Finite Group Databasebeta

← C11×#2716 #13065554

Subgroups — C11×#2716 #13065554

Order 1408.

450 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×C11×#126C211yesmaximal, characteristic
3C11×#400C211yesmaximal, characteristic, complemented
4C11×#398C211yesmaximal, characteristic, complemented
5C11×#397C211yesmaximal, characteristic
6C11×#396C211yesmaximal, characteristic
7C11×#393C211yesmaximal, characteristic
8C11×#393C211yesmaximal, characteristic
9C11×#391C211yesmaximal, characteristic, complemented
10C11×#391C211yesmaximal, characteristic, complemented
11C11×#388C211yesmaximal, characteristic
12C11×#388C211yesmaximal, characteristic
13C11×#387C211yesmaximal, characteristic, complemented
14C11×#387C211yesmaximal, characteristic, complemented
15C11×#387C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C11×C4⋊Q8—24no—
19C11×#126—24no—
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C4⋊C4C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C11×C22⋊C4C2211yescharacteristic
35C2×C11×C22⋊C4C2211yescharacteristic
36C2×C42×C11C2211yescharacteristic
37C2×C42×C11C2211yescharacteristic
38C2×C42×C11C2211yescharacteristic
39C11×#95C2211yescharacteristic
40C11×#95C2211yescharacteristic
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11×#95C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C2×Q8×C11—22no—
55C2×Q8×C11—22no—
56C2×Q8×C11—22no—
57C2×Q8×C11—22no—
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4D414yes—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—22no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—22no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C42×C11—22no—
91C42×C11—22no—
92C42×C11—41no—
93#2716C1111yesmaximal, characteristic, direct product factor, Sylow
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11C2411yescharacteristic
102Q8×C11—44no—
103Q8×C11—44no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11C2×D412yes—
142C2×C4×C11C2×D412yes—
143C2×C4×C11C2×D412yes—
144C2×C4×C11#4112yes—
145C2×C4×C11#4112yes—
146C2×C4⋊Q8C2×C1111yescharacteristic, complemented
147C2×#126C2×C1111yescharacteristic
148#400C2×C1111yescharacteristic, complemented
149#398C2×C1111yescharacteristic, complemented
150#397C2×C1111yescharacteristic
151#396C2×C1111yescharacteristic
152#393C2×C1111yescharacteristic
153#393C2×C1111yescharacteristic
154#391C2×C1111yescharacteristic, complemented
155#391C2×C1111yescharacteristic, complemented
156#388C2×C1111yescharacteristic
157#388C2×C1111yescharacteristic
158#387C2×C1111yescharacteristic, complemented
159#387C2×C1111yescharacteristic, complemented
160#387C2×C1111yescharacteristic, complemented
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11C22×D411yescharacteristic
169C22×C11C2×#4111yescharacteristic
170C22×C11C2×#4111yescharacteristic
171C22×C11H(5,𝔽2)11yescharacteristic
172C22×C112−1+411yescharacteristic
173C22×C112−1+411yescharacteristic
174C22×C112−1+411yescharacteristic
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—22no—
179C4×C11—22no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C22×Q8C22×C1111yescharacteristic
190C22×Q8C22×C1111yescharacteristic
191C4⋊Q8—24no—
192#126—24no—
193C2×C4⋊C4C22×C1111yescharacteristic
194C2×C4⋊C4C22×C1111yescharacteristic
195C2×C4⋊C4C22×C1111yescharacteristic
196C2×C4⋊C4C22×C1111yescharacteristic
197C2×C4⋊C4C22×C1111yescharacteristic
198C2×C4⋊C4C22×C1111yescharacteristic
199C2×C4⋊C4C22×C1111yescharacteristic
200C2×C4⋊C4C22×C1111yescharacteristic
201C2×C4⋊C4C22×C1111yescharacteristic
202C2×C22⋊C4C22×C1111yescharacteristic
203C2×C22⋊C4C22×C1111yescharacteristic
204C2×C22⋊C4C22×C1111yescharacteristic
205C2×C22⋊C4C22×C1111yescharacteristic
206C2×C22⋊C4C22×C1111yescharacteristic
207C2×C22⋊C4C22×C1111yescharacteristic
208C2×C22⋊C4C22×C1111yescharacteristic
209C2×C42C22×C1111yescharacteristic
210C2×C42C22×C1111yescharacteristic
211C2×C42C22×C1111yescharacteristic
212#95C22×C1111yescharacteristic
213#95C22×C1111yescharacteristic
214#95C22×C1111yescharacteristic
215#95C22×C1111yescharacteristic
216#95C22×C1111yescharacteristic
217#95C22×C1111yescharacteristic
218#95C22×C1111yescharacteristic
219#95C22×C1111yescharacteristic
220#95C22×C1111yescharacteristic
221#95C22×C1111yescharacteristic
222#95C22×C1111yescharacteristic
223#95C22×C1111yescharacteristic
224#95C22×C1111yescharacteristic
225#95C22×C1111yescharacteristic
226C2×C11—81no—
227C2×C11#53611yescharacteristic
228C2×C11#54111yescharacteristic
229C2×C11#54211yescharacteristic
230C2×C11#54611yescharacteristic
231C2×C11#54811yescharacteristic
232C2×C11#55611yescharacteristic
233C2×C11#56311yescharacteristic
234C24C23×C1111yescharacteristic
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C22×C4C23×C1111yescharacteristic
242C22×C4C23×C1111yescharacteristic
243C22×C4C23×C1111yescharacteristic
244C22×C4C23×C1111yescharacteristic
245C22×C4C23×C1111yescharacteristic
246C22×C4C23×C1111yescharacteristic
247C22×C4C23×C1111yescharacteristic
248C22×C4C23×C1111yescharacteristic
249C22×C4C23×C1111yescharacteristic
250C22×C4C23×C1111yescharacteristic
251C22×C4C23×C1111yescharacteristic
252C22×C4C23×C1111yescharacteristic
253C22×C4C23×C1111yescharacteristic
254C22×C4C23×C1111yescharacteristic
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4D4×C1114yes—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C42—22no—
272C42—22no—
273C42—41no—
274C11#271611yescharacteristic, direct product factor, Sylow
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23C24×C1111yescharacteristic
283Q8—44no—
284Q8—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4C2×D4×C1112yes—
323C2×C4C2×D4×C1112yes—
324C2×C4C2×D4×C1112yes—
325C2×C4C11×#4112yes—
326C2×C4C11×#4112yes—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C22×D4×C1111yescharacteristic
335C22C2×C11×#4111yescharacteristic
336C22C2×C11×#4111yescharacteristic
337C22C11×H(5,𝔽2)11yescharacteristic
338C22C11×2−1+411yescharacteristic
339C22C11×2−1+411yescharacteristic
340C22C11×2−1+411yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—22no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C2—81no—
356C2C11×#53611yescharacteristic
357C2C11×#54111yescharacteristic
358C2C11×#54211yescharacteristic
359C2C11×#54611yescharacteristic
360C2C11×#54811yescharacteristic
361C2C11×#55611yescharacteristic
362C2C11×#56311yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC24×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×C4⋊Q8C2semidirect
3. C11×#400C2semidirect
4. C11×#398C2semidirect
9. C11×#391C2semidirect
10. C11×#391C2semidirect
13. C11×#387C2semidirect
14. C11×#387C2semidirect
15. C11×#387C2semidirect
93. #2716C11direct (N × H)
146. C2×C4⋊Q8C2×C11semidirect
148. #400C2×C11semidirect
149. #398C2×C11semidirect
154. #391C2×C11semidirect
155. #391C2×C11semidirect
158. #387C2×C11semidirect
159. #387C2×C11semidirect
160. #387C2×C11semidirect
274. C11#2716direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×C4⋊Q82
C2×C11×#1262
C11×#4002
C11×#3982
C11×#3972
C11×#3962
C11×#3932
C11×#3912
C11×#3882
C11×#3872
#271611