Finite Group Databasebeta

← #13076641

Subgroups — #13076641

Order 1408.

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

normal subgroups only

This group has 644 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×#66992C212yesmaximal, complemented
2C11×#392C211yesmaximal, characteristic, complemented
3#10622836C212yesmaximal, complemented
4#10622836C212yesmaximal, complemented
5#10622573C212yesmaximal, complemented
6#10622573C211yesmaximal, characteristic, complemented
7#10622565C212yesmaximal, complemented
8#10622556C211yesmaximal, characteristic, complemented
9#10622288C212yesmaximal, complemented
10C22×D4×C11C2212yes—
11C22×D4×C11C2211yescharacteristic
12C22×C22⋊D11C2212yes—
13C22×C22⋊D11C2212yes—
14C22×C22⋊D11C2212yes—
15C23×Dic11C2211yescharacteristic
16C22×D44C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊Dic11C2212yes—
22#66992—28no—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C11×#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2211yescharacteristic
32C24×C11C2312yes—
33C24×C11C2311yescharacteristic
34C23×D11C2312yes—
35C2×D4×C11—24no—
36C2×D4×C11—42no—
37C2×D4×C11—42no—
38C2×D4×C11—42no—
39C2×D4×C11—41no—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2312yes—
43C2×C22⋊D11—24no—
44C2×C22⋊D11—24no—
45C2×C22⋊D11—42no—
46C2×C22⋊D11—42no—
47C2×C22⋊D11—42no—
48C2×C22⋊D11—42no—
49C2×C22⋊D11—42no—
50C2×C22⋊D11—42no—
51C2×C22⋊D11—42no—
52C22×Dic11—41no—
53C22×Dic11—41no—
54C22×Dic11D414yescomplemented
55C22×Dic11C2312yes—
56C22×Dic11C2312yes—
57C22×Dic11C2312yes—
58C2×D44—41no—
59C2×D44—42no—
60C11×C22⋊C4—41no—
61C11×C22⋊C4—42no—
62C22⋊Dic11—24no—
63C22⋊Dic11—41no—
64C22⋊Dic11—42no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—42no—
67(C2×D11)⋊C4—42no—
68Dic11⋊C4—24no—
69#2815—111nomaximal, Sylow
70C23×C11—21no—
71C23×C11—21no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11—22no—
81C23×C11C2×D412yes—
82C23×C11C2411yescharacteristic
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90D4×C11—48no—
91D4×C11—44no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—21no—
99C22⋊D11—48no—
100C22⋊D11—48no—
101C22⋊D11—48no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—44no—
111C2×Dic11C2×D414yes—
112D44—44no—
113C2×#121—112no—
114#397—112no—
115#397—112no—
116#392—112no—
117#392—112no—
118#392—112no—
119#392—111no—
120#392D1111yescharacteristic, complemented
121#381—111no—
122C22×C11—22no—
123C22×C11—24no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11—42no—
134C22×C11C22×D411yescharacteristic
135C22×C11H(5,𝔽2)11yescharacteristic
136C22×C11H(5,𝔽2)12yes—
137C22×C11H(5,𝔽2)12yes—
138C22×C11H(5,𝔽2)11yescharacteristic
139C2×D11—42no—
140C2×D11—42no—
141C2×D11—42no—
142C2×D11—42no—
143C2×D11—42no—
144C2×D11—42no—
145C2×D11—42no—
146C4×C11—42no—
147C4×C11—41no—
148C4×C11—41no—
149Dic11—24no—
150Dic11—42no—
151Dic11—42no—
152C22×D4—112no—
153C22×D4—112no—
154C22×D4—112no—
155C22×D4—111no—
156C22×D4C2×D1112yes—
157C22×D4C2×D1111yescharacteristic
158C23×C4—111no—
159#121—228no—
160C2×C4⋊C4—112no—
161C2×C22⋊C4—112no—
162C2×C22⋊C4—112no—
163C2×C22⋊C4—111no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4—112no—
167C2×C22⋊C4C2×D1111yescharacteristic
168C2×C22⋊C4C2×D1112yes—
169#95—112no—
170#95—112no—
171#95—112no—
172#95—111no—
173#95C2×D1111yescharacteristic
174C2×C11—42no—
175C2×C11—82no—
176C2×C11#53411yescharacteristic
177C2×C11#53512yes—
178C2×C11#56011yescharacteristic
179C2×C11#56011yescharacteristic
180C2×C11#56012yes—
181D11—82no—
182C24—112no—
183C24C22×D1112yes—
184C24C22×D1111yescharacteristic
185C2×D4—24no—
186C2×D4—42no—
187C2×D4—41no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4—224no—
191C2×D4—224no—
192C2×D4—442no—
193C2×D4—441no—
194C2×D4—442no—
195C2×D4—442no—
196C2×D4—442no—
197C2×D4—442no—
198C2×D4—442no—
199C2×D4—442no—
200C2×D4—442no—
201C22×C4—112no—
202C22×C4—114no—
203C22×C4—112no—
204C22×C4—112no—
205C22×C4—441no—
206C22×C4—441no—
207C22×C4C22×D1111yescharacteristic
208C22×C4C22×D1111yescharacteristic
209C22×C4C22×D1112yes—
210C4⋊C4—224no—
211C22⋊C4—41no—
212C22⋊C4—42no—
213C22⋊C4—224no—
214C22⋊C4—224no—
215C22⋊C4—442no—
216C22⋊C4—442no—
217C22⋊C4—442no—
218C22⋊C4—441no—
219C11#281511yescharacteristic, complemented, Sylow
220C23—21no—
221C23—22no—
222C23—22no—
223C23—21no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—222no—
232C23—222no—
233C23—222no—
234C23—222no—
235C23—222no—
236C23—222no—
237C23—222no—
238C23D4×D1112yes—
239C23C23×D1111yescharacteristic
240D4—48no—
241D4—44no—
242D4—444no—
243D4—448no—
244D4—448no—
245D4—448no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—114no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—222no—
257C2×C4—222no—
258C2×C4—222no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—444no—
263C22—24no—
264C22—22no—
265C22—41no—
266C22—41no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—442no—
276C22—442no—
277C22—442no—
278C22—442no—
279C22—442no—
280C22—442no—
281C22—442no—
282C22C2×D4×D1111yescharacteristic
283C22#6703712yes—
284C22#6703711yescharacteristic
285C22#6703712yes—
286C22#6704211yescharacteristic
287C4—41no—
288C4—42no—
289C4—41no—
290C4—224no—
291C4—442no—
292C4—442no—
293C2—42no—
294C2—82no—
295C2—882no—
296C2#1062312312yes—
297C2#1062312611yescharacteristic
298C2#1062313611yescharacteristic
299C2#1062315112yes—
300C2#1062325111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#392C2
hypercenter#392D11
hypocenterC11#2815
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#66992C2semidirect
2. C11×#392C2semidirect
3. #10622836C2semidirect
4. #10622836C2semidirect
5. #10622573C2semidirect
6. #10622573C2semidirect
7. #10622565C2semidirect
8. #10622556C2semidirect
9. #10622288C2semidirect
54. C22×Dic11D4semidirect
120. #392D11semidirect
219. C11#2815semidirect

Maximal subgroups

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

subgroupindex
C2×#669922
C11×#3922
#106228362
#106225732
#106225652
#106225562
#106222882
#281511