Finite Group Databasebeta

← C11×#10154 #14587347

Subgroups — C11×#10154 #14587347

Order 2816.

574 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×#3206C211yesmaximal, characteristic
2C2×C11×#494C211yesmaximal, characteristic, complemented
3C11×#3141C211yesmaximal, characteristic
4C11×#1997C211yesmaximal, characteristic, complemented
5C11×#1549C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic, complemented
8C22×C11×Q16—22no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C11×#494—22no—
13C11×#494—22no—
14C11×#492—21no—
15C11×#489—22no—
16C11×#487—21no—
17C11×#487—21no—
18C11×#486—21no—
19C11×#461—22no—
20C11×#448—22no—
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C11×#417—22no—
24C4×C11×M16C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#343—22no—
27C11×#332—22no—
28C11×D4⋊C8—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11D412yes—
32C2×C11×Q16—28no—
33C2×C11×Q16—48no—
34C2×C11×SD16—24no—
35C2×C11×M16—21no—
36C2×C11×M16D412yes—
37C22×C8×C11—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8D412yes—
46C11×C4⋊Q8D411yescharacteristic
47C11×#127D411yescharacteristic
48C11×#124—21no—
49C11×#121—21no—
50C11×#121—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×#103—24no—
62C11×#103—24no—
63C11×#102—24no—
64C11×C22⋊C8—21no—
65C11×#97—21no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C4×C8×C11D412yes—
70#10154C1111yesmaximal, characteristic, direct product factor, Sylow
71C11×#41—42no—
72C11×#41—42no—
73C2×Q8×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—44no—
78C2×Q8×C11—44no—
79C2×Q8×C11—41no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C22×C4×C11—22no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C11×Q16—416no—
91C11×SD16—84no—
92C11×M16—22no—
93C11×M16—22no—
94C11×M16—42no—
95C2×C8×C11—24no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116#3206C2×C1111yescharacteristic
117C2×#494C2×C1111yescharacteristic, complemented
118#3141C2×C1111yescharacteristic
119#1997C2×C1111yescharacteristic, complemented
120#1549C2×C1111yescharacteristic, complemented
121#1492C2×C1111yescharacteristic
122#1278C2×C1111yescharacteristic, complemented
123C23×C11—41no—
124C23×C11#12111yescharacteristic
125Q8×C11—44no—
126Q8×C11—44no—
127Q8×C11—42no—
128Q8×C11—44no—
129Q8×C11—82no—
130D4×C11—42no—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—82no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—82no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—82no—
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12711yescharacteristic
149C2×C4×C11#13512yes—
150C2×C4×C11#13712yes—
151C8×C11—24no—
152C8×C11—42no—
153C8×C11—42no—
154C8×C11—81no—
155C22×Q16—22no—
156#532C22×C1111yescharacteristic
157C2×C4⋊Q8C22×C1111yescharacteristic
158C2×C4⋊Q8C22×C1111yescharacteristic
159#494—22no—
160#494—22no—
161#492—21no—
162#489—22no—
163#487—21no—
164#487—21no—
165#486—21no—
166#461—22no—
167#448—22no—
168#431C22×C1111yescharacteristic
169#423C22×C1111yescharacteristic
170#417—22no—
171C4×M16C22×C1111yescharacteristic
172C2×C4×C8C22×C1111yescharacteristic
173#343—22no—
174#332—22no—
175D4⋊C8—22no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11#39211yescharacteristic
182C22×C11#46412yes—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—82no—
186C4×C11—82no—
187C4×C11—81no—
188C4×C11#45212yes—
189C4×C11#45312yes—
190C4×C11#47312yes—
191C4×C11#49511yescharacteristic
192C4×C11#49711yescharacteristic
193C2×#41—21no—
194C22×Q8—21no—
195C22×Q8D4×C1112yes—
196C2×Q16—28no—
197C2×Q16—48no—
198C2×SD16—24no—
199C2×M16—21no—
200C2×M16D4×C1112yes—
201C22×C8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8D4×C1112yes—
210C4⋊Q8D4×C1111yescharacteristic
211#127D4×C1111yescharacteristic
212#124—21no—
213#121—21no—
214#121—21no—
215C4×D4—21no—
216C4×D4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C42C23×C1111yescharacteristic
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8D4×C1112yes—
225#103—24no—
226#103—24no—
227#102—24no—
228C22⋊C8—21no—
229#97—21no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—21no—
233C4×C8D4×C1112yes—
234C2×C11—22no—
235C2×C11—161no—
236C2×C11#200211yescharacteristic
237C2×C11#201511yescharacteristic
238C2×C11#202011yescharacteristic
239#41—42no—
240#41—42no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8—44no—
246C2×Q8—44no—
247C2×Q8—41no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—41no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4C2×D4×C1111yescharacteristic
256C22×C4C2×D4×C1111yescharacteristic
257C22×C4C11×#4111yescharacteristic
258Q16—416no—
259SD16—84no—
260M16—22no—
261M16—22no—
262M16—42no—
263C2×C8—24no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C42C2×D4×C1111yescharacteristic
281C42C2×D4×C1111yescharacteristic
282C42C2×D4×C1111yescharacteristic
283C42C2×D4×C1111yescharacteristic
284C11#1015411yescharacteristic, direct product factor, Sylow
285C23—41no—
286C23C11×#12111yescharacteristic
287Q8—44no—
288Q8—44no—
289Q8—42no—
290Q8—44no—
291Q8—82no—
292D4—42no—
293D4—42no—
294D4—42no—
295D4—82no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—82no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—82no—
305C2×C4C11×#12011yescharacteristic
306C2×C4C11×#12011yescharacteristic
307C2×C4C11×#12011yescharacteristic
308C2×C4C11×#12111yescharacteristic
309C2×C4C11×#12111yescharacteristic
310C2×C4C11×#12711yescharacteristic
311C2×C4C11×#13512yes—
312C2×C4C11×#13712yes—
313C8—24no—
314C8—42no—
315C8—42no—
316C8—81no—
317C22—21no—
318C22—21no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22C11×#39211yescharacteristic
323C22C11×#46412yes—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—82no—
328C4—81no—
329C4C11×#45212yes—
330C4C11×#45312yes—
331C4C11×#47312yes—
332C4C11×#49511yescharacteristic
333C4C11×#49711yescharacteristic
334C2—22no—
335C2—161no—
336C2C11×#200211yescharacteristic
337C2C11×#201511yescharacteristic
338C2C11×#202011yescharacteristic
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×#494C2semidirect
4. C11×#1997C2semidirect
5. C11×#1549C2semidirect
7. C11×#1278C2semidirect
70. #10154C11direct (N × H)
117. C2×#494C2×C11semidirect
119. #1997C2×C11semidirect
120. #1549C2×C11semidirect
122. #1278C2×C11semidirect
284. C11#10154direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32062
C2×C11×#4942
C11×#31412
C11×#19972
C11×#15492
C11×#14922
C11×#12782
#1015411