Finite Group Databasebeta

← #11774058

Subgroups — #11774058

Order 1152.

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

normal subgroups only

This group has 467 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#10592417C211yesmaximal, characteristic
3#10591066C211yesmaximal, 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#63641—21no—
19C8×C3⋊Dic3—21no—
20C3×#830C2212yes—
21#63572—21no—
22#63555—21no—
23C2×#889—32no—
24#4719—32no—
25#4718—32no—
26#4718—61no—
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—
71Dic3⋊C8—62no—
72Dic3⋊C8—62no—
73Dic3⋊C8—62no—
74C8×Dic3—62no—
75C8×Dic3—62no—
76C23×C32C22×C411yescharacteristic
77C2×C32×C4—41no—
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3×Dic3—22no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—42no—
92C32×C8—41no—
93C3⋊(C3⋊C8)—41no—
94C3×C3⋊C8—42no—
95C2×#125—91no—
96#432—91no—
97#431—91no—
98#324—32no—
99#324—92no—
100C22×C3×C4—21no—
101C22×C3×C4—32no—
102C22×C3×C4—32no—
103C22×C3×C4C22×D312yes—
104C22×Dic3—32no—
105C22×Dic3—32no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C22×Dic3C4×D312yes—
109C22×Dic3C4×D312yes—
110C2×C3×C8—22no—
111C2×C3×C8—22no—
112C2×C3×C8—62no—
113C3×C4⋊C4—62no—
114C3×C4⋊C4—62no—
115C4⋊Dic3—62no—
116C4⋊Dic3—62no—
117Dic3⋊C4—22no—
118Dic3⋊C4—22no—
119Dic3⋊C4—62no—
120Dic3⋊C4—62no—
121Dic3⋊C4—62no—
122Dic3⋊C4—62no—
123Dic3⋊C4—62no—
124Dic3⋊C4—62no—
125C4×Dic3—32no—
126C4×Dic3—32no—
127C4×Dic3—32no—
128C4×Dic3—32no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C4×Dic3—61no—
132C4×Dic3—61no—
133C2×C3⋊C8—22no—
134C2×C3⋊C8—62no—
135C2×C3⋊C8—62no—
136C22×C32—21no—
137C22×C32—21no—
138C22×C32C2×C22⋊C411yescharacteristic
139C22×C32#13111yescharacteristic
140C22×C32#13111yescharacteristic
141C32×C4—21no—
142C32×C4—21no—
143C3⋊Dic3—21no—
144C3⋊Dic3—21no—
145C3⋊Dic3—21no—
146C3⋊Dic3#10112yes—
147C3×Dic3—42no—
148C3×Dic3—42no—
149#125—181no—
150#125—181no—
151#125—181no—
152#125—181no—
153C2×C4⋊C4—32no—
154C2×C4⋊C4—91no—
155C2×C4⋊C4—91no—
156C2×C4⋊C4—92no—
157C2×C42—91no—
158C4⋊C8—181no—
159C4⋊C8—181no—
160C22⋊C8—32no—
161C22⋊C8—91no—
162C22⋊C8D3211yescharacteristic
163#97—181no—
164C4×C8—181no—
165C23×C3—21no—
166C23×C3C2×C4×D312yes—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—42no—
170C2×C3×C4—42no—
171C2×C3×C4—62no—
172C2×C3×C4—62no—
173C2×C3×C4—62no—
174C2×C3×C4—62no—
175C2×C3×C4—122no—
176C2×C3×C4D3×D412yes—
177C2×C3×C4D3×D412yes—
178C2×Dic3—22no—
179C2×Dic3—22no—
180C2×Dic3—22no—
181C2×Dic3—22no—
182C2×Dic3—32no—
183C2×Dic3—32no—
184C2×Dic3—32no—
185C2×Dic3—32no—
186C2×Dic3—42no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—64no—
192C2×Dic3—62no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—122no—
197C3×C8—42no—
198C3×C8—42no—
199C3×C8—122no—
200C3⋊C8—42no—
201C3⋊C8—122no—
202C3⋊C8—122no—
203C2×C32—21no—
204C2×C32—21no—
205C2×C32#40811yescharacteristic
206C2×C32#41011yescharacteristic
207C2×C32C2×#10111yescharacteristic
208C22×C4—32no—
209C22×C4—32no—
210C22×C4—91no—
211C22×C4—91no—
212C22×C4C2×D3211yescharacteristic
213C2×C8—21no—
214C2×C8—62no—
215C2×C8—181no—
216C4⋊C4—62no—
217C4⋊C4—62no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C4⋊C4—182no—
223C4⋊C4—182no—
224C42—91no—
225C42—91no—
226C42—91no—
227C42—91no—
228C22×C3—22no—
229C22×C3—22no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—41no—
234C22×C3—41no—
235C22×C3D3×C22⋊C412yes—
236C22×C3#90112yes—
237C22×C3#90712yes—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—22no—
241C3×C4—41no—
242C3×C4—122no—
243C3×C4—122no—
244Dic3—34no—
245Dic3—42no—
246Dic3—42no—
247Dic3—62no—
248Dic3—62no—
249Dic3—62no—
250Dic3—62no—
251Dic3—62no—
252Dic3—62no—
253Dic3—121no—
254C32#147011yescharacteristic, complemented, Sylow
255C23C4×D3211yescharacteristic
256C2×C4—41no—
257C2×C4—62no—
258C2×C4—62no—
259C2×C4—62no—
260C2×C4—62no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—122no—
266C2×C4—182no—
267C2×C4—181no—
268C2×C4—181no—
269C2×C4#380211yescharacteristic
270C2×C4#381111yescharacteristic
271C8—41no—
272C8—122no—
273C8—361no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—41no—
280C2×C3—41no—
281C2×C3#472712yes—
282C2×C3#474012yes—
283C2×C3D3×#10112yes—
284C22—21no—
285C22—21no—
286C22#6380311yescharacteristic
287C22#6380511yescharacteristic
288C22#6392111yescharacteristic
289C4—21no—
290C4—21no—
291C4—92no—
292C4—122no—
293C4—122no—
294C4—181no—
295C4—181no—
296C4—181no—
297C3—21no—
298C3#6812812yescomplemented
299C2—21no—
300C2—21no—
301C2#1059040611yescharacteristic
302C2#1059095811yescharacteristic
303C2#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
254. C32#1470semidirect
298. C3#68128semidirect

Maximal subgroups

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

subgroupindex
C2×#638702
#105924172
#105910662
C3×#44692
#105891472
#681283