Finite Group Databasebeta

← C11×#10170 #14587363

Subgroups — C11×#10170 #14587363

Order 2816.

574 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×#3206C211yesmaximal, characteristic
2C11×#3152C211yesmaximal, characteristic
3C2×C11×#487C211yesmaximal, characteristic, complemented
4C11×#1997C211yesmaximal, characteristic, complemented
5C11×#1546C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic, complemented
8C2×C11×#137—22no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C11×#497—22no—
13C11×#494—21no—
14C11×#492—21no—
15C11×#492—21no—
16C11×#487—21no—
17C11×#487—22no—
18C11×#487—22no—
19C11×#461—22no—
20C11×#448—22no—
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C2×C11×#103—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—
32C11×#137—44no—
33C11×#137—44no—
34C2×C11×Q16—24no—
35C2×C11×SD16—24no—
36C2×C11×SD16—24no—
37C2×C11×M16—21no—
38C2×C11×M16D412yes—
39C22×C8×C11—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8D411yescharacteristic
48C11×C4⋊Q8D412yes—
49C11×#127D411yescharacteristic
50C11×#124—21no—
51C11×#121—21no—
52C11×#121—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×#103—28no—
64C11×#103—24no—
65C11×C22⋊C8—21no—
66C11×#97—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70C4×C8×C11D412yes—
71#10170C1111yesmaximal, characteristic, direct product factor, Sylow
72C11×#41—42no—
73C11×#41—42no—
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—21no—
77C2×Q8×C11—22no—
78C2×Q8×C11—44no—
79C2×Q8×C11—41no—
80C2×Q8×C11—42no—
81C2×Q8×C11—42no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C22×C4×C11—22no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C11×Q16—48no—
93C11×SD16—48no—
94C11×SD16—84no—
95C11×M16—22no—
96C11×M16—42no—
97C11×M16SD1614yescomplemented
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—42no—
102C2×C8×C11—41no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119#3206C2×C1111yescharacteristic
120#3152C2×C1111yescharacteristic
121C2×#487C2×C1111yescharacteristic, complemented
122#1997C2×C1111yescharacteristic, complemented
123#1546C2×C1111yescharacteristic, complemented
124#1492C2×C1111yescharacteristic
125#1278C2×C1111yescharacteristic, complemented
126C23×C11—41no—
127C23×C11#12111yescharacteristic
128Q8×C11—44no—
129Q8×C11—44no—
130Q8×C11—42no—
131Q8×C11—44no—
132Q8×C11—81no—
133Q8×C11—81no—
134D4×C11—42no—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—82no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—82no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—82no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12711yescharacteristic
153C2×C4×C11C2×SD1612yes—
154C2×C4×C11AGL(1,ℤ/8)12yes—
155C8×C11—24no—
156C8×C11—42no—
157C8×C11—42no—
158C8×C11—81no—
159C2×#137—22no—
160#532C22×C1111yescharacteristic
161C2×C4⋊Q8C22×C1111yescharacteristic
162C2×C4⋊Q8C22×C1111yescharacteristic
163#497—22no—
164#494—21no—
165#492—21no—
166#492—21no—
167#487—22no—
168#487—21no—
169#487—22no—
170#461—22no—
171#448—22no—
172#431C22×C1111yescharacteristic
173#423C22×C1111yescharacteristic
174C2×#103—22no—
175C4×M16C22×C1111yescharacteristic
176C2×C4×C8C22×C1111yescharacteristic
177#343—22no—
178#332—22no—
179D4⋊C8—22no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11#39211yescharacteristic
186C22×C11#46012yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11—81no—
191C4×C11—82no—
192C4×C11#45012yes—
193C4×C11#45512yes—
194C4×C11#47312yes—
195C4×C11#49211yescharacteristic
196C4×C11#49611yescharacteristic
197C2×#41—21no—
198C22×Q8—21no—
199C22×Q8D4×C1112yes—
200#137—44no—
201#137—44no—
202C2×Q16—24no—
203C2×SD16—24no—
204C2×SD16—24no—
205C2×M16—21no—
206C2×M16D4×C1112yes—
207C22×C8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8D4×C1112yes—
216C4⋊Q8D4×C1111yescharacteristic
217#127D4×C1111yescharacteristic
218#124—21no—
219#121—21no—
220#121—21no—
221C4×D4—21no—
222C4×D4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C42C23×C1111yescharacteristic
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8D4×C1112yes—
231#103—28no—
232#103—24no—
233C22⋊C8—21no—
234#97—21no—
235C4×C8—21no—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8D4×C1112yes—
239C2×C11—22no—
240C2×C11—161no—
241C2×C11#200411yescharacteristic
242C2×C11#201411yescharacteristic
243C2×C11#202011yescharacteristic
244#41—42no—
245#41—42no—
246C2×Q8—22no—
247C2×Q8—22no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—41no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4C2×D4×C1111yescharacteristic
262C22×C4C2×D4×C1111yescharacteristic
263C22×C4C11×#4111yescharacteristic
264Q16—48no—
265SD16—48no—
266SD16—84no—
267M16—22no—
268M16—42no—
269M16C11×SD1614yescomplemented
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—42no—
274C2×C8—41no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42C2×D4×C1111yescharacteristic
288C42C2×D4×C1111yescharacteristic
289C42C2×D4×C1111yescharacteristic
290C42C2×D4×C1111yescharacteristic
291C11#1017011yescharacteristic, direct product factor, Sylow
292C23—41no—
293C23C11×#12111yescharacteristic
294Q8—44no—
295Q8—44no—
296Q8—42no—
297Q8—44no—
298Q8—81no—
299Q8—81no—
300D4—42no—
301D4—42no—
302D4—42no—
303D4—82no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—82no—
313C2×C4C11×#12011yescharacteristic
314C2×C4C11×#12011yescharacteristic
315C2×C4C11×#12011yescharacteristic
316C2×C4C11×#12111yescharacteristic
317C2×C4C11×#12111yescharacteristic
318C2×C4C11×#12711yescharacteristic
319C2×C4C2×C11×SD1612yes—
320C2×C4C11×AGL(1,ℤ/8)12yes—
321C8—24no—
322C8—42no—
323C8—42no—
324C8—81no—
325C22—21no—
326C22—21no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22C11×#39211yescharacteristic
331C22C11×#46012yes—
332C4—21no—
333C4—21no—
334C4—82no—
335C4—81no—
336C4—82no—
337C4C11×#45012yes—
338C4C11×#45512yes—
339C4C11×#47312yes—
340C4C11×#49211yescharacteristic
341C4C11×#49611yescharacteristic
342C2—22no—
343C2—161no—
344C2C11×#200411yescharacteristic
345C2C11×#201411yescharacteristic
346C2C11×#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
3. C2×C11×#487C2semidirect
4. C11×#1997C2semidirect
5. C11×#1546C2semidirect
7. C11×#1278C2semidirect
71. #10170C11direct (N × H)
97. C11×M16SD16semidirect
121. C2×#487C2×C11semidirect
122. #1997C2×C11semidirect
123. #1546C2×C11semidirect
125. #1278C2×C11semidirect
269. M16C11×SD16semidirect
291. C11#10170direct (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×#31522
C2×C11×#4872
C11×#19972
C11×#15462
C11×#14922
C11×#12782
#1017011