Finite Group Databasebeta

← C11×#7816 #14585009

Subgroups — C11×#7816 #14585009

Order 2816.

362 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2806C211yesmaximal, characteristic
2C11×#2099C211yesmaximal, characteristic
3C11×#2072C211yesmaximal, characteristic
4C11×#2072C211yesmaximal, characteristic
5C11×#1272C211yesmaximal, characteristic
6C11×#1272C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C2×C11×#103—21no—
9C2×C11×#103—21no—
10C11×#398—21no—
11C11×#398—21no—
12C11×#395—21no—
13C11×#391—21no—
14C11×#391C2211yescharacteristic
15C11×#391C2211yescharacteristic
16C11×#389—21no—
17C11×#389C2211yescharacteristic
18C11×#387—21no—
19C11×#384C2211yescharacteristic
20C11×#340—21no—
21C11×#340—21no—
22C11×#340—21no—
23C11×#340—21no—
24C11×#336C2211yescharacteristic
25C11×#336C2211yescharacteristic
26C11×#336C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
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⋊C4D411yescharacteristic
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C42×C11—21no—
45C2×C42×C11C2311yescharacteristic
46C11×#103—42no—
47C11×#103—42no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56#7816C1111yesmaximal, characteristic, direct product factor, Sylow
57C2×Q8×C11—21no—
58C2×Q8×C11—21no—
59C2×Q8×C11—21no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×Q8×C11SD1612yes—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—81no—
96C11×C4⋊C4—81no—
97C11×C4⋊C4—81no—
98C11×C4⋊C4—81no—
99C11×C4⋊C4Q1612yes—
100C42×C11—41no—
101C42×C11—81no—
102#2806C2×C1111yescharacteristic
103#2099C2×C1111yescharacteristic
104#2072C2×C1111yescharacteristic
105#2072C2×C1111yescharacteristic
106#1272C2×C1111yescharacteristic
107#1272C2×C1111yescharacteristic
108#1271C2×C1111yescharacteristic
109C23×C11#12011yescharacteristic
110Q8×C11—42no—
111Q8×C11—42no—
112Q8×C11—81no—
113Q8×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
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—81no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11C2×SD1611yescharacteristic
142C2×C4×C11C2×Q1611yescharacteristic
143C2×C4×C11#13511yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C8×C11—81no—
148C8×C11—81no—
149C8×C11—81no—
150C2×#103—21no—
151C2×#103—21no—
152#398—21no—
153#398—21no—
154#395—21no—
155#391—21no—
156#391C22×C1111yescharacteristic
157#391C22×C1111yescharacteristic
158#389—21no—
159#389C22×C1111yescharacteristic
160#387—21no—
161#384C22×C1111yescharacteristic
162#340—21no—
163#340—21no—
164#340—21no—
165#340—21no—
166#336C22×C1111yescharacteristic
167#336C22×C1111yescharacteristic
168#336C22×C1111yescharacteristic
169C22×C11#44811yescharacteristic
170C22×C11#44911yescharacteristic
171C22×C11#45111yescharacteristic
172C22×C11#45411yescharacteristic
173C22×C11#45511yescharacteristic
174C22×C11#45511yescharacteristic
175C22×C11#45811yescharacteristic
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—42no—
183C4×C11—42no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11—161no—
189C22×Q8D4×C1111yescharacteristic
190C22×Q8D4×C1111yescharacteristic
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4D4×C1111yescharacteristic
203C2×C4⋊C4D4×C1111yescharacteristic
204C2×C4⋊C4D4×C1111yescharacteristic
205C2×C4⋊C4D4×C1111yescharacteristic
206C2×C42—21no—
207C2×C42C23×C1111yescharacteristic
208#103—42no—
209#103—42no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218C2×C11#160811yescharacteristic
219C2×C11#161211yescharacteristic
220C2×C11#161711yescharacteristic
221C2×C11#162611yescharacteristic
222C2×C11#164411yescharacteristic
223C2×C11#164511yescharacteristic
224C2×C11#166211yescharacteristic
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8C11×SD1612yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—41no—
240C22×C4C2×D4×C1111yescharacteristic
241C22×C4C2×D4×C1111yescharacteristic
242C22×C4C2×D4×C1111yescharacteristic
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4C11×Q1612yes—
268C42—41no—
269C42—81no—
270C11#781611yescharacteristic, direct product factor, Sylow
271C23C11×#12011yescharacteristic
272Q8—42no—
273Q8—42no—
274Q8—81no—
275Q8—81no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4C2×C11×SD1611yescharacteristic
304C2×C4C2×C11×Q1611yescharacteristic
305C2×C4C11×#13511yescharacteristic
306C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
307C2×C4C11×#13711yescharacteristic
308C2×C4C11×#13711yescharacteristic
309C8—81no—
310C8—81no—
311C8—81no—
312C22C11×#44811yescharacteristic
313C22C11×#44911yescharacteristic
314C22C11×#45111yescharacteristic
315C22C11×#45411yescharacteristic
316C22C11×#45511yescharacteristic
317C22C11×#45511yescharacteristic
318C22C11×#45811yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—42no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—161no—
332C2C11×#160811yescharacteristic
333C2C11×#161211yescharacteristic
334C2C11×#161711yescharacteristic
335C2C11×#162611yescharacteristic
336C2C11×#164411yescharacteristic
337C2C11×#164511yescharacteristic
338C2C11×#166211yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
56. #7816C11direct (N × H)
270. C11#7816direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28062
C11×#20992
C11×#20722
C11×#12722
C11×#12712
#781611