Finite Group Databasebeta

← C11×#10147 #14587340

Subgroups — C11×#10147 #14587340

Order 2816.

604 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3209C211yesmaximal, characteristic, complemented
2C2×C11×#492C211yesmaximal, characteristic
3C11×#3138C211yesmaximal, characteristic
4C11×#1997C211yesmaximal, characteristic, complemented
5C11×#1545C211yesmaximal, characteristic
6C11×#1493C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C22×C11×SD16—22no—
9C11×#533C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C11×#494—21no—
13C11×#492—22no—
14C11×#492—22no—
15C11×#490—22no—
16C11×#487—21no—
17C11×#486—21no—
18C11×#486—21no—
19C11×#462—22no—
20C11×#451—22no—
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C11×#418—22no—
24C4×C11×M16C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#343—22no—
27C11×#331—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11D412yes—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C2×C11×Q16—24no—
34C2×C11×SD16—28no—
35C2×C11×SD16—48no—
36C2×C11×M16—21no—
37C2×C11×M16D412yes—
38C22×C8×C11—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8D411yescharacteristic
44C11×C4⋊Q8D411yescharacteristic
45C11×#127—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127D412yes—
49C11×#125—21no—
50C11×C22⋊Q8—21no—
51C11×C22⋊Q8—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C11×#117—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×#102—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#10147C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11—41no—
72C2×Q8×C11—22no—
73C2×Q8×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—21no—
76C2×Q8×C11—44no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—44no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—42no—
85C2×D4×C11—42no—
86C2×D4×C11—82no—
87C22×C4×C11—22no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C11×Q16—84no—
92C11×SD16—416no—
93C11×M16—22no—
94C11×M16—22no—
95C11×M16—42no—
96C2×C8×C11—24no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117#3209C2×C1111yescharacteristic, complemented
118C2×#492C2×C1111yescharacteristic
119#3138C2×C1111yescharacteristic
120#1997C2×C1111yescharacteristic, complemented
121#1545C2×C1111yescharacteristic
122#1493C2×C1111yescharacteristic, complemented
123#1278C2×C1111yescharacteristic, complemented
124C23×C11—42no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11—82no—
128C23×C11#12111yescharacteristic
129Q8×C11—44no—
130Q8×C11—42no—
131Q8×C11—44no—
132Q8×C11—42no—
133D4×C11—44no—
134D4×C11—44no—
135D4×C11—82no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—81no—
139D4×C11—81no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—82no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12711yescharacteristic
152C2×C4×C11#13512yes—
153C2×C4×C11#13712yes—
154C8×C11—24no—
155C8×C11—42no—
156C8×C11—42no—
157C8×C11—81no—
158C22×SD16—22no—
159#533C22×C1111yescharacteristic
160C2×C4⋊Q8C22×C1111yescharacteristic
161C2×#127C22×C1111yescharacteristic
162#494—21no—
163#492—22no—
164#492—22no—
165#490—22no—
166#487—21no—
167#486—21no—
168#486—21no—
169#462—22no—
170#451—22no—
171#431C22×C1111yescharacteristic
172#423C22×C1111yescharacteristic
173#418—22no—
174C4×M16C22×C1111yescharacteristic
175C2×C4×C8C22×C1111yescharacteristic
176#343—22no—
177#331—22no—
178Q8⋊C8—22no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—164no—
185C22×C11#39211yescharacteristic
186C22×C11#46412yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11#45212yes—
193C4×C11#45312yes—
194C4×C11#47112yes—
195C4×C11#49511yescharacteristic
196C4×C11#49711yescharacteristic
197C22×Q8D4×C1112yes—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C2×Q16—24no—
202C2×SD16—28no—
203C2×SD16—48no—
204C2×M16—21no—
205C2×M16D4×C1112yes—
206C22×C8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8D4×C1111yescharacteristic
212C4⋊Q8D4×C1111yescharacteristic
213#127—21no—
214#127—21no—
215#127—21no—
216#127D4×C1112yes—
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222#117—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C42C23×C1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8D4×C1112yes—
229#103—24no—
230#102—24no—
231#102—24no—
232C22⋊C8—21no—
233#97—21no—
234C4×C8—21no—
235C4×C8—21no—
236C4×C8—21no—
237C4×C8D4×C1112yes—
238C2×C11—22no—
239C2×C11—162no—
240C2×C11#200211yescharacteristic
241C2×C11#201511yescharacteristic
242C2×C11#201911yescharacteristic
243C24—41no—
244C2×Q8—22no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—21no—
248C2×Q8—44no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—44no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—82no—
259C22×C4—22no—
260C22×C4C2×D4×C1111yescharacteristic
261C22×C4C2×D4×C1111yescharacteristic
262C22×C4C11×#4111yescharacteristic
263Q16—84no—
264SD16—416no—
265M16—22no—
266M16—22no—
267M16—42no—
268C2×C8—24no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—41no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—41no—
284C42—41no—
285C42C2×D4×C1111yescharacteristic
286C42C2×D4×C1111yescharacteristic
287C42C2×D4×C1111yescharacteristic
288C42C2×D4×C1111yescharacteristic
289C11#1014711yescharacteristic, direct product factor, Sylow
290C23—42no—
291C23—82no—
292C23—82no—
293C23—82no—
294C23C11×#12111yescharacteristic
295Q8—44no—
296Q8—42no—
297Q8—44no—
298Q8—42no—
299D4—44no—
300D4—44no—
301D4—82no—
302D4—81no—
303D4—81no—
304D4—82no—
305D4—82no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—82no—
312C2×C4C11×#12011yescharacteristic
313C2×C4C11×#12011yescharacteristic
314C2×C4C11×#12011yescharacteristic
315C2×C4C11×#12111yescharacteristic
316C2×C4C11×#12111yescharacteristic
317C2×C4C11×#12711yescharacteristic
318C2×C4C11×#13512yes—
319C2×C4C11×#13712yes—
320C8—24no—
321C8—42no—
322C8—42no—
323C8—81no—
324C22—21no—
325C22—21no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—164no—
330C22C11×#39211yescharacteristic
331C22C11×#46412yes—
332C4—21no—
333C4—21no—
334C4—82no—
335C4—81no—
336C4—81no—
337C4C11×#45212yes—
338C4C11×#45312yes—
339C4C11×#47112yes—
340C4C11×#49511yescharacteristic
341C4C11×#49711yescharacteristic
342C2—22no—
343C2—162no—
344C2C11×#200211yescharacteristic
345C2C11×#201511yescharacteristic
346C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
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
1. C11×#3209C2semidirect
4. C11×#1997C2semidirect
6. C11×#1493C2semidirect
7. C11×#1278C2semidirect
70. #10147C11direct (N × H)
117. #3209C2×C11semidirect
120. #1997C2×C11semidirect
122. #1493C2×C11semidirect
123. #1278C2×C11semidirect
289. C11#10147direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32092
C2×C11×#4922
C11×#31382
C11×#19972
C11×#15452
C11×#14932
C11×#12782
#1014711