Finite Group Databasebeta

← C11×#11502 #14588695

Subgroups — C11×#11502 #14588695

Order 2816.

714 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2308C211yesmaximal, characteristic
2C11×#1462C212yesmaximal, complemented
3C11×#1317C212yesmaximal, complemented
4C11×#1316C212yesmaximal, complemented
5C23×D4×C11C411yescharacteristic
6C22×C11×C22⋊C4C411yescharacteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C11×#407—22no—
9C11×#386—22no—
10C11×#386—22no—
11C11×#381C411yescharacteristic
12C11×#381C2211yescharacteristic
13C11×#379C411yescharacteristic
14C11×#379C2211yescharacteristic
15C11×#323—22no—
16C11×#323C2214yes—
17C25×C11C2×C411yescharacteristic
18C25×C11C2×C411yescharacteristic
19C22×D4×C11—21no—
20C22×D4×C11—21no—
21C22×D4×C11—22no—
22C22×D4×C11—22no—
23C22×D4×C11—41no—
24C22×D4×C11—41no—
25C22×D4×C11—42no—
26C23×C4×C11—21no—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D412yes—
29C2×C11×M16—42no—
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—41no—
34C2×C11×C22⋊C4—41no—
35C2×C11×C22⋊C4—42no—
36C2×C11×C22⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4D412yes—
40C2×C11×C22⋊C4C2311yescharacteristic
41C11×C22⋊C8—24no—
42C11×C22⋊C8—42no—
43C11×#95—22no—
44C11×#95—22no—
45#11502C1111yesmaximal, characteristic, direct product factor, Sylow
46C24×C11—21no—
47C24×C11—21no—
48C24×C11—22no—
49C24×C11—21no—
50C24×C11—21no—
51C24×C11—21no—
52C24×C11—21no—
53C24×C11—41no—
54C24×C11—41no—
55C24×C11—82no—
56C24×C11—82no—
57C24×C11C22⋊C411yescharacteristic
58C24×C11C22⋊C411yescharacteristic
59C24×C11M1612yescomplemented
60C24×C11C22×C411yescharacteristic
61C2×D4×C11—24no—
62C2×D4×C11—24no—
63C2×D4×C11—44no—
64C2×D4×C11—44no—
65C2×D4×C11—42no—
66C2×D4×C11—42no—
67C2×D4×C11—44no—
68C2×D4×C11—44no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—42no—
72C22×C4×C11—22no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—42no—
81C22×C4×C11—82no—
82C22×C4×C11—82no—
83C22×C4×C11C22⋊C412yes—
84C22×C4×C11M1612yescomplemented
85C22×C4×C11C2×D412yes—
86C11×M16—84no—
87C2×C8×C11—44no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—82no—
95C11×C22⋊C4—82no—
96#2308C2×C1111yescharacteristic
97#1462C2×C1112yescomplemented
98#1317C2×C1112yescomplemented
99#1316C2×C1112yescomplemented
100C23×C11—22no—
101C23×C11—22no—
102C23×C11—22no—
103C23×C11—22no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—22no—
111C23×C11—42no—
112C23×C11—42no—
113C23×C11—42no—
114C23×C11—42no—
115C23×C11—42no—
116C23×C11—42no—
117C23×C11—42no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—82no—
121C23×C11—82no—
122C23×C11—82no—
123C23×C11—84no—
124C23×C11—82no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11—84no—
128C23×C11—84no—
129C23×C11#9911yescharacteristic
130C23×C11#9911yescharacteristic
131C23×C11#10012yes—
132C23×C11C2×C22⋊C411yescharacteristic
133C23×C11C2×M1611yescharacteristic
134C23×C11C2×M1611yescharacteristic
135D4×C11—44no—
136D4×C11—44no—
137D4×C11—48no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—44no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—82no—
153C2×C4×C11—84no—
154C8×C11—84no—
155C23×D4C4×C1111yescharacteristic
156C22×C22⋊C4C4×C1111yescharacteristic
157C22×C22⋊C4C22×C1111yescharacteristic
158#407—22no—
159#386—22no—
160#386—22no—
161#381C4×C1111yescharacteristic
162#381C22×C1111yescharacteristic
163#379C4×C1111yescharacteristic
164#379C22×C1111yescharacteristic
165#323—22no—
166#323C22×C1114yes—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—22no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—22no—
175C22×C11—42no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—84no—
193C22×C11—84no—
194C22×C11—82no—
195C22×C11#40711yescharacteristic
196C22×C11C2×#9911yescharacteristic
197C22×C11C2×#10011yescharacteristic
198C4×C11—42no—
199C4×C11—42no—
200C4×C11—42no—
201C4×C11—81no—
202C4×C11—81no—
203C25C2×C4×C1111yescharacteristic
204C25C2×C4×C1111yescharacteristic
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—41no—
210C22×D4—41no—
211C22×D4—42no—
212C23×C4—21no—
213C23×C4C2×C4×C1111yescharacteristic
214C23×C4D4×C1112yes—
215C2×M16—42no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—41no—
220C2×C22⋊C4—41no—
221C2×C22⋊C4—42no—
222C2×C22⋊C4C2×C4×C1111yescharacteristic
223C2×C22⋊C4C2×C4×C1111yescharacteristic
224C2×C22⋊C4C2×C4×C1111yescharacteristic
225C2×C22⋊C4D4×C1112yes—
226C2×C22⋊C4C23×C1111yescharacteristic
227C22⋊C8—24no—
228C22⋊C8—42no—
229#95—22no—
230#95—22no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11—41no—
234C2×C11—41no—
235C2×C11—42no—
236C2×C11—41no—
237C2×C11—41no—
238C2×C11—82no—
239C2×C11#146211yescharacteristic
240C2×C11#212112yes—
241C24—21no—
242C24—21no—
243C24—22no—
244C24—21no—
245C24—21no—
246C24—21no—
247C24—21no—
248C24—41no—
249C24—41no—
250C24—82no—
251C24—82no—
252C24C11×C22⋊C411yescharacteristic
253C24C11×C22⋊C411yescharacteristic
254C24C11×M1612yescomplemented
255C24C22×C4×C1111yescharacteristic
256C2×D4—24no—
257C2×D4—24no—
258C2×D4—44no—
259C2×D4—44no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—44no—
263C2×D4—44no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—42no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—42no—
276C22×C4—82no—
277C22×C4—82no—
278C22×C4C11×C22⋊C412yes—
279C22×C4C11×M1612yescomplemented
280C22×C4C2×D4×C1112yes—
281M16—84no—
282C2×C8—44no—
283C22⋊C4—41no—
284C22⋊C4—42no—
285C22⋊C4—41no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—82no—
290C22⋊C4—82no—
291C11#1150211yescharacteristic, direct product factor, Sylow
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23—41no—
311C23—41no—
312C23—82no—
313C23—82no—
314C23—82no—
315C23—84no—
316C23—82no—
317C23—82no—
318C23—82no—
319C23—84no—
320C23—84no—
321C23C11×#9911yescharacteristic
322C23C11×#9911yescharacteristic
323C23C11×#10012yes—
324C23C2×C11×C22⋊C411yescharacteristic
325C23C2×C11×M1611yescharacteristic
326C23C2×C11×M1611yescharacteristic
327D4—44no—
328D4—44no—
329D4—48no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—84no—
346C8—84no—
347C22—22no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—84no—
373C22—84no—
374C22—82no—
375C22C11×#40711yescharacteristic
376C22C2×C11×#9911yescharacteristic
377C22C2×C11×#10011yescharacteristic
378C4—42no—
379C4—42no—
380C4—42no—
381C4—81no—
382C4—81no—
383C2—21no—
384C2—21no—
385C2—41no—
386C2—41no—
387C2—41no—
388C2—41no—
389C2—42no—
390C2—82no—
391C2C11×#146211yescharacteristic
392C2C11×#212112yes—
subgroupG/H
center, socleC22×C11C2×#99
commutatorC24C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC23×D4×C11C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1462C2semidirect
3. C11×#1317C2semidirect
4. C11×#1316C2semidirect
45. #11502C11direct (N × H)
59. C24×C11M16semidirect
84. C22×C4×C11M16semidirect
97. #1462C2×C11semidirect
98. #1317C2×C11semidirect
99. #1316C2×C11semidirect
254. C24C11×M16semidirect
279. C22×C4C11×M16semidirect
291. C11#11502direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23082
C11×#14622
C11×#13172
C11×#13162
#1150211