Finite Group Databasebeta

← C11×#12201 #14589394

Subgroups — C11×#12201 #14589394

Order 2816.

380 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2833C211yesmaximal, characteristic, complemented
2C11×#2007C211yesmaximal, characteristic
3C11×#1616C211yesmaximal, characteristic
4C11×#1610C211yesmaximal, characteristic
5C11×#1353C211yesmaximal, characteristic, complemented
6C11×#1346C211yesmaximal, characteristic, complemented
7C11×#1319C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#537C2211yescharacteristic
10C11×#481—21no—
11C11×#480—21no—
12C2×C11×#104—21no—
13C11×#401—21no—
14C11×#400—21no—
15C11×#400—21no—
16C11×#400C2211yescharacteristic
17C11×#398—21no—
18C11×#398C2211yescharacteristic
19C11×#395—21no—
20C11×#391C2211yescharacteristic
21C11×#387—21no—
22C11×#343C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#324C2211yescharacteristic
26C11×#324C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Q8×C11D411yescharacteristic
29C11×#137—42no—
30C11×#137—42no—
31C2×C11×Q16—41no—
32C2×C11×SD16—41no—
33C2×C11×M16—21no—
34C11×C22⋊Q8—41no—
35C11×#121—21no—
36C11×#121—21no—
37C11×#121—41no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4C2311yescharacteristic
45C2×C42×C11D411yescharacteristic
46C11×#107—41no—
47C11×#106—41no—
48C11×#104—42no—
49C11×#102—41no—
50C11×#102—41no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65#12201C1111yesmaximal, characteristic, direct product factor, Sylow
66C11×#41—41no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C11×Q16—44no—
90C11×SD16—44no—
91C11×M16—22no—
92C11×M16—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—81no—
104C11×C4⋊C4—81no—
105C11×C4⋊C4—81no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11—41no—
109#2833C2×C1111yescharacteristic, complemented
110#2007C2×C1111yescharacteristic
111#1616C2×C1111yescharacteristic
112#1610C2×C1111yescharacteristic
113#1353C2×C1111yescharacteristic, complemented
114#1346C2×C1111yescharacteristic, complemented
115#1319C2×C1111yescharacteristic, complemented
116C23×C11—41no—
117C23×C11#12011yescharacteristic
118Q8×C11—42no—
119Q8×C11—41no—
120Q8×C11—41no—
121Q8×C11—81no—
122D4×C11—41no—
123D4×C11—41no—
124D4×C11—81no—
125D4×C11—81no—
126D4×C11—81no—
127D4×C11—81no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
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—42no—
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—41no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C8×C11—42no—
157C8×C11—81no—
158C8×C11—81no—
159C2×#137—21no—
160#537C22×C1111yescharacteristic
161#481—21no—
162#480—21no—
163C2×#104—21no—
164#401—21no—
165#400—21no—
166#400—21no—
167#400C22×C1111yescharacteristic
168#398—21no—
169#398C22×C1111yescharacteristic
170#395—21no—
171#391C22×C1111yescharacteristic
172#387—21no—
173#343C22×C1111yescharacteristic
174#327—21no—
175#327—21no—
176#324C22×C1111yescharacteristic
177#324C22×C1111yescharacteristic
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11#44911yescharacteristic
184C22×C11#45311yescharacteristic
185C22×C11B(4,𝔽2)11yescharacteristic
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197C2×#41—21no—
198C22×Q8D4×C1111yescharacteristic
199#137—42no—
200#137—42no—
201C2×Q16—41no—
202C2×SD16—41no—
203C2×M16—21no—
204C22⋊Q8—41no—
205#121—21no—
206#121—21no—
207#121—41no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4D4×C1111yescharacteristic
213C2×C4⋊C4D4×C1111yescharacteristic
214C2×C4⋊C4C23×C1111yescharacteristic
215C2×C42D4×C1111yescharacteristic
216#107—41no—
217#106—41no—
218#104—42no—
219#102—41no—
220#102—41no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95D4×C1111yescharacteristic
234#95D4×C1111yescharacteristic
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—161no—
238C2×C11#160011yescharacteristic
239C2×C11#220111yescharacteristic
240C2×C11#220311yescharacteristic
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4C2×D4×C1111yescharacteristic
262C22×C4C2×D4×C1111yescharacteristic
263C22×C4C2×D4×C1111yescharacteristic
264Q16—44no—
265SD16—44no—
266M16—22no—
267M16—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C4⋊C4—81no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—41no—
284C11#1220111yescharacteristic, direct product factor, Sylow
285C23—41no—
286C23C11×#12011yescharacteristic
287Q8—42no—
288Q8—41no—
289Q8—41no—
290Q8—81no—
291D4—41no—
292D4—41no—
293D4—81no—
294D4—81no—
295D4—81no—
296D4—81no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
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—42no—
310C2×C4—41no—
311C2×C4—41no—
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—81no—
322C2×C4—81no—
323C2×C4C11×#13511yescharacteristic
324C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
325C8—42no—
326C8—81no—
327C8—81no—
328C22—21no—
329C22—21no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22C11×#44911yescharacteristic
334C22C11×#45311yescharacteristic
335C22C11×B(4,𝔽2)11yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C2—21no—
348C2—21no—
349C2—161no—
350C2C11×#160011yescharacteristic
351C2C11×#220111yescharacteristic
352C2C11×#220311yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC11×#537C22
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2833C2semidirect
5. C11×#1353C2semidirect
6. C11×#1346C2semidirect
7. C11×#1319C2semidirect
65. #12201C11direct (N × H)
109. #2833C2×C11semidirect
113. #1353C2×C11semidirect
114. #1346C2×C11semidirect
115. #1319C2×C11semidirect
284. C11#12201direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28332
C11×#20072
C11×#16162
C11×#16102
C11×#13532
C11×#13462
C11×#13192
#1220111