Finite Group Databasebeta

← C11×#12134 #14589327

Subgroups — C11×#12134 #14589327

Order 2816.

424 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2523C211yesmaximal, characteristic, complemented
2C11×#2044C211yesmaximal, characteristic
3C11×#1607C211yesmaximal, characteristic
4C11×#1601C211yesmaximal, characteristic
5C11×#1351C211yesmaximal, characteristic, complemented
6C11×#1344C211yesmaximal, characteristic, complemented
7C11×#1326C211yesmaximal, characteristic, complemented
8C11×#534C2211yescharacteristic
9C11×#480—21no—
10C11×#448—21no—
11C2×C11×#99—21no—
12C11×#397—21no—
13C11×#397C2211yescharacteristic
14C11×#393C2211yescharacteristic
15C11×#391—21no—
16C11×#387—21no—
17C11×#387—21no—
18C11×#386—21no—
19C11×#385C2211yescharacteristic
20C11×#383—21no—
21C4×C11×C22⋊C4—21no—
22C11×#342C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11—21no—
29C23×C4×C11D411yescharacteristic
30C2×C11×SD16—41no—
31C11×#123—41no—
32C11×#121—21no—
33C11×#121—21no—
34C11×#120—41no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—41no—
42C2×C11×C22⋊C4D411yescharacteristic
43C2×C11×C22⋊C4C2311yescharacteristic
44C2×C42×C11—21no—
45C2×C42×C11—21no—
46C11×#107—41no—
47C11×#103—41no—
48C11×#102—41no—
49C11×#99—42no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—41no—
61C11×#95D411yescharacteristic
62C11×#95D411yescharacteristic
63#12134C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—21no—
65C24×C11C2×D411yescharacteristic
66C2×Q8×C11—42no—
67C2×Q8×C11—41no—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—42no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C11×SD16—82no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—42no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—21no—
97C11×C22⋊C4—21no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—82no—
107C42×C11—42no—
108C42×C11—81no—
109#2523C2×C1111yescharacteristic, complemented
110#2044C2×C1111yescharacteristic
111#1607C2×C1111yescharacteristic
112#1601C2×C1111yescharacteristic
113#1351C2×C1111yescharacteristic, complemented
114#1344C2×C1111yescharacteristic, complemented
115#1326C2×C1111yescharacteristic, complemented
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—81no—
124C23×C11—81no—
125C23×C11#12011yescharacteristic
126C23×C11#13511yescharacteristic
127C23×C11AGL(1,ℤ/8)11yescharacteristic
128Q8×C11—42no—
129Q8×C11—81no—
130D4×C11—81no—
131D4×C11—81no—
132D4×C11—81no—
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C8×C11—81no—
167C8×C11—81no—
168#534C22×C1111yescharacteristic
169#480—21no—
170#448—21no—
171C2×#99—21no—
172#397—21no—
173#397C22×C1111yescharacteristic
174#393C22×C1111yescharacteristic
175#391—21no—
176#387—21no—
177#387—21no—
178#386—21no—
179#385C22×C1111yescharacteristic
180#383—21no—
181C4×C22⋊C4—21no—
182#342C22×C1111yescharacteristic
183#327—21no—
184#327—21no—
185#323C22×C1111yescharacteristic
186#323C22×C1111yescharacteristic
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—81no—
196C22×C11—82no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—161no—
201C22×C11#44911yescharacteristic
202C22×C11#45411yescharacteristic
203C22×C11B(4,𝔽2)11yescharacteristic
204C4×C11—42no—
205C4×C11—42no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11—161no—
214C22×Q8D4×C1111yescharacteristic
215C22×D4—21no—
216C23×C4D4×C1111yescharacteristic
217C2×SD16—41no—
218#123—41no—
219#121—21no—
220#121—21no—
221#120—41no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4D4×C1111yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—41no—
229C2×C22⋊C4D4×C1111yescharacteristic
230C2×C22⋊C4C23×C1111yescharacteristic
231C2×C42—21no—
232C2×C42—21no—
233#107—41no—
234#103—41no—
235#102—41no—
236#99—42no—
237C22⋊C8—21no—
238C22⋊C8—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—41no—
248#95D4×C1111yescharacteristic
249#95D4×C1111yescharacteristic
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—41no—
253C2×C11—41no—
254C2×C11—161no—
255C2×C11#159711yescharacteristic
256C2×C11#219711yescharacteristic
257C2×C11#219711yescharacteristic
258C24—21no—
259C24C2×D4×C1111yescharacteristic
260C2×Q8—42no—
261C2×Q8—41no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4C2×D4×C1111yescharacteristic
281C22×C4C2×D4×C1111yescharacteristic
282SD16—82no—
283C2×C8—41no—
284C2×C8—41no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—41no—
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—82no—
301C42—42no—
302C42—81no—
303C11#1213411yescharacteristic, direct product factor, Sylow
304C23—21no—
305C23—21no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—81no—
312C23—81no—
313C23C11×#12011yescharacteristic
314C23C11×#13511yescharacteristic
315C23C11×AGL(1,ℤ/8)11yescharacteristic
316Q8—42no—
317Q8—81no—
318D4—81no—
319D4—81no—
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C8—81no—
355C8—81no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—81no—
365C22—82no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—161no—
370C22C11×#44911yescharacteristic
371C22C11×#45411yescharacteristic
372C22C11×B(4,𝔽2)11yescharacteristic
373C4—41no—
374C4—41no—
375C4—42no—
376C4—42no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—161no—
383C2—21no—
384C2—21no—
385C2—41no—
386C2—41no—
387C2—161no—
388C2C11×#159711yescharacteristic
389C2C11×#219711yescharacteristic
390C2C11×#219711yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC11×#534C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2523C2semidirect
5. C11×#1351C2semidirect
6. C11×#1344C2semidirect
7. C11×#1326C2semidirect
63. #12134C11direct (N × H)
109. #2523C2×C11semidirect
113. #1351C2×C11semidirect
114. #1344C2×C11semidirect
115. #1326C2×C11semidirect
303. C11#12134direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25232
C11×#20442
C11×#16072
C11×#16012
C11×#13512
C11×#13442
C11×#13262
#1213411