Finite Group Databasebeta

← C11×#10271 #14587464

Subgroups — C11×#10271 #14587464

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#498C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic
3C2×C11×#461C211yesmaximal, characteristic
4C11×#1954C211yesmaximal, characteristic
5C2×C11×#333C211yesmaximal, characteristic, complemented
6C2×C11×#332C211yesmaximal, characteristic, complemented
7C11×#1277C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#498—22no—
13C11×#498—22no—
14C11×#476—22no—
15C11×#476—22no—
16C11×#461—22no—
17C11×#461—22no—
18C2×C11×#106—22no—
19C2×C11×#106—21no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103—21no—
24C2×C11×#102—21no—
25C2×C11×C22⋊C8—22no—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#333—22no—
28C11×#332—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C2×C11×SD16—24no—
34C2×C11×SD16—42no—
35C2×C11×SD16—42no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C22×C8×C11D412yes—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8D412yes—
47C11×C4⋊Q8D412yes—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59C11×#106—28no—
60C11×#106—24no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×C4⋊C8D412yes—
67C11×#103—24no—
68C11×#102—24no—
69C11×C22⋊C8—44no—
70C4×C8×C11—21no—
71C4×C8×C11—21no—
72#10271C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—82no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11SD1612yes—
89C22×C4×C11—21no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C11×SD16—48no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—42no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11SD1614yescomplemented
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C2×#498C2×C1111yescharacteristic, complemented
128C2×#476C2×C1111yescharacteristic
129C2×#461C2×C1111yescharacteristic
130#1954C2×C1111yescharacteristic
131C2×#333C2×C1111yescharacteristic, complemented
132C2×#332C2×C1111yescharacteristic, complemented
133#1277C2×C1111yescharacteristic, complemented
134C23×C11—22no—
135C23×C11—41no—
136C23×C11—42no—
137C23×C11—41no—
138C23×C11—42no—
139C23×C11#12111yescharacteristic
140Q8×C11—42no—
141Q8×C11—42no—
142Q8×C11—82no—
143Q8×C11—82no—
144Q8×C11—81no—
145Q8×C11—81no—
146D4×C11—22no—
147D4×C11—22no—
148D4×C11—41no—
149D4×C11—41no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11—82no—
158C2×C4×C11—82no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12711yescharacteristic
167C2×C4×C11C2×SD1611yescharacteristic
168C2×C4×C11C2×SD1612yes—
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C11#13711yescharacteristic
172C2×C4×C11#13712yes—
173C8×C11—24no—
174C8×C11—42no—
175C8×C11—42no—
176C8×C11—81no—
177C22×SD16—21no—
178C2×C4⋊Q8C22×C1111yescharacteristic
179C2×C4⋊Q8C22×C1111yescharacteristic
180C2×C4×D4C22×C1111yescharacteristic
181#498—22no—
182#498—22no—
183#476—22no—
184#476—22no—
185#461—22no—
186#461—22no—
187C2×#106—22no—
188C2×#106—21no—
189C2×C4⋊C8C22×C1111yescharacteristic
190C2×C4⋊C8C22×C1111yescharacteristic
191C2×C4⋊C8C22×C1111yescharacteristic
192C2×#103—21no—
193C2×#102—21no—
194C2×C22⋊C8—22no—
195C2×C4×C8C22×C1111yescharacteristic
196#333—22no—
197#332—22no—
198C22×C11—44no—
199C22×C11—42no—
200C22×C11—82no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11#39211yescharacteristic
204C22×C11#46112yes—
205C22×C11#46511yescharacteristic
206C22×C11#46811yescharacteristic
207C22×C11#47112yes—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—82no—
211C4×C11—81no—
212C4×C11—82no—
213C4×C11#44811yescharacteristic
214C4×C11#44812yes—
215C4×C11#44911yescharacteristic
216C4×C11#45011yescharacteristic
217C4×C11#45211yescharacteristic
218C4×C11#49211yescharacteristic
219C4×C11#49711yescharacteristic
220C22×Q8—21no—
221C22×Q8—21no—
222C22×D4D4×C1111yescharacteristic
223C23×C4—21no—
224C2×SD16—24no—
225C2×SD16—42no—
226C2×SD16—42no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8D4×C1112yes—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8D4×C1112yes—
238C4⋊Q8D4×C1112yes—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4D4×C1111yescharacteristic
248C2×C22⋊C4—21no—
249C2×C42C23×C1111yescharacteristic
250#106—24no—
251#106—28no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8D4×C1112yes—
257C4⋊C8D4×C1112yes—
258#103—24no—
259#102—24no—
260C22⋊C8—44no—
261C4×C8—21no—
262C4×C8—21no—
263C2×C11—82no—
264C2×C11#167112yes—
265C2×C11#169112yes—
266C2×C11#200011yescharacteristic
267C2×C11#201311yescharacteristic
268C2×C11#201911yescharacteristic
269C24—21no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—82no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4C11×SD1612yes—
285C22×C4—21no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4C2×D4×C1111yescharacteristic
293C22×C4C2×D4×C1111yescharacteristic
294C22×C4C11×#4111yescharacteristic
295SD16—48no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—42no—
306C2×C8C11×SD1614yescomplemented
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C42C2×D4×C1111yescharacteristic
320C42C2×D4×C1111yescharacteristic
321C42C2×D4×C1111yescharacteristic
322C42C2×D4×C1111yescharacteristic
323C11#1027111yescharacteristic, direct product factor, Sylow
324C23—22no—
325C23—41no—
326C23—42no—
327C23—41no—
328C23—42no—
329C23C11×#12111yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—82no—
333Q8—82no—
334Q8—81no—
335Q8—81no—
336D4—22no—
337D4—22no—
338D4—41no—
339D4—41no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—82no—
351C2×C4C11×#12011yescharacteristic
352C2×C4C11×#12011yescharacteristic
353C2×C4C11×#12011yescharacteristic
354C2×C4C11×#12111yescharacteristic
355C2×C4C11×#12111yescharacteristic
356C2×C4C11×#12711yescharacteristic
357C2×C4C2×C11×SD1612yes—
358C2×C4C2×C11×SD1611yescharacteristic
359C2×C4C11×#13511yescharacteristic
360C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
361C2×C4C11×#13712yes—
362C2×C4C11×#13711yescharacteristic
363C8—24no—
364C8—42no—
365C8—42no—
366C8—81no—
367C22—44no—
368C22—42no—
369C22—82no—
370C22—81no—
371C22—81no—
372C22C11×#39211yescharacteristic
373C22C11×#46112yes—
374C22C11×#46511yescharacteristic
375C22C11×#46811yescharacteristic
376C22C11×#47112yes—
377C4—21no—
378C4—21no—
379C4—82no—
380C4—81no—
381C4—82no—
382C4C11×#44811yescharacteristic
383C4C11×#44812yes—
384C4C11×#44911yescharacteristic
385C4C11×#45011yescharacteristic
386C4C11×#45211yescharacteristic
387C4C11×#49211yescharacteristic
388C4C11×#49711yescharacteristic
389C2—82no—
390C2C11×#167112yes—
391C2C11×#169112yes—
392C2C11×#200011yescharacteristic
393C2C11×#201311yescharacteristic
394C2C11×#201911yescharacteristic
subgroupG/H
center, socleC23×C11#121
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×#498C2semidirect
5. C2×C11×#333C2semidirect
6. C2×C11×#332C2semidirect
7. C11×#1277C2semidirect
72. #10271C11direct (N × H)
110. C2×C8×C11SD16semidirect
127. C2×#498C2×C11semidirect
131. C2×#333C2×C11semidirect
132. C2×#332C2×C11semidirect
133. #1277C2×C11semidirect
306. C2×C8C11×SD16semidirect
323. C11#10271direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4982
C2×C11×#4762
C2×C11×#4612
C11×#19542
C2×C11×#3332
C2×C11×#3322
C11×#12772
#1027111