Finite Group Databasebeta

← #11774065

Subgroups — #11774065

Order 1152.

463 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 463 conjugacy classes of subgroups — too many to draw. Only its 92 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×#63870C211yesmaximal, characteristic
2#10592418C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4C3×#4469C212yesmaximal
5#10589147C212yesmaximal
6#68128—32nomaximal
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×Dic3⋊C4C2212yes—
9C2×#3724C411yescharacteristic
10C2×#3724C411yescharacteristic
11C2×Dic3⋊Dic3C412yes—
12#63870—21no—
13#63870—21no—
14#63870—21no—
15#63870—21no—
16C32×C22⋊C8C2211yescharacteristic
17#63657C2211yescharacteristic
18#63642—21no—
19#63641—21no—
20C3×#830C2212yes—
21#63572—21no—
22#63553—21no—
23C2×#889—32no—
24#4719—32no—
25#4719—61no—
26#4718—32no—
27C3×#324—32no—
28#4528—32no—
29#4469—32no—
30#4469D312yes—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3×Dic3C2×C412yes—
35C22×C3×Dic3C2×C412yes—
36C2×C32×C8—21no—
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C2×C3⋊(C3⋊C8)—21no—
42C3×Dic3⋊C4—22no—
43C3×Dic3⋊C4—22no—
44C2×C3×C3⋊C8—22no—
45#3724—21no—
46#3724—21no—
47#3724—21no—
48#3724—21no—
49Dic3⋊Dic3—22no—
50Dic3⋊Dic3—22no—
51#1470—91noSylow
52C2×C3×C4⋊C4—32no—
53C2×C4⋊Dic3—32no—
54C2×Dic3⋊C4—32no—
55C2×Dic3⋊C4—32no—
56C2×Dic3⋊C4—32no—
57C2×Dic3⋊C4C2×D312yes—
58C2×C4×Dic3—32no—
59C2×C4×Dic3—61no—
60#889—62no—
61#889—62no—
62#889—62no—
63#889—62no—
64C3×C22⋊C8—21no—
65C3×C22⋊C8—32no—
66C3×C22⋊C8C2×D312yes—
67#830—32no—
68#830—61no—
69#830C2×D312yes—
70#815—62no—
71#815—62no—
72Dic3⋊C8—62no—
73Dic3⋊C8—62no—
74Dic3⋊C8—62no—
75C8×Dic3—62no—
76C23×C32C22×C411yescharacteristic
77C2×C32×C4—41no—
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3×Dic3—22no—
87C2×C3×Dic3—22no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—42no—
91C32×C8—41no—
92C3⋊(C3⋊C8)—41no—
93C3×C3⋊C8—42no—
94C2×#125—91no—
95#432—91no—
96#431—91no—
97#324—32no—
98#324—92no—
99C22×C3×C4—21no—
100C22×C3×C4—32no—
101C22×C3×C4—32no—
102C22×C3×C4C22×D312yes—
103C22×Dic3—32no—
104C22×Dic3—32no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107C22×Dic3C4×D312yes—
108C22×Dic3C4×D312yes—
109C2×C3×C8—22no—
110C2×C3×C8—22no—
111C2×C3×C8—62no—
112C3×C4⋊C4—62no—
113C3×C4⋊C4—62no—
114C4⋊Dic3—62no—
115C4⋊Dic3—62no—
116Dic3⋊C4—22no—
117Dic3⋊C4—22no—
118Dic3⋊C4—62no—
119Dic3⋊C4—62no—
120Dic3⋊C4—62no—
121Dic3⋊C4—62no—
122Dic3⋊C4—62no—
123Dic3⋊C4—62no—
124C4×Dic3—32no—
125C4×Dic3—32no—
126C4×Dic3—32no—
127C4×Dic3—32no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C4×Dic3—61no—
132C2×C3⋊C8—22no—
133C2×C3⋊C8—62no—
134C2×C3⋊C8—62no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32C2×C22⋊C411yescharacteristic
138C22×C32#13112yes—
139C32×C4—21no—
140C32×C4—21no—
141C3⋊Dic3—21no—
142C3⋊Dic3—21no—
143C3⋊Dic3—21no—
144C3⋊Dic3#10112yes—
145C3×Dic3—42no—
146C3×Dic3—42no—
147#125—181no—
148#125—181no—
149#125—181no—
150#125—181no—
151C2×C4⋊C4—32no—
152C2×C4⋊C4—91no—
153C2×C4⋊C4—91no—
154C2×C4⋊C4—92no—
155C2×C42—91no—
156C4⋊C8—181no—
157C4⋊C8—181no—
158C22⋊C8—32no—
159C22⋊C8—91no—
160C22⋊C8D3211yescharacteristic
161#97—181no—
162C4×C8—181no—
163C23×C3—21no—
164C23×C3C2×C4×D312yes—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—42no—
168C2×C3×C4—42no—
169C2×C3×C4—62no—
170C2×C3×C4—62no—
171C2×C3×C4—62no—
172C2×C3×C4—62no—
173C2×C3×C4—122no—
174C2×C3×C4D3×D412yes—
175C2×C3×C4D3×D412yes—
176C2×Dic3—22no—
177C2×Dic3—22no—
178C2×Dic3—22no—
179C2×Dic3—22no—
180C2×Dic3—32no—
181C2×Dic3—32no—
182C2×Dic3—32no—
183C2×Dic3—32no—
184C2×Dic3—42no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—64no—
190C2×Dic3—62no—
191C2×Dic3—62no—
192C2×Dic3—122no—
193C2×Dic3—122no—
194C3×C8—42no—
195C3×C8—42no—
196C3×C8—122no—
197C3⋊C8—42no—
198C3⋊C8—122no—
199C3⋊C8—122no—
200C2×C32—22no—
201C2×C32#40811yescharacteristic
202C2×C32#41011yescharacteristic
203C2×C32C2×#10111yescharacteristic
204C22×C4—32no—
205C22×C4—32no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4C2×D3211yescharacteristic
209C2×C8—21no—
210C2×C8—62no—
211C2×C8—181no—
212C4⋊C4—62no—
213C4⋊C4—62no—
214C4⋊C4—181no—
215C4⋊C4—181no—
216C4⋊C4—181no—
217C4⋊C4—181no—
218C4⋊C4—182no—
219C4⋊C4—182no—
220C42—91no—
221C42—91no—
222C42—91no—
223C42—91no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—21no—
228C22×C3—41no—
229C22×C3—41no—
230C22×C3D3×C22⋊C412yes—
231C22×C3#90112yes—
232C22×C3#90712yes—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—41no—
237C3×C4—122no—
238C3×C4—122no—
239Dic3—34no—
240Dic3—42no—
241Dic3—42no—
242Dic3—62no—
243Dic3—62no—
244Dic3—62no—
245Dic3—62no—
246Dic3—121no—
247Dic3—121no—
248Dic3—121no—
249C32#147011yescharacteristic, complemented, Sylow
250C23C4×D3211yescharacteristic
251C2×C4—41no—
252C2×C4—62no—
253C2×C4—62no—
254C2×C4—62no—
255C2×C4—62no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—91no—
260C2×C4—122no—
261C2×C4—182no—
262C2×C4—182no—
263C2×C4#380211yescharacteristic
264C2×C4#381111yescharacteristic
265C8—41no—
266C8—122no—
267C8—361no—
268C2×C3—22no—
269C2×C3—22no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—42no—
274C2×C3#472712yes—
275C2×C3#474012yes—
276C2×C3D3×#10112yes—
277C22—21no—
278C22—21no—
279C22#6380412yes—
280C22#6392111yescharacteristic
281C4—21no—
282C4—21no—
283C4—92no—
284C4—122no—
285C4—122no—
286C4—181no—
287C4—181no—
288C4—181no—
289C3—21no—
290C3#6812812yescomplemented
291C2—22no—
292C2#1059040611yescharacteristic
293C2#1059095911yescharacteristic
294C2#1059100311yescharacteristic
subgroupG/H
centerC22#63921
commutator, prime radicalC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1470
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
249. C32#1470semidirect
290. C3#68128semidirect

Maximal subgroups

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

subgroupindex
C2×#638702
#105924182
#105910612
C3×#44692
#105891472
#681283