Finite Group Databasebeta

← #14667013

Subgroups — #14667013

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#13070813C211yesmaximal, characteristic, complemented
3#13070057C211yesmaximal, characteristic, complemented
4#13066635C211yesmaximal, characteristic, complemented
5#13066631C211yesmaximal, characteristic, complemented
6#13066541C211yesmaximal, characteristic, complemented
7C11×#2233C211yesmaximal, characteristic, complemented
8#10623139—21no—
9C11×#466C2211yescharacteristic
10C2×C11×#107C2211yescharacteristic
11#10622771—21no—
12#10622729C2211yescharacteristic
13#10622723C2211yescharacteristic
14#10622655—21no—
15#10622579—21no—
16#10622497—21no—
17#10622396—21no—
18#10622387—21no—
19C11×#367—21no—
20C11×#357—21no—
21C11×C22⋊C16C2211yescharacteristic
22#10622190C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622168—21no—
25#10622130—21no—
26#10622128—21no—
27C2×#4341—21no—
28C2×#4339D411yescharacteristic
29C2×C11×D8D411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C11×#121—21no—
32C2×C11×C4⋊C4—21no—
33#66992—41no—
34#66991—21no—
35#66991—41no—
36C2×#4324—21no—
37#66977—21no—
38C2×#4318—21no—
39C2×#4318D411yescharacteristic
40C2×Dic44D411yescharacteristic
41#66950—21no—
42C4⋊C4×D11—21no—
43#66937—41no—
44#66931—41no—
45C2×C11×C16—21no—
46C11×#107—21no—
47C11×#107—21no—
48C11×#107D411yescharacteristic
49C11×#102—21no—
50#66896—21no—
51(C2×D11)⋊C8—21no—
52(C2×D11)⋊C8—21no—
53#66882D411yescharacteristic
54#66880—21no—
55C2×C11⋊C16—21no—
56#66874—21no—
57#66874—41no—
58#66873—41no—
59#66871—21no—
60#12285—111nomaximal, Sylow
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C2×C22⋊D11—21no—
66C2×C22⋊D11—41no—
67C2×C22⋊D11—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—
79C2×C8×C11—41no—
80C2×C8×C11C2×D411yescharacteristic
81C2×C8×C11C2×D411yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C22⋊Dic11—41no—
87C22⋊Dic11—41no—
88#4324—81no—
89(C2×D11)⋊C4—41no—
90C4⋊Dic11—21no—
91C4⋊Dic11—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94#4318—41no—
95#4318—41no—
96#4318—41no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—41no—
99Dic44—41no—
100C11×C16—41no—
101C11⋊C16—41no—
102#3203—111no—
103#2235—111no—
104#2233D1111yescharacteristic, complemented
105#2078—111no—
106#1350—111no—
107#1349—111no—
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—81no—
119C2×C4×C11—161no—
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11C2×D811yescharacteristic
122C22⋊D11—81no—
123C22⋊D11—82no—
124C22⋊D11—161no—
125C2×Dic11—21no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—82no—
129D44—41no—
130C4×D11—41no—
131C4×D11—41no—
132C4×D11—161no—
133Dic22—41no—
134Dic22—41no—
135Dic22—41no—
136C8×C11—21no—
137C8×C11—21no—
138C11⋊C8—41no—
139C11⋊C8—81no—
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×#107C2×D1111yescharacteristic
149#417—221no—
150#408—111no—
151#367—21no—
152#367—221no—
153#358—221no—
154#357—21no—
155C22⋊C16—111no—
156C22⋊C16C2×D1111yescharacteristic
157#343—221no—
158#341—111no—
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—161no—
172C4×C11#45511yescharacteristic
173C4×C11#45811yescharacteristic
174Dic11—41no—
175Dic11—81no—
176Dic11—81no—
177C2×#41—111no—
178C2×#41—221no—
179C2×Q16—111no—
180C2×SD16—221no—
181C2×D8C22⋊D1111yescharacteristic
182C2×M16—111no—
183C2×M16—221no—
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—21no—
194C2×C4⋊C4—221no—
195C2×C16—21no—
196C2×C16—221no—
197#107—21no—
198#107—21no—
199#107—111no—
200#107—221no—
201#107C22⋊D1111yescharacteristic
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—41no—
229C22×C4—221no—
230C22×C4—441no—
231C22×C4—441no—
232C22×C4D4×D1111yescharacteristic
233Q16—441no—
234SD16—881no—
235D8—41no—
236M16—441no—
237M16—441no—
238M16—441no—
239C2×C8—41no—
240C2×C8—221no—
241C2×C8—441no—
242C2×C8D4×D1111yescharacteristic
243C2×C8C2×C22⋊D1111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—221no—
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#6696411yescharacteristic
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—81no—
275C2×C4—161no—
276C2×C4—221no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—882no—
282C2×C4—1761no—
283C2×C4D8×D1111yescharacteristic
284C2×C4#6699011yescharacteristic
285C8—21no—
286C8—21no—
287C8—441no—
288C8—881no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—81no—
293C22—81no—
294C22—81no—
295C22—441no—
296C22—441no—
297C22—441no—
298C22#1062276911yescharacteristic
299C4—21no—
300C4—81no—
301C4—161no—
302C4—441no—
303C4—881no—
304C4—881no—
305C4#1062266611yescharacteristic
306C4#1062281511yescharacteristic
307C2—41no—
308C2—161no—
309C2—881no—
310C2#1306760011yescharacteristic
311C2#1307057711yescharacteristic
312C2#1307058611yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2233C2
socleC22×C11#447
prime radical#13079512C2
hypercenter#2233D11
hypocenterC11#12285
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
2. #13070813C2semidirect
3. #13070057C2semidirect
4. #13066635C2semidirect
5. #13066631C2semidirect
6. #13066541C2semidirect
7. C11×#2233C2semidirect
104. #2233D11semidirect
257. C11#12285semidirect

Maximal subgroups

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

subgroupindex
#130795122
#130708132
#130700572
#130666352
#130666312
#130665412
C11×#22332
#1228511