Finite Group Databasebeta

← C11×#11808 #14589001

Subgroups — C11×#11808 #14589001

Order 2816.

680 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C2×C11×#393C211yesmaximal, characteristic
2C11×#1819C211yesmaximal, characteristic
3C11×#1462C211yesmaximal, characteristic
4C11×#1351C214yesmaximal, complemented
5C23×Q8×C11C411yescharacteristic, complemented
6C22×C11×C22⋊C4—21no—
7C22×C11×C22⋊C4C2211yescharacteristic
8C11×#407—21no—
9C11×#393—21no—
10C11×#393—21no—
11C11×#393C412yescomplemented
12C11×#393C2212yes—
13C11×#379—21no—
14C2×C11×#95—21no—
15C2×C11×#95C411yescharacteristic, complemented
16C11×#342—21no—
17C11×#342C2212yes—
18C11×#323—21no—
19C11×#323C2212yes—
20C25×C11D411yescharacteristic
21C22×Q8×C11—21no—
22C22×Q8×C11—44no—
23C22×Q8×C11—41no—
24C22×Q8×C11—41no—
25C22×Q8×C11C2×C412yes—
26C23×C4×C11—21no—
27C23×C4×C11—21no—
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C2×C11×M16—41no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4—41no—
35C2×C11×C22⋊C4—41no—
36C2×C11×C22⋊C4—44no—
37C2×C11×C22⋊C4—41no—
38C2×C11×C22⋊C4—41no—
39C2×C11×C22⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4D411yescharacteristic
41C2×C11×C22⋊C4D411yescharacteristic
42C2×C11×C22⋊C4C2311yescharacteristic
43C11×C22⋊C8—22no—
44C11×C22⋊C8—41no—
45C11×#95—22no—
46C11×#95—21no—
47C11×#95—22no—
48C11×#95C2×C412yes—
49#11808C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11—22no—
51C24×C11—21no—
52C24×C11—21no—
53C24×C11—41no—
54C24×C11—42no—
55C24×C11—42no—
56C24×C11C22⋊C411yescharacteristic
57C24×C11C22⋊C411yescharacteristic
58C24×C11C2×D411yescharacteristic
59C2×Q8×C11—44no—
60C2×Q8×C11—42no—
61C2×Q8×C11—44no—
62C2×Q8×C11—42no—
63C2×Q8×C11—48no—
64C2×Q8×C11—44no—
65C2×Q8×C11—44no—
66C22×C4×C11—24no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—22no—
73C22×C4×C11—42no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C11×M16—82no—
87C2×C8×C11—42no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—44no—
93C11×C22⋊C4—44no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—42no—
96C11×C22⋊C4—82no—
97C11×C22⋊C4—82no—
98C2×#393C2×C1111yescharacteristic
99#1819C2×C1111yescharacteristic
100#1462C2×C1111yescharacteristic
101#1351C2×C1114yescomplemented
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—21no—
111C23×C11—42no—
112C23×C11—42no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—48no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—81no—
121C23×C11—81no—
122C23×C11—84no—
123C23×C11#9911yescharacteristic
124C23×C11#9911yescharacteristic
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11#13712yes—
127Q8×C11—44no—
128Q8×C11—48no—
129Q8×C11—44no—
130C2×C4×C11—24no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—42no—
136C2×C4×C11—44no—
137C2×C4×C11—42no—
138C2×C4×C11—44no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—81no—
150C2×C4×C11—84no—
151C2×C4×C11—82no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C8×C11—82no—
155C23×Q8C4×C1111yescharacteristic, complemented
156C22×C22⋊C4—21no—
157C22×C22⋊C4C22×C1111yescharacteristic
158#407—21no—
159#393—21no—
160#393—21no—
161#393C4×C1112yescomplemented
162#393C22×C1112yes—
163#379—21no—
164C2×#95—21no—
165C2×#95C4×C1111yescharacteristic, complemented
166#342—21no—
167#342C22×C1112yes—
168#323—21no—
169#323C22×C1112yes—
170C22×C11—24no—
171C22×C11—24no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—22no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—81no—
187C22×C11—84no—
188C22×C11—84no—
189C22×C11—81no—
190C22×C11AΣL(1,𝔽16)12yes—
191C22×C11#35412yes—
192C22×C11C2×#9911yescharacteristic
193C22×C11#41911yescharacteristic
194C22×C11#42111yescharacteristic
195C4×C11—44no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11—82no—
201C4×C11—162no—
202C25D4×C1111yescharacteristic
203C22×Q8—21no—
204C22×Q8—44no—
205C22×Q8—41no—
206C22×Q8—41no—
207C22×Q8C2×C4×C1112yes—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4C2×C4×C1111yescharacteristic
211C23×C4D4×C1111yescharacteristic
212C2×M16—41no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—41no—
217C2×C22⋊C4—41no—
218C2×C22⋊C4—44no—
219C2×C22⋊C4—41no—
220C2×C22⋊C4—41no—
221C2×C22⋊C4C2×C4×C1111yescharacteristic
222C2×C22⋊C4D4×C1111yescharacteristic
223C2×C22⋊C4D4×C1111yescharacteristic
224C2×C22⋊C4C23×C1111yescharacteristic
225C22⋊C8—22no—
226C22⋊C8—41no—
227#95—22no—
228#95—21no—
229#95—22no—
230#95C2×C4×C1112yes—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11—22no—
234C2×C11—22no—
235C2×C11—42no—
236C2×C11—81no—
237C2×C11#151111yescharacteristic
238C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
239C2×C11C2×#35411yescharacteristic
240C24—22no—
241C24—21no—
242C24—21no—
243C24—41no—
244C24—42no—
245C24—42no—
246C24C11×C22⋊C411yescharacteristic
247C24C11×C22⋊C411yescharacteristic
248C24C2×D4×C1111yescharacteristic
249C2×Q8—44no—
250C2×Q8—44no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—48no—
254C2×Q8—44no—
255C2×Q8—44no—
256C22×C4—24no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—42no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4C11×C22⋊C411yescharacteristic
273C22×C4C11×C22⋊C411yescharacteristic
274C22×C4C22×C4×C1111yescharacteristic
275C22×C4C2×D4×C1111yescharacteristic
276M16—82no—
277C2×C8—42no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—44no—
283C22⋊C4—44no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—82no—
287C22⋊C4—82no—
288C11#1180811yescharacteristic, direct product factor, Sylow
289C23—22no—
290C23—22no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—42no—
299C23—42no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—48no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—81no—
309C23—84no—
310C23C11×#9911yescharacteristic
311C23C11×#9911yescharacteristic
312C23C2×C11×C22⋊C411yescharacteristic
313C23C11×#13712yes—
314Q8—44no—
315Q8—44no—
316Q8—48no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—81no—
337C2×C4—84no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C8—82no—
342C22—24no—
343C22—24no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—42no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—84no—
360C22—84no—
361C22—81no—
362C22C11×AΣL(1,𝔽16)12yes—
363C22C11×#35412yes—
364C22C2×C11×#9911yescharacteristic
365C22C11×#41911yescharacteristic
366C22C11×#42111yescharacteristic
367C4—41no—
368C4—41no—
369C4—44no—
370C4—41no—
371C4—41no—
372C4—82no—
373C4—162no—
374C2—21no—
375C2—21no—
376C2—22no—
377C2—22no—
378C2—42no—
379C2—81no—
380C2C11×#151111yescharacteristic
381C2C2×C11×AΣL(1,𝔽16)11yescharacteristic
382C2C2×C11×#35411yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC25×C11D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
4. C11×#1351C2semidirect
5. C23×Q8×C11C4semidirect
11. C11×#393C4semidirect
15. C2×C11×#95C4semidirect
49. #11808C11direct (N × H)
101. #1351C2×C11semidirect
155. C23×Q8C4×C11semidirect
161. #393C4×C11semidirect
165. C2×#95C4×C11semidirect
288. C11#11808direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3932
C11×#18192
C11×#14622
C11×#13512
#1180811