Finite Group Databasebeta

← C11×#14297 #14591490

Subgroups — C11×#14297 #14591490

Order 2816.

1566 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#381C211yesmaximal, characteristic
2C2×C11×#380C211yesmaximal, characteristic
3C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
4C11×#1441C214yesmaximal, complemented
5C11×#1439C214yesmaximal
6C11×#1436C214yesmaximal, complemented
7C24×C4×C11C2211yescharacteristic
8C22×C11×C4⋊C4C2214yes—
9C22×C11×C4⋊C4C2212yes—
10C22×C11×C22⋊C4C2212yes—
11C22×C11×C22⋊C4C2212yes—
12C22×C11×C22⋊C4C2212yes—
13C22×C42×C11C2212yes—
14C11×#381—24no—
15C11×#380C418yescomplemented
16C4×C11×C22⋊C4—24no—
17C2×C11×#95C2212yes—
18C2×C11×#95C2214yes—
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2214yes—
22C2×C11×#95C2214yes—
23C2×C11×#95C2212yes—
24C25×C11C2311yescharacteristic
25C23×C4×C11—42no—
26C23×C4×C11—42no—
27C23×C4×C11C2×C414yes—
28C23×C4×C11D414yes—
29C23×C4×C11Q814yes—
30C23×C4×C11C2314yes—
31C23×C4×C11C2314yes—
32C23×C4×C11C2314yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C2×C11×C4⋊C4—28no—
36C2×C11×C4⋊C4—42no—
37C2×C11×C4⋊C4—42no—
38C2×C11×C4⋊C4—44no—
39C2×C11×C4⋊C4—44no—
40C2×C11×C4⋊C4C2×C418yes—
41C2×C11×C22⋊C4—24no—
42C2×C11×C22⋊C4—28no—
43C2×C11×C22⋊C4—24no—
44C2×C11×C22⋊C4—42no—
45C2×C11×C22⋊C4—42no—
46C2×C11×C22⋊C4—42no—
47C2×C11×C22⋊C4—42no—
48C2×C11×C22⋊C4C2×C418yes—
49C2×C42×C11—24no—
50C2×C42×C11—42no—
51C2×C42×C11—42no—
52C11×#95—24no—
53C11×#95—24no—
54C11×#95—24no—
55C11×#95—28no—
56C11×#95—44no—
57C11×#95—44no—
58C11×#95C2×C418yes—
59#14297C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11—24no—
61C24×C11—22no—
62C24×C11—22no—
63C24×C11—22no—
64C24×C11—22no—
65C24×C11C22×C412yes—
66C24×C11C2×D412yes—
67C24×C11C2×Q812yes—
68C24×C11C2411yescharacteristic
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—24no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—48no—
93C22×C4×C11—48no—
94C22×C4×C11—44no—
95C22×C4×C11—44no—
96C22×C4×C11C4⋊C4116yescomplemented
97C22×C4×C11C22×C418yes—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×Q812yes—
103C22×C4×C11C2×Q812yes—
104C22×C4×C11#4118yes—
105C11×C4⋊C4—48no—
106C11×C4⋊C4—416no—
107C11×C22⋊C4—216no—
108C11×C22⋊C4—48no—
109C11×C22⋊C4—48no—
110C42×C11—48no—
111C2×#381C2×C1111yescharacteristic
112C2×#380C2×C1111yescharacteristic
113C2×C4×C22⋊C4C2×C1111yescharacteristic
114#1441C2×C1114yescomplemented
115#1439C2×C1114yes—
116#1436C2×C1114yescomplemented
117C23×C11—24no—
118C23×C11—22no—
119C23×C11—24no—
120C23×C11—22no—
121C23×C11—24no—
122C23×C11—24no—
123C23×C11—24no—
124C23×C11—24no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—24no—
128C23×C11—44no—
129C23×C11—44no—
130C23×C11—44no—
131C23×C11—44no—
132C23×C11C2×C4⋊C414yes—
133C23×C11C23×C411yescharacteristic
134C23×C11C22×D411yescharacteristic
135C23×C11C22×Q811yescharacteristic
136C23×C11C2×#4114yes—
137C23×C11H(5,𝔽2)12yes—
138C23×C11H(5,𝔽2)12yes—
139C23×C11H(5,𝔽2)12yes—
140C23×C112−1+412yes—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—28no—
150C2×C4×C11—28no—
151C2×C4×C11—28no—
152C2×C4×C11—28no—
153C2×C4×C11—28no—
154C2×C4×C11—28no—
155C2×C4×C11—416no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C2×C4×C11—44no—
159C2×C4×C11—44no—
160C2×C4×C11—44no—
161C2×C4×C11—44no—
162C2×C4×C11—44no—
163C2×C4×C11—44no—
164C2×C4×C11—44no—
165C2×C4×C11—44no—
166C2×C4×C11—44no—
167C2×C4×C11—44no—
168C2×C4×C11—44no—
169C2×C4×C11—44no—
170C2×C4×C11—44no—
171C2×C4×C11C2×C4⋊C414yes—
172C2×C4×C11C2×C4⋊C414yes—
173C24×C4C22×C1111yescharacteristic
174C22×C4⋊C4C22×C1114yes—
175C22×C4⋊C4C22×C1112yes—
176C22×C22⋊C4C22×C1112yes—
177C22×C22⋊C4C22×C1112yes—
178C22×C22⋊C4C22×C1112yes—
179C22×C42C22×C1112yes—
180#381—24no—
181#380C4×C1118yescomplemented
182C4×C22⋊C4—24no—
183C2×#95C22×C1112yes—
184C2×#95C22×C1114yes—
185C2×#95C22×C1112yes—
186C2×#95C22×C1112yes—
187C2×#95C22×C1114yes—
188C2×#95C22×C1114yes—
189C2×#95C22×C1112yes—
190C22×C11—24no—
191C22×C11—24no—
192C22×C11—24no—
193C22×C11—44no—
194C22×C11—44no—
195C22×C11—48no—
196C22×C11—44no—
197C22×C11—44no—
198C22×C11C22×C4⋊C411yescharacteristic
199C22×C11C4×#4112yes—
200C22×C11#51812yes—
201C22×C11#51811yescharacteristic
202C22×C11#51911yescharacteristic
203C22×C11#52512yes—
204C22×C11#53312yes—
205C22×C11#53412yes—
206C22×C11#53712yes—
207C22×C11#53814yes—
208C22×C11#53914yes—
209C22×C11#54014yes—
210C22×C11#54214yes—
211C22×C11#54311yescharacteristic
212C22×C11#54311yescharacteristic
213C22×C11#54412yes—
214C4×C11—24no—
215C4×C11—24no—
216C4×C11—48no—
217C4×C11—48no—
218C4×C11—84no—
219C25C23×C1111yescharacteristic
220C23×C4—42no—
221C23×C4—42no—
222C23×C4C2×C4×C1114yes—
223C23×C4D4×C1114yes—
224C23×C4Q8×C1114yes—
225C23×C4C23×C1114yes—
226C23×C4C23×C1114yes—
227C23×C4C23×C1114yes—
228C23×C4C23×C1111yescharacteristic
229C23×C4C23×C1111yescharacteristic
230C2×C4⋊C4—28no—
231C2×C4⋊C4—42no—
232C2×C4⋊C4—42no—
233C2×C4⋊C4—44no—
234C2×C4⋊C4—44no—
235C2×C4⋊C4C2×C4×C1118yes—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—28no—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—42no—
240C2×C22⋊C4—42no—
241C2×C22⋊C4—42no—
242C2×C22⋊C4—42no—
243C2×C22⋊C4C2×C4×C1118yes—
244C2×C42—24no—
245C2×C42—42no—
246C2×C42—42no—
247#95—24no—
248#95—24no—
249#95—24no—
250#95—28no—
251#95—44no—
252#95—44no—
253#95C2×C4×C1118yes—
254C2×C11—44no—
255C2×C11#229611yescharacteristic
256C2×C11#231511yescharacteristic
257C2×C11#231611yescharacteristic
258C2×C11#233212yes—
259C2×C11#233312yes—
260C2×C11#263014yes—
261C2×C11#266512yes—
262C2×C11#266712yes—
263C24—24no—
264C24—22no—
265C24—22no—
266C24—22no—
267C24—22no—
268C24C22×C4×C1112yes—
269C24C2×D4×C1112yes—
270C24C2×Q8×C1112yes—
271C24C24×C1111yescharacteristic
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—48no—
296C22×C4—48no—
297C22×C4—44no—
298C22×C4—44no—
299C22×C4C11×C4⋊C4116yescomplemented
300C22×C4C22×C4×C1118yes—
301C22×C4C22×C4×C1112yes—
302C22×C4C22×C4×C1112yes—
303C22×C4C2×D4×C1112yes—
304C22×C4C2×D4×C1112yes—
305C22×C4C2×Q8×C1112yes—
306C22×C4C2×Q8×C1112yes—
307C22×C4C11×#4118yes—
308C4⋊C4—48no—
309C4⋊C4—416no—
310C22⋊C4—216no—
311C22⋊C4—48no—
312C22⋊C4—48no—
313C42—48no—
314C11#1429711yescharacteristic, direct product factor, Sylow
315C23—24no—
316C23—22no—
317C23—24no—
318C23—22no—
319C23—24no—
320C23—24no—
321C23—24no—
322C23—24no—
323C23—22no—
324C23—22no—
325C23—24no—
326C23—44no—
327C23—44no—
328C23—44no—
329C23—44no—
330C23C2×C11×C4⋊C414yes—
331C23C23×C4×C1111yescharacteristic
332C23C22×D4×C1111yescharacteristic
333C23C22×Q8×C1111yescharacteristic
334C23C2×C11×#4114yes—
335C23C11×H(5,𝔽2)12yes—
336C23C11×H(5,𝔽2)12yes—
337C23C11×H(5,𝔽2)12yes—
338C23C11×2−1+412yes—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—28no—
348C2×C4—28no—
349C2×C4—28no—
350C2×C4—28no—
351C2×C4—28no—
352C2×C4—28no—
353C2×C4—416no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4C2×C11×C4⋊C414yes—
370C2×C4C2×C11×C4⋊C414yes—
371C22—24no—
372C22—24no—
373C22—24no—
374C22—44no—
375C22—44no—
376C22—44no—
377C22—44no—
378C22—48no—
379C22C22×C11×C4⋊C411yescharacteristic
380C22C4×C11×#4112yes—
381C22C11×#51812yes—
382C22C11×#51811yescharacteristic
383C22C11×#51911yescharacteristic
384C22C11×#52512yes—
385C22C11×#53312yes—
386C22C11×#53412yes—
387C22C11×#53712yes—
388C22C11×#53814yes—
389C22C11×#53914yes—
390C22C11×#54014yes—
391C22C11×#54214yes—
392C22C11×#54311yescharacteristic
393C22C11×#54311yescharacteristic
394C22C11×#54412yes—
395C4—24no—
396C4—24no—
397C4—48no—
398C4—48no—
399C4—84no—
400C2—44no—
401C2C11×#229611yescharacteristic
402C2C11×#231511yescharacteristic
403C2C11×#231611yescharacteristic
404C2C11×#233212yes—
405C2C11×#233312yes—
406C2C11×#263014yes—
407C2C11×#266512yes—
408C2C11×#266712yes—
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1441C2semidirect
6. C11×#1436C2semidirect
15. C11×#380C4semidirect
59. #14297C11direct (N × H)
96. C22×C4×C11C4⋊C4semidirect
114. #1441C2×C11semidirect
116. #1436C2×C11semidirect
181. #380C4×C11semidirect
299. C22×C4C11×C4⋊C4semidirect
314. C11#14297direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3812
C2×C11×#3802
C2×C4×C11×C22⋊C42
C11×#14412
C11×#14392
C11×#14362
#1429711