Finite Group Databasebeta

← #11784224

Subgroups — #11784224

Order 1152.

438 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 108 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×C4⋊#622C211yesmaximal, characteristic
4C2×C4×#622C211yesmaximal, characteristic
5#10592347C211yesmaximal, characteristic
6#10590207C211yesmaximal, characteristic
7#10590207C211yesmaximal, characteristic
8C22×#622C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#63779C414yescomplemented
16#63777—22no—
17C4⋊#622C414yescomplemented
18C4×#622—22no—
19C32×#95C411yescharacteristic
20#63658C411yescharacteristic
21#63658C411yescharacteristic
22#63658C411yescharacteristic
23#4648—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×#622—21no—
38C2×#622—21no—
39C2×#622C2×C412yes—
40C2×#622C2×C412yes—
41C2×#622C2×C412yes—
42C2×#622C2×C412yes—
43C4×C3⋊Dic3—21no—
44C4×C3⋊Dic3—21no—
45C4×C3⋊Dic3C2×C412yes—
46C4×C3⋊Dic3C2×C412yes—
47C4×C3⋊Dic3D412yes—
48C4×C3⋊Dic3Q812yes—
49#1768—91nomaximal, Sylow
50C2×C4×Dic3—62no—
51C2×C4×Dic3—62no—
52C2×C4×Dic3—62no—
53C3×#95—22no—
54C3⋊#95—62no—
55C3⋊#95—62no—
56C3⋊#95—62no—
57C23×C32C22×C411yescharacteristic
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—21no—
65C2×C32×C4C4212yes—
66C2×C32×C4C4⋊C412yes—
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3C4212yes—
75C2×C3⋊Dic3C4⋊C412yes—
76C2×C3⋊Dic3C22×C411yescharacteristic
77C2×C3⋊Dic3C22×C411yescharacteristic
78C2×C3⋊Dic3C2×D411yescharacteristic
79C2×C3⋊Dic3C2×Q811yescharacteristic
80C2×C3⋊Dic3#4111yescharacteristic
81C2×C3⋊Dic3#4111yescharacteristic
82#622—22no—
83#622—22no—
84#622—22no—
85#622—22no—
86C2×C4⋊C8—91no—
87C2×C4⋊C8—91no—
88C2×#97—91no—
89C2×C4×C8—91no—
90#376—91no—
91#336—91no—
92#336—91no—
93C22×C3×C4—22no—
94C22×C3×C4—22no—
95C22×C3×C4—22no—
96C22×Dic3—62no—
97C22×Dic3—62no—
98C22×Dic3—62no—
99C22×Dic3—62no—
100C4×Dic3—64no—
101C4×Dic3—64no—
102C4×Dic3—64no—
103C4×Dic3—64no—
104C4×Dic3—64no—
105C4×Dic3—64no—
106C22×C32C2×C4211yescharacteristic
107C22×C32C2×C4⋊C411yescharacteristic
108C22×C32#11711yescharacteristic
109C22×C32#13111yescharacteristic
110C22×C32#13111yescharacteristic
111C22×C32#13111yescharacteristic
112C22×C32#13111yescharacteristic
113C32×C4—22no—
114C32×C4—22no—
115C32×C4—41no—
116C3⋊Dic3—22no—
117C3⋊Dic3—22no—
118C3⋊Dic3—41no—
119C3⋊Dic3C4×D411yescharacteristic
120C3⋊Dic3C4×D411yescharacteristic
121C3⋊Dic3C4×Q811yescharacteristic
122C3⋊Dic3C4×Q811yescharacteristic
123C22×C8—91no—
124C22×C8—91no—
125C22×C8—91no—
126C22×C8—91no—
127C2×C42—91no—
128C2×C42—91no—
129C2×C42—91no—
130C4⋊C8—94no—
131C4⋊C8—94no—
132#97—182no—
133C4×C8—182no—
134#95—91no—
135#95—91no—
136#95—91no—
137#95#15711yescharacteristic
138C23×C3—22no—
139C2×C3×C4—24no—
140C2×C3×C4—24no—
141C2×C3×C4—24no—
142C2×C3×C4—42no—
143C2×C3×C4—42no—
144C2×C3×C4—42no—
145C2×C3×C4—42no—
146C2×C3×C4—42no—
147C2×C3×C4—42no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150C2×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—64no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—122no—
158C2×Dic3—122no—
159C2×Dic3—122no—
160C2×Dic3—122no—
161C2×Dic3—122no—
162C2×Dic3—122no—
163C2×C32C4×C4⋊C411yescharacteristic
164C2×C32#40511yescharacteristic
165C2×C32#40511yescharacteristic
166C2×C32#42411yescharacteristic
167C2×C32#42411yescharacteristic
168C2×C32#43311yescharacteristic
169C2×C32#43311yescharacteristic
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4C2×#15711yescharacteristic
175C22×C4C2×#15711yescharacteristic
176C22×C4C2×#15711yescharacteristic
177C2×C8—92no—
178C2×C8—92no—
179C2×C8—92no—
180C2×C8—92no—
181C2×C8—181no—
182C2×C8—181no—
183C2×C8—181no—
184C2×C8—181no—
185C2×C8—181no—
186C2×C8—181no—
187C2×C8—181no—
188C2×C8—181no—
189C42—92no—
190C42—92no—
191C42—92no—
192C42—92no—
193C42—181no—
194C42—181no—
195C22×C3—22no—
196C22×C3—22no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3—22no—
200C22×C3—22no—
201C22×C3—22no—
202C3×C4—44no—
203C3×C4—44no—
204C3×C4—44no—
205Dic3—62no—
206Dic3—62no—
207Dic3—62no—
208Dic3—62no—
209Dic3—124no—
210Dic3—124no—
211Dic3—124no—
212C32#176811yescharacteristic, complemented, Sylow
213C23C22×#15711yescharacteristic
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—91no—
226C2×C4—91no—
227C2×C4—92no—
228C2×C4—92no—
229C2×C4—181no—
230C2×C4—181no—
231C2×C4—181no—
232C2×C4—181no—
233C2×C4—181no—
234C2×C4—181no—
235C2×C4—181no—
236C2×C4C4×#15712yes—
237C2×C4C4⋊#15712yes—
238C8—182no—
239C8—182no—
240C8—182no—
241C8—182no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—22no—
247C2×C3—22no—
248C2×C3—22no—
249C22C2×C4×#15711yescharacteristic
250C22C2×C4⋊#15711yescharacteristic
251C22#6428611yescharacteristic
252C22#6428711yescharacteristic
253C22#6428711yescharacteristic
254C22#6428711yescharacteristic
255C22#6428911yescharacteristic
256C4—22no—
257C4—22no—
258C4—41no—
259C4—91no—
260C4—91no—
261C4—91no—
262C4—91no—
263C4—182no—
264C4—182no—
265C4—361no—
266C3—22no—
267C2C4×C4⋊#15711yescharacteristic
268C2#1059373811yescharacteristic
269C2#1059374311yescharacteristic
270C2#1059374411yescharacteristic
271C2#1059374811yescharacteristic
272C2#1059375311yescharacteristic
273C2#1059375511yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC32×#95C4
socle, prime radicalC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenter#95#157
hypocenterC32#1768
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
15. #63779C4semidirect
17. C4⋊#622C4semidirect
212. C32#1768semidirect

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
C2×C4×#6222
#105923472
#105902072
#17689