Finite Group Databasebeta

← #15673844

Subgroups — #15673844

Order 2944.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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×#10625043C211yesmaximal, 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×D23C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C23×#117C2211yescharacteristic
12C2×C42×C23C2211yescharacteristic
13C2×(C2×D23)⋊C4—21no—
14C2×Dic23⋊C4—21no—
15C2×C4×Dic23C2211yescharacteristic
16C2×#67267C2211yescharacteristic
17#10625068C412yescomplemented
18#10625066C412yescomplemented
19#10625057—21no—
20#10625053—21no—
21C4×D92—22no—
22#10625043—22no—
23#10625043—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
39C2×C4×D23—21no—
40C2×C4×D23—21no—
41C2×C4×D23—21no—
42C2×C4×D23—21no—
43C2×C4×D23—21no—
44C2×C4×D23C2×C412yes—
45C2×C4×D23D412yes—
46C2×Dic46C2×C411yescharacteristic
47M16×C23—21no—
48M16×C23—21no—
49C2×C8×C23—21no—
50C4⋊C4×C23C2×C412yes—
51C22⋊C4×C23—21no—
52C42×C23—21no—
53C42×C23—21no—
54C42×C23D412yescomplemented
55(C2×D23)⋊C4—24no—
56(C2×D23)⋊C4—22no—
57(C2×D23)⋊C4—22no—
58C4⋊Dic23—22no—
59Dic23⋊C4—24no—
60C4×Dic23—21no—
61C4×Dic23D412yescomplemented
62#67267—21no—
63#67267—21no—
64C2×C23⋊C8—21no—
65C23×C23C2×D411yescharacteristic
66C22×D23—21no—
67C22×D23—21no—
68C22×D23—21no—
69C22×D23—42no—
70C22×D23C22⋊C412yes—
71C2×C4×C23—22no—
72C2×C4×C23—22no—
73C2×C4×C23—42no—
74C2×C4×C23C22×C411yescharacteristic
75C2×C4×C23C2×D411yescharacteristic
76C2×C4×C23C2×D411yescharacteristic
77C2×C4×C23C2×D411yescharacteristic
78C2×C4×C23#4111yescharacteristic
79C2×C4×C23#4111yescharacteristic
80C22⋊D23—41no—
81C22⋊D23—41no—
82C2×Dic23—21no—
83C2×Dic23—21no—
84C2×Dic23—21no—
85C2×Dic23—22no—
86C2×Dic23—42no—
87C2×Dic23C22⋊C412yes—
88D92—21no—
89D92—21no—
90D92—44no—
91C4×D23—22no—
92C4×D23—22no—
93C4×D23—22no—
94C4×D23—22no—
95C4×D23—41no—
96C4×D23—41no—
97Dic46—21no—
98Dic46—21no—
99C8×C23—41no—
100C23⋊C8—41no—
101#1897—231nomaximal, Sylow
102C22×C23—22no—
103C22×C23C2×C22⋊C411yescharacteristic
104C22×C23#12011yescharacteristic
105C22×C23#12311yescharacteristic
106C2×D23—22no—
107C2×D23—22no—
108C2×D23—22no—
109C2×D23—42no—
110C2×D23—42no—
111C2×D23—41no—
112C2×D23—42no—
113C4×C23—42no—
114C4×C23—42no—
115C4×C23C4×D411yescharacteristic
116C4×C23C4×D411yescharacteristic
117C4×C23#12111yescharacteristic
118C4×C23#12111yescharacteristic
119Dic23—22no—
120Dic23—42no—
121Dic23—41no—
122#525—231no—
123C2×#117—231no—
124C2×#104—231no—
125C2×#104—231no—
126#407—231no—
127#339—231no—
128#339D2311yescharacteristic, complemented
129C2×C23—21no—
130C2×C23—21no—
131C2×C23#38611yescharacteristic
132C2×C23#42112yes—
133D23—42no—
134D23—81no—
135C2×#41—231no—
136C23×C4—231no—
137C2×M16—231no—
138C2×M16C2×D2311yescharacteristic
139#123—461no—
140C22⋊Q8—232no—
141#121—232no—
142#120—461no—
143C4×D4—462no—
144#117—462no—
145#117—462no—
146#117C2×D2311yescharacteristic
147C2×C4⋊C4—461no—
148C2×C22⋊C4—461no—
149C2×C42—231no—
150C2×C42C2×D2311yescharacteristic
151#104—462no—
152#104—462no—
153C22⋊C8—462no—
154C23#189711yescharacteristic, complemented, Sylow
155C24—231no—
156#41—461no—
157#41—461no—
158#41—461no—
159#41—461no—
160C2×Q8—231no—
161C2×D4—231no—
162C2×D4—462no—
163C2×D4—461no—
164C22×C4—21no—
165C22×C4—231no—
166C22×C4—232no—
167C22×C4—232no—
168C22×C4—461no—
169C22×C4—461no—
170C22×C4—461no—
171C22×C4—461no—
172C22×C4—461no—
173C22×C4—461no—
174C22×C4C22×D2311yescharacteristic
175M16—21no—
176M16—21no—
177M16—461no—
178M16—461no—
179C2×C8—21no—
180C2×C8—461no—
181C4⋊C4—462no—
182C4⋊C4—464no—
183C4⋊C4C4×D2312yes—
184C22⋊C4—21no—
185C22⋊C4—462no—
186C22⋊C4—462no—
187C22⋊C4—464no—
188C42—21no—
189C42—21no—
190C42—232no—
191C42—461no—
192C42D9212yescomplemented
193C23—232no—
194C23—461no—
195C23—461no—
196C23—461no—
197C23—922no—
198C23D4×D2311yescharacteristic
199Q8—461no—
200Q8—461no—
201D4—461no—
202D4—461no—
203D4—924no—
204D4—921no—
205D4—921no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—232no—
210C2×C4—461no—
211C2×C4—461no—
212C2×C4—462no—
213C2×C4—462no—
214C2×C4—462no—
215C2×C4—462no—
216C2×C4—461no—
217C2×C4—462no—
218C2×C4—922no—
219C2×C4—921no—
220C2×C4—921no—
221C2×C4C2×C4×D2311yescharacteristic
222C2×C4C2×D9211yescharacteristic
223C2×C4#6728811yescharacteristic
224C2×C4D4×D2311yescharacteristic
225C2×C4D4×D2311yescharacteristic
226C2×C4#6729211yescharacteristic
227C8—41no—
228C8—921no—
229C22—22no—
230C22—462no—
231C22—462no—
232C22—462no—
233C22—922no—
234C22—922no—
235C22—922no—
236C22—921no—
237C22C22⋊C4×D2311yescharacteristic
238C22#1062505311yescharacteristic
239C22#1062506511yescharacteristic
240C4—42no—
241C4—42no—
242C4—462no—
243C4—922no—
244C4—921no—
245C4C4×D9211yescharacteristic
246C4#1062505511yescharacteristic
247C4#1062506411yescharacteristic
248C4#1062506611yescharacteristic
249C2—21no—
250C2—21no—
251C2—922no—
252C2—1841no—
253C2#1309229511yescharacteristic
254C2#1309243212yes—
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#1897
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×#10625043C2semidirect
3. C2×#10624987C2semidirect
4. C2×#10625007C2semidirect
5. #13092380C2semidirect
6. #13092176C2semidirect
7. C23×#339C2semidirect
17. #10625068C4semidirect
18. #10625066C4semidirect
54. C42×C23D4semidirect
61. C4×Dic23D4semidirect
128. #339D23semidirect
154. C23#1897semidirect
192. C42D92semidirect

Maximal subgroups

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

subgroupindex
#130929292
C2×#106250432
C2×#106249872
C2×#106250072
#130923802
#130921762
C23×#3392
#189723