Finite Group Databasebeta

← C11×#2695 #13065533

Subgroups — C11×#2695 #13065533

Order 1408.

504 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#126C211yesmaximal, characteristic, complemented
2C2×C11×#123C211yesmaximal, characteristic
3C11×#400C211yesmaximal, characteristic, complemented
4C11×#398C211yesmaximal, characteristic, complemented
5C11×#398C211yesmaximal, characteristic, complemented
6C11×#397C211yesmaximal, characteristic, complemented
7C11×#396C211yesmaximal, characteristic, complemented
8C11×#394C211yesmaximal, characteristic
9C11×#389C211yesmaximal, characteristic, complemented
10C11×#388C211yesmaximal, characteristic, complemented
11C11×#386C211yesmaximal, characteristic
12C11×#385C211yesmaximal, characteristic, complemented
13C11×#385C211yesmaximal, characteristic, complemented
14C11×#380C211yesmaximal, characteristic, complemented
15C11×#380C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic
19C11×#126—24no—
20C11×#123—24no—
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×C4⋊C4C2211yescharacteristic
30C2×C11×C4⋊C4C2211yescharacteristic
31C2×C11×C4⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C11×C22⋊C4C2211yescharacteristic
35C2×C11×C22⋊C4C2211yescharacteristic
36C2×C11×C22⋊C4C2211yescharacteristic
37C2×C11×C22⋊C4C2211yescharacteristic
38C2×C11×C22⋊C4C2211yescharacteristic
39C2×C11×C22⋊C4C2211yescharacteristic
40C2×C11×C22⋊C4C2211yescharacteristic
41C2×C11×C22⋊C4C2211yescharacteristic
42C2×C42×C11C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11×#95C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C2×D4×C11—22no—
56C2×D4×C11—22no—
57C2×D4×C11—41no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
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
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4—22no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4D414yes—
98C42×C11—22no—
99#2695C1111yesmaximal, characteristic, direct product factor, Sylow
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11C2×D412yes—
113C23×C11#4112yes—
114C23×C11C2411yescharacteristic
115D4×C11—44no—
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×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11C2×D412yes—
155C2×C4×C11C2×D412yes—
156C2×C4×C11#4112yes—
157C2×#126C2×C1111yescharacteristic, complemented
158C2×#123C2×C1111yescharacteristic
159#400C2×C1111yescharacteristic, complemented
160#398C2×C1111yescharacteristic, complemented
161#398C2×C1111yescharacteristic, complemented
162#397C2×C1111yescharacteristic, complemented
163#396C2×C1111yescharacteristic, complemented
164#394C2×C1111yescharacteristic
165#389C2×C1111yescharacteristic, complemented
166#388C2×C1111yescharacteristic, complemented
167#386C2×C1111yescharacteristic
168#385C2×C1111yescharacteristic, complemented
169#385C2×C1111yescharacteristic, complemented
170#380C2×C1111yescharacteristic, complemented
171#380C2×C1111yescharacteristic, complemented
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11C22×D411yescharacteristic
187C22×C11C2×#4111yescharacteristic
188C22×C11C2×#4111yescharacteristic
189C22×C11H(5,𝔽2)11yescharacteristic
190C22×C11H(5,𝔽2)11yescharacteristic
191C22×C112−1+411yescharacteristic
192C22×C112−1+411yescharacteristic
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—41no—
206C22×D4C22×C1111yescharacteristic
207C23×C4C22×C1111yescharacteristic
208C23×C4C22×C1111yescharacteristic
209#126—24no—
210#123—24no—
211C2×C4⋊C4C22×C1111yescharacteristic
212C2×C4⋊C4C22×C1111yescharacteristic
213C2×C4⋊C4C22×C1111yescharacteristic
214C2×C4⋊C4C22×C1111yescharacteristic
215C2×C4⋊C4C22×C1111yescharacteristic
216C2×C4⋊C4C22×C1111yescharacteristic
217C2×C4⋊C4C22×C1111yescharacteristic
218C2×C4⋊C4C22×C1111yescharacteristic
219C2×C4⋊C4C22×C1111yescharacteristic
220C2×C4⋊C4C22×C1111yescharacteristic
221C2×C4⋊C4C22×C1111yescharacteristic
222C2×C22⋊C4C22×C1111yescharacteristic
223C2×C22⋊C4C22×C1111yescharacteristic
224C2×C22⋊C4C22×C1111yescharacteristic
225C2×C22⋊C4C22×C1111yescharacteristic
226C2×C22⋊C4C22×C1111yescharacteristic
227C2×C22⋊C4C22×C1111yescharacteristic
228C2×C22⋊C4C22×C1111yescharacteristic
229C2×C22⋊C4C22×C1111yescharacteristic
230C2×C22⋊C4C22×C1111yescharacteristic
231C2×C22⋊C4C22×C1111yescharacteristic
232C2×C42C22×C1111yescharacteristic
233#95C22×C1111yescharacteristic
234#95C22×C1111yescharacteristic
235#95C22×C1111yescharacteristic
236#95C22×C1111yescharacteristic
237#95C22×C1111yescharacteristic
238#95C22×C1111yescharacteristic
239#95C22×C1111yescharacteristic
240#95C22×C1111yescharacteristic
241#95C22×C1111yescharacteristic
242#95C22×C1111yescharacteristic
243C2×C11—42no—
244C2×C11—42no—
245C2×C11#53711yescharacteristic
246C2×C11#53811yescharacteristic
247C2×C11#53911yescharacteristic
248C2×C11#54611yescharacteristic
249C2×C11#54711yescharacteristic
250C2×C11#55211yescharacteristic
251C2×C11#56311yescharacteristic
252C24C23×C1111yescharacteristic
253C24C23×C1111yescharacteristic
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—41no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4C23×C1111yescharacteristic
264C22×C4C23×C1111yescharacteristic
265C22×C4C23×C1111yescharacteristic
266C22×C4C23×C1111yescharacteristic
267C22×C4C23×C1111yescharacteristic
268C22×C4C23×C1111yescharacteristic
269C22×C4C23×C1111yescharacteristic
270C22×C4C23×C1111yescharacteristic
271C22×C4C23×C1111yescharacteristic
272C22×C4C23×C1111yescharacteristic
273C22×C4C23×C1111yescharacteristic
274C22×C4C23×C1111yescharacteristic
275C22×C4C23×C1111yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4D4×C1114yes—
297C42—22no—
298C11#269511yescharacteristic, direct product factor, Sylow
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23C2×D4×C1112yes—
312C23C11×#4112yes—
313C23C24×C1111yescharacteristic
314D4—44no—
315C2×C4—21no—
316C2×C4—21no—
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—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4C2×D4×C1112yes—
354C2×C4C2×D4×C1112yes—
355C2×C4C11×#4112yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C22×D4×C1111yescharacteristic
371C22C2×C11×#4111yescharacteristic
372C22C2×C11×#4111yescharacteristic
373C22C11×H(5,𝔽2)11yescharacteristic
374C22C11×H(5,𝔽2)11yescharacteristic
375C22C11×2−1+411yescharacteristic
376C22C11×2−1+411yescharacteristic
377C4—22no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—41no—
390C2—42no—
391C2—42no—
392C2C11×#53711yescharacteristic
393C2C11×#53811yescharacteristic
394C2C11×#53911yescharacteristic
395C2C11×#54611yescharacteristic
396C2C11×#54711yescharacteristic
397C2C11×#55211yescharacteristic
398C2C11×#56311yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC22×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#126C2semidirect
3. C11×#400C2semidirect
4. C11×#398C2semidirect
5. C11×#398C2semidirect
6. C11×#397C2semidirect
7. C11×#396C2semidirect
9. C11×#389C2semidirect
10. C11×#388C2semidirect
12. C11×#385C2semidirect
13. C11×#385C2semidirect
14. C11×#380C2semidirect
15. C11×#380C2semidirect
99. #2695C11direct (N × H)
157. C2×#126C2×C11semidirect
159. #400C2×C11semidirect
160. #398C2×C11semidirect
161. #398C2×C11semidirect
162. #397C2×C11semidirect
163. #396C2×C11semidirect
165. #389C2×C11semidirect
166. #388C2×C11semidirect
168. #385C2×C11semidirect
169. #385C2×C11semidirect
170. #380C2×C11semidirect
171. #380C2×C11semidirect
298. C11#2695direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1262
C2×C11×#1232
C11×#4002
C11×#3982
C11×#3972
C11×#3962
C11×#3942
C11×#3892
C11×#3882
C11×#3862
C11×#3852
C11×#3802
#269511