Finite Group Databasebeta

← #13080714

Subgroups — #13080714

Order 1408.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623082C211yesmaximal, characteristic
2#10623072C211yesmaximal, characteristic, complemented
3C11×#435C211yesmaximal, characteristic, complemented
4#10622750C211yesmaximal, characteristic, complemented
5#10622746C211yesmaximal, characteristic, complemented
6#10622729C211yesmaximal, characteristic, complemented
7#10622726C211yesmaximal, characteristic, complemented
8#10622462C211yesmaximal, characteristic, complemented
9#10622460C211yesmaximal, characteristic, complemented
10#10622346C211yesmaximal, characteristic, complemented
11#10622346C211yesmaximal, characteristic, complemented
12#10622336C211yesmaximal, characteristic, complemented
13#10622335C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622316C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C22×C8×C11C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic
21#66991—21no—
22#66988—21no—
23#66979C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25#66977C2211yescharacteristic
26#66977C2211yescharacteristic
27#66977C2211yescharacteristic
28#66977C2211yescharacteristic
29C2×Dic44C2211yescharacteristic
30C2×Dic44C2211yescharacteristic
31C2×#4314C2211yescharacteristic
32C4⋊C4×D11—21no—
33#66942—21no—
34#66936—21no—
35#66936—21no—
36#66932—21no—
37#66930—21no—
38C4×D44C2211yescharacteristic
39#66923C2211yescharacteristic
40#66922C2211yescharacteristic
41C4×Dic22C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45C11×#97C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C2×D4×C11D411yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65#4339—22no—
66#4339—22no—
67#4339—41no—
68#4339—41no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×Dic22C2311yescharacteristic
74C2×Dic22C2311yescharacteristic
75C2×Dic22C2311yescharacteristic
76C11×M16—41no—
77C2×C8×C11—41no—
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4D411yescharacteristic
83C11×C22⋊C4D411yescharacteristic
84C11×C22⋊C4D411yescharacteristic
85C42×C11C2311yescharacteristic
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91(C2×D11)⋊C4—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108Dic44—41no—
109Dic44—41no—
110#4314—22no—
111#3315—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115D4×C11—41no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C22⋊D11—42no—
126C22⋊D11—42no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—42no—
135D44—21no—
136D44#4112yes—
137C4×D11—42no—
138C4×D11—42no—
139C4×D11—42no—
140Dic22—21no—
141Dic22—21no—
142Dic22—21no—
143Dic22—21no—
144Dic22—21no—
145Dic22—21no—
146C8×C11—21no—
147C8×C11—21no—
148C8×C11—21no—
149C8×C11—21no—
150#552—111no—
151#547—111no—
152#491—111no—
153#485—111no—
154#484—111no—
155#478—111no—
156#470—111no—
157#467—111no—
158#462—111no—
159#452—111no—
160#452—111no—
161#440—111no—
162#435D1111yescharacteristic, complemented
163#417—111no—
164#416—111no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11C22×D411yescharacteristic
172C2×D11—22no—
173C2×D11—41no—
174C2×D11—41no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11C2×#4111yescharacteristic
180C4×C11H(5,𝔽2)11yescharacteristic
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188C2×#41—111no—
189C2×#41—111no—
190C2×Q16—111no—
191C2×Q16—111no—
192C2×SD16—111no—
193C2×M16C2×D1111yescharacteristic
194C22×C8C2×D1111yescharacteristic
195C4⋊Q8—111no—
196#126—221no—
197#125—111no—
198#125—221no—
199#123—221no—
200#123—221no—
201#123—221no—
202C22⋊Q8—111no—
203C22⋊Q8—111no—
204C22⋊Q8—111no—
205C22⋊Q8—111no—
206#121—221no—
207C4×Q8—111no—
208C4×D4—111no—
209C4×D4C2×D1111yescharacteristic
210#117—111no—
211#117—221no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214#107—111no—
215#107—111no—
216#106—111no—
217C4⋊C8C2×D1111yescharacteristic
218#103—111no—
219#103—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#103—111no—
225#102—111no—
226#102—111no—
227#102—111no—
228C22⋊C8C2×D1111yescharacteristic
229C22⋊C8C2×D1111yescharacteristic
230#97C2×D1111yescharacteristic
231C2×C11—41no—
232C2×C11—41no—
233C2×C11#54611yescharacteristic
234C2×C11#57511yescharacteristic
235C2×C11#57811yescharacteristic
236D11—42no—
237#41—222no—
238#41—222no—
239#41—441no—
240#41—441no—
241C2×Q8—111no—
242C2×Q8—111no—
243C2×Q8—111no—
244C2×D4—111no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4D4411yescharacteristic
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4C22×D1111yescharacteristic
253C22×C4C22×D1111yescharacteristic
254Q16—441no—
255Q16—441no—
256SD16—222no—
257M16—41no—
258C2×C8—41no—
259C2×C8C22×D1111yescharacteristic
260C2×C8C22×D1111yescharacteristic
261C2×C8C22×D1111yescharacteristic
262C2×C8C22×D1111yescharacteristic
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—111no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4D4411yescharacteristic
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4D4411yescharacteristic
285C22⋊C4D4411yescharacteristic
286C42—221no—
287C42—221no—
288C42C22×D1111yescharacteristic
289C11#331511yescharacteristic, complemented, Sylow
290C23—221no—
291C23C2×D4411yescharacteristic
292C23C2×D4411yescharacteristic
293Q8—221no—
294Q8—221no—
295Q8—221no—
296Q8—221no—
297Q8—221no—
298Q8—221no—
299D4—41no—
300D4—112no—
301D4—221no—
302D4—442no—
303D4—442no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4C2×D4411yescharacteristic
320C2×C4C2×D4411yescharacteristic
321C2×C4C2×D4411yescharacteristic
322C2×C4C2×D4411yescharacteristic
323C2×C4C23×D1111yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—222no—
335C22—441no—
336C22—441no—
337C22C22×D4411yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—441no—
343C4—441no—
344C4—441no—
345C4—441no—
346C4—441no—
347C4—441no—
348C4—441no—
349C4#6703711yescharacteristic
350C4#41×D1111yescharacteristic
351C2—41no—
352C2—41no—
353C2—442no—
354C2#1062308511yescharacteristic
355C2#1062327911yescharacteristic
356C2#1062328411yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#435C2
socleC22×C11C22×D4
prime radical#10623082C2
hypercenter#435D11
hypocenterC11#3315
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #10623072C2semidirect
3. C11×#435C2semidirect
4. #10622750C2semidirect
5. #10622746C2semidirect
6. #10622729C2semidirect
7. #10622726C2semidirect
8. #10622462C2semidirect
9. #10622460C2semidirect
10. #10622346C2semidirect
11. #10622346C2semidirect
12. #10622336C2semidirect
13. #10622335C2semidirect
14. #10622323C2semidirect
15. #10622316C2semidirect
162. #435D11semidirect
289. C11#3315semidirect

Maximal subgroups

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

subgroupindex
#106230822
#106230722
C11×#4352
#106227502
#106227462
#106227292
#106227262
#106224622
#106224602
#106223462
#106223362
#106223352
#106223232
#106223162
#331511