Finite Group Databasebeta

← C11×#19634 #14596827

Subgroups — C11×#19634 #14596827

Order 2816.

698 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×#3230C211yesmaximal, characteristic
2C11×#3209C211yesmaximal, characteristic
3C11×#3170C211yesmaximal, characteristic
4C11×#3165C211yesmaximal, characteristic
5C11×#3165C211yesmaximal, characteristic
6C2×C11×#487C211yesmaximal, characteristic
7C11×#1723C212yesmaximal, complemented
8C11×#1723C212yesmaximal, complemented
9C11×#1710C212yesmaximal, complemented
10C11×#1707C212yesmaximal, complemented
11C8×C11×M16C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13C11×#533C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C11×#501—22no—
17C11×#501—22no—
18C11×#500C2212yes—
19C11×#500C2212yes—
20C11×#500C2211yescharacteristic
21C11×#500C2212yes—
22C11×#498C2212yes—
23C11×#498C2212yes—
24C11×#494C2211yescharacteristic
25C11×#494C2212yes—
26C11×#487—22no—
27C11×#487C2211yescharacteristic
28C11×#487C2211yescharacteristic
29C11×#487C2212yes—
30C11×#487C2212yes—
31C11×#487C2212yes—
32C11×#487C2212yes—
33C11×#484—22no—
34C11×#477—22no—
35C11×#467—22no—
36C11×#462—22no—
37C11×#451—22no—
38C4×C11×Q16—22no—
39C11×#431C2211yescharacteristic
40C11×#428—22no—
41C11×#428—22no—
42C2×C11×#103—22no—
43C4×C11×M16C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45C11×#322C2212yes—
46C82×C11C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C2×C11×Q16—22no—
50C2×C11×Q16—24no—
51C2×C11×M16D412yes—
52C22×C8×C11D412yes—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8C2311yescharacteristic
60C11×C4⋊Q8C2311yescharacteristic
61C11×C4⋊Q8C2312yes—
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2312yes—
64C11×C4⋊Q8C2311yescharacteristic
65C11×#125—21no—
66C11×#125—21no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C4×Q8×C11—21no—
72C4×Q8×C11—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C11×#117—21no—
76C11×#117—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C11×#107—24no—
83C11×#107—24no—
84C11×#107—22no—
85C11×#107—24no—
86C11×#106—24no—
87C11×#106—24no—
88C11×C4⋊C8D412yes—
89C11×#103—24no—
90C11×#103—24no—
91C11×#103—22no—
92C11×#103—22no—
93C11×#103—24no—
94C11×#103—24no—
95C11×C22⋊C8D412yes—
96C11×#97D412yes—
97C4×C8×C11D412yes—
98C4×C8×C11C2311yescharacteristic
99C4×C8×C11C2312yes—
100C4×C8×C11C2312yes—
101C4×C8×C11C2311yescharacteristic
102#19634C1111yesmaximal, characteristic, direct product factor, Sylow
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—21no—
109C2×Q8×C11—44no—
110C2×Q8×C11—41no—
111C2×Q8×C11—41no—
112C2×Q8×C11—82no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C11×Q16—44no—
119C11×Q16—84no—
120C11×M16Q1618yescomplemented
121C2×C8×C11—42no—
122C2×C8×C11C2×D412yes—
123C2×C8×C11C2×D412yes—
124C2×C8×C11C2×D414yes—
125C2×C8×C11C2×D414yes—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C42×C11—41no—
149C42×C11—41no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2411yescharacteristic
154#3230C2×C1111yescharacteristic
155#3209C2×C1111yescharacteristic
156#3170C2×C1111yescharacteristic
157#3165C2×C1111yescharacteristic
158#3165C2×C1111yescharacteristic
159C2×#487C2×C1111yescharacteristic
160#1723C2×C1112yescomplemented
161#1723C2×C1112yescomplemented
162#1710C2×C1112yescomplemented
163#1707C2×C1112yescomplemented
164C8×M16C2×C1111yescharacteristic
165C23×C11#12711yescharacteristic
166Q8×C11—42no—
167Q8×C11—42no—
168Q8×C11—44no—
169Q8×C11—42no—
170Q8×C11—44no—
171Q8×C11—42no—
172Q8×C11—82no—
173Q8×C11—82no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—82no—
183C2×C4×C11—82no—
184C2×C4×C11#12711yescharacteristic
185C2×C4×C11#12711yescharacteristic
186C2×C4×C11#12711yescharacteristic
187C2×C4×C11C2×Q1614yes—
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C8×C11—22no—
192C8×C11—22no—
193C8×C11—24no—
194C8×C11C2×Q1618yes—
195#533C22×C1111yescharacteristic
196#533C22×C1111yescharacteristic
197C2×C4⋊Q8C22×C1111yescharacteristic
198C2×C4⋊Q8C22×C1111yescharacteristic
199#501—22no—
200#501—22no—
201#500C22×C1112yes—
202#500C22×C1112yes—
203#500C22×C1111yescharacteristic
204#500C22×C1112yes—
205#498C22×C1112yes—
206#498C22×C1112yes—
207#494C22×C1111yescharacteristic
208#494C22×C1112yes—
209#487—22no—
210#487C22×C1112yes—
211#487C22×C1112yes—
212#487C22×C1111yescharacteristic
213#487C22×C1111yescharacteristic
214#487C22×C1112yes—
215#487C22×C1112yes—
216#484—22no—
217#477—22no—
218#467—22no—
219#462—22no—
220#451—22no—
221C4×Q16—22no—
222#431C22×C1111yescharacteristic
223#428—22no—
224#428—22no—
225C2×#103—22no—
226C4×M16C22×C1111yescharacteristic
227C2×C4×C8C22×C1111yescharacteristic
228#322C22×C1112yes—
229C82C22×C1112yes—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11#49412yes—
233C22×C11C2×#12711yescharacteristic
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—82no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11—82no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11#49412yes—
243C4×C11C22×Q1612yes—
244C4×C11#57512yes—
245C4×C11#57712yes—
246C22×Q8—21no—
247C22×Q8—21no—
248C2×Q16—22no—
249C2×Q16—24no—
250C2×M16D4×C1112yes—
251C22×C8D4×C1112yes—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8C23×C1112yes—
259C4⋊Q8C23×C1112yes—
260C4⋊Q8C23×C1111yescharacteristic
261C4⋊Q8C23×C1111yescharacteristic
262C4⋊Q8C23×C1111yescharacteristic
263C4⋊Q8C23×C1111yescharacteristic
264#125—21no—
265#125—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274#117—21no—
275#117—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C42C23×C1111yescharacteristic
281#107—24no—
282#107—24no—
283#107—22no—
284#107—24no—
285#106—24no—
286#106—24no—
287C4⋊C8D4×C1112yes—
288#103—24no—
289#103—24no—
290#103—22no—
291#103—22no—
292#103—24no—
293#103—24no—
294C22⋊C8D4×C1112yes—
295#97D4×C1112yes—
296C4×C8D4×C1112yes—
297C4×C8C23×C1111yescharacteristic
298C4×C8C23×C1112yes—
299C4×C8C23×C1112yes—
300C4×C8C23×C1111yescharacteristic
301C2×C11—22no—
302C2×C11C2×#49411yescharacteristic
303C2×C11#315311yescharacteristic
304C2×C11#315411yescharacteristic
305C2×Q8—21no—
306C2×Q8—22no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—22no—
310C2×Q8—21no—
311C2×Q8—44no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—82no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4C2×D4×C1111yescharacteristic
318C22×C4C2×D4×C1111yescharacteristic
319C22×C4C2×D4×C1111yescharacteristic
320Q16—44no—
321Q16—84no—
322M16C11×Q1618yescomplemented
323C2×C8—42no—
324C2×C8C2×D4×C1112yes—
325C2×C8C2×D4×C1112yes—
326C2×C8C2×D4×C1114yes—
327C2×C8C2×D4×C1114yes—
328C4⋊C4—22no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C42—41no—
351C42—41no—
352C42C2×D4×C1111yescharacteristic
353C42C2×D4×C1111yescharacteristic
354C42C2×D4×C1111yescharacteristic
355C42C24×C1111yescharacteristic
356C11#1963411yescharacteristic, direct product factor, Sylow
357C23C11×#12711yescharacteristic
358Q8—42no—
359Q8—42no—
360Q8—44no—
361Q8—42no—
362Q8—44no—
363Q8—42no—
364Q8—82no—
365Q8—82no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4C11×#12711yescharacteristic
377C2×C4C11×#12711yescharacteristic
378C2×C4C11×#12711yescharacteristic
379C2×C4C2×C11×Q1614yes—
380C2×C4C22×D4×C1111yescharacteristic
381C2×C4C22×D4×C1111yescharacteristic
382C2×C4C22×D4×C1111yescharacteristic
383C8—22no—
384C8—22no—
385C8—24no—
386C8C2×C11×Q1618yes—
387C22—21no—
388C22—21no—
389C22C11×#49412yes—
390C22C2×C11×#12711yescharacteristic
391C4—21no—
392C4—21no—
393C4—82no—
394C4—81no—
395C4—81no—
396C4—82no—
397C4—81no—
398C4—81no—
399C4C11×#49412yes—
400C4C22×C11×Q1612yes—
401C4C11×#57512yes—
402C4C11×#57712yes—
403C2—22no—
404C2C2×C11×#49411yescharacteristic
405C2C11×#315311yescharacteristic
406C2C11×#315411yescharacteristic
subgroupG/H
center, socleC22×C11C2×#127
commutator, Frattini, cosocleC42C24×C11
prime radicalC23×C11#127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
7. C11×#1723C2semidirect
8. C11×#1723C2semidirect
9. C11×#1710C2semidirect
10. C11×#1707C2semidirect
102. #19634C11direct (N × H)
120. C11×M16Q16semidirect
160. #1723C2×C11semidirect
161. #1723C2×C11semidirect
162. #1710C2×C11semidirect
163. #1707C2×C11semidirect
322. M16C11×Q16semidirect
356. C11#19634direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32302
C11×#32092
C11×#31702
C11×#31652
C2×C11×#4872
C11×#17232
C11×#17102
C11×#17072
C8×C11×M162
#1963411