Finite Group Databasebeta

← #14656081

Subgroups — #14656081

Order 2816.

676 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 131 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×#10622688C212yesmaximal
2#13073989C211yesmaximal, characteristic, complemented
3C2×#10622094C212yesmaximal, complemented
4#13066499C211yesmaximal, characteristic, complemented
5C11×#1957C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7C22×#4324—22no—
8C2×C4×Dic22C2212yes—
9C2×C11×#102—22no—
10C2×C4×C8×C11C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×#66896—22no—
13#10622688—24no—
14#10622688—24no—
15#10622598—22no—
16#10622596—22no—
17#10622587—22no—
18C2×C4⋊(C11⋊C8)C2212yes—
19#10622094—24no—
20C22×D4×C11—22no—
21C22×D4×C11—21no—
22C22×Dic22D412yes—
23C22×C8×C11—21no—
24C11×#127—22no—
25C11×#127—21no—
26C11×#127D412yes—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4D412yes—
29C2×C42×C11C2311yescharacteristic
30C2×#4324—28no—
31C2×#4324—44no—
32C2×#4324—44no—
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11D412yes—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11—22no—
37C22×C11⋊C8—22no—
38C4×Dic22—22no—
39C4×Dic22—22no—
40C4×Dic22—22no—
41C4×Dic22—22no—
42C11×#102—44no—
43C4×C8×C11—22no—
44#66896—28no—
45C11⋊#95—22no—
46C11⋊#95—24no—
47C4⋊(C11⋊C8)—22no—
48C4⋊(C11⋊C8)D414yes—
49#10230—111nomaximal, Sylow
50C24×C11—41no—
51C2×D4×C11—24no—
52C2×D4×C11—22no—
53C2×D4×C11—42no—
54C2×D4×C11—42no—
55C2×D4×C11—42no—
56C2×D4×C11—41no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C2×D4×C11—42no—
60C2×D4×C11—42no—
61C22×C4×C11—22no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C22×Dic11—22no—
65C22×Dic11—22no—
66C2×Dic22—22no—
67C2×Dic22—22no—
68C2×Dic22—22no—
69C2×Dic22—22no—
70C2×Dic22—22no—
71C2×Dic22SD1614yescomplemented
72C2×C8×C11—22no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C42×C11C2×D411yescharacteristic
79C42×C11C2×D412yes—
80C42×C11#4111yescharacteristic
81#4324—416no—
82C4⋊Dic11—22no—
83C4⋊Dic11—22no—
84C4⋊Dic11—82no—
85Dic11⋊C4—42no—
86Dic11⋊C4—42no—
87C4×Dic11—42no—
88C4×Dic11—42no—
89C2×C11⋊C8—24no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92C2×#460—112no—
93#2582—111no—
94#1957D1111yescharacteristic
95C2×Q8⋊C8—112no—
96#1296—111no—
97C23×C11—42no—
98C23×C11—82no—
99C23×C11—82no—
100C23×C11—81no—
101C23×C11—81no—
102C23×C11#12011yescharacteristic
103D4×C11—44no—
104D4×C11—44no—
105D4×C11—44no—
106D4×C11—82no—
107D4×C11—82no—
108D4×C11—82no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—44no—
112C2×C4×C11—42no—
113C2×C4×C11#12012yes—
114C2×C4×C11#12112yes—
115C2×C4×C11#12111yescharacteristic
116C2×C4×C11#12711yescharacteristic
117C2×C4×C11C2×SD1612yes—
118C2×C4×C11#13512yes—
119C2×C4×C11AGL(1,ℤ/8)12yes—
120C2×C4×C11#13712yes—
121C2×Dic11—24no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127Dic22—24no—
128Dic22—24no—
129Dic22—42no—
130Dic22—42no—
131C8×C11—42no—
132C11⋊C8—44no—
133C22×SD16—222no—
134C2×#127C2×D1111yescharacteristic
135C2×C4×Q8—112no—
136#460—224no—
137#460—224no—
138C2×C4⋊C8—112no—
139C2×#102—22no—
140C2×#102—222no—
141C2×C4×C8C2×D1111yescharacteristic
142#398—222no—
143#391—222no—
144#389—222no—
145#384C2×D1111yescharacteristic
146Q8⋊C8—224no—
147C22×C11—84no—
148C22×C11—82no—
149C22×C11—161no—
150C22×C11—161no—
151C22×C11—162no—
152C22×C11#39211yescharacteristic
153C22×C11#44812yes—
154C22×C11#44912yes—
155C22×C11#45311yescharacteristic
156C22×C11#45411yescharacteristic
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—22no—
168C22×D4—21no—
169C2×SD16—228no—
170C2×SD16—444no—
171C2×SD16—444no—
172C22×C8—21no—
173C22×C8—222no—
174#127—21no—
175#127—22no—
176#127D4412yes—
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⋊C4C22⋊D1112yes—
186C2×C42—222no—
187C2×C42C22×D1111yescharacteristic
188C4⋊C8—114no—
189C4⋊C8—222no—
190#102—44no—
191#102—228no—
192C4×C8—22no—
193#95—224no—
194#95—222no—
195C2×C11—162no—
196C2×C11#162011yescharacteristic
197C2×C11#162311yescharacteristic
198C2×C11#162612yes—
199C2×C11#200012yes—
200C2×C11#200611yescharacteristic
201C24—41no—
202C2×Q8—114no—
203C2×Q8—222no—
204C2×Q8—222no—
205C2×Q8—222no—
206C2×Q8—222no—
207C2×Q8—222no—
208C2×D4—24no—
209C2×D4—22no—
210C2×D4—42no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—41no—
218C22×C4—22no—
219C22×C4—222no—
220C22×C4—222no—
221C22×C4D4×D1112yes—
222C22×C4C2×C22⋊D1111yescharacteristic
223SD16—4416no—
224C2×C8—22no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—224no—
228C2×C8—442no—
229C2×C8—442no—
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×D4411yescharacteristic
241C42#433911yescharacteristic
242C42D4×D1112yes—
243C11#1023011yescharacteristic, complemented, Sylow
244C23—42no—
245C23—82no—
246C23—82no—
247C23—81no—
248C23—81no—
249C23#6699011yescharacteristic
250Q8—224no—
251Q8—224no—
252Q8—442no—
253Q8—442no—
254D4—44no—
255D4—44no—
256D4—44no—
257D4—82no—
258D4—82no—
259D4—82no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—44no—
263C2×C4—42no—
264C2×C4—224no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—442no—
268C2×C4—442no—
269C2×C4—442no—
270C2×C4#6693512yes—
271C2×C4#6693712yes—
272C2×C4#6696412yes—
273C2×C4#6696512yes—
274C2×C4SD16×D1112yes—
275C2×C4#6696812yes—
276C2×C4#6698311yescharacteristic
277C2×C4#6699311yescharacteristic
278C8—42no—
279C8—444no—
280C22—84no—
281C22—82no—
282C22—161no—
283C22—161no—
284C22—162no—
285C22#1062257311yescharacteristic
286C22#1062267511yescharacteristic
287C22#1062269011yescharacteristic
288C22#1062277112yes—
289C22#1062278312yes—
290C4—21no—
291C4—21no—
292C4—82no—
293C4—444no—
294C4—882no—
295C4#1062238912yes—
296C4#1062239112yes—
297C4#1062239312yes—
298C4#1062239612yes—
299C2—162no—
300C2#1306767311yescharacteristic
301C2#1306769211yescharacteristic
302C2#1306770912yes—
303C2#1306962012yes—
304C2#1306965711yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1957C2
socleC23×C11#120
prime radicalC2×C11×#127C22
hypercenter#1957D11
hypocenterC11#10230
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #13073989C2semidirect
3. C2×#10622094C2semidirect
4. #13066499C2semidirect
71. C2×Dic22SD16semidirect
243. C11#10230semidirect

Maximal subgroups

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

subgroupindex
C2×#106226882
#130739892
C2×#106220942
#130664992
C11×#19572
#1023011