Finite Group Databasebeta

← C11×#9512 #14586705

Subgroups — C11×#9512 #14586705

Order 2816.

558 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2921C211yesmaximal, characteristic, complemented
2C11×#2482C211yesmaximal, characteristic
3C11×#1822C211yesmaximal, characteristic, complemented
4C11×#1462C212yesmaximal
5C11×#1306C212yesmaximal, complemented
6C2×C11×#117C2211yescharacteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C11×#433—24no—
9C11×#423—21no—
10C11×#407C2212yes—
11C11×#407C2212yes—
12C4×C11×M16—21no—
13C11×#399—21no—
14C11×#397—21no—
15C11×#388—21no—
16C11×#388—21no—
17C11×#385C411yescharacteristic
18C11×#385C411yescharacteristic
19C11×#381C2211yescharacteristic
20C11×#379C411yescharacteristic
21C11×#379C411yescharacteristic
22C11×#343—21no—
23C11×#343—21no—
24C11×#323—24no—
25C25×C11C2×C411yescharacteristic
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C2×C11×M16—22no—
29C2×C11×M16—22no—
30C11×#117—22no—
31C11×#117—22no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—22no—
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⋊C4C2×C411yescharacteristic
46C2×C11×C22⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4C2×C411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C11×C4⋊C8—24no—
51C11×C22⋊C8—22no—
52C11×C22⋊C8—22no—
53C11×C22⋊C8—22no—
54C11×C22⋊C8D414yes—
55C11×#97—22no—
56C4×C8×C11—22no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61#9512C1111yesmaximal, characteristic, direct product factor, Sylow
62C24×C11—21no—
63C24×C11—22no—
64C24×C11—42no—
65C24×C11—41no—
66C24×C11—41no—
67C24×C11—81no—
68C24×C11C22×C411yescharacteristic
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—22no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—81no—
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D412yes—
83C22×C4×C11#4112yes—
84C11×M16—42no—
85C11×M16—42no—
86C11×M16—42no—
87C11×M16—42no—
88C2×C8×C11—24no—
89C2×C8×C11—42no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—81no—
93C11×C4⋊C4—81no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—81no—
104C11×C22⋊C4—81no—
105C42×C11—21no—
106C42×C11—21no—
107C42×C11—21no—
108C42×C11—21no—
109#2921C2×C1111yescharacteristic, complemented
110#2482C2×C1111yescharacteristic
111#1822C2×C1111yescharacteristic, complemented
112#1462C2×C1112yes—
113#1306C2×C1112yescomplemented
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—22no—
117C23×C11—24no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—42no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—82no—
128C23×C11—82no—
129C23×C11—84no—
130C23×C11—84no—
131C23×C11C2×C22⋊C411yescharacteristic
132C23×C11C4×D412yes—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—82no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12112yes—
159C2×C4×C11#12311yescharacteristic
160C8×C11—44no—
161C8×C11—82no—
162C2×#117C22×C1111yescharacteristic
163C22×C22⋊C4C22×C1111yescharacteristic
164#433—24no—
165#423—21no—
166#407C22×C1112yes—
167#407C22×C1112yes—
168C4×M16—21no—
169#399—21no—
170#397—21no—
171#388—21no—
172#388—21no—
173#385C4×C1111yescharacteristic
174#385C4×C1111yescharacteristic
175#381C22×C1111yescharacteristic
176#379C4×C1111yescharacteristic
177#379C4×C1111yescharacteristic
178#343—21no—
179#343—21no—
180#323—24no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—22no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—42no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—84no—
194C22×C11—84no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#38611yescharacteristic
198C22×C11#41011yescharacteristic
199C22×C11#41011yescharacteristic
200C4×C11—21no—
201C4×C11—22no—
202C4×C11—21no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C25C2×C4×C1111yescharacteristic
211C23×C4C2×C4×C1111yescharacteristic
212C23×C4C23×C1111yescharacteristic
213C2×M16—22no—
214C2×M16—22no—
215#117—22no—
216#117—22no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4D4×C1111yescharacteristic
220C2×C4⋊C4D4×C1111yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4C2×C4×C1111yescharacteristic
230C2×C22⋊C4C2×C4×C1111yescharacteristic
231C2×C22⋊C4C2×C4×C1111yescharacteristic
232C2×C22⋊C4C2×C4×C1111yescharacteristic
233C2×C42D4×C1111yescharacteristic
234C2×C42D4×C1111yescharacteristic
235C4⋊C8—24no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8—22no—
239C22⋊C8D4×C1114yes—
240#97—22no—
241C4×C8—22no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—42no—
249C2×C11—82no—
250C2×C11#189111yescharacteristic
251C2×C11#189911yescharacteristic
252C2×C11#191411yescharacteristic
253C24—21no—
254C24—22no—
255C24—42no—
256C24—41no—
257C24—41no—
258C24—81no—
259C24C22×C4×C1111yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—81no—
267C22×C4C11×C22⋊C411yescharacteristic
268C22×C4C11×C22⋊C411yescharacteristic
269C22×C4C11×C22⋊C411yescharacteristic
270C22×C4C11×C22⋊C411yescharacteristic
271C22×C4C2×D4×C1111yescharacteristic
272C22×C4C2×D4×C1111yescharacteristic
273C22×C4C2×D4×C1112yes—
274C22×C4C11×#4112yes—
275M16—42no—
276M16—42no—
277M16—42no—
278M16—42no—
279C2×C8—24no—
280C2×C8—42no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—81no—
284C4⋊C4—81no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—41no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—81no—
295C22⋊C4—81no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—21no—
300C11#951211yescharacteristic, direct product factor, Sylow
301C23—21no—
302C23—21no—
303C23—22no—
304C23—24no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—42no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—82no—
315C23—82no—
316C23—84no—
317C23—84no—
318C23C2×C11×C22⋊C411yescharacteristic
319C23C4×D4×C1112yes—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—82no—
344C2×C4C11×#12011yescharacteristic
345C2×C4C11×#12112yes—
346C2×C4C11×#12311yescharacteristic
347C8—44no—
348C8—82no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—42no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—81no—
360C22—81no—
361C22—84no—
362C22—84no—
363C22—81no—
364C22—81no—
365C22C11×#38611yescharacteristic
366C22C11×#41011yescharacteristic
367C22C11×#41011yescharacteristic
368C4—21no—
369C4—22no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C2—21no—
379C2—21no—
380C2—42no—
381C2—82no—
382C2C11×#189111yescharacteristic
383C2C11×#189911yescharacteristic
384C2C11×#191411yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC24C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC25×C11C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2921C2semidirect
3. C11×#1822C2semidirect
5. C11×#1306C2semidirect
61. #9512C11direct (N × H)
109. #2921C2×C11semidirect
111. #1822C2×C11semidirect
113. #1306C2×C11semidirect
300. C11#9512direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29212
C11×#24822
C11×#18222
C11×#14622
C11×#13062
#951211