Finite Group Databasebeta

← C11×#10505 #14587698

Subgroups — C11×#10505 #14587698

Order 2816.

402 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3209C211yesmaximal, characteristic
2C11×#1997C211yesmaximal, characteristic
3C11×#1986C211yesmaximal, characteristic
4C11×#1981C211yesmaximal, characteristic
5C11×#1565C211yesmaximal, characteristic
6C11×#1550C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#494—21no—
11C11×#487—21no—
12C11×#462—21no—
13C11×#462—21no—
14C11×#451—22no—
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#103—22no—
19C4×C11×M16C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C11×#343—21no—
22C11×#343—21no—
23C11×#339—21no—
24C11×#339—21no—
25C11×#335—21no—
26C11×#334—21no—
27C11×#333—21no—
28C11×#332—21no—
29C22×Q8×C11D412yes—
30C2×C11×Q16—22no—
31C2×C11×Q16—22no—
32C2×C11×M16—21no—
33C2×C11×M16D411yescharacteristic
34C2×C11×M16D411yescharacteristic
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C11×#117—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D411yescharacteristic
58C11×C4⋊C8D411yescharacteristic
59C11×#103—22no—
60C11×#103—22no—
61C11×#103—44no—
62C11×C22⋊C8—21no—
63C11×#97—21no—
64C4×C8×C11—21no—
65C4×C8×C11—21no—
66C11×#95—21no—
67#10505C1111yesmaximal, characteristic, direct product factor, Sylow
68C2×Q8×C11—22no—
69C2×Q8×C11—21no—
70C2×Q8×C11—22no—
71C2×Q8×C11—21no—
72C2×Q8×C11—42no—
73C2×Q8×C11—42no—
74C22×C4×C11—22no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C11×Q16—82no—
80C11×Q16—82no—
81C11×M16—21no—
82C11×M16—21no—
83C11×M16—21no—
84C11×M16—41no—
85C11×M16—41no—
86C11×M16Q1612yescomplemented
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—42no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114#3209C2×C1111yescharacteristic
115#1997C2×C1111yescharacteristic
116#1986C2×C1111yescharacteristic
117#1981C2×C1111yescharacteristic
118#1565C2×C1111yescharacteristic
119#1550C2×C1111yescharacteristic
120#1303C2×C1111yescharacteristic
121C23×C11#12111yescharacteristic
122Q8×C11—44no—
123Q8×C11—41no—
124Q8×C11—42no—
125Q8×C11—41no—
126Q8×C11—42no—
127Q8×C11—81no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—82no—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11#12411yescharacteristic
144C2×C4×C11C2×Q1611yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C8×C11—22no—
149C8×C11—41no—
150C8×C11—41no—
151C8×C11—41no—
152C8×C11—81no—
153C8×C11—81no—
154#533C22×C1111yescharacteristic
155C2×C4⋊Q8C22×C1111yescharacteristic
156#494—21no—
157#487—21no—
158#462—21no—
159#462—21no—
160#451—22no—
161#431C22×C1111yescharacteristic
162#423C22×C1111yescharacteristic
163C2×C4⋊C8C22×C1111yescharacteristic
164C2×#103—22no—
165C4×M16C22×C1111yescharacteristic
166C4×C4⋊C4C22×C1111yescharacteristic
167#343—21no—
168#343—21no—
169#339—21no—
170#339—21no—
171#335—21no—
172#334—21no—
173#333—21no—
174#332—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#39411yescharacteristic
178C22×C11#46211yescharacteristic
179C22×C11#46411yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—82no—
184C4×C11—81no—
185C4×C11—82no—
186C4×C11—81no—
187C4×C11#45311yescharacteristic
188C4×C11#45511yescharacteristic
189C4×C11#46211yescharacteristic
190C4×C11#46411yescharacteristic
191C4×C11#46711yescharacteristic
192C4×C11#47011yescharacteristic
193C22×Q8D4×C1112yes—
194C2×Q16—22no—
195C2×Q16—22no—
196C2×M16—21no—
197C2×M16D4×C1111yescharacteristic
198C2×M16D4×C1111yescharacteristic
199C22×C8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8D4×C1111yescharacteristic
205C4⋊Q8D4×C1111yescharacteristic
206#125—21no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211#117—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C42—21no—
216C2×C42C23×C1111yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8D4×C1111yescharacteristic
222C4⋊C8D4×C1111yescharacteristic
223#103—22no—
224#103—22no—
225#103—44no—
226C22⋊C8—21no—
227#97—21no—
228C4×C8—21no—
229C4×C8—21no—
230#95—21no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#203711yescharacteristic
234C2×C11#204911yescharacteristic
235C2×C11#205611yescharacteristic
236C2×Q8—22no—
237C2×Q8—21no—
238C2×Q8—22no—
239C2×Q8—21no—
240C2×Q8—42no—
241C2×Q8—42no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4C2×D4×C1111yescharacteristic
245C22×C4C2×D4×C1111yescharacteristic
246C22×C4C11×#4111yescharacteristic
247Q16—82no—
248Q16—82no—
249M16—21no—
250M16—21no—
251M16—21no—
252M16—41no—
253M16—41no—
254M16C11×Q1612yescomplemented
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—42no—
260C2×C8—41no—
261C2×C8—41no—
262C4⋊C4—22no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—41no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42C2×D4×C1111yescharacteristic
279C42C2×D4×C1111yescharacteristic
280C42C11×#4111yescharacteristic
281C42C11×#4111yescharacteristic
282C11#1050511yescharacteristic, direct product factor, Sylow
283C23C11×#12111yescharacteristic
284Q8—44no—
285Q8—41no—
286Q8—42no—
287Q8—41no—
288Q8—42no—
289Q8—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4C11×#12011yescharacteristic
301C2×C4C11×#12111yescharacteristic
302C2×C4C11×#12111yescharacteristic
303C2×C4C11×#12311yescharacteristic
304C2×C4C11×#12311yescharacteristic
305C2×C4C11×#12411yescharacteristic
306C2×C4C2×C11×Q1611yescharacteristic
307C2×C4C11×#13511yescharacteristic
308C2×C4C11×#13711yescharacteristic
309C2×C4C11×#13711yescharacteristic
310C8—22no—
311C8—41no—
312C8—41no—
313C8—41no—
314C8—81no—
315C8—81no—
316C22—21no—
317C22—21no—
318C22C11×#39411yescharacteristic
319C22C11×#46211yescharacteristic
320C22C11×#46411yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—82no—
325C4—82no—
326C4—81no—
327C4—81no—
328C4C11×#45311yescharacteristic
329C4C11×#45511yescharacteristic
330C4C11×#46211yescharacteristic
331C4C11×#46411yescharacteristic
332C4C11×#46711yescharacteristic
333C4C11×#47011yescharacteristic
334C2—21no—
335C2—21no—
336C2C11×#203711yescharacteristic
337C2C11×#204911yescharacteristic
338C2C11×#205611yescharacteristic
subgroupG/H
center, socleC22×C11#394
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
67. #10505C11direct (N × H)
86. C11×M16Q16semidirect
254. M16C11×Q16semidirect
282. C11#10505direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32092
C11×#19972
C11×#19862
C11×#19812
C11×#15652
C11×#15502
C11×#13032
#1050511