Finite Group Databasebeta

← C11×#13377 #14590570

Subgroups — C11×#13377 #14590570

Order 2816.

648 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2804C211yesmaximal, characteristic, complemented
2C11×#1792C211yesmaximal, characteristic
3C11×#1790C212yesmaximal
4C11×#1393C211yesmaximal, characteristic, complemented
5C11×#1390C212yesmaximal, complemented
6C2×C11×H(5,𝔽2)C2211yescharacteristic
7C2×C11×#104—21no—
8C11×#417—21no—
9C2×C11×#100C2211yescharacteristic
10C2×C11×#99—22no—
11C2×C11×#99C2212yes—
12C11×#400—21no—
13C11×#393—22no—
14C11×#391—21no—
15C11×#390C2211yescharacteristic
16C11×#386—22no—
17C11×#386C2212yes—
18C11×#385—22no—
19C11×H(5,𝔽2)—22no—
20C11×H(5,𝔽2)—21no—
21C11×H(5,𝔽2)—42no—
22C11×H(5,𝔽2)Q812yescomplemented
23C2×C11×#41—21no—
24C2×C11×#41—41no—
25C22×Q8×C11—21no—
26C22×D4×C11—22no—
27C22×D4×C11—41no—
28C22×D4×C11C2311yescharacteristic
29C23×C4×C11D412yes—
30C2×C11×M16—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—42no—
38C2×C11×C22⋊C4D412yes—
39C2×C42×C11D411yescharacteristic
40C11×#104—42no—
41C11×#103—41no—
42C11×#102—41no—
43C11×#100—22no—
44C11×#99—22no—
45C11×#99—22no—
46C11×#99—44no—
47C11×#95—22no—
48C11×#95—22no—
49C11×#95—21no—
50C11×#95—22no—
51C11×#95—42no—
52#13377C1111yesmaximal, characteristic, direct product factor, Sylow
53C24×C11—22no—
54C24×C11C2×D412yes—
55C11×#41—22no—
56C11×#41—22no—
57C11×#41—42no—
58C11×#41—41no—
59C11×#41—44no—
60C11×#41—42no—
61C11×#41—41no—
62C2×Q8×C11—21no—
63C2×Q8×C11—42no—
64C2×Q8×C11—81no—
65C2×Q8×C11—81no—
66C2×D4×C11—21no—
67C2×D4×C11—24no—
68C2×D4×C11—24no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—42no—
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C2×D4×C11—42no—
75C2×D4×C11—44no—
76C2×D4×C11—41no—
77C2×D4×C11—42no—
78C2×D4×C11C2×Q811yescharacteristic
79C2×D4×C11#4111yescharacteristic
80C2×D4×C11#4112yes—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—41no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—82no—
90C22×C4×C11C2×D411yescharacteristic
91C11×M16—41no—
92C11×M16—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—81no—
96C11×C4⋊C4—81no—
97C11×C22⋊C4—44no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—82no—
102C11×C22⋊C4—84no—
103C42×C11—41no—
104#2804C2×C1111yescharacteristic, complemented
105#1792C2×C1111yescharacteristic
106#1790C2×C1112yes—
107#1393C2×C1111yescharacteristic, complemented
108#1390C2×C1112yescomplemented
109C23×C11—22no—
110C23×C11—22no—
111C23×C11—24no—
112C23×C11—42no—
113C23×C11—42no—
114C23×C11—42no—
115C23×C11—41no—
116C23×C11—82no—
117C23×C11—82no—
118C23×C11#12011yescharacteristic
119C23×C11C22⋊Q812yes—
120C23×C11#12412yes—
121Q8×C11—22no—
122Q8×C11—41no—
123Q8×C11—84no—
124D4×C11—22no—
125D4×C11—41no—
126D4×C11—41no—
127D4×C11—42no—
128D4×C11—41no—
129D4×C11—44no—
130D4×C11—44no—
131D4×C11—42no—
132D4×C11—42no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—24no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—44no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C2×C4×C11—82no—
155C2×C4×C11—82no—
156C2×C4×C11C22⋊Q811yescharacteristic
157C2×C4×C11#12411yescharacteristic
158C8×C11—81no—
159C2×H(5,𝔽2)C22×C1111yescharacteristic
160C2×#104—21no—
161#417—21no—
162C2×#100C22×C1111yescharacteristic
163C2×#99—22no—
164C2×#99C22×C1112yes—
165#400—21no—
166#393—22no—
167#391—21no—
168#390C22×C1111yescharacteristic
169#386—22no—
170#386C22×C1112yes—
171#385—22no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—42no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—82no—
182C22×C11—84no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—162no—
186C22×C11#39311yescharacteristic
187C22×C11B(4,𝔽2)11yescharacteristic
188C22×C11B(4,𝔽2)11yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—42no—
192C4×C11—42no—
193C4×C11—82no—
194C4×C11—81no—
195C4×C11—82no—
196C4×C11—162no—
197H(5,𝔽2)—22no—
198H(5,𝔽2)—21no—
199H(5,𝔽2)—42no—
200H(5,𝔽2)Q8×C1112yescomplemented
201C2×#41—21no—
202C2×#41—41no—
203C22×Q8—21no—
204C22×D4—22no—
205C22×D4—41no—
206C22×D4C23×C1111yescharacteristic
207C23×C4D4×C1112yes—
208C2×M16—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4D4×C1111yescharacteristic
212C2×C22⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—42no—
216C2×C22⋊C4D4×C1112yes—
217C2×C42D4×C1111yescharacteristic
218#104—42no—
219#103—41no—
220#102—41no—
221#100—22no—
222#99—22no—
223#99—22no—
224#99—44no—
225#95—22no—
226#95—22no—
227#95—21no—
228#95—22no—
229#95—42no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—42no—
233C2×C11—42no—
234C2×C11—82no—
235C2×C11#202911yescharacteristic
236C2×C11#219811yescharacteristic
237C2×C11#219911yescharacteristic
238C24—22no—
239C24C2×D4×C1112yes—
240#41—22no—
241#41—22no—
242#41—42no—
243#41—41no—
244#41—44no—
245#41—42no—
246#41—41no—
247C2×Q8—21no—
248C2×Q8—42no—
249C2×Q8—81no—
250C2×Q8—81no—
251C2×D4—21no—
252C2×D4—24no—
253C2×D4—24no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—44no—
261C2×D4—41no—
262C2×D4—42no—
263C2×D4C2×Q8×C1111yescharacteristic
264C2×D4C11×#4111yescharacteristic
265C2×D4C11×#4112yes—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—41no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—82no—
275C22×C4C2×D4×C1111yescharacteristic
276M16—41no—
277M16—41no—
278C2×C8—41no—
279C4⋊C4—41no—
280C4⋊C4—81no—
281C4⋊C4—81no—
282C22⋊C4—44no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—82no—
287C22⋊C4—84no—
288C42—41no—
289C11#1337711yescharacteristic, direct product factor, Sylow
290C23—22no—
291C23—22no—
292C23—24no—
293C23—42no—
294C23—42no—
295C23—42no—
296C23—41no—
297C23—82no—
298C23—82no—
299C23C11×#12011yescharacteristic
300C23C11×C22⋊Q812yes—
301C23C11×#12412yes—
302Q8—22no—
303Q8—41no—
304Q8—84no—
305D4—22no—
306D4—41no—
307D4—42no—
308D4—41no—
309D4—41no—
310D4—44no—
311D4—44no—
312D4—42no—
313D4—42no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4C11×C22⋊Q811yescharacteristic
338C2×C4C11×#12411yescharacteristic
339C8—81no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—22no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—82no—
350C22—84no—
351C22—81no—
352C22—81no—
353C22—162no—
354C22C11×#39311yescharacteristic
355C22C11×B(4,𝔽2)11yescharacteristic
356C22C11×B(4,𝔽2)11yescharacteristic
357C4—21no—
358C4—21no—
359C4—42no—
360C4—42no—
361C4—82no—
362C4—81no—
363C4—82no—
364C4—162no—
365C2—21no—
366C2—21no—
367C2—42no—
368C2—42no—
369C2—82no—
370C2C11×#202911yescharacteristic
371C2C11×#219811yescharacteristic
372C2C11×#219911yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C11
prime radicalC2×C11×H(5,𝔽2)C22
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2804C2semidirect
4. C11×#1393C2semidirect
5. C11×#1390C2semidirect
22. C11×H(5,𝔽2)Q8semidirect
52. #13377C11direct (N × H)
104. #2804C2×C11semidirect
107. #1393C2×C11semidirect
108. #1390C2×C11semidirect
200. H(5,𝔽2)Q8×C11semidirect
289. C11#13377direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28042
C11×#17922
C11×#17902
C11×#13932
C11×#13902
#1337711