—
172C22×C4—461no—
173C22×C4—461no—
174C22×C4—461no—
175C22×C4—461no—
176C22×C4—461no—
177C22×C4—461no—
178C22×C4C22×D2311yescharacteristic
179M16—21no—
180M16—21no—
181M16—461no—
182M16—461no—
183C2×C8—21no—
184C2×C8—461no—
185C4⋊C4—462no—
186C4⋊C4C4×D2312yescomplemented
187C22⋊C4—21no—
188C22⋊C4—462no—
189C22⋊C4—462no—
190C42—21no—
191C42—21no—
192C42—232no—
193C42—464no—
194C42—461no—
195C42D9212yescomplemented
196C23—232no—
197C23—464no—
198C23—461no—
199C23—461no—
200C23—461no—
201C23D4×D2311yescharacteristic
202Q8—461no—
203Q8—461no—
204D4—461no—
205D4—461no—
206D4—924no—
207D4—921no—
208D4—921no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—232no—
213C2×C4—4616no—
214C2×C4—464no—
215C2×C4—462no—
216C2×C4—461no—
217C2×C4—461no—
218C2×C4—462no—
219C2×C4—462no—
220C2×C4—462no—
221C2×C4—462no—
222C2×C4—461no—
223C2×C4—921no—
224C2×C4—921no—
225C2×C4C2×C4×D2311yescharacteristic
226C2×C4C2×D9211yescharacteristic
227C2×C4#6728811yescharacteristic
228C2×C4D4×D2311yescharacteristic
229C2×C4D4×D2311yescharacteristic
230C2×C4#6729211yescharacteristic
231C8—41no—
232C8—921no—
233C22—22no—
234C22—234no—
235C22—464no—
236C22—464no—
237C22—462no—
238C22—462no—
239C22—922no—
240C22—921no—
241C22C22⋊C4×D2311yescharacteristic
242C22#1062505311yescharacteristic
243C22#1062506511yescharacteristic
244C4—24no—
245C4—42no—
246C4—464no—
247C4—462no—
248C4—921no—
249C4C4×D9211yescharacteristic
250C4#1062505511yescharacteristic
251C4#1062506411yescharacteristic
252C4#1062506611yescharacteristic
253C2—21no—
254C2—21no—
255C2—464no—
256C2—1841no—
257C2#1309229511yescharacteristic
258C2#104×D2312yes—
subgroupG/H
centerC2×C4D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#339C2
socleC22×C23C2×C22⋊C4
prime radical#13092929C2
cosocleC22×C4×C23C23
hypercenter#339D23
hypocenterC23#1896
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. C2×C42×D23C2semidirect
3. C2×#10624987C2semidirect
4. C2×#10625007C2semidirect
5. #13092380C2semidirect
6. #13092176C2semidirect
7. C23×#339C2semidirect
17. #10625068C4semidirect
18. #10625066C4semidirect
38. C2×D92C2×C4semidirect
48. C2×Dic46C2×C4semidirect
52. C4⋊C4×C23C2×C4semidirect
56. C42×C23D4semidirect
62. C4×Dic23D4semidirect
114. C2×D23#104semidirect
130. #339D23semidirect
156. C23#1896semidirect
186. C4⋊C4C4×D23semidirect
195. C42D92semidirect

Maximal subgroups

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

subgroupindex
#130929292
C2×C42×D232
C2×#106249872
C2×#106250072
#130923802
#130921762
C23×#3392
#189623