Finite Group Databasebeta

← #14658097

Subgroups — #14658097

Order 2816.

364 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 105 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#13069391C211yesmaximal, characteristic
2#13067306C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic
4C2×#10622184C211yesmaximal, characteristic
5#13067019C211yesmaximal, characteristic
6#13066467C211yesmaximal, characteristic
7C11×#3165C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#501—22no—
11C11×#500—21no—
12C11×#498—21no—
13C11×#428—21no—
14C11×#428—21no—
15C4×C11×M16C2211yescharacteristic
16C2×#66886—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622196—21no—
22#10622185—22no—
23#10622185—21no—
24#10622184—21no—
25#10622184—22no—
26Q8⋊(C11⋊C8)—22no—
27C22×Q8×C11—21no—
28C2×C11×M16D411yescharacteristic
29C2×C11×M16D411yescharacteristic
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8D411yescharacteristic
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D412yes—
36C11×#125—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C11×#117—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4318—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48C11×#107—22no—
49C11×#107—22no—
50C11×#106—22no—
51C11×#106—22no—
52C11×#97—21no—
53C4×C8×C11—21no—
54C22⋊(C11⋊C8)—21no—
55#66886—42no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)D412yes—
63C4×C11⋊C8—21no—
64#10555—111nomaximal, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11—22no—
67C2×Q8×C11—21no—
68C2×Q8×C11—41no—
69C2×Q8×C11—82no—
70C22×C4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C11×M16—21no—
75C11×M16—21no—
76C11×M16SD1612yes—
77C11×M16Q1612yes—
78C2×C8×C11—21no—
79C2×C8×C11—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C42×C11—41no—
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96#4318—41no—
97#4318—41no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—81no—
105#3165D1111yescharacteristic
106#1950—111no—
107#1550—111no—
108#1549—111no—
109C2×#333—111no—
110#1481—111no—
111#1283—111no—
112C23×C11#12411yescharacteristic
113Q8×C11—41no—
114Q8×C11—41no—
115Q8×C11—81no—
116Q8×C11—82no—
117Q8×C11—82no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—82no—
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12311yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C2×C4×C11C2×SD1611yescharacteristic
132C2×C4×C11C2×Q1611yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C8×C11—22no—
136C8×C11—22no—
137C11⋊C8—42no—
138C11⋊C8—81no—
139C11⋊C8—81no—
140C11⋊C8—81no—
141#533C2×D1111yescharacteristic
142C2×C4⋊Q8C2×D1111yescharacteristic
143#501—22no—
144#500—21no—
145#498—21no—
146#431—111no—
147C2×#108—221no—
148#428—21no—
149#428—21no—
150#423—111no—
151C2×C4⋊C8—111no—
152C2×C4⋊C8—111no—
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—82no—
169C4×C11—81no—
170C4×C11—81no—
171C4×C11#44811yescharacteristic
172C4×C11#45111yescharacteristic
173C4×C11#46111yescharacteristic
174C4×C11#46211yescharacteristic
175C4×C11#47111yescharacteristic
176C4×C11#47311yescharacteristic
177C22×Q8—21no—
178C2×M16—221no—
179C2×M16C22⋊D1111yescharacteristic
180C2×M16C22⋊D1111yescharacteristic
181C22×C8—221no—
182C22×C8—221no—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8C22⋊D1112yes—
187C4⋊Q8C22⋊D1111yescharacteristic
188C4⋊Q8C22⋊D1111yescharacteristic
189#125—21no—
190C22⋊Q8—21no—
191C22⋊Q8—21no—
192C4×Q8—21no—
193C4×Q8—21no—
194#117—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C42C22×D1111yescharacteristic
198#108—442no—
199#107—22no—
200#107—22no—
201#106—22no—
202#106—22no—
203C4⋊C8—112no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C22⋊C8—221no—
211#97—21no—
212C4×C8—21no—
213C4×C8—221no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#204311yescharacteristic
217C2×C11#204811yescharacteristic
218C2×C11#205211yescharacteristic
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—82no—
224C22×C4—41no—
225C22×C4#434111yescharacteristic
226C22×C4#434111yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228M16—21no—
229M16—21no—
230M16—441no—
231M16—441no—
232M16#432512yes—
233M16#432612yes—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—222no—
237C2×C8—441no—
238C2×C8—441no—
239C2×C8—441no—
240C2×C8—441no—
241C2×C8—441no—
242C2×C8—881no—
243C4⋊C4—22no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—22no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C22⋊C4—41no—
254C42—41no—
255C42D4×D1111yescharacteristic
256C42#434111yescharacteristic
257C42C2×C22⋊D1111yescharacteristic
258C42C2×C22⋊D1111yescharacteristic
259C11#1055511yescharacteristic, complemented, Sylow
260C23#6698911yescharacteristic
261Q8—41no—
262Q8—41no—
263Q8—81no—
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—82no—
273C2×C4#6698811yescharacteristic
274C2×C4#6698811yescharacteristic
275C2×C4#6699111yescharacteristic
276C2×C4#6699211yescharacteristic
277C2×C4#6699211yescharacteristic
278C2×C4C2×#432511yescharacteristic
279C2×C4#6699511yescharacteristic
280C2×C4#6699511yescharacteristic
281C2×C4C2×#432611yescharacteristic
282C2×C4#6700611yescharacteristic
283C8—22no—
284C8—22no—
285C8—442no—
286C8—881no—
287C8—881no—
288C8—881no—
289C22—21no—
290C22—21no—
291C22#1062269411yescharacteristic
292C22#1062269511yescharacteristic
293C22#1062283511yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—82no—
298C4—81no—
299C4—81no—
300C4#1062269611yescharacteristic
301C4#1062270311yescharacteristic
302C4#1062281611yescharacteristic
303C4#1062281711yescharacteristic
304C4#1062284011yescharacteristic
305C4#1062284111yescharacteristic
306C2—21no—
307C2—21no—
308C2#1306985911yescharacteristic
309C2#1306988611yescharacteristic
310C2#1306991211yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3165C2
socleC22×C11#394
prime radicalC23×C11#124
hypercenter#3165D11
hypocenterC11#10555
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

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
#130693912
#130673062
#130673012
C2×#106221842
#130670192
#130664672
C11×#31652
#1055511