Finite Group Databasebeta

← C11×#11793 #14588986

Subgroups — C11×#11793 #14588986

Order 2816.

444 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2564C211yesmaximal, characteristic
2C4×C11×#100C211yesmaximal, characteristic
3C11×#1465C211yesmaximal, characteristic
4C11×#1354C212yesmaximal, complemented
5C11×#1353C212yesmaximal, complemented
6C2×C11×C22⋊Q8C411yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C2×C11×#100—21no—
9C11×#407—21no—
10C4×C11×M16—21no—
11C11×#400C2211yescharacteristic
12C11×#399C411yescharacteristic
13C11×#395C2211yescharacteristic
14C11×#393C411yescharacteristic
15C11×#387—21no—
16C11×#386—21no—
17C11×#385—21no—
18C11×#380—21no—
19C2×C11×#95C411yescharacteristic
20C11×#343C2212yes—
21C11×#324C2212yes—
22C11×#323—21no—
23C22×Q8×C11C2×C411yescharacteristic
24C22×D4×C11D411yescharacteristic
25C23×C4×C11—21no—
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C2×C11×M16—22no—
29C2×C11×M16—41no—
30C11×C22⋊Q8—41no—
31C11×C22⋊Q8—41no—
32C4×D4×C11—41no—
33C4×D4×C11—41no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4C2311yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4D411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C11×#100—24no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—41no—
48C11×#97—41no—
49C4×C8×C11—41no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11×#95C2×C411yescharacteristic
57#11793C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C22⋊C411yescharacteristic
60C2×Q8×C11—41no—
61C2×Q8×C11—81no—
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—81no—
76C22×C4×C11—81no—
77C22×C4×C11—81no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C11×M16—24no—
84C11×M16—42no—
85C11×M16—82no—
86C2×C8×C11—42no—
87C2×C8×C11—42no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—81no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—81no—
99C42×C11—21no—
100C42×C11—21no—
101#2564C2×C1111yescharacteristic
102C4×#100C2×C1111yescharacteristic
103#1465C2×C1111yescharacteristic
104#1354C2×C1112yescomplemented
105#1353C2×C1112yescomplemented
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11#10412yes—
116C23×C11C2×C22⋊C411yescharacteristic
117Q8×C11—82no—
118D4×C11—44no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
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—81no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—84no—
145C2×C4×C11#9911yescharacteristic
146C2×C4×C11#9911yescharacteristic
147C2×C4×C11#13712yes—
148C8×C11—44no—
149C8×C11—82no—
150C2×C22⋊Q8C4×C1111yescharacteristic
151C2×C4×D4C22×C1111yescharacteristic
152C2×#100—21no—
153#407—21no—
154C4×M16—21no—
155#400C22×C1111yescharacteristic
156#399C4×C1111yescharacteristic
157#395C22×C1111yescharacteristic
158#393C4×C1111yescharacteristic
159#387—21no—
160#386—21no—
161#385—21no—
162#380—21no—
163C2×#95C4×C1111yescharacteristic
164#343C22×C1112yes—
165#324C22×C1112yes—
166#323—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—42no—
171C22×C11—42no—
172C22×C11—42no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—81no—
179C22×C11C2×#9911yescharacteristic
180C22×C11#41911yescharacteristic
181C22×C11C2×#10411yescharacteristic
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—42no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11—81no—
192C22×Q8C2×C4×C1111yescharacteristic
193C22×D4D4×C1111yescharacteristic
194C23×C4—21no—
195C23×C4C2×C4×C1111yescharacteristic
196C23×C4D4×C1111yescharacteristic
197C2×M16—22no—
198C2×M16—41no—
199C22⋊Q8—41no—
200C22⋊Q8—41no—
201C4×D4—41no—
202C4×D4—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C2×C4×C1111yescharacteristic
207C2×C4⋊C4C23×C1111yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4C2×C4×C1111yescharacteristic
212C2×C22⋊C4D4×C1111yescharacteristic
213C2×C42D4×C1111yescharacteristic
214#100—24no—
215C22⋊C8—22no—
216C22⋊C8—41no—
217#97—41no—
218C4×C8—41no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95C2×C4×C1111yescharacteristic
225#95C2×C4×C1111yescharacteristic
226C2×C11—21no—
227C2×C11—21no—
228C2×C11—42no—
229C2×C11—81no—
230C2×C11#150811yescharacteristic
231C2×C11#212111yescharacteristic
232C2×C11#213211yescharacteristic
233C24C11×C22⋊C411yescharacteristic
234C24C11×C22⋊C411yescharacteristic
235C2×Q8—41no—
236C2×Q8—81no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—41no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4C11×C22⋊C411yescharacteristic
254C22×C4C11×C22⋊C411yescharacteristic
255C22×C4C22×C4×C1111yescharacteristic
256C22×C4C2×D4×C1111yescharacteristic
257C22×C4C2×D4×C1111yescharacteristic
258M16—24no—
259M16—42no—
260M16—82no—
261C2×C8—42no—
262C2×C8—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—81no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—81no—
274C42—21no—
275C42—21no—
276C11#1179311yescharacteristic, direct product factor, Sylow
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23C11×#10412yes—
287C23C2×C11×C22⋊C411yescharacteristic
288Q8—82no—
289D4—44no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
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—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—84no—
316C2×C4C11×#9911yescharacteristic
317C2×C4C11×#9911yescharacteristic
318C2×C4C11×#13712yes—
319C8—44no—
320C8—82no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22C2×C11×#9911yescharacteristic
334C22C11×#41911yescharacteristic
335C22C2×C11×#10411yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—42no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—81no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—81no—
350C2C11×#150811yescharacteristic
351C2C11×#212111yescharacteristic
352C2C11×#213211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×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×#1354C2semidirect
5. C11×#1353C2semidirect
57. #11793C11direct (N × H)
104. #1354C2×C11semidirect
105. #1353C2×C11semidirect
276. C11#11793direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25642
C4×C11×#1002
C11×#14652
C11×#13542
C11×#13532
#1179311