Finite Group Databasebeta

← C11×#21423 #14598616

Subgroups — C11×#21423 #14598616

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#539C211yesmaximal, characteristic
2C11×#2313C211yesmaximal, characteristic, complemented
3C11×#2274C211yesmaximal, characteristic, complemented
4C11×#1996C212yesmaximal, complemented
5C11×#1964C212yesmaximal
6C11×#1899C214yesmaximal, complemented
7C4×C11×#99C214yesmaximal, complemented
8C11×#539—24no—
9C11×#539—24no—
10C2×C11×#126C412yescomplemented
11C2×C11×#125C412yescomplemented
12C2×C11×#123C412yescomplemented
13C2×C11×#123C2212yes—
14C2×C11×C22⋊Q8C412yescomplemented
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C2×C11×#117C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×C11×#99C2218yes—
21C11×#387—24no—
22C11×#381C2212yes—
23C11×#380C2212yes—
24C4×C11×C4⋊C4—24no—
25C4×C11×C22⋊C4C2212yes—
26C4×C11×C22⋊C4C2212yes—
27C4×C11×C22⋊C4C2212yes—
28C11×#342C2218yes—
29C22×Q8×C11C2×C411yescharacteristic
30C22×D4×C11C2×C411yescharacteristic
31C22×D4×C11C2312yes—
32C23×C4×C11C2×C412yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C11×#126—28no—
37C11×#125—28no—
38C11×#123—24no—
39C11×#123—24no—
40C11×#123—28no—
41C11×C22⋊Q8—22no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—28no—
44C11×#121—22no—
45C11×#121—22no—
46C4×D4×C11—24no—
47C4×D4×C11—24no—
48C11×#117—28no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2×C412yes—
52C2×C11×C4⋊C4C2×C411yescharacteristic
53C2×C11×C4⋊C4C2×C412yes—
54C2×C11×C4⋊C4C2×C412yes—
55C2×C11×C4⋊C4C2×C411yescharacteristic
56C2×C11×C4⋊C4C2×C412yes—
57C2×C11×C4⋊C4C2×C412yes—
58C2×C11×C4⋊C4C2×C412yes—
59C2×C11×C4⋊C4D414yes—
60C2×C11×C4⋊C4D414yes—
61C2×C11×C22⋊C4C2×C412yes—
62C2×C11×C22⋊C4C2×C412yes—
63C2×C11×C22⋊C4C2×C412yes—
64C2×C11×C22⋊C4C2×C412yes—
65C2×C11×C22⋊C4C2314yes—
66C2×C11×C22⋊C4C2312yes—
67C2×C11×C22⋊C4C2314yes—
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11C2×C412yes—
73C11×#99—216no—
74C11×#95—22no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—24no—
79#21423C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11C22×C412yes—
81C24×C11C2411yescharacteristic
82C2×Q8×C11—22no—
83C2×Q8×C11—81no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—28no—
87C2×D4×C11—22no—
88C2×D4×C11—81no—
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—81no—
94C22×C4×C11—81no—
95C22×C4×C11—82no—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C11×C4⋊C4—28no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—82no—
117C11×C4⋊C4C22⋊C418yes—
118C11×C4⋊C4C22⋊C418yes—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—22no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—24no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—28no—
127C11×C22⋊C4#4118yes—
128C42×C11—28no—
129C42×C11—24no—
130C42×C11—82no—
131C42×C11—82no—
132C42×C11—82no—
133C2×#539C2×C1111yescharacteristic
134#2313C2×C1111yescharacteristic, complemented
135#2274C2×C1111yescharacteristic, complemented
136#1996C2×C1112yescomplemented
137#1964C2×C1112yes—
138#1899C2×C1114yescomplemented
139C4×#99C2×C1114yescomplemented
140C23×C11—22no—
141C23×C11—24no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11C23×C411yescharacteristic
147C23×C11C22×D411yescharacteristic
148C23×C11C22×D411yescharacteristic
149C23×C11C2×#4114yes—
150Q8×C11—82no—
151D4×C11—44no—
152D4×C11—44no—
153D4×C11—82no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—28no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—44no—
171C2×C4×C11—44no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—44no—
175C2×C4×C11—44no—
176C2×C4×C11—44no—
177C2×C4×C11—84no—
178C2×C4×C11C2×C22⋊C414yes—
179C2×C4×C11C2×C22⋊C414yes—
180C2×C4×C11C2×C22⋊C412yes—
181C2×C4×C11C2×C22⋊C412yes—
182#539—24no—
183#539—24no—
184C2×#126C4×C1112yescomplemented
185C2×#125C4×C1112yescomplemented
186C2×#123C4×C1112yescomplemented
187C2×#123C22×C1112yes—
188C2×C22⋊Q8C4×C1112yescomplemented
189C2×C22⋊Q8C22×C1111yescharacteristic
190C2×#121C22×C1111yescharacteristic
191C2×C4×D4C22×C1112yes—
192C2×#117C22×C1112yes—
193C22×C4⋊C4C22×C1111yescharacteristic
194C2×#99C22×C1118yes—
195#387—24no—
196#381C22×C1112yes—
197#380C22×C1112yes—
198C4×C4⋊C4—24no—
199C4×C22⋊C4C22×C1112yes—
200C4×C22⋊C4C22×C1112yes—
201C4×C22⋊C4C22×C1112yes—
202#342C22×C1118yes—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—44no—
210C22×C11—42no—
211C22×C11—42no—
212C22×C11—42no—
213C22×C11—84no—
214C22×C11C22×C22⋊C411yescharacteristic
215C22×C11C4×#4112yes—
216C22×C11#52512yes—
217C22×C11#53212yes—
218C4×C11—24no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—24no—
222C4×C11—48no—
223C4×C11—42no—
224C4×C11—42no—
225C4×C11—42no—
226C4×C11—84no—
227C22×Q8C2×C4×C1111yescharacteristic
228C22×D4C2×C4×C1111yescharacteristic
229C22×D4C23×C1112yes—
230C23×C4C2×C4×C1112yes—
231C23×C4C23×C1111yescharacteristic
232C23×C4C23×C1111yescharacteristic
233C23×C4C23×C1111yescharacteristic
234#126—28no—
235#125—28no—
236#123—24no—
237#123—24no—
238#123—28no—
239C22⋊Q8—22no—
240C22⋊Q8—22no—
241C22⋊Q8—28no—
242#121—22no—
243#121—22no—
244C4×D4—24no—
245C4×D4—24no—
246#117—28no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4C2×C4×C1112yes—
250C2×C4⋊C4C2×C4×C1111yescharacteristic
251C2×C4⋊C4C2×C4×C1112yes—
252C2×C4⋊C4C2×C4×C1112yes—
253C2×C4⋊C4C2×C4×C1111yescharacteristic
254C2×C4⋊C4C2×C4×C1112yes—
255C2×C4⋊C4C2×C4×C1112yes—
256C2×C4⋊C4C2×C4×C1112yes—
257C2×C4⋊C4D4×C1114yes—
258C2×C4⋊C4D4×C1114yes—
259C2×C22⋊C4C2×C4×C1112yes—
260C2×C22⋊C4C2×C4×C1112yes—
261C2×C22⋊C4C2×C4×C1112yes—
262C2×C22⋊C4C2×C4×C1112yes—
263C2×C22⋊C4C23×C1114yes—
264C2×C22⋊C4C23×C1112yes—
265C2×C22⋊C4C23×C1114yes—
266C2×C42—22no—
267C2×C42—22no—
268C2×C42—22no—
269C2×C42—22no—
270C2×C42C2×C4×C1112yes—
271#99—216no—
272#95—22no—
273#95—22no—
274#95—22no—
275#95—22no—
276#95—24no—
277C2×C11—22no—
278C2×C11—22no—
279C2×C11—22no—
280C2×C11—82no—
281C2×C11#229711yescharacteristic
282C2×C11#288311yescharacteristic
283C2×C11#288411yescharacteristic
284C24C22×C4×C1112yes—
285C24C24×C1111yescharacteristic
286C2×Q8—22no—
287C2×Q8—81no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—28no—
291C2×D4—22no—
292C2×D4—81no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4—82no—
300C22×C4C22×C4×C1112yes—
301C22×C4C22×C4×C1112yes—
302C22×C4C22×C4×C1112yes—
303C22×C4C22×C4×C1112yes—
304C22×C4C22×C4×C1112yes—
305C22×C4C22×C4×C1111yescharacteristic
306C22×C4C22×C4×C1111yescharacteristic
307C22×C4C2×D4×C1112yes—
308C22×C4C2×D4×C1112yes—
309C22×C4C2×D4×C1112yes—
310C22×C4C2×D4×C1112yes—
311C22×C4C2×D4×C1112yes—
312C22×C4C2×D4×C1112yes—
313C4⋊C4—28no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—22no—
319C4⋊C4—24no—
320C4⋊C4—82no—
321C4⋊C4C11×C22⋊C418yes—
322C4⋊C4C11×C22⋊C418yes—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—24no—
326C22⋊C4—24no—
327C22⋊C4—24no—
328C22⋊C4—24no—
329C22⋊C4—24no—
330C22⋊C4—28no—
331C22⋊C4C11×#4118yes—
332C42—28no—
333C42—24no—
334C42—82no—
335C42—82no—
336C42—82no—
337C11#2142311yescharacteristic, direct product factor, Sylow
338C23—22no—
339C23—24no—
340C23—41no—
341C23—41no—
342C23—42no—
343C23—42no—
344C23C23×C4×C1111yescharacteristic
345C23C22×D4×C1111yescharacteristic
346C23C22×D4×C1111yescharacteristic
347C23C2×C11×#4114yes—
348Q8—82no—
349D4—44no—
350D4—44no—
351D4—82no—
352C2×C4—24no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—24no—
360C2×C4—28no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—84no—
376C2×C4C2×C11×C22⋊C414yes—
377C2×C4C2×C11×C22⋊C414yes—
378C2×C4C2×C11×C22⋊C412yes—
379C2×C4C2×C11×C22⋊C412yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—44no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—84no—
391C22C22×C11×C22⋊C411yescharacteristic
392C22C4×C11×#4112yes—
393C22C11×#52512yes—
394C22C11×#53212yes—
395C4—24no—
396C4—24no—
397C4—22no—
398C4—22no—
399C4—48no—
400C4—42no—
401C4—42no—
402C4—42no—
403C4—84no—
404C2—22no—
405C2—22no—
406C2—22no—
407C2—82no—
408C2C11×#229711yescharacteristic
409C2C11×#288311yescharacteristic
410C2C11×#288411yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2313C2semidirect
3. C11×#2274C2semidirect
4. C11×#1996C2semidirect
6. C11×#1899C2semidirect
7. C4×C11×#99C2semidirect
10. C2×C11×#126C4semidirect
11. C2×C11×#125C4semidirect
12. C2×C11×#123C4semidirect
14. C2×C11×C22⋊Q8C4semidirect
79. #21423C11direct (N × H)
134. #2313C2×C11semidirect
135. #2274C2×C11semidirect
136. #1996C2×C11semidirect
138. #1899C2×C11semidirect
139. C4×#99C2×C11semidirect
184. C2×#126C4×C11semidirect
185. C2×#125C4×C11semidirect
186. C2×#123C4×C11semidirect
188. C2×C22⋊Q8C4×C11semidirect
337. C11#21423direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5392
C11×#23132
C11×#22742
C11×#19962
C11×#19642
C11×#18992
C4×C11×#992
#2142311