Finite Group Databasebeta

← C11×#10597 #14587790

Subgroups — C11×#10597 #14587790

Order 2816.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#1990C211yesmaximal, characteristic
2C11×#1987C211yesmaximal, characteristic
3C11×#1948C211yesmaximal, characteristic
4C11×#1939C211yesmaximal, characteristic
5C2×C11×#334C211yesmaximal, characteristic
6C2×C11×#333C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#106—21no—
10C2×C11×C4⋊C8—21no—
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15C11×#384C2211yescharacteristic
16C4×C11×C4⋊C4C2211yescharacteristic
17C11×#340—21no—
18C11×#340—21no—
19C11×#340—21no—
20C11×#340—21no—
21C11×#340—21no—
22C11×#336—21no—
23C11×#334—22no—
24C11×#333—22no—
25C22×Q8×C11—21no—
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C22×C8×C11D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8Q812yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44C11×#106—42no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—42no—
51C11×C4⋊C8D412yes—
52C4×C8×C11—21no—
53C4×C8×C11—21no—
54C11×#95—21no—
55#10597C1111yesmaximal, characteristic, direct product factor, Sylow
56C2×Q8×C11—22no—
57C2×Q8×C11—41no—
58C2×Q8×C11—81no—
59C2×Q8×C11—81no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C2×C8×C11—21no—
68C2×C8×C11—21no—
69C2×C8×C11—22no—
70C2×C8×C11—21no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11SD1612yes—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—81no—
94C11×C4⋊C4SD1612yes—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×Q811yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101#1990C2×C1111yescharacteristic
102#1987C2×C1111yescharacteristic
103#1948C2×C1111yescharacteristic
104#1939C2×C1111yescharacteristic
105C2×#334C2×C1111yescharacteristic
106C2×#333C2×C1111yescharacteristic
107#1296C2×C1111yescharacteristic
108C23×C11#12111yescharacteristic
109Q8×C11—82no—
110Q8×C11—82no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11C22⋊Q811yescharacteristic
129C2×C4×C11C22⋊Q811yescharacteristic
130C2×C4×C11#12611yescharacteristic
131C2×C4×C11C2×SD1611yescharacteristic
132C2×C4×C11C2×SD1611yescharacteristic
133C2×C4×C11#13511yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C8×C11—22no—
140C8×C11—42no—
141C8×C11—41no—
142C8×C11—81no—
143C8×C11—81no—
144C2×C4⋊Q8C22×C1111yescharacteristic
145C2×#106—21no—
146C2×C4⋊C8—21no—
147C2×C4⋊C8C22×C1111yescharacteristic
148C2×C4⋊C8C22×C1111yescharacteristic
149C2×C4⋊C8C22×C1111yescharacteristic
150C2×C4×C8C22×C1111yescharacteristic
151#384C22×C1111yescharacteristic
152C4×C4⋊C4C22×C1111yescharacteristic
153#340—21no—
154#340—21no—
155#340—21no—
156#340—21no—
157#340—21no—
158#336—21no—
159#334—22no—
160#333—22no—
161C22×C11#39611yescharacteristic
162C22×C11#46111yescharacteristic
163C22×C11#46411yescharacteristic
164C22×C11#46511yescharacteristic
165C22×C11#47011yescharacteristic
166C22×C11#47111yescharacteristic
167C22×C11#47211yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—42no—
171C4×C11—82no—
172C4×C11—81no—
173C4×C11—161no—
174C4×C11#46111yescharacteristic
175C4×C11#46411yescharacteristic
176C4×C11#46511yescharacteristic
177C4×C11#47011yescharacteristic
178C4×C11#47511yescharacteristic
179C4×C11#47511yescharacteristic
180C4×C11#47911yescharacteristic
181C4×C11#47911yescharacteristic
182C22×Q8—21no—
183C22×C8—21no—
184C22×C8—21no—
185C22×C8—21no—
186C22×C8D4×C1111yescharacteristic
187C22×C8D4×C1111yescharacteristic
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8Q8×C1112yes—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4D4×C1111yescharacteristic
198C2×C4⋊C4D4×C1111yescharacteristic
199C2×C42—21no—
200C2×C42C23×C1111yescharacteristic
201#106—42no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—42no—
208C4⋊C8D4×C1112yes—
209C4×C8—21no—
210C4×C8—21no—
211#95—21no—
212C2×C11#167111yescharacteristic
213C2×C11#167811yescharacteristic
214C2×C11#169511yescharacteristic
215C2×C11#170411yescharacteristic
216C2×C11#206311yescharacteristic
217C2×C11#206611yescharacteristic
218C2×C11#206611yescharacteristic
219C2×Q8—22no—
220C2×Q8—41no—
221C2×Q8—81no—
222C2×Q8—81no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4C2×D4×C1111yescharacteristic
228C22×C4C2×D4×C1111yescharacteristic
229C22×C4C11×#4111yescharacteristic
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—22no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8C11×SD1612yes—
245C4⋊C4—21no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—81no—
257C4⋊C4C11×SD1612yes—
258C42—41no—
259C42—41no—
260C42C2×D4×C1111yescharacteristic
261C42C2×Q8×C1111yescharacteristic
262C42C11×#4111yescharacteristic
263C42C11×#4111yescharacteristic
264C11#1059711yescharacteristic, direct product factor, Sylow
265C23C11×#12111yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4C11×#12111yescharacteristic
283C2×C4C11×#12111yescharacteristic
284C2×C4C11×C22⋊Q811yescharacteristic
285C2×C4C11×C22⋊Q811yescharacteristic
286C2×C4C11×C22⋊Q811yescharacteristic
287C2×C4C11×#12611yescharacteristic
288C2×C4C2×C11×SD1611yescharacteristic
289C2×C4C2×C11×SD1611yescharacteristic
290C2×C4C11×#13511yescharacteristic
291C2×C4C11×#13511yescharacteristic
292C2×C4C11×#13711yescharacteristic
293C2×C4C11×#13711yescharacteristic
294C2×C4C11×#13711yescharacteristic
295C2×C4C11×#13711yescharacteristic
296C8—22no—
297C8—42no—
298C8—41no—
299C8—81no—
300C8—81no—
301C22C11×#39611yescharacteristic
302C22C11×#46111yescharacteristic
303C22C11×#46411yescharacteristic
304C22C11×#46511yescharacteristic
305C22C11×#47011yescharacteristic
306C22C11×#47111yescharacteristic
307C22C11×#47211yescharacteristic
308C4—21no—
309C4—21no—
310C4—42no—
311C4—81no—
312C4—82no—
313C4—161no—
314C4C11×#46111yescharacteristic
315C4C11×#46411yescharacteristic
316C4C11×#46511yescharacteristic
317C4C11×#47011yescharacteristic
318C4C11×#47511yescharacteristic
319C4C11×#47511yescharacteristic
320C4C11×#47911yescharacteristic
321C4C11×#47911yescharacteristic
322C2C11×#167111yescharacteristic
323C2C11×#167811yescharacteristic
324C2C11×#169511yescharacteristic
325C2C11×#170411yescharacteristic
326C2C11×#206311yescharacteristic
327C2C11×#206611yescharacteristic
328C2C11×#206611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#121
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
55. #10597C11direct (N × H)
264. C11#10597direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#19902
C11×#19872
C11×#19482
C11×#19392
C2×C11×#3342
C2×C11×#3332
C11×#12962
#1059711