Finite Group Databasebeta

← C11×#11879 #14589072

Subgroups — C11×#11879 #14589072

Order 2816.

440 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2536C211yesmaximal, characteristic
2C11×#1801C211yesmaximal, characteristic, complemented
3C11×#1461C211yesmaximal, characteristic, complemented
4C11×#1346C212yesmaximal, complemented
5C11×#1345C212yesmaximal
6C2×C11×C22⋊Q8—21no—
7C2×C4×Q8×C11C2211yescharacteristic
8C2×C4×D4×C11C411yescharacteristic
9C11×#431—21no—
10C11×#423—21no—
11C2×C11×#101—21no—
12C11×#398C411yescharacteristic
13C11×#398C2211yescharacteristic
14C11×#394C411yescharacteristic
15C11×#394C2211yescharacteristic
16C11×#388—21no—
17C11×#388—21no—
18C11×#382C411yescharacteristic
19C11×#380—21no—
20C11×#343C2212yes—
21C11×#324—21no—
22C11×#324C2212yes—
23C22×Q8×C11D411yescharacteristic
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11—21no—
26C2×C11×M16—22no—
27C11×C22⋊Q8—42no—
28C11×C22⋊Q8—42no—
29C4×Q8×C11—41no—
30C4×Q8×C11—41no—
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4C2311yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C42×C11C2×C411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C11×C4⋊C8—41no—
49C11×C4⋊C8—41no—
50C11×C4⋊C8—41no—
51C11×#101—42no—
52C11×C22⋊C8—22no—
53C4×C8×C11—41no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95C2×C411yescharacteristic
58C11×#95C2×C411yescharacteristic
59#11879C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11—21no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C2×Q8×C11D812yes—
64C2×Q8×C11SD1612yes—
65C2×D4×C11—41no—
66C2×D4×C11—42no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—42no—
71C22×C4×C11—42no—
72C22×C4×C11—42no—
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C11×M16—42no—
81C11×M16—42no—
82C2×C8×C11—42no—
83C2×C8×C11—42no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—42no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11—21no—
100C42×C11—21no—
101C42×C11—21no—
102C42×C11—21no—
103C42×C11—21no—
104C42×C11—21no—
105#2536C2×C1111yescharacteristic
106#1801C2×C1111yescharacteristic, complemented
107#1461C2×C1111yescharacteristic, complemented
108#1346C2×C1112yescomplemented
109#1345C2×C1112yes—
110C23×C11—22no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11C2×C22⋊C411yescharacteristic
118Q8×C11—42no—
119Q8×C11—42no—
120D4×C11—42no—
121D4×C11—42no—
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—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—84no—
145C2×C4×C11#9911yescharacteristic
146C2×C4×C11#9911yescharacteristic
147C2×C4×C11#10212yes—
148C2×C4×C11#10212yes—
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×SD1611yescharacteristic
151C8×C11—82no—
152C8×C11—82no—
153C2×C22⋊Q8—21no—
154C2×C4×Q8C22×C1111yescharacteristic
155C2×C4×D4C4×C1111yescharacteristic
156#431—21no—
157#423—21no—
158C2×#101—21no—
159#398C4×C1111yescharacteristic
160#398C22×C1111yescharacteristic
161#394C4×C1111yescharacteristic
162#394C22×C1111yescharacteristic
163#388—21no—
164#388—21no—
165#382C4×C1111yescharacteristic
166#380—21no—
167#343C22×C1112yes—
168#324—21no—
169#324C22×C1112yes—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11—81no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11C2×#9911yescharacteristic
180C22×C11C2×#10211yescharacteristic
181C22×C11#42111yescharacteristic
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11—81no—
194C22×Q8D4×C1111yescharacteristic
195C22×D4C2×C4×C1111yescharacteristic
196C23×C4—21no—
197C2×M16—22no—
198C22⋊Q8—42no—
199C22⋊Q8—42no—
200C4×Q8—41no—
201C4×Q8—41no—
202C4×D4—41no—
203C4×D4—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×C4×C1111yescharacteristic
208C2×C4⋊C4C2×C4×C1111yescharacteristic
209C2×C4⋊C4D4×C1111yescharacteristic
210C2×C4⋊C4C23×C1111yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C42C2×C4×C1111yescharacteristic
217C2×C42D4×C1111yescharacteristic
218C2×C42D4×C1111yescharacteristic
219C4⋊C8—41no—
220C4⋊C8—41no—
221C4⋊C8—41no—
222#101—42no—
223C22⋊C8—22no—
224C4×C8—41no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95C2×C4×C1111yescharacteristic
229#95C2×C4×C1111yescharacteristic
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—82no—
233C2×C11#151911yescharacteristic
234C2×C11#212011yescharacteristic
235C2×C11#213311yescharacteristic
236C24—21no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8C11×D812yes—
240C2×Q8C11×SD1612yes—
241C2×D4—41no—
242C2×D4—42no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4C11×C22⋊C411yescharacteristic
250C22×C4C11×C22⋊C411yescharacteristic
251C22×C4C11×C22⋊C411yescharacteristic
252C22×C4C11×C22⋊C411yescharacteristic
253C22×C4C22×C4×C1111yescharacteristic
254C22×C4C2×D4×C1111yescharacteristic
255C22×C4C2×D4×C1111yescharacteristic
256M16—42no—
257M16—42no—
258C2×C8—42no—
259C2×C8—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—42no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C11#1187911yescharacteristic, direct product factor, Sylow
282C23—22no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×C11×C22⋊C411yescharacteristic
290Q8—42no—
291Q8—42no—
292D4—42no—
293D4—42no—
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—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—84no—
317C2×C4C11×#9911yescharacteristic
318C2×C4C11×#9911yescharacteristic
319C2×C4C11×#10212yes—
320C2×C4C11×#10212yes—
321C2×C4C2×C11×D811yescharacteristic
322C2×C4C2×C11×SD1611yescharacteristic
323C8—82no—
324C8—82no—
325C22—21no—
326C22—21no—
327C22—42no—
328C22—42no—
329C22—42no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22C2×C11×#9911yescharacteristic
335C22C2×C11×#10211yescharacteristic
336C22C11×#42111yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—22no—
341C4—22no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C2—21no—
350C2—21no—
351C2—82no—
352C2C11×#151911yescharacteristic
353C2C11×#212011yescharacteristic
354C2C11×#213311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC22×D4×C11C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1801C2semidirect
3. C11×#1461C2semidirect
4. C11×#1346C2semidirect
59. #11879C11direct (N × H)
106. #1801C2×C11semidirect
107. #1461C2×C11semidirect
108. #1346C2×C11semidirect
281. C11#11879direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25362
C11×#18012
C11×#14612
C11×#13462
C11×#13452
#1187911