Finite Group Databasebeta

← #13069023

Subgroups — #13069023

Order 1408.

578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 83 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×#66935C211yesmaximal, characteristic
2#10623017C211yesmaximal, characteristic, complemented
3#10622568C211yesmaximal, characteristic, complemented
4#10622568C211yesmaximal, characteristic, complemented
5C2×#66870C211yesmaximal, characteristic, complemented
6C11×#342C211yesmaximal, characteristic, complemented
7#10622165C211yesmaximal, characteristic, complemented
8C24×D11C2211yescharacteristic
9C22×C22⋊D11C2211yescharacteristic
10C22×D44—21no—
11C2×C11×C22⋊C4C2211yescharacteristic
12C2×C11×C22⋊C4C2211yescharacteristic
13C2×C11×C22⋊C4C2211yescharacteristic
14C2×C22⋊Dic11C2211yescharacteristic
15C2×C22⋊Dic11C2211yescharacteristic
16C4×C22⋊D11—22no—
17C2×(C2×D11)⋊C4—21no—
18C2×(C2×D11)⋊C4—22no—
19C2×(C2×D11)⋊C4—22no—
20#66935—22no—
21#66935C414yescomplemented
22(C22⋊D11)⋊C4—22no—
23C22⋊C4×D11—21no—
24#66930—21no—
25#66870—22no—
26C24×C11C2311yescharacteristic
27C23×D11—21no—
28C23×D11—21no—
29C23×D11—21no—
30C23×D11—21no—
31C23×D11—21no—
32C23×D11—21no—
33C23×D11—44no—
34C23×D11C2×C412yescomplemented
35C23×D11D411yescharacteristic
36C22×C4×C11—21no—
37C22×C4×C11—21no—
38C22×C4×C11D412yescomplemented
39C2×C22⋊D11—21no—
40C2×C22⋊D11—21no—
41C2×C22⋊D11—21no—
42C2×C22⋊D11—21no—
43C2×C22⋊D11C2×C412yes—
44C2×C22⋊D11D412yes—
45C22×Dic11—21no—
46C22×Dic11D411yescharacteristic
47C22×Dic11D412yescomplemented
48C2×D44—24no—
49C2×D44—44no—
50C2×C4×D11—22no—
51C11×C22⋊C4—21no—
52C11×C22⋊C4—21no—
53C11×C22⋊C4—21no—
54C11×C22⋊C4—21no—
55C11×C22⋊C4—21no—
56C11×C22⋊C4C2×C412yescomplemented
57C22⋊Dic11—21no—
58C22⋊Dic11—21no—
59C22⋊Dic11—21no—
60C22⋊Dic11—21no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—24no—
63(C2×D11)⋊C4—44no—
64(C2×D11)⋊C4—44no—
65Dic11⋊C4—22no—
66C4×Dic11—22no—
67#1889—111nomaximal, Sylow
68C23×C11—42no—
69C23×C11C22×C411yescharacteristic
70C23×C11C2×D411yescharacteristic
71C23×C11C2×D411yescharacteristic
72C23×C11C2×D411yescharacteristic
73C23×C11C2×D411yescharacteristic
74C23×C11#4111yescharacteristic
75C23×C11#4111yescharacteristic
76C22×D11—24no—
77C22×D11—24no—
78C22×D11—24no—
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—44no—
85C22×D11—44no—
86C22×D11—44no—
87C22×D11—44no—
88C22×D11—42no—
89C22×D11—42no—
90C22×D11—42no—
91C22×D11—41no—
92C22×D11—41no—
93C22×D11—41no—
94C22×D11—41no—
95C22×D11—42no—
96C22×D11C22⋊C412yescomplemented
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—41no—
103C22⋊D11—22no—
104C22⋊D11—22no—
105C22⋊D11—22no—
106C22⋊D11—22no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—22no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—41no—
113C2×Dic11C22⋊C412yescomplemented
114D44—48no—
115C4×D11—82no—
116C2×#120—111no—
117#518—111no—
118C2×#99—111no—
119#379—111no—
120#379—111no—
121#342—111no—
122#342D1111yescharacteristic, complemented
123C22×C11—22no—
124C22×C11—22no—
125C22×C11—22no—
126C22×C11—41no—
127C22×C11—41no—
128C22×C11—41no—
129C22×C11—41no—
130C22×C11C2×C22⋊C411yescharacteristic
131C22×C11C4×D411yescharacteristic
132C22×C11C4×D411yescharacteristic
133C22×C11#12011yescharacteristic
134C22×C11#12111yescharacteristic
135C22×C11#12111yescharacteristic
136C22×C11#12311yescharacteristic
137C2×D11—24no—
138C2×D11—24no—
139C2×D11—24no—
140C2×D11—22no—
141C2×D11—44no—
142C2×D11—42no—
143C2×D11—44no—
144C2×D11—42no—
145C2×D11—42no—
146C2×D11—44no—
147C2×D11—42no—
148C2×D11—44no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—81no—
152C4×C11—42no—
153C4×C11—42no—
154C4×C11—81no—
155Dic11—22no—
156Dic11—42no—
157Dic11—81no—
158C25—111no—
159C22×D4—111no—
160C22×D4—221no—
161#120—114no—
162#120—222no—
163C4×D4—222no—
164C4×D4—222no—
165#117—221no—
166C2×C22⋊C4—111no—
167C2×C22⋊C4—111no—
168C2×C22⋊C4—221no—
169C2×C22⋊C4—221no—
170C2×C22⋊C4—222no—
171C2×C22⋊C4—222no—
172C2×C22⋊C4C2×D1111yescharacteristic
173C2×C22⋊C4C2×D1111yescharacteristic
174C2×C22⋊C4C2×D1111yescharacteristic
175#99—222no—
176C2×C11—21no—
177C2×C11—21no—
178C2×C11—21no—
179C2×C11—21no—
180C2×C11—21no—
181C2×C11—21no—
182C2×C11#38611yescharacteristic
183C2×C11B(4,𝔽2)12yes—
184D11—44no—
185D11—42no—
186C24—111no—
187C24—112no—
188C24—221no—
189C24—221no—
190C24—221no—
191C24—221no—
192C24—221no—
193C24—221no—
194C24—444no—
195C24C22×D1111yescharacteristic
196C2×D4—112no—
197C2×D4—112no—
198C2×D4—224no—
199C2×D4—221no—
200C2×D4—221no—
201C2×D4—221no—
202C2×D4—221no—
203C2×D4—444no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—111no—
207C22×C4—112no—
208C22×C4—222no—
209C22×C4—221no—
210C22×C4D4412yescomplemented
211C4⋊C4—222no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—224no—
218C22⋊C4—222no—
219C22⋊C4—221no—
220C22⋊C4—221no—
221C22⋊C4—221no—
222C22⋊C4—221no—
223C22⋊C4—444no—
224C22⋊C4—444no—
225C22⋊C4C4×D1112yescomplemented
226C42—222no—
227C11#188911yescharacteristic, complemented, Sylow
228C23—42no—
229C23—112no—
230C23—224no—
231C23—224no—
232C23—224no—
233C23—222no—
234C23—222no—
235C23—221no—
236C23—222no—
237C23—221no—
238C23—442no—
239C23—442no—
240C23—442no—
241C23—442no—
242C23—444no—
243C23—444no—
244C23—444no—
245C23—444no—
246C23—441no—
247C23—441no—
248C23—441no—
249C23—441no—
250C23C2×C4×D1111yescharacteristic
251C23C2×D4411yescharacteristic
252C23#433911yescharacteristic
253C23D4×D1111yescharacteristic
254C23D4×D1111yescharacteristic
255C23D4×D1111yescharacteristic
256C23#434311yescharacteristic
257D4—222no—
258D4—222no—
259D4—222no—
260D4—222no—
261D4—448no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—112no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—222no—
272C2×C4—442no—
273C2×C4—442no—
274C2×C4—441no—
275C2×C4—882no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—224no—
284C22—224no—
285C22—224no—
286C22—222no—
287C22—442no—
288C22—442no—
289C22—444no—
290C22—444no—
291C22—442no—
292C22—442no—
293C22—444no—
294C22—442no—
295C22—442no—
296C22—444no—
297C22—881no—
298C22C4×D4411yescharacteristic
299C22C22⋊C4×D1111yescharacteristic
300C22#6693511yescharacteristic
301C22#6693711yescharacteristic
302C22#6694611yescharacteristic
303C22#6694711yescharacteristic
304C22#6694811yescharacteristic
305C4—42no—
306C4—42no—
307C4—81no—
308C4—222no—
309C4—442no—
310C4—881no—
311C2—21no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—444no—
318C2—442no—
319C2#1062227811yescharacteristic
320C2#1062235412yes—
subgroupG/H
centerC22#66935
commutatorC23×C11C22×C4
FrattiniC24C22×D11
FittingC11×#342C2
socleC22×C11#120
prime radicalC2×#66935C2
cosocleC24×C11C23
hypercenter#342D11
hypocenterC11#1889
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. #10623017C2semidirect
3. #10622568C2semidirect
4. #10622568C2semidirect
5. C2×#66870C2semidirect
6. C11×#342C2semidirect
7. #10622165C2semidirect
21. #66935C4semidirect
34. C23×D11C2×C4semidirect
38. C22×C4×C11D4semidirect
47. C22×Dic11D4semidirect
56. C11×C22⋊C4C2×C4semidirect
96. C22×D11C22⋊C4semidirect
113. C2×Dic11C22⋊C4semidirect
122. #342D11semidirect
210. C22×C4D44semidirect
225. C22⋊C4C4×D11semidirect
227. C11#1889semidirect

Maximal subgroups

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

subgroupindex
C2×#669352
#106230172
#106225682
C2×#668702
C11×#3422
#106221652
#188911