Finite Group Databasebeta

← C11×#7915 #14585108

Subgroups — C11×#7915 #14585108

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#407C211yesmaximal, characteristic
2C22×C11×C22⋊C8C211yesmaximal, characteristic
3C2×C11×#380C211yesmaximal, characteristic
4C11×#1280C214yesmaximal, complemented
5C24×C4×C11C2211yescharacteristic
6C22×C11×M16—21no—
7C23×C8×C11—21no—
8C22×C11×C4⋊C4C412yes—
9C22×C11×C22⋊C4C412yes—
10C11×#407—22no—
11C11×#407C414yescomplemented
12C2×C11×C22⋊C8—21no—
13C2×C11×C22⋊C8—22no—
14C2×C11×C22⋊C8—21no—
15C2×C11×C22⋊C8C414yescomplemented
16C2×C11×C22⋊C8C2212yes—
17C2×C11×C22⋊C8C2212yes—
18C11×#380—21no—
19C11×#380—21no—
20C11×#380—21no—
21C11×#380—21no—
22C2×C11×#95C2212yes—
23C25×C11C2×C411yescharacteristic
24C23×C4×C11—44no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11C2×C414yes—
27C23×C4×C11C2×C412yes—
28C23×C4×C11C2×C412yes—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11D412yes—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11Q812yes—
35C23×C4×C11C2311yescharacteristic
36C2×C11×M16—24no—
37C2×C11×M16—44no—
38C22×C8×C11—24no—
39C22×C8×C11—22no—
40C22×C8×C11—22no—
41C22×C8×C11—44no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—44no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—44no—
48C11×C22⋊C8—24no—
49C11×C22⋊C8—24no—
50C11×C22⋊C8—22no—
51C11×C22⋊C8—22no—
52C11×C22⋊C8C2×C414yes—
53C11×C22⋊C8C2×C414yes—
54C11×#95—22no—
55C11×#95—22no—
56#7915C1111yesmaximal, characteristic, direct product factor, Sylow
57C24×C11—22no—
58C24×C11—22no—
59C24×C11—24no—
60C24×C11—42no—
61C24×C11C4212yes—
62C24×C11C22⋊C411yescharacteristic
63C24×C11C22⋊C411yescharacteristic
64C24×C11C4⋊C412yes—
65C24×C11C22×C411yescharacteristic
66C22×C4×C11—24no—
67C22×C4×C11—24no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—28no—
71C22×C4×C11—44no—
72C22×C4×C11—44no—
73C22×C4×C11—44no—
74C22×C4×C11—44no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—44no—
79C22×C4×C11—44no—
80C22×C4×C11C4212yes—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C412yes—
83C22×C4×C11C22⋊C412yes—
84C22×C4×C11C22⋊C412yes—
85C22×C4×C11C22⋊C412yes—
86C22×C4×C11C22⋊C411yescharacteristic
87C22×C4×C11C4⋊C412yes—
88C22×C4×C11C4⋊C412yes—
89C22×C4×C11C4⋊C412yes—
90C22×C4×C11C4⋊C412yes—
91C22×C4×C11C4⋊C412yes—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×Q811yescharacteristic
98C11×M16—48no—
99C2×C8×C11—24no—
100C2×C8×C11—24no—
101C2×C8×C11—44no—
102C2×C8×C11—48no—
103C2×C8×C11—44no—
104C11×C4⋊C4—44no—
105C11×C4⋊C4—44no—
106C11×C22⋊C4—44no—
107C11×C22⋊C4—44no—
108C2×#407C2×C1111yescharacteristic
109C22×C22⋊C8C2×C1111yescharacteristic
110C2×#380C2×C1111yescharacteristic
111#1280C2×C1114yescomplemented
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—22no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—24no—
118C23×C11—24no—
119C23×C11—24no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—24no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11—48no—
128C23×C11—48no—
129C23×C11#9512yes—
130C23×C11#9512yes—
131C23×C11#10012yes—
132C23×C11#10112yes—
133C23×C11C2×C4211yescharacteristic
134C23×C11C2×C22⋊C411yescharacteristic
135C23×C11C2×C4⋊C411yescharacteristic
136C23×C11#13114yes—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—44no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—88no—
158C2×C4×C11#9512yes—
159C2×C4×C11#9512yes—
160C2×C4×C11#9914yes—
161C2×C4×C11C2×C22⋊C411yescharacteristic
162C2×C4×C11C2×C22⋊C411yescharacteristic
163C2×C4×C11C2×C4⋊C411yescharacteristic
164C2×C4×C11C2×C4⋊C411yescharacteristic
165C8×C11—44no—
166C8×C11—44no—
167C24×C4C22×C1111yescharacteristic
168C22×M16—21no—
169C23×C8—21no—
170C22×C4⋊C4C4×C1112yes—
171C22×C22⋊C4C4×C1112yes—
172#407—22no—
173#407C4×C1114yescomplemented
174C2×C22⋊C8—21no—
175C2×C22⋊C8—22no—
176C2×C22⋊C8—21no—
177C2×C22⋊C8C4×C1114yescomplemented
178C2×C22⋊C8C22×C1112yes—
179C2×C22⋊C8C22×C1112yes—
180#380—21no—
181#380—21no—
182#380—21no—
183#380—21no—
184C2×#95C22×C1112yes—
185C22×C11—24no—
186C22×C11—24no—
187C22×C11—24no—
188C22×C11—24no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—22no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—48no—
199C22×C11—48no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11#34314yes—
203C22×C11C2×#9511yescharacteristic
204C22×C11#40512yes—
205C22×C11#40812yes—
206C22×C11C2×#9912yes—
207C22×C11C2×#10011yescharacteristic
208C22×C11C2×#10111yescharacteristic
209C22×C11#42412yes—
210C4×C11—22no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—84no—
216C4×C11#34214yes—
217C25C2×C4×C1111yescharacteristic
218C23×C4—44no—
219C23×C4C2×C4×C1111yescharacteristic
220C23×C4C2×C4×C1114yes—
221C23×C4C2×C4×C1112yes—
222C23×C4C2×C4×C1112yes—
223C23×C4D4×C1111yescharacteristic
224C23×C4D4×C1111yescharacteristic
225C23×C4D4×C1112yes—
226C23×C4D4×C1111yescharacteristic
227C23×C4D4×C1111yescharacteristic
228C23×C4Q8×C1112yes—
229C23×C4C23×C1111yescharacteristic
230C2×M16—24no—
231C2×M16—44no—
232C22×C8—24no—
233C22×C8—22no—
234C22×C8—22no—
235C22×C8—44no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—44no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—44no—
242C22⋊C8—24no—
243C22⋊C8—24no—
244C22⋊C8—22no—
245C22⋊C8—22no—
246C22⋊C8C2×C4×C1114yes—
247C22⋊C8C2×C4×C1114yes—
248#95—22no—
249#95—22no—
250C2×C11—24no—
251C2×C11—22no—
252C2×C11—22no—
253C2×C11—42no—
254C2×C11#147112yes—
255C2×C11#147212yes—
256C2×C11#172911yescharacteristic
257C2×C11C2×#34211yescharacteristic
258C2×C11C2×#34311yescharacteristic
259C24—22no—
260C24—22no—
261C24—24no—
262C24—42no—
263C24C42×C1112yes—
264C24C11×C22⋊C411yescharacteristic
265C24C11×C22⋊C411yescharacteristic
266C24C11×C4⋊C412yes—
267C24C22×C4×C1111yescharacteristic
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—28no—
273C22×C4—44no—
274C22×C4—44no—
275C22×C4—44no—
276C22×C4—44no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—44no—
281C22×C4—44no—
282C22×C4C42×C1112yes—
283C22×C4C11×C22⋊C411yescharacteristic
284C22×C4C11×C22⋊C412yes—
285C22×C4C11×C22⋊C412yes—
286C22×C4C11×C22⋊C412yes—
287C22×C4C11×C22⋊C412yes—
288C22×C4C11×C22⋊C411yescharacteristic
289C22×C4C11×C4⋊C412yes—
290C22×C4C11×C4⋊C412yes—
291C22×C4C11×C4⋊C412yes—
292C22×C4C11×C4⋊C412yes—
293C22×C4C11×C4⋊C412yes—
294C22×C4C22×C4×C1111yescharacteristic
295C22×C4C22×C4×C1111yescharacteristic
296C22×C4C2×D4×C1111yescharacteristic
297C22×C4C2×D4×C1111yescharacteristic
298C22×C4C2×D4×C1111yescharacteristic
299C22×C4C2×Q8×C1111yescharacteristic
300M16—48no—
301C2×C8—24no—
302C2×C8—24no—
303C2×C8—44no—
304C2×C8—48no—
305C2×C8—44no—
306C4⋊C4—44no—
307C4⋊C4—44no—
308C22⋊C4—44no—
309C22⋊C4—44no—
310C11#791511yescharacteristic, direct product factor, Sylow
311C23—22no—
312C23—22no—
313C23—22no—
314C23—21no—
315C23—21no—
316C23—24no—
317C23—24no—
318C23—24no—
319C23—22no—
320C23—22no—
321C23—21no—
322C23—21no—
323C23—24no—
324C23—42no—
325C23—42no—
326C23—48no—
327C23—48no—
328C23C11×#9512yes—
329C23C11×#9512yes—
330C23C11×#10012yes—
331C23C11×#10112yes—
332C23C2×C42×C1111yescharacteristic
333C23C2×C11×C22⋊C411yescharacteristic
334C23C2×C11×C4⋊C411yescharacteristic
335C23C11×#13114yes—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—88no—
357C2×C4C11×#9512yes—
358C2×C4C11×#9512yes—
359C2×C4C11×#9914yes—
360C2×C4C2×C11×C22⋊C411yescharacteristic
361C2×C4C2×C11×C22⋊C411yescharacteristic
362C2×C4C2×C11×C4⋊C411yescharacteristic
363C2×C4C2×C11×C4⋊C411yescharacteristic
364C8—44no—
365C8—44no—
366C22—24no—
367C22—24no—
368C22—24no—
369C22—24no—
370C22—22no—
371C22—22no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—48no—
380C22—48no—
381C22—42no—
382C22—42no—
383C22C11×#34314yes—
384C22C2×C11×#9511yescharacteristic
385C22C11×#40512yes—
386C22C11×#40812yes—
387C22C2×C11×#9912yes—
388C22C2×C11×#10011yescharacteristic
389C22C2×C11×#10111yescharacteristic
390C22C11×#42412yes—
391C4—21no—
392C4—21no—
393C4—22no—
394C4—21no—
395C4—21no—
396C4—84no—
397C4C11×#34214yes—
398C2—24no—
399C2—22no—
400C2—22no—
401C2—42no—
402C2C11×#147112yes—
403C2C11×#147212yes—
404C2C11×#172911yescharacteristic
405C2C2×C11×#34211yescharacteristic
406C2C2×C11×#34311yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC23C2×C42×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC25×C11C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1280C2semidirect
11. C11×#407C4semidirect
15. C2×C11×C22⋊C8C4semidirect
56. #7915C11direct (N × H)
111. #1280C2×C11semidirect
173. #407C4×C11semidirect
177. C2×C22⋊C8C4×C11semidirect
310. C11#7915direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4072
C22×C11×C22⋊C82
C2×C11×#3802
C11×#12802
#791511