Finite Group Databasebeta

← C11×#3225 #13066063

Subgroups — C11×#3225 #13066063

Order 1408.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#542C211yesmaximal, characteristic, complemented
2C11×#536C211yesmaximal, characteristic, complemented
3C11×#497C211yesmaximal, characteristic, complemented
4C11×#495C211yesmaximal, characteristic, complemented
5C11×#489C211yesmaximal, characteristic, complemented
6C11×#487C211yesmaximal, characteristic, complemented
7C11×#464C211yesmaximal, characteristic, complemented
8C11×#463C211yesmaximal, characteristic, complemented
9C11×#462C211yesmaximal, characteristic, complemented
10C11×#461C211yesmaximal, characteristic, complemented
11C11×#452C211yesmaximal, characteristic, complemented
12C11×#451C211yesmaximal, characteristic, complemented
13C11×#449C211yesmaximal, characteristic
14C11×#448C211yesmaximal, characteristic, complemented
15C11×#433C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C2×C11×Q16C2211yescharacteristic
21C2×C11×SD16C2211yescharacteristic
22C2×C11×SD16C2211yescharacteristic
23C2×C11×SD16C2211yescharacteristic
24C2×C11×SD16C2211yescharacteristic
25C2×C11×D8C2211yescharacteristic
26C11×C4⋊Q8C2211yescharacteristic
27C11×C4⋊Q8C2211yescharacteristic
28C11×C4⋊Q8C2211yescharacteristic
29C11×#126—21no—
30C11×#124—21no—
31C11×#124C2211yescharacteristic
32C11×#124C2211yescharacteristic
33C11×#124C2211yescharacteristic
34C11×#123—21no—
35C11×#123—21no—
36C11×#123—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8C2211yescharacteristic
41C11×#121C2211yescharacteristic
42C4×Q8×C11C2211yescharacteristic
43C4×D4×C11C2211yescharacteristic
44C11×#117C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×C4⋊C8C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#103C2211yescharacteristic
49C11×#103C2211yescharacteristic
50C11×#103C2211yescharacteristic
51C11×#103C2211yescharacteristic
52C11×#103C2211yescharacteristic
53C11×#102C2211yescharacteristic
54C11×#102C2211yescharacteristic
55C11×C22⋊C8C2211yescharacteristic
56C11×C22⋊C8C2211yescharacteristic
57C11×#97C2211yescharacteristic
58C4×C8×C11C2211yescharacteristic
59C11×#41—41no—
60C11×#41—41no—
61C2×Q8×C11—21no—
62C2×Q8×C11—21no—
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C2×Q8×C11C2311yescharacteristic
66C2×Q8×C11C2311yescharacteristic
67C2×Q8×C11C2311yescharacteristic
68C2×Q8×C11C2311yescharacteristic
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11C2311yescharacteristic
72C2×D4×C11C2311yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11C2311yescharacteristic
77C11×Q16—41no—
78C11×Q16—41no—
79C11×Q16—41no—
80C11×SD16—41no—
81C11×SD16—41no—
82C11×SD16—41no—
83C11×SD16—41no—
84C11×D8—41no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C2×C8×C11C2311yescharacteristic
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4D411yescharacteristic
97C11×C4⋊C4D411yescharacteristic
98C11×C4⋊C4C2311yescharacteristic
99C11×C4⋊C4C2311yescharacteristic
100C11×C22⋊C4—21no—
101C11×C22⋊C4—21no—
102C11×C22⋊C4—21no—
103C11×C22⋊C4—21no—
104C11×C22⋊C4—21no—
105C11×C22⋊C4—21no—
106C11×C22⋊C4—21no—
107C11×C22⋊C4—21no—
108C11×C22⋊C4—21no—
109C11×C22⋊C4D411yescharacteristic
110C11×C22⋊C4D411yescharacteristic
111C42×C11—21no—
112C42×C11C2311yescharacteristic
113C42×C11C2311yescharacteristic
114#3225C1111yesmaximal, characteristic, direct product factor, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C23×C11C2×D411yescharacteristic
118Q8×C11—21no—
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122Q8×C11—21no—
123Q8×C11—21no—
124Q8×C11—21no—
125Q8×C11—21no—
126Q8×C11—42no—
127Q8×C11—81no—
128D4×C11—21no—
129D4×C11—21no—
130D4×C11—21no—
131D4×C11—21no—
132D4×C11—42no—
133D4×C11—81no—
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×C11—21no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—81no—
145C2×C4×C11C2×D411yescharacteristic
146C2×C4×C11C2×D411yescharacteristic
147C2×C4×C11C2×D411yescharacteristic
148C2×C4×C11C2×D411yescharacteristic
149C2×C4×C11C2×D411yescharacteristic
150C2×C4×C11C2411yescharacteristic
151C8×C11—21no—
152C8×C11—21no—
153C8×C11—21no—
154C8×C11—21no—
155#542C2×C1111yescharacteristic, complemented
156#536C2×C1111yescharacteristic, complemented
157#497C2×C1111yescharacteristic, complemented
158#495C2×C1111yescharacteristic, complemented
159#489C2×C1111yescharacteristic, complemented
160#487C2×C1111yescharacteristic, complemented
161#464C2×C1111yescharacteristic, complemented
162#463C2×C1111yescharacteristic, complemented
163#462C2×C1111yescharacteristic, complemented
164#461C2×C1111yescharacteristic, complemented
165#452C2×C1111yescharacteristic, complemented
166#451C2×C1111yescharacteristic, complemented
167#449C2×C1111yescharacteristic
168#448C2×C1111yescharacteristic, complemented
169#433C2×C1111yescharacteristic, complemented
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11C22×D411yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11H(5,𝔽2)11yescharacteristic
192C4×C11H(5,𝔽2)11yescharacteristic
193C2×#41C22×C1111yescharacteristic
194C22×Q8C22×C1111yescharacteristic
195C2×Q16C22×C1111yescharacteristic
196C2×Q16C22×C1111yescharacteristic
197C2×Q16C22×C1111yescharacteristic
198C2×SD16C22×C1111yescharacteristic
199C2×SD16C22×C1111yescharacteristic
200C2×SD16C22×C1111yescharacteristic
201C2×SD16C22×C1111yescharacteristic
202C2×D8C22×C1111yescharacteristic
203C4⋊Q8C22×C1111yescharacteristic
204C4⋊Q8C22×C1111yescharacteristic
205C4⋊Q8C22×C1111yescharacteristic
206#126—21no—
207#124—21no—
208#124C22×C1111yescharacteristic
209#124C22×C1111yescharacteristic
210#124C22×C1111yescharacteristic
211#123—21no—
212#123—21no—
213#123—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8C22×C1111yescharacteristic
218#121C22×C1111yescharacteristic
219C4×Q8C22×C1111yescharacteristic
220C4×D4C22×C1111yescharacteristic
221#117C22×C1111yescharacteristic
222C4⋊C8C22×C1111yescharacteristic
223C4⋊C8C22×C1111yescharacteristic
224#103C22×C1111yescharacteristic
225#103C22×C1111yescharacteristic
226#103C22×C1111yescharacteristic
227#103C22×C1111yescharacteristic
228#103C22×C1111yescharacteristic
229#103C22×C1111yescharacteristic
230#102C22×C1111yescharacteristic
231#102C22×C1111yescharacteristic
232C22⋊C8C22×C1111yescharacteristic
233C22⋊C8C22×C1111yescharacteristic
234#97C22×C1111yescharacteristic
235C4×C8C22×C1111yescharacteristic
236C2×C11—41no—
237C2×C11—81no—
238C2×C11—81no—
239C2×C11#53511yescharacteristic
240C2×C11#57711yescharacteristic
241C2×C11#57811yescharacteristic
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8C23×C1111yescharacteristic
249C2×Q8C23×C1111yescharacteristic
250C2×Q8C23×C1111yescharacteristic
251C2×Q8C23×C1111yescharacteristic
252C2×D4—21no—
253C2×D4—21no—
254C2×D4C23×C1111yescharacteristic
255C2×D4C23×C1111yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4C23×C1111yescharacteristic
260Q16—41no—
261Q16—41no—
262Q16—41no—
263SD16—41no—
264SD16—41no—
265SD16—41no—
266SD16—41no—
267D8—41no—
268C2×C8C23×C1111yescharacteristic
269C2×C8C23×C1111yescharacteristic
270C2×C8C23×C1111yescharacteristic
271C2×C8C23×C1111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4D4×C1111yescharacteristic
280C4⋊C4D4×C1111yescharacteristic
281C4⋊C4C23×C1111yescharacteristic
282C4⋊C4C23×C1111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4D4×C1111yescharacteristic
293C22⋊C4D4×C1111yescharacteristic
294C42—21no—
295C42C23×C1111yescharacteristic
296C42C23×C1111yescharacteristic
297C11#322511yescharacteristic, direct product factor, Sylow
298C23—21no—
299C23—21no—
300C23C2×D4×C1111yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—42no—
310Q8—81no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—81no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4C2×D4×C1111yescharacteristic
329C2×C4C2×D4×C1111yescharacteristic
330C2×C4C2×D4×C1111yescharacteristic
331C2×C4C2×D4×C1111yescharacteristic
332C2×C4C2×D4×C1111yescharacteristic
333C2×C4C24×C1111yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22C22×D4×C1111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4C11×H(5,𝔽2)11yescharacteristic
360C4C11×H(5,𝔽2)11yescharacteristic
361C2—41no—
362C2—81no—
363C2—81no—
364C2C11×#53511yescharacteristic
365C2C11×#57711yescharacteristic
366C2C11×#57811yescharacteristic
subgroupG/H
center, socleC22×C11C22×D4
commutator, Frattini, cosocleC2×C4C24×C11
prime radicalC11×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#542C2semidirect
2. C11×#536C2semidirect
3. C11×#497C2semidirect
4. C11×#495C2semidirect
5. C11×#489C2semidirect
6. C11×#487C2semidirect
7. C11×#464C2semidirect
8. C11×#463C2semidirect
9. C11×#462C2semidirect
10. C11×#461C2semidirect
11. C11×#452C2semidirect
12. C11×#451C2semidirect
14. C11×#448C2semidirect
15. C11×#433C2semidirect
114. #3225C11direct (N × H)
155. #542C2×C11semidirect
156. #536C2×C11semidirect
157. #497C2×C11semidirect
158. #495C2×C11semidirect
159. #489C2×C11semidirect
160. #487C2×C11semidirect
161. #464C2×C11semidirect
162. #463C2×C11semidirect
163. #462C2×C11semidirect
164. #461C2×C11semidirect
165. #452C2×C11semidirect
166. #451C2×C11semidirect
168. #448C2×C11semidirect
169. #433C2×C11semidirect
297. C11#3225direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5422
C11×#5362
C11×#4972
C11×#4952
C11×#4892
C11×#4872
C11×#4642
C11×#4632
C11×#4622
C11×#4612
C11×#4522
C11×#4512
C11×#4492
C11×#4482
C11×#4332
#322511