Finite Group Databasebeta

← C11×#10164 #14587357

Subgroups — C11×#10164 #14587357

Order 2816.

498 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3227C211yesmaximal, characteristic
2C2×C11×#500C211yesmaximal, characteristic, complemented
3C11×#3141C211yesmaximal, characteristic
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×#500—22no—
12C11×#500—22no—
13C11×#498—21no—
14C11×#489—22no—
15C11×#487—21no—
16C11×#486—21no—
17C11×#486—21no—
18C11×#481—22no—
19C11×#476—22no—
20C11×#431C2211yescharacteristic
21C2×C11×#107—22no—
22C11×#423C2211yescharacteristic
23C11×#417—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×C11—21no—
32C2×C11×M16—21no—
33C2×C11×M16D412yes—
34C22×C8×C11—21no—
35C11×C4⋊Q8—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⋊Q8D412yes—
43C11×C4⋊Q8D411yescharacteristic
44C11×#127D411yescharacteristic
45C11×#124—21no—
46C11×#121—21no—
47C11×#121—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D412yes—
54C2×C42×C11C2311yescharacteristic
55C11×#107—28no—
56C11×#106—24no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60C11×#103—24no—
61C11×#102—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#10164C1111yesmaximal, characteristic, direct product factor, Sylow
70C11×#41—42no—
71C11×#41—42no—
72C2×Q8×C11—21no—
73C2×Q8×C11—22no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—82no—
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×M16—22no—
90C11×M16—22no—
91C11×M16—42no—
92C2×C8×C11—24no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113#3227C2×C1111yescharacteristic
114C2×#500C2×C1111yescharacteristic, complemented
115#3141C2×C1111yescharacteristic
116#1997C2×C1111yescharacteristic, complemented
117#1548C2×C1111yescharacteristic, complemented
118#1492C2×C1111yescharacteristic
119#1278C2×C1111yescharacteristic, complemented
120C23×C11—41no—
121C23×C11#12111yescharacteristic
122Q8×C11—42no—
123Q8×C11—82no—
124Q8×C11—82no—
125Q8×C11—82no—
126Q8×C11—82no—
127D4×C11—42no—
128D4×C11—42no—
129D4×C11—42no—
130D4×C11—82no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—82no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11—82no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×C4×C11#13512yes—
147C2×C4×C11#13712yes—
148C8×C11—24no—
149C8×C11—42no—
150C8×C11—42no—
151C8×C11—81no—
152#532C22×C1111yescharacteristic
153C2×C4⋊Q8C22×C1111yescharacteristic
154C2×C4⋊Q8C22×C1111yescharacteristic
155#500—22no—
156#500—22no—
157#498—21no—
158#489—22no—
159#487—21no—
160#486—21no—
161#486—21no—
162#481—22no—
163#476—22no—
164#431C22×C1111yescharacteristic
165C2×#107—22no—
166#423C22×C1111yescharacteristic
167#417—22no—
168C4×M16C22×C1111yescharacteristic
169C2×C4×C8C22×C1111yescharacteristic
170#343—22no—
171#333—22no—
172D4⋊C8—22no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—81no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11#39211yescharacteristic
179C22×C11#46412yes—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—81no—
183C4×C11—82no—
184C4×C11—82no—
185C4×C11#45212yes—
186C4×C11#45612yes—
187C4×C11#47212yes—
188C4×C11#49511yescharacteristic
189C4×C11#49711yescharacteristic
190C2×#41—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C2×M16—21no—
194C2×M16D4×C1112yes—
195C22×C8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8D4×C1112yes—
204C4⋊Q8D4×C1111yescharacteristic
205#127D4×C1111yescharacteristic
206#124—21no—
207#121—21no—
208#121—21no—
209C4×D4—21no—
210C4×D4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4D4×C1112yes—
215C2×C42C23×C1111yescharacteristic
216#107—28no—
217#106—24no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8D4×C1112yes—
221#103—24no—
222#102—24no—
223#102—24no—
224C22⋊C8—21no—
225#97—21no—
226C4×C8—21no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8D4×C1112yes—
230C2×C11—22no—
231C2×C11—161no—
232C2×C11#200511yescharacteristic
233C2×C11#201511yescharacteristic
234C2×C11#201811yescharacteristic
235#41—42no—
236#41—42no—
237C2×Q8—21no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—82no—
243C2×Q8—82no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C2×D4×C1111yescharacteristic
252C22×C4C2×D4×C1111yescharacteristic
253C22×C4C11×#4111yescharacteristic
254M16—22no—
255M16—22no—
256M16—42no—
257C2×C8—24no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—41no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42C2×D4×C1111yescharacteristic
275C42C2×D4×C1111yescharacteristic
276C42C2×D4×C1111yescharacteristic
277C42C2×D4×C1111yescharacteristic
278C11#1016411yescharacteristic, direct product factor, Sylow
279C23—41no—
280C23C11×#12111yescharacteristic
281Q8—42no—
282Q8—82no—
283Q8—82no—
284Q8—82no—
285Q8—82no—
286D4—42no—
287D4—42no—
288D4—42no—
289D4—82no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—82no—
299C2×C4C11×#12011yescharacteristic
300C2×C4C11×#12011yescharacteristic
301C2×C4C11×#12011yescharacteristic
302C2×C4C11×#12111yescharacteristic
303C2×C4C11×#12111yescharacteristic
304C2×C4C11×#12711yescharacteristic
305C2×C4C11×#13512yes—
306C2×C4C11×#13712yes—
307C8—24no—
308C8—42no—
309C8—42no—
310C8—81no—
311C22—21no—
312C22—21no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22C11×#39211yescharacteristic
317C22C11×#46412yes—
318C4—21no—
319C4—21no—
320C4—81no—
321C4—82no—
322C4—82no—
323C4C11×#45212yes—
324C4C11×#45612yes—
325C4C11×#47212yes—
326C4C11×#49511yescharacteristic
327C4C11×#49711yescharacteristic
328C2—22no—
329C2—161no—
330C2C11×#200511yescharacteristic
331C2C11×#201511yescharacteristic
332C2C11×#201811yescharacteristic
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
2. C2×C11×#500C2semidirect
4. C11×#1997C2semidirect
5. C11×#1548C2semidirect
7. C11×#1278C2semidirect
69. #10164C11direct (N × H)
114. C2×#500C2×C11semidirect
116. #1997C2×C11semidirect
117. #1548C2×C11semidirect
119. #1278C2×C11semidirect
278. C11#10164direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32272
C2×C11×#5002
C11×#31412
C11×#19972
C11×#15482
C11×#14922
C11×#12782
#1016411