Finite Group Databasebeta

← C11×#8990 #14586183

Subgroups — C11×#8990 #14586183

Order 2816.

462 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3104C211yesmaximal, characteristic
2Q8×C11×M16C211yesmaximal, characteristic
3C11×#1986C211yesmaximal, characteristic
4C4×C11×#103C211yesmaximal, characteristic
5C11×#1493C211yesmaximal, characteristic
6C11×#1303C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C11×#484—21no—
11C11×#477C411yescharacteristic, complemented
12C11×#477C411yescharacteristic, complemented
13C11×#462C411yescharacteristic, complemented
14C11×#462C411yescharacteristic, complemented
15C11×#451—21no—
16C11×#446—21no—
17C11×#446—22no—
18C8×Q8×C11—21no—
19C4×C11×Q16—21no—
20C4×C11×Q16—21no—
21C11×#431C2211yescharacteristic
22C11×#423—21no—
23C11×#423C2211yescharacteristic
24C2×C11×#103—21no—
25C4×C11×M16—21no—
26C4×C11×M16C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C11×#340—21no—
30C11×#339—21no—
31C11×#339—21no—
32C11×Q8⋊C8—22no—
33C22×Q8×C11D411yescharacteristic
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×M16—21no—
37C2×C11×M16D411yescharacteristic
38C2×C11×M16D411yescharacteristic
39C22×C8×C11—21no—
40C11×C4⋊Q8C2×C411yescharacteristic
41C11×C4⋊Q8C2×C411yescharacteristic
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11C2×C411yescharacteristic
50C4×Q8×C11C2×C411yescharacteristic
51C4×Q8×C11D411yescharacteristic
52C4×Q8×C11D411yescharacteristic
53C11×#117—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C11×#107—21no—
61C11×#107—21no—
62C11×C4⋊C8—22no—
63C11×C4⋊C8—22no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8C2×C411yescharacteristic
66C11×C4⋊C8C2×C411yescharacteristic
67C11×C4⋊C8D412yes—
68C11×#103—24no—
69C11×#103—21no—
70C11×#103—21no—
71C11×#103—21no—
72C11×#103—21no—
73C11×C22⋊C8—21no—
74C11×#97—22no—
75C11×#97—21no—
76C4×C8×C11—22no—
77C4×C8×C11—21no—
78C4×C8×C11—21no—
79C4×C8×C11—21no—
80C4×C8×C11—21no—
81C11×#95—21no—
82#8990C1111yesmaximal, characteristic, direct product factor, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—41no—
88C2×Q8×C11C22⋊C411yescharacteristic
89C2×Q8×C11C22⋊C411yescharacteristic
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×Q16—42no—
97C11×Q16—42no—
98C11×M16—21no—
99C11×M16—21no—
100C11×M16—21no—
101C11×M16—41no—
102C11×M16—41no—
103C11×M16Q1612yescomplemented
104C2×C8×C11—22no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C2×C8×C11—21no—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C2×C8×C11—41no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4C22⋊C411yescharacteristic
126C11×C4⋊C4C22⋊C411yescharacteristic
127C11×C22⋊C4—41no—
128C42×C11—21no—
129C42×C11—21no—
130C42×C11—21no—
131C42×C11—21no—
132C42×C11—41no—
133C42×C11—41no—
134C42×C11—41no—
135C42×C11C22×C411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139#3104C2×C1111yescharacteristic
140Q8×M16C2×C1111yescharacteristic
141#1986C2×C1111yescharacteristic
142C4×#103C2×C1111yescharacteristic
143#1493C2×C1111yescharacteristic
144#1303C2×C1111yescharacteristic
145#1278C2×C1111yescharacteristic
146C23×C11#12111yescharacteristic
147Q8×C11—21no—
148Q8×C11—21no—
149Q8×C11—21no—
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—41no—
153Q8×C11—41no—
154Q8×C11#10412yes—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11C2×C22⋊C411yescharacteristic
170C2×C4×C11C4×D411yescharacteristic
171C2×C4×C11C4×D411yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12311yescharacteristic
175C2×C4×C11C2×Q1611yescharacteristic
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11#13711yescharacteristic
178C2×C4×C11#13711yescharacteristic
179C8×C11—22no—
180C8×C11—42no—
181C8×C11—41no—
182C8×C11—41no—
183C8×C11—41no—
184C8×C11—42no—
185#533C22×C1111yescharacteristic
186C2×C4×Q8C22×C1111yescharacteristic
187#484—21no—
188#477C4×C1111yescharacteristic, complemented
189#477C4×C1111yescharacteristic, complemented
190#462C4×C1111yescharacteristic, complemented
191#462C4×C1111yescharacteristic, complemented
192#451—21no—
193#446—21no—
194#446—22no—
195C8×Q8—21no—
196C4×Q16—21no—
197C4×Q16—21no—
198#431C22×C1111yescharacteristic
199#423—21no—
200#423C22×C1111yescharacteristic
201C2×#103—21no—
202C4×M16—21no—
203C4×M16C22×C1111yescharacteristic
204C2×C4×C8C22×C1111yescharacteristic
205C4×C4⋊C4C22×C1111yescharacteristic
206#340—21no—
207#339—21no—
208#339—21no—
209Q8⋊C8—22no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11#38611yescharacteristic
213C22×C11#46211yescharacteristic
214C22×C11#46411yescharacteristic
215C4×C11—21no—
216C4×C11—22no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11—82no—
223C4×C11—81no—
224C4×C11—81no—
225C4×C11C2×#10411yescharacteristic
226C4×C11#42111yescharacteristic
227C4×C11C4×Q1611yescharacteristic
228C4×C11#44111yescharacteristic
229C4×C11#45111yescharacteristic
230C4×C11#45211yescharacteristic
231C22×Q8D4×C1111yescharacteristic
232C2×Q16—21no—
233C2×Q16—21no—
234C2×M16—21no—
235C2×M16D4×C1111yescharacteristic
236C2×M16D4×C1111yescharacteristic
237C22×C8—21no—
238C4⋊Q8C2×C4×C1111yescharacteristic
239C4⋊Q8C2×C4×C1111yescharacteristic
240#125—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8C2×C4×C1111yescharacteristic
248C4×Q8C2×C4×C1111yescharacteristic
249C4×Q8D4×C1111yescharacteristic
250C4×Q8D4×C1111yescharacteristic
251#117—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4D4×C1111yescharacteristic
255C2×C42—21no—
256C2×C42—21no—
257C2×C42C23×C1111yescharacteristic
258#107—21no—
259#107—21no—
260C4⋊C8—22no—
261C4⋊C8—22no—
262C4⋊C8—21no—
263C4⋊C8C2×C4×C1111yescharacteristic
264C4⋊C8C2×C4×C1111yescharacteristic
265C4⋊C8D4×C1112yes—
266#103—24no—
267#103—21no—
268#103—21no—
269#103—21no—
270#103—21no—
271C22⋊C8—21no—
272#97—22no—
273#97—21no—
274C4×C8—22no—
275C4×C8—21no—
276C4×C8—21no—
277C4×C8—21no—
278C4×C8—21no—
279#95—21no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11#187111yescharacteristic
283C2×C11#187811yescharacteristic
284C2×C11#188111yescharacteristic
285C2×Q8—21no—
286C2×Q8—22no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—41no—
290C2×Q8C11×C22⋊C411yescharacteristic
291C2×Q8C11×C22⋊C411yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—41no—
295C22×C4C2×D4×C1111yescharacteristic
296C22×C4C2×D4×C1111yescharacteristic
297C22×C4C11×#4111yescharacteristic
298Q16—42no—
299Q16—42no—
300M16—21no—
301M16—21no—
302M16—21no—
303M16—41no—
304M16—41no—
305M16C11×Q1612yescomplemented
306C2×C8—21no—
307C2×C8—22no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—41no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4C11×C22⋊C411yescharacteristic
328C4⋊C4C11×C22⋊C411yescharacteristic
329C22⋊C4—41no—
330C42—21no—
331C42—21no—
332C42—21no—
333C42—21no—
334C42—41no—
335C42—41no—
336C42—41no—
337C42C22×C4×C1111yescharacteristic
338C42C2×D4×C1111yescharacteristic
339C42C2×D4×C1111yescharacteristic
340C42C11×#4111yescharacteristic
341C11#899011yescharacteristic, direct product factor, Sylow
342C23C11×#12111yescharacteristic
343Q8—21no—
344Q8—21no—
345Q8—21no—
346Q8—42no—
347Q8—42no—
348Q8—41no—
349Q8—41no—
350Q8C11×#10412yes—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4C2×C11×C22⋊C411yescharacteristic
366C2×C4C4×D4×C1111yescharacteristic
367C2×C4C4×D4×C1111yescharacteristic
368C2×C4C11×#12011yescharacteristic
369C2×C4C11×#12111yescharacteristic
370C2×C4C11×#12311yescharacteristic
371C2×C4C2×C11×Q1611yescharacteristic
372C2×C4C11×#13511yescharacteristic
373C2×C4C11×#13711yescharacteristic
374C2×C4C11×#13711yescharacteristic
375C8—22no—
376C8—42no—
377C8—41no—
378C8—41no—
379C8—41no—
380C8—42no—
381C22—21no—
382C22—21no—
383C22C11×#38611yescharacteristic
384C22C11×#46211yescharacteristic
385C22C11×#46411yescharacteristic
386C4—21no—
387C4—22no—
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—82no—
394C4—81no—
395C4—81no—
396C4C2×C11×#10411yescharacteristic
397C4C11×#42111yescharacteristic
398C4C4×C11×Q1611yescharacteristic
399C4C11×#44111yescharacteristic
400C4C11×#45111yescharacteristic
401C4C11×#45211yescharacteristic
402C2—21no—
403C2—21no—
404C2C11×#187111yescharacteristic
405C2C11×#187811yescharacteristic
406C2C11×#188111yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
socleC22×C11#386
prime radicalC23×C11#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
11. C11×#477C4semidirect
12. C11×#477C4semidirect
13. C11×#462C4semidirect
14. C11×#462C4semidirect
82. #8990C11direct (N × H)
103. C11×M16Q16semidirect
188. #477C4×C11semidirect
189. #477C4×C11semidirect
190. #462C4×C11semidirect
191. #462C4×C11semidirect
305. M16C11×Q16semidirect
341. C11#8990direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31042
Q8×C11×M162
C11×#19862
C4×C11×#1032
C11×#14932
C11×#13032
C11×#12782
#899011