Finite Group Databasebeta

← C11×#61936 #14639129

Subgroups — C11×#61936 #14639129

Order 2816.

1634 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3556C211yesmaximal, characteristic, complemented
2C11×#3509C211yesmaximal, characteristic
3C11×#3398C214yesmaximal, complemented
4C11×#3395C214yesmaximal, complemented
5C11×#3374C214yesmaximal, complemented
6C11×#3364C214yesmaximal, complemented
7C11×#3223C214yesmaximal
8C11×#3209C212yesmaximal, complemented
9C11×#3127C214yesmaximal, complemented
10C11×#3107C212yesmaximal
11C11×#2986C211yesmaximal, characteristic, complemented
12C11×#564—22no—
13C11×#557—22no—
14C11×#557C2214yes—
15C11×#557C2214yes—
16C11×#557C2214yes—
17C11×#556C2214yes—
18C11×#552—24no—
19C11×#541—22no—
20C11×#541—24no—
21C11×#541C2214yes—
22C11×#536C2212yes—
23C11×#533—22no—
24C11×#533C2212yes—
25C11×#533C2211yescharacteristic
26C2×C11×C4⋊Q8C2211yescharacteristic
27C11×#519C2212yes—
28C4×C11×#41C2211yescharacteristic
29C11×#497C2214yes—
30C11×#494C2214yes—
31C11×#494C2214yes—
32C11×#491C2214yes—
33C11×#488C2214yes—
34C11×#487C2214yes—
35C11×#485C2214yes—
36C11×#479C2218yes—
37C11×#475C2212yes—
38C11×#474C2212yes—
39C11×#464C2218yes—
40C11×#462C2214yes—
41C11×#462C2214yes—
42C11×#462C2218yes—
43C11×#462C2212yes—
44C11×#462C2218yes—
45C11×#461C2212yes—
46C11×#452C2214yes—
47C11×#451C2218yes—
48C11×#446C2214yes—
49C8×Q8×C11C2214yes—
50C11×#441C2218yes—
51C4×C11×Q16C2214yes—
52C4×C11×Q16C2218yes—
53C4×C11×SD16C2214yes—
54C11×#433C2214yes—
55C11×#431C2212yes—
56C2×C11×#41C2311yescharacteristic
57C22×Q8×C11C2312yes—
58C2×C11×Q16C2318yes—
59C2×C11×Q16C2314yes—
60C2×C11×Q16C2318yes—
61C2×C11×SD16C2314yes—
62C11×C4⋊Q8—24no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8D412yes—
66C11×C4⋊Q8C2314yes—
67C11×C4⋊Q8C2312yes—
68C11×C4⋊Q8C2314yes—
69C11×C4⋊Q8C2314yes—
70C11×C4⋊Q8C2312yes—
71C11×#126—28no—
72C11×#126—28no—
73C11×#125—24no—
74C11×#125—28no—
75C11×#125—24no—
76C11×#125—28no—
77C11×#125—28no—
78C11×#125—28no—
79C11×#125—22no—
80C11×#125D412yes—
81C11×#125C2314yes—
82C11×#124C2314yes—
83C11×#123—24no—
84C11×C22⋊Q8—24no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—24no—
87C11×C22⋊Q8D414yes—
88C11×C22⋊Q8C2314yes—
89C4×Q8×C11—24no—
90C4×Q8×C11—24no—
91C4×Q8×C11—24no—
92C4×Q8×C11—24no—
93C4×Q8×C11—22no—
94C4×Q8×C11C2312yes—
95C4×Q8×C11C2318yes—
96C4×Q8×C11C2314yes—
97C4×Q8×C11C2318yes—
98C4×Q8×C11C2314yes—
99C4×D4×C11—22no—
100C4×D4×C11C2312yes—
101C11×#117—22no—
102C11×#117—24no—
103C11×#117—24no—
104C11×#117—21no—
105C11×#117C2311yescharacteristic
106C11×#117C2312yes—
107C2×C11×C4⋊C4—22no—
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110C11×#107C2314yes—
111C11×#106C2314yes—
112C11×C4⋊C8C2312yes—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2318yes—
115C11×#103C2314yes—
116C11×#103C2318yes—
117C11×#103C2314yes—
118C11×#103C2314yes—
119C11×#103C2318yes—
120C11×#102C2314yes—
121C11×C22⋊C8C2314yes—
122C11×#97C2314yes—
123C4×C8×C11C2314yes—
124C4×C8×C11C2314yes—
125#61936C1111yesmaximal, characteristic, direct product factor, Sylow
126C11×#41—42no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—44no—
130C2×Q8×C11C2×D414yes—
131C2×Q8×C11C2414yes—
132C2×Q8×C11C2411yescharacteristic
133C2×Q8×C11C2414yes—
134C2×D4×C11—21no—
135C2×D4×C11C2411yescharacteristic
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2411yescharacteristic
141C11×Q16—48no—
142C11×Q16—48no—
143C11×Q16—44no—
144C11×SD16—44no—
145C2×C8×C11C2414yes—
146C2×C8×C11C2414yes—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—28no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—28no—
160C11×C4⋊C4C2×D414yes—
161C11×C4⋊C4C2×D414yes—
162C11×C4⋊C4C2×D418yes—
163C11×C4⋊C4C2414yes—
164C11×C4⋊C4C2412yes—
165C11×C22⋊C4—21no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—28no—
169C11×C22⋊C4C2×D414yes—
170C42×C11—21no—
171C42×C11—22no—
172C42×C11—28no—
173C42×C11—24no—
174C42×C11—28no—
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2412yes—
178C42×C11C2414yes—
179#3556C2×C1111yescharacteristic, complemented
180#3509C2×C1111yescharacteristic
181#3398C2×C1114yescomplemented
182#3395C2×C1114yescomplemented
183#3374C2×C1114yescomplemented
184#3364C2×C1114yescomplemented
185#3223C2×C1114yes—
186#3209C2×C1112yescomplemented
187#3127C2×C1114yescomplemented
188#3107C2×C1112yes—
189#2986C2×C1111yescharacteristic, complemented
190C23×C11—21no—
191C23×C11C22×D411yescharacteristic
192Q8×C11—28no—
193Q8×C11—24no—
194Q8×C11—24no—
195Q8×C11—28no—
196Q8×C11—22no—
197Q8×C11—44no—
198Q8×C11—44no—
199D4×C11—22no—
200D4×C11—42no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—21no—
208C2×C4×C11—42no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11C22×D418yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D412yes—
214C2×C4×C11C22×D412yes—
215C2×C4×C11C2511yescharacteristic
216C8×C11—24no—
217C8×C11—24no—
218#564—22no—
219#557—22no—
220#557C22×C1114yes—
221#557C22×C1114yes—
222#557C22×C1114yes—
223#556C22×C1114yes—
224#552—24no—
225#541—22no—
226#541—24no—
227#541C22×C1114yes—
228#536C22×C1112yes—
229#533—22no—
230#533C22×C1112yes—
231#533C22×C1111yescharacteristic
232C2×C4⋊Q8C22×C1111yescharacteristic
233#519C22×C1112yes—
234C4×#41C22×C1111yescharacteristic
235#497C22×C1114yes—
236#494C22×C1114yes—
237#494C22×C1114yes—
238#491C22×C1114yes—
239#488C22×C1114yes—
240#487C22×C1114yes—
241#485C22×C1114yes—
242#479C22×C1118yes—
243#475C22×C1112yes—
244#474C22×C1112yes—
245#464C22×C1118yes—
246#462C22×C1112yes—
247#462C22×C1114yes—
248#462C22×C1118yes—
249#462C22×C1114yes—
250#462C22×C1118yes—
251#461C22×C1112yes—
252#452C22×C1114yes—
253#451C22×C1118yes—
254#446C22×C1114yes—
255C8×Q8C22×C1114yes—
256#441C22×C1118yes—
257C4×Q16C22×C1114yes—
258C4×Q16C22×C1118yes—
259C4×SD16C22×C1114yes—
260#433C22×C1114yes—
261#431C22×C1112yes—
262C22×C11—21no—
263C22×C11—22no—
264C22×C11—41no—
265C22×C11—42no—
266C22×C11C23×D411yescharacteristic
267C4×C11—21no—
268C4×C11—22no—
269C4×C11—28no—
270C4×C11—41no—
271C4×C11—44no—
272C4×C11—44no—
273C4×C11—42no—
274C4×C11—44no—
275C4×C11#57814yes—
276C4×C11#58512yes—
277C2×#41C23×C1111yescharacteristic
278C22×Q8C23×C1112yes—
279C2×Q16C23×C1118yes—
280C2×Q16C23×C1114yes—
281C2×Q16C23×C1118yes—
282C2×SD16C23×C1114yes—
283C4⋊Q8—24no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8D4×C1112yes—
287C4⋊Q8C23×C1114yes—
288C4⋊Q8C23×C1112yes—
289C4⋊Q8C23×C1114yes—
290C4⋊Q8C23×C1114yes—
291C4⋊Q8C23×C1112yes—
292#126—28no—
293#126—28no—
294#125—24no—
295#125—28no—
296#125—24no—
297#125—28no—
298#125—28no—
299#125—28no—
300#125—22no—
301#125D4×C1112yes—
302#125C23×C1114yes—
303#124C23×C1114yes—
304#123—24no—
305C22⋊Q8—24no—
306C22⋊Q8—22no—
307C22⋊Q8—24no—
308C22⋊Q8D4×C1114yes—
309C22⋊Q8C23×C1114yes—
310C4×Q8—24no—
311C4×Q8—24no—
312C4×Q8—24no—
313C4×Q8—24no—
314C4×Q8—22no—
315C4×Q8C23×C1112yes—
316C4×Q8C23×C1118yes—
317C4×Q8C23×C1114yes—
318C4×Q8C23×C1118yes—
319C4×Q8C23×C1114yes—
320C4×D4—22no—
321C4×D4C23×C1112yes—
322#117—22no—
323#117—24no—
324#117—24no—
325#117—21no—
326#117C23×C1111yescharacteristic
327#117C23×C1112yes—
328C2×C4⋊C4—22no—
329C2×C42—21no—
330C2×C42C23×C1111yescharacteristic
331#107C23×C1114yes—
332#106C23×C1114yes—
333C4⋊C8C23×C1112yes—
334C4⋊C8C23×C1112yes—
335C4⋊C8C23×C1118yes—
336#103C23×C1114yes—
337#103C23×C1114yes—
338#103C23×C1118yes—
339#103C23×C1114yes—
340#103C23×C1118yes—
341#102C23×C1114yes—
342C22⋊C8C23×C1114yes—
343#97C23×C1114yes—
344C4×C8C23×C1114yes—
345C4×C8C23×C1114yes—
346C2×C11—41no—
347C2×C11—81no—
348C2×C11#348711yescharacteristic
349C2×C11C2×#57812yes—
350#41—42no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—44no—
354C2×Q8C2×D4×C1114yes—
355C2×Q8C24×C1114yes—
356C2×Q8C24×C1111yescharacteristic
357C2×Q8C24×C1114yes—
358C2×D4—21no—
359C2×D4C24×C1111yescharacteristic
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4C2×D4×C1112yes—
364C22×C4C24×C1111yescharacteristic
365Q16—48no—
366Q16—48no—
367Q16—44no—
368SD16—44no—
369C2×C8C24×C1114yes—
370C2×C8C24×C1114yes—
371C4⋊C4—24no—
372C4⋊C4—24no—
373C4⋊C4—22no—
374C4⋊C4—28no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—28no—
379C4⋊C4—24no—
380C4⋊C4—28no—
381C4⋊C4—28no—
382C4⋊C4—24no—
383C4⋊C4—28no—
384C4⋊C4C2×D4×C1114yes—
385C4⋊C4C2×D4×C1114yes—
386C4⋊C4C2×D4×C1118yes—
387C4⋊C4C24×C1114yes—
388C4⋊C4C24×C1112yes—
389C22⋊C4—21no—
390C22⋊C4—24no—
391C22⋊C4—22no—
392C22⋊C4—28no—
393C22⋊C4C2×D4×C1114yes—
394C42—21no—
395C42—22no—
396C42—28no—
397C42—24no—
398C42—28no—
399C42C2×D4×C1111yescharacteristic
400C42C2×D4×C1111yescharacteristic
401C42C24×C1112yes—
402C42C24×C1114yes—
403C11#6193611yescharacteristic, direct product factor, Sylow
404C23—21no—
405C23C22×D4×C1111yescharacteristic
406Q8—28no—
407Q8—24no—
408Q8—24no—
409Q8—28no—
410Q8—22no—
411Q8—44no—
412Q8—44no—
413D4—22no—
414D4—42no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—21no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4C22×D4×C1118yes—
426C2×C4C22×D4×C1111yescharacteristic
427C2×C4C22×D4×C1112yes—
428C2×C4C22×D4×C1112yes—
429C2×C4C25×C1111yescharacteristic
430C8—24no—
431C8—24no—
432C22—21no—
433C22—22no—
434C22—41no—
435C22—42no—
436C22C23×D4×C1111yescharacteristic
437C4—21no—
438C4—22no—
439C4—28no—
440C4—41no—
441C4—44no—
442C4—44no—
443C4—42no—
444C4—44no—
445C4C11×#57814yes—
446C4C11×#58512yes—
447C2—41no—
448C2—81no—
449C2C11×#348711yescharacteristic
450C2C2×C11×#57812yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3556C2semidirect
3. C11×#3398C2semidirect
4. C11×#3395C2semidirect
5. C11×#3374C2semidirect
6. C11×#3364C2semidirect
8. C11×#3209C2semidirect
9. C11×#3127C2semidirect
11. C11×#2986C2semidirect
125. #61936C11direct (N × H)
179. #3556C2×C11semidirect
181. #3398C2×C11semidirect
182. #3395C2×C11semidirect
183. #3374C2×C11semidirect
184. #3364C2×C11semidirect
186. #3209C2×C11semidirect
187. #3127C2×C11semidirect
189. #2986C2×C11semidirect
403. C11#61936direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35562
C11×#35092
C11×#33982
C11×#33952
C11×#33742
C11×#33642
C11×#32232
C11×#32092
C11×#31272
C11×#31072
C11×#29862
#6193611