Finite Group Databasebeta

← C11×#10056 #14587249

Subgroups — C11×#10056 #14587249

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#494C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic
4C11×#1987C211yesmaximal, characteristic, complemented
5C2×C11×#333C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×Q16—22no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#494—22no—
13C11×#494—22no—
14C11×#476—22no—
15C11×#476—22no—
16C2×C11×#106—21no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102—21no—
20C2×C4×C8×C11C2211yescharacteristic
21C11×#393—22no—
22C11×#390—21no—
23C11×#382—21no—
24C11×#380—22no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×#333—22no—
28C11×D4⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D412yes—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C2×C11×Q16—28no—
34C2×C11×Q16—48no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8D412yes—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—24no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C11×#106—24no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#102—24no—
66C4×C8×C11—21no—
67C4×C8×C11D412yes—
68C11×#95—24no—
69C11×#95—21no—
70#10056C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11—21no—
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—44no—
76C2×Q8×C11—44no—
77C2×Q8×C11—41no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11Q1612yescomplemented
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C11×Q16—416no—
96C2×C8×C11—24no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—42no—
102C2×C8×C11—41no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—84no—
118C42×C11—41no—
119C42×C11—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C2×#494C2×C1111yescharacteristic, complemented
125C2×#476C2×C1111yescharacteristic
126#2563C2×C1111yescharacteristic
127#1987C2×C1111yescharacteristic, complemented
128C2×#333C2×C1111yescharacteristic, complemented
129C2×D4⋊C8C2×C1111yescharacteristic
130#1279C2×C1111yescharacteristic, complemented
131C23×C11—22no—
132C23×C11—41no—
133C23×C11—42no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11#12011yescharacteristic
137Q8×C11—44no—
138Q8×C11—44no—
139Q8×C11—82no—
140Q8×C11—82no—
141D4×C11—22no—
142D4×C11—22no—
143D4×C11—41no—
144D4×C11—41no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—82no—
155C2×C4×C11—82no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12711yescharacteristic
164C2×C4×C11C2×Q1611yescharacteristic
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11#13512yes—
167C2×C4×C11#13711yescharacteristic
168C2×C4×C11#13711yescharacteristic
169C2×C4×C11#13712yes—
170C8×C11—24no—
171C8×C11—42no—
172C8×C11—81no—
173C22×Q16—22no—
174C2×C4⋊Q8C22×C1111yescharacteristic
175C2×C4⋊Q8C22×C1111yescharacteristic
176C2×C4×D4C22×C1111yescharacteristic
177#494—22no—
178#494—22no—
179#476—22no—
180#476—22no—
181C2×#106—21no—
182C2×C4⋊C8C22×C1111yescharacteristic
183C2×C4⋊C8C22×C1111yescharacteristic
184C2×#102—21no—
185C2×C4×C8C22×C1111yescharacteristic
186#393—22no—
187#390—21no—
188#382—21no—
189#380—22no—
190C4×C4⋊C4C22×C1111yescharacteristic
191#340—22no—
192#333—22no—
193D4⋊C8—22no—
194C22×C11—44no—
195C22×C11—42no—
196C22×C11—82no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11#39211yescharacteristic
200C22×C11#45111yescharacteristic
201C22×C11#45212yes—
202C22×C11#45211yescharacteristic
203C22×C11#45312yes—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—82no—
207C4×C11—82no—
208C4×C11—82no—
209C4×C11—81no—
210C4×C11#45111yescharacteristic
211C4×C11#45211yescharacteristic
212C4×C11#46412yes—
213C4×C11#46711yescharacteristic
214C4×C11#47011yescharacteristic
215C4×C11#49511yescharacteristic
216C4×C11#49711yescharacteristic
217C22×Q8—21no—
218C22×Q8D4×C1112yes—
219C22×D4D4×C1111yescharacteristic
220C23×C4—21no—
221C2×Q16—28no—
222C2×Q16—48no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8D4×C1112yes—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4D4×C1111yescharacteristic
243C2×C4⋊C4D4×C1112yes—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—24no—
246C2×C42—21no—
247C2×C42C23×C1111yescharacteristic
248#106—24no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8D4×C1112yes—
253#102—24no—
254C4×C8—21no—
255C4×C8D4×C1112yes—
256#95—24no—
257#95—21no—
258C2×C11—82no—
259C2×C11#163212yes—
260C2×C11#163412yes—
261C2×C11#200111yescharacteristic
262C2×C11#200211yescharacteristic
263C2×C11#201511yescharacteristic
264C24—21no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—44no—
269C2×Q8—44no—
270C2×Q8—41no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4C11×Q1612yescomplemented
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C2×D4×C1111yescharacteristic
287C22×C4C2×D4×C1111yescharacteristic
288Q16—416no—
289C2×C8—24no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—42no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—84no—
311C42—41no—
312C42—41no—
313C42C2×D4×C1111yescharacteristic
314C42C2×D4×C1111yescharacteristic
315C42C2×D4×C1111yescharacteristic
316C42C11×#4111yescharacteristic
317C11#1005611yescharacteristic, direct product factor, Sylow
318C23—22no—
319C23—41no—
320C23—42no—
321C23—41no—
322C23—42no—
323C23C11×#12011yescharacteristic
324Q8—44no—
325Q8—44no—
326Q8—82no—
327Q8—82no—
328D4—22no—
329D4—22no—
330D4—41no—
331D4—41no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—82no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—82no—
345C2×C4C11×#12011yescharacteristic
346C2×C4C11×#12011yescharacteristic
347C2×C4C11×#12111yescharacteristic
348C2×C4C11×#12111yescharacteristic
349C2×C4C11×#12111yescharacteristic
350C2×C4C11×#12711yescharacteristic
351C2×C4C2×C11×Q1611yescharacteristic
352C2×C4C11×#13512yes—
353C2×C4C11×#13511yescharacteristic
354C2×C4C11×#13712yes—
355C2×C4C11×#13711yescharacteristic
356C2×C4C11×#13711yescharacteristic
357C8—24no—
358C8—42no—
359C8—81no—
360C22—44no—
361C22—42no—
362C22—82no—
363C22—81no—
364C22—81no—
365C22C11×#39211yescharacteristic
366C22C11×#45111yescharacteristic
367C22C11×#45212yes—
368C22C11×#45211yescharacteristic
369C22C11×#45312yes—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—82no—
374C4—82no—
375C4—81no—
376C4C11×#45111yescharacteristic
377C4C11×#45211yescharacteristic
378C4C11×#46412yes—
379C4C11×#46711yescharacteristic
380C4C11×#47011yescharacteristic
381C4C11×#49511yescharacteristic
382C4C11×#49711yescharacteristic
383C2—82no—
384C2C11×#163212yes—
385C2C11×#163412yes—
386C2C11×#200111yescharacteristic
387C2C11×#200211yescharacteristic
388C2C11×#201511yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#494C2semidirect
4. C11×#1987C2semidirect
5. C2×C11×#333C2semidirect
7. C11×#1279C2semidirect
70. #10056C11direct (N × H)
83. C2×D4×C11Q16semidirect
124. C2×#494C2×C11semidirect
127. #1987C2×C11semidirect
128. C2×#333C2×C11semidirect
130. #1279C2×C11semidirect
276. C2×D4C11×Q16semidirect
317. C11#10056direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4942
C2×C11×#4762
C11×#25632
C11×#19872
C2×C11×#3332
C2×C11×D4⋊C82
C11×#12792
#1005611