Finite Group Databasebeta

← #14643075

Subgroups — #14643075

Order 2816.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#13075647C211yesmaximal, characteristic
2#13070180C211yesmaximal, characteristic
3#13070179C211yesmaximal, characteristic
4#13070153C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic
6#13066440C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C2×#66941—21no—
9C11×#389C2211yescharacteristic
10C2×#66882—21no—
11C2×#66880—21no—
12#10622597—21no—
13#10622594—21no—
14#10622592—21no—
15#10622548C2211yescharacteristic
16#10622542C2211yescharacteristic
17#10622541C2211yescharacteristic
18#10622269—21no—
19#10622267—21no—
20C11×#336C2211yescharacteristic
21C11×#336C2211yescharacteristic
22#10622189—21no—
23#10622189—21no—
24#10622167—21no—
25#10622167—21no—
26#10622162C2211yescharacteristic
27C22×Dic22—21no—
28C22×Dic22D411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×C4⋊Dic11D411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C22×C11⋊C8—21no—
47#66941—42no—
48#66941—42no—
49C11×#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56#66882—42no—
57#66880—42no—
58#7829—111nomaximal, Sylow
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11—41no—
69C2×Dic22—21no—
70C2×Dic22—41no—
71C2×Dic22—41no—
72C2×Dic22—42no—
73C2×Dic22—81no—
74C2×Dic22—81no—
75C2×Dic22SD1612yes—
76C2×C8×C11—22no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4Q1612yes—
87C42×C11—41no—
88C4⋊Dic11—21no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—42no—
94C4⋊Dic11—42no—
95C4⋊Dic11—42no—
96C4⋊Dic11Q1612yes—
97Dic11⋊C4—42no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100Dic11⋊C4—81no—
101C4×Dic11—42no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2734—111no—
106#2100—111no—
107#2100—111no—
108#2095—111no—
109#1272—111no—
110#1271—111no—
111#1271D1111yescharacteristic
112C23×C11#12011yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11C2×SD1611yescharacteristic
126C2×C4×C11C2×Q1611yescharacteristic
127C2×C4×C11C2×Q1611yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×Dic11—22no—
132C2×Dic11—22no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—81no—
144C2×Dic11—81no—
145C2×Dic11—81no—
146Dic22—42no—
147Dic22—81no—
148Dic22—84no—
149C8×C11—42no—
150C8×C11—81no—
151C11⋊C8—81no—
152C2×C4⋊Q8—221no—
153C2×#107—221no—
154C2×#103—221no—
155#398—221no—
156#395—221no—
157#395—221no—
158#391—111no—
159#389—111no—
160#389C2×D1111yescharacteristic
161#387—221no—
162#387—221no—
163#384—111no—
164#340—221no—
165#340—221no—
166#340—221no—
167#340—221no—
168#336—111no—
169#336C2×D1111yescharacteristic
170#336C2×D1111yescharacteristic
171C22×C11#45011yescharacteristic
172C22×C11#45111yescharacteristic
173C22×C11#45111yescharacteristic
174C22×C11#45311yescharacteristic
175C22×C11#45411yescharacteristic
176C22×C11#45411yescharacteristic
177C22×C11#45811yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—42no—
185C4×C11—81no—
186Dic11—42no—
187Dic11—42no—
188Dic11—81no—
189Dic11—81no—
190Dic11—161no—
191C22×Q8—111no—
192C22×Q8—221no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—221no—
196C4⋊Q8—442no—
197C4⋊Q8—442no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4D4411yescharacteristic
210C2×C4⋊C4D4411yescharacteristic
211C2×C42—221no—
212C2×C42C22×D1111yescharacteristic
213#107—442no—
214#103—442no—
215#95—21no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222C2×C11#161311yescharacteristic
223C2×C11#161711yescharacteristic
224C2×C11#161711yescharacteristic
225C2×C11#163311yescharacteristic
226C2×C11#163711yescharacteristic
227C2×C11#163711yescharacteristic
228C2×C11#165711yescharacteristic
229C2×Q8—112no—
230C2×Q8—221no—
231C2×Q8—441no—
232C2×Q8—441no—
233C2×Q8—442no—
234C2×Q8—881no—
235C2×Q8—881no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—441no—
243C22×C4C2×D4411yescharacteristic
244C22×C4D4×D1111yescharacteristic
245C22×C4D4×D1111yescharacteristic
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—441no—
253C2×C8—441no—
254C2×C8—441no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—112no—
260C4⋊C4—221no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C4⋊C4—442no—
268C4⋊C4—442no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—881no—
272C4⋊C4Dic4412yes—
273C42—41no—
274C42—442no—
275C11#782911yescharacteristic, complemented, Sylow
276C23#6693511yescharacteristic
277Q8—442no—
278Q8—881no—
279Q8—884no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—222no—
293C2×C4—222no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—881no—
305C2×C4—881no—
306C2×C4—881no—
307C2×C4C2×Dic4411yescharacteristic
308C2×C4#6696211yescharacteristic
309C2×C4#6696411yescharacteristic
310C2×C4SD16×D1111yescharacteristic
311C2×C4#6696811yescharacteristic
312C2×C4Q16×D1111yescharacteristic
313C8—42no—
314C8—81no—
315C8—881no—
316C22#1062235211yescharacteristic
317C22#1062235511yescharacteristic
318C22#1062236611yescharacteristic
319C22#1062238911yescharacteristic
320C22#1062242111yescharacteristic
321C22#1062243511yescharacteristic
322C22#1062244011yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4—81no—
331C4—442no—
332C4—442no—
333C4—881no—
334C4—881no—
335C4—1761no—
336C2#1306763711yescharacteristic
337C2#1306765911yescharacteristic
338C2#1306766011yescharacteristic
339C2#1306775811yescharacteristic
340C2#1306778211yescharacteristic
341C2#1306778411yescharacteristic
342C2#1306791611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socle, prime radicalC23×C11#120
hypercenter#1271D11
hypocenterC11#7829
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
275. C11#7829semidirect

Maximal subgroups

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

subgroupindex
#130756472
#130701802
#130701792
#130701532
#130664412
#130664402
C11×#12712
#782911