Finite Group Databasebeta

← #11773838

Subgroups — #11773838

Order 1152.

645 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 645 conjugacy classes of subgroups — too many to draw. Only its 116 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×#64096C211yesmaximal, characteristic
2#10591061C212yesmaximal
3C3×#4528C212yesmaximal
4#10589148C212yesmaximal
5#68125—32nomaximal
6C22×#634C411yescharacteristic
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×#3750C411yescharacteristic
9C2×#3750C2211yescharacteristic
10C2×C4×C3⋊Dic3C411yescharacteristic
11C2×C4×C3⋊Dic3C411yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#64096—22no—
14#64096—22no—
15C3×#830C2214yes—
16#63572—22no—
17#63553—22no—
18C2×#887—32no—
19C2×#887—61no—
20#4718—34no—
21C3×#324—32no—
22#4528D312yes—
23#4469—34no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C2×#634—22no—
32C2×#634—22no—
33C2×#634C814yescomplemented
34C32×C4⋊C4—22no—
35#3750—22no—
36#3750—22no—
37C4×C3⋊Dic3—21no—
38C4×C3⋊Dic3—21no—
39C4×C3⋊Dic3—21no—
40C4×C3⋊Dic3—21no—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3D412yes—
43C2×C3×C3⋊C8—24no—
44#1461—91noSylow
45C22×Dic6—32no—
46C22×Dic6—61no—
47C2×C3×C4⋊C4—21no—
48C2×C3×C4⋊C4C2×D312yes—
49C2×Dic3⋊C4—32no—
50C2×Dic3⋊C4—32no—
51C2×Dic3⋊C4—61no—
52C2×Dic3⋊C4—61no—
53C2×C4×Dic3—32no—
54C2×C4×Dic3—32no—
55C2×C4×Dic3—32no—
56C2×C4×Dic3—61no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—61no—
59#887—64no—
60#887—64no—
61#887—64no—
62#887—64no—
63C3×C22⋊C8—34no—
64#830C2×D314yes—
65Dic3⋊C8—64no—
66C8×Dic3—64no—
67C23×C32C22×C411yescharacteristic
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4C2×C812yes—
74C2×C32×C4C2×D412yes—
75C2×C3⋊Dic3—21no—
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22⋊C412yes—
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C2×C812yes—
84C2×C3⋊Dic3C2×C812yes—
85C2×C3⋊Dic3M1612yes—
86#634—28no—
87C3×C3⋊C8—44no—
88C2×C4×Q8—91no—
89#431—92no—
90#324—32no—
91#324—92no—
92C22×C3×C4—21no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4C4×D312yes—
96C22×C3×C4C4×D312yes—
97C22×C3×C4C22×D312yes—
98C22×Dic3—32no—
99C22×Dic3—32no—
100C22×Dic3—32no—
101C22×Dic3—32no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C2×Dic6—38no—
107C2×Dic6—64no—
108C2×Dic6—64no—
109C2×Dic6—64no—
110C2×Dic6—64no—
111C2×Dic6—64no—
112C2×C3×C8—64no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4—24no—
115Dic3⋊C4—64no—
116Dic3⋊C4—64no—
117Dic3⋊C4—64no—
118Dic3⋊C4—64no—
119C4×Dic3—34no—
120C4×Dic3—34no—
121C4×Dic3—62no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C4×Dic3—62no—
126C4×Dic3—62no—
127C4×Dic3—62no—
128C4×Dic3—62no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C2×C3⋊C8—24no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32C2×C22⋊C411yescharacteristic
135C22×C32C22×C811yescharacteristic
136C22×C32C2×M1611yescharacteristic
137C32×C4—22no—
138C32×C4—22no—
139C32×C4—41no—
140C3⋊Dic3—22no—
141C3⋊Dic3—21no—
142C3⋊Dic3—41no—
143C3⋊Dic3C22⋊C814yes—
144C3⋊Dic3#10112yes—
145C22×Q8—91no—
146C4×Q8—182no—
147C4×Q8—182no—
148C2×C4⋊C4—91no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4D3211yescharacteristic
151C2×C42—91no—
152C2×C42—91no—
153C2×C42—91no—
154C4⋊C8—182no—
155C22⋊C8—34no—
156C4×C8—182no—
157C23×C3—21no—
158C23×C3C2×C4×D312yes—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—22no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—42no—
168C2×C3×C4—42no—
169C2×C3×C4—42no—
170C2×C3×C4—42no—
171C2×C3×C4D3×C814yes—
172C2×C3×C4D3×D414yes—
173C2×Dic3—32no—
174C2×Dic3—34no—
175C2×Dic3—34no—
176C2×Dic3—34no—
177C2×Dic3—32no—
178C2×Dic3—34no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—62no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—64no—
186C2×Dic3—62no—
187C2×Dic3—62no—
188C2×Dic3—64no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—62no—
192C2×Dic3—62no—
193C2×Dic3—122no—
194C2×Dic3—122no—
195Dic6—616no—
196Dic6—616no—
197C3×C8—124no—
198C3⋊C8—44no—
199C2×C32—21no—
200C2×C32—21no—
201C2×C32C2×C22⋊C811yescharacteristic
202C2×C32#41011yescharacteristic
203C2×C32C2×#10111yescharacteristic
204C2×Q8—94no—
205C2×Q8—182no—
206C2×Q8—182no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4#62411yescharacteristic
212C22×C4#62411yescharacteristic
213C22×C4C2×D3211yescharacteristic
214C2×C8—64no—
215C4⋊C4—22no—
216C4⋊C4—182no—
217C4⋊C4—182no—
218C42—92no—
219C42—92no—
220C42—181no—
221C42—181no—
222C42—181no—
223C42—181no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3D3×C22⋊C412yes—
232C22×C3C2×D3×C812yes—
233C22×C3D3×M1612yes—
234C3×C4—24no—
235C3×C4—24no—
236C3×C4—24no—
237C3×C4—42no—
238C3×C4—42no—
239C3×C4—42no—
240Dic3—38no—
241Dic3—34no—
242Dic3—64no—
243Dic3—62no—
244Dic3—64no—
245Dic3—62no—
246Dic3—64no—
247Dic3—62no—
248Dic3—122no—
249Dic3—122no—
250C32#146111yescharacteristic, complemented, Sylow
251C23C2×#62411yescharacteristic
252Q8—188no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—92no—
259C2×C4—92no—
260C2×C4—91no—
261C2×C4—92no—
262C2×C4—92no—
263C2×C4—91no—
264C2×C4—182no—
265C2×C4—181no—
266C2×C4—181no—
267C2×C4—181no—
268C2×C4—361no—
269C2×C4#371012yes—
270C2×C4#381112yes—
271C8—124no—
272C2×C3—22no—
273C2×C3—22no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3D3×C22⋊C812yes—
280C2×C3#474012yes—
281C2×C3D3×#10112yes—
282C22—21no—
283C22—21no—
284C22C2×#371011yescharacteristic
285C22#6381811yescharacteristic
286C22#6397411yescharacteristic
287C4—22no—
288C4—22no—
289C4—41no—
290C4—92no—
291C4—94no—
292C4—181no—
293C4—182no—
294C4—361no—
295C3—21no—
296C3#6812512yescomplemented
297C2—21no—
298C2—21no—
299C2#1059115211yescharacteristic
300C2#1059152911yescharacteristic
301C2#1059163911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1461
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
33. C2×#634C8semidirect
250. C32#1461semidirect
296. C3#68125semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
#105910612
C3×#45282
#105891482
#681253