Finite Group Databasebeta

← #13080711

Subgroups — #13080711

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#10623257C211yesmaximal, characteristic
2#10623225C211yesmaximal, characteristic, complemented
3C11×#491C211yesmaximal, characteristic, complemented
4#10622703C211yesmaximal, characteristic, complemented
5#10622679C211yesmaximal, characteristic, complemented
6#10622429C211yesmaximal, characteristic, complemented
7#10622427C211yesmaximal, characteristic, complemented
8#10622426C211yesmaximal, characteristic, complemented
9#10622423C211yesmaximal, characteristic, complemented
10#10622423C211yesmaximal, characteristic, complemented
11#10622422C211yesmaximal, characteristic, complemented
12#10622417C211yesmaximal, characteristic, complemented
13#10622416C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C11×C4⋊Q8C2211yescharacteristic
19C11×#125C2211yescharacteristic
20#66999C2211yescharacteristic
21#66999C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23C2×#4326C2211yescharacteristic
24C2×#4314C2211yescharacteristic
25C2×#4313C2211yescharacteristic
26C2×C8×D11C2211yescharacteristic
27#66951—21no—
28#66950C2211yescharacteristic
29#66950C2211yescharacteristic
30#66948—21no—
31#66947—21no—
32#66947—21no—
33#66947—21no—
34#66945—21no—
35#66945C2211yescharacteristic
36C4⋊C4×D11—21no—
37C4⋊C4×D11C2211yescharacteristic
38#66943—21no—
39C4×D44C2211yescharacteristic
40C4×D44C2211yescharacteristic
41C4×Dic22C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46C11×#97C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66882C2211yescharacteristic
53#66880C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61#4343—22no—
62#4343—22no—
63#4343—41no—
64#4343—41no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44D411yescharacteristic
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11C2311yescharacteristic
74C2×C4×D11C2311yescharacteristic
75C2×Dic22C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C42×C11C2311yescharacteristic
85#4326—41no—
86#4326—41no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4D411yescharacteristic
94(C2×D11)⋊C4D411yescharacteristic
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11D411yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#4314—22no—
109#4313—41no—
110C8×D11—41no—
111#3315—111nomaximal, Sylow
112C22×D11—21no—
113C22×D11C2×D411yescharacteristic
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131D44—21no—
132D44—41no—
133D44—42no—
134D44—42no—
135D44#4112yes—
136C4×D11—21no—
137C4×D11—21no—
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—42no—
141C4×D11—42no—
142C4×D11—42no—
143C4×D11—42no—
144Dic22—21no—
145Dic22—21no—
146C8×C11—21no—
147C8×C11—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#552—111no—
151#547—111no—
152#491D1111yescharacteristic, complemented
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#435—111no—
163#417—111no—
164#416—111no—
165C22×C11C22×D411yescharacteristic
166C2×D11—22no—
167C2×D11—21no—
168C2×D11—21no—
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—21no—
173C2×D11—41no—
174C2×D11—41no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11C2×#4111yescharacteristic
182C4×C11H(5,𝔽2)11yescharacteristic
183Dic11—21no—
184Dic11—21no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188C2×#41—111no—
189C2×#41—111no—
190C2×Q16—111no—
191C2×Q16—111no—
192C2×SD16—111no—
193C2×M16—111no—
194C22×C8—111no—
195C4⋊Q8C2×D1111yescharacteristic
196#126—221no—
197#125—221no—
198#125C2×D1111yescharacteristic
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×D4—111no—
210#117—111no—
211#117—221no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214#107—111no—
215#107—111no—
216#106—111no—
217C4⋊C8—111no—
218#103—111no—
219#103—111no—
220#103—111no—
221#103C2×D1111yescharacteristic
222#103C2×D1111yescharacteristic
223#103C2×D1111yescharacteristic
224#103C2×D1111yescharacteristic
225#102—111no—
226#102—111no—
227#102—111no—
228C22⋊C8—111no—
229C22⋊C8—111no—
230#97C2×D1111yescharacteristic
231C2×C11#54611yescharacteristic
232C2×C11#57511yescharacteristic
233C2×C11#57811yescharacteristic
234D11—41no—
235D11—41no—
236D11—42no—
237#41—222no—
238#41—222no—
239#41—441no—
240#41—441no—
241C2×Q8—111no—
242C2×Q8C22×D1111yescharacteristic
243C2×Q8C22×D1111yescharacteristic
244C2×D4—111no—
245C2×D4—111no—
246C2×D4—221no—
247C2×D4—221no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254Q16—441no—
255Q16—441no—
256SD16—222no—
257M16—441no—
258C2×C8—111no—
259C2×C8—111no—
260C2×C8—441no—
261C2×C8C22×D1111yescharacteristic
262C2×C8C22×D1111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—111no—
268C4⋊C4—111no—
269C4⋊C4—111no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4C22×D1111yescharacteristic
277C4⋊C4C22×D1111yescharacteristic
278C22⋊C4—111no—
279C22⋊C4—111no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C42—221no—
287C42—221no—
288C42C22×D1111yescharacteristic
289C11#331511yescharacteristic, complemented, Sylow
290C23—111no—
291C23—111no—
292C23—221no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—221no—
298Q8—221no—
299D4—112no—
300D4—221no—
301D4—441no—
302D4—442no—
303D4—442no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—111no—
309C2×C4—111no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4D4×D1111yescharacteristic
322C2×C4D4×D1111yescharacteristic
323C2×C4C23×D1111yescharacteristic
324C8—21no—
325C8—21no—
326C8—221no—
327C8—221no—
328C22—221no—
329C22—221no—
330C22—221no—
331C22—221no—
332C22—221no—
333C22—221no—
334C22—222no—
335C22—441no—
336C22—441no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—221no—
345C4—221no—
346C4—441no—
347C4—441no—
348C4—441no—
349C4#41×D1111yescharacteristic
350C4#6704211yescharacteristic
351C2—441no—
352C2—441no—
353C2—442no—
354C2#1062320711yescharacteristic
355C2#1062330811yescharacteristic
356C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#491C2
socleC22×C11C22×D4
prime radical#10623257C2
hypercenter#491D11
hypocenterC11#3315
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #10623225C2semidirect
3. C11×#491C2semidirect
4. #10622703C2semidirect
5. #10622679C2semidirect
6. #10622429C2semidirect
7. #10622427C2semidirect
8. #10622426C2semidirect
9. #10622423C2semidirect
10. #10622423C2semidirect
11. #10622422C2semidirect
12. #10622417C2semidirect
13. #10622416C2semidirect
14. #10622323C2semidirect
15. #10622319C2semidirect
152. #491D11semidirect
289. C11#3315semidirect

Maximal subgroups

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

subgroupindex
#106232572
#106232252
C11×#4912
#106227032
#106226792
#106224292
#106224272
#106224262
#106224232
#106224222
#106224172
#106224162
#106223232
#106223192
#331511