Finite Group Databasebeta

← C11×#10463 #14587656

Subgroups — C11×#10463 #14587656

Order 2816.

374 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×#3078C211yesmaximal, characteristic
2C11×#1801C211yesmaximal, characteristic
3C11×#1567C211yesmaximal, characteristic
4C11×#1550C211yesmaximal, characteristic
5C11×#1493C211yesmaximal, characteristic
6C2×C11×Q8⋊C8C211yesmaximal, characteristic
7C11×#1292C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C11×#479—22no—
11C11×#477—21no—
12C11×#475—21no—
13C11×#428—21no—
14C11×#423C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C11×#419—21no—
19C2×C11×#101—21no—
20C2×C4×C8×C11C2211yescharacteristic
21C11×#343—21no—
22C11×#335—22no—
23C11×#333—21no—
24C11×#332—21no—
25C11×Q8⋊C8—21no—
26C11×Q8⋊C8—21no—
27C11×Q8⋊C8—21no—
28C11×Q8⋊C8—21no—
29C22×Q8×C11D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×M16—21no—
32C2×C11×M16—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C11×#117—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C11×#107—22no—
52C11×#106—22no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×#103—22no—
62C11×#103—22no—
63C11×#101—42no—
64C4×C8×C11—21no—
65C4×C8×C11D411yescharacteristic
66C4×C8×C11D411yescharacteristic
67#10463C1111yesmaximal, characteristic, direct product factor, Sylow
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11Q1612yes—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C11×M16—41no—
82C11×M16—41no—
83C11×M16—41no—
84C11×M16—41no—
85C11×M16—41no—
86C11×M16—41no—
87C2×C8×C11—22no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—42no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—81no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113#3078C2×C1111yescharacteristic
114#1801C2×C1111yescharacteristic
115#1567C2×C1111yescharacteristic
116#1550C2×C1111yescharacteristic
117#1493C2×C1111yescharacteristic
118C2×Q8⋊C8C2×C1111yescharacteristic
119#1292C2×C1111yescharacteristic
120C23×C11#12311yescharacteristic
121Q8×C11—22no—
122Q8×C11—22no—
123Q8×C11—41no—
124Q8×C11—41no—
125Q8×C11—41no—
126Q8×C11—41no—
127Q8×C11—81no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
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#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11#12411yescharacteristic
144C2×C4×C11C2×Q1611yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C8×C11—22no—
149C8×C11—41no—
150C8×C11—42no—
151C8×C11—81no—
152C8×C11—81no—
153C8×C11—81no—
154#533C22×C1111yescharacteristic
155C2×C4×Q8C22×C1111yescharacteristic
156#479—22no—
157#477—21no—
158#475—21no—
159#428—21no—
160#423C22×C1111yescharacteristic
161#423C22×C1111yescharacteristic
162#423C22×C1111yescharacteristic
163C2×C4⋊C8C22×C1111yescharacteristic
164#419—21no—
165C2×#101—21no—
166C2×C4×C8C22×C1111yescharacteristic
167#343—21no—
168#335—22no—
169#333—21no—
170#332—21no—
171Q8⋊C8—21no—
172Q8⋊C8—21no—
173Q8⋊C8—21no—
174Q8⋊C8—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#39411yescharacteristic
178C22×C11#48411yescharacteristic
179C22×C11#48511yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—42no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11#44911yescharacteristic
188C4×C11#45111yescharacteristic
189C4×C11#46711yescharacteristic
190C4×C11#46811yescharacteristic
191C4×C11#47111yescharacteristic
192C4×C11#47311yescharacteristic
193C22×Q8D4×C1111yescharacteristic
194C2×M16—21no—
195C2×M16—21no—
196C2×M16—21no—
197C22×C8—21no—
198C22×C8—21no—
199C4⋊Q8D4×C1111yescharacteristic
200C4⋊Q8D4×C1111yescharacteristic
201#125—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210#117—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4D4×C1111yescharacteristic
213C2×C42—21no—
214C2×C42C23×C1111yescharacteristic
215#107—22no—
216#106—22no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8D4×C1112yes—
225#103—22no—
226#103—22no—
227#101—42no—
228C4×C8—21no—
229C4×C8D4×C1111yescharacteristic
230C4×C8D4×C1111yescharacteristic
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#203611yescharacteristic
234C2×C11#205011yescharacteristic
235C2×C11#205211yescharacteristic
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8C11×Q1612yes—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4C2×D4×C1111yescharacteristic
247C22×C4C11×#4111yescharacteristic
248C22×C4C11×#4111yescharacteristic
249M16—41no—
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—41no—
255C2×C8—21no—
256C2×C8—22no—
257C2×C8—21no—
258C2×C8—42no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—81no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C22⋊C4—41no—
274C42—41no—
275C42—41no—
276C42—41no—
277C42C2×D4×C1111yescharacteristic
278C42C2×D4×C1111yescharacteristic
279C42C2×D4×C1111yescharacteristic
280C42C11×#4111yescharacteristic
281C11#1046311yescharacteristic, direct product factor, Sylow
282C23C11×#12311yescharacteristic
283Q8—22no—
284Q8—22no—
285Q8—41no—
286Q8—41no—
287Q8—41no—
288Q8—41no—
289Q8—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4C11×#12011yescharacteristic
301C2×C4C11×#12111yescharacteristic
302C2×C4C11×#12111yescharacteristic
303C2×C4C11×#12111yescharacteristic
304C2×C4C11×#12311yescharacteristic
305C2×C4C11×#12411yescharacteristic
306C2×C4C2×C11×Q1611yescharacteristic
307C2×C4C11×#13511yescharacteristic
308C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
309C2×C4C11×#13711yescharacteristic
310C8—22no—
311C8—41no—
312C8—42no—
313C8—81no—
314C8—81no—
315C8—81no—
316C22—21no—
317C22—21no—
318C22C11×#39411yescharacteristic
319C22C11×#48411yescharacteristic
320C22C11×#48511yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4C11×#44911yescharacteristic
329C4C11×#45111yescharacteristic
330C4C11×#46711yescharacteristic
331C4C11×#46811yescharacteristic
332C4C11×#47111yescharacteristic
333C4C11×#47311yescharacteristic
334C2—21no—
335C2—21no—
336C2C11×#203611yescharacteristic
337C2C11×#205011yescharacteristic
338C2C11×#205211yescharacteristic
subgroupG/H
center, socleC22×C11#394
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#123
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. #10463C11direct (N × H)
281. C11#10463direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30782
C11×#18012
C11×#15672
C11×#15502
C11×#14932
C2×C11×Q8⋊C82
C11×#12922
#1046311