Finite Group Databasebeta

← C11×#10937 #14588130

Subgroups — C11×#10937 #14588130

Order 2816.

1066 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×#407C212yesmaximal
2C11×#2873C211yesmaximal, characteristic, complemented
3C11×#2280C211yesmaximal, characteristic
4C2×C11×#344C212yesmaximal, complemented
5C11×#1742C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C22×C11×M16C2212yes—
8C22×C11×M16C2212yes—
9C2×C11×#117C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C11×#407—24no—
12C11×#407C418yescomplemented
13C2×C11×C22⋊C8—24no—
14C11×#405—24no—
15C4×C11×M16—22no—
16C11×#381C412yes—
17C11×#380—22no—
18C11×#379C412yes—
19C4×C11×C22⋊C4—22no—
20C11×#344—24no—
21C11×#343—22no—
22C25×C11C2×C411yescharacteristic
23C23×C4×C11—21no—
24C23×C4×C11—21no—
25C23×C4×C11—22no—
26C23×C4×C11—22no—
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11—22no—
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C414yes—
32C23×C4×C11C2311yescharacteristic
33C2×C11×M16—22no—
34C2×C11×M16—22no—
35C2×C11×M16—22no—
36C2×C11×M16—22no—
37C2×C11×M16—22no—
38C2×C11×M16—22no—
39C2×C11×M16—22no—
40C2×C11×M16—22no—
41C2×C11×M16—22no—
42C2×C11×M16C2×C414yes—
43C2×C11×M16C2×C414yes—
44C2×C11×M16D414yes—
45C22×C8×C11—22no—
46C22×C8×C11D414yes—
47C11×#117—22no—
48C11×#117—22no—
49C11×#117—22no—
50C11×#117—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4C2×C412yes—
55C2×C11×C22⋊C4C2×C412yes—
56C2×C42×C11—21no—
57C2×C42×C11D412yes—
58C11×C22⋊C8—216no—
59C11×#97—24no—
60C4×C8×C11—24no—
61C11×#95—24no—
62#10937C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11—21no—
64C24×C11—22no—
65C24×C11—21no—
66C24×C11—22no—
67C24×C11—44no—
68C24×C11C4212yes—
69C24×C11C22×C411yescharacteristic
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
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—22no—
81C22×C4×C11—41no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11—42no—
85C22×C4×C11—41no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—41no—
89C22×C4×C11—42no—
90C22×C4×C11—41no—
91C22×C4×C11C4212yes—
92C22×C4×C11C22⋊C414yes—
93C22×C4×C11C22×C412yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4112yes—
99C22×C4×C11#4112yes—
100C22×C4×C11#4112yes—
101C11×M16—24no—
102C11×M16—24no—
103C11×M16—24no—
104C11×M16—24no—
105C11×M16—24no—
106C11×M16—24no—
107C11×M16—42no—
108C11×M16—42no—
109C2×C8×C11—24no—
110C2×C8×C11—24no—
111C2×C8×C11—24no—
112C2×C8×C11—42no—
113C2×C8×C11—42no—
114C2×C8×C11C22⋊C418yescomplemented
115C11×C4⋊C4—24no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—48no—
121C42×C11—22no—
122C42×C11—22no—
123C42×C11—42no—
124C2×#407C2×C1112yes—
125#2873C2×C1111yescharacteristic, complemented
126#2280C2×C1111yescharacteristic
127C2×#344C2×C1112yescomplemented
128#1742C2×C1111yescharacteristic, complemented
129C23×C11—24no—
130C23×C11—28no—
131C23×C11—24no—
132C23×C11—22no—
133C23×C11—44no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—44no—
137C23×C11—44no—
138C23×C11—48no—
139C23×C11—41no—
140C23×C11—42no—
141C23×C11—41no—
142C23×C11C2×C4211yescharacteristic
143C23×C11C2×C22⋊C411yescharacteristic
144C23×C11#11711yescharacteristic
145C23×C11C4×D412yes—
146C23×C11C4×D412yes—
147C2×C4×C11—24no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C2×C4×C11—44no—
159C2×C4×C11—42no—
160C2×C4×C11C2×C22⋊C412yes—
161C2×C4×C11#11712yes—
162C2×C4×C11C4×D412yes—
163C2×C4×C11C4×D412yes—
164C2×C4×C11C4×D412yes—
165C2×C4×C11C4×D412yes—
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12112yes—
168C2×C4×C11#12112yes—
169C2×C4×C11#12112yes—
170C2×C4×C11#12312yes—
171C2×C4×C11#12311yescharacteristic
172C2×C4×C11#12411yescharacteristic
173C2×C4×C11#12412yes—
174C2×C4×C11#12612yes—
175C2×C4×C11#12711yescharacteristic
176C8×C11—28no—
177C8×C11—44no—
178C24×C4C22×C1111yescharacteristic
179C22×M16C22×C1112yes—
180C22×M16C22×C1112yes—
181C2×#117C22×C1111yescharacteristic
182C2×#117C22×C1111yescharacteristic
183#407—24no—
184#407C4×C1118yescomplemented
185C2×C22⋊C8—24no—
186#405—24no—
187C4×M16—22no—
188#381C4×C1112yes—
189#380—22no—
190#379C4×C1112yes—
191C4×C22⋊C4—22no—
192#344—24no—
193#343—22no—
194C22×C11—22no—
195C22×C11—24no—
196C22×C11—24no—
197C22×C11—28no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—42no—
201C22×C11—44no—
202C22×C11—42no—
203C22×C11—44no—
204C22×C11—48no—
205C22×C11—44no—
206C22×C11—42no—
207C22×C11C4×C22⋊C412yes—
208C22×C11C4×C22⋊C411yescharacteristic
209C22×C11#38611yescharacteristic
210C22×C11#38812yes—
211C22×C11#39011yescharacteristic
212C4×C11—44no—
213C4×C11—42no—
214C4×C11—82no—
215C4×C11#38612yes—
216C4×C11#38812yes—
217C4×C11#38812yes—
218C4×C11#39012yes—
219C25C2×C4×C1111yescharacteristic
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4C2×C4×C1111yescharacteristic
228C23×C4C2×C4×C1114yes—
229C23×C4C23×C1111yescharacteristic
230C2×M16—22no—
231C2×M16—22no—
232C2×M16—22no—
233C2×M16—22no—
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—22no—
238C2×M16—22no—
239C2×M16C2×C4×C1114yes—
240C2×M16C2×C4×C1114yes—
241C2×M16D4×C1114yes—
242C22×C8—22no—
243C22×C8D4×C1114yes—
244#117—22no—
245#117—22no—
246#117—22no—
247#117—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4D4×C1112yes—
250C2×C22⋊C4—24no—
251C2×C22⋊C4C2×C4×C1112yes—
252C2×C22⋊C4C2×C4×C1112yes—
253C2×C42—21no—
254C2×C42D4×C1112yes—
255C22⋊C8—216no—
256#97—24no—
257C4×C8—24no—
258#95—24no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—22no—
262C2×C11—22no—
263C2×C11—44no—
264C2×C11#143711yescharacteristic
265C2×C11#189112yes—
266C24—21no—
267C24—22no—
268C24—21no—
269C24—22no—
270C24—44no—
271C24C42×C1112yes—
272C24C22×C4×C1111yescharacteristic
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—41no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4C42×C1112yes—
295C22×C4C11×C22⋊C414yes—
296C22×C4C22×C4×C1112yes—
297C22×C4C2×D4×C1112yes—
298C22×C4C2×D4×C1112yes—
299C22×C4C2×D4×C1111yescharacteristic
300C22×C4C2×D4×C1111yescharacteristic
301C22×C4C11×#4112yes—
302C22×C4C11×#4112yes—
303C22×C4C11×#4112yes—
304M16—24no—
305M16—24no—
306M16—24no—
307M16—24no—
308M16—24no—
309M16—24no—
310M16—42no—
311M16—42no—
312C2×C8—24no—
313C2×C8—24no—
314C2×C8—24no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8C11×C22⋊C418yescomplemented
318C4⋊C4—24no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C22⋊C4—24no—
322C22⋊C4—24no—
323C22⋊C4—48no—
324C42—22no—
325C42—22no—
326C42—42no—
327C11#1093711yescharacteristic, direct product factor, Sylow
328C23—24no—
329C23—28no—
330C23—24no—
331C23—22no—
332C23—44no—
333C23—42no—
334C23—42no—
335C23—44no—
336C23—44no—
337C23—48no—
338C23—41no—
339C23—42no—
340C23—41no—
341C23C2×C42×C1111yescharacteristic
342C23C2×C11×C22⋊C411yescharacteristic
343C23C11×#11711yescharacteristic
344C23C4×D4×C1112yes—
345C23C4×D4×C1112yes—
346C2×C4—24no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—42no—
359C2×C4C2×C11×C22⋊C412yes—
360C2×C4C11×#11712yes—
361C2×C4C4×D4×C1112yes—
362C2×C4C4×D4×C1112yes—
363C2×C4C4×D4×C1112yes—
364C2×C4C4×D4×C1112yes—
365C2×C4C11×#12011yescharacteristic
366C2×C4C11×#12112yes—
367C2×C4C11×#12112yes—
368C2×C4C11×#12112yes—
369C2×C4C11×#12312yes—
370C2×C4C11×#12311yescharacteristic
371C2×C4C11×#12411yescharacteristic
372C2×C4C11×#12412yes—
373C2×C4C11×#12612yes—
374C2×C4C11×#12711yescharacteristic
375C8—28no—
376C8—44no—
377C22—22no—
378C22—24no—
379C22—24no—
380C22—28no—
381C22—41no—
382C22—41no—
383C22—42no—
384C22—44no—
385C22—42no—
386C22—44no—
387C22—48no—
388C22—44no—
389C22—42no—
390C22C4×C11×C22⋊C412yes—
391C22C4×C11×C22⋊C411yescharacteristic
392C22C11×#38611yescharacteristic
393C22C11×#38812yes—
394C22C11×#39011yescharacteristic
395C4—44no—
396C4—42no—
397C4—82no—
398C4C11×#38612yes—
399C4C11×#38812yes—
400C4C11×#38812yes—
401C4C11×#39012yes—
402C2—21no—
403C2—21no—
404C2—22no—
405C2—22no—
406C2—44no—
407C2C11×#143711yescharacteristic
408C2C11×#189112yes—
subgroupG/H
centerC2×C4×C11#120
commutatorC23C2×C42×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#386
prime radicalC25×C11C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2873C2semidirect
4. C2×C11×#344C2semidirect
5. C11×#1742C2semidirect
12. C11×#407C4semidirect
62. #10937C11direct (N × H)
114. C2×C8×C11C22⋊C4semidirect
125. #2873C2×C11semidirect
127. C2×#344C2×C11semidirect
128. #1742C2×C11semidirect
184. #407C4×C11semidirect
317. C2×C8C11×C22⋊C4semidirect
327. C11#10937direct (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
C11×#28732
C11×#22802
C2×C11×#3442
C11×#17422
#1093711