Finite Group Databasebeta

← C11×#10097 #14587290

Subgroups — C11×#10097 #14587290

Order 2816.

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

normal subgroups only

This group has 542 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×#3236C211yesmaximal, characteristic, complemented
2C11×#3138C211yesmaximal, characteristic
3C11×#2641C211yesmaximal, characteristic
4C11×#1555C211yesmaximal, characteristic
5C11×#1528C211yesmaximal, characteristic, complemented
6C11×#1506C211yesmaximal, characteristic, complemented
7C11×#1300C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×C11×#125C2211yescharacteristic
11C11×#501—21no—
12C11×#491—21no—
13C11×#490—22no—
14C11×#486—21no—
15C11×#486—21no—
16C11×#484—21no—
17C11×#483—21no—
18C11×#479—22no—
19C11×#432C2211yescharacteristic
20C11×#432C2211yescharacteristic
21C11×#418—22no—
22C4×C11×M16C2211yescharacteristic
23C11×#394—22no—
24C11×#394—22no—
25C11×#390—21no—
26C11×#390—21no—
27C11×#376C2211yescharacteristic
28C11×#331—22no—
29C11×#330—22no—
30C11×#328—22no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D412yes—
34C2×C11×M16—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#125—21no—
42C11×#125—21no—
43C11×#125—21no—
44C11×#125—21no—
45C11×#125—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C11×#117—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—24no—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C11×#107—22no—
60C11×#106—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×#103—22no—
64C11×#103—22no—
65C11×#102—24no—
66C11×#102—24no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×#97—21no—
70C11×#97—21no—
71C11×#97D412yes—
72C4×C8×C11—21no—
73C11×#95—21no—
74C11×#95D412yes—
75#10097C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—44no—
82C2×D4×C11—44no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—82no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C11×M16—42no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—84no—
114C11×C22⋊C4—84no—
115C42×C11—42no—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121#3236C2×C1111yescharacteristic, complemented
122#3138C2×C1111yescharacteristic
123#2641C2×C1111yescharacteristic
124#1555C2×C1111yescharacteristic
125#1528C2×C1111yescharacteristic, complemented
126#1506C2×C1111yescharacteristic, complemented
127#1300C2×C1111yescharacteristic, complemented
128C23×C11—44no—
129C23×C11—44no—
130C23×C11—42no—
131C23×C11—44no—
132C23×C11#12011yescharacteristic
133Q8×C11—42no—
134Q8×C11—81no—
135D4×C11—44no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—82no—
139D4×C11—82no—
140D4×C11—82no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C8×C11—42no—
160C8×C11—42no—
161C8×C11—81no—
162#533C22×C1111yescharacteristic
163C2×#127C22×C1111yescharacteristic
164C2×#125C22×C1111yescharacteristic
165#501—21no—
166#491—21no—
167#490—22no—
168#486—21no—
169#486—21no—
170#484—21no—
171#483—21no—
172#479—22no—
173#432C22×C1111yescharacteristic
174#432C22×C1111yescharacteristic
175#418—22no—
176C4×M16C22×C1111yescharacteristic
177#394—22no—
178#394—22no—
179#390—21no—
180#390—21no—
181#376C22×C1111yescharacteristic
182#331—22no—
183#330—22no—
184#328—22no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—88no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11#39211yescharacteristic
192C22×C11#45512yes—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—82no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11—81no—
203C4×C11#45412yes—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4D4×C1112yes—
207C2×M16—21no—
208C4⋊Q8D4×C1111yescharacteristic
209C4⋊Q8D4×C1111yescharacteristic
210#127—21no—
211#127—21no—
212#127—21no—
213#127—21no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—21no—
218#125—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223#117—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4D4×C1111yescharacteristic
227C2×C4⋊C4D4×C1111yescharacteristic
228C2×C22⋊C4—24no—
229C2×C22⋊C4—24no—
230C2×C42—21no—
231C2×C42C23×C1111yescharacteristic
232#107—22no—
233#106—22no—
234C4⋊C8—21no—
235C4⋊C8D4×C1112yes—
236#103—22no—
237#103—22no—
238#102—24no—
239#102—24no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242#97—21no—
243#97—21no—
244#97D4×C1112yes—
245C4×C8—21no—
246#95—21no—
247#95D4×C1112yes—
248C2×C11—22no—
249C2×C11—162no—
250C2×C11#200311yescharacteristic
251C2×C11#200411yescharacteristic
252C2×C11#200811yescharacteristic
253C24—22no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—44no—
259C2×D4—44no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—82no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4C2×D4×C1111yescharacteristic
269C22×C4C2×D4×C1111yescharacteristic
270C22×C4C2×D4×C1111yescharacteristic
271M16—42no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—41no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—84no—
291C22⋊C4—84no—
292C42—42no—
293C42—41no—
294C42C2×D4×C1111yescharacteristic
295C42C2×D4×C1111yescharacteristic
296C42C2×D4×C1111yescharacteristic
297C42C11×#4111yescharacteristic
298C11#1009711yescharacteristic, direct product factor, Sylow
299C23—44no—
300C23—44no—
301C23—42no—
302C23—44no—
303C23C11×#12011yescharacteristic
304Q8—42no—
305Q8—81no—
306D4—44no—
307D4—82no—
308D4—82no—
309D4—82no—
310D4—82no—
311D4—82no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4C11×#12011yescharacteristic
325C2×C4C11×#12011yescharacteristic
326C2×C4C11×#12111yescharacteristic
327C2×C4C11×#12111yescharacteristic
328C2×C4C11×#12111yescharacteristic
329C2×C4C11×#12711yescharacteristic
330C8—42no—
331C8—42no—
332C8—81no—
333C22—21no—
334C22—21no—
335C22—88no—
336C22—82no—
337C22—82no—
338C22—82no—
339C22C11×#39211yescharacteristic
340C22C11×#45512yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—82no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4C11×#45412yes—
352C2—22no—
353C2—162no—
354C2C11×#200311yescharacteristic
355C2C11×#200411yescharacteristic
356C2C11×#200811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
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×#3236C2semidirect
5. C11×#1528C2semidirect
6. C11×#1506C2semidirect
7. C11×#1300C2semidirect
75. #10097C11direct (N × H)
121. #3236C2×C11semidirect
125. #1528C2×C11semidirect
126. #1506C2×C11semidirect
127. #1300C2×C11semidirect
298. C11#10097direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32362
C11×#31382
C11×#26412
C11×#15552
C11×#15282
C11×#15062
C11×#13002
#1009711