Finite Group Databasebeta

← #15671924

Subgroups — #15671924

Order 2944.

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

normal subgroups only

This group has 326 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#121×D23C211yesmaximal, characteristic
2#13092379C211yesmaximal, characteristic, complemented
3#13092279C211yesmaximal, characteristic, complemented
4#13092152C211yesmaximal, characteristic, complemented
5#13092151C211yesmaximal, characteristic, complemented
6#13092150C211yesmaximal, characteristic, complemented
7C23×#327C211yesmaximal, characteristic, complemented
8C2×D4×D23—21no—
9C2×D4×D23C411yescharacteristic, complemented
10C22×C4×D23C2211yescharacteristic
11C23×#121C2211yescharacteristic
12#10625110—21no—
13#10625109C411yescharacteristic, complemented
14#10625101C2211yescharacteristic
15C2×(C2×D23)⋊C4—21no—
16C2×#67262—21no—
17#10625066C411yescharacteristic, complemented
18C4⋊C4×D23C411yescharacteristic, complemented
19#10625055—21no—
20C22⋊C4×D23—21no—
21C23×C22⋊C8C2211yescharacteristic, complemented
22C23×#95C2211yescharacteristic, complemented
23C23⋊#95—21no—
24C23⋊#95C2211yescharacteristic, complemented
25C22⋊(C23⋊C8)C2211yescharacteristic, complemented
26(C2×D23)⋊C8—21no—
27C23×D23—21no—
28C23×D23D411yescharacteristic
29C2×D4×C23—21no—
30C2×D4×C23C2×C411yescharacteristic
31C22×C4×C23—21no—
32C22×C4×C23C2311yescharacteristic
33C2×C22⋊D23—21no—
34C2×C22⋊D23—21no—
35C2×C22⋊D23—21no—
36C22×Dic23—21no—
37C22×Dic23D411yescharacteristic
38D4×D23—42no—
39D4×D23—42no—
40D4×D23—42no—
41C2×D92—21no—
42C2×D92C2×C411yescharacteristic
43C2×C4×D23—21no—
44C2×C4×D23—42no—
45C2×C4×D23C2×C411yescharacteristic
46C2×C4×D23C2×C411yescharacteristic
47C2×C4×D23D411yescharacteristic
48C2×C4×D23D411yescharacteristic
49C2×C8×C23—21no—
50C4⋊C4×C23C2×C411yescharacteristic
51C22⋊C4×C23—21no—
52C22⋊Dic23—21no—
53(C2×D23)⋊C4—21no—
54(C2×D23)⋊C4—21no—
55(C2×D23)⋊C4—42no—
56C4⋊Dic23C2×C411yescharacteristic
57Dic23⋊C4—21no—
58C2×C23⋊C8—21no—
59#67262—42no—
60C23×C23—21no—
61C23×C23C2×D411yescharacteristic
62C22×D23—21no—
63C22×D23—21no—
64C22×D23—22no—
65C22×D23—21no—
66C22×D23—41no—
67C22×D23—42no—
68C22×D23—42no—
69C22×D23—42no—
70C22×D23C22⋊C411yescharacteristic
71C22×D23C22⋊C411yescharacteristic
72D4×C23—41no—
73D4×C23—41no—
74D4×C23—41no—
75C2×C4×C23—21no—
76C2×C4×C23—41no—
77C2×C4×C23—41no—
78C2×C4×C23—41no—
79C2×C4×C23—41no—
80C2×C4×C23C22×C411yescharacteristic
81C2×C4×C23C2×D411yescharacteristic
82C22⋊D23—42no—
83C22⋊D23—42no—
84C22⋊D23—41no—
85C22⋊D23—41no—
86C2×Dic23—21no—
87C2×Dic23—41no—
88C2×Dic23—41no—
89C2×Dic23—41no—
90C2×Dic23—41no—
91C2×Dic23C22⋊C411yescharacteristic
92C2×Dic23C22⋊C411yescharacteristic
93D92—41no—
94D92—42no—
95C4×D23—22no—
96C4×D23—22no—
97C4×D23—41no—
98C4×D23—41no—
99C4×D23—42no—
100C8×C23—41no—
101C23⋊C8—41no—
102#1510—231nomaximal, Sylow
103C22×C23—21no—
104C22×C23—21no—
105C22×C23—41no—
106C22×C23—41no—
107C22×C23—41no—
108C22×C23C2×C22⋊C411yescharacteristic
109C22×C23AGL(1,ℤ/8)11yescharacteristic
110C22×C23AGL(1,ℤ/8)11yescharacteristic
111C2×D23—21no—
112C2×D23—21no—
113C2×D23—21no—
114C2×D23—21no—
115C2×D23—21no—
116C2×D23—42no—
117C2×D23—42no—
118C2×D23—41no—
119C2×D23—41no—
120C2×D23—41no—
121C2×D23—84no—
122C2×D23#9912yes—
123C4×C23—21no—
124C4×C23—21no—
125C4×C23—41no—
126C4×C23—81no—
127Dic23—21no—
128Dic23—21no—
129Dic23—41no—
130Dic23—81no—
131C2×#121—231no—
132#407—231no—
133#381—231no—
134#327—231no—
135#327—231no—
136#327—231no—
137#327D2311yescharacteristic, complemented
138C2×C23—21no—
139C2×C23—21no—
140C2×C23—81no—
141C2×C23C2×#9911yescharacteristic
142C2×C23#41811yescharacteristic
143C2×C23#42111yescharacteristic
144D23—22no—
145D23—41no—
146D23—81no—
147C22×D4—231no—
148C22×D4—461no—
149C23×C4—231no—
150C2×M16—461no—
151#121—231no—
152#121—231no—
153#121—231no—
154#121—461no—
155#121—461no—
156#121C2×D2311yescharacteristic
157C2×C4⋊C4—231no—
158C2×C22⋊C4—461no—
159C2×C22⋊C4—461no—
160C22⋊C8—231no—
161C22⋊C8—461no—
162C22⋊C8C2×D2311yescharacteristic, complemented
163#95—231no—
164#95—461no—
165#95C2×D2311yescharacteristic, complemented
166C23#151011yescharacteristic, complemented, Sylow
167C24—231no—
168C24—461no—
169C2×D4—21no—
170C2×D4—231no—
171C2×D4—461no—
172C2×D4—461no—
173C2×D4—461no—
174C2×D4—461no—
175C2×D4—922no—
176C2×D4—922no—
177C2×D4—922no—
178C2×D4C4×D2311yescharacteristic
179C22×C4—21no—
180C22×C4—231no—
181C22×C4—231no—
182C22×C4—231no—
183C22×C4—231no—
184C22×C4—231no—
185C22×C4—461no—
186C22×C4—461no—
187C22×C4—922no—
188C22×C4C22×D2311yescharacteristic
189M16—922no—
190C2×C8—21no—
191C2×C8—461no—
192C4⋊C4—231no—
193C4⋊C4—461no—
194C4⋊C4C4×D2311yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—461no—
197C22⋊C4—461no—
198C22⋊C4—461no—
199C22⋊C4—922no—
200C23—21no—
201C23—231no—
202C23—231no—
203C23—462no—
204C23—461no—
205C23—461no—
206C23—461no—
207C23—921no—
208C23—922no—
209C23—922no—
210C23—922no—
211C23D4×D2311yescharacteristic
212D4—41no—
213D4—41no—
214D4—41no—
215D4—921no—
216D4—922no—
217D4—922no—
218D4—922no—
219D4—921no—
220D4—921no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—231no—
227C2×C4—231no—
228C2×C4—462no—
229C2×C4—462no—
230C2×C4—461no—
231C2×C4—921no—
232C2×C4—921no—
233C2×C4—922no—
234C2×C4—921no—
235C2×C4—921no—
236C2×C4—921no—
237C2×C4—921no—
238C2×C4C2×C4×D2311yescharacteristic
239C2×C4D4×D2311yescharacteristic
240C8—41no—
241C8—921no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—232no—
248C22—461no—
249C22—461no—
250C22—461no—
251C22—461no—
252C22—461no—
253C22—922no—
254C22—922no—
255C22—921no—
256C22—921no—
257C22—921no—
258C22—1844no—
259C22C22⋊C4×D2311yescharacteristic
260C22#1062508211yescharacteristic
261C22#1062508511yescharacteristic
262C4—21no—
263C4—21no—
264C4—41no—
265C4—81no—
266C4—461no—
267C4—461no—
268C4—921no—
269C4—1841no—
270C2—21no—
271C2—21no—
272C2—81no—
273C2—462no—
274C2—921no—
275C2—1841no—
276C2#99×D2311yescharacteristic
277C2#1309242011yescharacteristic
278C2#1309243211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#327C2
socleC22×C23C2×C22⋊C4
prime radical#121×D23C2
cosocleC22×C4×C23C23
hypercenter#327D23
hypocenterC23#1510
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #13092379C2semidirect
3. #13092279C2semidirect
4. #13092152C2semidirect
5. #13092151C2semidirect
6. #13092150C2semidirect
7. C23×#327C2semidirect
9. C2×D4×D23C4semidirect
13. #10625109C4semidirect
17. #10625066C4semidirect
18. C4⋊C4×D23C4semidirect
21. C23×C22⋊C8C22semidirect
22. C23×#95C22semidirect
24. C23⋊#95C22semidirect
25. C22⋊(C23⋊C8)C22semidirect
137. #327D23semidirect
162. C22⋊C8C2×D23semidirect
165. #95C2×D23semidirect
166. C23#1510semidirect

Maximal subgroups

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

subgroupindex
#121×D232
#130923792
#130922792
#130921522
#130921512
#130921502
C23×#3272
#151023