Finite Group Databasebeta

← C11×#7807 #14585000

Subgroups — C11×#7807 #14585000

Order 2816.

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

normal subgroups only

This group has 366 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×#2805C211yesmaximal, characteristic
2C11×#2096C211yesmaximal, characteristic
3C11×#2084C211yesmaximal, characteristic
4C11×#2083C211yesmaximal, characteristic
5C11×#1272C211yesmaximal, characteristic
6C11×#1271C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C2×C11×#107—21no—
9C2×C11×#106—21no—
10C2×C11×#106—21no—
11C2×C11×#103—21no—
12C11×#400—21no—
13C11×#400—21no—
14C11×#395—21no—
15C11×#391C2211yescharacteristic
16C11×#389—21no—
17C11×#389C2211yescharacteristic
18C11×#389C2211yescharacteristic
19C11×#387—21no—
20C11×#387—21no—
21C11×#384C2211yescharacteristic
22C11×#340—21no—
23C11×#340—21no—
24C11×#336C2211yescharacteristic
25C11×#336C2211yescharacteristic
26C11×#336C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45C11×#107—42no—
46C11×#106—42no—
47C11×#106—42no—
48C11×#103—42no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58#7807C1111yesmaximal, characteristic, direct product factor, Sylow
59C2×Q8×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C8×C11—22no—
74C2×C8×C11—22no—
75C2×C8×C11—22no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—81no—
99C11×C4⋊C4—81no—
100C11×C4⋊C4SD1612yes—
101C42×C11—41no—
102C42×C11—81no—
103#2805C2×C1111yescharacteristic
104#2096C2×C1111yescharacteristic
105#2084C2×C1111yescharacteristic
106#2083C2×C1111yescharacteristic
107#1272C2×C1111yescharacteristic
108#1271C2×C1111yescharacteristic
109#1271C2×C1111yescharacteristic
110C23×C11#12011yescharacteristic
111Q8×C11—42no—
112Q8×C11—81no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
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—81no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11#13711yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C8×C11—42no—
147C8×C11—42no—
148C8×C11—42no—
149C2×#107—21no—
150C2×#106—21no—
151C2×#106—21no—
152C2×#103—21no—
153#400—21no—
154#400—21no—
155#395—21no—
156#391C22×C1111yescharacteristic
157#389—21no—
158#389C22×C1111yescharacteristic
159#389C22×C1111yescharacteristic
160#387—21no—
161#387—21no—
162#384C22×C1111yescharacteristic
163#340—21no—
164#340—21no—
165#336C22×C1111yescharacteristic
166#336C22×C1111yescharacteristic
167#336C22×C1111yescharacteristic
168C22×C11#44811yescharacteristic
169C22×C11#44911yescharacteristic
170C22×C11#45211yescharacteristic
171C22×C11#45311yescharacteristic
172C22×C11#45611yescharacteristic
173C22×C11#45611yescharacteristic
174C22×C11#45811yescharacteristic
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—42no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11—161no—
188C22×Q8D4×C1111yescharacteristic
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4D4×C1111yescharacteristic
200C2×C4⋊C4D4×C1111yescharacteristic
201C2×C4⋊C4D4×C1111yescharacteristic
202C2×C4⋊C4D4×C1111yescharacteristic
203C2×C4⋊C4D4×C1111yescharacteristic
204C2×C42—21no—
205C2×C42C23×C1111yescharacteristic
206#107—42no—
207#106—42no—
208#106—42no—
209#103—42no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219C2×C11#160911yescharacteristic
220C2×C11#161111yescharacteristic
221C2×C11#161811yescharacteristic
222C2×C11#162211yescharacteristic
223C2×C11#165011yescharacteristic
224C2×C11#165311yescharacteristic
225C2×C11#166011yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—41no—
229C2×Q8—41no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4C2×D4×C1111yescharacteristic
238C22×C4C2×D4×C1111yescharacteristic
239C22×C4C2×D4×C1111yescharacteristic
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4C11×SD1612yes—
268C42—41no—
269C42—81no—
270C11#780711yescharacteristic, direct product factor, Sylow
271C23C11×#12011yescharacteristic
272Q8—42no—
273Q8—81no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4C2×C11×SD1611yescharacteristic
302C2×C4C11×#13511yescharacteristic
303C2×C4C11×#13511yescharacteristic
304C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
305C2×C4C11×#13711yescharacteristic
306C2×C4C11×#13711yescharacteristic
307C8—42no—
308C8—42no—
309C8—42no—
310C22C11×#44811yescharacteristic
311C22C11×#44911yescharacteristic
312C22C11×#45211yescharacteristic
313C22C11×#45311yescharacteristic
314C22C11×#45611yescharacteristic
315C22C11×#45611yescharacteristic
316C22C11×#45811yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—81no—
329C4—161no—
330C2C11×#160911yescharacteristic
331C2C11×#161111yescharacteristic
332C2C11×#161811yescharacteristic
333C2C11×#162211yescharacteristic
334C2C11×#165011yescharacteristic
335C2C11×#165311yescharacteristic
336C2C11×#166011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
58. #7807C11direct (N × H)
270. C11#7807direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28052
C11×#20962
C11×#20842
C11×#20832
C11×#12722
C11×#12712
#780711