Finite Group Databasebeta

← #13076649

Subgroups — #13076649

Order 1408.

528 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 125 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×#66949C211yesmaximal, characteristic, complemented
2C2×#66948C211yesmaximal, characteristic
3C11×#398C211yesmaximal, characteristic, complemented
4#10622605C212yesmaximal, complemented
5#10622604C211yesmaximal, characteristic, complemented
6#10622604C212yesmaximal, complemented
7#10622593C211yesmaximal, characteristic, complemented
8#10622286C212yesmaximal, complemented
9#10622285C211yesmaximal, characteristic, complemented
10#10622285C212yesmaximal, complemented
11#10622277C211yesmaximal, characteristic, complemented
12C22×D44C2212yes—
13C22×D44C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C22×Dic22C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30#66949—24no—
31#66948—24no—
32C11×#95C2211yescharacteristic
33C11×#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C23×D11C2312yes—
38C23×D11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×D44—24no—
49C2×D44—22no—
50C2×D44—42no—
51C2×D44—42no—
52C2×D44—42no—
53C2×C4×D11—42no—
54C2×C4×D11D414yes—
55C2×Dic22—22no—
56C2×Dic22—42no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—42no—
60(C2×D11)⋊C4—24no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—42no—
64(C2×D11)⋊C4—42no—
65(C2×D11)⋊C4—42no—
66(C2×D11)⋊C4—42no—
67(C2×D11)⋊C4—42no—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70Dic11⋊C4—42no—
71#2816—111nomaximal, Sylow
72C23×C11C2411yescharacteristic
73C22×D11—22no—
74C22×D11—21no—
75C22×D11—21no—
76C22×D11—22no—
77C22×D11—22no—
78C22×D11—22no—
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11C2×D412yes—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11C2×D412yes—
98C2×Dic11—22no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11C2×D412yes—
108D44—44no—
109D44—48no—
110C4×D11—44no—
111Dic22—44no—
112C2×C22⋊Q8—111no—
113C2×#121—111no—
114#399—112no—
115#398—111no—
116#398D1111yescharacteristic, complemented
117#394—111no—
118#394—112no—
119#394—111no—
120#394—112no—
121#393—112no—
122#381—111no—
123C22×C11C22×D411yescharacteristic
124C22×C11H(5,𝔽2)11yescharacteristic
125C22×C11H(5,𝔽2)12yes—
126C22×C11H(5,𝔽2)11yescharacteristic
127C22×C112−1+412yes—
128C2×D11—22no—
129C2×D11—22no—
130C2×D11—22no—
131C2×D11—42no—
132C2×D11—42no—
133C2×D11—42no—
134C2×D11—42no—
135C2×D11—42no—
136C2×D11—42no—
137C2×D11—42no—
138C2×D11—42no—
139C2×D11—42no—
140C4×C11—22no—
141C4×C11—41no—
142C4×C11—41no—
143C4×C11—42no—
144C4×C11—42no—
145Dic11—22no—
146Dic11—41no—
147Dic11—41no—
148Dic11—42no—
149C22×Q8—111no—
150C22×D4—112no—
151C22×D4—111no—
152C23×C4—111no—
153C22⋊Q8—224no—
154#121—224no—
155C2×C4⋊C4—111no—
156C2×C4⋊C4—111no—
157C2×C4⋊C4—112no—
158C2×C4⋊C4C2×D1111yescharacteristic
159C2×C4⋊C4C2×D1111yescharacteristic
160C2×C4⋊C4C2×D1112yes—
161C2×C22⋊C4—112no—
162C2×C22⋊C4—111no—
163C2×C22⋊C4—111no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4—112no—
167C2×C22⋊C4—112no—
168C2×C22⋊C4—112no—
169#95—112no—
170#95—111no—
171#95—112no—
172#95C2×D1111yescharacteristic
173#95C2×D1112yes—
174C2×C11#53411yescharacteristic
175C2×C11#53511yescharacteristic
176C2×C11#53611yescharacteristic
177C2×C11#56212yes—
178C2×C11#56212yes—
179D11—42no—
180D11—82no—
181C24—111no—
182C24—112no—
183C2×Q8—222no—
184C2×Q8—442no—
185C2×D4—224no—
186C2×D4—222no—
187C2×D4—442no—
188C2×D4—442no—
189C2×D4—442no—
190C22×C4—111no—
191C22×C4—114no—
192C22×C4—112no—
193C22×C4—111no—
194C22×C4—111no—
195C22×C4—442no—
196C22×C4C22×D1112yes—
197C22×C4C22×D1112yes—
198C22×C4C22×D1111yescharacteristic
199C22×C4C22×D1111yescharacteristic
200C22×C4C22×D1111yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—42no—
204C4⋊C4—222no—
205C4⋊C4—222no—
206C4⋊C4—442no—
207C22⋊C4—224no—
208C22⋊C4—222no—
209C22⋊C4—222no—
210C22⋊C4—442no—
211C22⋊C4—442no—
212C22⋊C4—442no—
213C22⋊C4—442no—
214C22⋊C4—442no—
215C11#281611yescharacteristic, complemented, Sylow
216C23—112no—
217C23—221no—
218C23—222no—
219C23—222no—
220C23—221no—
221C23—222no—
222C23—222no—
223C23—222no—
224C23—222no—
225C23—222no—
226C23—222no—
227C23—222no—
228C23C23×D1111yescharacteristic
229Q8—444no—
230D4—444no—
231D4—448no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—112no—
245C2×C4—222no—
246C2×C4—221no—
247C2×C4—221no—
248C2×C4—221no—
249C2×C4—222no—
250C2×C4—222no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—221no—
254C2×C4—444no—
255C2×C4D4×D1112yes—
256C22—222no—
257C22—222no—
258C22—222no—
259C22—442no—
260C22—442no—
261C22—442no—
262C22—442no—
263C22—442no—
264C22—442no—
265C22—442no—
266C22—442no—
267C22—442no—
268C22C2×D4×D1111yescharacteristic
269C22#6703711yescharacteristic
270C22#6704012yes—
271C22#6704211yescharacteristic
272C22#6704212yes—
273C4—22no—
274C4—42no—
275C4—41no—
276C4—42no—
277C4—41no—
278C4—222no—
279C4—441no—
280C4—441no—
281C4—442no—
282C2—442no—
283C2—882no—
284C2#1062313811yescharacteristic
285C2#1062317812yes—
286C2#1062318411yescharacteristic
287C2#1062323112yes—
288C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#398C2
prime radicalC2×#66948C2
hypercenter#398D11
hypocenterC11#2816
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#66949C2semidirect
3. C11×#398C2semidirect
4. #10622605C2semidirect
5. #10622604C2semidirect
6. #10622604C2semidirect
7. #10622593C2semidirect
8. #10622286C2semidirect
9. #10622285C2semidirect
10. #10622285C2semidirect
11. #10622277C2semidirect
116. #398D11semidirect
215. C11#2816semidirect

Maximal subgroups

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

subgroupindex
C2×#669492
C2×#669482
C11×#3982
#106226052
#106226042
#106225932
#106222862
#106222852
#106222772
#281611