Finite Group Databasebeta

← C11×#10129 #14587322

Subgroups — C11×#10129 #14587322

Order 2816.

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

normal subgroups only

This group has 600 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×#3215C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic, complemented
3C2×C11×#496C211yesmaximal, characteristic
4C11×#1555C211yesmaximal, characteristic, complemented
5C11×#1531C211yesmaximal, characteristic, complemented
6C11×#1469C211yesmaximal, characteristic, complemented
7C11×#1302C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C22×C11×D8—21no—
10C11×#533C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×C11×#124C2211yescharacteristic
13C11×#497—21no—
14C11×#496—22no—
15C11×#496—22no—
16C11×#492—21no—
17C11×#489—21no—
18C11×#486—21no—
19C11×#464—22no—
20C11×#460—22no—
21C11×#451—21no—
22C11×#450—21no—
23C11×#450—22no—
24C11×#432C2211yescharacteristic
25C11×#432C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C11×#331—22no—
29C11×#330—22no—
30C11×#323—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11D411yescharacteristic
36C2×C11×Q16—22no—
37C2×C11×SD16—24no—
38C2×C11×SD16—24no—
39C2×C11×SD16—22no—
40C2×C11×SD16—44no—
41C2×C11×D8—24no—
42C2×C11×D8—44no—
43C22×C8×C11—21no—
44C11×C4⋊Q8D411yescharacteristic
45C11×C4⋊Q8D411yescharacteristic
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127D412yes—
50C11×#125—21no—
51C11×#124—21no—
52C11×#124—21no—
53C11×#124—21no—
54C11×#124—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C11×#117—21no—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C42×C11C2311yescharacteristic
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×#103—22no—
67C11×#102—22no—
68C11×#102—24no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8D412yes—
72C11×#97—21no—
73C11×#97—21no—
74C11×#97—21no—
75C11×#97D412yes—
76C4×C8×C11—21no—
77#10129C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C24×C11—41no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—42no—
85C2×D4×C11—21no—
86C2×D4×C11—22no—
87C2×D4×C11—21no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11—42no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—82no—
97C2×D4×C11—82no—
98C22×C4×C11—21no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C11×Q16—82no—
103C11×SD16—48no—
104C11×SD16—84no—
105C11×SD16—82no—
106C11×D8—48no—
107C2×C8×C11—24no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—41no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128#3215C2×C1111yescharacteristic, complemented
129#3208C2×C1111yescharacteristic, complemented
130C2×#496C2×C1111yescharacteristic
131#1555C2×C1111yescharacteristic, complemented
132#1531C2×C1111yescharacteristic, complemented
133#1469C2×C1111yescharacteristic, complemented
134#1302C2×C1111yescharacteristic, complemented
135C23×C11—41no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11—82no—
139C23×C11—82no—
140C23×C11—81no—
141C23×C11—81no—
142C23×C11—82no—
143C23×C11#12111yescharacteristic
144Q8×C11—42no—
145Q8×C11—42no—
146Q8×C11—42no—
147Q8×C11—42no—
148D4×C11—42no—
149D4×C11—42no—
150D4×C11—42no—
151D4×C11—44no—
152D4×C11—42no—
153D4×C11—82no—
154D4×C11—82no—
155D4×C11—82no—
156D4×C11—82no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—81no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12711yescharacteristic
170C8×C11—24no—
171C8×C11—42no—
172C8×C11—42no—
173C8×C11—81no—
174C22×SD16—21no—
175C22×D8—21no—
176#533C22×C1111yescharacteristic
177C2×#127C22×C1111yescharacteristic
178C2×#124C22×C1111yescharacteristic
179#497—21no—
180#496—22no—
181#496—22no—
182#492—21no—
183#489—21no—
184#486—21no—
185#464—22no—
186#460—22no—
187#451—21no—
188#450—21no—
189#450—22no—
190#432C22×C1111yescharacteristic
191#432C22×C1111yescharacteristic
192#431C22×C1111yescharacteristic
193C2×#97C22×C1111yescharacteristic
194#331—22no—
195#330—22no—
196#323—22no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—81no—
200C22×C11—82no—
201C22×C11—82no—
202C22×C11—81no—
203C22×C11—82no—
204C22×C11—81no—
205C22×C11—162no—
206C22×C11—164no—
207C22×C11#39211yescharacteristic
208C22×C11#47112yes—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11#45312yes—
218C22×Q8D4×C1111yescharacteristic
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4D4×C1111yescharacteristic
223C2×Q16—22no—
224C2×SD16—24no—
225C2×SD16—24no—
226C2×SD16—22no—
227C2×SD16—44no—
228C2×D8—24no—
229C2×D8—44no—
230C22×C8—21no—
231C4⋊Q8D4×C1111yescharacteristic
232C4⋊Q8D4×C1111yescharacteristic
233#127—21no—
234#127—21no—
235#127—21no—
236#127D4×C1112yes—
237#125—21no—
238#124—21no—
239#124—21no—
240#124—21no—
241#124—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246#117—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C42C23×C1111yescharacteristic
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8D4×C1112yes—
253#103—22no—
254#102—24no—
255#102—22no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8D4×C1112yes—
259#97—21no—
260#97—21no—
261#97—21no—
262#97D4×C1112yes—
263C4×C8—21no—
264C2×C11—22no—
265C2×C11—161no—
266C2×C11—162no—
267C2×C11#200211yescharacteristic
268C2×C11#200811yescharacteristic
269C2×C11#201911yescharacteristic
270C24—21no—
271C24—41no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—42no—
277C2×D4—21no—
278C2×D4—22no—
279C2×D4—21no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—82no—
289C2×D4—82no—
290C22×C4—21no—
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C2×D4×C1111yescharacteristic
293C22×C4C11×#4111yescharacteristic
294Q16—82no—
295SD16—48no—
296SD16—84no—
297SD16—82no—
298D8—48no—
299C2×C8—24no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—41no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C42—41no—
316C42C2×D4×C1111yescharacteristic
317C42C2×D4×C1111yescharacteristic
318C42C2×D4×C1111yescharacteristic
319C42C2×D4×C1111yescharacteristic
320C11#1012911yescharacteristic, direct product factor, Sylow
321C23—41no—
322C23—42no—
323C23—42no—
324C23—82no—
325C23—82no—
326C23—81no—
327C23—81no—
328C23—82no—
329C23C11×#12111yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—42no—
333Q8—42no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—44no—
338D4—42no—
339D4—82no—
340D4—82no—
341D4—82no—
342D4—82no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4C11×#12011yescharacteristic
351C2×C4C11×#12011yescharacteristic
352C2×C4C11×#12011yescharacteristic
353C2×C4C11×#12111yescharacteristic
354C2×C4C11×#12111yescharacteristic
355C2×C4C11×#12711yescharacteristic
356C8—24no—
357C8—42no—
358C8—42no—
359C8—81no—
360C22—21no—
361C22—21no—
362C22—81no—
363C22—82no—
364C22—82no—
365C22—81no—
366C22—82no—
367C22—81no—
368C22—162no—
369C22—164no—
370C22C11×#39211yescharacteristic
371C22C11×#47112yes—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4C11×#45312yes—
381C2—22no—
382C2—162no—
383C2—161no—
384C2C11×#200211yescharacteristic
385C2C11×#200811yescharacteristic
386C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#496C2
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×#3215C2semidirect
2. C11×#3208C2semidirect
4. C11×#1555C2semidirect
5. C11×#1531C2semidirect
6. C11×#1469C2semidirect
7. C11×#1302C2semidirect
77. #10129C11direct (N × H)
128. #3215C2×C11semidirect
129. #3208C2×C11semidirect
131. #1555C2×C11semidirect
132. #1531C2×C11semidirect
133. #1469C2×C11semidirect
134. #1302C2×C11semidirect
320. C11#10129direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32152
C11×#32082
C2×C11×#4962
C11×#15552
C11×#15312
C11×#14692
C11×#13022
#1012911