Finite Group Databasebeta

← C11×#10474 #14587667

Subgroups — C11×#10474 #14587667

Order 2816.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#460C211yesmaximal, characteristic
2C11×#1984C211yesmaximal, characteristic, complemented
3C11×#1957C211yesmaximal, characteristic
4C11×#1803C211yesmaximal, characteristic, complemented
5C2×C11×#335C211yesmaximal, characteristic, complemented
6C2×C11×#331C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C11×#460—22no—
12C11×#460—22no—
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103—21no—
17C2×C11×#102—21no—
18C2×C11×#102—21no—
19C2×C11×#102—21no—
20C2×C4×C8×C11C2211yescharacteristic
21C11×#384C2211yescharacteristic
22C11×#340—21no—
23C11×#336—21no—
24C11×#336—21no—
25C11×#335—22no—
26C11×#331—22no—
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C2×C11×SD16—24no—
32C2×C11×SD16—42no—
33C2×C11×SD16—42no—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—21no—
42C11×#127D412yes—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60C11×#103—42no—
61C11×#102—24no—
62C11×#102—42no—
63C11×#102—42no—
64C4×C8×C11—21no—
65C4×C8×C11—21no—
66#10474C1111yesmaximal, characteristic, direct product factor, Sylow
67C24×C11—41no—
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11D812yes—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—81no—
89C2×D4×C11—81no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C11×SD16—48no—
97C2×C8×C11—22no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11—21no—
102C2×C8×C11—21no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C2×C8×C11SD1612yescomplemented
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—81no—
121C42×C11—41no—
122C42×C11—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C42×C11#4111yescharacteristic
127C2×#460C2×C1111yescharacteristic
128#1984C2×C1111yescharacteristic, complemented
129#1957C2×C1111yescharacteristic
130#1803C2×C1111yescharacteristic, complemented
131C2×#335C2×C1111yescharacteristic, complemented
132C2×#331C2×C1111yescharacteristic
133#1296C2×C1111yescharacteristic, complemented
134C23×C11—42no—
135C23×C11—81no—
136C23×C11—81no—
137C23×C11—81no—
138C23×C11—81no—
139C23×C11—81no—
140C23×C11—81no—
141C23×C11#12111yescharacteristic
142Q8×C11—22no—
143Q8×C11—22no—
144Q8×C11—41no—
145Q8×C11—41no—
146D4×C11—42no—
147D4×C11—42no—
148D4×C11—42no—
149D4×C11—42no—
150D4×C11—82no—
151D4×C11—82no—
152D4×C11—81no—
153D4×C11—81no—
154D4×C11—81no—
155D4×C11—81no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12311yescharacteristic
171C2×C4×C11#12311yescharacteristic
172C2×C4×C11#12411yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×SD1611yescharacteristic
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C11#13711yescharacteristic
180C2×C4×C11#13711yescharacteristic
181C8×C11—22no—
182C8×C11—42no—
183C8×C11—41no—
184C8×C11—81no—
185C8×C11—81no—
186C22×SD16—21no—
187C2×#127C22×C1111yescharacteristic
188C2×C4×Q8C22×C1111yescharacteristic
189#460—22no—
190#460—22no—
191C2×C4⋊C8C22×C1111yescharacteristic
192C2×C4⋊C8C22×C1111yescharacteristic
193C2×C4⋊C8C22×C1111yescharacteristic
194C2×#103—21no—
195C2×#102—21no—
196C2×#102—21no—
197C2×#102—21no—
198C2×C4×C8C22×C1111yescharacteristic
199#384C22×C1111yescharacteristic
200#340—21no—
201#336—21no—
202#336—21no—
203#335—22no—
204#331—22no—
205C22×C11—82no—
206C22×C11—82no—
207C22×C11—82no—
208C22×C11—161no—
209C22×C11—161no—
210C22×C11—161no—
211C22×C11—161no—
212C22×C11#39411yescharacteristic
213C22×C11#46011yescharacteristic
214C22×C11#46411yescharacteristic
215C22×C11#46611yescharacteristic
216C22×C11#46811yescharacteristic
217C22×C11#47111yescharacteristic
218C22×C11#47211yescharacteristic
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—42no—
222C4×C11—81no—
223C4×C11—161no—
224C4×C11#44711yescharacteristic
225C4×C11#45211yescharacteristic
226C4×C11#46111yescharacteristic
227C4×C11#46311yescharacteristic
228C4×C11#46511yescharacteristic
229C4×C11#46811yescharacteristic
230C4×C11#48011yescharacteristic
231C4×C11#48211yescharacteristic
232C22×Q8D4×C1111yescharacteristic
233C22×D4—21no—
234C22×D4—21no—
235C22×D4—21no—
236C2×SD16—24no—
237C2×SD16—42no—
238C2×SD16—42no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8D4×C1111yescharacteristic
243C22×C8D4×C1111yescharacteristic
244#127—21no—
245#127—21no—
246#127—21no—
247#127D4×C1112yes—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C1111yescharacteristic
257C2×C42—21no—
258C2×C42C23×C1111yescharacteristic
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8D4×C1112yes—
265#103—42no—
266#102—24no—
267#102—42no—
268#102—42no—
269C4×C8—21no—
270C4×C8—21no—
271C2×C11—162no—
272C2×C11#166811yescharacteristic
273C2×C11#168211yescharacteristic
274C2×C11#168611yescharacteristic
275C2×C11#169811yescharacteristic
276C2×C11#203311yescharacteristic
277C2×C11#205111yescharacteristic
278C2×C11#205511yescharacteristic
279C24—41no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8C11×D812yes—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—81no—
301C2×D4—81no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4C2×D4×C1111yescharacteristic
306C22×C4C2×D4×C1111yescharacteristic
307C22×C4C11×#4111yescharacteristic
308SD16—48no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8C11×SD1612yescomplemented
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—81no—
333C42—41no—
334C42—41no—
335C42C2×D4×C1111yescharacteristic
336C42C2×D4×C1111yescharacteristic
337C42C11×#4111yescharacteristic
338C42C11×#4111yescharacteristic
339C11#1047411yescharacteristic, direct product factor, Sylow
340C23—42no—
341C23—81no—
342C23—81no—
343C23—81no—
344C23—81no—
345C23—81no—
346C23—81no—
347C23C11×#12111yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—41no—
351Q8—41no—
352D4—42no—
353D4—42no—
354D4—42no—
355D4—42no—
356D4—82no—
357D4—82no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4C11×#12011yescharacteristic
374C2×C4C11×#12111yescharacteristic
375C2×C4C11×#12111yescharacteristic
376C2×C4C11×#12311yescharacteristic
377C2×C4C11×#12311yescharacteristic
378C2×C4C11×#12411yescharacteristic
379C2×C4C2×C11×D811yescharacteristic
380C2×C4C2×C11×SD1611yescharacteristic
381C2×C4C11×#13511yescharacteristic
382C2×C4C11×#13511yescharacteristic
383C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
384C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
385C2×C4C11×#13711yescharacteristic
386C2×C4C11×#13711yescharacteristic
387C8—22no—
388C8—42no—
389C8—41no—
390C8—81no—
391C8—81no—
392C22—82no—
393C22—82no—
394C22—82no—
395C22—161no—
396C22—161no—
397C22—161no—
398C22—161no—
399C22C11×#39411yescharacteristic
400C22C11×#46011yescharacteristic
401C22C11×#46411yescharacteristic
402C22C11×#46611yescharacteristic
403C22C11×#46811yescharacteristic
404C22C11×#47111yescharacteristic
405C22C11×#47211yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—161no—
411C4C11×#44711yescharacteristic
412C4C11×#45211yescharacteristic
413C4C11×#46111yescharacteristic
414C4C11×#46311yescharacteristic
415C4C11×#46511yescharacteristic
416C4C11×#46811yescharacteristic
417C4C11×#48011yescharacteristic
418C4C11×#48211yescharacteristic
419C2—162no—
420C2C11×#166811yescharacteristic
421C2C11×#168211yescharacteristic
422C2C11×#168611yescharacteristic
423C2C11×#169811yescharacteristic
424C2C11×#203311yescharacteristic
425C2C11×#205111yescharacteristic
426C2C11×#205511yescharacteristic
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. C11×#1984C2semidirect
4. C11×#1803C2semidirect
5. C2×C11×#335C2semidirect
7. C11×#1296C2semidirect
66. #10474C11direct (N × H)
111. C2×C8×C11SD16semidirect
128. #1984C2×C11semidirect
130. #1803C2×C11semidirect
131. C2×#335C2×C11semidirect
133. #1296C2×C11semidirect
323. C2×C8C11×SD16semidirect
339. C11#10474direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4602
C11×#19842
C11×#19572
C11×#18032
C2×C11×#3352
C2×C11×#3312
C11×#12962
#1047411