Finite Group Databasebeta

← C11×#9995 #14587188

Subgroups — C11×#9995 #14587188

Order 2816.

510 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3195C211yesmaximal, characteristic
2C2×C11×#484C211yesmaximal, characteristic
3C2×C11×#483C211yesmaximal, characteristic
4C11×#1821C211yesmaximal, characteristic
5C11×#1472C211yesmaximal, characteristic
6C11×#1472C211yesmaximal, characteristic
7C11×#1298C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C11×#484—22no—
12C11×#484—22no—
13C11×#483—21no—
14C11×#483—21no—
15C11×#483—22no—
16C11×#483—22no—
17C11×#470—22no—
18C11×#451—21no—
19C11×#451—21no—
20C2×C11×#107—21no—
21C2×C11×#106—21no—
22C2×C11×#103—21no—
23C2×C11×#103—21no—
24C11×#407C2211yescharacteristic
25C11×#407C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#343—22no—
29C11×#324—22no—
30C11×#324—22no—
31C22×Q8×C11D411yescharacteristic
32C22×Q8×C11D411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C2×C11×Q16—22no—
36C2×C11×M16—21no—
37C2×C11×M16D412yes—
38C22×C8×C11—21no—
39C22×C8×C11—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C11×#107—24no—
61C11×#106—24no—
62C11×#106—22no—
63C11×#103—24no—
64C11×#103—24no—
65C11×#103—22no—
66C11×#103—22no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8—21no—
73C11×C22⋊C8D412yes—
74C11×C22⋊C8D412yes—
75#9995C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11#4111yescharacteristic
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—42no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—82no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C11×Q16—82no—
99C11×M16—42no—
100C11×M16—42no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—42no—
105C2×C8×C11—42no—
106C2×C8×C11—41no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123#3195C2×C1111yescharacteristic
124C2×#484C2×C1111yescharacteristic
125C2×#483C2×C1111yescharacteristic
126#1821C2×C1111yescharacteristic
127#1472C2×C1111yescharacteristic
128#1472C2×C1111yescharacteristic
129#1298C2×C1111yescharacteristic
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—41no—
133C23×C11#12111yescharacteristic
134C23×C11#12111yescharacteristic
135C23×C11#12111yescharacteristic
136Q8×C11—42no—
137Q8×C11—42no—
138Q8×C11—42no—
139Q8×C11—42no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—82no—
154C2×C4×C11—82no—
155C2×C4×C11—82no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12711yescharacteristic
162C8×C11—42no—
163C8×C11—42no—
164C8×C11—42no—
165C8×C11—81no—
166C2×C22⋊Q8C22×C1111yescharacteristic
167C2×C22⋊Q8C22×C1111yescharacteristic
168C22×C4⋊C4C22×C1111yescharacteristic
169#484—22no—
170#484—22no—
171#483—22no—
172#483—21no—
173#483—21no—
174#483—22no—
175#470—22no—
176#451—21no—
177#451—21no—
178C2×#107—21no—
179C2×#106—21no—
180C2×#103—21no—
181C2×#103—21no—
182#407C22×C1111yescharacteristic
183#407C22×C1111yescharacteristic
184C2×C22⋊C8C22×C1111yescharacteristic
185C2×C22⋊C8C22×C1111yescharacteristic
186#343—22no—
187#324—22no—
188#324—22no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—44no—
197C22×C11#39211yescharacteristic
198C22×C11#47112yes—
199C22×C11#47312yes—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—82no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11#45812yes—
209C22×Q8D4×C1111yescharacteristic
210C22×Q8D4×C1111yescharacteristic
211C23×C4—21no—
212C23×C4C23×C1111yescharacteristic
213C2×Q16—22no—
214C2×M16—21no—
215C2×M16D4×C1112yes—
216C22×C8—21no—
217C22×C8—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4D4×C1112yes—
234C2×C4⋊C4D4×C1111yescharacteristic
235C2×C4⋊C4D4×C1111yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238#107—24no—
239#106—24no—
240#106—22no—
241#103—24no—
242#103—24no—
243#103—22no—
244#103—22no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8D4×C1112yes—
252C22⋊C8D4×C1112yes—
253C2×C11—22no—
254C2×C11—22no—
255C2×C11—41no—
256C2×C11#201911yescharacteristic
257C2×C11#202011yescharacteristic
258C2×C11#202211yescharacteristic
259C24C11×#4111yescharacteristic
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—42no—
265C2×Q8—42no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—42no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—82no—
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C2×D4×C1111yescharacteristic
277C22×C4C2×D4×C1111yescharacteristic
278C22×C4C2×D4×C1111yescharacteristic
279C22×C4C2×D4×C1111yescharacteristic
280C22×C4C2×D4×C1111yescharacteristic
281Q16—82no—
282M16—42no—
283M16—42no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—41no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C11#999511yescharacteristic, direct product factor, Sylow
307C23—22no—
308C23—22no—
309C23—41no—
310C23C11×#12111yescharacteristic
311C23C11×#12111yescharacteristic
312C23C11×#12111yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—42no—
316Q8—42no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4C11×#12011yescharacteristic
336C2×C4C11×#12011yescharacteristic
337C2×C4C11×#12011yescharacteristic
338C2×C4C11×#12711yescharacteristic
339C8—42no—
340C8—42no—
341C8—42no—
342C8—81no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—44no—
351C22C11×#39211yescharacteristic
352C22C11×#47112yes—
353C22C11×#47312yes—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—82no—
359C4—81no—
360C4—81no—
361C4—81no—
362C4C11×#45812yes—
363C2—22no—
364C2—22no—
365C2—41no—
366C2C11×#201911yescharacteristic
367C2C11×#202011yescharacteristic
368C2C11×#202211yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
75. #9995C11direct (N × H)
306. C11#9995direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31952
C2×C11×#4842
C2×C11×#4832
C11×#18212
C11×#14722
C11×#12982
#999511