Finite Group Databasebeta

← #11783257

Subgroups — #11783257

Order 1152.

754 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 138 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×#64286C211yesmaximal, characteristic
2C22×#3787C211yesmaximal, characteristic
3C3⋊D3×#117C211yesmaximal, characteristic
4#10590163C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×C22⋊#157—21no—
7C22×#622—21no—
8#64286—22no—
9#64286C414yescomplemented
10C2×C4⋊#157C2212yes—
11C2×C4×#157—21no—
12C2×#3787—21no—
13C2×#3787—22no—
14C2×#3787C414yescomplemented
15C2×#3787C2212yes—
16C32×#117C411yescharacteristic, complemented
17#64135C411yescharacteristic, complemented
18#64101C412yescomplemented
19C4⋊C4×C3⋊D3C2212yes—
20C22⋊C4×C3⋊D3—21no—
21#64086—21no—
22#64081—21no—
23C42×C3⋊D3—21no—
24D3×#117—62no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—22no—
27C22×C32×C4C2×C411yescharacteristic
28C22×C3⋊Dic3D411yescharacteristic
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C4×C3⋊D3C2×C412yes—
32C2×C4×C3⋊D3C2×C412yes—
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D412yes—
36C2×C4×C3⋊D3Q812yes—
37C2×C4×C3⋊D3C2311yescharacteristic
38C22⋊#157—24no—
39C2×#622—24no—
40C2×#622—22no—
41C4⋊#157—22no—
42C4⋊#157C2×C414yes—
43C4×#157—24no—
44#3787—24no—
45#3787—22no—
46#3787C2×C414yes—
47C32×C4⋊C4C2×C412yes—
48C32×C22⋊C4—21no—
49C32×C42—21no—
50#3757—21no—
51#3752—22no—
52C4⋊(C3⋊Dic3)C2×C412yes—
53#3750—22no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3—22no—
56#1735—91nomaximal, Sylow
57C22×C4×D3—62no—
58C3×#117—22no—
59#926—62no—
60#892—64no—
61D3×C4⋊C4—64no—
62D3×C22⋊C4—64no—
63#877—64no—
64#872—64no—
65C42×D3—64no—
66C23×C32C22⋊C411yescharacteristic
67C22×C3⋊D3—24no—
68C22×C3⋊D3C22⋊C411yescharacteristic
69C22×C3⋊D3C22⋊C412yes—
70C22×C3⋊D3C4⋊C412yes—
71C22×C3⋊D3C2×D411yescharacteristic
72C2×#157—24no—
73C2×#157—44no—
74C2×C32×C4—22no—
75C2×C32×C4C4212yes—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C4⋊C412yes—
78C2×C32×C4C22×C411yescharacteristic
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22⋊C412yes—
82C2×C3⋊Dic3C4⋊C412yes—
83C2×C3⋊Dic3C2×D411yescharacteristic
84C4×C3⋊D3—44no—
85C4×C3⋊D3C4212yes—
86C4×C3⋊D3C22⋊C412yes—
87C4×C3⋊D3C22⋊C412yes—
88C4×C3⋊D3C4⋊C412yes—
89C4×C3⋊D3C4⋊C412yes—
90C4×C3⋊D3C4⋊C412yes—
91C4×C3⋊D3C22×C411yescharacteristic
92C4×C3⋊D3C22×C411yescharacteristic
93C4×C3⋊D3C2×D411yescharacteristic
94C4×C3⋊D3C2×Q811yescharacteristic
95#622—24no—
96C23×C8—91no—
97C2×#117—91no—
98C2×#117—91no—
99#340—94no—
100C23×D3—62no—
101C22×C3×C4—22no—
102C22×Dic3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—64no—
108C2×C4×D3—64no—
109C2×C4×D3—64no—
110C2×C4×D3—64no—
111C2×C4×D3—68no—
112C3×C4⋊C4—24no—
113C3×C22⋊C4—24no—
114C3×C42—24no—
115#217—64no—
116(C2×D3)⋊C4—68no—
117C4⋊Dic3—64no—
118Dic3⋊C4—68no—
119C4×Dic3—64no—
120C4×Dic3—68no—
121C22×C32—22no—
122C22×C32#9512yes—
123C22×C32C2×C22⋊C411yescharacteristic
124C2×C3⋊D3—22no—
125C2×C3⋊D3—24no—
126C2×C3⋊D3—24no—
127C2×C3⋊D3#9512yes—
128C2×C3⋊D3C2×C22⋊C411yescharacteristic
129C2×C3⋊D3C2×C4⋊C411yescharacteristic
130C2×C3⋊D3#13514yes—
131#157—44no—
132C32×C4—42no—
133C32×C4#9512yes—
134C32×C4C2×C4211yescharacteristic
135C32×C4C2×C4⋊C411yescharacteristic
136C3⋊Dic3—42no—
137C3⋊Dic3#9512yes—
138C3⋊Dic3C2×C22⋊C411yescharacteristic
139C3⋊Dic3C2×C4⋊C411yescharacteristic
140C23×C4—91no—
141C22×C8—94no—
142C22×C8—92no—
143C22×C8—182no—
144C22×C8—181no—
145C22×C8—181no—
146#117—94no—
147#117—91no—
148#117—92no—
149#117—181no—
150#117—181no—
151#117—182no—
152#117#15711yescharacteristic, complemented
153C2×C4⋊C4—92no—
154C2×C4⋊C4—92no—
155C2×C22⋊C4—181no—
156C2×C22⋊C4—181no—
157C2×C42—181no—
158C2×C42—181no—
159C23×C3—22no—
160C22×D3—62no—
161C22×D3—62no—
162C22×D3—64no—
163C22×D3—64no—
164C22×D3—128no—
165C2×C3×C4—28no—
166C2×C3×C4—22no—
167C2×C3×C4—24no—
168C2×C3×C4—24no—
169C2×C3×C4—22no—
170C2×Dic3—62no—
171C2×Dic3—64no—
172C2×Dic3—64no—
173C2×Dic3—62no—
174C2×Dic3—68no—
175C4×D3—64no—
176C4×D3—64no—
177C4×D3—64no—
178C4×D3—64no—
179C4×D3—64no—
180C4×D3—64no—
181C4×D3—62no—
182C4×D3—62no—
183C4×D3—62no—
184C4×D3—62no—
185C4×D3—1216no—
186C2×C32—22no—
187C2×C32C2×#9511yescharacteristic
188C2×C32#41612yes—
189C3⋊D3—22no—
190C3⋊D3#41612yes—
191C3⋊D3#42712yes—
192C24—91no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—91no—
196C22×C4—92no—
197C22×C4—92no—
198C22×C4—92no—
199C22×C4—92no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—182no—
203C22×C4—182no—
204C22×C4C2×#15711yescharacteristic
205C2×C8—94no—
206C2×C8—182no—
207C2×C8—184no—
208C2×C8—184no—
209C2×C8—182no—
210C4⋊C4—94no—
211C4⋊C4—92no—
212C4⋊C4—182no—
213C4⋊C4—182no—
214C4⋊C4C2×#15712yes—
215C22⋊C4—21no—
216C22⋊C4—182no—
217C22⋊C4—184no—
218C22⋊C4—181no—
219C42—21no—
220C42—182no—
221C42—184no—
222C42—181no—
223C22×C3—24no—
224C22×C3—22no—
225C22×C3—44no—
226C2×D3—62no—
227C2×D3—62no—
228C2×D3—68no—
229C2×D3—64no—
230C2×D3—128no—
231C2×D3—128no—
232C2×D3—124no—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—24no—
236C3×C4—48no—
237Dic3—64no—
238Dic3—62no—
239Dic3—62no—
240Dic3—128no—
241C32#173511yescharacteristic, complemented, Sylow
242C23—91no—
243C23—92no—
244C23—92no—
245C23—91no—
246C23—184no—
247C23C22⋊#15711yescharacteristic
248C2×C4—22no—
249C2×C4—92no—
250C2×C4—92no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—92no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—92no—
259C2×C4—92no—
260C2×C4—92no—
261C2×C4—92no—
262C2×C4—92no—
263C2×C4—184no—
264C2×C4—182no—
265C2×C4—364no—
266C2×C4—364no—
267C2×C4C4×#15712yes—
268C2×C4C4⋊#15712yes—
269C2×C4C22⋊#15711yescharacteristic
270C2×C4C22×#15711yescharacteristic
271C8—184no—
272C2×C3—22no—
273C2×C3—24no—
274C2×C3—44no—
275D3—64no—
276D3—64no—
277D3—124no—
278C22—22no—
279C22—91no—
280C22—91no—
281C22—94no—
282C22—92no—
283C22—184no—
284C22—184no—
285C22—182no—
286C22#6378112yes—
287C22C2×C22⋊#15711yescharacteristic
288C4—42no—
289C4—91no—
290C4—92no—
291C4—91no—
292C4—364no—
293C4—362no—
294C4#6378112yes—
295C4C2×C4×#15711yescharacteristic
296C4C2×C4⋊#15711yescharacteristic
297C3—22no—
298C2—22no—
299C2—92no—
300C2—92no—
301C2—182no—
302C2C2×#6378111yescharacteristic
303C2#1059384112yes—
subgroupG/H
centerC2×C4C22⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×#117C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenter#117#157
hypocenterC32#1735
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10590163C2semidirect
9. #64286C4semidirect
14. C2×#3787C4semidirect
16. C32×#117C4semidirect
17. #64135C4semidirect
18. #64101C4semidirect
152. #117#157semidirect
241. C32#1735semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
C22×#37872
C3⋊D3×#1172
#105901632
#17359