Finite Group Databasebeta

← #13073566

Subgroups — #13073566

Order 1408.

676 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic, complemented
3C2×#66997C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D11C211yesmaximal, characteristic
5C2×#66977C211yesmaximal, characteristic, complemented
6C2×#66950C211yesmaximal, characteristic, complemented
7#10622605C212yesmaximal, complemented
8#10622589C212yesmaximal, complemented
9C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10#10622570C212yesmaximal
11#10622562C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C22×Dic22C2211yescharacteristic
17C11×C22⋊Q8—24no—
18C2×C11×C4⋊C4C2212yes—
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2211yescharacteristic
23#66999—24no—
24#66997—24no—
25C4×C22⋊D11—24no—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2212yes—
29C2×C4⋊Dic11C2212yes—
30C2×C4⋊Dic11C2211yescharacteristic
31#66977—24no—
32C2×Dic11⋊C4C2212yes—
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2212yes—
35C2×Dic11⋊C4C2212yes—
36C2×Dic11⋊C4C2212yes—
37C2×C4×Dic11C2212yes—
38C2×C4×Dic11C2211yescharacteristic
39#66950—24no—
40C11⋊#95C2212yes—
41C24×C11C2311yescharacteristic
42C23×D11C2311yescharacteristic
43C2×Q8×C11—22no—
44C2×Q8×C11—22no—
45C2×Q8×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11C2312yes—
50C22×C4×C11C2311yescharacteristic
51C22×C4×C11C2312yes—
52C22×C4×C11C2311yescharacteristic
53C2×C22⋊D11—22no—
54C2×C22⋊D11—22no—
55C2×C22⋊D11Q814yescomplemented
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2312yes—
58C22×Dic11C2311yescharacteristic
59C22×Dic11C2312yes—
60C22×Dic11C2311yescharacteristic
61C2×C4×D11—22no—
62C2×C4×D11—22no—
63C2×C4×D11—22no—
64C2×Dic22—22no—
65C2×Dic22—22no—
66C2×Dic22—22no—
67C11×C4⋊C4—24no—
68C11×C4⋊C4D414yescomplemented
69C11×C22⋊C4—24no—
70C22⋊Dic11—24no—
71C22⋊Dic11—22no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—24no—
74(C2×D11)⋊C4—24no—
75C4⋊Dic11—24no—
76C4⋊Dic11D414yescomplemented
77Dic11⋊C4—24no—
78Dic11⋊C4—22no—
79Dic11⋊C4—24no—
80Dic11⋊C4—24no—
81Dic11⋊C4—24no—
82C4×Dic11—24no—
83C4×Dic11D414yes—
84#2542—111nomaximal, Sylow
85C23×C11—21no—
86C23×C11—21no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11C2×Q812yes—
92C23×C11C2411yescharacteristic
93C22×D11—21no—
94C22×D11—21no—
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—21no—
98C22×D11—21no—
99C22×D11C2×Q812yes—
100Q8×C11—44no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—44no—
110C2×C4×C11C2×D412yes—
111C2×C4×C11C2×D412yes—
112C2×C4×C11C2×D414yes—
113C2×C4×C11C2×D412yes—
114C22⋊D11—28no—
115C2×Dic11—22no—
116C2×Dic11—21no—
117C2×Dic11—22no—
118C2×Dic11—21no—
119C2×Dic11—22no—
120C2×Dic11—21no—
121C2×Dic11—22no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—22no—
125C2×Dic11C2×D412yes—
126C2×Dic11C2×D414yes—
127C2×Dic11C2×D412yes—
128C2×Dic11C2×Q812yes—
129C2×Dic11#4112yes—
130C4×D11—44no—
131Dic22—44no—
132C2×C4⋊Q8—111no—
133C2×C22⋊Q8—111no—
134C2×C22⋊Q8—111no—
135C2×C22⋊Q8—111no—
136C2×C22⋊Q8D1111yescharacteristic, complemented
137C2×C4×D4—111no—
138#399—112no—
139#399—112no—
140#390—112no—
141#384—112no—
142C4×C4⋊C4—111no—
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11C22×D411yescharacteristic
151C22×C11C22×D411yescharacteristic
152C22×C11C22×D411yescharacteristic
153C22×C11C22×Q811yescharacteristic
154C22×C11C2×#4111yescharacteristic
155C22×C112−1+411yescharacteristic
156C22×C112−1+411yescharacteristic
157C2×D11—22no—
158C2×D11—22no—
159C2×D11—22no—
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C4×C11—24no—
165C4×C11—41no—
166C4×C11—42no—
167C4×C11#12714yes—
168Dic11—22no—
169Dic11—24no—
170Dic11—42no—
171Dic11—41no—
172Dic11C22⋊Q814yescomplemented
173C22×Q8—111no—
174C22×Q8C2×D1111yescharacteristic
175C22×D4—111no—
176C23×C4—111no—
177C23×C4C2×D1111yescharacteristic
178C4⋊Q8—224no—
179C22⋊Q8—24no—
180C22⋊Q8—224no—
181C22⋊Q8—224no—
182C22⋊Q8—224no—
183C4×D4—224no—
184C2×C4⋊C4—111no—
185C2×C4⋊C4—111no—
186C2×C4⋊C4—112no—
187C2×C4⋊C4—112no—
188C2×C4⋊C4—112no—
189C2×C4⋊C4—112no—
190C2×C4⋊C4—112no—
191C2×C4⋊C4C2×D1112yes—
192C2×C4⋊C4C2×D1111yescharacteristic
193C2×C22⋊C4—111no—
194C2×C22⋊C4—112no—
195C2×C22⋊C4—111no—
196C2×C22⋊C4—112no—
197C2×C22⋊C4—112no—
198C2×C22⋊C4C2×D1112yes—
199C2×C42—111no—
200C2×C42—112no—
201#95—112no—
202C2×C11—42no—
203C2×C11C2×C22⋊Q811yescharacteristic
204C2×C11C2×#12711yescharacteristic
205C2×C11#53611yescharacteristic
206C2×C11#54711yescharacteristic
207C2×C11#54711yescharacteristic
208C2×C11D4×Q811yescharacteristic
209C2×C11D4×Q811yescharacteristic
210D11—42no—
211C24—111no—
212C24C22×D1111yescharacteristic
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—22no—
216C2×Q8—222no—
217C2×Q8—222no—
218C2×Q8—222no—
219C2×D4—114no—
220C2×D4—222no—
221C2×D4—222no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—111no—
226C22×C4—111no—
227C22×C4—112no—
228C22×C4—112no—
229C22×C4—111no—
230C22×C4—222no—
231C22×C4—222no—
232C22×C4—222no—
233C22×C4C22×D1112yes—
234C22×C4C22×D1111yescharacteristic
235C22×C4C22×D1112yes—
236C22×C4C22×D1111yescharacteristic
237C4⋊C4—24no—
238C4⋊C4—114no—
239C4⋊C4—222no—
240C4⋊C4—224no—
241C4⋊C4—224no—
242C4⋊C4—224no—
243C4⋊C4—224no—
244C4⋊C4—224no—
245C4⋊C4C22⋊D1114yescomplemented
246C22⋊C4—24no—
247C22⋊C4—222no—
248C22⋊C4—224no—
249C22⋊C4—222no—
250C22⋊C4—224no—
251C22⋊C4—224no—
252C42—114no—
253C42—224no—
254C11#254211yescharacteristic, complemented, Sylow
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—112no—
262C23—221no—
263C23—221no—
264C23—221no—
265C23—221no—
266C23—221no—
267C23—221no—
268C23Q8×D1112yes—
269C23C23×D1111yescharacteristic
270Q8—44no—
271Q8—444no—
272D4—228no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—44no—
282C2×C4—112no—
283C2×C4—112no—
284C2×C4—112no—
285C2×C4—112no—
286C2×C4—114no—
287C2×C4—221no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—222no—
293C2×C4—221no—
294C2×C4—222no—
295C2×C4—222no—
296C2×C4—221no—
297C2×C4—444no—
298C2×C4D4×D1112yes—
299C2×C4D4×D1112yes—
300C2×C4C2×C22⋊D1114yes—
301C2×C4C2×C22⋊D1112yes—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—222no—
310C22—222no—
311C22—222no—
312C22—441no—
313C22—441no—
314C22—441no—
315C22—441no—
316C22C2×D4×D1111yescharacteristic
317C22C2×D4×D1111yescharacteristic
318C22C2×Q8×D1111yescharacteristic
319C22#6704011yescharacteristic
320C22#41×D1111yescharacteristic
321C22#6704311yescharacteristic
322C22C22×C22⋊D1111yescharacteristic
323C4—24no—
324C4—41no—
325C4—42no—
326C4—114no—
327C4—222no—
328C4—224no—
329C4—441no—
330C4—442no—
331C4#6699314yes—
332C2—42no—
333C2—442no—
334C2D11×C22⋊Q811yescharacteristic
335C2#1062315911yescharacteristic
336C2#1062316211yescharacteristic
337C2#1062316311yescharacteristic
338C2C2×#6699311yescharacteristic
339C2Q8×C22⋊D1111yescharacteristic
340C2#1062335511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC22×C22⋊D11C22
hypercenterC2×C22⋊Q8D11
hypocenterC11#2542
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C22⋊Q8C2semidirect
2. C2×#66999C2semidirect
3. C2×#66997C2semidirect
5. C2×#66977C2semidirect
6. C2×#66950C2semidirect
7. #10622605C2semidirect
8. #10622589C2semidirect
9. C4⋊C4×Dic11C2semidirect
11. #10622562C2semidirect
55. C2×C22⋊D11Q8semidirect
68. C11×C4⋊C4D4semidirect
76. C4⋊Dic11D4semidirect
136. C2×C22⋊Q8D11semidirect
172. Dic11C22⋊Q8semidirect
245. C4⋊C4C22⋊D11semidirect
254. C11#2542semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#669992
C2×#669972
C2×C4×C22⋊D112
C2×#669772
C2×#669502
#106226052
#106225892
C4⋊C4×Dic112
#106225702
#106225622
#254211