Finite Group Databasebeta

← C11×#10106 #14587299

Subgroups — C11×#10106 #14587299

Order 2816.

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

normal subgroups only

This group has 574 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×#3253C211yesmaximal, characteristic
2C11×#3206C211yesmaximal, characteristic, complemented
3C11×#3152C211yesmaximal, characteristic, complemented
4C11×#1997C211yesmaximal, characteristic, complemented
5C11×#1525C211yesmaximal, characteristic, complemented
6C11×#1484C211yesmaximal, characteristic, complemented
7C11×#1299C211yesmaximal, characteristic, complemented
8C2×C11×#137—22no—
9C11×#532C2211yescharacteristic
10C11×#532C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C11×#497—22no—
13C11×#494—21no—
14C11×#492—21no—
15C11×#492—21no—
16C11×#487—21no—
17C11×#476—21no—
18C11×#476—21no—
19C11×#469—22no—
20C11×#461—22no—
21C11×#459—21no—
22C11×#459—21no—
23C11×#448—22no—
24C11×#431C2211yescharacteristic
25C11×#423C2211yescharacteristic
26C4×C11×M16C2211yescharacteristic
27C4×C11×M16C2211yescharacteristic
28C11×#343—22no—
29C11×#329—22no—
30C11×D4⋊C8—22no—
31C2×C11×#41—21no—
32C2×C11×#41—21no—
33C22×Q8×C11D412yes—
34C11×#137—48no—
35C2×C11×Q16—24no—
36C2×C11×SD16—24no—
37C2×C11×SD16—24no—
38C2×C11×D8—22no—
39C2×C11×M16—21no—
40C2×C11×M16—21no—
41C2×C11×M16D412yes—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8D411yescharacteristic
47C11×C4⋊Q8D411yescharacteristic
48C11×#127D411yescharacteristic
49C11×#127D411yescharacteristic
50C11×#124—21no—
51C11×#124—21no—
52C11×#121—21no—
53C11×#121—21no—
54C11×#121—21no—
55C11×#121—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C42×C11C2311yescharacteristic
63C11×#106—22no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#103—24no—
68C11×#102—22no—
69C11×#102—22no—
70C11×C22⋊C8—21no—
71C11×#97—21no—
72C11×#97D412yes—
73C4×C8×C11—21no—
74C4×C8×C11—21no—
75C4×C8×C11—21no—
76#10106C1111yesmaximal, characteristic, direct product factor, Sylow
77C11×#41—44no—
78C11×#41—82no—
79C2×Q8×C11—22no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—21no—
83C2×Q8×C11—44no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C22×C4×C11—22no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C11×Q16—48no—
99C11×SD16—48no—
100C11×SD16—84no—
101C11×D8—82no—
102C11×M16—24no—
103C11×M16—22no—
104C11×M16—42no—
105C11×M16—41no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—41no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126#3253C2×C1111yescharacteristic
127#3206C2×C1111yescharacteristic, complemented
128#3152C2×C1111yescharacteristic, complemented
129#1997C2×C1111yescharacteristic, complemented
130#1525C2×C1111yescharacteristic, complemented
131#1484C2×C1111yescharacteristic, complemented
132#1299C2×C1111yescharacteristic, complemented
133C23×C11—41no—
134C23×C11—41no—
135C23×C11#12111yescharacteristic
136Q8×C11—44no—
137Q8×C11—42no—
138Q8×C11—44no—
139Q8×C11—81no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—41no—
143D4×C11—41no—
144D4×C11—41no—
145D4×C11—41no—
146D4×C11—42no—
147D4×C11—81no—
148D4×C11—82no—
149D4×C11—82no—
150C2×C4×C11—22no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12711yescharacteristic
166C8×C11—24no—
167C8×C11—42no—
168C8×C11—42no—
169C8×C11—42no—
170C2×#137—22no—
171#532C22×C1111yescharacteristic
172#532C22×C1111yescharacteristic
173C2×C4⋊Q8C22×C1111yescharacteristic
174#497—22no—
175#494—21no—
176#492—21no—
177#492—21no—
178#487—21no—
179#476—21no—
180#476—21no—
181#469—22no—
182#461—22no—
183#459—21no—
184#459—21no—
185#448—22no—
186#431C22×C1111yescharacteristic
187#423C22×C1111yescharacteristic
188C4×M16C22×C1111yescharacteristic
189C4×M16C22×C1111yescharacteristic
190#343—22no—
191#329—22no—
192D4⋊C8—22no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11#39211yescharacteristic
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—81no—
207C4×C11—82no—
208C4×C11—81no—
209C4×C11#45312yes—
210C4×C11#45511yescharacteristic
211C4×C11#45611yescharacteristic
212C4×C11#47112yes—
213C2×#41—21no—
214C2×#41—21no—
215C22×Q8D4×C1112yes—
216#137—48no—
217C2×Q16—24no—
218C2×SD16—24no—
219C2×SD16—24no—
220C2×D8—22no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16D4×C1112yes—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8D4×C1111yescharacteristic
229C4⋊Q8D4×C1111yescharacteristic
230#127D4×C1111yescharacteristic
231#127D4×C1111yescharacteristic
232#124—21no—
233#124—21no—
234#121—21no—
235#121—21no—
236#121—21no—
237#121—21no—
238C4×D4—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C42C23×C1111yescharacteristic
245#106—22no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8D4×C1112yes—
249#103—24no—
250#102—22no—
251#102—22no—
252C22⋊C8—21no—
253#97—21no—
254#97D4×C1112yes—
255C4×C8—21no—
256C4×C8—21no—
257C4×C8—21no—
258C2×C11—41no—
259C2×C11—161no—
260C2×C11—161no—
261C2×C11#200211yescharacteristic
262C2×C11#200711yescharacteristic
263C2×C11#201911yescharacteristic
264#41—44no—
265#41—82no—
266C2×Q8—22no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—21no—
270C2×Q8—44no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—22no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4C2×D4×C1111yescharacteristic
283C22×C4C2×D4×C1111yescharacteristic
284C22×C4C11×#4111yescharacteristic
285Q16—48no—
286SD16—48no—
287SD16—84no—
288D8—82no—
289M16—24no—
290M16—22no—
291M16—41no—
292M16—42no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—41no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42C2×D4×C1111yescharacteristic
310C42C2×D4×C1111yescharacteristic
311C42C2×D4×C1111yescharacteristic
312C42C2×D4×C1111yescharacteristic
313C11#1010611yescharacteristic, direct product factor, Sylow
314C23—41no—
315C23—41no—
316C23C11×#12111yescharacteristic
317Q8—44no—
318Q8—42no—
319Q8—44no—
320Q8—81no—
321D4—42no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—41no—
327D4—42no—
328D4—81no—
329D4—82no—
330D4—82no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4C11×#12011yescharacteristic
342C2×C4C11×#12011yescharacteristic
343C2×C4C11×#12011yescharacteristic
344C2×C4C11×#12111yescharacteristic
345C2×C4C11×#12111yescharacteristic
346C2×C4C11×#12711yescharacteristic
347C8—24no—
348C8—42no—
349C8—42no—
350C8—42no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22C11×#39211yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—82no—
366C4—81no—
367C4C11×#45312yes—
368C4C11×#45511yescharacteristic
369C4C11×#45611yescharacteristic
370C4C11×#47112yes—
371C2—41no—
372C2—161no—
373C2—161no—
374C2C11×#200211yescharacteristic
375C2C11×#200711yescharacteristic
376C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3253C2
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
2. C11×#3206C2semidirect
3. C11×#3152C2semidirect
4. C11×#1997C2semidirect
5. C11×#1525C2semidirect
6. C11×#1484C2semidirect
7. C11×#1299C2semidirect
76. #10106C11direct (N × H)
127. #3206C2×C11semidirect
128. #3152C2×C11semidirect
129. #1997C2×C11semidirect
130. #1525C2×C11semidirect
131. #1484C2×C11semidirect
132. #1299C2×C11semidirect
313. C11#10106direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32532
C11×#32062
C11×#31522
C11×#19972
C11×#15252
C11×#14842
C11×#12992
#1010611