Finite Group Databasebeta

← C11×#10127 #14587320

Subgroups — C11×#10127 #14587320

Order 2816.

420 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3237C211yesmaximal, characteristic
2C11×#3236C211yesmaximal, characteristic
3C11×#3166C211yesmaximal, characteristic
4C11×#1497C211yesmaximal, characteristic
5C11×#1485C211yesmaximal, characteristic
6C11×#1470C211yesmaximal, characteristic
7C11×#1291C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#533C2211yescharacteristic
10C2×C11×#125C2211yescharacteristic
11C11×#501—21no—
12C11×#501—21no—
13C11×#501—21no—
14C11×#501—21no—
15C11×#499—22no—
16C11×#491—21no—
17C11×#491—21no—
18C11×#485—22no—
19C11×#484—21no—
20C11×#483—21no—
21C11×#479—22no—
22C11×#477—21no—
23C11×#475—21no—
24C11×#432C2211yescharacteristic
25C11×#432C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C11×#428—21no—
28C11×#428—21no—
29C4×C11×M16C2211yescharacteristic
30C11×Q8⋊C8—22no—
31C11×Q8⋊C8—22no—
32C11×#324—22no—
33C2×C11×M16—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#125—21no—
39C11×#125—21no—
40C11×#125—21no—
41C11×#125—21no—
42C11×#125—21no—
43C11×#125—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C11×#117—21no—
53C11×#117—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C11×#107—22no—
60C11×#107—22no—
61C11×#107—22no—
62C11×#107—22no—
63C11×#106—22no—
64C11×#106—22no—
65C11×#106—22no—
66C11×#106—22no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yes—
70C11×#103—22no—
71C11×#103—22no—
72C11×#103—22no—
73C11×#103—22no—
74C11×C22⋊C8—21no—
75C11×C22⋊C8—21no—
76C11×C22⋊C8D412yes—
77C11×#97—21no—
78C11×#97—21no—
79C11×#97—21no—
80C4×C8×C11—21no—
81C4×C8×C11D412yes—
82#10127C1111yesmaximal, characteristic, direct product factor, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C11×M16—24no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11—41no—
120C42×C11—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125#3237C2×C1111yescharacteristic
126#3236C2×C1111yescharacteristic
127#3166C2×C1111yescharacteristic
128#1497C2×C1111yescharacteristic
129#1485C2×C1111yescharacteristic
130#1470C2×C1111yescharacteristic
131#1291C2×C1111yescharacteristic
132C23×C11#12111yescharacteristic
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—42no—
136Q8×C11—42no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—81no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12711yescharacteristic
154C8×C11—24no—
155C8×C11—42no—
156C8×C11—42no—
157C8×C11—81no—
158#533C22×C1111yescharacteristic
159#533C22×C1111yescharacteristic
160C2×#125C22×C1111yescharacteristic
161#501—21no—
162#501—21no—
163#501—21no—
164#501—21no—
165#499—22no—
166#491—21no—
167#491—21no—
168#485—22no—
169#484—21no—
170#483—21no—
171#479—22no—
172#477—21no—
173#475—21no—
174#432C22×C1111yescharacteristic
175#432C22×C1111yescharacteristic
176#431C22×C1111yescharacteristic
177#428—21no—
178#428—21no—
179C4×M16C22×C1111yescharacteristic
180Q8⋊C8—22no—
181Q8⋊C8—22no—
182#324—22no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11#39211yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—81no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11#45612yes—
199C2×M16—21no—
200C4⋊Q8D4×C1111yescharacteristic
201C4⋊Q8D4×C1111yescharacteristic
202C4⋊Q8D4×C1111yescharacteristic
203C4⋊Q8D4×C1111yescharacteristic
204#125—21no—
205#125—21no—
206#125—21no—
207#125—21no—
208#125—21no—
209#125—21no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213C22⋊Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218#117—21no—
219#117—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4D4×C1111yescharacteristic
223C2×C4⋊C4D4×C1111yescharacteristic
224C2×C42C23×C1111yescharacteristic
225#107—22no—
226#107—22no—
227#107—22no—
228#107—22no—
229#106—22no—
230#106—22no—
231#106—22no—
232#106—22no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8D4×C1112yes—
236#103—22no—
237#103—22no—
238#103—22no—
239#103—22no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8D4×C1112yes—
243#97—21no—
244#97—21no—
245#97—21no—
246C4×C8—21no—
247C4×C8D4×C1112yes—
248C2×C11—41no—
249C2×C11#200511yescharacteristic
250C2×C11#200911yescharacteristic
251C2×C11#201711yescharacteristic
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4C2×D4×C1111yescharacteristic
259C22×C4C2×D4×C1111yescharacteristic
260C22×C4C11×#4111yescharacteristic
261M16—24no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C42—41no—
289C42—41no—
290C42C2×D4×C1111yescharacteristic
291C42C2×D4×C1111yescharacteristic
292C42C2×D4×C1111yescharacteristic
293C42C2×D4×C1111yescharacteristic
294C11#1012711yescharacteristic, direct product factor, Sylow
295C23C11×#12111yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—42no—
299Q8—42no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4C11×#12011yescharacteristic
312C2×C4C11×#12011yescharacteristic
313C2×C4C11×#12011yescharacteristic
314C2×C4C11×#12111yescharacteristic
315C2×C4C11×#12111yescharacteristic
316C2×C4C11×#12711yescharacteristic
317C8—24no—
318C8—42no—
319C8—42no—
320C8—81no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22C11×#39211yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4C11×#45612yes—
337C2—41no—
338C2C11×#200511yescharacteristic
339C2C11×#200911yescharacteristic
340C2C11×#201711yescharacteristic
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
82. #10127C11direct (N × H)
294. C11#10127direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32372
C11×#32362
C11×#31662
C11×#14972
C11×#14852
C11×#14702
C11×#12912
#1012711