Finite Group Databasebeta

← #14667779

Subgroups — #14667779

Order 2816.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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#13081221C211yesmaximal, characteristic
2#13070902C211yesmaximal, characteristic, complemented
3#13070754C211yesmaximal, characteristic, complemented
4#13068139C211yesmaximal, characteristic, complemented
5#13066667C211yesmaximal, characteristic, complemented
6#13066584C211yesmaximal, characteristic, complemented
7C11×#1330C211yesmaximal, characteristic, complemented
8#10623096—21no—
9C11×#436C2211yescharacteristic
10#10622748—21no—
11#10622734—21no—
12#10622621—21no—
13#10622460—21no—
14#10622350—21no—
15#10622349—21no—
16C4×D88C2211yescharacteristic
17#10622296C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C11×#346C2211yescharacteristic
21#10622147—21no—
22#10622143—21no—
23#10622142—21no—
24#10622142—21no—
25#10622119—21no—
26#10622095C2211yescharacteristic
27C2×C11×M16—21no—
28C4×D4×C11D411yescharacteristic
29#66992—41no—
30#66983—21no—
31#66983—21no—
32#66979—21no—
33C2×C4⋊Dic11—21no—
34C2×D88D411yescharacteristic
35#66951—41no—
36#66936—41no—
37(C22⋊D11)⋊C4—41no—
38C4×D44—21no—
39#66923—21no—
40#66922—21no—
41C2×C11×C16—21no—
42C2×C11×C16—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×C22⋊C8—21no—
45C4×C8×C11C2311yescharacteristic
46#66896—41no—
47#66885—21no—
48#66885—21no—
49#66885—21no—
50#66882—21no—
51#66882—21no—
52#66882—21no—
53#66882D411yescharacteristic
54#66882D411yescharacteristic
55#66882D411yescharacteristic
56#66881—21no—
57#66881—21no—
58#66872—41no—
59C4⋊(C11⋊C8)—21no—
60#12400—111nomaximal, Sylow
61C2×D4×C11D811yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—41no—
64C2×C22⋊D11—41no—
65C22×Dic11—41no—
66C2×D44—21no—
67C2×C4×D11—41no—
68C2×Dic22—41no—
69C11×M16—41no—
70C11×M16—41no—
71C2×C8×C11—21no—
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4D811yescharacteristic
75C11×C22⋊C4—21no—
76C42×C11C2×D411yescharacteristic
77C22⋊Dic11—41no—
78(C2×D11)⋊C4—41no—
79(C2×D11)⋊C4—41no—
80(C2×D11)⋊C4—41no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89C4×Dic11—41no—
90C2×C11⋊C8—41no—
91D88—21no—
92D88—21no—
93C11×C16—22no—
94C11×C16—41no—
95#3355—111no—
96#2255—111no—
97#2224—111no—
98#1695—111no—
99#1363—111no—
100#1333—111no—
101#1330D1111yescharacteristic, complemented
102C23×C11—21no—
103C22×D11—41no—
104D4×C11—41no—
105C2×C4×C11—21no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11C2×D811yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C22⋊D11—82no—
112C22⋊D11—161no—
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116C2×Dic11—81no—
117C2×Dic11—161no—
118D44—41no—
119D44—41no—
120C4×D11—161no—
121Dic22—161no—
122C8×C11—21no—
123C8×C11—41no—
124C8×C11#13511yescharacteristic
125C8×C11#13711yescharacteristic
126C11⋊C8—81no—
127#553—221no—
128#500—111no—
129#499—111no—
130#482—221no—
131#480—221no—
132#478—221no—
133#476—221no—
134#469—221no—
135C4×D8—111no—
136#436C2×D1111yescharacteristic
137#428—221no—
138#367—221no—
139#366—221no—
140#366—221no—
141C4⋊C16C2×D1111yescharacteristic
142#357—221no—
143#346C2×D1111yescharacteristic
144#334—111no—
145#333—221no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11#44711yescharacteristic
150C2×D11—81no—
151C2×D11—81no—
152C2×D11—81no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—41no—
156C4×C11#45211yescharacteristic
157C4×C11#45611yescharacteristic
158Dic11—81no—
159Dic11—81no—
160Dic11—81no—
161Dic11—161no—
162C2×D8—111no—
163C2×M16—21no—
164C4⋊Q8—221no—
165#126—441no—
166#125—221no—
167#123—441no—
168#121—221no—
169#121—221no—
170#121—441no—
171C4×D4—221no—
172C4×D4—441no—
173C4×D4D4411yescharacteristic
174#117—221no—
175C2×C4⋊C4—221no—
176C2×C16—21no—
177C2×C16—21no—
178#107—111no—
179#107—111no—
180#107—111no—
181#107—221no—
182#107—221no—
183#107—221no—
184#106—221no—
185#106—221no—
186#106—441no—
187C4⋊C8—221no—
188C4⋊C8D4411yescharacteristic
189#102—221no—
190#102—221no—
191#102—221no—
192#102—441no—
193C22⋊C8—21no—
194C4×C8C22×D1111yescharacteristic
195C2×C11—81no—
196C2×C11#164711yescharacteristic
197C2×C11#219111yescharacteristic
198C2×C11#219211yescharacteristic
199D11—161no—
200C2×Q8—441no—
201C2×D4—221no—
202C2×D4—441no—
203C2×D4—441no—
204C2×D4D8811yescharacteristic
205C22×C4—21no—
206C22×C4—441no—
207C22×C4—441no—
208D8—221no—
209D8—221no—
210M16—41no—
211M16—41no—
212C2×C8—21no—
213C2×C8—441no—
214C2×C8D4×D1111yescharacteristic
215C2×C8D4×D1111yescharacteristic
216C4⋊C4—221no—
217C4⋊C4—221no—
218C4⋊C4—221no—
219C4⋊C4—441no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4D8811yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—441no—
227C22⋊C4—441no—
228C22⋊C4—441no—
229C22⋊C4—441no—
230C42—441no—
231C42C2×D4411yescharacteristic
232C16—22no—
233C16—41no—
234C11#1240011yescharacteristic, complemented, Sylow
235C23—21no—
236C23—441no—
237Q8—1761no—
238D4—41no—
239D4—441no—
240D4—441no—
241D4—882no—
242D4—1761no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—441no—
247C2×C4—441no—
248C2×C4—441no—
249C2×C4—881no—
250C2×C4—1761no—
251C2×C4—1761no—
252C2×C4#6693511yescharacteristic
253C2×C4C2×D8811yescharacteristic
254C2×C4#6696111yescharacteristic
255C8—21no—
256C8—41no—
257C8—881no—
258C8#6696511yescharacteristic
259C8#6696811yescharacteristic
260C22—41no—
261C22—41no—
262C22—41no—
263C22—881no—
264C22—881no—
265C22—881no—
266C22#1062234511yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—881no—
271C4—881no—
272C4—881no—
273C4—1761no—
274C4#1062239611yescharacteristic
275C4#1062243911yescharacteristic
276C2—81no—
277C2—1761no—
278C2#1306785311yescharacteristic
279C2#1307056911yescharacteristic
280C2#1307057511yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1330C2
socleC22×C11#447
prime radical#13081221C2
hypercenter#1330D11
hypocenterC11#12400
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #13070902C2semidirect
3. #13070754C2semidirect
4. #13068139C2semidirect
5. #13066667C2semidirect
6. #13066584C2semidirect
7. C11×#1330C2semidirect
101. #1330D11semidirect
234. C11#12400semidirect

Maximal subgroups

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

subgroupindex
#130812212
#130709022
#130707542
#130681392
#130666672
#130665842
C11×#13302
#1240011