Finite Group Databasebeta

← #13075346

Subgroups — #13075346

Order 1408.

612 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 137 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×#66993C211yesmaximal, characteristic
2C2×#66988C211yesmaximal, characteristic, complemented
3C11×#386C211yesmaximal, characteristic, complemented
4#10622826C212yesmaximal, complemented
5#10622574C212yesmaximal, complemented
6#10622574C212yesmaximal, complemented
7#10622571C212yesmaximal, complemented
8#10622285C212yesmaximal, complemented
9#10622266C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C22×C22⋊D11C2212yes—
13C22×C22⋊D11C2212yes—
14C23×Dic11C2211yescharacteristic
15C22×D44C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2211yescharacteristic
20#66993—24no—
21#66988—24no—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×C4×Dic11C2211yescharacteristic
29C11×#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C24×C11C2311yescharacteristic
34C24×C11C2311yescharacteristic
35C23×D11C2312yes—
36C2×D4×C11—41no—
37C2×D4×C11—41no—
38C2×D4×C11D414yes—
39C22×C4×C11—41no—
40C22×C4×C11—42no—
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C2×C22⋊D11—24no—
45C2×C22⋊D11—24no—
46C2×C22⋊D11—24no—
47C2×C22⋊D11—24no—
48C2×C22⋊D11—42no—
49C2×C22⋊D11—42no—
50C22×Dic11—22no—
51C22×Dic11—41no—
52C22×Dic11—41no—
53C22×Dic11C2312yes—
54C22×Dic11C2312yes—
55C22×Dic11C2312yes—
56C2×D44—22no—
57C2×D44—41no—
58C2×D44—41no—
59C11×C22⋊C4—41no—
60C11×C22⋊C4—42no—
61C22⋊Dic11—24no—
62C22⋊Dic11—22no—
63(C2×D11)⋊C4—42no—
64(C2×D11)⋊C4—42no—
65(C2×D11)⋊C4—42no—
66(C2×D11)⋊C4—42no—
67C4⋊Dic11—24no—
68Dic11⋊C4—24no—
69C4×Dic11—22no—
70#2709—111nomaximal, Sylow
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11—21no—
77C23×C11—22no—
78C23×C11—21no—
79C23×C11C2×D412yes—
80C23×C11C2×D412yes—
81C23×C11C2411yescharacteristic
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89D4×C11—44no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—44no—
99C2×C4×C11C2×D412yes—
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×Dic11#4114yes—
112D44—44no—
113C2×#127—111no—
114C2×#123—111no—
115#394—112no—
116#394—112no—
117#394—112no—
118#387—112no—
119#386—112no—
120#386—112no—
121#386D1111yescharacteristic, complemented
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—24no—
125C22×C11—24no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11—41no—
129C22×C11—41no—
130C22×C11—41no—
131C22×C11—41no—
132C22×C11C22×D411yescharacteristic
133C22×C11C2×#4112yes—
134C22×C11H(5,𝔽2)11yescharacteristic
135C22×C11H(5,𝔽2)11yescharacteristic
136C22×C11H(5,𝔽2)12yes—
137C2×D11—42no—
138C2×D11—42no—
139C2×D11—42no—
140C2×D11—42no—
141C2×D11—42no—
142C2×D11—42no—
143C2×D11—42no—
144C4×C11—22no—
145C4×C11—42no—
146C4×C11—42no—
147Dic11—24no—
148Dic11—42no—
149Dic11—42no—
150C22×D4—112no—
151C22×D4—112no—
152C22×D4—111no—
153C22×D4C2×D1111yescharacteristic
154C23×C4—111no—
155C23×C4C2×D1111yescharacteristic
156#127—224no—
157#123—224no—
158C2×C4⋊C4—112no—
159C2×C4⋊C4—112no—
160C2×C22⋊C4—112no—
161C2×C22⋊C4—111no—
162C2×C22⋊C4—112no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4C2×D1112yes—
167C2×C22⋊C4C2×D1111yescharacteristic
168C2×C42—111no—
169#95—112no—
170#95—112no—
171#95—112no—
172#95C2×D1112yes—
173C2×C11—42no—
174C2×C11—42no—
175C2×C11#53411yescharacteristic
176C2×C11#54012yes—
177C2×C11#54612yes—
178C2×C11#55911yescharacteristic
179C2×C11#56011yescharacteristic
180D11—82no—
181C24—112no—
182C24C22×D1111yescharacteristic
183C24C22×D1111yescharacteristic
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—224no—
187C2×D4—224no—
188C2×D4—224no—
189C2×D4—224no—
190C2×D4—222no—
191C2×D4—441no—
192C2×D4—441no—
193C2×D4—442no—
194C2×D4—442no—
195C2×D4D4414yes—
196C22×C4—42no—
197C22×C4—41no—
198C22×C4—112no—
199C22×C4—112no—
200C22×C4—112no—
201C22×C4—222no—
202C22×C4—441no—
203C22×C4—441no—
204C22×C4C22×D1112yes—
205C22×C4C22×D1112yes—
206C22×C4C22×D1111yescharacteristic
207C4⋊C4—224no—
208C4⋊C4—224no—
209C22⋊C4—41no—
210C22⋊C4—42no—
211C22⋊C4—222no—
212C22⋊C4—224no—
213C22⋊C4—442no—
214C22⋊C4—442no—
215C22⋊C4—442no—
216C22⋊C4—442no—
217C42—222no—
218C11#270911yescharacteristic, complemented, Sylow
219C23—21no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—21no—
224C23—21no—
225C23—22no—
226C23—22no—
227C23—222no—
228C23—222no—
229C23—222no—
230C23—222no—
231C23—222no—
232C23—222no—
233C23—222no—
234C23C2×D4412yes—
235C23C2×D4412yes—
236C23C23×D1111yescharacteristic
237D4—44no—
238D4—444no—
239D4—448no—
240D4—448no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—44no—
250C2×C4—114no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—222no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—222no—
257C2×C4—222no—
258C2×C4—222no—
259C2×C4—444no—
260C2×C4C2×D4412yes—
261C22—22no—
262C22—22no—
263C22—24no—
264C22—24no—
265C22—41no—
266C22—41no—
267C22—42no—
268C22—42no—
269C22—41no—
270C22—41no—
271C22—442no—
272C22—442no—
273C22—442no—
274C22—442no—
275C22—442no—
276C22—442no—
277C22—442no—
278C22C22×D4411yescharacteristic
279C22#6703711yescharacteristic
280C22#6703711yescharacteristic
281C22#6703712yes—
282C22#41×D1112yes—
283C4—22no—
284C4—42no—
285C4—42no—
286C4—224no—
287C4—442no—
288C4—442no—
289C2—42no—
290C2—42no—
291C2—882no—
292C2#1062302411yescharacteristic
293C2#1062308512yes—
294C2#1062312611yescharacteristic
295C2#1062314612yes—
296C2#1062319511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC2×#66993C2
hypercenter#386D11
hypocenterC11#2709
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#66988C2semidirect
3. C11×#386C2semidirect
4. #10622826C2semidirect
5. #10622574C2semidirect
6. #10622574C2semidirect
7. #10622571C2semidirect
8. #10622285C2semidirect
9. #10622266C2semidirect
121. #386D11semidirect
218. C11#2709semidirect

Maximal subgroups

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

subgroupindex
C2×#669932
C2×#669882
C11×#3862
#106228262
#106225742
#106225712
#106222852
#106222662
#270911