Finite Group Databasebeta

← C11×#11897 #14589090

Subgroups — C11×#11897 #14589090

Order 2816.

452 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2580C211yesmaximal, characteristic
2C11×#1799C211yesmaximal, characteristic
3C11×#1459C211yesmaximal, characteristic
4C11×#1352C212yesmaximal, complemented
5C11×#1351C212yesmaximal, complemented
6C2×C4×Q8×C11C411yescharacteristic, complemented
7C2×C4×D4×C11C2211yescharacteristic
8C2×C11×#99—21no—
9C2×C11×C22⋊C8—21no—
10C11×#399C411yescharacteristic, complemented
11C11×#399C2211yescharacteristic
12C11×#393C411yescharacteristic, complemented
13C11×#393C2211yescharacteristic
14C11×#390—21no—
15C11×#389—21no—
16C11×#385—21no—
17C11×#385—21no—
18C11×#382C411yescharacteristic, complemented
19C11×#380—21no—
20C11×#342C2212yes—
21C11×#324—21no—
22C11×#323C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×D4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C22×C8×C11—41no—
28C4×Q8×C11—41no—
29C4×Q8×C11—41no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—41no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4C2311yescharacteristic
46C2×C42×C11—21no—
47C2×C42×C11C2×C411yescharacteristic
48C11×#99—42no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—41no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—41no—
55C11×#95C2×C411yescharacteristic
56C11×#95C2×C411yescharacteristic
57#11897C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C2×Q8×C11—42no—
61C2×Q8×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11SD1612yes—
65C2×D4×C11Q1612yes—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—42no—
75C22×C4×C11—81no—
76C22×C4×C11—81no—
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C8×C11—42no—
83C2×C8×C11—82no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—81no—
90C11×C4⋊C4—81no—
91C11×C4⋊C4—82no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—42no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—81no—
99C11×C22⋊C4—81no—
100C42×C11—21no—
101C42×C11—21no—
102C42×C11—42no—
103#2580C2×C1111yescharacteristic
104#1799C2×C1111yescharacteristic
105#1459C2×C1111yescharacteristic
106#1352C2×C1112yescomplemented
107#1351C2×C1112yescomplemented
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11#10312yes—
117C23×C11C2×C22⋊C411yescharacteristic
118C23×C11C2×SD1611yescharacteristic
119C23×C11C2×Q1611yescharacteristic
120Q8×C11—42no—
121Q8×C11—42no—
122D4×C11—42no—
123D4×C11—42no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—22no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11—82no—
150C2×C4×C11—82no—
151C2×C4×C11—82no—
152C2×C4×C11#9911yescharacteristic
153C2×C4×C11#9911yescharacteristic
154C2×C4×C11#10312yes—
155C8×C11—82no—
156C2×C4×Q8C4×C1111yescharacteristic, complemented
157C2×C4×D4C22×C1111yescharacteristic
158C2×#99—21no—
159C2×C22⋊C8—21no—
160#399C4×C1111yescharacteristic, complemented
161#399C22×C1111yescharacteristic
162#393C4×C1111yescharacteristic, complemented
163#393C22×C1111yescharacteristic
164#390—21no—
165#389—21no—
166#385—21no—
167#385—21no—
168#382C4×C1111yescharacteristic, complemented
169#380—21no—
170#342C22×C1112yes—
171#324—21no—
172#323C22×C1112yes—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—22no—
177C22×C11—21no—
178C22×C11—42no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11C2×#9911yescharacteristic
188C22×C11C2×#10311yescharacteristic
189C22×C11#42111yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—22no—
193C4×C11—42no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11—81no—
200C4×C11—162no—
201C22×Q8C2×C4×C1111yescharacteristic
202C22×D4D4×C1111yescharacteristic
203C23×C4D4×C1111yescharacteristic
204C23×C4D4×C1111yescharacteristic
205C22×C8—41no—
206C4×Q8—41no—
207C4×Q8—41no—
208C4×D4—41no—
209C4×D4—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4C2×C4×C1111yescharacteristic
216C2×C4⋊C4D4×C1111yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4C2×C4×C1111yescharacteristic
223C2×C22⋊C4C23×C1111yescharacteristic
224C2×C42—21no—
225C2×C42C2×C4×C1111yescharacteristic
226#99—42no—
227C22⋊C8—22no—
228C22⋊C8—41no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—41no—
233#95C2×C4×C1111yescharacteristic
234#95C2×C4×C1111yescharacteristic
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—41no—
238C2×C11—42no—
239C2×C11—41no—
240C2×C11#152011yescharacteristic
241C2×C11#212011yescharacteristic
242C2×C11#212711yescharacteristic
243C24C11×C22⋊C411yescharacteristic
244C24C2×D4×C1111yescharacteristic
245C2×Q8—42no—
246C2×Q8—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4C11×SD1612yes—
250C2×D4C11×Q1612yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—42no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4C11×C22⋊C411yescharacteristic
263C22×C4C11×C22⋊C411yescharacteristic
264C22×C4C11×C22⋊C411yescharacteristic
265C22×C4C22×C4×C1111yescharacteristic
266C22×C4C2×D4×C1111yescharacteristic
267C2×C8—42no—
268C2×C8—82no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—81no—
275C4⋊C4—81no—
276C4⋊C4—82no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—81no—
284C22⋊C4—81no—
285C42—21no—
286C42—21no—
287C42—42no—
288C11#1189711yescharacteristic, direct product factor, Sylow
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C11×#10312yes—
298C23C2×C11×C22⋊C411yescharacteristic
299C23C2×C11×SD1611yescharacteristic
300C23C2×C11×Q1611yescharacteristic
301Q8—42no—
302Q8—42no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4C11×#9911yescharacteristic
334C2×C4C11×#9911yescharacteristic
335C2×C4C11×#10312yes—
336C8—82no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22C2×C11×#9911yescharacteristic
352C22C2×C11×#10311yescharacteristic
353C22C11×#42111yescharacteristic
354C4—21no—
355C4—21no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—42no—
360C4—41no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—162no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—42no—
369C2—41no—
370C2C11×#152011yescharacteristic
371C2C11×#212011yescharacteristic
372C2C11×#212711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C11×#1352C2semidirect
5. C11×#1351C2semidirect
6. C2×C4×Q8×C11C4semidirect
10. C11×#399C4semidirect
12. C11×#393C4semidirect
18. C11×#382C4semidirect
57. #11897C11direct (N × H)
106. #1352C2×C11semidirect
107. #1351C2×C11semidirect
156. C2×C4×Q8C4×C11semidirect
160. #399C4×C11semidirect
162. #393C4×C11semidirect
168. #382C4×C11semidirect
288. C11#11897direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25802
C11×#17992
C11×#14592
C11×#13522
C11×#13512
#1189711