Finite Group Databasebeta

← C11×#61393 #14638586

Subgroups — C11×#61393 #14638586

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3480C212yesmaximal, complemented
2C11×#3396C213yesmaximal, complemented
3C11×#3395C211yesmaximal, characteristic, complemented
4C11×#3394C216yesmaximal, complemented
5C11×#3393C213yesmaximal, complemented
6C11×#3392C212yesmaximal, complemented
7C11×#3391C211yesmaximal, characteristic, complemented
8C11×#3147C213yesmaximal, complemented
9C11×#3035C216yesmaximal, complemented
10C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
11C4×C11×#135C213yesmaximal, complemented
12C2×C11×#135C2213yes—
13C2×C11×#135C2216yes—
14C11×#559C2216yes—
15C11×#557C2212yes—
16C11×#556C2216yes—
17C11×#553—26no—
18C11×#550C2212yes—
19C11×#548—22no—
20C11×#532C2216yes—
21C11×#529—26no—
22C4×C11×#41—22no—
23C4×C11×#41C2216yes—
24C2×C4×Q8×C11C2211yescharacteristic
25C11×#495C2216yes—
26C11×#495C2216yes—
27C11×#494C2213yes—
28C11×#493C2213yes—
29C11×#492C2216yes—
30C11×#464C22112yes—
31C11×#463C22112yes—
32C11×#462C2216yes—
33C11×#461C2216yes—
34C11×#460C2216yes—
35C11×#459C2216yes—
36C8×Q8×C11C2211yescharacteristic
37C8×Q8×C11C2211yescharacteristic
38C8×Q8×C11C2213yes—
39C8×Q8×C11C2213yes—
40C4×C11×Q16C2213yes—
41C4×C11×Q16C2213yes—
42C4×C11×SD16C2216yes—
43C4×C11×SD16C2216yes—
44C4×C11×D8C2213yes—
45C4×C11×D8C2213yes—
46C11×#427C2211yescharacteristic
47C2×C11×C4⋊C8C2213yes—
48C11×#416C2216yes—
49C2×C4×C8×C11C2213yes—
50C2×C11×#41—22no—
51C2×C11×#41C2316yes—
52C22×Q8×C11D411yescharacteristic
53C11×#135—212no—
54C11×#135—412no—
55C2×C11×Q16C2313yes—
56C2×C11×Q16C2316yes—
57C2×C11×SD16C2316yes—
58C2×C11×SD16C23112yes—
59C2×C11×D8C2313yes—
60C2×C11×D8C2316yes—
61C22×C8×C11C2313yes—
62C22×C8×C11C2311yescharacteristic
63C11×C4⋊Q8C2316yes—
64C11×#127C2316yes—
65C11×#126—212no—
66C11×#125—26no—
67C11×#124—26no—
68C11×#124C23112yes—
69C11×#123—212no—
70C11×C22⋊Q8—26no—
71C11×#121—26no—
72C11×#121—26no—
73C11×#121—26no—
74C4×Q8×C11—22no—
75C4×Q8×C11D411yescharacteristic
76C4×Q8×C11D413yes—
77C4×Q8×C11C2316yes—
78C4×Q8×C11C2316yes—
79C4×Q8×C11C2311yescharacteristic
80C4×Q8×C11C2313yes—
81C4×D4×C11—26no—
82C4×D4×C11—26no—
83C4×D4×C11—26no—
84C4×D4×C11—26no—
85C4×D4×C11—26no—
86C4×D4×C11C2316yes—
87C4×D4×C11C2316yes—
88C11×#117—26no—
89C11×#117—26no—
90C11×#117C2312yes—
91C2×C11×C4⋊C4D413yes—
92C2×C42×C11—26no—
93C2×C42×C11C2313yes—
94C11×#107C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#106C2312yes—
97C11×C4⋊C8C2313yes—
98C11×C4⋊C8C2313yes—
99C11×C4⋊C8C2316yes—
100C11×#103C2316yes—
101C11×#103C2316yes—
102C11×#102C2316yes—
103C11×#102C2316yes—
104C4×C8×C11C2313yes—
105C4×C8×C11C2313yes—
106C4×C8×C11C2313yes—
107C4×C8×C11C2313yes—
108#61393C1111yesmaximal, characteristic, direct product factor, Sylow
109C11×#41—212no—
110C11×#41—212no—
111C11×#41—48no—
112C2×Q8×C11—24no—
113C2×Q8×C11C2×D413yes—
114C2×Q8×C11C2×D411yescharacteristic
115C2×Q8×C11C2416yes—
116C2×D4×C11—26no—
117C2×D4×C11—26no—
118C2×D4×C11—26no—
119C2×D4×C11C2416yes—
120C22×C4×C11—26no—
121C22×C4×C11—26no—
122C22×C4×C11—26no—
123C22×C4×C11C2×D413yes—
124C22×C4×C11C2×D413yes—
125C22×C4×C11C2411yescharacteristic
126C11×Q16—26no—
127C11×Q16—46no—
128C11×SD16—212no—
129C11×SD16—412no—
130C11×D8—26no—
131C11×D8—46no—
132C2×C8×C11—26no—
133C2×C8×C11#4114yescomplemented
134C2×C8×C11C2413yes—
135C2×C8×C11C2413yes—
136C2×C8×C11C2411yescharacteristic
137C2×C8×C11C2411yescharacteristic
138C11×C4⋊C4—26no—
139C11×C4⋊C4—26no—
140C11×C4⋊C4—26no—
141C11×C4⋊C4—26no—
142C11×C4⋊C4C2×D413yes—
143C11×C4⋊C4C2×D413yes—
144C11×C4⋊C4C2×D416yes—
145C11×C4⋊C4C2412yes—
146C11×C4⋊C4C2412yes—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—212no—
149C11×C22⋊C4—26no—
150C11×C22⋊C4—26no—
151C11×C22⋊C4—212no—
152C42×C11—26no—
153C42×C11—26no—
154C42×C11—22no—
155C42×C11C2×D413yes—
156C42×C11C2×D413yes—
157C42×C11C2413yes—
158C42×C11C2413yes—
159#3480C2×C1112yescomplemented
160#3396C2×C1113yescomplemented
161#3395C2×C1111yescharacteristic, complemented
162#3394C2×C1116yescomplemented
163#3393C2×C1113yescomplemented
164#3392C2×C1112yescomplemented
165#3391C2×C1111yescharacteristic, complemented
166#3147C2×C1113yescomplemented
167#3035C2×C1116yescomplemented
168C2×C8×Q8C2×C1111yescharacteristic, complemented
169C4×#135C2×C1113yescomplemented
170C23×C11—26no—
171C23×C11C22×D411yescharacteristic
172Q8×C11—26no—
173Q8×C11—26no—
174Q8×C11—26no—
175Q8×C11#13514yescomplemented
176D4×C11—26no—
177D4×C11—26no—
178D4×C11—412no—
179D4×C11—412no—
180D4×C11—86no—
181C2×C4×C11—26no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—26no—
185C2×C4×C11—43no—
186C2×C4×C11—412no—
187C2×C4×C11—412no—
188C2×C4×C11—86no—
189C2×C4×C11C22×D413yes—
190C2×C4×C11C22×D413yes—
191C2×C4×C11C22×D413yes—
192C2×C4×C11C22×D413yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C2×#4112yes—
195C2×C4×C11H(5,𝔽2)12yes—
196C2×C4×C11C2511yescharacteristic
197C8×C11—23no—
198C8×C11—23no—
199C8×C11C2×#4112yes—
200C8×C11C2×#4112yes—
201C2×#135C22×C1113yes—
202C2×#135C22×C1116yes—
203#559C22×C1116yes—
204#557C22×C1112yes—
205#556C22×C1116yes—
206#553—26no—
207#550C22×C1112yes—
208#548—22no—
209#532C22×C1116yes—
210#529—26no—
211C4×#41—22no—
212C4×#41C22×C1116yes—
213C2×C4×Q8C22×C1111yescharacteristic
214#495C22×C1116yes—
215#495C22×C1116yes—
216#494C22×C1113yes—
217#493C22×C1113yes—
218#492C22×C1116yes—
219#464C22×C11112yes—
220#463C22×C11112yes—
221#462C22×C1116yes—
222#461C22×C1116yes—
223#460C22×C1116yes—
224#459C22×C1116yes—
225C8×Q8C22×C1111yescharacteristic
226C8×Q8C22×C1111yescharacteristic
227C8×Q8C22×C1113yes—
228C8×Q8C22×C1113yes—
229C4×Q16C22×C1113yes—
230C4×Q16C22×C1113yes—
231C4×SD16C22×C1116yes—
232C4×SD16C22×C1116yes—
233C4×D8C22×C1113yes—
234C4×D8C22×C1113yes—
235#427C22×C1111yescharacteristic
236C2×C4⋊C8C22×C1113yes—
237#416C22×C1116yes—
238C2×C4×C8C22×C1113yes—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—46no—
242C22×C11—46no—
243C22×C11—46no—
244C22×C11#55012yes—
245C22×C11C23×D411yescharacteristic
246C4×C11—23no—
247C4×C11—23no—
248C4×C11—23no—
249C4×C11—42no—
250C4×C11—46no—
251C4×C11—42no—
252C4×C11#55012yes—
253C4×C11C2×#13516yes—
254C4×C11C22×#4111yescharacteristic
255C4×C11C2×H(5,𝔽2)11yescharacteristic
256C2×#41—22no—
257C2×#41C23×C1116yes—
258C22×Q8D4×C1111yescharacteristic
259#135—212no—
260#135—412no—
261C2×Q16C23×C1113yes—
262C2×Q16C23×C1116yes—
263C2×SD16C23×C1116yes—
264C2×SD16C23×C11112yes—
265C2×D8C23×C1113yes—
266C2×D8C23×C1116yes—
267C22×C8C23×C1113yes—
268C22×C8C23×C1111yescharacteristic
269C4⋊Q8C23×C1116yes—
270#127C23×C1116yes—
271#126—212no—
272#125—26no—
273#124—26no—
274#124C23×C11112yes—
275#123—212no—
276C22⋊Q8—26no—
277#121—26no—
278#121—26no—
279#121—26no—
280C4×Q8—22no—
281C4×Q8D4×C1111yescharacteristic
282C4×Q8D4×C1113yes—
283C4×Q8C23×C1116yes—
284C4×Q8C23×C1116yes—
285C4×Q8C23×C1111yescharacteristic
286C4×Q8C23×C1113yes—
287C4×D4—26no—
288C4×D4—26no—
289C4×D4—26no—
290C4×D4—26no—
291C4×D4—26no—
292C4×D4C23×C1116yes—
293C4×D4C23×C1116yes—
294#117—26no—
295#117—26no—
296#117C23×C1112yes—
297C2×C4⋊C4D4×C1113yes—
298C2×C42—26no—
299C2×C42C23×C1113yes—
300#107C23×C1111yescharacteristic
301#107C23×C1111yescharacteristic
302#106C23×C1112yes—
303C4⋊C8C23×C1113yes—
304C4⋊C8C23×C1113yes—
305C4⋊C8C23×C1116yes—
306#103C23×C1116yes—
307#103C23×C1116yes—
308#102C23×C1116yes—
309#102C23×C1116yes—
310C4×C8C23×C1113yes—
311C4×C8C23×C1113yes—
312C4×C8C23×C1113yes—
313C4×C8C23×C1113yes—
314C2×C11—22no—
315C2×C11—86no—
316C2×C11C2×#55011yescharacteristic
317C2×C11C22×#13511yescharacteristic
318C2×C11#358411yescharacteristic
319#41—212no—
320#41—212no—
321#41—48no—
322C2×Q8—24no—
323C2×Q8C2×D4×C1113yes—
324C2×Q8C2×D4×C1111yescharacteristic
325C2×Q8C24×C1116yes—
326C2×D4—26no—
327C2×D4—26no—
328C2×D4—26no—
329C2×D4C24×C1116yes—
330C22×C4—26no—
331C22×C4—26no—
332C22×C4—26no—
333C22×C4C2×D4×C1113yes—
334C22×C4C2×D4×C1113yes—
335C22×C4C24×C1111yescharacteristic
336Q16—26no—
337Q16—46no—
338SD16—212no—
339SD16—412no—
340D8—26no—
341D8—46no—
342C2×C8—26no—
343C2×C8C11×#4114yescomplemented
344C2×C8C24×C1113yes—
345C2×C8C24×C1113yes—
346C2×C8C24×C1111yescharacteristic
347C2×C8C24×C1111yescharacteristic
348C4⋊C4—26no—
349C4⋊C4—26no—
350C4⋊C4—26no—
351C4⋊C4—26no—
352C4⋊C4C2×D4×C1113yes—
353C4⋊C4C2×D4×C1113yes—
354C4⋊C4C2×D4×C1116yes—
355C4⋊C4C24×C1112yes—
356C4⋊C4C24×C1112yes—
357C22⋊C4—22no—
358C22⋊C4—212no—
359C22⋊C4—26no—
360C22⋊C4—26no—
361C22⋊C4—212no—
362C42—22no—
363C42—26no—
364C42—26no—
365C42C2×D4×C1113yes—
366C42C2×D4×C1113yes—
367C42C24×C1113yes—
368C42C24×C1113yes—
369C11#6139311yescharacteristic, direct product factor, Sylow
370C23—26no—
371C23C22×D4×C1111yescharacteristic
372Q8—26no—
373Q8—26no—
374Q8—26no—
375Q8C11×#13514yescomplemented
376D4—26no—
377D4—26no—
378D4—412no—
379D4—412no—
380D4—86no—
381C2×C4—26no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—26no—
385C2×C4—43no—
386C2×C4—412no—
387C2×C4—412no—
388C2×C4—86no—
389C2×C4C22×D4×C1113yes—
390C2×C4C22×D4×C1113yes—
391C2×C4C22×D4×C1113yes—
392C2×C4C22×D4×C1111yescharacteristic
393C2×C4C22×D4×C1113yes—
394C2×C4C2×C11×#4112yes—
395C2×C4C11×H(5,𝔽2)12yes—
396C2×C4C25×C1111yescharacteristic
397C8—23no—
398C8—23no—
399C8C2×C11×#4112yes—
400C8C2×C11×#4112yes—
401C22—21no—
402C22—21no—
403C22—46no—
404C22—46no—
405C22—46no—
406C22C11×#55012yes—
407C22C23×D4×C1111yescharacteristic
408C4—23no—
409C4—23no—
410C4—23no—
411C4—46no—
412C4—42no—
413C4—42no—
414C4C11×#55012yes—
415C4C2×C11×#13516yes—
416C4C22×C11×#4111yescharacteristic
417C4C2×C11×H(5,𝔽2)11yescharacteristic
418C2—22no—
419C2—86no—
420C2C2×C11×#55011yescharacteristic
421C2C22×C11×#13511yescharacteristic
422C2C11×#358411yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3480C2semidirect
2. C11×#3396C2semidirect
3. C11×#3395C2semidirect
4. C11×#3394C2semidirect
5. C11×#3393C2semidirect
6. C11×#3392C2semidirect
7. C11×#3391C2semidirect
8. C11×#3147C2semidirect
9. C11×#3035C2semidirect
10. C2×C8×Q8×C11C2semidirect
11. C4×C11×#135C2semidirect
108. #61393C11direct (N × H)
133. C2×C8×C11#41semidirect
159. #3480C2×C11semidirect
160. #3396C2×C11semidirect
161. #3395C2×C11semidirect
162. #3394C2×C11semidirect
163. #3393C2×C11semidirect
164. #3392C2×C11semidirect
165. #3391C2×C11semidirect
166. #3147C2×C11semidirect
167. #3035C2×C11semidirect
168. C2×C8×Q8C2×C11semidirect
169. C4×#135C2×C11semidirect
175. Q8×C11#135semidirect
343. C2×C8C11×#41semidirect
369. C11#61393direct (N × H)
375. Q8C11×#135semidirect

Maximal subgroups

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

subgroupindex
C11×#34802
C11×#33962
C11×#33952
C11×#33942
C11×#33932
C11×#33922
C11×#33912
C11×#31472
C11×#30352
C2×C8×Q8×C112
C4×C11×#1352
#6139311