Finite Group Databasebeta

← C11×#7818 #14585011

Subgroups — C11×#7818 #14585011

Order 2816.

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

normal subgroups only

This group has 350 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×#2099C211yesmaximal, characteristic
3C11×#2084C211yesmaximal, characteristic
4C11×#2072C211yesmaximal, characteristic
5C11×#1272C211yesmaximal, characteristic
6C11×#1271C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C2×C11×#106—21no—
9C2×C11×#103—21no—
10C11×#400—21no—
11C11×#400—21no—
12C11×#395—21no—
13C11×#391C2211yescharacteristic
14C11×#389—21no—
15C11×#389C2211yescharacteristic
16C11×#389C2211yescharacteristic
17C11×#387—21no—
18C11×#387—21no—
19C11×#384C2211yescharacteristic
20C11×#340—21no—
21C11×#340—21no—
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×#106—42no—
46C11×#103—42no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56#7818C1111yesmaximal, characteristic, direct product factor, Sylow
57C2×Q8×C11—21no—
58C2×Q8×C11—21no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C2×C8×C11—22no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—42no—
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—81no—
96C11×C4⋊C4—81no—
97C11×C4⋊C4SD1612yes—
98C42×C11—41no—
99C42×C11—81no—
100#2805C2×C1111yescharacteristic
101#2099C2×C1111yescharacteristic
102#2084C2×C1111yescharacteristic
103#2072C2×C1111yescharacteristic
104#1272C2×C1111yescharacteristic
105#1271C2×C1111yescharacteristic
106#1271C2×C1111yescharacteristic
107C23×C11#12011yescharacteristic
108Q8×C11—42no—
109Q8×C11—81no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
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—81no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C8×C11—42no—
144C8×C11—81no—
145C8×C11—81no—
146C2×#106—21no—
147C2×#103—21no—
148#400—21no—
149#400—21no—
150#395—21no—
151#391C22×C1111yescharacteristic
152#389—21no—
153#389C22×C1111yescharacteristic
154#389C22×C1111yescharacteristic
155#387—21no—
156#387—21no—
157#384C22×C1111yescharacteristic
158#340—21no—
159#340—21no—
160#340—21no—
161#340—21no—
162#336C22×C1111yescharacteristic
163#336C22×C1111yescharacteristic
164#336C22×C1111yescharacteristic
165C22×C11#44811yescharacteristic
166C22×C11#44911yescharacteristic
167C22×C11#45211yescharacteristic
168C22×C11#45411yescharacteristic
169C22×C11#45511yescharacteristic
170C22×C11#45611yescharacteristic
171C22×C11#45811yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—42no—
179C4×C11—81no—
180C4×C11—81no—
181C4×C11—81no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—161no—
185C22×Q8D4×C1111yescharacteristic
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4D4×C1111yescharacteristic
197C2×C4⋊C4D4×C1111yescharacteristic
198C2×C4⋊C4D4×C1111yescharacteristic
199C2×C4⋊C4D4×C1111yescharacteristic
200C2×C4⋊C4D4×C1111yescharacteristic
201C2×C42—21no—
202C2×C42C23×C1111yescharacteristic
203#106—42no—
204#103—42no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214C2×C11#161111yescharacteristic
215C2×C11#161211yescharacteristic
216C2×C11#161511yescharacteristic
217C2×C11#162611yescharacteristic
218C2×C11#164311yescharacteristic
219C2×C11#165211yescharacteristic
220C2×C11#166411yescharacteristic
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—41no—
224C2×Q8—41no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4C2×D4×C1111yescharacteristic
233C22×C4C2×D4×C1111yescharacteristic
234C22×C4C2×D4×C1111yescharacteristic
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C4⋊C4C11×SD1612yes—
262C42—41no—
263C42—81no—
264C11#781811yescharacteristic, direct product factor, Sylow
265C23C11×#12011yescharacteristic
266Q8—42no—
267Q8—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
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—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4C2×C11×SD1611yescharacteristic
296C2×C4C11×#13511yescharacteristic
297C2×C4C11×#13511yescharacteristic
298C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
299C2×C4C11×#13711yescharacteristic
300C2×C4C11×#13711yescharacteristic
301C8—42no—
302C8—81no—
303C8—81no—
304C22C11×#44811yescharacteristic
305C22C11×#44911yescharacteristic
306C22C11×#45211yescharacteristic
307C22C11×#45411yescharacteristic
308C22C11×#45511yescharacteristic
309C22C11×#45611yescharacteristic
310C22C11×#45811yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—161no—
324C2C11×#161111yescharacteristic
325C2C11×#161211yescharacteristic
326C2C11×#161511yescharacteristic
327C2C11×#162611yescharacteristic
328C2C11×#164311yescharacteristic
329C2C11×#165211yescharacteristic
330C2C11×#166411yescharacteristic
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
56. #7818C11direct (N × H)
264. C11#7818direct (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×#20992
C11×#20842
C11×#20722
C11×#12722
C11×#12712
#781811