Finite Group Databasebeta

← C11×#11804 #14588997

Subgroups — C11×#11804 #14588997

Order 2816.

472 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2392C211yesmaximal, characteristic
2C11×#1822C211yesmaximal, characteristic, complemented
3C11×#1464C211yesmaximal, characteristic, complemented
4C11×#1346C212yesmaximal, complemented
5C11×#1345C212yesmaximal, complemented
6C2×C4×D4×C11—21no—
7C2×C4×D4×C11C411yescharacteristic
8C2×C11×#117C2211yescharacteristic
9C11×#432—21no—
10C11×#407—21no—
11C11×#398C2211yescharacteristic
12C11×#397C411yescharacteristic
13C11×#396—21no—
14C11×#394—21no—
15C11×#394C2211yescharacteristic
16C11×#392C411yescharacteristic
17C4×C11×C4⋊C4C411yescharacteristic
18C4×C11×C22⋊C4—21no—
19C11×#343—21no—
20C11×#343C2212yes—
21C11×#324C2212yes—
22C11×#323—21no—
23C22×D4×C11—21no—
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11—21no—
26C23×C4×C11D411yescharacteristic
27C2×C11×M16—22no—
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C4×D4×C11—44no—
31C11×#117—41no—
32C11×#117—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4C2×C411yescharacteristic
44C2×C11×C22⋊C4D411yescharacteristic
45C2×C42×C11—21no—
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C11×C4⋊C8—41no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—41no—
51C11×C22⋊C8—41no—
52C11×#97—41no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11×#95C2×C411yescharacteristic
57#11804C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11—21no—
59C24×C11C22⋊C411yescharacteristic
60C2×D4×C11—42no—
61C2×D4×C11—41no—
62C2×D4×C11—42no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—41no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C11×M16—42no—
83C11×M16—42no—
84C2×C8×C11—42no—
85C2×C8×C11—42no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—42no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—42no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—42no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—42no—
98C42×C11—21no—
99C42×C11—21no—
100C42×C11—21no—
101C42×C11—21no—
102C42×C11—42no—
103#2392C2×C1111yescharacteristic
104#1822C2×C1111yescharacteristic, complemented
105#1464C2×C1111yescharacteristic, complemented
106#1346C2×C1112yescomplemented
107#1345C2×C1112yescomplemented
108C23×C11—22no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11C2×C22⋊C411yescharacteristic
121D4×C11—42no—
122D4×C11—48no—
123D4×C11—42no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
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—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—82no—
148C2×C4×C11—82no—
149C2×C4×C11#9911yescharacteristic
150C2×C4×C11#9911yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)12yes—
152C8×C11—82no—
153C8×C11—82no—
154C2×C4×D4—21no—
155C2×C4×D4C4×C1111yescharacteristic
156C2×#117C22×C1111yescharacteristic
157#432—21no—
158#407—21no—
159#398C22×C1111yescharacteristic
160#397C4×C1111yescharacteristic
161#396—21no—
162#394—21no—
163#394C22×C1111yescharacteristic
164#392C4×C1111yescharacteristic
165C4×C4⋊C4C4×C1111yescharacteristic
166C4×C22⋊C4—21no—
167#343—21no—
168#343C22×C1112yes—
169#324C22×C1112yes—
170#323—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11—42no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11C2×#9911yescharacteristic
186C22×C11#41811yescharacteristic
187C22×C11#42111yescharacteristic
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—22no—
191C4×C11—42no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—81no—
197C4×C11—81no—
198C22×D4—21no—
199C22×D4C2×C4×C1111yescharacteristic
200C23×C4—21no—
201C23×C4D4×C1111yescharacteristic
202C2×M16—22no—
203C4×D4—41no—
204C4×D4—41no—
205C4×D4—44no—
206#117—41no—
207#117—41no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C2×C4×C1111yescharacteristic
211C2×C4⋊C4D4×C1111yescharacteristic
212C2×C4⋊C4C23×C1111yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4C2×C4×C1111yescharacteristic
219C2×C22⋊C4D4×C1111yescharacteristic
220C2×C42—21no—
221C2×C42C2×C4×C1111yescharacteristic
222C2×C42D4×C1111yescharacteristic
223C4⋊C8—41no—
224C22⋊C8—22no—
225C22⋊C8—41no—
226C22⋊C8—41no—
227#97—41no—
228#95—21no—
229#95—21no—
230#95C2×C4×C1111yescharacteristic
231#95C2×C4×C1111yescharacteristic
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—81no—
235C2×C11—82no—
236C2×C11#151011yescharacteristic
237C2×C11#212011yescharacteristic
238C2×C11#213211yescharacteristic
239C24—21no—
240C24C11×C22⋊C411yescharacteristic
241C2×D4—41no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—42no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4C11×C22⋊C411yescharacteristic
258C22×C4C11×C22⋊C411yescharacteristic
259C22×C4C11×C22⋊C411yescharacteristic
260C22×C4C22×C4×C1111yescharacteristic
261C22×C4C2×D4×C1111yescharacteristic
262C22×C4C2×D4×C1111yescharacteristic
263M16—42no—
264M16—42no—
265C2×C8—42no—
266C2×C8—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C42—21no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42—42no—
284C11#1180411yescharacteristic, direct product factor, Sylow
285C23—22no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×C11×C22⋊C411yescharacteristic
298D4—42no—
299D4—48no—
300D4—42no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4C11×#9911yescharacteristic
327C2×C4C11×#9911yescharacteristic
328C2×C4C11×AGL(1,ℤ/8)12yes—
329C8—82no—
330C8—82no—
331C22—21no—
332C22—21no—
333C22—42no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—42no—
339C22—41no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22C2×C11×#9911yescharacteristic
346C22C11×#41811yescharacteristic
347C22C11×#42111yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—42no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—81no—
357C4—81no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—82no—
362C2C11×#151011yescharacteristic
363C2C11×#212011yescharacteristic
364C2C11×#213211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC11×#392C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1822C2semidirect
3. C11×#1464C2semidirect
4. C11×#1346C2semidirect
5. C11×#1345C2semidirect
57. #11804C11direct (N × H)
104. #1822C2×C11semidirect
105. #1464C2×C11semidirect
106. #1346C2×C11semidirect
107. #1345C2×C11semidirect
284. C11#11804direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23922
C11×#18222
C11×#14642
C11×#13462
C11×#13452
#1180411