Finite Group Databasebeta

← #14667018

Subgroups — #14667018

Order 2816.

318 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 59 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#13079518C211yesmaximal, characteristic
2#13070814C211yesmaximal, characteristic, complemented
3#13070802C211yesmaximal, characteristic, complemented
4#13070056C211yesmaximal, characteristic, complemented
5#13066635C211yesmaximal, characteristic, complemented
6#13066632C211yesmaximal, characteristic, complemented
7C11×#1315C211yesmaximal, characteristic, complemented
8#10623364—21no—
9C11×#408C2211yescharacteristic
10#10622845—21no—
11#10622747—21no—
12#10622729C2211yescharacteristic
13#10622728C2211yescharacteristic
14C2×#66882C2211yescharacteristic
15#10622349—21no—
16#10622347—21no—
17#10622346—21no—
18#10622335—21no—
19C11×C22⋊C16C2211yescharacteristic
20C11×C22⋊C16C2211yescharacteristic
21#10622192—21no—
22#10622190C2211yescharacteristic
23#10622147—21no—
24#10622143—21no—
25#10622143—21no—
26#10622141—21no—
27C2×C11×#41D411yescharacteristic
28C2×#4339—21no—
29C2×C11×M16D411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31#66999—41no—
32#66992—41no—
33#66992—41no—
34#66991—41no—
35#66983—21no—
36#66983—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39#66977—21no—
40#66977—21no—
41C2×#4318—21no—
42C2×Dic44D411yescharacteristic
43C2×D88D411yescharacteristic
44C2×#4314—21no—
45C2×C11×C16—21no—
46C2×C11×C16—21no—
47C11×C22⋊C8—21no—
48C11×C22⋊C8—21no—
49#66899—41no—
50#66896—41no—
51#66885—21no—
52#66885—21no—
53#66882—21no—
54#66882—21no—
55#66882—21no—
56#66882D411yescharacteristic
57#66882D411yescharacteristic
58#66880—21no—
59#66880—21no—
60#12285—111nomaximal, Sylow
61C11×#41—41no—
62C11×#41—41no—
63C2×Q8×C11D811yescharacteristic
64C2×D4×C11—21no—
65C2×D4×C11D811yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C2×C22⋊D11—41no—
69C2×C22⋊D11—41no—
70C2×C22⋊D11—41no—
71C22×Dic11—41no—
72C22×Dic11—41no—
73#4339—81no—
74#4339—81no—
75C2×D44—21no—
76C2×C4×D11—41no—
77C2×Dic22—21no—
78C11×M16—41no—
79C2×C8×C11—21no—
80C2×C8×C11—41no—
81C2×C8×C11C2×D411yescharacteristic
82C2×C8×C11C2×D411yescharacteristic
83C22⋊Dic11—41no—
84C22⋊Dic11—41no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94#4318—41no—
95#4318—41no—
96C2×C11⋊C8—41no—
97Dic44—41no—
98D88—41no—
99#4314—81no—
100C11×C16—41no—
101C11×C16—41no—
102#3203—111no—
103#2235—111no—
104#2233—111no—
105#2078—111no—
106#1350—111no—
107#1349—111no—
108#1315D1111yescharacteristic, complemented
109C23×C11—21no—
110C23×C11AGL(1,ℤ/8)11yescharacteristic
111C22×D11—41no—
112Q8×C11—41no—
113D4×C11—41no—
114D4×C11—81no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11C2×D811yescharacteristic
122C22⋊D11—82no—
123C22⋊D11—161no—
124C22⋊D11—161no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—81no—
129C2×Dic11—161no—
130C2×Dic11—161no—
131D44—41no—
132D44—41no—
133C4×D11—82no—
134Dic22—41no—
135Dic22—41no—
136C8×C11—21no—
137C8×C11—21no—
138C8×C11—41no—
139C11⋊C8—81no—
140#537—221no—
141#484—221no—
142#480—221no—
143#468—221no—
144#467—111no—
145#466—111no—
146#452—221no—
147#449—221no—
148C2×#107—111no—
149#417—221no—
150#408C2×D1111yescharacteristic
151#367—221no—
152#367—221no—
153#358—221no—
154#357—221no—
155C22⋊C16C2×D1111yescharacteristic
156C22⋊C16C2×D1111yescharacteristic
157#343—221no—
158#341—111no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11#44711yescharacteristic
166C2×D11—81no—
167C2×D11—81no—
168C2×D11—81no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11#45511yescharacteristic
172C4×C11#45811yescharacteristic
173Dic11—81no—
174Dic11—81no—
175Dic11—81no—
176Dic11—161no—
177C2×#41—221no—
178C2×#41D4411yescharacteristic
179C2×Q16—111no—
180C2×SD16—221no—
181C2×D8—111no—
182C2×M16—221no—
183C2×M16D4411yescharacteristic
184C22×C8C22×D1111yescharacteristic
185C22⋊Q8—221no—
186C22⋊Q8—221no—
187C22⋊Q8—441no—
188#121—221no—
189#121—221no—
190#121—441no—
191#121—441no—
192#121—441no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4—221no—
195C2×C16—21no—
196C2×C16—21no—
197#107—111no—
198#107—111no—
199#107—221no—
200#107—221no—
201#107—221no—
202#103—221no—
203#103—221no—
204#103—441no—
205#102—221no—
206#102—221no—
207#102—441no—
208C22⋊C8—21no—
209C22⋊C8—21no—
210C2×C11—41no—
211C2×C11—81no—
212C2×C11#160711yescharacteristic
213C2×C11#219311yescharacteristic
214C2×C11#219411yescharacteristic
215D11—161no—
216#41—41no—
217#41—41no—
218#41—881no—
219#41—881no—
220C2×Q8—221no—
221C2×Q8D8811yescharacteristic
222C2×D4—21no—
223C2×D4—221no—
224C2×D4—441no—
225C2×D4—441no—
226C2×D4—441no—
227C2×D4D8811yescharacteristic
228C22×C4—21no—
229C22×C4—441no—
230C22×C4—441no—
231C22×C4—441no—
232C22×C4C2×D4411yescharacteristic
233Q16—441no—
234SD16—881no—
235D8—441no—
236M16—41no—
237M16—441no—
238M16—441no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—441no—
242C2×C8D4×D1111yescharacteristic
243C2×C8D4×D1111yescharacteristic
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C4⋊C4—441no—
250C4⋊C4—441no—
251C22⋊C4—441no—
252C22⋊C4—441no—
253C22⋊C4—441no—
254C22⋊C4—441no—
255C16—41no—
256C16—41no—
257C11#1228511yescharacteristic, complemented, Sylow
258C23—21no—
259C23—441no—
260C23#6696111yescharacteristic
261Q8—41no—
262Q8—441no—
263Q8—441no—
264D4—41no—
265D4—81no—
266D4—441no—
267D4—441no—
268D4—882no—
269D4—1761no—
270D4—1761no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—882no—
280C2×C4—881no—
281C2×C4—1761no—
282C2×C4—1761no—
283C2×C4#6693511yescharacteristic
284C2×C4C2×D8811yescharacteristic
285C8—21no—
286C8—21no—
287C8—41no—
288C8—881no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—881no—
296C22—881no—
297C22—881no—
298C22#1062234511yescharacteristic
299C4—21no—
300C4—41no—
301C4—881no—
302C4—881no—
303C4—881no—
304C4—1761no—
305C4#1062235511yescharacteristic
306C4#1062235911yescharacteristic
307C2—41no—
308C2—81no—
309C2—1761no—
310C2#1306760411yescharacteristic
311C2#1307058211yescharacteristic
312C2#1307058911yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1315C2
socleC22×C11#447
prime radical#13079518C2
hypercenter#1315D11
hypocenterC11#12285
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #408 ◁ #1315

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13070814C2semidirect
3. #13070802C2semidirect
4. #13070056C2semidirect
5. #13066635C2semidirect
6. #13066632C2semidirect
7. C11×#1315C2semidirect
108. #1315D11semidirect
257. C11#12285semidirect

Maximal subgroups

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

subgroupindex
#130795182
#130708142
#130708022
#130700562
#130666352
#130666322
C11×#13152
#1228511