Finite Group Databasebeta

← #14656084

Subgroups — #14656084

Order 2816.

676 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#10622461C212yesmaximal
2#13073989C211yesmaximal, characteristic, complemented
3#13069421C211yesmaximal, characteristic
4C2×#10622122C212yesmaximal, complemented
5C11×#1296C211yesmaximal, characteristic, complemented
6C22×#4314—22no—
7C2×#66927C2211yescharacteristic
8C2×C4×Dic22C2212yes—
9C2×C11×C4⋊C8C2212yes—
10C11×#384C2211yescharacteristic
11C2×#66885—22no—
12#10622598—22no—
13#10622596—22no—
14#10622587—22no—
15C2×#66873—22no—
16C2×C4×C11⋊C8C2211yescharacteristic
17#10622461—24no—
18#10622461—24no—
19#10622122—24no—
20C22×D44—22no—
21C22×D44—21no—
22C22×Dic22D412yes—
23C22×C8×C11—22no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4D412yes—
26C2×C42×C11C2311yescharacteristic
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11D412yes—
29C2×Dic11⋊C4—22no—
30C2×C4×Dic11—22no—
31C22×C11⋊C8—21no—
32C2×#4314—28no—
33C2×#4314—44no—
34C2×#4314—44no—
35#66927—22no—
36#66927—21no—
37#66927D412yes—
38C4×Dic22—22no—
39C4×Dic22—22no—
40C4×Dic22—22no—
41C4×Dic22—22no—
42C11×C4⋊C8—22no—
43C11×C4⋊C8D414yes—
44C11⋊#95—22no—
45C11⋊#95—24no—
46#66885—28no—
47#66873—44no—
48C4×C11⋊C8—22no—
49#10230—111nomaximal, Sylow
50C23×D11—41no—
51C22×C4×C11—22no—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11C2×D412yes—
54C22×Dic11—22no—
55C22×Dic11—22no—
56C2×D44—24no—
57C2×D44—22no—
58C2×D44—42no—
59C2×D44—42no—
60C2×D44—42no—
61C2×D44—41no—
62C2×D44—42no—
63C2×D44—42no—
64C2×D44—42no—
65C2×D44—42no—
66C2×Dic22—22no—
67C2×Dic22—22no—
68C2×Dic22—22no—
69C2×Dic22—22no—
70C2×Dic22—22no—
71C2×Dic22SD1614yescomplemented
72C2×C8×C11—24no—
73C2×C8×C11—42no—
74C2×C8×C11—42no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C42×C11C2×D411yescharacteristic
79C42×C11C2×D412yes—
80C42×C11#4111yescharacteristic
81C4⋊Dic11—22no—
82C4⋊Dic11—22no—
83C4⋊Dic11—82no—
84Dic11⋊C4—42no—
85Dic11⋊C4—42no—
86C4×Dic11—42no—
87C4×Dic11—42no—
88C2×C11⋊C8—22no—
89C2×C11⋊C8—41no—
90C2×C11⋊C8—41no—
91#4314—416no—
92C2×#460—112no—
93#2582—111no—
94#1957—111no—
95C2×Q8⋊C8—112no—
96#1296D1111yescharacteristic, complemented
97C23×C11#12011yescharacteristic
98C22×D11—42no—
99C22×D11—82no—
100C22×D11—82no—
101C22×D11—81no—
102C22×D11—81no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—44no—
106C2×C4×C11—42no—
107C2×C4×C11#12012yes—
108C2×C4×C11#12111yescharacteristic
109C2×C4×C11#12112yes—
110C2×C4×C11#12711yescharacteristic
111C2×C4×C11C2×SD1612yes—
112C2×C4×C11#13512yes—
113C2×C4×C11AGL(1,ℤ/8)12yes—
114C2×C4×C11#13712yes—
115C2×Dic11—24no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121D44—44no—
122D44—44no—
123D44—44no—
124D44—82no—
125D44—82no—
126D44—82no—
127Dic22—24no—
128Dic22—24no—
129Dic22—42no—
130Dic22—42no—
131C8×C11—44no—
132C11⋊C8—42no—
133C22×SD16—222no—
134C2×#127—111no—
135C2×C4×Q8—112no—
136#460—224no—
137#460—224no—
138C2×C4⋊C8C2×D1112yes—
139C2×#102—222no—
140C2×#102—222no—
141C2×C4×C8—111no—
142#398—222no—
143#391—222no—
144#389—222no—
145#384C2×D1111yescharacteristic
146Q8⋊C8—224no—
147C22×C11#39211yescharacteristic
148C22×C11#44812yes—
149C22×C11#44912yes—
150C22×C11#45311yescharacteristic
151C22×C11#45411yescharacteristic
152C2×D11—84no—
153C2×D11—82no—
154C2×D11—161no—
155C2×D11—161no—
156C2×D11—162no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—82no—
160C4×C11#45012yes—
161C4×C11#45212yes—
162C4×C11#46512yes—
163C4×C11#46812yes—
164Dic11—44no—
165Dic11—82no—
166C22×Q8—112no—
167C22×D4—221no—
168C22×D4—222no—
169C2×SD16—228no—
170C2×SD16—444no—
171C2×SD16—444no—
172C22×C8—22no—
173C22×C8—221no—
174#127—112no—
175#127—222no—
176#127—221no—
177C4×Q8—222no—
178C4×Q8—222no—
179C4×Q8—222no—
180C4×Q8—222no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—112no—
183C2×C4⋊C4—222no—
184C2×C4⋊C4—222no—
185C2×C4⋊C4D4412yes—
186C2×C42—222no—
187C2×C42C22×D1111yescharacteristic
188C4⋊C8—22no—
189C4⋊C8D4414yes—
190#102—228no—
191#102—444no—
192C4×C8—222no—
193#95—224no—
194#95—222no—
195C2×C11#162011yescharacteristic
196C2×C11#162311yescharacteristic
197C2×C11#162612yes—
198C2×C11#200012yes—
199C2×C11#200611yescharacteristic
200D11—162no—
201C24—441no—
202C2×Q8—114no—
203C2×Q8—222no—
204C2×Q8—222no—
205C2×Q8—222no—
206C2×Q8—222no—
207C2×Q8—222no—
208C2×D4—224no—
209C2×D4—222no—
210C2×D4—442no—
211C2×D4—442no—
212C2×D4—441no—
213C2×D4—442no—
214C2×D4—442no—
215C2×D4—442no—
216C2×D4—442no—
217C2×D4—442no—
218C22×C4—22no—
219C22×C4—222no—
220C22×C4—222no—
221C22×C4C2×D4411yescharacteristic
222C22×C4D4×D1112yes—
223SD16—4416no—
224C2×C8—24no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—222no—
228C2×C8—441no—
229C2×C8—441no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—222no—
234C4⋊C4—222no—
235C4⋊C4—442no—
236C4⋊C4—442no—
237C4⋊C4—882no—
238C42—442no—
239C42—442no—
240C42C2×D4412yes—
241C42D4×D1111yescharacteristic
242C42#434311yescharacteristic
243C11#1023011yescharacteristic, complemented, Sylow
244C23—442no—
245C23—881no—
246C23—881no—
247C23—882no—
248C23—882no—
249C23#6693511yescharacteristic
250Q8—224no—
251Q8—224no—
252Q8—442no—
253Q8—442no—
254D4—444no—
255D4—444no—
256D4—444no—
257D4—882no—
258D4—882no—
259D4—882no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—44no—
264C2×C4—224no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—442no—
268C2×C4—442no—
269C2×C4—442no—
270C2×C4#6692711yescharacteristic
271C2×C4#6693512yes—
272C2×C4#6694811yescharacteristic
273C2×C4#6694812yes—
274C2×C4#6696412yes—
275C2×C4SD16×D1112yes—
276C2×C4#6696912yes—
277C2×C4#6697112yes—
278C8—44no—
279C8—442no—
280C22—884no—
281C22—882no—
282C22—1761no—
283C22—1761no—
284C22—1762no—
285C22#1062228411yescharacteristic
286C22#1062236011yescharacteristic
287C22#1062236611yescharacteristic
288C22#1062239412yes—
289C22#1062241912yes—
290C4—21no—
291C4—21no—
292C4—82no—
293C4—444no—
294C4—882no—
295C4#1062238912yes—
296C4#1062242312yes—
297C4#1062247712yes—
298C4#1062249912yes—
299C2—1762no—
300C2#1306767611yescharacteristic
301C2#1306769511yescharacteristic
302C2#1306771312yes—
303C2#1306962212yes—
304C2#1306966011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenter#1296D11
hypocenterC11#10230
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #13073989C2semidirect
4. C2×#10622122C2semidirect
5. C11×#1296C2semidirect
71. C2×Dic22SD16semidirect
96. #1296D11semidirect
243. C11#10230semidirect

Maximal subgroups

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

subgroupindex
C2×#106224612
#130739892
#130694212
C2×#106221222
C11×#12962
#1023011