Finite Group Databasebeta

← C11×#61378 #14638571

Subgroups — C11×#61378 #14638571

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C212yesmaximal, complemented
2C11×#3389C218yesmaximal, complemented
3C11×#3384C218yesmaximal, complemented
4C11×#3163C212yesmaximal, complemented
5C11×#3162C211yesmaximal, characteristic, complemented
6C11×#3081C214yesmaximal, complemented
7C11×#3077C212yesmaximal, complemented
8C11×#2961C211yesmaximal, characteristic, complemented
9C11×#2948C212yesmaximal
10C2×C11×#442C211yesmaximal, characteristic
11C22×C11×D8C2211yescharacteristic
12C11×#554—22no—
13C11×#554—24no—
14C11×#554C2218yescomplemented
15C11×#554C2214yescomplemented
16D4×Q8×C11—22no—
17D4×Q8×C11C2214yescomplemented
18C11×#544C2214yes—
19C11×#543—24no—
20C11×#533C2212yes—
21C11×#533C2211yescharacteristic
22C2×C11×C22⋊Q8—24no—
23C11×#518C2214yes—
24C2×C4×D4×C11C2212yes—
25C11×#501C2214yescomplemented
26C11×#501C2214yescomplemented
27C11×#501C2218yescomplemented
28C11×#499C2214yescomplemented
29C11×#498C2214yescomplemented
30C11×#478C2218yescomplemented
31C11×#478C2218yescomplemented
32C11×#478C2218yescomplemented
33C11×#476C2214yescomplemented
34C11×#476C2218yescomplemented
35C11×#474C2214yescomplemented
36C11×#474C2218yescomplemented
37C11×#446C2218yescomplemented
38C11×#442C2218yes—
39C11×#442C2214yes—
40C11×#442C2214yes—
41C4×C11×D8C2218yes—
42C11×#428C2214yes—
43C11×#427C2212yes—
44C11×#427C2212yes—
45C2×C11×#106C2211yescharacteristic
46C11×#424C2212yes—
47C11×#423C2211yescharacteristic
48C11×#418C2214yes—
49C2×C11×#102C2212yes—
50C11×#405C2212yes—
51C2×C11×#97C2211yescharacteristic
52C22×Q8×C11—24no—
53C22×D4×C11C2312yes—
54C23×C4×C11—22no—
55C2×C11×D8Q818yescomplemented
56C2×C11×D8C2314yes—
57C2×C11×M16C2312yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—24no—
61C11×C4⋊Q8D412yes—
62C11×C4⋊Q8C2318yes—
63C11×C4⋊Q8C2312yes—
64C11×C4⋊Q8C2312yes—
65C11×#125—24no—
66C11×#125D412yes—
67C11×#125C2318yes—
68C11×#125C2314yes—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—28no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—28no—
75C11×C22⋊Q8—28no—
76C11×C22⋊Q8—28no—
77C11×C22⋊Q8—28no—
78C11×C22⋊Q8—28no—
79C11×C22⋊Q8D414yes—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11C2314yes—
83C4×D4×C11—24no—
84C4×D4×C11—24no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11C2314yes—
88C4×D4×C11C2314yes—
89C4×D4×C11C2318yes—
90C4×D4×C11C2318yes—
91C11×#117C2314yes—
92C11×#117C2312yes—
93C2×C11×C4⋊C4—28no—
94C2×C11×C4⋊C4—24no—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—28no—
98C2×C42×C11C2311yescharacteristic
99C11×#107C2318yes—
100C11×#107C2314yes—
101C11×#107C2314yes—
102C11×#106C2312yes—
103C11×#106C2314yes—
104C11×#106C2318yes—
105C11×#106C2312yes—
106C11×#106C2312yes—
107C11×#106C2312yes—
108C11×C4⋊C8C2314yes—
109C11×C4⋊C8C2318yes—
110C11×#102C2318yes—
111C11×#102C2318yes—
112C11×#102C2318yes—
113C11×#97C2314yes—
114C11×#97C2314yes—
115C4×C8×C11C2314yes—
116#61378C1111yesmaximal, characteristic, direct product factor, Sylow
117C24×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—28no—
121C2×Q8×C11—88no—
122C2×Q8×C11C2×D414yes—
123C2×D4×C11—22no—
124C2×D4×C11—24no—
125C2×D4×C11C2×Q818yescomplemented
126C2×D4×C11C2414yes—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—28no—
130C22×C4×C11—28no—
131C22×C4×C11—24no—
132C22×C4×C11—84no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2411yescharacteristic
135C11×D8C2×Q8116yescomplemented
136C11×M16—24no—
137C2×C8×C11—22no—
138C2×C8×C11C2×Q814yescomplemented
139C2×C8×C11C2414yes—
140C2×C8×C11C2412yes—
141C2×C8×C11C2412yes—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4C2×D418yes—
151C11×C4⋊C4C2×D414yes—
152C11×C4⋊C4C2×D414yes—
153C11×C4⋊C4C2414yes—
154C11×C4⋊C4C2414yes—
155C11×C4⋊C4C2414yes—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—28no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4C2×D414yes—
162C42×C11—24no—
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2414yes—
166C42×C11C2412yes—
167#3501C2×C1112yescomplemented
168#3389C2×C1118yescomplemented
169#3384C2×C1118yescomplemented
170#3163C2×C1112yescomplemented
171#3162C2×C1111yescharacteristic, complemented
172#3081C2×C1114yescomplemented
173#3077C2×C1112yescomplemented
174#2961C2×C1111yescharacteristic, complemented
175#2948C2×C1112yes—
176C2×#442C2×C1111yescharacteristic
177C23×C11—24no—
178C23×C11—28no—
179C23×C11—82no—
180C23×C11—82no—
181C23×C11C22×D411yescharacteristic
182Q8×C11—44no—
183Q8×C11—44no—
184Q8×C11—82no—
185Q8×C11—88no—
186D4×C11—28no—
187D4×C11—24no—
188D4×C11C22×Q818yes—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—42no—
193C2×C4×C11—48no—
194C2×C4×C11—88no—
195C2×C4×C11—84no—
196C2×C4×C11—88no—
197C2×C4×C11—82no—
198C2×C4×C11C22×D412yes—
199C2×C4×C11C22×D412yes—
200C2×C4×C11C22×D418yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×Q812yes—
203C2×C4×C112−1+412yes—
204C2×C4×C11C2511yescharacteristic
205C8×C11—22no—
206C8×C11—24no—
207C8×C11C22×Q814yes—
208C22×D8C22×C1111yescharacteristic
209#554—22no—
210#554—24no—
211#554C22×C1118yescomplemented
212#554C22×C1114yescomplemented
213D4×Q8—22no—
214D4×Q8C22×C1114yescomplemented
215#544C22×C1114yes—
216#543—24no—
217#533C22×C1112yes—
218#533C22×C1111yescharacteristic
219C2×C22⋊Q8—24no—
220#518C22×C1114yes—
221C2×C4×D4C22×C1112yes—
222#501C22×C1114yescomplemented
223#501C22×C1118yescomplemented
224#501C22×C1114yescomplemented
225#499C22×C1114yescomplemented
226#498C22×C1114yescomplemented
227#478C22×C1118yescomplemented
228#478C22×C1118yescomplemented
229#478C22×C1118yescomplemented
230#476C22×C1114yescomplemented
231#476C22×C1118yescomplemented
232#474C22×C1114yescomplemented
233#474C22×C1118yescomplemented
234#446C22×C1118yescomplemented
235#442C22×C1114yes—
236#442C22×C1118yes—
237#442C22×C1114yes—
238C4×D8C22×C1118yes—
239#428C22×C1114yes—
240#427C22×C1112yes—
241#427C22×C1112yes—
242C2×#106C22×C1111yescharacteristic
243#424C22×C1112yes—
244#423C22×C1111yescharacteristic
245#418C22×C1114yes—
246C2×#102C22×C1112yes—
247#405C22×C1112yes—
248C2×#97C22×C1111yescharacteristic
249C22×C11—22no—
250C22×C11—28no—
251C22×C11—44no—
252C22×C11—44no—
253C22×C11—88no—
254C22×C11D4×Q812yes—
255C22×C11C23×D411yescharacteristic
256C4×C11—22no—
257C4×C11—22no—
258C4×C11—28no—
259C4×C11—44no—
260C4×C11—44no—
261C4×C11—44no—
262C4×C11D4×Q812yes—
263C4×C11C23×Q811yescharacteristic
264C4×C11C2×2−1+411yescharacteristic
265C22×Q8—24no—
266C22×D4C23×C1112yes—
267C23×C4—22no—
268C2×D8Q8×C1118yescomplemented
269C2×D8C23×C1114yes—
270C2×M16C23×C1112yes—
271C22×C8C23×C1111yescharacteristic
272C22×C8C23×C1111yescharacteristic
273C4⋊Q8—24no—
274C4⋊Q8D4×C1112yes—
275C4⋊Q8C23×C1112yes—
276C4⋊Q8C23×C1112yes—
277C4⋊Q8C23×C1118yes—
278#125—24no—
279#125D4×C1112yes—
280#125C23×C1114yes—
281#125C23×C1118yes—
282C22⋊Q8—24no—
283C22⋊Q8—28no—
284C22⋊Q8—22no—
285C22⋊Q8—22no—
286C22⋊Q8—24no—
287C22⋊Q8—28no—
288C22⋊Q8—28no—
289C22⋊Q8—28no—
290C22⋊Q8—28no—
291C22⋊Q8—28no—
292C22⋊Q8D4×C1114yes—
293C4×Q8—22no—
294C4×Q8—22no—
295C4×Q8C23×C1114yes—
296C4×D4—24no—
297C4×D4—24no—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4C23×C1114yes—
301C4×D4C23×C1114yes—
302C4×D4C23×C1118yes—
303C4×D4C23×C1118yes—
304#117C23×C1114yes—
305#117C23×C1112yes—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4C23×C1112yes—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—28no—
311C2×C42C23×C1111yescharacteristic
312#107C23×C1114yes—
313#107C23×C1114yes—
314#107C23×C1118yes—
315#106C23×C1114yes—
316#106C23×C1112yes—
317#106C23×C1112yes—
318#106C23×C1112yes—
319#106C23×C1112yes—
320#106C23×C1118yes—
321C4⋊C8C23×C1114yes—
322C4⋊C8C23×C1118yes—
323#102C23×C1118yes—
324#102C23×C1118yes—
325#102C23×C1118yes—
326#97C23×C1114yes—
327#97C23×C1114yes—
328C4×C8C23×C1114yes—
329C2×C11—22no—
330C2×C11—48no—
331C2×C11C2×D4×Q811yescharacteristic
332C2×C11#358512yes—
333C24—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—28no—
337C2×Q8—88no—
338C2×Q8C2×D4×C1114yes—
339C2×D4—22no—
340C2×D4—24no—
341C2×D4C2×Q8×C1118yescomplemented
342C2×D4C24×C1114yes—
343C22×C4—22no—
344C22×C4—24no—
345C22×C4—28no—
346C22×C4—28no—
347C22×C4—24no—
348C22×C4—84no—
349C22×C4C2×D4×C1112yes—
350C22×C4C24×C1111yescharacteristic
351D8C2×Q8×C11116yescomplemented
352M16—24no—
353C2×C8—22no—
354C2×C8C2×Q8×C1114yescomplemented
355C2×C8C24×C1114yes—
356C2×C8C24×C1112yes—
357C2×C8C24×C1112yes—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—28no—
361C4⋊C4—28no—
362C4⋊C4—28no—
363C4⋊C4—22no—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4C2×D4×C1118yes—
367C4⋊C4C2×D4×C1114yes—
368C4⋊C4C2×D4×C1114yes—
369C4⋊C4C24×C1114yes—
370C4⋊C4C24×C1114yes—
371C4⋊C4C24×C1114yes—
372C22⋊C4—24no—
373C22⋊C4—28no—
374C22⋊C4—28no—
375C22⋊C4—24no—
376C22⋊C4—24no—
377C22⋊C4C2×D4×C1114yes—
378C42—24no—
379C42C2×D4×C1111yescharacteristic
380C42C2×D4×C1111yescharacteristic
381C42C24×C1114yes—
382C42C24×C1112yes—
383C11#6137811yescharacteristic, direct product factor, Sylow
384C23—24no—
385C23—28no—
386C23—82no—
387C23—82no—
388C23C22×D4×C1111yescharacteristic
389Q8—44no—
390Q8—44no—
391Q8—82no—
392Q8—88no—
393D4—28no—
394D4—24no—
395D4C22×Q8×C1118yes—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—42no—
400C2×C4—48no—
401C2×C4—88no—
402C2×C4—84no—
403C2×C4—88no—
404C2×C4—82no—
405C2×C4C22×D4×C1112yes—
406C2×C4C22×D4×C1112yes—
407C2×C4C22×D4×C1118yes—
408C2×C4C22×D4×C1111yescharacteristic
409C2×C4C22×Q8×C1112yes—
410C2×C4C11×2−1+412yes—
411C2×C4C25×C1111yescharacteristic
412C8—22no—
413C8—24no—
414C8C22×Q8×C1114yes—
415C22—22no—
416C22—28no—
417C22—44no—
418C22—44no—
419C22—88no—
420C22D4×Q8×C1112yes—
421C22C23×D4×C1111yescharacteristic
422C4—22no—
423C4—22no—
424C4—28no—
425C4—44no—
426C4—44no—
427C4—44no—
428C4D4×Q8×C1112yes—
429C4C23×Q8×C1111yescharacteristic
430C4C2×C11×2−1+411yescharacteristic
431C2—22no—
432C2—48no—
433C2C2×D4×Q8×C1111yescharacteristic
434C2C11×#358512yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC22×C11×D8C22
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×#3501C2semidirect
2. C11×#3389C2semidirect
3. C11×#3384C2semidirect
4. C11×#3163C2semidirect
5. C11×#3162C2semidirect
6. C11×#3081C2semidirect
7. C11×#3077C2semidirect
8. C11×#2961C2semidirect
14. C11×#554C22semidirect
15. C11×#554C22semidirect
17. D4×Q8×C11C22semidirect
25. C11×#501C22semidirect
26. C11×#501C22semidirect
27. C11×#501C22semidirect
28. C11×#499C22semidirect
29. C11×#498C22semidirect
30. C11×#478C22semidirect
31. C11×#478C22semidirect
32. C11×#478C22semidirect
33. C11×#476C22semidirect
34. C11×#476C22semidirect
35. C11×#474C22semidirect
36. C11×#474C22semidirect
37. C11×#446C22semidirect
55. C2×C11×D8Q8semidirect
116. #61378C11direct (N × H)
125. C2×D4×C11C2×Q8semidirect
135. C11×D8C2×Q8semidirect
138. C2×C8×C11C2×Q8semidirect
167. #3501C2×C11semidirect
168. #3389C2×C11semidirect
169. #3384C2×C11semidirect
170. #3163C2×C11semidirect
171. #3162C2×C11semidirect
172. #3081C2×C11semidirect
173. #3077C2×C11semidirect
174. #2961C2×C11semidirect
211. #554C22×C11semidirect
212. #554C22×C11semidirect
214. D4×Q8C22×C11semidirect
222. #501C22×C11semidirect
223. #501C22×C11semidirect
224. #501C22×C11semidirect
225. #499C22×C11semidirect
226. #498C22×C11semidirect
227. #478C22×C11semidirect
228. #478C22×C11semidirect
229. #478C22×C11semidirect
230. #476C22×C11semidirect
231. #476C22×C11semidirect
232. #474C22×C11semidirect
233. #474C22×C11semidirect
234. #446C22×C11semidirect
268. C2×D8Q8×C11semidirect
341. C2×D4C2×Q8×C11semidirect
351. D8C2×Q8×C11semidirect
354. C2×C8C2×Q8×C11semidirect
383. C11#61378direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#33892
C11×#33842
C11×#31632
C11×#31622
C11×#30812
C11×#30772
C11×#29612
C11×#29482
C2×C11×#4422
#6137811