Finite Group Databasebeta

← C11×#23657 #14600850

Subgroups — C11×#23657 #14600850

Order 2816.

946 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×#428C212yesmaximal
2C2×C11×#389C211yesmaximal, characteristic
3C11×#2285C211yesmaximal, characteristic
4C11×#2085C214yesmaximal, complemented
5C11×#2084C212yesmaximal, complemented
6C11×#2083C212yesmaximal, complemented
7C11×#1736C212yesmaximal
8C11×#1728C211yesmaximal, characteristic
9C22×C11×M16C2212yes—
10C2×C11×#117C2212yes—
11C22×C11×C4⋊C4—21no—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C11×#428—28no—
16C2×C11×#107C2214yes—
17C2×C11×#106C2214yes—
18C11×#389—21no—
19C11×#389—21no—
20C11×#389C2212yes—
21C11×#389C2212yes—
22C11×#384C2211yescharacteristic
23C11×#384C2211yescharacteristic
24C11×#382C2212yes—
25C11×#380—21no—
26C11×#380—21no—
27C4×C11×C4⋊C4—21no—
28C4×C11×C4⋊C4—21no—
29C2×C11×#95—21no—
30C11×#340C2214yes—
31C11×#340C2214yes—
32C11×#336C2212yes—
33C11×#336C2212yes—
34C23×C4×C11—21no—
35C23×C4×C11—21no—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C2×C11×M16—24no—
40C2×C11×M16—24no—
41C2×C11×M16Q818yes—
42C22×C8×C11C2314yes—
43C11×#117—24no—
44C11×#117—24no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—44no—
56C2×C11×C4⋊C4D414yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—24no—
63C2×C42×C11—22no—
64C2×C42×C11D411yescharacteristic
65C2×C42×C11D411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C11×#107—28no—
69C11×#106—28no—
70C11×#95—22no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95—22no—
74#23657C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11C2×D411yescharacteristic
76C22×C4×C11—24no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×Q814yes—
99C22×C4×C11#4112yes—
100C22×C4×C11#4114yes—
101C22×C4×C11C2411yescharacteristic
102C11×M16—216no—
103C2×C8×C11—24no—
104C2×C8×C11—24no—
105C2×C8×C11C2×Q818yes—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—42no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4—44no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—44no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4C2×D414yes—
121C11×C22⋊C4—44no—
122C42×C11—22no—
123C42×C11—22no—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11—44no—
127C2×#428C2×C1112yes—
128C2×#389C2×C1111yescharacteristic
129#2285C2×C1111yescharacteristic
130#2085C2×C1114yescomplemented
131#2084C2×C1112yescomplemented
132#2083C2×C1112yescomplemented
133#1736C2×C1112yes—
134#1728C2×C1111yescharacteristic
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11#12112yes—
140C23×C11#12312yes—
141C23×C11C4⋊Q812yes—
142C23×C11C22×D411yescharacteristic
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—24no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—44no—
155C2×C4×C11—44no—
156C2×C4×C11—48no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—84no—
169C2×C4×C11#12112yes—
170C2×C4×C11C22⋊Q818yes—
171C2×C4×C11#12312yes—
172C2×C4×C11#12518yes—
173C2×C4×C11C4⋊Q812yes—
174C2×C4×C11AGL(1,ℤ/8)12yes—
175C2×C4×C11#13712yes—
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×Q812yes—
178C2×C4×C11C2×#4112yes—
179C2×C4×C11C2×#4111yescharacteristic
180C8×C11—28no—
181C22×M16C22×C1112yes—
182C2×#117C22×C1112yes—
183C22×C4⋊C4—21no—
184C22×C4⋊C4C22×C1111yescharacteristic
185C22×C4⋊C4C22×C1111yescharacteristic
186C22×C42C22×C1111yescharacteristic
187#428—28no—
188C2×#107C22×C1114yes—
189C2×#106C22×C1114yes—
190#389—21no—
191#389—21no—
192#389C22×C1112yes—
193#389C22×C1112yes—
194#384C22×C1111yescharacteristic
195#384C22×C1111yescharacteristic
196#382C22×C1112yes—
197#380—21no—
198#380—21no—
199C4×C4⋊C4—21no—
200C4×C4⋊C4—21no—
201C2×#95—21no—
202#340C22×C1114yes—
203#340C22×C1114yes—
204#336C22×C1112yes—
205#336C22×C1112yes—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11#39814yes—
213C22×C11C2×#12111yescharacteristic
214C22×C11C2×#12311yescharacteristic
215C22×C11C2×C4⋊Q811yescharacteristic
216C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
217C22×C11C2×#13711yescharacteristic
218C22×C11#57511yescharacteristic
219C22×C11#57511yescharacteristic
220C4×C11—22no—
221C4×C11—22no—
222C4×C11—41no—
223C4×C11—41no—
224C4×C11—44no—
225C4×C11—82no—
226C4×C11—82no—
227C4×C11—82no—
228C4×C11#39814yes—
229C4×C11C2×C22⋊Q812yes—
230C4×C11C2×#12512yes—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4D4×C1111yescharacteristic
234C23×C4D4×C1111yescharacteristic
235C23×C4C23×C1111yescharacteristic
236C2×M16—24no—
237C2×M16—24no—
238C2×M16Q8×C1118yes—
239C22×C8C23×C1114yes—
240#117—24no—
241#117—24no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—44no—
253C2×C4⋊C4D4×C1114yes—
254C2×C4⋊C4C23×C1112yes—
255C2×C4⋊C4C23×C1112yes—
256C2×C4⋊C4C23×C1112yes—
257C2×C4⋊C4C23×C1112yes—
258C2×C22⋊C4—22no—
259C2×C42—24no—
260C2×C42—22no—
261C2×C42D4×C1111yescharacteristic
262C2×C42D4×C1111yescharacteristic
263C2×C42C23×C1111yescharacteristic
264C2×C42C23×C1111yescharacteristic
265#107—28no—
266#106—28no—
267#95—22no—
268#95—22no—
269#95—22no—
270#95—22no—
271C2×C11—24no—
272C2×C11C2×#39811yescharacteristic
273C2×C11#303611yescharacteristic
274C2×C11#303711yescharacteristic
275C2×C11#309411yescharacteristic
276C2×C11#309511yescharacteristic
277C2×C11#316511yescharacteristic
278C2×C11#316611yescharacteristic
279C24C2×D4×C1111yescharacteristic
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4C2×D4×C1111yescharacteristic
297C22×C4C2×D4×C1111yescharacteristic
298C22×C4C2×D4×C1111yescharacteristic
299C22×C4C2×D4×C1111yescharacteristic
300C22×C4C2×D4×C1111yescharacteristic
301C22×C4C2×D4×C1112yes—
302C22×C4C2×Q8×C1114yes—
303C22×C4C11×#4112yes—
304C22×C4C11×#4114yes—
305C22×C4C24×C1111yescharacteristic
306M16—216no—
307C2×C8—24no—
308C2×C8—24no—
309C2×C8C2×Q8×C1118yes—
310C4⋊C4—24no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—44no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—44no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4C2×D4×C1114yes—
325C22⋊C4—44no—
326C42—22no—
327C42—22no—
328C42—22no—
329C42—22no—
330C42—44no—
331C11#2365711yescharacteristic, direct product factor, Sylow
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23C11×#12112yes—
337C23C11×#12312yes—
338C23C11×C4⋊Q812yes—
339C23C22×D4×C1111yescharacteristic
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—24no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—48no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—84no—
366C2×C4C11×#12112yes—
367C2×C4C11×C22⋊Q818yes—
368C2×C4C11×#12312yes—
369C2×C4C11×#12518yes—
370C2×C4C11×C4⋊Q812yes—
371C2×C4C11×AGL(1,ℤ/8)12yes—
372C2×C4C11×#13712yes—
373C2×C4C22×D4×C1111yescharacteristic
374C2×C4C22×Q8×C1112yes—
375C2×C4C2×C11×#4112yes—
376C2×C4C2×C11×#4111yescharacteristic
377C8—28no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22C11×#39814yes—
385C22C2×C11×#12111yescharacteristic
386C22C2×C11×#12311yescharacteristic
387C22C2×C11×C4⋊Q811yescharacteristic
388C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
389C22C2×C11×#13711yescharacteristic
390C22C11×#57511yescharacteristic
391C22C11×#57511yescharacteristic
392C4—22no—
393C4—22no—
394C4—44no—
395C4—41no—
396C4—41no—
397C4—82no—
398C4—82no—
399C4—82no—
400C4C11×#39814yes—
401C4C2×C11×C22⋊Q812yes—
402C4C2×C11×#12512yes—
403C2—24no—
404C2C2×C11×#39811yescharacteristic
405C2C11×#303611yescharacteristic
406C2C11×#303711yescharacteristic
407C2C11×#309411yescharacteristic
408C2C11×#309511yescharacteristic
409C2C11×#316511yescharacteristic
410C2C11×#316611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2085C2semidirect
5. C11×#2084C2semidirect
6. C11×#2083C2semidirect
74. #23657C11direct (N × H)
130. #2085C2×C11semidirect
131. #2084C2×C11semidirect
132. #2083C2×C11semidirect
331. C11#23657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C2×C11×#3892
C11×#22852
C11×#20852
C11×#20842
C11×#20832
C11×#17362
C11×#17282
#2365711