Finite Group Databasebeta

← #13082692

Subgroups — #13082692

Order 1408.

1104 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#548C211yesmaximal, characteristic, complemented
2#10623365C211yesmaximal, characteristic, complemented
3#10623358C211yesmaximal, characteristic, complemented
4#10623348C211yesmaximal, characteristic, complemented
5C2×Q8×Dic11C211yesmaximal, characteristic, complemented
6#10623213C213yesmaximal, complemented
7#10623212C213yesmaximal, complemented
8#10623174C213yesmaximal, complemented
9#10623166C213yesmaximal, complemented
10#10623142C213yesmaximal, complemented
11#10623127C213yesmaximal, complemented
12#10623105C211yesmaximal, characteristic, complemented
13Q8×Dic22C211yesmaximal, characteristic, complemented
14#10623086C213yesmaximal, complemented
15#10623069C213yesmaximal, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C2×#4343C2211yescharacteristic
19C2×#4341C2216yes—
20C11×#124C2213yes—
21C11×C22⋊Q8C2213yes—
22C11×#121C2213yes—
23C4×Q8×C11C2211yescharacteristic
24C4×D4×C11C2213yes—
25#67000C2213yes—
26#66999C2213yes—
27Q8×Dic11C2211yescharacteristic
28Q8×Dic11C2211yescharacteristic
29Q8×Dic11C2213yes—
30Q8×Dic11C2213yes—
31Q8×Dic11C2211yescharacteristic
32#66993C2213yes—
33#66992C2213yes—
34#66991C2213yes—
35#66988C2213yes—
36D4×Dic11C2213yes—
37D4×Dic11C2213yes—
38#66983C2213yes—
39#66983C2213yes—
40C4×C22⋊D11C2213yes—
41C4×C22⋊D11C2213yes—
42#66979C2213yes—
43C2×C4⋊Dic11C2213yes—
44C2×C4⋊Dic11C2213yes—
45C2×C4×Dic11C2213yes—
46#66951C2213yes—
47#66950C2216yes—
48#66946C2213yes—
49C4⋊C4×D11C2213yes—
50#66942C2213yes—
51#66941C2213yes—
52#66941C2213yes—
53#66939C2213yes—
54#66939C2216yes—
55#66938C2213yes—
56#66938C2216yes—
57#66936C2216yes—
58(C22⋊D11)⋊C4C2216yes—
59#66932C2213yes—
60#66931C2211yescharacteristic
61#66931C2216yes—
62C4×D44C2213yes—
63#66925C2213yes—
64#66922C2213yes—
65C4×Dic22C2213yes—
66C11×#41—24no—
67C2×Q8×C11—24no—
68C2×Q8×C11C2313yes—
69C2×Q8×C11C2311yescharacteristic
70C2×D4×C11C2313yes—
71C2×D4×C11C2313yes—
72C22×C4×C11C2313yes—
73C22×C4×C11C2313yes—
74C2×C22⋊D11C2313yes—
75C2×C22⋊D11C2313yes—
76C2×C22⋊D11C2316yes—
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2313yes—
79C22×Dic11C2316yes—
80#4343—24no—
81#4341—412no—
82C2×D44C2313yes—
83C2×C4×D11C2313yes—
84C2×C4×D11C2316yes—
85C2×Dic22C2311yescharacteristic
86C2×Dic22C2316yes—
87C11×C4⋊C4C2313yes—
88C11×C4⋊C4C2313yes—
89C11×C22⋊C4C2316yes—
90C11×C22⋊C4C2311yescharacteristic
91C11×C22⋊C4C2313yes—
92C42×C11C2313yes—
93C22⋊Dic11C2313yes—
94C22⋊Dic11C2311yescharacteristic
95C22⋊Dic11C2313yes—
96C22⋊Dic11C2313yes—
97(C2×D11)⋊C4C2313yes—
98(C2×D11)⋊C4C2313yes—
99(C2×D11)⋊C4C2316yes—
100(C2×D11)⋊C4C2313yes—
101(C2×D11)⋊C4C2313yes—
102C4⋊Dic11C2313yes—
103C4⋊Dic11C2313yes—
104C4⋊Dic11C2313yes—
105C4⋊Dic11C2313yes—
106C4⋊Dic11C2316yes—
107C4⋊Dic11C2311yescharacteristic
108C4⋊Dic11C2313yes—
109Dic11⋊C4C2313yes—
110Dic11⋊C4C2313yes—
111Dic11⋊C4C2311yescharacteristic
112Dic11⋊C4C2313yes—
113Dic11⋊C4C2313yes—
114Dic11⋊C4C2311yescharacteristic
115C4×Dic11C2313yes—
116C4×Dic11C2313yes—
117C4×Dic11C2313yes—
118C4×Dic11C2313yes—
119C4×Dic11C2313yes—
120#3522—111nomaximal, Sylow
121C23×C11C2413yes—
122C23×C11C2411yescharacteristic
123C22×D11C2413yes—
124Q8×C11—26no—
125Q8×C11#4114yescomplemented
126D4×C11—26no—
127D4×C11—26no—
128C2×C4×C11—26no—
129C2×C4×C11—26no—
130C2×C4×C11C2413yes—
131C2×C4×C11C2413yes—
132C2×C4×C11C2411yescharacteristic
133C2×C4×C11C2411yescharacteristic
134C2×C4×C11C2413yes—
135C22⋊D11—26no—
136C22⋊D11—26no—
137C22⋊D11—46no—
138C2×Dic11—26no—
139C2×Dic11—22no—
140C2×Dic11—46no—
141C2×Dic11C2411yescharacteristic
142C2×Dic11C2411yescharacteristic
143C2×Dic11C2413yes—
144C2×Dic11C2413yes—
145C2×Dic11C2413yes—
146C2×Dic11C2411yescharacteristic
147C2×Dic11C2411yescharacteristic
148D44—26no—
149C4×D11—26no—
150C4×D11—46no—
151Dic22—22no—
152Dic22—46no—
153#559—113no—
154Q82—111no—
155#554—113no—
156#550—111no—
157#548—111no—
158#548D1111yescharacteristic, complemented
159#547—113no—
160#547—113no—
161#542—113no—
162#542—113no—
163#532—113no—
164#529—113no—
165#520—111no—
166#520—111no—
167C2×C4×Q8—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—23no—
171C22×C11—23no—
172C22×C11—23no—
173C22×C11H(5,𝔽2)12yes—
174C22×C11C2511yescharacteristic
175C2×D11—23no—
176C2×D11—23no—
177C2×D11—23no—
178C4×C11—21no—
179C4×C11—23no—
180C4×C11—23no—
181C4×C11—21no—
182C4×C11C2×#4116yes—
183Dic11—21no—
184Dic11—23no—
185Dic11—23no—
186Dic11—23no—
187Dic11—21no—
188Dic11—21no—
189Dic112−1+412yes—
190C2×#41—111no—
191C2×#41—116no—
192C2×#41C2×D1111yescharacteristic
193C22×Q8C2×D1111yescharacteristic
194C4⋊Q8—113no—
195C4⋊Q8—113no—
196C4⋊Q8—113no—
197#127—113no—
198#126—113no—
199#126—113no—
200#125—113no—
201#124—113no—
202#124—113no—
203#124—116no—
204#124C2×D1113yes—
205#123—113no—
206#123—113no—
207#123—116no—
208#123—116no—
209C22⋊Q8—113no—
210C22⋊Q8—116no—
211C22⋊Q8—111no—
212C22⋊Q8—116no—
213C22⋊Q8C2×D1113yes—
214#121—113no—
215#121—113no—
216#121—113no—
217#121—113no—
218#121C2×D1113yes—
219C4×Q8—111no—
220C4×Q8—113no—
221C4×Q8—111no—
222C4×Q8—113no—
223C4×Q8—111no—
224C4×Q8—113no—
225C4×Q8C2×D1111yescharacteristic
226C4×D4—113no—
227C4×D4—113no—
228C4×D4—113no—
229C4×D4—113no—
230C4×D4—113no—
231C4×D4—116no—
232C4×D4—113no—
233C4×D4C2×D1113yes—
234#117—113no—
235#117—113no—
236C2×C4⋊C4—113no—
237C2×C4⋊C4—113no—
238C2×C4⋊C4—113no—
239C2×C42—113no—
240C2×C11—22no—
241C2×C11—43no—
242C2×C11C22×#4111yescharacteristic
243C2×C11C2×H(5,𝔽2)11yescharacteristic
244C2×C11C2×2−1+411yescharacteristic
245D11—43no—
246#41—24no—
247#41—224no—
248#41—4412no—
249C2×Q8—24no—
250C2×Q8—111no—
251C2×Q8—116no—
252C2×Q8C22×D1113yes—
253C2×Q8C22×D1111yescharacteristic
254C2×D4—113no—
255C2×D4—113no—
256C2×D4—116no—
257C2×D4—113no—
258C2×D4C22×D1113yes—
259C2×D4C22×D1113yes—
260C22×C4—111no—
261C22×C4—113no—
262C22×C4—116no—
263C22×C4—113no—
264C22×C4—116no—
265C22×C4C22×D1113yes—
266C22×C4C22×D1113yes—
267C4⋊C4—113no—
268C4⋊C4—113no—
269C4⋊C4—113no—
270C4⋊C4—113no—
271C4⋊C4—113no—
272C4⋊C4—116no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—113no—
277C4⋊C4—113no—
278C4⋊C4—113no—
279C4⋊C4—113no—
280C4⋊C4C22×D1113yes—
281C4⋊C4C22×D1113yes—
282C22⋊C4—113no—
283C22⋊C4—113no—
284C22⋊C4—111no—
285C22⋊C4—113no—
286C22⋊C4—113no—
287C22⋊C4—113no—
288C22⋊C4—113no—
289C22⋊C4—116no—
290C22⋊C4—113no—
291C22⋊C4C22×D1116yes—
292C22⋊C4C22×D1111yescharacteristic
293C22⋊C4C22×D1113yes—
294C42—113no—
295C42—113no—
296C42—113no—
297C42—113no—
298C42—113no—
299C42C22×D1113yes—
300C11#352211yescharacteristic, complemented, Sylow
301C23—113no—
302C23C23×D1113yes—
303C23C23×D1111yescharacteristic
304Q8—26no—
305Q8—222no—
306Q8—446no—
307Q8#434114yescomplemented
308D4—26no—
309D4—26no—
310D4—226no—
311D4—226no—
312D4—226no—
313D4—446no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—111no—
317C2×C4—111no—
318C2×C4—111no—
319C2×C4—113no—
320C2×C4—113no—
321C2×C4—113no—
322C2×C4—111no—
323C2×C4—222no—
324C2×C4—226no—
325C2×C4—226no—
326C2×C4—446no—
327C2×C4—446no—
328C2×C4C23×D1113yes—
329C2×C4C23×D1111yescharacteristic
330C2×C4C23×D1113yes—
331C2×C4C23×D1111yescharacteristic
332C2×C4C23×D1113yes—
333C22—21no—
334C22—21no—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—223no—
339C22—223no—
340C22—223no—
341C22#6704212yes—
342C22C24×D1111yescharacteristic
343C4—21no—
344C4—23no—
345C4—23no—
346C4—21no—
347C4—112no—
348C4—221no—
349C4—223no—
350C4—223no—
351C4—223no—
352C4—221no—
353C4—221no—
354C4C2×#434116yes—
355C2—22no—
356C2—43no—
357C2—443no—
358C2C22×#434111yescharacteristic
359C2C2×#6704211yescharacteristic
360C2D11×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#548C2
hypercenter#548D11
hypocenterC11#3522
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C11×#548C2semidirect
2. #10623365C2semidirect
3. #10623358C2semidirect
4. #10623348C2semidirect
5. C2×Q8×Dic11C2semidirect
6. #10623213C2semidirect
7. #10623212C2semidirect
8. #10623174C2semidirect
9. #10623166C2semidirect
10. #10623142C2semidirect
11. #10623127C2semidirect
12. #10623105C2semidirect
13. Q8×Dic22C2semidirect
14. #10623086C2semidirect
15. #10623069C2semidirect
125. Q8×C11#41semidirect
158. #548D11semidirect
300. C11#3522semidirect
307. Q8#4341semidirect

Maximal subgroups

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

subgroupindex
C11×#5482
#106233652
#106233582
#106233482
C2×Q8×Dic112
#106232132
#106232122
#106231742
#106231662
#106231422
#106231272
#106231052
Q8×Dic222
#106230862
#106230692
#352211