Finite Group Databasebeta

← C11×#10162 #14587355

Subgroups — C11×#10162 #14587355

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3206C211yesmaximal, characteristic
2C11×#3141C211yesmaximal, characteristic
3C2×C11×#487C211yesmaximal, characteristic, complemented
4C11×#1997C211yesmaximal, characteristic, complemented
5C11×#1548C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C11×#492—21no—
12C11×#489—22no—
13C11×#487—21no—
14C11×#487—22no—
15C11×#487—21no—
16C11×#487—22no—
17C11×#486—21no—
18C11×#461—22no—
19C11×#448—22no—
20C11×#431C2211yescharacteristic
21C11×#423C2211yescharacteristic
22C11×#417—22no—
23C2×C11×#103—22no—
24C4×C11×M16C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#343—22no—
27C11×#333—22no—
28C11×D4⋊C8—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11D412yes—
32C2×C11×SD16—24no—
33C2×C11×M16—21no—
34C2×C11×M16D412yes—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8D412yes—
44C11×C4⋊Q8D411yescharacteristic
45C11×#127D411yescharacteristic
46C11×#124—21no—
47C11×#121—21no—
48C11×#121—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×#103—24no—
60C11×#103—28no—
61C11×#103—24no—
62C11×#102—24no—
63C11×C22⋊C8—21no—
64C11×#97—21no—
65C4×C8×C11—21no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68C4×C8×C11D412yes—
69#10162C1111yesmaximal, characteristic, direct product factor, Sylow
70C11×#41—42no—
71C11×#41—42no—
72C2×Q8×C11—21no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—44no—
77C2×Q8×C11—41no—
78C2×Q8×C11—82no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C22×C4×C11—22no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C11×SD16—84no—
90C11×M16—22no—
91C11×M16—22no—
92C11×M16—42no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—42no—
97C2×C8×C11—41no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114#3206C2×C1111yescharacteristic
115#3141C2×C1111yescharacteristic
116C2×#487C2×C1111yescharacteristic, complemented
117#1997C2×C1111yescharacteristic, complemented
118#1548C2×C1111yescharacteristic, complemented
119#1492C2×C1111yescharacteristic
120#1278C2×C1111yescharacteristic, complemented
121C23×C11—41no—
122C23×C11#12111yescharacteristic
123Q8×C11—44no—
124Q8×C11—42no—
125Q8×C11—44no—
126Q8×C11—82no—
127Q8×C11—82no—
128D4×C11—42no—
129D4×C11—42no—
130D4×C11—42no—
131D4×C11—82no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—82no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11—82no—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12711yescharacteristic
147C2×C4×C11#13512yes—
148C2×C4×C11#13712yes—
149C8×C11—42no—
150C8×C11—42no—
151C8×C11—42no—
152C8×C11—81no—
153#532C22×C1111yescharacteristic
154C2×C4⋊Q8C22×C1111yescharacteristic
155C2×C4⋊Q8C22×C1111yescharacteristic
156#492—21no—
157#489—22no—
158#487—22no—
159#487—21no—
160#487—21no—
161#487—22no—
162#486—21no—
163#461—22no—
164#448—22no—
165#431C22×C1111yescharacteristic
166#423C22×C1111yescharacteristic
167#417—22no—
168C2×#103—22no—
169C4×M16C22×C1111yescharacteristic
170C2×C4×C8C22×C1111yescharacteristic
171#343—22no—
172#333—22no—
173D4⋊C8—22no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11#39211yescharacteristic
180C22×C11#46412yes—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—82no—
184C4×C11—81no—
185C4×C11—82no—
186C4×C11#45212yes—
187C4×C11#45512yes—
188C4×C11#47112yes—
189C4×C11#49511yescharacteristic
190C4×C11#49711yescharacteristic
191C2×#41—21no—
192C22×Q8—21no—
193C22×Q8D4×C1112yes—
194C2×SD16—24no—
195C2×M16—21no—
196C2×M16D4×C1112yes—
197C22×C8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8D4×C1112yes—
206C4⋊Q8D4×C1111yescharacteristic
207#127D4×C1111yescharacteristic
208#124—21no—
209#121—21no—
210#121—21no—
211C4×D4—21no—
212C4×D4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C42C23×C1111yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8D4×C1112yes—
221#103—28no—
222#103—24no—
223#103—24no—
224#102—24no—
225C22⋊C8—21no—
226#97—21no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8D4×C1112yes—
231C2×C11—22no—
232C2×C11—161no—
233C2×C11#200411yescharacteristic
234C2×C11#201511yescharacteristic
235C2×C11#201911yescharacteristic
236#41—42no—
237#41—42no—
238C2×Q8—21no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8—44no—
243C2×Q8—41no—
244C2×Q8—82no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—41no—
249C22×C4—22no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4C2×D4×C1111yescharacteristic
253C22×C4C2×D4×C1111yescharacteristic
254C22×C4C11×#4111yescharacteristic
255SD16—84no—
256M16—22no—
257M16—22no—
258M16—42no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—42no—
263C2×C8—41no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C42C2×D4×C1111yescharacteristic
277C42C2×D4×C1111yescharacteristic
278C42C2×D4×C1111yescharacteristic
279C42C2×D4×C1111yescharacteristic
280C11#1016211yescharacteristic, direct product factor, Sylow
281C23—41no—
282C23C11×#12111yescharacteristic
283Q8—44no—
284Q8—42no—
285Q8—44no—
286Q8—82no—
287Q8—82no—
288D4—42no—
289D4—42no—
290D4—42no—
291D4—82no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—82no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—82no—
301C2×C4C11×#12011yescharacteristic
302C2×C4C11×#12011yescharacteristic
303C2×C4C11×#12011yescharacteristic
304C2×C4C11×#12111yescharacteristic
305C2×C4C11×#12111yescharacteristic
306C2×C4C11×#12711yescharacteristic
307C2×C4C11×#13512yes—
308C2×C4C11×#13712yes—
309C8—42no—
310C8—42no—
311C8—42no—
312C8—81no—
313C22—21no—
314C22—21no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22C11×#39211yescharacteristic
319C22C11×#46412yes—
320C4—21no—
321C4—21no—
322C4—82no—
323C4—81no—
324C4—82no—
325C4C11×#45212yes—
326C4C11×#45512yes—
327C4C11×#47112yes—
328C4C11×#49511yescharacteristic
329C4C11×#49711yescharacteristic
330C2—22no—
331C2—161no—
332C2C11×#200411yescharacteristic
333C2C11×#201511yescharacteristic
334C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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. C2×C11×#487C2semidirect
4. C11×#1997C2semidirect
5. C11×#1548C2semidirect
7. C11×#1278C2semidirect
69. #10162C11direct (N × H)
116. C2×#487C2×C11semidirect
117. #1997C2×C11semidirect
118. #1548C2×C11semidirect
120. #1278C2×C11semidirect
280. C11#10162direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32062
C11×#31412
C2×C11×#4872
C11×#19972
C11×#15482
C11×#14922
C11×#12782
#1016211