Finite Group Databasebeta

← C11×#10268 #14587461

Subgroups — C11×#10268 #14587461

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#492C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic
4C11×#1984C211yesmaximal, characteristic, complemented
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×#331C211yesmaximal, characteristic
7C11×#1277C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C22×C11×SD16—22no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C11×#492—22no—
14C11×#492—22no—
15C11×#475—22no—
16C11×#475—22no—
17C11×#460—22no—
18C11×#460—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×C4×C8×C11C2211yescharacteristic
26C11×#336—22no—
27C11×#332—22no—
28C11×#331—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C2×C11×SD16—28no—
35C2×C11×SD16—24no—
36C2×C11×SD16—44no—
37C2×C11×SD16—42no—
38C2×C11×SD16—42no—
39C2×C11×SD16—44no—
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42C22×C8×C11—21no—
43C22×C8×C11D412yes—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8D412yes—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127—21no—
51C11×#127D412yes—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C11×#106—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8D412yes—
69C11×#103—24no—
70C11×#102—24no—
71C4×C8×C11—21no—
72C4×C8×C11—21no—
73#10268C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11—41no—
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×Q8×C11SD1612yescomplemented
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—42no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—42no—
96C2×D4×C11—41no—
97C2×D4×C11—82no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C11×SD16—48no—
105C11×SD16—416no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—42no—
116C2×C8×C11SD1614yescomplemented
117C11×C4⋊C4—21no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C42×C11—41no—
126C42×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C2×#492C2×C1111yescharacteristic
132C2×#475C2×C1111yescharacteristic, complemented
133C2×#460C2×C1111yescharacteristic
134#1984C2×C1111yescharacteristic, complemented
135C2×#332C2×C1111yescharacteristic, complemented
136C2×#331C2×C1111yescharacteristic
137#1277C2×C1111yescharacteristic, complemented
138C23×C11—42no—
139C23×C11—82no—
140C23×C11—81no—
141C23×C11—81no—
142C23×C11—82no—
143C23×C11#12111yescharacteristic
144Q8×C11—22no—
145Q8×C11—22no—
146Q8×C11—41no—
147Q8×C11—41no—
148Q8×C11—44no—
149Q8×C11—81no—
150Q8×C11—81no—
151D4×C11—42no—
152D4×C11—44no—
153D4×C11—42no—
154D4×C11—82no—
155D4×C11—82no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159D4×C11—81no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—82no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12711yescharacteristic
174C2×C4×C11C2×SD1611yescharacteristic
175C2×C4×C11C2×SD1612yes—
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)12yes—
179C2×C4×C11#13711yescharacteristic
180C8×C11—24no—
181C8×C11—42no—
182C8×C11—42no—
183C8×C11—81no—
184C22×SD16—21no—
185C22×SD16—22no—
186C2×C4⋊Q8C22×C1111yescharacteristic
187C2×#127C22×C1111yescharacteristic
188C2×C4×Q8C22×C1111yescharacteristic
189#492—22no—
190#492—22no—
191#475—22no—
192#475—22no—
193#460—22no—
194#460—22no—
195C2×#106—21no—
196C2×C4⋊C8C22×C1111yescharacteristic
197C2×C4⋊C8C22×C1111yescharacteristic
198C2×C4⋊C8C22×C1111yescharacteristic
199C2×#103—21no—
200C2×#102—21no—
201C2×C4×C8C22×C1111yescharacteristic
202#336—22no—
203#332—22no—
204#331—22no—
205C22×C11—82no—
206C22×C11—82no—
207C22×C11—82no—
208C22×C11—162no—
209C22×C11—162no—
210C22×C11#39211yescharacteristic
211C22×C11#46012yes—
212C22×C11#46511yescharacteristic
213C22×C11#46811yescharacteristic
214C22×C11#47112yes—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—42no—
218C4×C11—82no—
219C4×C11—81no—
220C4×C11#44811yescharacteristic
221C4×C11#44911yescharacteristic
222C4×C11#45011yescharacteristic
223C4×C11#45012yes—
224C4×C11#45211yescharacteristic
225C4×C11#49211yescharacteristic
226C4×C11#49611yescharacteristic
227C22×Q8—21no—
228C22×Q8D4×C1111yescharacteristic
229C22×D4—21no—
230C22×D4—21no—
231C22×D4—21no—
232C2×SD16—24no—
233C2×SD16—28no—
234C2×SD16—44no—
235C2×SD16—42no—
236C2×SD16—42no—
237C2×SD16—44no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8D4×C1112yes—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8D4×C1112yes—
246#127—21no—
247#127—21no—
248#127—21no—
249#127D4×C1112yes—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4D4×C1111yescharacteristic
258C2×C42—21no—
259C2×C42C23×C1111yescharacteristic
260#106—24no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8D4×C1112yes—
266C4⋊C8D4×C1112yes—
267#103—24no—
268#102—24no—
269C4×C8—21no—
270C4×C8—21no—
271C2×C11—162no—
272C2×C11#166612yes—
273C2×C11#168612yes—
274C2×C11#200011yescharacteristic
275C2×C11#201411yescharacteristic
276C2×C11#201911yescharacteristic
277C24—41no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—22no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—41no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×Q8C11×SD1612yescomplemented
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—82no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4C2×D4×C1111yescharacteristic
305C22×C4C2×D4×C1111yescharacteristic
306C22×C4C11×#4111yescharacteristic
307SD16—416no—
308SD16—48no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—42no—
319C2×C8C11×SD1614yescomplemented
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C42—41no—
329C42—41no—
330C42C2×D4×C1111yescharacteristic
331C42C2×D4×C1111yescharacteristic
332C42C2×D4×C1111yescharacteristic
333C42C2×D4×C1111yescharacteristic
334C11#1026811yescharacteristic, direct product factor, Sylow
335C23—42no—
336C23—82no—
337C23—81no—
338C23—81no—
339C23—82no—
340C23C11×#12111yescharacteristic
341Q8—22no—
342Q8—22no—
343Q8—41no—
344Q8—41no—
345Q8—44no—
346Q8—81no—
347Q8—81no—
348D4—42no—
349D4—44no—
350D4—42no—
351D4—82no—
352D4—82no—
353D4—81no—
354D4—81no—
355D4—81no—
356D4—81no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4C11×#12011yescharacteristic
366C2×C4C11×#12011yescharacteristic
367C2×C4C11×#12011yescharacteristic
368C2×C4C11×#12111yescharacteristic
369C2×C4C11×#12111yescharacteristic
370C2×C4C11×#12711yescharacteristic
371C2×C4C2×C11×SD1612yes—
372C2×C4C2×C11×SD1611yescharacteristic
373C2×C4C11×#13511yescharacteristic
374C2×C4C11×AGL(1,ℤ/8)12yes—
375C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
376C2×C4C11×#13711yescharacteristic
377C8—24no—
378C8—42no—
379C8—42no—
380C8—81no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—162no—
385C22—162no—
386C22C11×#39211yescharacteristic
387C22C11×#46012yes—
388C22C11×#46511yescharacteristic
389C22C11×#46811yescharacteristic
390C22C11×#47112yes—
391C4—21no—
392C4—21no—
393C4—42no—
394C4—82no—
395C4—81no—
396C4C11×#44811yescharacteristic
397C4C11×#44911yescharacteristic
398C4C11×#45011yescharacteristic
399C4C11×#45012yes—
400C4C11×#45211yescharacteristic
401C4C11×#49211yescharacteristic
402C4C11×#49611yescharacteristic
403C2—162no—
404C2C11×#166612yes—
405C2C11×#168612yes—
406C2C11×#200011yescharacteristic
407C2C11×#201411yescharacteristic
408C2C11×#201911yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
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
2. C2×C11×#475C2semidirect
4. C11×#1984C2semidirect
5. C2×C11×#332C2semidirect
7. C11×#1277C2semidirect
73. #10268C11direct (N × H)
84. C2×Q8×C11SD16semidirect
116. C2×C8×C11SD16semidirect
132. C2×#475C2×C11semidirect
134. #1984C2×C11semidirect
135. C2×#332C2×C11semidirect
137. #1277C2×C11semidirect
287. C2×Q8C11×SD16semidirect
319. C2×C8C11×SD16semidirect
334. C11#10268direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4922
C2×C11×#4752
C2×C11×#4602
C11×#19842
C2×C11×#3322
C2×C11×#3312
C11×#12772
#1026811