Finite Group Databasebeta

← C11×#13375 #14590568

Subgroups — C11×#13375 #14590568

Order 2816.

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

normal subgroups only

This group has 704 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×#2683C211yesmaximal, characteristic, complemented
2C11×#1792C211yesmaximal, characteristic
3C11×#1790C212yesmaximal
4C11×#1393C211yesmaximal, characteristic, complemented
5C11×#1390C212yesmaximal, complemented
6C2×C11×H(5,𝔽2)C2211yescharacteristic
7C2×C11×C22⋊Q8—22no—
8C2×C11×#104—21no—
9C11×#417—21no—
10C2×C11×#100C2211yescharacteristic
11C2×C11×#99—22no—
12C2×C11×#99C2212yes—
13C11×#396—22no—
14C11×#395—21no—
15C11×#390C2211yescharacteristic
16C11×#389—21no—
17C11×#386—22no—
18C11×#386C2212yes—
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—
31C11×C22⋊Q8—48no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—42no—
41C2×C11×C22⋊C4D412yes—
42C2×C42×C11D411yescharacteristic
43C11×#104—42no—
44C11×#103—41no—
45C11×#102—41no—
46C11×#100—22no—
47C11×#99—22no—
48C11×#99—22no—
49C11×#99—44no—
50C11×#95—21no—
51C11×#95—22no—
52C11×#95—42no—
53#13375C1111yesmaximal, characteristic, direct product factor, Sylow
54C24×C11—22no—
55C24×C11C2×D412yes—
56C11×#41—22no—
57C11×#41—22no—
58C11×#41—42no—
59C11×#41—41no—
60C11×#41—44no—
61C11×#41—42no—
62C11×#41—41no—
63C2×Q8×C11—21no—
64C2×Q8×C11—44no—
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—22no—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—44no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11C2×D411yescharacteristic
91C11×M16—41no—
92C11×M16—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—44no—
96C11×C4⋊C4—44no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—81no—
99C11×C22⋊C4—44no—
100C11×C22⋊C4—44no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—84no—
105C42×C11—41no—
106#2683C2×C1111yescharacteristic, complemented
107#1792C2×C1111yescharacteristic
108#1790C2×C1112yes—
109#1393C2×C1111yescharacteristic, complemented
110#1390C2×C1112yescomplemented
111C23×C11—22no—
112C23×C11—22no—
113C23×C11—24no—
114C23×C11—42no—
115C23×C11—42no—
116C23×C11—42no—
117C23×C11—41no—
118C23×C11—82no—
119C23×C11—82no—
120C23×C11#12011yescharacteristic
121C23×C11C22⋊Q812yes—
122C23×C11#12412yes—
123Q8×C11—22no—
124Q8×C11—41no—
125Q8×C11—84no—
126D4×C11—22no—
127D4×C11—41no—
128D4×C11—41no—
129D4×C11—42no—
130D4×C11—41no—
131D4×C11—44no—
132D4×C11—44no—
133D4×C11—42no—
134D4×C11—42no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—22no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—44no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—82no—
155C2×C4×C11—82no—
156C2×C4×C11—82no—
157C2×C4×C11—82no—
158C2×C4×C11C22⋊Q811yescharacteristic
159C2×C4×C11#12411yescharacteristic
160C8×C11—81no—
161C2×H(5,𝔽2)C22×C1111yescharacteristic
162C2×C22⋊Q8—22no—
163C2×#104—21no—
164#417—21no—
165C2×#100C22×C1111yescharacteristic
166C2×#99—22no—
167C2×#99C22×C1112yes—
168#396—22no—
169#395—21no—
170#390C22×C1111yescharacteristic
171#389—21no—
172#386—22no—
173#386C22×C1112yes—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11—82no—
184C22×C11—84no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—162no—
188C22×C11#39311yescharacteristic
189C22×C11B(4,𝔽2)11yescharacteristic
190C22×C11B(4,𝔽2)11yescharacteristic
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—42no—
194C4×C11—44no—
195C4×C11—42no—
196C4×C11—82no—
197C4×C11—81no—
198C4×C11—162no—
199H(5,𝔽2)—22no—
200H(5,𝔽2)—21no—
201H(5,𝔽2)—42no—
202H(5,𝔽2)Q8×C1112yescomplemented
203C2×#41—21no—
204C2×#41—41no—
205C22×Q8—21no—
206C22×D4—22no—
207C22×D4—41no—
208C22×D4C23×C1111yescharacteristic
209C23×C4D4×C1112yes—
210C2×M16—21no—
211C22⋊Q8—48no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4D4×C1111yescharacteristic
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—42no—
221C2×C22⋊C4D4×C1112yes—
222C2×C42D4×C1111yescharacteristic
223#104—42no—
224#103—41no—
225#102—41no—
226#100—22no—
227#99—22no—
228#99—22no—
229#99—44no—
230#95—21no—
231#95—22no—
232#95—42no—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—42no—
236C2×C11—42no—
237C2×C11—82no—
238C2×C11#202911yescharacteristic
239C2×C11#219611yescharacteristic
240C2×C11#220111yescharacteristic
241C24—22no—
242C24C2×D4×C1112yes—
243#41—22no—
244#41—22no—
245#41—42no—
246#41—41no—
247#41—44no—
248#41—42no—
249#41—41no—
250C2×Q8—21no—
251C2×Q8—44no—
252C2×Q8—81no—
253C2×D4—21no—
254C2×D4—24no—
255C2×D4—24no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—44no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4C2×Q8×C1111yescharacteristic
266C2×D4C11×#4111yescharacteristic
267C2×D4C11×#4112yes—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—44no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4C2×D4×C1111yescharacteristic
278M16—41no—
279M16—41no—
280C2×C8—41no—
281C4⋊C4—24no—
282C4⋊C4—41no—
283C4⋊C4—44no—
284C4⋊C4—44no—
285C4⋊C4—81no—
286C22⋊C4—44no—
287C22⋊C4—44no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—84no—
292C42—41no—
293C11#1337511yescharacteristic, direct product factor, Sylow
294C23—22no—
295C23—22no—
296C23—24no—
297C23—42no—
298C23—42no—
299C23—42no—
300C23—41no—
301C23—82no—
302C23—82no—
303C23C11×#12011yescharacteristic
304C23C11×C22⋊Q812yes—
305C23C11×#12412yes—
306Q8—22no—
307Q8—41no—
308Q8—84no—
309D4—22no—
310D4—41no—
311D4—42no—
312D4—41no—
313D4—41no—
314D4—44no—
315D4—44no—
316D4—42no—
317D4—42no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4C11×C22⋊Q811yescharacteristic
342C2×C4C11×#12411yescharacteristic
343C8—81no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—84no—
355C22—81no—
356C22—81no—
357C22—162no—
358C22C11×#39311yescharacteristic
359C22C11×B(4,𝔽2)11yescharacteristic
360C22C11×B(4,𝔽2)11yescharacteristic
361C4—21no—
362C4—21no—
363C4—42no—
364C4—44no—
365C4—42no—
366C4—82no—
367C4—81no—
368C4—162no—
369C2—21no—
370C2—21no—
371C2—42no—
372C2—42no—
373C2—82no—
374C2C11×#202911yescharacteristic
375C2C11×#219611yescharacteristic
376C2C11×#220111yescharacteristic
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×#2683C2semidirect
4. C11×#1393C2semidirect
5. C11×#1390C2semidirect
22. C11×H(5,𝔽2)Q8semidirect
53. #13375C11direct (N × H)
106. #2683C2×C11semidirect
109. #1393C2×C11semidirect
110. #1390C2×C11semidirect
202. H(5,𝔽2)Q8×C11semidirect
293. C11#13375direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26832
C11×#17922
C11×#17902
C11×#13932
C11×#13902
#1337511