Finite Group Databasebeta

← C11×#12183 #14589376

Subgroups — C11×#12183 #14589376

Order 2816.

362 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2843C211yesmaximal, characteristic, complemented
2C11×#2039C211yesmaximal, characteristic
3C11×#1616C211yesmaximal, characteristic
4C11×#1604C211yesmaximal, characteristic
5C11×#1354C211yesmaximal, characteristic, complemented
6C11×#1353C211yesmaximal, characteristic, complemented
7C11×#1325C211yesmaximal, characteristic, complemented
8C11×#537C2211yescharacteristic
9C11×#481—21no—
10C11×#448—21no—
11C2×C11×#104—21no—
12C11×#417—21no—
13C11×#400—21no—
14C11×#400C2211yescharacteristic
15C11×#398—21no—
16C11×#398—21no—
17C11×#398—21no—
18C11×#395—21no—
19C11×#395C2211yescharacteristic
20C11×#384C2211yescharacteristic
21C11×#383—21no—
22C11×#343C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#324C2211yescharacteristic
26C11×#324C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Q8×C11D411yescharacteristic
29C2×C11×SD16—41no—
30C2×C11×M16—21no—
31C11×C22⋊Q8—41no—
32C11×#121—21no—
33C11×#121—21no—
34C11×#121—41no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4C2311yescharacteristic
44C2×C42×C11D411yescharacteristic
45C11×#106—41no—
46C11×#104—42no—
47C11×#103—41no—
48C11×#103—41no—
49C11×#102—41no—
50C11×#102—41no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95D411yescharacteristic
62C11×#95D411yescharacteristic
63#12183C1111yesmaximal, characteristic, direct product factor, Sylow
64C11×#41—41no—
65C11×#41—41no—
66C11×#41—41no—
67C11×#41—41no—
68C2×Q8×C11—21no—
69C2×Q8×C11—41no—
70C2×Q8×C11—81no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—41no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C11×SD16—82no—
86C11×M16—41no—
87C11×M16—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—81no—
97C11×C4⋊C4—81no—
98C11×C4⋊C4—81no—
99C11×C4⋊C4—81no—
100C11×C4⋊C4—81no—
101C11×C4⋊C4—81no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—21no—
105C42×C11SD1612yescomplemented
106#2843C2×C1111yescharacteristic, complemented
107#2039C2×C1111yescharacteristic
108#1616C2×C1111yescharacteristic
109#1604C2×C1111yescharacteristic
110#1354C2×C1111yescharacteristic, complemented
111#1353C2×C1111yescharacteristic, complemented
112#1325C2×C1111yescharacteristic, complemented
113C23×C11—41no—
114C23×C11#12011yescharacteristic
115Q8×C11—41no—
116Q8×C11—41no—
117Q8×C11—42no—
118Q8×C11—81no—
119D4×C11—41no—
120D4×C11—41no—
121D4×C11—81no—
122D4×C11—81no—
123D4×C11—81no—
124D4×C11—81no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—22no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11C2×SD1611yescharacteristic
152C2×C4×C11#13711yescharacteristic
153C8×C11—81no—
154C8×C11—81no—
155C8×C11—81no—
156#537C22×C1111yescharacteristic
157#481—21no—
158#448—21no—
159C2×#104—21no—
160#417—21no—
161#400—21no—
162#400C22×C1111yescharacteristic
163#398—21no—
164#398—21no—
165#398—21no—
166#395—21no—
167#395C22×C1111yescharacteristic
168#384C22×C1111yescharacteristic
169#383—21no—
170#343C22×C1111yescharacteristic
171#327—21no—
172#327—21no—
173#324C22×C1111yescharacteristic
174#324C22×C1111yescharacteristic
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11#44811yescharacteristic
181C22×C11#45411yescharacteristic
182C22×C11B(4,𝔽2)11yescharacteristic
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—81no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11—81no—
194C2×#41—21no—
195C22×Q8D4×C1111yescharacteristic
196C2×SD16—41no—
197C2×M16—21no—
198C22⋊Q8—41no—
199#121—21no—
200#121—21no—
201#121—41no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4D4×C1111yescharacteristic
209C2×C4⋊C4D4×C1111yescharacteristic
210C2×C4⋊C4C23×C1111yescharacteristic
211C2×C42D4×C1111yescharacteristic
212#106—41no—
213#104—42no—
214#103—41no—
215#103—41no—
216#102—41no—
217#102—41no—
218C22⋊C8—21no—
219C22⋊C8—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95D4×C1111yescharacteristic
229#95D4×C1111yescharacteristic
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—161no—
233C2×C11#159911yescharacteristic
234C2×C11#220011yescharacteristic
235C2×C11#220311yescharacteristic
236#41—41no—
237#41—41no—
238#41—41no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—41no—
242C2×Q8—81no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4C2×D4×C1111yescharacteristic
255C22×C4C2×D4×C1111yescharacteristic
256C22×C4C2×D4×C1111yescharacteristic
257SD16—82no—
258M16—41no—
259M16—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C42—21no—
277C42C11×SD1612yescomplemented
278C11#1218311yescharacteristic, direct product factor, Sylow
279C23—41no—
280C23C11×#12011yescharacteristic
281Q8—41no—
282Q8—41no—
283Q8—42no—
284Q8—81no—
285D4—41no—
286D4—41no—
287D4—81no—
288D4—81no—
289D4—81no—
290D4—81no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4C2×C11×SD1611yescharacteristic
318C2×C4C11×#13711yescharacteristic
319C8—81no—
320C8—81no—
321C8—81no—
322C22—21no—
323C22—21no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22C11×#44811yescharacteristic
328C22C11×#45411yescharacteristic
329C22C11×B(4,𝔽2)11yescharacteristic
330C4—21no—
331C4—21no—
332C4—42no—
333C4—41no—
334C4—41no—
335C4—81no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—81no—
341C2—21no—
342C2—21no—
343C2—161no—
344C2C11×#159911yescharacteristic
345C2C11×#220011yescharacteristic
346C2C11×#220311yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC11×#537C22
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2843C2semidirect
5. C11×#1354C2semidirect
6. C11×#1353C2semidirect
7. C11×#1325C2semidirect
63. #12183C11direct (N × H)
105. C42×C11SD16semidirect
106. #2843C2×C11semidirect
110. #1354C2×C11semidirect
111. #1353C2×C11semidirect
112. #1325C2×C11semidirect
277. C42C11×SD16semidirect
278. C11#12183direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28432
C11×#20392
C11×#16162
C11×#16042
C11×#13542
C11×#13532
C11×#13252
#1218311