Finite Group Databasebeta

← C11×#33703 #14610896

Subgroups — C11×#33703 #14610896

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3164C211yesmaximal, characteristic, complemented
2C11×#3156C211yesmaximal, characteristic
3C11×#2245C212yesmaximal, complemented
4C11×#2243C212yesmaximal, complemented
5C11×#2242C212yesmaximal, complemented
6C11×#2241C212yesmaximal, complemented
7C11×#2141C211yesmaximal, characteristic, complemented
8C11×#2139C211yesmaximal, characteristic
9C11×#2138C211yesmaximal, characteristic
10C2×C11×#358C211yesmaximal, characteristic, complemented
11C11×#2108C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C2×C11×#135C2211yescharacteristic
14C22×C11×Q16C2211yescharacteristic
15C11×#544—21no—
16C11×#536—21no—
17C2×C11×M32C2211yescharacteristic
18C22×C11×C16C2211yescharacteristic
19C11×#501—22no—
20C11×#500C2212yes—
21C11×#499C2212yes—
22C11×#497—22no—
23C11×#495C2212yes—
24C11×#494C2212yes—
25C11×#428—21no—
26C11×#427C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C11×#405C2211yescharacteristic
29C11×#358C2212yes—
30C11×#358C2212yes—
31C11×#358C2211yescharacteristic
32C11×#358C2211yescharacteristic
33C11×#358C2212yes—
34C11×#358C2212yes—
35C11×#358C2212yes—
36C11×#357C2211yescharacteristic
37C11×#357C2211yescharacteristic
38C11×#357C2212yes—
39C11×#346C2212yes—
40C4×C11×C16C2212yes—
41C2×C11×#41—21no—
42C22×Q8×C11—21no—
43C11×#137—44no—
44C11×#135—22no—
45C11×#135—22no—
46C2×C11×Q16—22no—
47C2×C11×Q16—21no—
48C2×C11×Q16—22no—
49C2×C11×Q16—22no—
50C2×C11×Q16C2311yescharacteristic
51C2×C11×Q16C2312yes—
52C2×C11×SD16—22no—
53C2×C11×SD16—21no—
54C2×C11×D8C2311yescharacteristic
55C2×C11×M16D411yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—41no—
60C11×#125—22no—
61C11×#125—41no—
62C11×#124—22no—
63C11×#123—42no—
64C11×C22⋊Q8—41no—
65C11×C22⋊Q8—41no—
66C11×C22⋊Q8—42no—
67C11×#117—21no—
68C11×#117D411yescharacteristic
69C2×C11×C4⋊C4—21no—
70C11×M32—22no—
71C2×C11×C16—22no—
72C2×C11×C16C2311yescharacteristic
73C2×C11×C16C2311yescharacteristic
74C2×C11×C16C2312yes—
75C11×#107—22no—
76C11×#107—21no—
77C11×#107C2311yescharacteristic
78C11×#107C2312yes—
79C11×#107C2311yescharacteristic
80C11×#106—22no—
81C11×#106—21no—
82C11×#97D412yes—
83C4×C8×C11C2312yes—
84#33703C1111yesmaximal, characteristic, direct product factor, Sylow
85C11×#41—42no—
86C11×#41—42no—
87C2×Q8×C11—22no—
88C2×Q8×C11—21no—
89C2×Q8×C11—41no—
90C2×Q8×C11—42no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C11×Q16—22no—
100C11×Q16—22no—
101C11×Q16—21no—
102C11×Q16—21no—
103C11×Q16—42no—
104C11×Q16—44no—
105C11×SD16—42no—
106C11×SD16—44no—
107C11×D8—21no—
108C11×D8—21no—
109C11×M16SD1614yes—
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D412yes—
112C2×C8×C11#4112yes—
113C2×C8×C11#4112yes—
114C2×C8×C11C2411yescharacteristic
115C11×C4⋊C4—21no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—42no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4D811yescharacteristic
125C11×C4⋊C4D811yescharacteristic
126C11×C22⋊C4—41no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4D812yes—
130C42×C11—41no—
131C42×C11C2×D412yes—
132C11×C16—21no—
133C11×C16—21no—
134C11×C16—22no—
135#3164C2×C1111yescharacteristic, complemented
136#3156C2×C1111yescharacteristic
137#2245C2×C1112yescomplemented
138#2243C2×C1112yescomplemented
139#2242C2×C1112yescomplemented
140#2241C2×C1112yescomplemented
141#2141C2×C1111yescharacteristic, complemented
142#2139C2×C1111yescharacteristic
143#2138C2×C1111yescharacteristic
144C2×#358C2×C1111yescharacteristic, complemented
145#2108C2×C1111yescharacteristic, complemented
146C23×C11—41no—
147C23×C11C2×D811yescharacteristic
148Q8×C11—41no—
149Q8×C11—42no—
150Q8×C11—42no—
151Q8×C11—41no—
152Q8×C11—82no—
153Q8×C11—162no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—82no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—82no—
163C2×C4×C11—82no—
164C2×C4×C11—161no—
165C2×C4×C11#12412yes—
166C2×C4×C11C2×D812yes—
167C2×C4×C11C2×D812yes—
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×SD1612yes—
170C2×C4×C11C22×D411yescharacteristic
171C8×C11#12412yes—
172C8×C11C2×SD1614yes—
173C8×C11C2×#4111yescharacteristic
174C8×C11C2×#4111yescharacteristic
175C2×#137—21no—
176C2×#135C22×C1111yescharacteristic
177C22×Q16C22×C1111yescharacteristic
178#544—21no—
179#536—21no—
180C2×M32C22×C1111yescharacteristic
181C22×C16C22×C1111yescharacteristic
182#501—22no—
183#500C22×C1112yes—
184#499C22×C1112yes—
185#497—22no—
186#495C22×C1112yes—
187#494C22×C1112yes—
188#428—21no—
189#427C22×C1111yescharacteristic
190C2×#107C22×C1111yescharacteristic
191#405C22×C1111yescharacteristic
192#358C22×C1112yes—
193#358C22×C1112yes—
194#358C22×C1111yescharacteristic
195#358C22×C1111yescharacteristic
196#358C22×C1112yes—
197#358C22×C1112yes—
198#358C22×C1112yes—
199#357C22×C1111yescharacteristic
200#357C22×C1111yescharacteristic
201#357C22×C1112yes—
202#346C22×C1112yes—
203C4×C16C22×C1112yes—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11#48612yes—
210C22×C11C22×D811yescharacteristic
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—81no—
214C4×C11—82no—
215C4×C11—82no—
216C4×C11—81no—
217C4×C11—81no—
218C4×C11#48612yes—
219C4×C11C2×#12411yescharacteristic
220C4×C11C22×SD1611yescharacteristic
221C2×#41—21no—
222C22×Q8—21no—
223#137—44no—
224#135—22no—
225#135—22no—
226C2×Q16—21no—
227C2×Q16—22no—
228C2×Q16—22no—
229C2×Q16—22no—
230C2×Q16C23×C1112yes—
231C2×Q16C23×C1111yescharacteristic
232C2×SD16—21no—
233C2×SD16—22no—
234C2×D8C23×C1111yescharacteristic
235C2×M16D4×C1111yescharacteristic
236C22×C8C23×C1111yescharacteristic
237C4⋊Q8—22no—
238C4⋊Q8—22no—
239C4⋊Q8—41no—
240#125—22no—
241#125—41no—
242#124—22no—
243#123—42no—
244C22⋊Q8—41no—
245C22⋊Q8—41no—
246C22⋊Q8—42no—
247#117—21no—
248#117D4×C1111yescharacteristic
249C2×C4⋊C4—21no—
250M32—22no—
251C2×C16—22no—
252C2×C16C23×C1111yescharacteristic
253C2×C16C23×C1112yes—
254C2×C16C23×C1111yescharacteristic
255#107—21no—
256#107—22no—
257#107C23×C1112yes—
258#107C23×C1111yescharacteristic
259#107C23×C1111yescharacteristic
260#106—21no—
261#106—22no—
262#97D4×C1112yes—
263C4×C8C23×C1112yes—
264C2×C11—22no—
265C2×C11—161no—
266C2×C11C2×#48611yescharacteristic
267C2×C11#341611yescharacteristic
268C2×C11#341711yescharacteristic
269#41—42no—
270#41—42no—
271C2×Q8—22no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—42no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×D4—21no—
278C2×D4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4C2×D4×C1111yescharacteristic
283Q16—22no—
284Q16—22no—
285Q16—21no—
286Q16—21no—
287Q16—42no—
288Q16—44no—
289SD16—42no—
290SD16—44no—
291D8—21no—
292D8—21no—
293M16C11×SD1614yes—
294C2×C8C2×D4×C1111yescharacteristic
295C2×C8C2×D4×C1112yes—
296C2×C8C11×#4112yes—
297C2×C8C11×#4112yes—
298C2×C8C24×C1111yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4C11×D811yescharacteristic
309C4⋊C4C11×D811yescharacteristic
310C22⋊C4—41no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4C11×D812yes—
314C42—41no—
315C42C2×D4×C1112yes—
316C16—21no—
317C16—21no—
318C16—22no—
319C11#3370311yescharacteristic, direct product factor, Sylow
320C23—41no—
321C23C2×C11×D811yescharacteristic
322Q8—41no—
323Q8—42no—
324Q8—42no—
325Q8—41no—
326Q8—82no—
327Q8—162no—
328D4—41no—
329D4—41no—
330D4—82no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—161no—
339C2×C4C11×#12412yes—
340C2×C4C2×C11×D812yes—
341C2×C4C2×C11×D812yes—
342C2×C4C2×C11×D811yescharacteristic
343C2×C4C2×C11×SD1612yes—
344C2×C4C22×D4×C1111yescharacteristic
345C8C11×#12412yes—
346C8C2×C11×SD1614yes—
347C8C2×C11×#4111yescharacteristic
348C8C2×C11×#4111yescharacteristic
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22C11×#48612yes—
355C22C22×C11×D811yescharacteristic
356C4—22no—
357C4—22no—
358C4—82no—
359C4—81no—
360C4—81no—
361C4—81no—
362C4—82no—
363C4C11×#48612yes—
364C4C2×C11×#12411yescharacteristic
365C4C22×C11×SD1611yescharacteristic
366C2—22no—
367C2—161no—
368C2C2×C11×#48611yescharacteristic
369C2C11×#341611yescharacteristic
370C2C11×#341711yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC2×C11×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3164C2semidirect
3. C11×#2245C2semidirect
4. C11×#2243C2semidirect
5. C11×#2242C2semidirect
6. C11×#2241C2semidirect
7. C11×#2141C2semidirect
10. C2×C11×#358C2semidirect
11. C11×#2108C2semidirect
84. #33703C11direct (N × H)
135. #3164C2×C11semidirect
137. #2245C2×C11semidirect
138. #2243C2×C11semidirect
139. #2242C2×C11semidirect
140. #2241C2×C11semidirect
141. #2141C2×C11semidirect
144. C2×#358C2×C11semidirect
145. #2108C2×C11semidirect
319. C11#33703direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31642
C11×#31562
C11×#22452
C11×#22432
C11×#22422
C11×#22412
C11×#21412
C11×#21392
C11×#21382
C2×C11×#3582
C11×#21082
#3370311