Finite Group Databasebeta

← C11×#11805 #14588998

Subgroups — C11×#11805 #14588998

Order 2816.

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

normal subgroups only

This group has 448 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×#2618C211yesmaximal, characteristic
2C11×#1821C211yesmaximal, characteristic, complemented
3C11×#1463C211yesmaximal, characteristic, complemented
4C11×#1346C212yesmaximal, complemented
5C11×#1345C212yesmaximal, complemented
6C2×C11×#123—21no—
7C2×C11×#121C411yescharacteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C11×#407—21no—
10C11×#407—21no—
11C11×#398C411yescharacteristic
12C11×#398C2211yescharacteristic
13C11×#396—21no—
14C11×#396—21no—
15C11×#394C411yescharacteristic
16C11×#394C2211yescharacteristic
17C11×#386—21no—
18C11×#380C411yescharacteristic
19C11×#343—21no—
20C11×#343C2212yes—
21C11×#324—21no—
22C11×#324C2212yes—
23C22×D4×C11—21no—
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C2×C11×M16—22no—
29C2×C11×M16—41no—
30C11×#123—44no—
31C11×#121—41no—
32C11×#121—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—41no—
37C2×C11×C4⋊C4—41no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4C2311yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—41no—
51C11×C22⋊C8—41no—
52C11×C22⋊C8—41no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11×#95C2×C411yescharacteristic
57#11805C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11—21no—
59C24×C11C22⋊C411yescharacteristic
60C2×D4×C11—41no—
61C2×D4×C11—42no—
62C2×D4×C11—42no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—81no—
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—22no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—41no—
77C22×C4×C11—81no—
78C22×C4×C11—81no—
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C11×M16—42no—
86C11×M16—42no—
87C11×M16—82no—
88C2×C8×C11—42no—
89C2×C8×C11—42no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—81no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—81no—
103C11×C22⋊C4—81no—
104#2618C2×C1111yescharacteristic
105#1821C2×C1111yescharacteristic, complemented
106#1463C2×C1111yescharacteristic, complemented
107#1346C2×C1112yescomplemented
108#1345C2×C1112yescomplemented
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—41no—
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×C11#9911yescharacteristic
121C23×C11#9911yescharacteristic
122C23×C11C2×C22⋊C411yescharacteristic
123D4×C11—82no—
124D4×C11—82no—
125D4×C11—82no—
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—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
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—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11AGL(1,ℤ/8)12yes—
155C8×C11—82no—
156C8×C11—82no—
157C2×#123—21no—
158C2×#121C4×C1111yescharacteristic
159C22×C4⋊C4C22×C1111yescharacteristic
160#407—21no—
161#407—21no—
162#398C4×C1111yescharacteristic
163#398C22×C1111yescharacteristic
164#396—21no—
165#396—21no—
166#394C4×C1111yescharacteristic
167#394C22×C1111yescharacteristic
168#386—21no—
169#380C4×C1111yescharacteristic
170#343—21no—
171#343C22×C1112yes—
172#324—21no—
173#324C22×C1112yes—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11C2×#9911yescharacteristic
192C22×C11#41811yescharacteristic
193C22×C11#42111yescharacteristic
194C4×C11—22no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11—81no—
203C22×D4—21no—
204C22×D4C2×C4×C1111yescharacteristic
205C23×C4C2×C4×C1111yescharacteristic
206C23×C4D4×C1111yescharacteristic
207C23×C4D4×C1111yescharacteristic
208C2×M16—22no—
209C2×M16—41no—
210#123—44no—
211#121—41no—
212#121—41no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4C2×C4×C1111yescharacteristic
219C2×C4⋊C4C2×C4×C1111yescharacteristic
220C2×C4⋊C4D4×C1111yescharacteristic
221C2×C4⋊C4D4×C1111yescharacteristic
222C2×C4⋊C4C23×C1111yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C22⋊C8—22no—
230C22⋊C8—41no—
231C22⋊C8—41no—
232C22⋊C8—41no—
233#95—21no—
234#95—21no—
235#95C2×C4×C1111yescharacteristic
236#95C2×C4×C1111yescharacteristic
237C2×C11—21no—
238C2×C11—21no—
239C2×C11—41no—
240C2×C11—41no—
241C2×C11—161no—
242C2×C11#151011yescharacteristic
243C2×C11#212111yescharacteristic
244C2×C11#213311yescharacteristic
245C24—21no—
246C24C11×C22⋊C411yescharacteristic
247C2×D4—41no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—81no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—81no—
265C22×C4—81no—
266C22×C4C11×C22⋊C411yescharacteristic
267C22×C4C11×C22⋊C411yescharacteristic
268C22×C4C11×C22⋊C411yescharacteristic
269C22×C4C22×C4×C1111yescharacteristic
270C22×C4C2×D4×C1111yescharacteristic
271C22×C4C2×D4×C1111yescharacteristic
272M16—42no—
273M16—42no—
274M16—82no—
275C2×C8—42no—
276C2×C8—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—81no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C11#1180511yescharacteristic, direct product factor, Sylow
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23C11×#9911yescharacteristic
304C23C11×#9911yescharacteristic
305C23C2×C11×C22⋊C411yescharacteristic
306D4—82no—
307D4—82no—
308D4—82no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4C11×AGL(1,ℤ/8)12yes—
338C8—82no—
339C8—82no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C2×C11×#9911yescharacteristic
358C22C11×#41811yescharacteristic
359C22C11×#42111yescharacteristic
360C4—22no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—81no—
367C4—81no—
368C4—81no—
369C2—21no—
370C2—21no—
371C2—41no—
372C2—41no—
373C2—161no—
374C2C11×#151011yescharacteristic
375C2C11×#212111yescharacteristic
376C2C11×#213311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC2×C11×#121C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1821C2semidirect
3. C11×#1463C2semidirect
4. C11×#1346C2semidirect
5. C11×#1345C2semidirect
57. #11805C11direct (N × H)
105. #1821C2×C11semidirect
106. #1463C2×C11semidirect
107. #1346C2×C11semidirect
108. #1345C2×C11semidirect
291. C11#11805direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26182
C11×#18212
C11×#14632
C11×#13462
C11×#13452
#1180511