Finite Group Databasebeta

← #13074296

Subgroups — #13074296

Order 1408.

576 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#66989C211yesmaximal, characteristic, complemented
2C2×#66930C211yesmaximal, characteristic, complemented
3C11×#392C211yesmaximal, characteristic
4#10622835C211yesmaximal, characteristic, complemented
5#10622834C212yesmaximal, complemented
6#10622833C212yesmaximal, complemented
7#10622564C212yesmaximal, complemented
8#10622560C211yesmaximal, characteristic, complemented
9#10622557C212yesmaximal, complemented
10#10622269C211yesmaximal, characteristic, complemented
11#10622261C211yesmaximal, characteristic, complemented
12C22×D4×C11C2212yes—
13C22×D4×C11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C22×Dic22C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2212yes—
24#66989—24no—
25C2×C4⋊Dic11C2212yes—
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×C4×Dic11C2211yescharacteristic
29C2×C4×Dic11C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31#66930—24no—
32C11×#95C2211yescharacteristic
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2312yes—
38C24×C11C2311yescharacteristic
39C2×D4×C11—24no—
40C2×D4×C11—22no—
41C2×D4×C11—24no—
42C2×D4×C11—42no—
43C2×D4×C11—42no—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2312yes—
47C22×Dic11—22no—
48C22×Dic11—22no—
49C22×Dic11—22no—
50C22×Dic11C2312yes—
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C2×Dic22—22no—
57C2×Dic22—42no—
58C11×C22⋊C4—22no—
59C11×C22⋊C4—24no—
60C22⋊Dic11—22no—
61C22⋊Dic11—24no—
62C22⋊Dic11—24no—
63C22⋊Dic11—24no—
64C22⋊Dic11—42no—
65C22⋊Dic11—42no—
66C4⋊Dic11—42no—
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69C4×Dic11—22no—
70C4×Dic11—24no—
71C4×Dic11D414yescomplemented
72#2610—111nomaximal, Sylow
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11#4112yes—
85C23×C11C2411yescharacteristic
86D4×C11—48no—
87D4×C11—44no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11C2×D412yes—
94C2×C4×C11#4114yes—
95C2×Dic11—28no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11C2×D412yes—
110C2×Dic11C2×D412yes—
111C2×Dic11#4112yes—
112Dic22—44no—
113C2×#124—111no—
114C2×#117—111no—
115#395—111no—
116#394—111no—
117#393—111no—
118#392D1111yescharacteristic
119#390—112no—
120#388—112no—
121#388—112no—
122#386—112no—
123#376—111no—
124C22×C11—22no—
125C22×C11—24no—
126C22×C11—41no—
127C22×C11—41no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11—42no—
136C22×C11C22×D411yescharacteristic
137C22×C11C2×#4111yescharacteristic
138C22×C11C2×#4112yes—
139C22×C11C2×#4111yescharacteristic
140C22×C11H(5,𝔽2)12yes—
141C4×C11—22no—
142C4×C11—24no—
143C4×C11—41no—
144Dic11—22no—
145Dic11—22no—
146Dic11—22no—
147Dic11—42no—
148Dic11—41no—
149Dic11—42no—
150C22×Q8—111no—
151C22×D4C2×D1112yes—
152C22×D4C2×D1111yescharacteristic
153C23×C4—111no—
154#124—224no—
155#117—224no—
156C2×C4⋊C4—111no—
157C2×C4⋊C4—111no—
158C2×C4⋊C4—112no—
159C2×C22⋊C4—111no—
160C2×C22⋊C4—112no—
161C2×C22⋊C4—112no—
162C2×C22⋊C4—112no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4C2×D1111yescharacteristic
166C2×C22⋊C4C2×D1112yes—
167C2×C42—111no—
168C2×C42—111no—
169C2×C42—112no—
170#95—112no—
171#95—111no—
172#95—112no—
173#95—112no—
174#95C2×D1111yescharacteristic
175C2×C11—42no—
176C2×C11—82no—
177C2×C11#52511yescharacteristic
178C2×C11#53211yescharacteristic
179C2×C11#53511yescharacteristic
180C2×C11#55112yes—
181C2×C11#55512yes—
182C24C22×D1112yes—
183C24C22×D1111yescharacteristic
184C2×Q8—222no—
185C2×Q8—442no—
186C2×D4—24no—
187C2×D4—22no—
188C2×D4—24no—
189C2×D4—42no—
190C2×D4—42no—
191C22×C4—111no—
192C22×C4—111no—
193C22×C4—111no—
194C22×C4—112no—
195C22×C4—112no—
196C22×C4—111no—
197C22×C4—222no—
198C22×C4—222no—
199C22×C4—222no—
200C22×C4C22×D1111yescharacteristic
201C22×C4C22×D1111yescharacteristic
202C22×C4C22×D1112yes—
203C4⋊C4—222no—
204C4⋊C4—222no—
205C4⋊C4—442no—
206C22⋊C4—22no—
207C22⋊C4—24no—
208C22⋊C4—222no—
209C22⋊C4—224no—
210C22⋊C4—224no—
211C22⋊C4—224no—
212C22⋊C4—442no—
213C22⋊C4—442no—
214C42—114no—
215C42—222no—
216C42—224no—
217C11#261011yescharacteristic, complemented, Sylow
218C23—21no—
219C23—22no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23#434112yes—
230C23C23×D1111yescharacteristic
231Q8—444no—
232D4—48no—
233D4—44no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—112no—
240C2×C4—112no—
241C2×C4—112no—
242C2×C4—228no—
243C2×C4—221no—
244C2×C4—222no—
245C2×C4—221no—
246C2×C4—221no—
247C2×C4—221no—
248C2×C4—221no—
249C2×C4—222no—
250C2×C4—222no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—222no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4D4×D1112yes—
257C2×C4#434114yes—
258C22—24no—
259C22—22no—
260C22—41no—
261C22—41no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22C2×D4×D1111yescharacteristic
271C22C2×#434112yes—
272C22C2×#434111yescharacteristic
273C22#6703712yes—
274C22#41×D1111yescharacteristic
275C4—24no—
276C4—22no—
277C4—41no—
278C4—222no—
279C4—222no—
280C4—222no—
281C4—442no—
282C4—441no—
283C4—442no—
284C2—42no—
285C2—82no—
286C2#1062311812yes—
287C2#1062312311yescharacteristic
288C2#1062313711yescharacteristic
289C2#1062314712yes—
290C2#1062324711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC11×#392C2
hypercenter#392D11
hypocenterC11#2610
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#66989C2semidirect
2. C2×#66930C2semidirect
4. #10622835C2semidirect
5. #10622834C2semidirect
6. #10622833C2semidirect
7. #10622564C2semidirect
8. #10622560C2semidirect
9. #10622557C2semidirect
10. #10622269C2semidirect
11. #10622261C2semidirect
71. C4×Dic11D4semidirect
217. C11#2610semidirect

Maximal subgroups

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

subgroupindex
C2×#669892
C2×#669302
C11×#3922
#106228352
#106228342
#106228332
#106225642
#106225602
#106225572
#106222692
#106222612
#261011