Finite Group Databasebeta

← #14658107

Subgroups — #14658107

Order 2816.

364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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#13079158C211yesmaximal, characteristic
2#13069389C211yesmaximal, characteristic
3#13067307C211yesmaximal, characteristic
4C2×#10622185C211yesmaximal, characteristic
5#13067020C211yesmaximal, characteristic
6#13066465C211yesmaximal, characteristic
7C11×#1548C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×#66886—21no—
13#10622693—22no—
14#10622692—21no—
15#10622691—21no—
16#10622577—21no—
17#10622577—21no—
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21C11×#333—22no—
22#10622196—21no—
23#10622185—22no—
24#10622124—21no—
25#10622119—21no—
26#10622094—22no—
27C22×Q8×C11—21no—
28C2×C11×M16—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8D412yes—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36#66979—21no—
37#66977—21no—
38#66977—21no—
39C2×#4318D411yescharacteristic
40C2×#4318D411yescharacteristic
41C22×C11⋊C8—21no—
42C22×C11⋊C8—21no—
43#66923—21no—
44#66922D411yescharacteristic
45#66922D411yescharacteristic
46C4×Dic22—21no—
47C4×Dic22—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C22⋊C8—21no—
52C4×C8×C11—21no—
53#66886—42no—
54#66872—22no—
55#66872—22no—
56#66871—22no—
57#66871—22no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)D412yes—
62#66867—21no—
63C4×C11⋊C8—21no—
64#10556—111nomaximal, Sylow
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—81no—
68C2×Q8×C11—81no—
69C22×C4×C11—41no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C2×Dic22—21no—
74C2×Dic22—21no—
75C11×M16—41no—
76C11×M16—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11#4111yescharacteristic
87C22⋊Dic11—41no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94C4×Dic11—41no—
95#4318—21no—
96#4318—21no—
97#4318SD1612yes—
98#4318Q1612yes—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—81no—
106#3165—111no—
107#1950—111no—
108#1550—111no—
109#1548D1111yescharacteristic
110C2×#332—111no—
111#1481—111no—
112#1283—111no—
113C23×C11#12411yescharacteristic
114Q8×C11—82no—
115Q8×C11—81no—
116Q8×C11—81no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—82no—
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12311yescharacteristic
127C2×C4×C11#12311yescharacteristic
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11C2×Q1611yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×Dic11—41no—
133C2×Dic11—41no—
134Dic22—41no—
135Dic22—41no—
136Dic22—81no—
137C8×C11—81no—
138C8×C11—81no—
139C11⋊C8—22no—
140C11⋊C8—22no—
141C11⋊C8—42no—
142C11⋊C8—81no—
143#533—111no—
144C2×C4⋊Q8C2×D1111yescharacteristic
145#501—222no—
146#500—221no—
147#498—221no—
148#431C2×D1111yescharacteristic
149C2×#108—221no—
150#428—221no—
151#428—221no—
152#423C2×D1111yescharacteristic
153C2×C4⋊C8—111no—
154C2×C4⋊C8—111no—
155C4×M16—111no—
156#341—221no—
157#333—22no—
158#333—221no—
159#332—221no—
160#332—222no—
161Q8⋊C8—222no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11#39411yescharacteristic
165C22×C11#48711yescharacteristic
166C22×C11#49111yescharacteristic
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—82no—
171C4×C11#44811yescharacteristic
172C4×C11#45111yescharacteristic
173C4×C11#46111yescharacteristic
174C4×C11#46211yescharacteristic
175C4×C11#47111yescharacteristic
176C4×C11#47211yescharacteristic
177Dic11—81no—
178Dic11—81no—
179C22×Q8—21no—
180C2×M16—21no—
181C2×M16—111no—
182C2×M16—111no—
183C22×C8—221no—
184C22×C8—221no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8—111no—
189C4⋊Q8—111no—
190C4⋊Q8C22⋊D1112yes—
191#125—221no—
192C22⋊Q8—221no—
193C22⋊Q8—221no—
194C4×Q8—221no—
195C4×Q8—221no—
196#117—221no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C42C22×D1111yescharacteristic
200#108—442no—
201#107—222no—
202#107—222no—
203#106—222no—
204#106—222no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—112no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212C22⋊C8—21no—
213#97—221no—
214C4×C8—21no—
215C4×C8—221no—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11#204311yescharacteristic
219C2×C11#204911yescharacteristic
220C2×C11#205111yescharacteristic
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—81no—
224C2×Q8—81no—
225C2×Q8—221no—
226C2×Q8—221no—
227C22×C4—41no—
228C22×C4#433911yescharacteristic
229C22×C4D4×D1111yescharacteristic
230C22×C4#434111yescharacteristic
231M16—41no—
232M16—41no—
233M16—112no—
234M16—112no—
235M16—221no—
236M16—221no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—221no—
240C2×C8—221no—
241C2×C8—222no—
242C2×C8—441no—
243C2×C8—441no—
244C2×C8—441no—
245C2×C8—881no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C22⋊C4—441no—
257C42—441no—
258C42#433911yescharacteristic
259C42D4×D1111yescharacteristic
260C42D4×D1111yescharacteristic
261C42C2×C22⋊D1111yescharacteristic
262C11#1055611yescharacteristic, complemented, Sylow
263C23#6693811yescharacteristic
264Q8—82no—
265Q8—81no—
266Q8—81no—
267Q8—441no—
268Q8—441no—
269Q8—881no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—82no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4#6693611yescharacteristic
278C2×C4#6693711yescharacteristic
279C2×C4#6693711yescharacteristic
280C2×C4SD16×D1111yescharacteristic
281C2×C4#6696811yescharacteristic
282C2×C4Q16×D1111yescharacteristic
283C2×C4#6697111yescharacteristic
284C2×C4#6698211yescharacteristic
285C2×C4#6699011yescharacteristic
286C2×C4#6699211yescharacteristic
287C8—81no—
288C8—81no—
289C8—222no—
290C8—222no—
291C8—442no—
292C8—881no—
293C22—21no—
294C22—21no—
295C22#1062240511yescharacteristic
296C22#1062241011yescharacteristic
297C22#1062257211yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—82no—
302C4—881no—
303C4—881no—
304C4#1062236111yescharacteristic
305C4#1062236211yescharacteristic
306C4#1062240611yescharacteristic
307C4#1062243111yescharacteristic
308C4#1062278311yescharacteristic
309C4#1062279911yescharacteristic
310C2—21no—
311C2—21no—
312C2#1306986011yescharacteristic
313C2#1306989411yescharacteristic
314C2#1306990811yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#394
prime radicalC23×C11#124
hypercenter#1548D11
hypocenterC11#10556
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
262. C11#10556semidirect

Maximal subgroups

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

subgroupindex
#130791582
#130693892
#130673072
C2×#106221852
#130670202
#130664652
C11×#15482
#1055611