Finite Group Databasebeta

← #14658104

Subgroups — #14658104

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#13067297C211yesmaximal, characteristic
4C2×#10622185C211yesmaximal, 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—21no—
23#10622185—22no—
24#10622184—22no—
25#10622184—21no—
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#10556—111nomaximal, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—22no—
68C2×Q8×C11—41no—
69C2×Q8×C11—81no—
70C2×Q8×C11—81no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C11×M16—21no—
76C11×M16—21no—
77C11×M16SD1612yes—
78C11×M16Q1612yes—
79C2×C8×C11—21no—
80C2×C8×C11—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11—41no—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97#4318—41no—
98#4318—41no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—81no—
106#3165D1111yescharacteristic
107#1950—111no—
108#1550—111no—
109#1548—111no—
110C2×#332—111no—
111#1481—111no—
112#1283—111no—
113C23×C11#12411yescharacteristic
114Q8×C11—41no—
115Q8×C11—41no—
116Q8×C11—81no—
117Q8×C11—82no—
118Q8×C11—81no—
119Q8×C11—81no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—82no—
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11C2×SD1611yescharacteristic
134C2×C4×C11C2×Q1611yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C8×C11—22no—
138C8×C11—22no—
139C11⋊C8—42no—
140C11⋊C8—81no—
141C11⋊C8—81no—
142C11⋊C8—81no—
143#533C2×D1111yescharacteristic
144C2×C4⋊Q8C2×D1111yescharacteristic
145#501—22no—
146#500—21no—
147#498—21no—
148#431—111no—
149C2×#108—221no—
150#428—21no—
151#428—21no—
152#423—111no—
153C2×C4⋊C8—111no—
154C2×C4⋊C8—111no—
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—81no—
171C4×C11—82no—
172C4×C11—81no—
173C4×C11#44811yescharacteristic
174C4×C11#45111yescharacteristic
175C4×C11#46111yescharacteristic
176C4×C11#46211yescharacteristic
177C4×C11#47111yescharacteristic
178C4×C11#47211yescharacteristic
179C22×Q8—21no—
180C2×M16—221no—
181C2×M16C22⋊D1111yescharacteristic
182C2×M16C22⋊D1111yescharacteristic
183C22×C8—221no—
184C22×C8—221no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8C22⋊D1112yes—
189C4⋊Q8C22⋊D1111yescharacteristic
190C4⋊Q8C22⋊D1111yescharacteristic
191#125—21no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194C4×Q8—21no—
195C4×Q8—21no—
196#117—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C42C22×D1111yescharacteristic
200#108—442no—
201#107—22no—
202#107—22no—
203#106—22no—
204#106—22no—
205C4⋊C8—112no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212C22⋊C8—221no—
213#97—21no—
214C4×C8—21no—
215C4×C8—221no—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11#204311yescharacteristic
219C2×C11#204911yescharacteristic
220C2×C11#205111yescharacteristic
221C2×Q8—21no—
222C2×Q8—22no—
223C2×Q8—21no—
224C2×Q8—41no—
225C2×Q8—81no—
226C2×Q8—81no—
227C22×C4—41no—
228C22×C4#434111yescharacteristic
229C22×C4#434111yescharacteristic
230C22×C4C2×C22⋊D1111yescharacteristic
231M16—21no—
232M16—21no—
233M16—441no—
234M16—441no—
235M16#432512yes—
236M16#432612yes—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—222no—
240C2×C8—441no—
241C2×C8—441no—
242C2×C8—441no—
243C2×C8—441no—
244C2×C8—441no—
245C2×C8—881no—
246C4⋊C4—21no—
247C4⋊C4—22no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—22no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C22⋊C4—41no—
257C42—41no—
258C42D4×D1111yescharacteristic
259C42#434111yescharacteristic
260C42C2×C22⋊D1111yescharacteristic
261C42C2×C22⋊D1111yescharacteristic
262C11#1055611yescharacteristic, complemented, Sylow
263C23#6698911yescharacteristic
264Q8—41no—
265Q8—41no—
266Q8—81no—
267Q8—82no—
268Q8—81no—
269Q8—81no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—82no—
277C2×C4#6698811yescharacteristic
278C2×C4#6698811yescharacteristic
279C2×C4#6699111yescharacteristic
280C2×C4#6699211yescharacteristic
281C2×C4#6699211yescharacteristic
282C2×C4C2×#432511yescharacteristic
283C2×C4#6699511yescharacteristic
284C2×C4#6699511yescharacteristic
285C2×C4C2×#432611yescharacteristic
286C2×C4#6700611yescharacteristic
287C8—22no—
288C8—22no—
289C8—442no—
290C8—881no—
291C8—881no—
292C8—881no—
293C22—21no—
294C22—21no—
295C22#1062269411yescharacteristic
296C22#1062269511yescharacteristic
297C22#1062283511yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—81no—
302C4—82no—
303C4—81no—
304C4#1062269611yescharacteristic
305C4#1062270311yescharacteristic
306C4#1062281211yescharacteristic
307C4#1062281311yescharacteristic
308C4#1062284011yescharacteristic
309C4#1062284111yescharacteristic
310C2—21no—
311C2—21no—
312C2#1306985911yescharacteristic
313C2#1306989311yescharacteristic
314C2#1306990511yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3165C2
socleC22×C11#394
prime radicalC23×C11#124
hypercenter#3165D11
hypocenterC11#10556
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
262. C11#10556semidirect

Maximal subgroups

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

subgroupindex
#130693912
#130673062
#130672972
C2×#106221852
#130670192
#130664672
C11×#31652
#1055611