Finite Group Databasebeta

← #15671952

Subgroups — #15671952

Order 2944.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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#13092930C211yesmaximal, characteristic
2C22⋊C8×D23C211yesmaximal, characteristic, complemented
3#13092279C211yesmaximal, characteristic, complemented
4#13092154C211yesmaximal, characteristic, complemented
5#13092152C211yesmaximal, characteristic, complemented
6#13092150C211yesmaximal, characteristic, complemented
7C23×#328C211yesmaximal, characteristic, complemented
8C2×#67292C411yescharacteristic, complemented
9C22×C4×D23C2211yescharacteristic
10C23×C22⋊Q8C2211yescharacteristic
11#10625117C411yescharacteristic, complemented
12#10625101C2211yescharacteristic
13C2×(C2×D23)⋊C4—21no—
14C2×C8×D23—21no—
15#10625066C411yescharacteristic, complemented
16#10625065—21no—
17#10625064—21no—
18#10625063C411yescharacteristic, complemented
19#10625053—21no—
20(C22⋊D23)⋊C4—21no—
21C23×C22⋊C8C2211yescharacteristic
22C23×#95C2211yescharacteristic
23C23⋊#95—21no—
24C23⋊#95C2211yescharacteristic
25C22⋊(C23⋊C8)C2211yescharacteristic
26(C2×D23)⋊C8—21no—
27C23×D23D411yescharacteristic
28C2×Q8×C23C2×C411yescharacteristic
29C22×C4×C23—21no—
30C22×C4×C23C2311yescharacteristic
31C2×C22⋊D23—21no—
32C22×Dic23—21no—
33C22×Dic23D411yescharacteristic
34#67292—42no—
35C2×D92—21no—
36C2×D92—21no—
37C2×D92C2×C411yescharacteristic
38C2×C4×D23—21no—
39C2×C4×D23—42no—
40C2×C4×D23C2×C411yescharacteristic
41C2×C4×D23C2×C411yescharacteristic
42C2×C4×D23D411yescharacteristic
43C2×C4×D23D411yescharacteristic
44C2×C8×C23—21no—
45C4⋊C4×C23—21no—
46C4⋊C4×C23C2×C411yescharacteristic
47C22⋊C4×C23—21no—
48(C2×D23)⋊C4—21no—
49(C2×D23)⋊C4—21no—
50(C2×D23)⋊C4—21no—
51(C2×D23)⋊C4—21no—
52(C2×D23)⋊C4—42no—
53C4⋊Dic23C2×C411yescharacteristic
54Dic23⋊C4—21no—
55C4×Dic23—21no—
56C2×C23⋊C8—21no—
57C8×D23—42no—
58C23×C23C2×D411yescharacteristic
59C22×D23—21no—
60C22×D23—21no—
61C22×D23—22no—
62C22×D23—21no—
63C22×D23—41no—
64C22×D23C22⋊C411yescharacteristic
65C22×D23C22⋊C411yescharacteristic
66Q8×C23—41no—
67C2×C4×C23—21no—
68C2×C4×C23—21no—
69C2×C4×C23—41no—
70C2×C4×C23—41no—
71C2×C4×C23—41no—
72C2×C4×C23—41no—
73C2×C4×C23C22×C411yescharacteristic
74C2×C4×C23C2×D411yescharacteristic
75C22⋊D23—41no—
76C22⋊D23—41no—
77C2×Dic23—21no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80C2×Dic23—41no—
81C2×Dic23—41no—
82C2×Dic23C22⋊C411yescharacteristic
83C2×Dic23C22⋊C411yescharacteristic
84D92—41no—
85D92—42no—
86D92—42no—
87C4×D23—22no—
88C4×D23—22no—
89C4×D23—41no—
90C4×D23—41no—
91C4×D23—42no—
92C8×C23—41no—
93C23⋊C8—41no—
94#1516—231nomaximal, Sylow
95C22×C23—21no—
96C22×C23—21no—
97C22×C23C2×C22⋊C411yescharacteristic
98C22×C23#13511yescharacteristic
99C22×C23#13511yescharacteristic
100C2×D23—21no—
101C2×D23—21no—
102C2×D23—21no—
103C2×D23—21no—
104C2×D23—21no—
105C2×D23—42no—
106C2×D23—42no—
107C2×D23—41no—
108C2×D23—41no—
109C2×D23—41no—
110C2×D23#9912yes—
111C4×C23—21no—
112C4×C23—21no—
113C4×C23—41no—
114C4×C23—41no—
115C4×C23—81no—
116Dic23—21no—
117Dic23—21no—
118Dic23—41no—
119Dic23—81no—
120#525—231no—
121C2×C22⋊C8—231no—
122#381—231no—
123#328—231no—
124#328D2311yescharacteristic, complemented
125#327—231no—
126#327—231no—
127C2×C23—21no—
128C2×C23—21no—
129C2×C23C2×#9911yescharacteristic
130C2×C23#41611yescharacteristic
131C2×C23#42111yescharacteristic
132D23—22no—
133D23—41no—
134D23—81no—
135C2×#41—231no—
136C23×C4—231no—
137C22×C8—461no—
138#123—461no—
139C22⋊Q8—231no—
140C22⋊Q8C2×D2311yescharacteristic
141#121—231no—
142#121—231no—
143#120—461no—
144C4×D4—461no—
145C4×D4—461no—
146#117—231no—
147C2×C22⋊C4—461no—
148C22⋊C8—231no—
149C22⋊C8—461no—
150C22⋊C8C2×D2311yescharacteristic
151#95—231no—
152#95—461no—
153#95C2×D2311yescharacteristic
154C23#151611yescharacteristic, complemented, Sylow
155C24—231no—
156#41—922no—
157C2×Q8C4×D2311yescharacteristic
158C2×D4—231no—
159C2×D4—461no—
160C2×D4—461no—
161C2×D4—461no—
162C22×C4—21no—
163C22×C4—231no—
164C22×C4—231no—
165C22×C4—231no—
166C22×C4—231no—
167C22×C4—231no—
168C22×C4—461no—
169C22×C4—461no—
170C22×C4—922no—
171C22×C4C22×D2311yescharacteristic
172C2×C8—21no—
173C2×C8—461no—
174C2×C8—922no—
175C4⋊C4—21no—
176C4⋊C4—231no—
177C4⋊C4—461no—
178C4⋊C4C4×D2311yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—461no—
181C22⋊C4—461no—
182C22⋊C4—461no—
183C22⋊C4—461no—
184C22⋊C4—922no—
185C42—461no—
186C23—231no—
187C23—231no—
188C23—462no—
189C23—461no—
190C23—461no—
191C23—461no—
192C23—921no—
193C23D4×D2311yescharacteristic
194Q8—41no—
195D4—921no—
196D4—922no—
197D4—922no—
198D4—921no—
199D4—921no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—231no—
207C2×C4—231no—
208C2×C4—462no—
209C2×C4—462no—
210C2×C4—461no—
211C2×C4—921no—
212C2×C4—921no—
213C2×C4—922no—
214C2×C4—921no—
215C2×C4—921no—
216C2×C4—921no—
217C2×C4—921no—
218C2×C4C2×C4×D2311yescharacteristic
219C2×C4D4×D2311yescharacteristic
220C8—41no—
221C8—921no—
222C22—21no—
223C22—21no—
224C22—232no—
225C22—461no—
226C22—461no—
227C22—461no—
228C22—461no—
229C22—461no—
230C22—922no—
231C22—922no—
232C22—921no—
233C22—921no—
234C22—921no—
235C22C22⋊C4×D2311yescharacteristic
236C22#1062508711yescharacteristic
237C22#1062509011yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—81no—
243C4—461no—
244C4—461no—
245C4—921no—
246C4—1841no—
247C2—21no—
248C2—21no—
249C2—462no—
250C2—921no—
251C2—1841no—
252C2#99×D2311yescharacteristic
253C2#1309241211yescharacteristic
254C2#1309243211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23C2×C22⋊C4
prime radical#13092930C2
cosocleC22×C4×C23C23
hypercenter#328D23
hypocenterC23#1516
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D23C2semidirect
3. #13092279C2semidirect
4. #13092154C2semidirect
5. #13092152C2semidirect
6. #13092150C2semidirect
7. C23×#328C2semidirect
8. C2×#67292C4semidirect
11. #10625117C4semidirect
15. #10625066C4semidirect
18. #10625063C4semidirect
124. #328D23semidirect
154. C23#1516semidirect

Maximal subgroups

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

subgroupindex
#130929302
C22⋊C8×D232
#130922792
#130921542
#130921522
#130921502
C23×#3282
#151623