Finite Group Databasebeta

← C11×#11546 #14588739

Subgroups — C11×#11546 #14588739

Order 2816.

460 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2482C211yesmaximal, characteristic
2C11×#1464C211yesmaximal, characteristic, complemented
3C11×#1458C211yesmaximal, characteristic, complemented
4C11×#1326C212yesmaximal, complemented
5C11×#1316C212yesmaximal
6C2×C11×#117C2211yescharacteristic
7C22×C11×C22⋊C4C411yescharacteristic
8C11×#432—21no—
9C11×#431—21no—
10C11×#399—21no—
11C11×#397—21no—
12C11×#388—21no—
13C11×#388—21no—
14C11×#385C411yescharacteristic
15C11×#385C2211yescharacteristic
16C11×#381C411yescharacteristic
17C11×#379C411yescharacteristic
18C11×#379C2211yescharacteristic
19C11×#324—21no—
20C11×#324—21no—
21C11×#323C2212yes—
22C11×#323C2212yes—
23C25×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C11×#117—41no—
27C11×#117—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—41no—
39C2×C11×C22⋊C4—41no—
40C2×C11×C22⋊C4C2×C411yescharacteristic
41C2×C11×C22⋊C4C2×C411yescharacteristic
42C2×C11×C22⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4C2311yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C11×C4⋊C8—41no—
47C11×C4⋊C8—41no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—22no—
50C11×#97—41no—
51C4×C8×C11—41no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56#11546C1111yesmaximal, characteristic, direct product factor, Sylow
57C24×C11—21no—
58C24×C11—22no—
59C24×C11—41no—
60C24×C11—42no—
61C24×C11—41no—
62C24×C11—81no—
63C24×C11C22×C411yescharacteristic
64C22×C4×C11—22no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—81no—
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C2×C8×C11—42no—
80C2×C8×C11—42no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—81no—
84C11×C4⋊C4—81no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—42no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—42no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—81no—
95C11×C22⋊C4—81no—
96C42×C11—21no—
97C42×C11—21no—
98C42×C11—21no—
99C42×C11—21no—
100#2482C2×C1111yescharacteristic
101#1464C2×C1111yescharacteristic, complemented
102#1458C2×C1111yescharacteristic, complemented
103#1326C2×C1112yescomplemented
104#1316C2×C1112yes—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—22no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—42no—
114C23×C11—42no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—82no—
119C23×C11—84no—
120C23×C11—84no—
121C23×C11—82no—
122C23×C11C2×C22⋊C411yescharacteristic
123C23×C11#13112yes—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
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—41no—
148C2×C4×C11—82no—
149C2×C4×C11#9911yescharacteristic
150C2×C4×C11#9911yescharacteristic
151C8×C11—82no—
152C8×C11—82no—
153C2×#117C22×C1111yescharacteristic
154C22×C22⋊C4C4×C1111yescharacteristic
155#432—21no—
156#431—21no—
157#399—21no—
158#397—21no—
159#388—21no—
160#388—21no—
161#385C4×C1111yescharacteristic
162#385C22×C1111yescharacteristic
163#381C4×C1111yescharacteristic
164#379C4×C1111yescharacteristic
165#379C22×C1111yescharacteristic
166#324—21no—
167#324—21no—
168#323C22×C1112yes—
169#323C22×C1112yes—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—22no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11—42no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—42no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—84no—
183C22×C11—84no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11#40811yescharacteristic
187C22×C11C2×#9911yescharacteristic
188C22×C11#41311yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—81no—
199C25C2×C4×C1111yescharacteristic
200C23×C4C2×C4×C1111yescharacteristic
201C23×C4C2×C4×C1111yescharacteristic
202#117—41no—
203#117—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4D4×C1111yescharacteristic
207C2×C4⋊C4D4×C1111yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—41no—
215C2×C22⋊C4—41no—
216C2×C22⋊C4C2×C4×C1111yescharacteristic
217C2×C22⋊C4C2×C4×C1111yescharacteristic
218C2×C22⋊C4C2×C4×C1111yescharacteristic
219C2×C22⋊C4C23×C1111yescharacteristic
220C2×C42D4×C1111yescharacteristic
221C2×C42D4×C1111yescharacteristic
222C4⋊C8—41no—
223C4⋊C8—41no—
224C22⋊C8—22no—
225C22⋊C8—22no—
226#97—41no—
227C4×C8—41no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—42no—
235C2×C11—82no—
236C2×C11#146811yescharacteristic
237C2×C11#212011yescharacteristic
238C2×C11#212211yescharacteristic
239C24—21no—
240C24—22no—
241C24—41no—
242C24—42no—
243C24—41no—
244C24—81no—
245C24C22×C4×C1111yescharacteristic
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—81no—
255C22×C4C11×C22⋊C411yescharacteristic
256C22×C4C11×C22⋊C411yescharacteristic
257C22×C4C11×C22⋊C411yescharacteristic
258C22×C4C11×C22⋊C411yescharacteristic
259C22×C4C2×D4×C1111yescharacteristic
260C22×C4C2×D4×C1111yescharacteristic
261C2×C8—42no—
262C2×C8—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C22⋊C4—22no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—81no—
277C22⋊C4—81no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—21no—
282C11#1154611yescharacteristic, direct product factor, Sylow
283C23—21no—
284C23—21no—
285C23—22no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—42no—
292C23—42no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—82no—
297C23—84no—
298C23—84no—
299C23—82no—
300C23C2×C11×C22⋊C411yescharacteristic
301C23C11×#13112yes—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
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—82no—
327C2×C4C11×#9911yescharacteristic
328C2×C4C11×#9911yescharacteristic
329C8—82no—
330C8—82no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—42no—
341C22—81no—
342C22—81no—
343C22—84no—
344C22—84no—
345C22—81no—
346C22—81no—
347C22C11×#40811yescharacteristic
348C22C2×C11×#9911yescharacteristic
349C22C11×#41311yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—82no—
364C2C11×#146811yescharacteristic
365C2C11×#212011yescharacteristic
366C2C11×#212211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC24C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC25×C11C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1464C2semidirect
3. C11×#1458C2semidirect
4. C11×#1326C2semidirect
56. #11546C11direct (N × H)
101. #1464C2×C11semidirect
102. #1458C2×C11semidirect
103. #1326C2×C11semidirect
282. C11#11546direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24822
C11×#14642
C11×#14582
C11×#13262
C11×#13162
#1154611