Finite Group Databasebeta

← C11×#61375 #14638568

Subgroups — C11×#61375 #14638568

Order 2816.

1706 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3504C212yesmaximal, complemented
2C11×#3390C214yesmaximal, complemented
3C11×#3389C214yesmaximal, complemented
4C11×#3381C218yesmaximal, complemented
5C11×#3163C212yesmaximal, complemented
6C2×C11×#499C211yesmaximal, characteristic, complemented
7C11×#3083C214yesmaximal, complemented
8C11×#3080C212yesmaximal, complemented
9C11×#2960C211yesmaximal, characteristic, complemented
10C11×#2952C212yesmaximal
11C4×C11×#135C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13C11×#557C2218yes—
14C11×#554—28no—
15C11×#554C2218yes—
16C11×#544—24no—
17C11×#544C2214yes—
18C11×#533—22no—
19C11×#533C2211yescharacteristic
20C2×C11×#125—22no—
21C2×C11×#125C2212yes—
22C11×#520C2214yes—
23C4×C11×#41C2212yes—
24C11×#501C2218yes—
25C11×#499C2214yes—
26C11×#499C2214yes—
27C11×#499C2214yes—
28C11×#498C2214yes—
29C11×#479C2218yes—
30C11×#479C2218yes—
31C11×#478C2218yes—
32C11×#478C2218yes—
33C11×#477C2218yes—
34C11×#474C2218yes—
35C11×#446C2214yes—
36C8×Q8×C11C2214yes—
37C11×#442C2214yes—
38C11×#441C2214yes—
39C4×C11×Q16C2212yes—
40C4×C11×SD16C2214yes—
41C4×C11×SD16C2218yes—
42C4×C11×D8C2212yes—
43C11×#428C2214yes—
44C11×#427C2211yescharacteristic
45C2×C11×#107C2212yes—
46C2×C11×#106C2212yes—
47C11×#424C2212yes—
48C11×#423C2211yescharacteristic
49C11×#417C2214yes—
50C11×#416C2212yes—
51C11×#405C2212yes—
52C2×C4×C8×C11C2211yescharacteristic
53C2×C11×#41C2312yes—
54C11×#135Q818yescomplemented
55C2×C11×Q16C2311yescharacteristic
56C2×C11×SD16C2312yes—
57C2×C11×D8C2311yescharacteristic
58C2×C11×M16C2312yes—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×C4⋊Q8—28no—
62C11×C4⋊Q8—24no—
63C11×C4⋊Q8D412yes—
64C11×C4⋊Q8C2318yes—
65C11×#125—24no—
66C11×#125—28no—
67C11×#125—28no—
68C11×#125—22no—
69C11×#125—22no—
70C11×#125D412yes—
71C11×#125C2318yes—
72C11×#125C2318yes—
73C11×C22⋊Q8—28no—
74C11×C22⋊Q8—28no—
75C11×C22⋊Q8—28no—
76C11×C22⋊Q8—28no—
77C11×C22⋊Q8D414yes—
78C4×Q8×C11—28no—
79C4×Q8×C11C2314yes—
80C4×Q8×C11C2318yes—
81C4×Q8×C11C2314yes—
82C4×D4×C11—24no—
83C4×D4×C11—28no—
84C4×D4×C11C2314yes—
85C4×D4×C11C2318yes—
86C11×#117—24no—
87C11×#117—22no—
88C11×#117C2312yes—
89C11×#117C2312yes—
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4—24no—
92C2×C11×C4⋊C4—28no—
93C2×C11×C4⋊C4C2314yes—
94C2×C42×C11—22no—
95C2×C42×C11C2311yescharacteristic
96C11×#107C2314yes—
97C11×#107C2314yes—
98C11×#107C2318yes—
99C11×#107C2312yes—
100C11×#106C2312yes—
101C11×#106C2314yes—
102C11×#106C2318yes—
103C11×#106C2314yes—
104C11×C4⋊C8C2314yes—
105C11×C4⋊C8C2318yes—
106C11×#103C2314yes—
107C11×#103C2318yes—
108C11×#102C2314yes—
109C11×#102C2318yes—
110C11×#97C2314yes—
111C4×C8×C11C2314yes—
112C4×C8×C11C2312yes—
113C4×C8×C11C2312yes—
114#61375C1111yesmaximal, characteristic, direct product factor, Sylow
115C11×#41—24no—
116C11×#41C2×Q818yes—
117C2×Q8×C11—28no—
118C2×Q8×C11C2×D414yes—
119C2×Q8×C11C2412yes—
120C2×D4×C11—22no—
121C2×D4×C11C2412yes—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—28no—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2411yescharacteristic
128C11×Q16C2×Q814yes—
129C11×SD16C2×Q818yes—
130C11×D8C2×Q814yes—
131C11×M16—24no—
132C2×C8×C11—22no—
133C2×C8×C11C2×Q814yes—
134C2×C8×C11C2412yes—
135C2×C8×C11C2414yes—
136C2×C8×C11C2411yescharacteristic
137C2×C8×C11C2411yescharacteristic
138C11×C4⋊C4—28no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—28no—
146C11×C4⋊C4C2×D414yes—
147C11×C4⋊C4C2×D418yes—
148C11×C4⋊C4C2×D414yes—
149C11×C4⋊C4C2418yes—
150C11×C4⋊C4C2414yes—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—28no—
154C11×C22⋊C4C2×D414yes—
155C42×C11—22no—
156C42×C11—24no—
157C42×C11—28no—
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2412yes—
161C42×C11C2414yes—
162#3504C2×C1112yescomplemented
163#3390C2×C1114yescomplemented
164#3389C2×C1114yescomplemented
165#3381C2×C1118yescomplemented
166#3163C2×C1112yescomplemented
167C2×#499C2×C1111yescharacteristic, complemented
168#3083C2×C1114yescomplemented
169#3080C2×C1112yescomplemented
170#2960C2×C1111yescharacteristic, complemented
171#2952C2×C1112yes—
172C4×#135C2×C1111yescharacteristic
173C23×C11—22no—
174C23×C11C22×D411yescharacteristic
175Q8×C11—22no—
176Q8×C11—44no—
177Q8×C11—88no—
178Q8×C11C22×Q814yes—
179D4×C11—28no—
180D4×C11—22no—
181D4×C11C22×Q814yes—
182C2×C4×C11—22no—
183C2×C4×C11—28no—
184C2×C4×C11—24no—
185C2×C4×C11—28no—
186C2×C4×C11—42no—
187C2×C4×C11—84no—
188C2×C4×C11—88no—
189C2×C4×C11—84no—
190C2×C4×C11C22×D412yes—
191C2×C4×C11C22×D418yes—
192C2×C4×C11C22×D412yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×Q812yes—
195C2×C4×C112−1+412yes—
196C2×C4×C11C2511yescharacteristic
197C8×C11—22no—
198C8×C11—24no—
199C8×C11C22×Q812yes—
200C8×C11C22×Q812yes—
201C2×#135C22×C1111yescharacteristic
202#557C22×C1118yes—
203#554—28no—
204#554C22×C1118yes—
205#544—24no—
206#544C22×C1114yes—
207#533—22no—
208#533C22×C1111yescharacteristic
209C2×#125—22no—
210C2×#125C22×C1112yes—
211#520C22×C1114yes—
212C4×#41C22×C1112yes—
213#501C22×C1118yes—
214#499C22×C1114yes—
215#499C22×C1114yes—
216#499C22×C1114yes—
217#498C22×C1114yes—
218#479C22×C1118yes—
219#479C22×C1118yes—
220#478C22×C1118yes—
221#478C22×C1118yes—
222#477C22×C1118yes—
223#474C22×C1118yes—
224#446C22×C1114yes—
225C8×Q8C22×C1114yes—
226#442C22×C1114yes—
227#441C22×C1114yes—
228C4×Q16C22×C1112yes—
229C4×SD16C22×C1114yes—
230C4×SD16C22×C1118yes—
231C4×D8C22×C1112yes—
232#428C22×C1114yes—
233#427C22×C1111yescharacteristic
234C2×#107C22×C1112yes—
235C2×#106C22×C1112yes—
236#424C22×C1112yes—
237#423C22×C1111yescharacteristic
238#417C22×C1114yes—
239#416C22×C1112yes—
240#405C22×C1112yes—
241C2×C4×C8C22×C1111yescharacteristic
242C22×C11—22no—
243C22×C11—24no—
244C22×C11—44no—
245C22×C11D4×Q812yes—
246C22×C11C23×D411yescharacteristic
247C4×C11—22no—
248C4×C11—22no—
249C4×C11—28no—
250C4×C11—24no—
251C4×C11—48no—
252C4×C11—44no—
253C4×C11D4×Q812yes—
254C4×C11C23×Q811yescharacteristic
255C4×C11C2×2−1+411yescharacteristic
256C2×#41C23×C1112yes—
257#135Q8×C1118yescomplemented
258C2×Q16C23×C1111yescharacteristic
259C2×SD16C23×C1112yes—
260C2×D8C23×C1111yescharacteristic
261C2×M16C23×C1112yes—
262C22×C8C23×C1111yescharacteristic
263C22×C8C23×C1111yescharacteristic
264C4⋊Q8—28no—
265C4⋊Q8—24no—
266C4⋊Q8D4×C1112yes—
267C4⋊Q8C23×C1118yes—
268#125—24no—
269#125—28no—
270#125—28no—
271#125—22no—
272#125—22no—
273#125D4×C1112yes—
274#125C23×C1118yes—
275#125C23×C1118yes—
276C22⋊Q8—28no—
277C22⋊Q8—28no—
278C22⋊Q8—28no—
279C22⋊Q8—28no—
280C22⋊Q8D4×C1114yes—
281C4×Q8—28no—
282C4×Q8C23×C1114yes—
283C4×Q8C23×C1118yes—
284C4×Q8C23×C1114yes—
285C4×D4—24no—
286C4×D4—28no—
287C4×D4C23×C1114yes—
288C4×D4C23×C1118yes—
289#117—24no—
290#117—22no—
291#117C23×C1112yes—
292#117C23×C1112yes—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4C23×C1114yes—
297C2×C42—22no—
298C2×C42C23×C1111yescharacteristic
299#107C23×C1114yes—
300#107C23×C1114yes—
301#107C23×C1112yes—
302#107C23×C1118yes—
303#106C23×C1114yes—
304#106C23×C1114yes—
305#106C23×C1112yes—
306#106C23×C1118yes—
307C4⋊C8C23×C1114yes—
308C4⋊C8C23×C1118yes—
309#103C23×C1114yes—
310#103C23×C1118yes—
311#102C23×C1114yes—
312#102C23×C1118yes—
313#97C23×C1114yes—
314C4×C8C23×C1112yes—
315C4×C8C23×C1112yes—
316C4×C8C23×C1114yes—
317C2×C11—22no—
318C2×C11—44no—
319C2×C11C2×D4×Q811yescharacteristic
320C2×C11#358412yes—
321#41—24no—
322#41C2×Q8×C1118yes—
323C2×Q8—28no—
324C2×Q8C2×D4×C1114yes—
325C2×Q8C24×C1112yes—
326C2×D4—22no—
327C2×D4C24×C1112yes—
328C22×C4—22no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—28no—
332C22×C4C2×D4×C1112yes—
333C22×C4C24×C1111yescharacteristic
334Q16C2×Q8×C1114yes—
335SD16C2×Q8×C1118yes—
336D8C2×Q8×C1114yes—
337M16—24no—
338C2×C8—22no—
339C2×C8C2×Q8×C1114yes—
340C2×C8C24×C1112yes—
341C2×C8C24×C1114yes—
342C2×C8C24×C1111yescharacteristic
343C2×C8C24×C1111yescharacteristic
344C4⋊C4—28no—
345C4⋊C4—24no—
346C4⋊C4—28no—
347C4⋊C4—28no—
348C4⋊C4—28no—
349C4⋊C4—28no—
350C4⋊C4—24no—
351C4⋊C4—28no—
352C4⋊C4C2×D4×C1114yes—
353C4⋊C4C2×D4×C1118yes—
354C4⋊C4C2×D4×C1114yes—
355C4⋊C4C24×C1118yes—
356C4⋊C4C24×C1114yes—
357C22⋊C4—22no—
358C22⋊C4—24no—
359C22⋊C4—28no—
360C22⋊C4C2×D4×C1114yes—
361C42—22no—
362C42—24no—
363C42—28no—
364C42C2×D4×C1111yescharacteristic
365C42C2×D4×C1111yescharacteristic
366C42C24×C1112yes—
367C42C24×C1114yes—
368C11#6137511yescharacteristic, direct product factor, Sylow
369C23—22no—
370C23C22×D4×C1111yescharacteristic
371Q8—22no—
372Q8—44no—
373Q8—88no—
374Q8C22×Q8×C1114yes—
375D4—28no—
376D4—22no—
377D4C22×Q8×C1114yes—
378C2×C4—22no—
379C2×C4—28no—
380C2×C4—24no—
381C2×C4—28no—
382C2×C4—42no—
383C2×C4—84no—
384C2×C4—88no—
385C2×C4—84no—
386C2×C4C22×D4×C1112yes—
387C2×C4C22×D4×C1118yes—
388C2×C4C22×D4×C1112yes—
389C2×C4C22×D4×C1111yescharacteristic
390C2×C4C22×Q8×C1112yes—
391C2×C4C11×2−1+412yes—
392C2×C4C25×C1111yescharacteristic
393C8—22no—
394C8—24no—
395C8C22×Q8×C1112yes—
396C8C22×Q8×C1112yes—
397C22—22no—
398C22—24no—
399C22—44no—
400C22D4×Q8×C1112yes—
401C22C23×D4×C1111yescharacteristic
402C4—24no—
403C4—22no—
404C4—22no—
405C4—28no—
406C4—48no—
407C4—44no—
408C4D4×Q8×C1112yes—
409C4C23×Q8×C1111yescharacteristic
410C4C2×C11×2−1+411yescharacteristic
411C2—22no—
412C2—44no—
413C2C2×D4×Q8×C1111yescharacteristic
414C2C11×#358412yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#135C22
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×#3504C2semidirect
2. C11×#3390C2semidirect
3. C11×#3389C2semidirect
4. C11×#3381C2semidirect
5. C11×#3163C2semidirect
6. C2×C11×#499C2semidirect
7. C11×#3083C2semidirect
8. C11×#3080C2semidirect
9. C11×#2960C2semidirect
54. C11×#135Q8semidirect
114. #61375C11direct (N × H)
162. #3504C2×C11semidirect
163. #3390C2×C11semidirect
164. #3389C2×C11semidirect
165. #3381C2×C11semidirect
166. #3163C2×C11semidirect
167. C2×#499C2×C11semidirect
168. #3083C2×C11semidirect
169. #3080C2×C11semidirect
170. #2960C2×C11semidirect
257. #135Q8×C11semidirect
368. C11#61375direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35042
C11×#33902
C11×#33892
C11×#33812
C11×#31632
C2×C11×#4992
C11×#30832
C11×#30802
C11×#29602
C11×#29522
C4×C11×#1352
#6137511