Finite Group Databasebeta

← C11×#11728 #14588921

Subgroups — C11×#11728 #14588921

Order 2816.

470 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2398C211yesmaximal, characteristic
2C4×C11×#99C211yesmaximal, characteristic
3C11×#1459C211yesmaximal, characteristic
4C11×#1351C212yesmaximal, complemented
5C11×#1344C212yesmaximal, complemented
6C2×C4×Q8×C11C411yescharacteristic, complemented
7C2×C4×D4×C11C2211yescharacteristic
8C2×C11×#99—21no—
9C2×C11×C22⋊C8—21no—
10C11×#400—21no—
11C11×#397C411yescharacteristic, complemented
12C11×#397C2211yescharacteristic
13C11×#394—21no—
14C11×#393C411yescharacteristic, complemented
15C11×#393C2211yescharacteristic
16C4×C11×C22⋊C4—21no—
17C4×C11×C22⋊C4—21no—
18C4×C11×C22⋊C4—21no—
19C11×#376C411yescharacteristic, complemented
20C11×#342C2212yes—
21C11×#324—21no—
22C11×#323C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×D4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C22×C8×C11—41no—
28C4×Q8×C11—41no—
29C4×Q8×C11—41no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4C2×C411yescharacteristic
41C2×C11×C22⋊C4C2311yescharacteristic
42C2×C42×C11—21no—
43C2×C42×C11—21no—
44C2×C42×C11—41no—
45C2×C42×C11C2×C411yescharacteristic
46C11×#99—24no—
47C11×C22⋊C8—22no—
48C11×C22⋊C8—41no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—41no—
55C11×#95C2×C411yescharacteristic
56C11×#95C2×C411yescharacteristic
57#11728C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C2×Q8×C11—42no—
61C2×Q8×C11—41no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C2×C8×C11—42no—
82C2×C8×C11—82no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—24no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—42no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—42no—
94C42×C11—21no—
95C42×C11—21no—
96C42×C11—42no—
97C42×C11—41no—
98C42×C11—41no—
99C42×C11—82no—
100#2398C2×C1111yescharacteristic
101C4×#99C2×C1111yescharacteristic
102#1459C2×C1111yescharacteristic
103#1351C2×C1112yescomplemented
104#1344C2×C1112yescomplemented
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11#10412yes—
114C23×C11C2×C22⋊C411yescharacteristic
115C23×C11#13512yes—
116Q8×C11—42no—
117Q8×C11—42no—
118D4×C11—44no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
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—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—44no—
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—81no—
145C2×C4×C11—81no—
146C2×C4×C11—82no—
147C2×C4×C11—82no—
148C2×C4×C11#9911yescharacteristic
149C2×C4×C11#9911yescharacteristic
150C8×C11—82no—
151C2×C4×Q8C4×C1111yescharacteristic, complemented
152C2×C4×D4C22×C1111yescharacteristic
153C2×#99—21no—
154C2×C22⋊C8—21no—
155#400—21no—
156#397C4×C1111yescharacteristic, complemented
157#397C22×C1111yescharacteristic
158#394—21no—
159#393C4×C1111yescharacteristic, complemented
160#393C22×C1111yescharacteristic
161C4×C22⋊C4—21no—
162C4×C22⋊C4—21no—
163C4×C22⋊C4—21no—
164#376C4×C1111yescharacteristic, complemented
165#342C22×C1112yes—
166#324—21no—
167#323C22×C1112yes—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—22no—
171C22×C11—22no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11C2×#9911yescharacteristic
181C22×C11#41611yescharacteristic
182C22×C11C2×#10411yescharacteristic
183C4×C11—21no—
184C4×C11—42no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11—84no—
192C4×C11—81no—
193C4×C11#35412yes—
194C22×Q8C2×C4×C1111yescharacteristic
195C22×D4D4×C1111yescharacteristic
196C23×C4D4×C1111yescharacteristic
197C23×C4D4×C1111yescharacteristic
198C22×C8—41no—
199C4×Q8—41no—
200C4×Q8—41no—
201C4×D4—41no—
202C4×D4—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×C4×C1111yescharacteristic
205C2×C4⋊C4D4×C1111yescharacteristic
206C2×C22⋊C4—22no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4C2×C4×C1111yescharacteristic
212C2×C22⋊C4C23×C1111yescharacteristic
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—41no—
216C2×C42C2×C4×C1111yescharacteristic
217#99—24no—
218C22⋊C8—22no—
219C22⋊C8—41no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—41no—
226#95C2×C4×C1111yescharacteristic
227#95C2×C4×C1111yescharacteristic
228C2×C11—21no—
229C2×C11—21no—
230C2×C11—42no—
231C2×C11—42no—
232C2×C11#150111yescharacteristic
233C2×C11#212011yescharacteristic
234C2×C11C2×#35411yescharacteristic
235C24C11×C22⋊C411yescharacteristic
236C24C2×D4×C1111yescharacteristic
237C2×Q8—42no—
238C2×Q8—41no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—41no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4C11×C22⋊C411yescharacteristic
254C22×C4C11×C22⋊C411yescharacteristic
255C22×C4C11×C22⋊C411yescharacteristic
256C22×C4C22×C4×C1111yescharacteristic
257C22×C4C2×D4×C1111yescharacteristic
258C2×C8—42no—
259C2×C8—82no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C22⋊C4—24no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C42—21no—
272C42—21no—
273C42—42no—
274C42—41no—
275C42—41no—
276C42—82no—
277C11#1172811yescharacteristic, direct product factor, Sylow
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23C11×#10412yes—
287C23C2×C11×C22⋊C411yescharacteristic
288C23C11×#13512yes—
289Q8—42no—
290Q8—42no—
291D4—44no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—44no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4C11×#9911yescharacteristic
322C2×C4C11×#9911yescharacteristic
323C8—82no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—22no—
328C22—42no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22C2×C11×#9911yescharacteristic
337C22C11×#41611yescharacteristic
338C22C2×C11×#10411yescharacteristic
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—42no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—84no—
348C4—81no—
349C4C11×#35412yes—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—42no—
354C2C11×#150111yescharacteristic
355C2C11×#212011yescharacteristic
356C2C2×C11×#35411yescharacteristic
subgroupG/H
centerC2×C4×C11#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1351C2semidirect
5. C11×#1344C2semidirect
6. C2×C4×Q8×C11C4semidirect
11. C11×#397C4semidirect
14. C11×#393C4semidirect
19. C11×#376C4semidirect
57. #11728C11direct (N × H)
103. #1351C2×C11semidirect
104. #1344C2×C11semidirect
151. C2×C4×Q8C4×C11semidirect
156. #397C4×C11semidirect
159. #393C4×C11semidirect
164. #376C4×C11semidirect
277. C11#11728direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23982
C4×C11×#992
C11×#14592
C11×#13512
C11×#13442
#1172811