Finite Group Databasebeta

← C11×#10469 #14587662

Subgroups — C11×#10469 #14587662

Order 2816.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3077C211yesmaximal, characteristic
2C11×#1804C211yesmaximal, characteristic
3C11×#1571C211yesmaximal, characteristic, complemented
4C11×#1542C211yesmaximal, characteristic, complemented
5C11×#1518C211yesmaximal, characteristic, complemented
6C11×#1460C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C11×#478—22no—
11C11×#476—21no—
12C11×#474—21no—
13C11×#431C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#428—21no—
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C11×#418—21no—
19C2×C11×#102—21no—
20C11×#382C2211yescharacteristic
21C11×#340—21no—
22C11×#335—22no—
23C11×#333—21no—
24C11×#332—21no—
25C11×#328—22no—
26C11×#323—22no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11—21no—
29C2×C11×M16—21no—
30C22×C8×C11—21no—
31C11×C4⋊Q8D411yescharacteristic
32C11×C4⋊Q8D411yescharacteristic
33C11×#125—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C11×#117—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C11×#107—22no—
48C11×#106—22no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8D412yes—
55C11×#102—22no—
56C11×#102—22no—
57C11×#102—42no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8D412yes—
60C4×C8×C11—21no—
61C4×C8×C11—21no—
62C11×#95—21no—
63C11×#95—21no—
64#10469C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11Q1612yes—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—82no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C11×M16—41no—
83C11×M16—41no—
84C2×C8×C11—22no—
85C2×C8×C11—22no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108#3077C2×C1111yescharacteristic
109#1804C2×C1111yescharacteristic
110#1571C2×C1111yescharacteristic, complemented
111#1542C2×C1111yescharacteristic, complemented
112#1518C2×C1111yescharacteristic, complemented
113#1460C2×C1111yescharacteristic
114#1286C2×C1111yescharacteristic, complemented
115C23×C11—22no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—81no—
119C23×C11—81no—
120C23×C11#12111yescharacteristic
121Q8×C11—81no—
122Q8×C11—81no—
123D4×C11—22no—
124D4×C11—22no—
125D4×C11—41no—
126D4×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—82no—
133C2×C4×C11—82no—
134C2×C4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
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×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C8×C11—42no—
149C8×C11—42no—
150C8×C11—81no—
151C8×C11—81no—
152#533C22×C1111yescharacteristic
153C2×C4×D4C22×C1111yescharacteristic
154#478—22no—
155#476—21no—
156#474—21no—
157#431C22×C1111yescharacteristic
158#431C22×C1111yescharacteristic
159#428—21no—
160#423C22×C1111yescharacteristic
161C2×C4⋊C8C22×C1111yescharacteristic
162#418—21no—
163C2×#102—21no—
164#382C22×C1111yescharacteristic
165#340—21no—
166#335—22no—
167#333—21no—
168#332—21no—
169#328—22no—
170#323—22no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—42no—
174C22×C11—82no—
175C22×C11—82no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11#39411yescharacteristic
179C22×C11#46711yescharacteristic
180C22×C11#46811yescharacteristic
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11—161no—
189C4×C11#44911yescharacteristic
190C4×C11#45111yescharacteristic
191C4×C11#48411yescharacteristic
192C4×C11#48511yescharacteristic
193C22×D4D4×C1111yescharacteristic
194C23×C4—21no—
195C2×M16—21no—
196C22×C8—21no—
197C4⋊Q8D4×C1111yescharacteristic
198C4⋊Q8D4×C1111yescharacteristic
199#125—21no—
200C22⋊Q8—21no—
201C22⋊Q8—21no—
202C4×Q8—21no—
203C4×Q8—21no—
204C4×D4—21no—
205C4×D4—21no—
206C4×D4—21no—
207C4×D4—21no—
208#117—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4D4×C1111yescharacteristic
211C2×C22⋊C4—21no—
212C2×C42C23×C1111yescharacteristic
213#107—22no—
214#106—22no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8D4×C1112yes—
221#102—22no—
222#102—22no—
223#102—42no—
224C22⋊C8—21no—
225C22⋊C8D4×C1112yes—
226C4×C8—21no—
227C4×C8—21no—
228#95—21no—
229#95—21no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—82no—
233C2×C11#203611yescharacteristic
234C2×C11#204811yescharacteristic
235C2×C11#205311yescharacteristic
236C24—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4C11×Q1612yes—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—82no—
250C22×C4C2×D4×C1111yescharacteristic
251C22×C4C2×D4×C1111yescharacteristic
252C22×C4C11×#4111yescharacteristic
253M16—41no—
254M16—41no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42—41no—
275C42C2×D4×C1111yescharacteristic
276C42C2×D4×C1111yescharacteristic
277C42C11×#4111yescharacteristic
278C42C11×#4111yescharacteristic
279C11#1046911yescharacteristic, direct product factor, Sylow
280C23—22no—
281C23—41no—
282C23—41no—
283C23—81no—
284C23—81no—
285C23C11×#12111yescharacteristic
286Q8—81no—
287Q8—81no—
288D4—22no—
289D4—22no—
290D4—41no—
291D4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4C11×#12011yescharacteristic
304C2×C4C11×#12111yescharacteristic
305C2×C4C11×#12111yescharacteristic
306C2×C4C11×#12311yescharacteristic
307C2×C4C11×#12311yescharacteristic
308C2×C4C11×#12411yescharacteristic
309C2×C4C2×C11×Q1611yescharacteristic
310C2×C4C11×#13511yescharacteristic
311C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
312C2×C4C11×#13711yescharacteristic
313C8—42no—
314C8—42no—
315C8—81no—
316C8—81no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—82no—
321C22—82no—
322C22—81no—
323C22—81no—
324C22C11×#39411yescharacteristic
325C22C11×#46711yescharacteristic
326C22C11×#46811yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—161no—
335C4C11×#44911yescharacteristic
336C4C11×#45111yescharacteristic
337C4C11×#48411yescharacteristic
338C4C11×#48511yescharacteristic
339C2—21no—
340C2—21no—
341C2—82no—
342C2C11×#203611yescharacteristic
343C2C11×#204811yescharacteristic
344C2C11×#205311yescharacteristic
subgroupG/H
center, socleC22×C11#394
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
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
3. C11×#1571C2semidirect
4. C11×#1542C2semidirect
5. C11×#1518C2semidirect
7. C11×#1286C2semidirect
64. #10469C11direct (N × H)
110. #1571C2×C11semidirect
111. #1542C2×C11semidirect
112. #1518C2×C11semidirect
114. #1286C2×C11semidirect
279. C11#10469direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30772
C11×#18042
C11×#15712
C11×#15422
C11×#15182
C11×#14602
C11×#12862
#1046911