Finite Group Databasebeta

← C11×#10102 #14587295

Subgroups — C11×#10102 #14587295

Order 2816.

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

normal subgroups only

This group has 568 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
2C11×#3165C211yesmaximal, characteristic, complemented
3C11×#2658C211yesmaximal, characteristic
4C11×#1556C211yesmaximal, characteristic, complemented
5C11×#1527C211yesmaximal, characteristic
6C11×#1506C211yesmaximal, characteristic, complemented
7C11×#1300C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#124—21no—
12C2×C11×#124C2211yescharacteristic
13C11×#501—22no—
14C11×#500—21no—
15C11×#498—21no—
16C11×#497—21no—
17C11×#489—21no—
18C11×#464—22no—
19C11×#451—21no—
20C11×#450—21no—
21C11×#432C2211yescharacteristic
22C11×#432C2211yescharacteristic
23C11×#428—22no—
24C4×C11×M16C2211yescharacteristic
25C11×#399—22no—
26C11×#399—22no—
27C11×#376C2211yescharacteristic
28C11×#332—22no—
29C11×#329—22no—
30C11×#328—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C2×C11×Q16—22no—
35C2×C11×SD16—22no—
36C2×C11×M16—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—44no—
42C11×C4⋊Q8D411yescharacteristic
43C11×C4⋊Q8D411yescharacteristic
44C11×#125—21no—
45C11×#124—21no—
46C11×#124—21no—
47C11×#124—21no—
48C11×#124—21no—
49C11×#124—44no—
50C11×C22⋊Q8—21no—
51C11×C22⋊Q8—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C11×#117—21no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C11×#107—24no—
64C11×#106—24no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#103—22no—
68C11×#102—22no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—21no—
71C11×#97—21no—
72C11×#97—21no—
73C11×#97D412yes—
74C4×C8×C11—21no—
75C11×#95—21no—
76C11×#95D412yes—
77#10102C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—42no—
84C2×Q8×C11—42no—
85C2×Q8×C11—42no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—42no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C11×Q16—82no—
98C11×SD16—82no—
99C11×M16—24no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—41no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—48no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—48no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C42×C11—24no—
121C42×C11—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126#3215C2×C1111yescharacteristic
127#3165C2×C1111yescharacteristic, complemented
128#2658C2×C1111yescharacteristic
129#1556C2×C1111yescharacteristic, complemented
130#1527C2×C1111yescharacteristic
131#1506C2×C1111yescharacteristic, complemented
132#1300C2×C1111yescharacteristic, complemented
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—41no—
136C23×C11—42no—
137C23×C11#12011yescharacteristic
138Q8×C11—42no—
139Q8×C11—42no—
140Q8×C11—81no—
141Q8×C11—81no—
142Q8×C11—82no—
143Q8×C11—82no—
144D4×C11—42no—
145D4×C11—81no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
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#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12711yescharacteristic
165C8×C11—24no—
166C8×C11—42no—
167C8×C11—81no—
168#533C22×C1111yescharacteristic
169C2×C4⋊Q8—21no—
170C2×C4⋊Q8C22×C1111yescharacteristic
171C2×#124—21no—
172C2×#124C22×C1111yescharacteristic
173#501—22no—
174#500—21no—
175#498—21no—
176#497—21no—
177#489—21no—
178#464—22no—
179#451—21no—
180#450—21no—
181#432C22×C1111yescharacteristic
182#432C22×C1111yescharacteristic
183#428—22no—
184C4×M16C22×C1111yescharacteristic
185#399—22no—
186#399—22no—
187#376C22×C1111yescharacteristic
188#332—22no—
189#329—22no—
190#328—22no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—84no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#39211yescharacteristic
198C22×C11#45612yes—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—44no—
205C4×C11—81no—
206C4×C11—82no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11#45312yes—
210C22×Q8—21no—
211C22×Q8D4×C1111yescharacteristic
212C22×D4D4×C1111yescharacteristic
213C2×Q16—22no—
214C2×SD16—22no—
215C2×M16—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—44no—
221C4⋊Q8D4×C1111yescharacteristic
222C4⋊Q8D4×C1111yescharacteristic
223#125—21no—
224#124—21no—
225#124—21no—
226#124—21no—
227#124—21no—
228#124—44no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233#117—21no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4D4×C1112yes—
237C2×C22⋊C4—24no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C42—21no—
241C2×C42C23×C1111yescharacteristic
242#107—24no—
243#106—24no—
244C4⋊C8—21no—
245C4⋊C8D4×C1112yes—
246#103—22no—
247#102—22no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250#97—21no—
251#97—21no—
252#97D4×C1112yes—
253C4×C8—21no—
254#95—21no—
255#95D4×C1112yes—
256C2×C11—22no—
257C2×C11—161no—
258C2×C11#200211yescharacteristic
259C2×C11#200511yescharacteristic
260C2×C11#200911yescharacteristic
261C24—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—42no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4C2×D4×C1111yescharacteristic
278C22×C4C2×D4×C1111yescharacteristic
279C22×C4C2×D4×C1111yescharacteristic
280Q16—82no—
281SD16—82no—
282M16—24no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—41no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—48no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C22⋊C4—48no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C42—24no—
304C42—41no—
305C42C2×D4×C1111yescharacteristic
306C42C2×D4×C1111yescharacteristic
307C42C2×D4×C1111yescharacteristic
308C42C11×#4111yescharacteristic
309C11#1010211yescharacteristic, direct product factor, Sylow
310C23—42no—
311C23—42no—
312C23—41no—
313C23—42no—
314C23C11×#12011yescharacteristic
315Q8—42no—
316Q8—42no—
317Q8—81no—
318Q8—81no—
319Q8—82no—
320Q8—82no—
321D4—42no—
322D4—81no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4C11×#12011yescharacteristic
337C2×C4C11×#12011yescharacteristic
338C2×C4C11×#12111yescharacteristic
339C2×C4C11×#12111yescharacteristic
340C2×C4C11×#12111yescharacteristic
341C2×C4C11×#12711yescharacteristic
342C8—24no—
343C8—42no—
344C8—81no—
345C22—21no—
346C22—21no—
347C22—84no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22C11×#39211yescharacteristic
352C22C11×#45612yes—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—44no—
359C4—81no—
360C4—82no—
361C4—81no—
362C4—81no—
363C4C11×#45312yes—
364C2—22no—
365C2—161no—
366C2C11×#200211yescharacteristic
367C2C11×#200511yescharacteristic
368C2C11×#200911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
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×#3165C2semidirect
4. C11×#1556C2semidirect
6. C11×#1506C2semidirect
7. C11×#1300C2semidirect
77. #10102C11direct (N × H)
127. #3165C2×C11semidirect
129. #1556C2×C11semidirect
131. #1506C2×C11semidirect
132. #1300C2×C11semidirect
309. C11#10102direct (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×#31652
C11×#26582
C11×#15562
C11×#15272
C11×#15062
C11×#13002
#1010211