Finite Group Databasebeta

← #14658101

Subgroups — #14658101

Order 2816.

364 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 99 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#13069392C211yesmaximal, characteristic
3#13067304C211yesmaximal, characteristic
4#13067301C211yesmaximal, characteristic
5#13067018C211yesmaximal, characteristic
6#13066466C211yesmaximal, characteristic
7C2×C11×#333C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66883—21no—
13#10622693—22no—
14#10622692—21no—
15#10622691—21no—
16#10622577—21no—
17#10622577—21no—
18#10622538C2211yescharacteristic
19#10622537C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21C11×#333—22no—
22#10622190—21no—
23#10622185—22no—
24#10622122—22no—
25#10622120—21no—
26#10622119—21no—
27C22×Q8×C11—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8D412yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37#66979—21no—
38#66977—21no—
39#66977—21no—
40C2×#4318—21no—
41C2×#4318D411yescharacteristic
42C2×#4318D411yescharacteristic
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×C4⋊C8D412yes—
52C22⋊(C11⋊C8)—21no—
53#66883—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—
61#66867—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#10555—111nomaximal, Sylow
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—82no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×C8×C11—22no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—81no—
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#4318—41no—
98#4318—41no—
99#4318SD1612yes—
100#4318Q1612yes—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#3165—111no—
106#1950—111no—
107#1550—111no—
108#1549—111no—
109C2×#333D1111yescharacteristic
110#1481—111no—
111#1283—111no—
112C23×C11#12411yescharacteristic
113Q8×C11—82no—
114Q8×C11—82no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—82no—
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11#12311yescharacteristic
125C2×C4×C11#12311yescharacteristic
126C2×C4×C11C2×SD1611yescharacteristic
127C2×C4×C11C2×Q1611yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×Dic11—41no—
131C2×Dic11—41no—
132Dic22—41no—
133Dic22—41no—
134Dic22—81no—
135C8×C11—42no—
136C8×C11—81no—
137C11⋊C8—22no—
138C11⋊C8—22no—
139C11⋊C8—81no—
140C11⋊C8—81no—
141#533—111no—
142C2×C4⋊Q8C2×D1111yescharacteristic
143#501—222no—
144#500—221no—
145#498—221no—
146#431—111no—
147C2×#108—221no—
148#428—221no—
149#428—221no—
150#423—111no—
151C2×C4⋊C8C2×D1111yescharacteristic
152C2×C4⋊C8C2×D1111yescharacteristic
153C4×M16—111no—
154#341—221no—
155#333—22no—
156#333—221no—
157#332—221no—
158#332—222no—
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—82no—
169C4×C11#44811yescharacteristic
170C4×C11#45111yescharacteristic
171C4×C11#46111yescharacteristic
172C4×C11#46211yescharacteristic
173C4×C11#47111yescharacteristic
174C4×C11#47311yescharacteristic
175Dic11—81no—
176Dic11—81no—
177C22×Q8—21no—
178C2×M16—111no—
179C2×M16—111no—
180C2×M16—221no—
181C22×C8—21no—
182C22×C8—21no—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—111no—
187C4⋊Q8—111no—
188C4⋊Q8D4412yes—
189#125—221no—
190C22⋊Q8—221no—
191C22⋊Q8—221no—
192C4×Q8—221no—
193C4×Q8—221no—
194#117—221no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
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—221no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C4⋊C8C22⋊D1112yes—
210C22⋊C8—221no—
211#97—221no—
212C4×C8—221no—
213C4×C8—221no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#204311yescharacteristic
217C2×C11#204811yescharacteristic
218C2×C11#205211yescharacteristic
219C2×Q8—22no—
220C2×Q8—41no—
221C2×Q8—82no—
222C2×Q8—221no—
223C2×Q8—221no—
224C22×C4—41no—
225C22×C4#433911yescharacteristic
226C22×C4D4×D1111yescharacteristic
227C22×C4#434111yescharacteristic
228M16—112no—
229M16—112no—
230M16—221no—
231M16—221no—
232M16—441no—
233M16—441no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—81no—
239C2×C8—221no—
240C2×C8—221no—
241C2×C8—441no—
242C2×C8—441no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C22⋊C4—441no—
254C42—441no—
255C42C2×D4411yescharacteristic
256C42D4×D1111yescharacteristic
257C42#434111yescharacteristic
258C42C2×C22⋊D1111yescharacteristic
259C11#1055511yescharacteristic, complemented, Sylow
260C23#6693811yescharacteristic
261Q8—82no—
262Q8—82no—
263Q8—441no—
264Q8—441no—
265Q8—881no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—82no—
271C2×C4—441no—
272C2×C4—441no—
273C2×C4#6693511yescharacteristic
274C2×C4#6693611yescharacteristic
275C2×C4#6693911yescharacteristic
276C2×C4SD16×D1111yescharacteristic
277C2×C4#6696811yescharacteristic
278C2×C4Q16×D1111yescharacteristic
279C2×C4#6697111yescharacteristic
280C2×C4#6698311yescharacteristic
281C2×C4#6699111yescharacteristic
282C2×C4#6699211yescharacteristic
283C8—42no—
284C8—81no—
285C8—222no—
286C8—222no—
287C8—881no—
288C8—881no—
289C22—21no—
290C22—21no—
291C22#1062240511yescharacteristic
292C22#1062241011yescharacteristic
293C22#1062257411yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—82no—
298C4—881no—
299C4—881no—
300C4#1062241911yescharacteristic
301C4#1062242111yescharacteristic
302C4#1062277511yescharacteristic
303C4#1062279011yescharacteristic
304C4#1062279511yescharacteristic
305C4#1062280511yescharacteristic
306C2—21no—
307C2—21no—
308C2#1306986111yescharacteristic
309C2#1306988811yescharacteristic
310C2#1306991611yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#333C2
socleC22×C11#394
prime radicalC23×C11#124
hypercenterC2×#333D11
hypocenterC11#10555
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

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
#130791582
#130693922
#130673042
#130673012
#130670182
#130664662
C2×C11×#3332
#1055511