Finite Group Databasebeta

← #11783177

Subgroups — #11783177

Order 1152.

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

normal subgroups only

This group has 818 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
1C22×C4×#157C211yesmaximal, characteristic
2C2×#64283C211yesmaximal, characteristic
3C3⋊D3×#117C211yesmaximal, characteristic
4#10590164C214yesmaximal, complemented
5C23×#157—21no—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3792—21no—
8C2×C4×#157—22no—
9C2×C4×#157—21no—
10C2×C4×#157C414yescomplemented
11C2×C4×#157C2212yes—
12#64283—22no—
13#64283C414yescomplemented
14C2×#3788C2212yes—
15C2×#3787—21no—
16C32×#117C411yescharacteristic, complemented
17#64135C411yescharacteristic, complemented
18#64101C2212yes—
19C4⋊C4×C3⋊D3C412yescomplemented
20C22⋊C4×C3⋊D3—21no—
21#64086—21no—
22#64081—21no—
23C42×C3⋊D3—21no—
24D3×#117—62no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—28no—
27C22×#157—24no—
28C22×#157—22no—
29C22×C32×C4C2×C411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3C2×C412yes—
34C2×C4×C3⋊D3C2×C412yes—
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D412yes—
38C2×C4×C3⋊D3Q812yes—
39C2×C4×C3⋊D3C2311yescharacteristic
40#3792—24no—
41C2×#622—22no—
42C4×#157—24no—
43C4×#157—22no—
44C4×#157C2×C414yescomplemented
45#3788—22no—
46#3788C2×C414yescomplemented
47#3787—24no—
48C32×C4⋊C4C2×C412yescomplemented
49C32×C22⋊C4—21no—
50C32×C42—21no—
51#3757—21no—
52#3752—22no—
53C4⋊(C3⋊Dic3)C2×C412yescomplemented
54#3750—22no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—22no—
57C2×#339—91nomaximal, Sylow
58C22×C4×D3—62no—
59C3×#117—22no—
60#926—62no—
61#892—64no—
62D3×C4⋊C4—64no—
63D3×C22⋊C4—64no—
64#877—64no—
65#872—64no—
66C42×D3—64no—
67C23×C32C22⋊C411yescharacteristic
68C22×C3⋊D3—24no—
69C22×C3⋊D3C22⋊C412yes—
70C22×C3⋊D3C22⋊C411yescharacteristic
71C22×C3⋊D3C4⋊C412yes—
72C22×C3⋊D3C2×D411yescharacteristic
73C2×#157—28no—
74C2×#157—216no—
75C2×#157—24no—
76C2×C32×C4—22no—
77C2×C32×C4C4212yes—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C4⋊C412yes—
80C2×C32×C4C22×C411yescharacteristic
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C412yes—
84C2×C3⋊Dic3C4⋊C412yes—
85C2×C3⋊Dic3C2×D411yescharacteristic
86C4×C3⋊D3—44no—
87C4×C3⋊D3C4212yes—
88C4×C3⋊D3C22⋊C412yes—
89C4×C3⋊D3C22⋊C412yes—
90C4×C3⋊D3C4⋊C412yes—
91C4×C3⋊D3C4⋊C412yes—
92C4×C3⋊D3C4⋊C412yes—
93C4×C3⋊D3C22×C411yescharacteristic
94C4×C3⋊D3C22×C411yescharacteristic
95C4×C3⋊D3C2×D411yescharacteristic
96C4×C3⋊D3C2×Q811yescharacteristic
97#622—24no—
98C22×M16—91no—
99C2×#117—91no—
100C22×C42—91no—
101#339—94no—
102C23×D3—62no—
103C22×C3×C4—22no—
104C22×Dic3—62no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—64no—
110C2×C4×D3—64no—
111C2×C4×D3—64no—
112C2×C4×D3—64no—
113C2×C4×D3—68no—
114C3×C4⋊C4—24no—
115C3×C22⋊C4—24no—
116C3×C42—24no—
117#217—64no—
118(C2×D3)⋊C4—68no—
119C4⋊Dic3—64no—
120Dic3⋊C4—68no—
121C4×Dic3—64no—
122C4×Dic3—68no—
123C22×C32—22no—
124C22×C32#9512yes—
125C22×C32C2×C22⋊C411yescharacteristic
126C2×C3⋊D3—22no—
127C2×C3⋊D3—24no—
128C2×C3⋊D3—24no—
129C2×C3⋊D3#9512yes—
130C2×C3⋊D3#10414yes—
131C2×C3⋊D3C2×C22⋊C411yescharacteristic
132C2×C3⋊D3C2×C4⋊C411yescharacteristic
133#157—28no—
134C32×C4—42no—
135C32×C4#9512yes—
136C32×C4C2×C4211yescharacteristic
137C32×C4C2×C4⋊C411yescharacteristic
138C3⋊Dic3—42no—
139C3⋊Dic3#9512yes—
140C3⋊Dic3C2×C22⋊C411yescharacteristic
141C3⋊Dic3C2×C4⋊C411yescharacteristic
142C23×C4—91no—
143C23×C4—181no—
144C2×M16—92no—
145C2×M16—94no—
146C2×M16—182no—
147C2×M16—181no—
148C22×C8—181no—
149#117—91no—
150#117—92no—
151#117—181no—
152#117—181no—
153#117#15711yescharacteristic, complemented
154C2×C4⋊C4—92no—
155C2×C22⋊C4—181no—
156C2×C42—94no—
157C2×C42—92no—
158C2×C42—181no—
159C2×C42—182no—
160C2×C42—181no—
161C23×C3—22no—
162C22×D3—62no—
163C22×D3—64no—
164C22×D3—64no—
165C22×D3—62no—
166C22×D3—128no—
167C2×C3×C4—28no—
168C2×C3×C4—22no—
169C2×C3×C4—24no—
170C2×C3×C4—24no—
171C2×C3×C4—22no—
172C2×Dic3—62no—
173C2×Dic3—64no—
174C2×Dic3—64no—
175C2×Dic3—62no—
176C2×Dic3—68no—
177C4×D3—64no—
178C4×D3—64no—
179C4×D3—64no—
180C4×D3—64no—
181C4×D3—64no—
182C4×D3—64no—
183C4×D3—62no—
184C4×D3—62no—
185C4×D3—62no—
186C4×D3—62no—
187C4×D3—1216no—
188C2×C32—22no—
189C2×C32C2×#9511yescharacteristic
190C2×C32C2×#10412yes—
191C3⋊D3—21no—
192C3⋊D3—21no—
193C3⋊D3#33914yescomplemented
194C24—91no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—92no—
199C22×C4—92no—
200C22×C4—92no—
201C22×C4—92no—
202C22×C4—91no—
203C22×C4—91no—
204C22×C4—182no—
205C22×C4—184no—
206C22×C4—182no—
207C22×C4—188no—
208C22×C4C2×#15711yescharacteristic
209M16—94no—
210M16—182no—
211M16—184no—
212C2×C8—184no—
213C2×C8—182no—
214C4⋊C4—92no—
215C4⋊C4—182no—
216C4⋊C4C2×#15712yescomplemented
217C22⋊C4—21no—
218C22⋊C4—182no—
219C22⋊C4—181no—
220C42—21no—
221C42—94no—
222C42—182no—
223C42—182no—
224C42—184no—
225C42—181no—
226C22×C3—24no—
227C22×C3—22no—
228C22×C3—44no—
229C2×D3—64no—
230C2×D3—68no—
231C2×D3—62no—
232C2×D3—62no—
233C2×D3—128no—
234C2×D3—128no—
235C2×D3—124no—
236C3×C4—22no—
237C3×C4—22no—
238C3×C4—24no—
239C3×C4—48no—
240Dic3—64no—
241Dic3—62no—
242Dic3—62no—
243Dic3—128no—
244C32C2×#33911yescharacteristic, complemented, Sylow
245C23—91no—
246C23—92no—
247C23—92no—
248C23—91no—
249C23—184no—
250C23C22⋊#15711yescharacteristic
251C2×C4—22no—
252C2×C4—92no—
253C2×C4—92no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—92no—
259C2×C4—91no—
260C2×C4—92no—
261C2×C4—91no—
262C2×C4—92no—
263C2×C4—92no—
264C2×C4—92no—
265C2×C4—92no—
266C2×C4—184no—
267C2×C4—1816no—
268C2×C4—188no—
269C2×C4—182no—
270C2×C4—364no—
271C2×C4C4×#15712yes—
272C2×C4C4⋊#15712yes—
273C2×C4C22⋊#15711yescharacteristic
274C2×C4C22×#15711yescharacteristic
275C8—184no—
276C2×C3—22no—
277C2×C3—24no—
278C2×C3—44no—
279D3—68no—
280D3—122no—
281D3—122no—
282C22—22no—
283C22—92no—
284C22—94no—
285C22—91no—
286C22—91no—
287C22—184no—
288C22—184no—
289C22—182no—
290C22#6378112yes—
291C22C2×C22⋊#15711yescharacteristic
292C4—42no—
293C4—91no—
294C4—92no—
295C4—91no—
296C4—188no—
297C4—362no—
298C4#6378112yes—
299C4C2×C4×#15711yescharacteristic
300C4C2×C4⋊#15711yescharacteristic
301C3—22no—
302C2—22no—
303C2—94no—
304C2—181no—
305C2—181no—
306C2C2×#6378111yescharacteristic
307C2#1059383912yes—
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
hypocenterC32C2×#339
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. #10590164C2semidirect
10. C2×C4×#157C4semidirect
13. #64283C4semidirect
16. C32×#117C4semidirect
17. #64135C4semidirect
19. C4⋊C4×C3⋊D3C4semidirect
44. C4×#157C2×C4semidirect
46. #3788C2×C4semidirect
48. C32×C4⋊C4C2×C4semidirect
53. C4⋊(C3⋊Dic3)C2×C4semidirect
153. #117#157semidirect
193. C3⋊D3#339semidirect
216. C4⋊C4C2×#157semidirect
244. C32C2×#339semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C2×#642832
C3⋊D3×#1172
#105901642
C2×#3399