Finite Group Databasebeta

← C11×#10100 #14587293

Subgroups — C11×#10100 #14587293

Order 2816.

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

normal subgroups only

This group has 512 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×#2640C211yesmaximal, characteristic
4C11×#1556C211yesmaximal, characteristic, complemented
5C11×#1527C211yesmaximal, characteristic
6C11×#1506C211yesmaximal, characteristic, complemented
7C11×#1300C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#124C2211yescharacteristic
11C11×#501—22no—
12C11×#500—21no—
13C11×#498—21no—
14C11×#497—21no—
15C11×#489—21no—
16C11×#464—22no—
17C11×#451—21no—
18C11×#450—21no—
19C11×#432C2211yescharacteristic
20C11×#432C2211yescharacteristic
21C11×#428—22no—
22C4×C11×M16C2211yescharacteristic
23C11×#397—22no—
24C11×#393—22no—
25C11×#391—21no—
26C11×#390—21no—
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⋊Q8D411yescharacteristic
42C11×C4⋊Q8D411yescharacteristic
43C11×#125—21no—
44C11×#124—21no—
45C11×#124—21no—
46C11×#124—21no—
47C11×#124—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C11×#117—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—24no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C11×#107—24no—
61C11×#106—24no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#103—22no—
65C11×#102—22no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68C11×#97—21no—
69C11×#97—21no—
70C11×#97D412yes—
71C4×C8×C11—21no—
72C11×#95—24no—
73C11×#95—21no—
74C11×#95D412yes—
75#10100C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—82no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C11×Q16—82no—
95C11×SD16—82no—
96C11×M16—24no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—84no—
116C42×C11—42no—
117C42×C11—41no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122#3215C2×C1111yescharacteristic
123#3165C2×C1111yescharacteristic, complemented
124#2640C2×C1111yescharacteristic
125#1556C2×C1111yescharacteristic, complemented
126#1527C2×C1111yescharacteristic
127#1506C2×C1111yescharacteristic, complemented
128#1300C2×C1111yescharacteristic, complemented
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—41no—
132C23×C11—42no—
133C23×C11#12011yescharacteristic
134Q8×C11—42no—
135Q8×C11—42no—
136Q8×C11—81no—
137Q8×C11—81no—
138Q8×C11—82no—
139Q8×C11—82no—
140D4×C11—42no—
141D4×C11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—44no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12711yescharacteristic
160C8×C11—24no—
161C8×C11—42no—
162C8×C11—81no—
163#533C22×C1111yescharacteristic
164C2×C4⋊Q8C22×C1111yescharacteristic
165C2×#124C22×C1111yescharacteristic
166#501—22no—
167#500—21no—
168#498—21no—
169#497—21no—
170#489—21no—
171#464—22no—
172#451—21no—
173#450—21no—
174#432C22×C1111yescharacteristic
175#432C22×C1111yescharacteristic
176#428—22no—
177C4×M16C22×C1111yescharacteristic
178#397—22no—
179#393—22no—
180#391—21no—
181#390—21no—
182#376C22×C1111yescharacteristic
183#332—22no—
184#329—22no—
185#328—22no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—84no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11#39211yescharacteristic
193C22×C11#45612yes—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—82no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11—82no—
203C4×C11—81no—
204C4×C11#45512yes—
205C22×Q8—21no—
206C22×Q8D4×C1111yescharacteristic
207C22×D4D4×C1111yescharacteristic
208C2×Q16—22no—
209C2×SD16—22no—
210C2×M16—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8D4×C1111yescharacteristic
216C4⋊Q8D4×C1111yescharacteristic
217#125—21no—
218#124—21no—
219#124—21no—
220#124—21no—
221#124—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226#117—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4D4×C1112yes—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—24no—
232C2×C42—21no—
233C2×C42C23×C1111yescharacteristic
234#107—24no—
235#106—24no—
236C4⋊C8—21no—
237C4⋊C8D4×C1112yes—
238#103—22no—
239#102—22no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242#97—21no—
243#97—21no—
244#97D4×C1112yes—
245C4×C8—21no—
246#95—24no—
247#95—21no—
248#95D4×C1112yes—
249C2×C11—22no—
250C2×C11—161no—
251C2×C11#200411yescharacteristic
252C2×C11#200511yescharacteristic
253C2×C11#200811yescharacteristic
254C24—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—42no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—82no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—42no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4C2×D4×C1111yescharacteristic
270C22×C4C2×D4×C1111yescharacteristic
271C22×C4C2×D4×C1111yescharacteristic
272Q16—82no—
273SD16—82no—
274M16—24no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—41no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—84no—
294C42—42no—
295C42—41no—
296C42C2×D4×C1111yescharacteristic
297C42C2×D4×C1111yescharacteristic
298C42C2×D4×C1111yescharacteristic
299C42C11×#4111yescharacteristic
300C11#1010011yescharacteristic, direct product factor, Sylow
301C23—42no—
302C23—42no—
303C23—41no—
304C23—42no—
305C23C11×#12011yescharacteristic
306Q8—42no—
307Q8—42no—
308Q8—81no—
309Q8—81no—
310Q8—82no—
311Q8—82no—
312D4—42no—
313D4—81no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4C11×#12011yescharacteristic
327C2×C4C11×#12011yescharacteristic
328C2×C4C11×#12111yescharacteristic
329C2×C4C11×#12111yescharacteristic
330C2×C4C11×#12111yescharacteristic
331C2×C4C11×#12711yescharacteristic
332C8—24no—
333C8—42no—
334C8—81no—
335C22—21no—
336C22—21no—
337C22—84no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22C11×#39211yescharacteristic
342C22C11×#45612yes—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—81no—
350C4—81no—
351C4—82no—
352C4—81no—
353C4C11×#45512yes—
354C2—22no—
355C2—161no—
356C2C11×#200411yescharacteristic
357C2C11×#200511yescharacteristic
358C2C11×#200811yescharacteristic
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
75. #10100C11direct (N × H)
123. #3165C2×C11semidirect
125. #1556C2×C11semidirect
127. #1506C2×C11semidirect
128. #1300C2×C11semidirect
300. C11#10100direct (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×#26402
C11×#15562
C11×#15272
C11×#15062
C11×#13002
#1010011