Finite Group Databasebeta

← #14658103

Subgroups — #14658103

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#13067300C211yesmaximal, characteristic
5C2×#10622119C211yesmaximal, 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—22no—
23#10622120—21no—
24#10622119—21no—
25#10622119—22no—
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#10555—111nomaximal, Sylow
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×Dic11—41no—
69C2×Dic22—21no—
70C2×Dic22—22no—
71C2×Dic22—21no—
72C2×Dic22—41no—
73C2×Dic22—82no—
74C11×M16—21no—
75C11×M16—21no—
76C11×M16SD1612yes—
77C11×M16Q1612yes—
78C2×C8×C11—21no—
79C2×C8×C11—21no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—81no—
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11#4111yescharacteristic
87C22⋊Dic11—41no—
88C4⋊Dic11—21no—
89C4⋊Dic11—22no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—22no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98C4×Dic11—41no—
99#4318—41no—
100#4318—41no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#3165—111no—
106#1950—111no—
107#1550—111no—
108#1549—111no—
109C2×#333—111no—
110#1481—111no—
111#1283D1111yescharacteristic
112C23×C11#12411yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11#12011yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12111yescharacteristic
120C2×C4×C11#12311yescharacteristic
121C2×C4×C11#12311yescharacteristic
122C2×C4×C11C2×SD1611yescharacteristic
123C2×C4×C11C2×Q1611yescharacteristic
124C2×C4×C11#13711yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—42no—
129C2×Dic11—82no—
130Dic22—41no—
131Dic22—41no—
132Dic22—82no—
133Dic22—81no—
134Dic22—82no—
135C8×C11—22no—
136C8×C11—22no—
137C8×C11—81no—
138C8×C11—81no—
139C11⋊C8—42no—
140C11⋊C8—81no—
141#533—111no—
142C2×C4⋊Q8—111no—
143#501—222no—
144#500—221no—
145#498—221no—
146#431C2×D1111yescharacteristic
147C2×#108—221no—
148#428—221no—
149#428—221no—
150#423—111no—
151C2×C4⋊C8—111no—
152C2×C4⋊C8C2×D1111yescharacteristic
153C4×M16C2×D1111yescharacteristic
154#341—221no—
155#333—222no—
156#333—221no—
157#332—222no—
158#332—221no—
159Q8⋊C8—222no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11#39411yescharacteristic
163C22×C11#48711yescharacteristic
164C22×C11#49111yescharacteristic
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11#44811yescharacteristic
169C4×C11#45111yescharacteristic
170C4×C11#46111yescharacteristic
171C4×C11#46211yescharacteristic
172C4×C11#47111yescharacteristic
173C4×C11#47311yescharacteristic
174Dic11—82no—
175Dic11—81no—
176Dic11—81no—
177C22×Q8—221no—
178C2×M16—221no—
179C2×M16D4411yescharacteristic
180C2×M16D4411yescharacteristic
181C22×C8—21no—
182C22×C8—221no—
183C4⋊Q8—112no—
184C4⋊Q8—111no—
185C4⋊Q8—111no—
186C4⋊Q8—221no—
187C4⋊Q8—221no—
188C4⋊Q8—221no—
189#125—221no—
190C22⋊Q8—221no—
191C22⋊Q8—221no—
192C4×Q8—221no—
193C4×Q8—221no—
194#117—221no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C42C22×D1111yescharacteristic
198#108—442no—
199#107—222no—
200#107—222no—
201#106—222no—
202#106—222no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—112no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C22⋊C8—21no—
211#97—21no—
212C4×C8—21no—
213C4×C8—21no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#204311yescharacteristic
217C2×C11#204811yescharacteristic
218C2×C11#205211yescharacteristic
219C2×Q8—221no—
220C2×Q8—222no—
221C2×Q8—221no—
222C2×Q8—441no—
223C2×Q8—882no—
224C22×C4—441no—
225C22×C4C2×D4411yescharacteristic
226C22×C4#433911yescharacteristic
227C22×C4#433911yescharacteristic
228M16—21no—
229M16—21no—
230M16—441no—
231M16—441no—
232M16#431412yes—
233M16Dic4412yes—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—81no—
239C2×C8—222no—
240C2×C8—441no—
241C2×C8—441no—
242C2×C8—441no—
243C4⋊C4—221no—
244C4⋊C4—222no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—222no—
248C4⋊C4—221no—
249C4⋊C4—441no—
250C4⋊C4—441no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C22⋊C4—441no—
254C42—441no—
255C42D4×D1111yescharacteristic
256C42D4×D1111yescharacteristic
257C42D4×D1111yescharacteristic
258C42#434311yescharacteristic
259C11#1055511yescharacteristic, complemented, Sylow
260C23#6692811yescharacteristic
261Q8—441no—
262Q8—441no—
263Q8—882no—
264Q8—881no—
265Q8—882no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—441no—
270C2×C4—441no—
271C2×C4—442no—
272C2×C4—882no—
273C2×C4#6693511yescharacteristic
274C2×C4#6693711yescharacteristic
275C2×C4#6693711yescharacteristic
276C2×C4#6694711yescharacteristic
277C2×C4#6694711yescharacteristic
278C2×C4#6694811yescharacteristic
279C2×C4C2×#431411yescharacteristic
280C2×C4C2×Dic4411yescharacteristic
281C2×C4#6696211yescharacteristic
282C2×C4#6696211yescharacteristic
283C8—22no—
284C8—22no—
285C8—81no—
286C8—81no—
287C8—442no—
288C8—881no—
289C22—21no—
290C22—21no—
291C22#1062228511yescharacteristic
292C22#1062229411yescharacteristic
293C22#1062231611yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—882no—
298C4—881no—
299C4—881no—
300C4#1062235111yescharacteristic
301C4#1062235211yescharacteristic
302C4#1062236111yescharacteristic
303C4#1062236811yescharacteristic
304C4#1062245411yescharacteristic
305C4#1062246211yescharacteristic
306C2—21no—
307C2—21no—
308C2#1306986311yescharacteristic
309C2#1306989211yescharacteristic
310C2#1306991811yescharacteristic
subgroupG/H
centerC22#10622285
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1283C2
socleC22×C11#394
prime radicalC23×C11#124
hypercenter#1283D11
hypocenterC11#10555
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
259. C11#10555semidirect

Maximal subgroups

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

subgroupindex
#130791622
#130693912
#130673042
#130673002
C2×#106221192
#130670202
C11×#12832
#1055511