Finite Group Databasebeta

← #14658096

Subgroups — #14658096

Order 2816.

364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078997C211yesmaximal, characteristic
2#13069391C211yesmaximal, characteristic
3#13067304C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic
5C2×#10622124C211yesmaximal, characteristic
6#13067020C211yesmaximal, characteristic
7C11×#1283C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13C2×#66886—21no—
14#10622733—21no—
15#10622733—21no—
16#10622537C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622316—22no—
19#10622294—21no—
20#10622294—21no—
21#10622196—21no—
22#10622124—22no—
23#10622124—22no—
24#10622120—21no—
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#66880—22no—
57#66880—22no—
58#66880—22no—
59#66880—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64#10554—111nomaximal, Sylow
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×Dic11—41no—
69C2×Dic22—22no—
70C2×Dic22—21no—
71C2×Dic22—21no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C11×M16—21no—
78C11×M16—21no—
79C11×M16—21no—
80C11×M16—21no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—81no—
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90C22⋊Dic11—41no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—22no—
95C4⋊Dic11—21no—
96C4⋊Dic11—22no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101C4×Dic11—41no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#3139—111no—
109#1950—111no—
110#1550—111no—
111#1546—111no—
112C2×#332—111no—
113#1481—111no—
114#1283D1111yescharacteristic
115C23×C11#12411yescharacteristic
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12311yescharacteristic
124C2×C4×C11#12311yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—42no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134Dic22—42no—
135Dic22—42no—
136Dic22—41no—
137Dic22—41no—
138Dic22—81no—
139Dic22—81no—
140Dic22—81no—
141C8×C11—41no—
142C8×C11—41no—
143C8×C11—81no—
144C8×C11—81no—
145C11⋊C8—42no—
146C11⋊C8—81no—
147#533—111no—
148C2×C4⋊Q8—111no—
149#491—222no—
150#487—221no—
151#487—221no—
152#431C2×D1111yescharacteristic
153C2×#108—221no—
154#423—111no—
155C2×C4⋊C8—111no—
156C2×C4⋊C8C2×D1111yescharacteristic
157#419—221no—
158#419—221no—
159C4×M16C2×D1111yescharacteristic
160#341—221no—
161#333—221no—
162#332—222no—
163#332—222no—
164#332—221no—
165Q8⋊C8—222no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#39411yescharacteristic
169C22×C11#48811yescharacteristic
170C22×C11#48911yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11#44911yescharacteristic
175C4×C11#45211yescharacteristic
176C4×C11#46311yescharacteristic
177C4×C11#46411yescharacteristic
178C4×C11#47111yescharacteristic
179C4×C11#47311yescharacteristic
180Dic11—81no—
181Dic11—81no—
182Dic11—82no—
183C22×Q8—221no—
184C2×M16—221no—
185C2×M16D4411yescharacteristic
186C2×M16D4411yescharacteristic
187C22×C8—21no—
188C22×C8—221no—
189C4⋊Q8—112no—
190C4⋊Q8—111no—
191C4⋊Q8—111no—
192C4⋊Q8—221no—
193C4⋊Q8—221no—
194C4⋊Q8—221no—
195#125—221no—
196C22⋊Q8—221no—
197C22⋊Q8—221no—
198C4×Q8—221no—
199C4×Q8—221no—
200#117—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C42C22×D1111yescharacteristic
204#108—442no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—112no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212#103—222no—
213#103—222no—
214#103—222no—
215#103—222no—
216C22⋊C8—21no—
217#97—21no—
218C4×C8—21no—
219C4×C8—21no—
220C2×C11—21no—
221C2×C11—21no—
222C2×C11#204211yescharacteristic
223C2×C11#204911yescharacteristic
224C2×C11#205211yescharacteristic
225C2×Q8—222no—
226C2×Q8—221no—
227C2×Q8—221no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×Q8—441no—
231C2×Q8—441no—
232C2×Q8—441no—
233C22×C4—441no—
234C22×C4C2×D4411yescharacteristic
235C22×C4#433911yescharacteristic
236C22×C4#433911yescharacteristic
237M16—21no—
238M16—21no—
239M16—21no—
240M16—21no—
241M16—441no—
242M16—441no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—81no—
248C2×C8—222no—
249C2×C8—441no—
250C2×C8—441no—
251C2×C8—441no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—222no—
255C4⋊C4—221no—
256C4⋊C4—222no—
257C4⋊C4—221no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C22⋊C4—441no—
263C42—441no—
264C42D4×D1111yescharacteristic
265C42D4×D1111yescharacteristic
266C42D4×D1111yescharacteristic
267C42#434311yescharacteristic
268C11#1055411yescharacteristic, complemented, Sylow
269C23#6692811yescharacteristic
270Q8—442no—
271Q8—442no—
272Q8—441no—
273Q8—441no—
274Q8—881no—
275Q8—881no—
276Q8—881no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—442no—
283C2×C4—881no—
284C2×C4—881no—
285C2×C4#6693511yescharacteristic
286C2×C4#6693711yescharacteristic
287C2×C4#6693711yescharacteristic
288C2×C4#6694711yescharacteristic
289C2×C4#6694711yescharacteristic
290C2×C4#6694811yescharacteristic
291C2×C4#6695711yescharacteristic
292C2×C4#6695711yescharacteristic
293C2×C4#6696111yescharacteristic
294C2×C4#6696211yescharacteristic
295C8—41no—
296C8—41no—
297C8—81no—
298C8—81no—
299C8—442no—
300C8—881no—
301C22—21no—
302C22—21no—
303C22#1062228511yescharacteristic
304C22#1062231011yescharacteristic
305C22#1062232711yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—882no—
310C4—881no—
311C4—881no—
312C4#1062234611yescharacteristic
313C4#1062234711yescharacteristic
314C4#1062236111yescharacteristic
315C4#1062236811yescharacteristic
316C4#1062245711yescharacteristic
317C4#1062245811yescharacteristic
318C2—21no—
319C2—21no—
320C2#1306985811yescharacteristic
321C2#1306989911yescharacteristic
322C2#1306991811yescharacteristic
subgroupG/H
centerC22#10622285
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1283C2
socleC22×C11#394
prime radicalC23×C11#124
hypercenter#1283D11
hypocenterC11#10554
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
268. C11#10554semidirect

Maximal subgroups

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

subgroupindex
#130789972
#130693912
#130673042
#130672872
C2×#106221242
#130670202
C11×#12832
#1055411