Finite Group Databasebeta

← #11784332

Subgroups — #11784332

Order 1152.

466 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×#63779C211yesmaximal, characteristic
2C2×#63777C211yesmaximal, characteristic
3C2×#63777C211yesmaximal, characteristic
4C2×C4×#622C211yesmaximal, characteristic
5C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
6#10590207C211yesmaximal, characteristic
7#10590207C211yesmaximal, characteristic
8C22×#622C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C2×C32×C4⋊C4C411yescharacteristic
13C2×C4⋊(C3⋊Dic3)C411yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17#63779C414yescomplemented
18#63777—22no—
19#63777C414yescomplemented
20C4×#622—22no—
21#63658C411yescharacteristic
22#63658C411yescharacteristic
23Dic3×C4⋊C4—62no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C2×#622—21no—
32C2×#622—21no—
33C2×#622—21no—
34C2×#622—21no—
35C2×#622—21no—
36C2×#622—21no—
37C2×#622C2×C412yes—
38C2×#622C2×C412yes—
39C2×#622C2×C412yes—
40C2×#622C2×C412yes—
41C2×#622D412yes—
42C2×#622Q812yes—
43C32×C4⋊C4—22no—
44C4⋊(C3⋊Dic3)—22no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3C2×C412yes—
50C4×C3⋊Dic3C2×C412yes—
51#1771—91nomaximal, Sylow
52C2×C3×C4⋊C4—22no—
53C2×C4⋊Dic3—62no—
54C2×C4×Dic3—62no—
55C2×C4×Dic3—62no—
56C2×C4×Dic3—62no—
57C3⋊#95—62no—
58C3⋊#95—62no—
59C23×C32C22×C411yescharacteristic
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C32×C4—21no—
67C2×C32×C4C4212yes—
68C2×C32×C4M1612yes—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3—21no—
76C2×C3⋊Dic3C4212yes—
77C2×C3⋊Dic3M1612yes—
78C2×C3⋊Dic3C22×C411yescharacteristic
79C2×C3⋊Dic3C22×C411yescharacteristic
80C2×C3⋊Dic3C2×D411yescharacteristic
81C2×C3⋊Dic3C2×Q811yescharacteristic
82C2×C3⋊Dic3#4111yescharacteristic
83C2×C3⋊Dic3#4111yescharacteristic
84#622—22no—
85#622—22no—
86#622—22no—
87#622C4⋊C414yescomplemented
88C2×C4⋊C8—91no—
89C2×#97—91no—
90C2×#97—91no—
91C2×C4×C8—91no—
92C4×C4⋊C4—91no—
93#336—91no—
94#336—91no—
95C22×C3×C4—22no—
96C22×C3×C4—22no—
97C22×C3×C4—22no—
98C22×Dic3—62no—
99C22×Dic3—62no—
100C22×Dic3—62no—
101C22×Dic3—62no—
102C3×C4⋊C4—28no—
103C4⋊Dic3—68no—
104C4×Dic3—64no—
105C4×Dic3—64no—
106C4×Dic3—122no—
107C4×Dic3—122no—
108C4×Dic3—122no—
109C4×Dic3—122no—
110C22×C32C2×C4211yescharacteristic
111C22×C32C4×D411yescharacteristic
112C22×C32C4×Q811yescharacteristic
113C22×C32C2×M1611yescharacteristic
114C22×C32C2×M1611yescharacteristic
115C22×C32#13111yescharacteristic
116C22×C32#13111yescharacteristic
117C32×C4—22no—
118C32×C4—22no—
119C32×C4—41no—
120C3⋊Dic3—22no—
121C3⋊Dic3—22no—
122C3⋊Dic3—41no—
123C3⋊Dic3C2×C4⋊C411yescharacteristic
124C3⋊Dic3#11711yescharacteristic
125C3⋊Dic3C4×D411yescharacteristic
126C3⋊Dic3C4×Q811yescharacteristic
127C22×C8—91no—
128C22×C8—91no—
129C22×C8—91no—
130C22×C8—91no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4#15711yescharacteristic
133C2×C42—91no—
134C2×C42—91no—
135C2×C42—91no—
136C4⋊C8—94no—
137#97—94no—
138#97—182no—
139C4×C8—182no—
140#95—91no—
141#95—91no—
142C23×C3—22no—
143C2×C3×C4—24no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—24no—
148C2×C3×C4—42no—
149C2×C3×C4—42no—
150C2×C3×C4—42no—
151C2×C3×C4—42no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C2×Dic3—64no—
159C2×Dic3—64no—
160C2×Dic3—64no—
161C2×Dic3—122no—
162C2×Dic3—122no—
163C2×Dic3—122no—
164C2×Dic3—122no—
165C2×Dic3—122no—
166C2×Dic3—122no—
167C2×C32C4×C4⋊C411yescharacteristic
168C2×C32C4×M1611yescharacteristic
169C2×C32#40511yescharacteristic
170C2×C32#43511yescharacteristic
171C2×C32#43511yescharacteristic
172C2×C32#44611yescharacteristic
173C2×C32#44611yescharacteristic
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4C2×#15711yescharacteristic
179C22×C4C2×#15711yescharacteristic
180C22×C4C2×#15711yescharacteristic
181C2×C8—92no—
182C2×C8—92no—
183C2×C8—92no—
184C2×C8—92no—
185C2×C8—92no—
186C2×C8—92no—
187C2×C8—181no—
188C2×C8—181no—
189C2×C8—181no—
190C2×C8—181no—
191C2×C8—181no—
192C2×C8—181no—
193C4⋊C4—22no—
194C4⋊C4—182no—
195C42—92no—
196C42—92no—
197C42—181no—
198C42—181no—
199C42—181no—
200C42—181no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—22no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—22no—
207C22×C3—22no—
208C3×C4—28no—
209C3×C4—44no—
210C3×C4—44no—
211Dic3—62no—
212Dic3—62no—
213Dic3—62no—
214Dic3—62no—
215Dic3—124no—
216Dic3—124no—
217Dic3—124no—
218C32#177111yescharacteristic, complemented, Sylow
219C23C22×#15711yescharacteristic
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—91no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—91no—
231C2×C4—91no—
232C2×C4—91no—
233C2×C4—92no—
234C2×C4—92no—
235C2×C4—181no—
236C2×C4—181no—
237C2×C4—181no—
238C2×C4—181no—
239C2×C4—181no—
240C2×C4—181no—
241C2×C4—181no—
242C2×C4C4×#15712yes—
243C2×C4#379212yes—
244C8—94no—
245C8—182no—
246C8—182no—
247C8—182no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—22no—
251C2×C3—22no—
252C2×C3—22no—
253C2×C3—22no—
254C2×C3—22no—
255C22#6428311yescharacteristic
256C22C2×C4×#15711yescharacteristic
257C22#6428711yescharacteristic
258C22D4×#15711yescharacteristic
259C22#6428911yescharacteristic
260C22Q8×#15711yescharacteristic
261C22C2×#379211yescharacteristic
262C4—22no—
263C4—22no—
264C4—41no—
265C4—91no—
266C4—91no—
267C4—91no—
268C4—91no—
269C4—182no—
270C4—182no—
271C4—361no—
272C3—22no—
273C2#1059374811yescharacteristic
274C2#1059375111yescharacteristic
275C2#1059375411yescharacteristic
276C2C4⋊C4×#15711yescharacteristic
277C2C4×#379211yescharacteristic
278C2#1059382011yescharacteristic
279C2#1059383511yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC2×C32×C4⋊C4C4
socle, prime radicalC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1771
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
17. #63779C4semidirect
19. #63777C4semidirect
87. #622C4⋊C4semidirect
218. C32#1771semidirect

Maximal subgroups

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

subgroupindex
C2×#637792
C2×#637772
C2×C4×#6222
C4⋊C4×C3⋊Dic32
#105902072
#17719