Finite Group Databasebeta

← #14667437

Subgroups — #14667437

Order 2816.

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

normal subgroups only

This group has 298 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#13070862C211yesmaximal, characteristic, complemented
3#13070662C211yesmaximal, characteristic, complemented
4#13068105C211yesmaximal, 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#10622620—21no—
13C2×#66864—21no—
14#10622460—21no—
15#10622350—21no—
16#10622349—21no—
17#10622312C2211yescharacteristic
18C4×D88C2211yescharacteristic
19#10622296C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#346C2211yescharacteristic
22#10622141—21no—
23#10622141—21no—
24#10622141—21no—
25#10622120—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×Dic44—21no—
35C2×Dic44—21no—
36C2×D88D411yescharacteristic
37#66951—41no—
38#66936—41no—
39(C22⋊D11)⋊C4—41no—
40C4×D44—21no—
41#66923—21no—
42#66922—21no—
43C2×C11×C16—21no—
44C2×C11×C16—21no—
45C11×C4⋊C8D411yescharacteristic
46C11×C22⋊C8—21no—
47C4×C8×C11C2311yescharacteristic
48#66896—41no—
49#66885—21no—
50#66885—21no—
51#66885—21no—
52#66882—21no—
53#66882D411yescharacteristic
54#66882D411yescharacteristic
55#66882D411yescharacteristic
56#66881—21no—
57#66881—21no—
58#66871—41no—
59C4⋊(C11⋊C8)—21no—
60#66864—42no—
61#12350—111nomaximal, Sylow
62C2×D4×C11D811yescharacteristic
63C22×C4×C11—21no—
64C2×C22⋊D11—41no—
65C2×C22⋊D11—41no—
66C22×Dic11—41no—
67C2×D44—21no—
68C2×C4×D11—41no—
69C2×Dic22—41no—
70C11×M16—41no—
71C11×M16—41no—
72C2×C8×C11—21no—
73C2×C8×C11C2×D411yescharacteristic
74C2×C8×C11C2×D411yescharacteristic
75C11×C4⋊C4D811yescharacteristic
76C11×C22⋊C4—21no—
77C42×C11C2×D411yescharacteristic
78C22⋊Dic11—41no—
79(C2×D11)⋊C4—41no—
80(C2×D11)⋊C4—41no—
81(C2×D11)⋊C4—41no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C4×Dic11—41no—
91C2×C11⋊C8—41no—
92Dic44—42no—
93Dic44—41no—
94Dic44—41no—
95D88—21no—
96D88—21no—
97C11×C16—41no—
98C11×C16—41no—
99#3355—111no—
100#2245—111no—
101#2208—111no—
102#1689—111no—
103#1363—111no—
104#1333—111no—
105#1330D1111yescharacteristic, complemented
106C23×C11—21no—
107C22×D11—41no—
108D4×C11—41no—
109C2×C4×C11—21no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11#12011yescharacteristic
113C2×C4×C11C2×D811yescharacteristic
114C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
115C22⋊D11—82no—
116C22⋊D11—161no—
117C2×Dic11—41no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—81no—
121C2×Dic11—161no—
122D44—41no—
123D44—41no—
124C4×D11—161no—
125Dic22—81no—
126Dic22—81no—
127C8×C11—21no—
128C8×C11—41no—
129C8×C11#13511yescharacteristic
130C8×C11AGL(1,ℤ/8)11yescharacteristic
131C11⋊C8—81no—
132#553—221no—
133C2×SD32—221no—
134#499—111no—
135#494—111no—
136#482—221no—
137#480—221no—
138#478—221no—
139#474—221no—
140#469—221no—
141C4×D8—111no—
142#436C2×D1111yescharacteristic
143#428—221no—
144C4⋊C16C2×D1111yescharacteristic
145#358—221no—
146#358—221no—
147#358—221no—
148#346C2×D1111yescharacteristic
149#334—111no—
150#332—221no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11#44711yescharacteristic
155C2×D11—81no—
156C2×D11—81no—
157C2×D11—81no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—41no—
161C4×C11#44911yescharacteristic
162C4×C11#45411yescharacteristic
163Dic11—81no—
164Dic11—81no—
165Dic11—81no—
166Dic11—161no—
167C2×Q16—221no—
168C2×Q16—221no—
169C2×D8—111no—
170C2×M16—21no—
171C4⋊Q8—221no—
172#126—441no—
173#125—221no—
174#123—441no—
175#121—221no—
176#121—221no—
177#121—441no—
178C4×D4—221no—
179C4×D4—441no—
180C4×D4D4411yescharacteristic
181#117—221no—
182C2×C4⋊C4—221no—
183SD32—442no—
184C2×C16—21no—
185C2×C16—21no—
186#107—111no—
187#107—111no—
188#107—111no—
189#107—221no—
190#107—441no—
191#106—221no—
192#106—221no—
193C4⋊C8—221no—
194C4⋊C8D4411yescharacteristic
195#102—221no—
196#102—221no—
197#102—221no—
198#102—441no—
199C22⋊C8—21no—
200C4×C8C22×D1111yescharacteristic
201C2×C11—81no—
202C2×C11#162511yescharacteristic
203C2×C11#219111yescharacteristic
204C2×C11#219411yescharacteristic
205D11—161no—
206C2×Q8—441no—
207C2×D4—221no—
208C2×D4—441no—
209C2×D4—441no—
210C2×D4D8811yescharacteristic
211C22×C4—21no—
212C22×C4—441no—
213C22×C4—441no—
214Q16—442no—
215Q16—441no—
216Q16—441no—
217D8—221no—
218D8—221no—
219M16—41no—
220M16—41no—
221C2×C8—21no—
222C2×C8—441no—
223C2×C8D4×D1111yescharacteristic
224C2×C8D4×D1111yescharacteristic
225C4⋊C4—221no—
226C4⋊C4—221no—
227C4⋊C4—221no—
228C4⋊C4—441no—
229C4⋊C4—441no—
230C4⋊C4—441no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C4⋊C4D8811yescharacteristic
234C22⋊C4—21no—
235C22⋊C4—441no—
236C22⋊C4—441no—
237C22⋊C4—441no—
238C22⋊C4—441no—
239C42—441no—
240C42C2×D4411yescharacteristic
241C16—41no—
242C16—41no—
243C11#1235011yescharacteristic, complemented, Sylow
244C23—21no—
245C23—441no—
246Q8—881no—
247Q8—881no—
248D4—41no—
249D4—441no—
250D4—441no—
251D4—882no—
252D4—1761no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—441no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4—881no—
260C2×C4—1761no—
261C2×C4—1761no—
262C2×C4#6693511yescharacteristic
263C2×C4C2×D8811yescharacteristic
264C2×C4#6696111yescharacteristic
265C8—21no—
266C8—41no—
267C8—881no—
268C8#6696411yescharacteristic
269C8#6696911yescharacteristic
270C22—41no—
271C22—41no—
272C22—41no—
273C22—881no—
274C22—881no—
275C22—881no—
276C22#1062234511yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—881no—
281C4—881no—
282C4—881no—
283C4—1761no—
284C4#1062239411yescharacteristic
285C4#1062244011yescharacteristic
286C2—81no—
287C2—1761no—
288C2#1306770711yescharacteristic
289C2#1307056911yescharacteristic
290C2#1307058911yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1330C2
socleC22×C11#447
prime radical#13081221C2
hypercenter#1330D11
hypocenterC11#12350
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. #13070862C2semidirect
3. #13070662C2semidirect
4. #13068105C2semidirect
5. #13066667C2semidirect
6. #13066584C2semidirect
7. C11×#1330C2semidirect
105. #1330D11semidirect
243. C11#12350semidirect

Maximal subgroups

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

subgroupindex
#130812212
#130708622
#130706622
#130681052
#130666672
#130665842
C11×#13302
#1235011