Finite Group Databasebeta

← #11778816

Subgroups — #11778816

Order 1152.

471 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 471 conjugacy classes of subgroups — too many to draw. Only its 80 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#10594813C211yesmaximal, characteristic
2#10592684C211yesmaximal, characteristic
3C3×#4970C212yesmaximal
4#10589152C212yesmaximal
5#10589148C211yesmaximal, characteristic
6#71179—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×#3750C2211yescharacteristic
9C3×#924C2212yes—
10#63982—21no—
11#63957—21no—
12#63847—22no—
13#63839—22no—
14#63658—21no—
15#63658—21no—
16#63658C2211yescharacteristic
17C3×#830C2212yes—
18C3×#810—22no—
19C3×#807—22no—
20#5623—32no—
21C3×#484—32no—
22#4985—32no—
23#4985—61no—
24#4970D312yes—
25#4538—32no—
26#4469—32no—
27#4467—32no—
28C22×C32×C4—21no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C2×C3×Dic6D412yes—
34C2×#627—21no—
35C32×C4⋊C4—22no—
36#3750—22no—
37C3×#217—22no—
38C3×C4⋊Dic3D412yes—
39C3×Dic3⋊C4—22no—
40C2×C3×C3⋊C8—22no—
41#3724—21no—
42#3724—21no—
43#3724—21no—
44Dic3⋊Dic3—22no—
45Dic32—22no—
46#1617—91noSylow
47C3×C22⋊Q8—32no—
48C2×C3×C4⋊C4—21no—
49C2×C3×C4⋊C4C2×D312yes—
50#944—62no—
51#924C2×D312yes—
52C2×Dic3⋊C4—32no—
53C2×Dic3⋊C4—61no—
54#889—62no—
55#889—62no—
56#888—62no—
57#878—62no—
58#877—62no—
59C3×#107—62no—
60C3×#103—62no—
61C3×C22⋊C8—32no—
62C3⋊#95—32no—
63C3⋊#95—61no—
64C3⋊#95—62no—
65C3⋊#95—62no—
66C3⋊#95—62no—
67C3⋊#95—62no—
68#830C2×D312yes—
69#810—22no—
70#807—22no—
71C23×C32C2×D411yescharacteristic
72C2×C32×C4—41no—
73C2×C32×C4—42no—
74C2×C32×C4—41no—
75C2×C32×C4C2×D412yes—
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3Q1612yes—
84C2×C3×Dic3—22no—
85C2×C3×Dic3—22no—
86C3×Dic6—42no—
87#627—81no—
88C3×C3⋊C8—42no—
89#544—91no—
90#484—32no—
91#400—91no—
92#328—92no—
93#324—91no—
94C2×C3×Q8—32no—
95C22×C3×C4—22no—
96C22×C3×C4—22no—
97C22×C3×C4—21no—
98C22×C3×C4C22×D312yes—
99C22×Dic3—32no—
100C22×Dic3—32no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103C22×Dic3—62no—
104C22×Dic3—62no—
105C2×Dic6—62no—
106C2×Dic6#6712yes—
107C2×C3×C8—62no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4—32no—
111C3×C4⋊C4—42no—
112C3×C4⋊C4—62no—
113C3×C22⋊C4—62no—
114#217—22no—
115C4⋊Dic3—62no—
116C4⋊Dic3#6712yes—
117Dic3⋊C4—22no—
118Dic3⋊C4—62no—
119Dic3⋊C4—62no—
120Dic3⋊C4—62no—
121Dic3⋊C4—62no—
122Dic3⋊C4—62no—
123Dic3⋊C4—62no—
124Dic3⋊C4—122no—
125C4×Dic3—62no—
126C4×Dic3—62no—
127C2×C3⋊C8—22no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32#12011yescharacteristic
131C22×C32C2×Q1611yescharacteristic
132C22×C32#13711yescharacteristic
133C32×C4—22no—
134C32×C4—81no—
135C3⋊Dic3—22no—
136C3⋊Dic3—41no—
137C3⋊Dic3—81no—
138C3×Dic3—42no—
139C3×Dic3—42no—
140C4⋊Q8—182no—
141#125—182no—
142C22⋊Q8—32no—
143C22⋊Q8—181no—
144#117—181no—
145C2×C4⋊C4—91no—
146C2×C4⋊C4D3211yescharacteristic
147#107—62no—
148#103—62no—
149C22⋊C8—32no—
150#95—91no—
151#95—181no—
152#95—181no—
153C23×C3—21no—
154C23×C3D3×D412yes—
155C3×Q8—122no—
156C2×C3×C4—22no—
157C2×C3×C4—42no—
158C2×C3×C4—42no—
159C2×C3×C4—42no—
160C2×C3×C4—44no—
161C2×C3×C4—44no—
162C2×C3×C4—42no—
163C2×C3×C4—62no—
164C2×C3×C4—62no—
165C2×C3×C4D3×D412yes—
166C2×C3×C4C2×#6712yes—
167C2×Dic3—22no—
168C2×Dic3—22no—
169C2×Dic3—34no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—121no—
175C2×Dic3—121no—
176C2×Dic3—121no—
177C2×Dic3—122no—
178C2×Dic3—122no—
179C2×Dic3—122no—
180C2×Dic3—122no—
181C2×Dic3—122no—
182C2×Dic3—122no—
183C2×Dic3—122no—
184C2×Dic3—122no—
185Dic6—42no—
186Dic6—242no—
187C3×C8—122no—
188C3⋊C8—42no—
189C2×C32—21no—
190C2×C32—21no—
191C2×C32#45111yescharacteristic
192C2×C32#45411yescharacteristic
193C2×C32#45811yescharacteristic
194C2×Q8—32no—
195C2×Q8—181no—
196C22×C4—21no—
197C22×C4—91no—
198C22×C4—91no—
199C22×C4—181no—
200C22×C4C2×D3211yescharacteristic
201C2×C8—62no—
202C4⋊C4—22no—
203C4⋊C4—32no—
204C4⋊C4—62no—
205C4⋊C4—181no—
206C4⋊C4—181no—
207C4⋊C4—181no—
208C4⋊C4—182no—
209C4⋊C4—182no—
210C22⋊C4—62no—
211C42—182no—
212C22×C3—22no—
213C22×C3—22no—
214C22×C3—22no—
215C22×C3—22no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3D3×Q1612yes—
220C22×C3#91812yes—
221C22×C3#93712yes—
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—42no—
225C3×C4—82no—
226C3×C4—82no—
227C3×C4—122no—
228C3×C4—122no—
229Dic3—42no—
230Dic3—42no—
231Dic3—64no—
232Dic3—122no—
233Dic3—122no—
234Dic3—241no—
235Dic3—242no—
236Dic3—242no—
237C32#161711yescharacteristic, complemented, Sylow
238C23#381111yescharacteristic
239Q8—122no—
240Q8—721no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—62no—
245C2×C4—62no—
246C2×C4—92no—
247C2×C4—181no—
248C2×C4—181no—
249C2×C4—181no—
250C2×C4—361no—
251C2×C4—361no—
252C2×C4—361no—
253C2×C4—361no—
254C2×C4D3×#6712yes—
255C8—122no—
256C2×C3—22no—
257C2×C3—22no—
258C2×C3—22no—
259C2×C3—22no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3#505312yes—
264C2×C3#518612yes—
265C2×C3#520112yes—
266C22—21no—
267C22—21no—
268C22#6394411yescharacteristic
269C22#6394511yescharacteristic
270C22#6398311yescharacteristic
271C4—22no—
272C4—81no—
273C4—122no—
274C4—122no—
275C4—182no—
276C4—361no—
277C4—721no—
278C3—21no—
279C3#7117912yescomplemented
280C2—21no—
281C2—21no—
282C2#1059139811yescharacteristic
283C2#1059152411yescharacteristic
284C2#1059165411yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#1617
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
237. C32#1617semidirect
279. C3#71179semidirect

Maximal subgroups

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

subgroupindex
#105948132
#105926842
C3×#49702
#105891522
#105891482
#711793