Finite Group Databasebeta

← C11×#14675 #14591868

Subgroups — C11×#14675 #14591868

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 414 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×C11×#380C211yesmaximal, characteristic
4C11×#1444C212yesmaximal, complemented
5C11×#1442C212yesmaximal, complemented
6C11×#1441C214yesmaximal, complemented
7C11×#1439C214yesmaximal
8C24×C4×C11C2211yescharacteristic
9C22×C11×C4⋊C4C2212yes—
10C22×C11×C4⋊C4C2214yes—
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C11×#381—24no—
16C11×#380—24no—
17C11×#380C418yescomplemented
18C2×C11×#95C2212yes—
19C2×C11×#95C2212yes—
20C2×C11×#95C2211yescharacteristic
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2214yes—
23C2×C11×#95C2214yes—
24C2×C11×#95C2214yes—
25C2×C11×#95C2212yes—
26C25×C11C2311yescharacteristic
27C23×C4×C11—44no—
28C23×C4×C11C2×C414yes—
29C23×C4×C11D414yes—
30C23×C4×C11Q814yes—
31C23×C4×C11C2312yes—
32C23×C4×C11C2312yes—
33C23×C4×C11C2314yes—
34C23×C4×C11C2314yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C2×C11×C4⋊C4—24no—
38C2×C11×C4⋊C4—44no—
39C2×C11×C4⋊C4—44no—
40C2×C11×C4⋊C4—44no—
41C2×C11×C4⋊C4—44no—
42C2×C11×C4⋊C4—44no—
43C2×C11×C4⋊C4C2×C418yes—
44C2×C11×C22⋊C4—24no—
45C2×C11×C22⋊C4—24no—
46C2×C11×C22⋊C4—44no—
47C2×C11×C22⋊C4—42no—
48C2×C11×C22⋊C4—44no—
49C2×C11×C22⋊C4—42no—
50C2×C11×C22⋊C4C2×C418yes—
51C11×#95—24no—
52C11×#95—24no—
53C11×#95—22no—
54C11×#95—22no—
55C11×#95—44no—
56C11×#95—44no—
57C11×#95—44no—
58C11×#95C2×C418yes—
59#14675C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11—22no—
61C24×C11—22no—
62C24×C11—24no—
63C24×C11—22no—
64C24×C11—22no—
65C24×C11C22×C412yes—
66C24×C11C2×D412yes—
67C24×C11C2×Q812yes—
68C24×C11C2411yescharacteristic
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—24no—
76C22×C4×C11—24no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11—22no—
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—22no—
90C22×C4×C11—24no—
91C22×C4×C11—22no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—48no—
95C22×C4×C11—48no—
96C22×C4×C11—48no—
97C22×C4×C11C4⋊C4116yescomplemented
98C22×C4×C11C22×C418yes—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×Q812yes—
104C22×C4×C11C2×Q812yes—
105C11×C4⋊C4—48no—
106C11×C4⋊C4—48no—
107C11×C4⋊C4—416no—
108C11×C22⋊C4—48no—
109C11×C22⋊C4—48no—
110C11×C22⋊C4—48no—
111C2×#381C2×C1111yescharacteristic
112C2×#380C2×C1111yescharacteristic
113C2×#380C2×C1111yescharacteristic
114#1444C2×C1112yescomplemented
115#1442C2×C1112yescomplemented
116#1441C2×C1114yescomplemented
117#1439C2×C1114yes—
118C23×C11—22no—
119C23×C11—24no—
120C23×C11—22no—
121C23×C11—24no—
122C23×C11—24no—
123C23×C11—22no—
124C23×C11—22no—
125C23×C11—24no—
126C23×C11—24no—
127C23×C11—24no—
128C23×C11—24no—
129C23×C11—44no—
130C23×C11—44no—
131C23×C11—44no—
132C23×C11—44no—
133C23×C11C2×C4⋊C414yes—
134C23×C11C23×C411yescharacteristic
135C23×C11C22×D411yescharacteristic
136C23×C11C22×Q811yescharacteristic
137C23×C11H(5,𝔽2)14yes—
138C23×C11H(5,𝔽2)12yes—
139C23×C11H(5,𝔽2)12yes—
140C23×C112−1+412yes—
141C23×C112−1+412yes—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—24no—
148C2×C4×C11—28no—
149C2×C4×C11—28no—
150C2×C4×C11—28no—
151C2×C4×C11—416no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—44no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—44no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—44no—
164C2×C4×C11—42no—
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×C11—44no—
172C2×C4×C11—44no—
173C2×C4×C11C2×C4⋊C414yes—
174C2×C4×C11C2×C4⋊C414yes—
175C24×C4C22×C1111yescharacteristic
176C22×C4⋊C4C22×C1112yes—
177C22×C4⋊C4C22×C1114yes—
178C22×C4⋊C4C22×C1112yes—
179C22×C22⋊C4C22×C1112yes—
180C22×C22⋊C4C22×C1112yes—
181C22×C22⋊C4C22×C1112yes—
182#381—24no—
183#380—24no—
184#380C4×C1118yescomplemented
185C2×#95C22×C1112yes—
186C2×#95C22×C1112yes—
187C2×#95C22×C1111yescharacteristic
188C2×#95C22×C1111yescharacteristic
189C2×#95C22×C1114yes—
190C2×#95C22×C1114yes—
191C2×#95C22×C1114yes—
192C2×#95C22×C1112yes—
193C22×C11—24no—
194C22×C11—24no—
195C22×C11—24no—
196C22×C11—48no—
197C22×C11—44no—
198C22×C11—44no—
199C22×C11—44no—
200C22×C11—44no—
201C22×C11C22×C4⋊C411yescharacteristic
202C22×C11#51812yes—
203C22×C11#51811yescharacteristic
204C22×C11#51911yescharacteristic
205C22×C11#52012yes—
206C22×C11#53412yes—
207C22×C11#53511yescharacteristic
208C22×C11#53611yescharacteristic
209C22×C11#53712yes—
210C22×C11#54312yes—
211C22×C11#54412yes—
212C22×C11#54412yes—
213C22×C11#56014yes—
214C22×C11#56214yes—
215C22×C11#56214yes—
216C22×C11#56314yes—
217C4×C11—24no—
218C4×C11—24no—
219C4×C11—48no—
220C4×C11—82no—
221C4×C11—84no—
222C4×C11—82no—
223C25C23×C1111yescharacteristic
224C23×C4—44no—
225C23×C4C2×C4×C1114yes—
226C23×C4D4×C1114yes—
227C23×C4Q8×C1114yes—
228C23×C4C23×C1112yes—
229C23×C4C23×C1114yes—
230C23×C4C23×C1112yes—
231C23×C4C23×C1114yes—
232C23×C4C23×C1111yescharacteristic
233C23×C4C23×C1111yescharacteristic
234C2×C4⋊C4—24no—
235C2×C4⋊C4—44no—
236C2×C4⋊C4—44no—
237C2×C4⋊C4—44no—
238C2×C4⋊C4—44no—
239C2×C4⋊C4—44no—
240C2×C4⋊C4C2×C4×C1118yes—
241C2×C22⋊C4—24no—
242C2×C22⋊C4—24no—
243C2×C22⋊C4—44no—
244C2×C22⋊C4—42no—
245C2×C22⋊C4—44no—
246C2×C22⋊C4—42no—
247C2×C22⋊C4C2×C4×C1118yes—
248#95—24no—
249#95—24no—
250#95—22no—
251#95—22no—
252#95—44no—
253#95—44no—
254#95—44no—
255#95C2×C4×C1118yes—
256C2×C11—44no—
257C2×C11#231511yescharacteristic
258C2×C11#231611yescharacteristic
259C2×C11#231711yescharacteristic
260C2×C11#237712yes—
261C2×C11#237812yes—
262C2×C11#281312yes—
263C2×C11#281412yes—
264C2×C11#284114yes—
265C24—22no—
266C24—22no—
267C24—24no—
268C24—22no—
269C24—22no—
270C24C22×C4×C1112yes—
271C24C2×D4×C1112yes—
272C24C2×Q8×C1112yes—
273C24C24×C1111yescharacteristic
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—22no—
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—22no—
295C22×C4—24no—
296C22×C4—22no—
297C22×C4—24no—
298C22×C4—22no—
299C22×C4—48no—
300C22×C4—48no—
301C22×C4—48no—
302C22×C4C11×C4⋊C4116yescomplemented
303C22×C4C22×C4×C1118yes—
304C22×C4C22×C4×C1112yes—
305C22×C4C22×C4×C1112yes—
306C22×C4C2×D4×C1112yes—
307C22×C4C2×D4×C1112yes—
308C22×C4C2×Q8×C1112yes—
309C22×C4C2×Q8×C1112yes—
310C4⋊C4—48no—
311C4⋊C4—48no—
312C4⋊C4—416no—
313C22⋊C4—48no—
314C22⋊C4—48no—
315C22⋊C4—48no—
316C11#1467511yescharacteristic, direct product factor, Sylow
317C23—22no—
318C23—24no—
319C23—22no—
320C23—24no—
321C23—24no—
322C23—22no—
323C23—22no—
324C23—24no—
325C23—24no—
326C23—24no—
327C23—24no—
328C23—44no—
329C23—44no—
330C23—44no—
331C23—44no—
332C23C2×C11×C4⋊C414yes—
333C23C23×C4×C1111yescharacteristic
334C23C22×D4×C1111yescharacteristic
335C23C22×Q8×C1111yescharacteristic
336C23C11×H(5,𝔽2)14yes—
337C23C11×H(5,𝔽2)12yes—
338C23C11×H(5,𝔽2)12yes—
339C23C11×2−1+412yes—
340C23C11×2−1+412yes—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—28no—
348C2×C4—28no—
349C2×C4—28no—
350C2×C4—416no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—44no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4C2×C11×C4⋊C414yes—
373C2×C4C2×C11×C4⋊C414yes—
374C22—24no—
375C22—24no—
376C22—24no—
377C22—44no—
378C22—44no—
379C22—44no—
380C22—48no—
381C22—44no—
382C22C22×C11×C4⋊C411yescharacteristic
383C22C11×#51812yes—
384C22C11×#51811yescharacteristic
385C22C11×#51911yescharacteristic
386C22C11×#52012yes—
387C22C11×#53412yes—
388C22C11×#53511yescharacteristic
389C22C11×#53611yescharacteristic
390C22C11×#53712yes—
391C22C11×#54312yes—
392C22C11×#54412yes—
393C22C11×#54412yes—
394C22C11×#56014yes—
395C22C11×#56214yes—
396C22C11×#56214yes—
397C22C11×#56314yes—
398C4—24no—
399C4—24no—
400C4—48no—
401C4—82no—
402C4—84no—
403C4—82no—
404C2—44no—
405C2C11×#231511yescharacteristic
406C2C11×#231611yescharacteristic
407C2C11×#231711yescharacteristic
408C2C11×#237712yes—
409C2C11×#237812yes—
410C2C11×#281312yes—
411C2C11×#281412yes—
412C2C11×#284114yes—
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×#1444C2semidirect
5. C11×#1442C2semidirect
6. C11×#1441C2semidirect
17. C11×#380C4semidirect
59. #14675C11direct (N × H)
97. C22×C4×C11C4⋊C4semidirect
114. #1444C2×C11semidirect
115. #1442C2×C11semidirect
116. #1441C2×C11semidirect
184. #380C4×C11semidirect
302. C22×C4C11×C4⋊C4semidirect
316. C11#14675direct (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
C11×#14442
C11×#14422
C11×#14412
C11×#14392
#1467511