Finite Group Databasebeta

← #14667017

Subgroups — #14667017

Order 2816.

318 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 57 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#13079512C211yesmaximal, characteristic
2#13070814C211yesmaximal, characteristic, complemented
3#13070799C211yesmaximal, characteristic, complemented
4#13070058C211yesmaximal, characteristic, complemented
5#13066633C211yesmaximal, characteristic, complemented
6#13066541C211yesmaximal, characteristic, complemented
7C11×#1349C211yesmaximal, characteristic, complemented
8#10623139—21no—
9C11×#466C2211yescharacteristic
10#10622771—21no—
11#10622746—21no—
12#10622729C2211yescharacteristic
13#10622723C2211yescharacteristic
14C2×#66882C2211yescharacteristic
15#10622655—21no—
16#10622497—21no—
17#10622396—21no—
18#10622387—21no—
19C11×C22⋊C16C2211yescharacteristic
20C11×#341C2211yescharacteristic
21#10622200—21no—
22#10622192—21no—
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622143—21no—
25#10622141—21no—
26#10622128—21no—
27C2×#4341—21no—
28C2×#4339D411yescharacteristic
29C2×C11×D8D411yescharacteristic
30C2×C11×M16—21no—
31C22×C8×C11C2311yescharacteristic
32C11×#121—21no—
33#66992—41no—
34#66991—21no—
35#66991—41no—
36C2×#4324—21no—
37C2×C4⋊Dic11—21no—
38#66977—21no—
39C2×#4318D411yescharacteristic
40C2×Dic44D411yescharacteristic
41#66950—21no—
42C4⋊C4×D11—21no—
43#66937—41no—
44#66931—41no—
45C2×C11×C16—21no—
46C11×#107D411yescharacteristic
47C11×#102—21no—
48#66896—21no—
49#66885—41no—
50(C2×D11)⋊C8—21no—
51(C2×D11)⋊C8—21no—
52#66882—21no—
53#66882—21no—
54#66882D411yescharacteristic
55#66880—21no—
56#66880—41no—
57C2×C11⋊C16—21no—
58#66874—21no—
59#66871—21no—
60#12285—111nomaximal, Sylow
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—41no—
66C2×C22⋊D11—41no—
67C22×Dic11—41no—
68C22×Dic11—41no—
69#4341—81no—
70#4341—81no—
71#4339—41no—
72#4339—41no—
73C2×D44D811yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—41no—
76C2×Dic22—21no—
77C2×Dic22D811yescharacteristic
78C11×D8—41no—
79C11×M16—41no—
80C11×M16—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11C2×D411yescharacteristic
84C2×C8×C11C2×D411yescharacteristic
85C11×C4⋊C4—21no—
86C11×C22⋊C4—41no—
87C22⋊Dic11—41no—
88C22⋊Dic11—41no—
89#4324—81no—
90(C2×D11)⋊C4—41no—
91C4⋊Dic11—21no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97#4318—41no—
98C2×C11⋊C8—21no—
99Dic44—41no—
100C11×C16—41no—
101C11⋊C16—41no—
102#3203—111no—
103#2235—111no—
104#2233—111no—
105#2078—111no—
106#1350—111no—
107#1349D1111yescharacteristic, complemented
108#1315—111no—
109C23×C11—41no—
110C23×C11AGL(1,ℤ/8)11yescharacteristic
111C22×D11—21no—
112D4×C11—41no—
113D4×C11—41no—
114D4×C11—161no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11C2×D811yescharacteristic
120C22⋊D11—81no—
121C22⋊D11—82no—
122C22⋊D11—161no—
123C2×Dic11—21no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—82no—
127C2×Dic11—81no—
128C2×Dic11—161no—
129D44—41no—
130C4×D11—41no—
131C4×D11—41no—
132C4×D11—161no—
133Dic22—41no—
134Dic22—41no—
135Dic22—41no—
136C8×C11—21no—
137C8×C11—21no—
138C8×C11—81no—
139C11⋊C8—41no—
140#537—221no—
141#484—221no—
142#480—221no—
143#468—221no—
144#467—111no—
145#466C2×D1111yescharacteristic
146#452—221no—
147#449—221no—
148C2×#107—111no—
149#417—221no—
150#408—111no—
151#367—221no—
152#367—221no—
153#358—221no—
154#357—221no—
155C22⋊C16—111no—
156C22⋊C16C2×D1111yescharacteristic
157#343—221no—
158#341C2×D1111yescharacteristic
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—81no—
163C22×C11—81no—
164C22×C11—81no—
165C22×C11#44711yescharacteristic
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C4×C11—21no—
170C4×C11—81no—
171C4×C11#45511yescharacteristic
172C4×C11#45811yescharacteristic
173Dic11—41no—
174Dic11—81no—
175Dic11—81no—
176Dic11—161no—
177C2×#41—111no—
178C2×#41—221no—
179C2×Q16—111no—
180C2×SD16—221no—
181C2×D8D4411yescharacteristic
182C2×M16—21no—
183C2×M16—111no—
184C22×C8C22×D1111yescharacteristic
185C22⋊Q8—221no—
186C22⋊Q8—221no—
187C22⋊Q8—441no—
188#121—21no—
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—221no—
197#107—111no—
198#107—221no—
199#107—221no—
200#107—221no—
201#107D4411yescharacteristic
202#103—221no—
203#103—221no—
204#103—441no—
205#102—21no—
206#102—221no—
207#102—441no—
208C22⋊C8—221no—
209C22⋊C8—221no—
210C2×C11—41no—
211C2×C11—161no—
212C2×C11#160711yescharacteristic
213C2×C11#219311yescharacteristic
214C2×C11#219411yescharacteristic
215D11—81no—
216#41—441no—
217#41—441no—
218#41—881no—
219#41—881no—
220C2×Q8—111no—
221C2×Q8—221no—
222C2×D4—21no—
223C2×D4—41no—
224C2×D4—111no—
225C2×D4—221no—
226C2×D4—441no—
227C2×D4—441no—
228C22×C4—221no—
229C22×C4—441no—
230C22×C4—441no—
231C22×C4—441no—
232C22×C4D4×D1111yescharacteristic
233Q16—441no—
234SD16—881no—
235D8—41no—
236M16—41no—
237M16—41no—
238M16—441no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—221no—
242C2×C8C2×D4411yescharacteristic
243C2×C8D4×D1111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—221no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C4⋊C4—441no—
250C4⋊C4—441no—
251C22⋊C4—41no—
252C22⋊C4—441no—
253C22⋊C4—441no—
254C22⋊C4—441no—
255C16—41no—
256C16—441no—
257C11#1228511yescharacteristic, complemented, Sylow
258C23—41no—
259C23—221no—
260C23#6696711yescharacteristic
261Q8—441no—
262Q8—441no—
263Q8—441no—
264D4—41no—
265D4—41no—
266D4—161no—
267D4—441no—
268D4—881no—
269D4—882no—
270D4—1761no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—221no—
275C2×C4—441no—
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×C4D8×D1111yescharacteristic
285C8—21no—
286C8—21no—
287C8—81no—
288C8—441no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—81no—
293C22—81no—
294C22—81no—
295C22—441no—
296C22—441no—
297C22—441no—
298C22#1062238611yescharacteristic
299C4—21no—
300C4—81no—
301C4—441no—
302C4—881no—
303C4—881no—
304C4—1761no—
305C4#1062235511yescharacteristic
306C4#1062243811yescharacteristic
307C2—41no—
308C2—161no—
309C2—881no—
310C2#1306760311yescharacteristic
311C2#1307058111yescharacteristic
312C2#1307059011yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1349C2
socleC22×C11#447
prime radical#13079512C2
hypercenter#1349D11
hypocenterC11#12285
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1349

Complements

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

NH ≅ G/Ntype
2. #13070814C2semidirect
3. #13070799C2semidirect
4. #13070058C2semidirect
5. #13066633C2semidirect
6. #13066541C2semidirect
7. C11×#1349C2semidirect
107. #1349D11semidirect
257. C11#12285semidirect

Maximal subgroups

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

subgroupindex
#130795122
#130708142
#130707992
#130700582
#130666332
#130665412
C11×#13492
#1228511