Finite Group Databasebeta

← C11×#10089 #14587282

Subgroups — C11×#10089 #14587282

Order 2816.

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

normal subgroups only

This group has 628 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×#3234C211yesmaximal, characteristic, complemented
2C11×#3151C211yesmaximal, characteristic
3C11×#2641C211yesmaximal, characteristic, complemented
4C11×#1555C211yesmaximal, characteristic, complemented
5C11×#1528C211yesmaximal, characteristic, complemented
6C11×#1505C211yesmaximal, characteristic, complemented
7C11×#1300C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—22no—
9C11×#532C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×#125C2211yescharacteristic
12C11×#501—21no—
13C11×#496—22no—
14C11×#493—21no—
15C11×#492—21no—
16C11×#490—21no—
17C11×#481—21no—
18C11×#480—21no—
19C11×#478—22no—
20C11×#432C2211yescharacteristic
21C11×#432C2211yescharacteristic
22C4×C11×M16C2211yescharacteristic
23C11×#394—22no—
24C11×#394—22no—
25C11×#390—21no—
26C11×#390—21no—
27C11×#376C2211yescharacteristic
28C11×#331—22no—
29C11×#330—22no—
30C11×#327—22no—
31C2×C11×#41—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11D412yes—
35C11×AGL(1,ℤ/8)—48no—
36C2×C11×SD16—24no—
37C2×C11×D8—24no—
38C2×C11×M16—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#127D411yescharacteristic
45C11×#125—21no—
46C11×#125—21no—
47C11×#125—21no—
48C11×#125—21no—
49C11×#124—21no—
50C11×#121—21no—
51C11×#121—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—24no—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C11×#107—22no—
63C11×#106—22no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×#102—22no—
67C11×#102—22no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8—21no—
70C11×#97—21no—
71C11×#97—21no—
72C11×#97D412yes—
73C4×C8×C11—21no—
74C11×#95—21no—
75C11×#95D412yes—
76#10089C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11—22no—
78C11×#41—44no—
79C2×Q8×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—44no—
86C2×D4×C11—44no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—82no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C11×SD16—48no—
101C11×D8—48no—
102C11×M16—24no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—84no—
119C11×C22⋊C4—84no—
120C42×C11—42no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125#3234C2×C1111yescharacteristic, complemented
126#3151C2×C1111yescharacteristic
127#2641C2×C1111yescharacteristic, complemented
128#1555C2×C1111yescharacteristic, complemented
129#1528C2×C1111yescharacteristic, complemented
130#1505C2×C1111yescharacteristic, complemented
131#1300C2×C1111yescharacteristic, complemented
132C23×C11—44no—
133C23×C11—44no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—44no—
137C23×C11#12011yescharacteristic
138Q8×C11—42no—
139D4×C11—42no—
140D4×C11—44no—
141D4×C11—42no—
142D4×C11—81no—
143D4×C11—82no—
144D4×C11—82no—
145D4×C11—82no—
146D4×C11—82no—
147D4×C11—82no—
148D4×C11—82no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—82no—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12711yescharacteristic
167C8×C11—24no—
168C8×C11—42no—
169C8×C11—81no—
170C2×AGL(1,ℤ/8)—22no—
171#532C22×C1111yescharacteristic
172C2×#127C22×C1111yescharacteristic
173C2×#125C22×C1111yescharacteristic
174#501—21no—
175#496—22no—
176#493—21no—
177#492—21no—
178#490—21no—
179#481—21no—
180#480—21no—
181#478—22no—
182#432C22×C1111yescharacteristic
183#432C22×C1111yescharacteristic
184C4×M16C22×C1111yescharacteristic
185#394—22no—
186#394—22no—
187#390—21no—
188#390—21no—
189#376C22×C1111yescharacteristic
190#331—22no—
191#330—22no—
192#327—22no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—88no—
196C22×C11—81no—
197C22×C11—82no—
198C22×C11—81no—
199C22×C11—82no—
200C22×C11—82no—
201C22×C11—81no—
202C22×C11#39211yescharacteristic
203C22×C11#45312yes—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—82no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11#45412yes—
214C2×#41—21no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4D4×C1112yes—
218AGL(1,ℤ/8)—48no—
219C2×SD16—24no—
220C2×D8—24no—
221C2×M16—21no—
222C4⋊Q8D4×C1111yescharacteristic
223#127—21no—
224#127—21no—
225#127—21no—
226#127—21no—
227#127D4×C1111yescharacteristic
228#125—21no—
229#125—21no—
230#125—21no—
231#125—21no—
232#124—21no—
233#121—21no—
234#121—21no—
235C4×D4—21no—
236C4×D4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4D4×C1111yescharacteristic
240C2×C4⋊C4D4×C1111yescharacteristic
241C2×C22⋊C4—24no—
242C2×C22⋊C4—24no—
243C2×C42—21no—
244C2×C42C23×C1111yescharacteristic
245#107—22no—
246#106—22no—
247C4⋊C8—21no—
248C4⋊C8D4×C1112yes—
249#102—22no—
250#102—22no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253#97—21no—
254#97—21no—
255#97D4×C1112yes—
256C4×C8—21no—
257#95—21no—
258#95D4×C1112yes—
259C2×C11—22no—
260C2×C11—161no—
261C2×C11—162no—
262C2×C11#200211yescharacteristic
263C2×C11#200311yescharacteristic
264C2×C11#200811yescharacteristic
265C24—22no—
266#41—44no—
267C2×Q8—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—22no—
271C2×D4—21no—
272C2×D4—22no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—82no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C2×D4×C1111yescharacteristic
287C22×C4C2×D4×C1111yescharacteristic
288SD16—48no—
289D8—48no—
290M16—24no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—41no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—84no—
307C22⋊C4—84no—
308C42—42no—
309C42C2×D4×C1111yescharacteristic
310C42C2×D4×C1111yescharacteristic
311C42C2×D4×C1111yescharacteristic
312C42C11×#4111yescharacteristic
313C11#1008911yescharacteristic, direct product factor, Sylow
314C23—44no—
315C23—44no—
316C23—41no—
317C23—42no—
318C23—44no—
319C23C11×#12011yescharacteristic
320Q8—42no—
321D4—42no—
322D4—44no—
323D4—42no—
324D4—81no—
325D4—82no—
326D4—82no—
327D4—82no—
328D4—82no—
329D4—82no—
330D4—82no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—82no—
343C2×C4C11×#12011yescharacteristic
344C2×C4C11×#12011yescharacteristic
345C2×C4C11×#12111yescharacteristic
346C2×C4C11×#12111yescharacteristic
347C2×C4C11×#12111yescharacteristic
348C2×C4C11×#12711yescharacteristic
349C8—24no—
350C8—42no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—88no—
355C22—81no—
356C22—82no—
357C22—81no—
358C22—82no—
359C22—82no—
360C22—81no—
361C22C11×#39211yescharacteristic
362C22C11×#45312yes—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—82no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4C11×#45412yes—
373C2—22no—
374C2—162no—
375C2—161no—
376C2C11×#200211yescharacteristic
377C2C11×#200311yescharacteristic
378C2C11×#200811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3151C2
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
1. C11×#3234C2semidirect
3. C11×#2641C2semidirect
4. C11×#1555C2semidirect
5. C11×#1528C2semidirect
6. C11×#1505C2semidirect
7. C11×#1300C2semidirect
76. #10089C11direct (N × H)
125. #3234C2×C11semidirect
127. #2641C2×C11semidirect
128. #1555C2×C11semidirect
129. #1528C2×C11semidirect
130. #1505C2×C11semidirect
131. #1300C2×C11semidirect
313. C11#10089direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32342
C11×#31512
C11×#26412
C11×#15552
C11×#15282
C11×#15052
C11×#13002
#1008911