Finite Group Databasebeta

← #14658110

Subgroups — #14658110

Order 2816.

364 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079162C211yesmaximal, characteristic
2#13069391C211yesmaximal, characteristic
3#13067304C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic
5C2×#10622120C211yesmaximal, characteristic
6#13067020C211yesmaximal, characteristic
7C11×#1283C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13C2×#66886—21no—
14#10622734—21no—
15#10622734—21no—
16#10622537C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622315—22no—
19#10622295—21no—
20#10622293—21no—
21#10622196—21no—
22#10622120—21no—
23#10622120—22no—
24#10622119—22no—
25#10622119—21no—
26#10622094—22no—
27C22×Dic22—21no—
28C2×C11×M16D411yescharacteristic
29C2×C11×M16D411yescharacteristic
30C22×C8×C11—21no—
31C2×C42×C11C2311yescharacteristic
32#66979—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35#66977—21no—
36#66977—21no—
37C2×#4318—21no—
38C22×C11⋊C8—21no—
39#66923—21no—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922D412yes—
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—
52C11×#97—21no—
53C4×C8×C11—21no—
54C4×C8×C11—21no—
55#66886—42no—
56#66882—22no—
57#66882—22no—
58#66881—22no—
59#66881—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64#10556—111nomaximal, Sylow
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×Dic11—41no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×Dic22—22no—
72C2×Dic22—41no—
73C2×Dic22—81no—
74C2×Dic22—81no—
75C11×M16—21no—
76C11×M16—21no—
77C11×M16SD1612yes—
78C11×M16Q1612yes—
79C2×C8×C11—21no—
80C2×C8×C11—21no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11—81no—
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11#4111yescharacteristic
88C22⋊Dic11—41no—
89C4⋊Dic11—21no—
90C4⋊Dic11—22no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—22no—
94C4⋊Dic11—21no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C4×Dic11—41no—
100#4318—41no—
101#4318—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#3165—111no—
107#1950—111no—
108#1550—111no—
109#1548—111no—
110C2×#332—111no—
111#1481—111no—
112#1283D1111yescharacteristic
113C23×C11#12411yescharacteristic
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—41no—
117C2×C4×C11#12011yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12111yescharacteristic
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11#12311yescharacteristic
122C2×C4×C11#12311yescharacteristic
123C2×C4×C11C2×SD1611yescharacteristic
124C2×C4×C11C2×Q1611yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—42no—
130C2×Dic11—82no—
131Dic22—41no—
132Dic22—41no—
133Dic22—81no—
134Dic22—81no—
135Dic22—81no—
136Dic22—82no—
137C8×C11—22no—
138C8×C11—22no—
139C8×C11—81no—
140C8×C11—81no—
141C11⋊C8—42no—
142C11⋊C8—81no—
143#533—111no—
144C2×C4⋊Q8—111no—
145#501—222no—
146#500—221no—
147#498—221no—
148#431C2×D1111yescharacteristic
149C2×#108—221no—
150#428—221no—
151#428—221no—
152#423—111no—
153C2×C4⋊C8—111no—
154C2×C4⋊C8C2×D1111yescharacteristic
155C4×M16C2×D1111yescharacteristic
156#341—221no—
157#333—222no—
158#333—221no—
159#332—222no—
160#332—221no—
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#44811yescharacteristic
171C4×C11#45111yescharacteristic
172C4×C11#46111yescharacteristic
173C4×C11#46211yescharacteristic
174C4×C11#47111yescharacteristic
175C4×C11#47211yescharacteristic
176Dic11—81no—
177Dic11—81no—
178Dic11—82no—
179C22×Q8—221no—
180C2×M16—221no—
181C2×M16D4411yescharacteristic
182C2×M16D4411yescharacteristic
183C22×C8—21no—
184C22×C8—221no—
185C4⋊Q8—112no—
186C4⋊Q8—111no—
187C4⋊Q8—111no—
188C4⋊Q8—221no—
189C4⋊Q8—221no—
190C4⋊Q8—221no—
191#125—221no—
192C22⋊Q8—221no—
193C22⋊Q8—221no—
194C4×Q8—221no—
195C4×Q8—221no—
196#117—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
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—21no—
214C4×C8—21no—
215C4×C8—21no—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11#204311yescharacteristic
219C2×C11#204911yescharacteristic
220C2×C11#205111yescharacteristic
221C2×Q8—221no—
222C2×Q8—221no—
223C2×Q8—222no—
224C2×Q8—441no—
225C2×Q8—881no—
226C2×Q8—881no—
227C22×C4—441no—
228C22×C4C2×D4411yescharacteristic
229C22×C4#433911yescharacteristic
230C22×C4#433911yescharacteristic
231M16—21no—
232M16—21no—
233M16—441no—
234M16—441no—
235M16#431412yes—
236M16Dic4412yes—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—81no—
242C2×C8—222no—
243C2×C8—441no—
244C2×C8—441no—
245C2×C8—441no—
246C4⋊C4—221no—
247C4⋊C4—222no—
248C4⋊C4—221no—
249C4⋊C4—222no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C22⋊C4—441no—
257C42—441no—
258C42D4×D1111yescharacteristic
259C42D4×D1111yescharacteristic
260C42D4×D1111yescharacteristic
261C42#434311yescharacteristic
262C11#1055611yescharacteristic, complemented, Sylow
263C23#6692811yescharacteristic
264Q8—441no—
265Q8—441no—
266Q8—882no—
267Q8—881no—
268Q8—881no—
269Q8—881no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—441no—
274C2×C4—441no—
275C2×C4—442no—
276C2×C4—882no—
277C2×C4#6693511yescharacteristic
278C2×C4#6693711yescharacteristic
279C2×C4#6693711yescharacteristic
280C2×C4#6694711yescharacteristic
281C2×C4#6694711yescharacteristic
282C2×C4#6694811yescharacteristic
283C2×C4C2×#431411yescharacteristic
284C2×C4C2×Dic4411yescharacteristic
285C2×C4#6696211yescharacteristic
286C2×C4#6696211yescharacteristic
287C8—22no—
288C8—22no—
289C8—81no—
290C8—81no—
291C8—442no—
292C8—881no—
293C22—21no—
294C22—21no—
295C22#1062228511yescharacteristic
296C22#1062229411yescharacteristic
297C22#1062231611yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—881no—
302C4—882no—
303C4—881no—
304C4#1062235111yescharacteristic
305C4#1062235211yescharacteristic
306C4#1062236211yescharacteristic
307C4#1062236711yescharacteristic
308C4#1062245411yescharacteristic
309C4#1062246211yescharacteristic
310C2—21no—
311C2—21no—
312C2#1306986311yescharacteristic
313C2#1306989911yescharacteristic
314C2#1306991111yescharacteristic
subgroupG/H
centerC22#10622285
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1283C2
socleC22×C11#394
prime radicalC23×C11#124
hypercenter#1283D11
hypocenterC11#10556
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1283

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
#130791622
#130693912
#130673042
#130672962
C2×#106221202
#130670202
C11×#12832
#1055611