Finite Group Databasebeta

← C11×#10139 #14587332

Subgroups — C11×#10139 #14587332

Order 2816.

446 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3236C211yesmaximal, characteristic
2C11×#3209C211yesmaximal, characteristic
3C2×C11×#501C211yesmaximal, characteristic
4C11×#1556C211yesmaximal, characteristic
5C11×#1531C211yesmaximal, characteristic
6C11×#1470C211yesmaximal, characteristic
7C11×#1302C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#125C2211yescharacteristic
11C11×#501—22no—
12C11×#501—21no—
13C11×#501—22no—
14C11×#494—21no—
15C11×#491—21no—
16C11×#487—21no—
17C11×#484—21no—
18C11×#483—21no—
19C11×#479—22no—
20C11×#462—22no—
21C11×#451—22no—
22C11×#432C2211yescharacteristic
23C11×#432C2211yescharacteristic
24C11×#431C2211yescharacteristic
25C2×C11×#107—21no—
26C2×C11×#106—21no—
27C2×C11×#97C2211yescharacteristic
28C11×#332—22no—
29C11×#330—22no—
30C11×#324—22no—
31C22×Q8×C11—21no—
32C2×C11×Q16—24no—
33C22×C8×C11—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D412yes—
40C11×#125—21no—
41C11×#125—21no—
42C11×#125—21no—
43C11×#125—21no—
44C11×#125—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C11×#117—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C11×#107—24no—
58C11×#107—22no—
59C11×#106—24no—
60C11×#106—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#103—22no—
65C11×#103—22no—
66C11×#103—24no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8D412yes—
70C11×#97—21no—
71C11×#97—21no—
72C11×#97—21no—
73C11×#97D412yes—
74C4×C8×C11—21no—
75#10139C1111yesmaximal, characteristic, direct product factor, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—22no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—82no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C11×Q16—84no—
88C2×C8×C11—24no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
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×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117#3236C2×C1111yescharacteristic
118#3209C2×C1111yescharacteristic
119C2×#501C2×C1111yescharacteristic
120#1556C2×C1111yescharacteristic
121#1531C2×C1111yescharacteristic
122#1470C2×C1111yescharacteristic
123#1302C2×C1111yescharacteristic
124C23×C11#12111yescharacteristic
125Q8×C11—42no—
126Q8×C11—44no—
127Q8×C11—42no—
128Q8×C11—82no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—82no—
139C2×C4×C11—81no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C8×C11—24no—
147C8×C11—42no—
148C8×C11—42no—
149C8×C11—81no—
150#533C22×C1111yescharacteristic
151C2×C4⋊Q8C22×C1111yescharacteristic
152C2×#125C22×C1111yescharacteristic
153#501—22no—
154#501—21no—
155#501—22no—
156#494—21no—
157#491—21no—
158#487—21no—
159#484—21no—
160#483—21no—
161#479—22no—
162#462—22no—
163#451—22no—
164#432C22×C1111yescharacteristic
165#432C22×C1111yescharacteristic
166#431C22×C1111yescharacteristic
167C2×#107—21no—
168C2×#106—21no—
169C2×#97C22×C1111yescharacteristic
170#332—22no—
171#330—22no—
172#324—22no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#39211yescharacteristic
176C22×C11#47312yes—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—82no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11#45612yes—
188C22×Q8—21no—
189C2×Q16—24no—
190C22×C8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8D4×C1112yes—
195C4⋊Q8D4×C1111yescharacteristic
196C4⋊Q8D4×C1111yescharacteristic
197#125—21no—
198#125—21no—
199#125—21no—
200#125—21no—
201#125—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206#117—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4D4×C1111yescharacteristic
212C2×C4⋊C4D4×C1111yescharacteristic
213C2×C42C23×C1111yescharacteristic
214#107—24no—
215#107—22no—
216#106—24no—
217#106—22no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8D4×C1112yes—
221#103—24no—
222#103—22no—
223#103—22no—
224C22⋊C8—21no—
225C22⋊C8—21no—
226C22⋊C8D4×C1112yes—
227#97—21no—
228#97—21no—
229#97—21no—
230#97D4×C1112yes—
231C4×C8—21no—
232C2×C11—22no—
233C2×C11#200511yescharacteristic
234C2×C11#200811yescharacteristic
235C2×C11#202011yescharacteristic
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—21no—
239C2×Q8—41no—
240C2×Q8—82no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4C2×D4×C1111yescharacteristic
245C22×C4C2×D4×C1111yescharacteristic
246C22×C4C11×#4111yescharacteristic
247Q16—84no—
248C2×C8—24no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—41no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—22no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—22no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C22⋊C4—41no—
272C42—41no—
273C42C2×D4×C1111yescharacteristic
274C42C2×D4×C1111yescharacteristic
275C42C2×D4×C1111yescharacteristic
276C42C2×D4×C1111yescharacteristic
277C11#1013911yescharacteristic, direct product factor, Sylow
278C23C11×#12111yescharacteristic
279Q8—42no—
280Q8—44no—
281Q8—42no—
282Q8—82no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—82no—
293C2×C4—81no—
294C2×C4C11×#12011yescharacteristic
295C2×C4C11×#12011yescharacteristic
296C2×C4C11×#12011yescharacteristic
297C2×C4C11×#12111yescharacteristic
298C2×C4C11×#12111yescharacteristic
299C2×C4C11×#12711yescharacteristic
300C8—24no—
301C8—42no—
302C8—42no—
303C8—81no—
304C22—21no—
305C22—21no—
306C22C11×#39211yescharacteristic
307C22C11×#47312yes—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—81no—
314C4—82no—
315C4—81no—
316C4—81no—
317C4—81no—
318C4C11×#45612yes—
319C2—22no—
320C2C11×#200511yescharacteristic
321C2C11×#200811yescharacteristic
322C2C11×#202011yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#121
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
75. #10139C11direct (N × H)
277. C11#10139direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32362
C11×#32092
C2×C11×#5012
C11×#15562
C11×#15312
C11×#14702
C11×#13022
#1013911