Finite Group Databasebeta

← #11785817

Subgroups — #11785817

Order 1152.

630 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C3⋊D3×#117C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3#10593800C211yesmaximal, characteristic
4#10590163C212yesmaximal, complemented
5#10590163C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157—21no—
8C2×C4⋊#157C2212yes—
9C2×#3787C2212yes—
10C32×#117C411yescharacteristic, complemented
11#64135C411yescharacteristic, complemented
12#64101C411yescharacteristic, complemented
13#64101C411yescharacteristic, complemented
14C4⋊C4×C3⋊D3C2211yescharacteristic
15C4⋊C4×C3⋊D3C2211yescharacteristic
16C22⋊C4×C3⋊D3—21no—
17#64086—21no—
18#64081—21no—
19C42×C3⋊D3—21no—
20C22⋊#622—21no—
21#63781—21no—
22#63778—21no—
23D3×#117—62no—
24C23×C3⋊D3D411yescharacteristic
25C22×#157—22no—
26C22×C32×C4C2×C411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×C4×C3⋊D3—24no—
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3C2311yescharacteristic
35C22⋊#157—42no—
36C2×#622—22no—
37C4⋊#157—24no—
38#3787—24no—
39C32×C4⋊C4C2×C411yescharacteristic
40C32×C4⋊C4C2×C411yescharacteristic
41C32×C22⋊C4—21no—
42C32×C42—21no—
43#3757—21no—
44#3752—21no—
45#3752—21no—
46C4⋊(C3⋊Dic3)C2×C411yescharacteristic
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48#3750—21no—
49#3750—21no—
50C4×C3⋊Dic3—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3—21no—
53#1825—91nomaximal, Sylow
54C22×C4×D3—62no—
55C3×#117—22no—
56#926—62no—
57#892—62no—
58#892—62no—
59D3×C4⋊C4—62no—
60D3×C4⋊C4—62no—
61D3×C22⋊C4—64no—
62#877—64no—
63#872—64no—
64C42×D3—64no—
65C23×C32C22⋊C411yescharacteristic
66C22×C3⋊D3—22no—
67C22×C3⋊D3—22no—
68C22×C3⋊D3—21no—
69C22×C3⋊D3—21no—
70C22×C3⋊D3C22⋊C411yescharacteristic
71C22×C3⋊D3C2×D411yescharacteristic
72C2×#157—42no—
73C2×#157—42no—
74C2×#157—42no—
75C2×C32×C4—22no—
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22×C411yescharacteristic
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C4×C3⋊D3—22no—
86C4×C3⋊D3—22no—
87C4×C3⋊D3—22no—
88C4×C3⋊D3—42no—
89C4×C3⋊D3—41no—
90C4×C3⋊D3—41no—
91C4×C3⋊D3#4114yes—
92#622—42no—
93C2×#117—91no—
94C2×C22⋊C8—91no—
95#380—91no—
96#340—92no—
97#340—92no—
98C23×D3—62no—
99C22×C3×C4—22no—
100C22×Dic3—62no—
101C2×C4×D3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—616no—
106C2×C4×D3—64no—
107C2×C4×D3—64no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4—22no—
110C3×C22⋊C4—24no—
111C3×C42—24no—
112#217—64no—
113(C2×D3)⋊C4—64no—
114(C2×D3)⋊C4—64no—
115C4⋊Dic3—62no—
116C4⋊Dic3—62no—
117Dic3⋊C4—64no—
118Dic3⋊C4—64no—
119C4×Dic3—64no—
120C4×Dic3—64no—
121C4×Dic3—64no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32C2×C22⋊C411yescharacteristic
126C2×C3⋊D3—21no—
127C2×C3⋊D3—21no—
128C2×C3⋊D3—21no—
129C2×C3⋊D3—42no—
130C2×C3⋊D3—42no—
131C2×C3⋊D3#12312yes—
132C2×C3⋊D3#13512yes—
133C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
134C2×C3⋊D3#13711yescharacteristic
135#157—82no—
136C32×C4—21no—
137C32×C4—41no—
138C32×C4—41no—
139C32×C4#11712yes—
140C3⋊Dic3—21no—
141C3⋊Dic3—41no—
142C3⋊Dic3—41no—
143C3⋊Dic3#12312yes—
144C23×C4—91no—
145C22×C8—92no—
146#117—91no—
147#117—91no—
148#117—91no—
149#117—181no—
150#117—181no—
151#117#15711yescharacteristic, complemented
152C2×C4⋊C4—91no—
153C2×C4⋊C4—91no—
154C2×C4⋊C4—92no—
155C2×C22⋊C4—181no—
156C2×C22⋊C4—181no—
157C2×C42—181no—
158C22⋊C8—181no—
159C22⋊C8—181no—
160#95—181no—
161C23×C3—22no—
162C22×D3—62no—
163C22×D3—62no—
164C22×D3—68no—
165C22×D3—122no—
166C22×D3—124no—
167C22×D3—122no—
168C2×C3×C4—28no—
169C2×C3×C4—24no—
170C2×C3×C4—24no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—68no—
176C2×Dic3—64no—
177C2×Dic3—64no—
178C4×D3—68no—
179C4×D3—68no—
180C4×D3—68no—
181C4×D3—68no—
182C4×D3—128no—
183C4×D3—124no—
184C4×D3—124no—
185C2×C32—41no—
186C2×C32#38111yescharacteristic
187C2×C32#41611yescharacteristic
188C2×C32#41711yescharacteristic
189C3⋊D3—41no—
190C3⋊D3#48212yes—
191C3⋊D3#48512yes—
192C24—91no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—184no—
199C22×C4—181no—
200C22×C4—181no—
201C22×C4—182no—
202C22×C4C2×#15711yescharacteristic
203C2×C8—182no—
204C2×C8—184no—
205C4⋊C4—91no—
206C4⋊C4—91no—
207C4⋊C4—181no—
208C4⋊C4—181no—
209C4⋊C4—184no—
210C4⋊C4C2×#15711yescharacteristic
211C4⋊C4C2×#15711yescharacteristic
212C22⋊C4—21no—
213C22⋊C4—181no—
214C22⋊C4—181no—
215C22⋊C4—181no—
216C22⋊C4—362no—
217C42—21no—
218C42—181no—
219C42—181no—
220C42—181no—
221C22×C3—24no—
222C22×C3—22no—
223C22×C3—42no—
224C22×C3—42no—
225C2×D3—64no—
226C2×D3—64no—
227C2×D3—62no—
228C2×D3—62no—
229C2×D3—64no—
230C2×D3—122no—
231C2×D3—122no—
232C2×D3—128no—
233C2×D3—128no—
234C3×C4—24no—
235C3×C4—24no—
236C3×C4—44no—
237C3×C4—44no—
238Dic3—64no—
239Dic3—64no—
240Dic3—124no—
241Dic3—124no—
242C32#182511yescharacteristic, complemented, Sylow
243C23—91no—
244C23—91no—
245C23—181no—
246C23—182no—
247C23—181no—
248C23—182no—
249C23C22⋊#15711yescharacteristic
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—91no—
254C2×C4—94no—
255C2×C4—91no—
256C2×C4—182no—
257C2×C4—182no—
258C2×C4—182no—
259C2×C4—182no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4—361no—
263C2×C4—361no—
264C2×C4—362no—
265C2×C4—362no—
266C2×C4—362no—
267C2×C4—362no—
268C2×C4C22⋊#15711yescharacteristic
269C2×C4C22×#15711yescharacteristic
270C8—362no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—22no—
274C2×C3—44no—
275D3—64no—
276D3—64no—
277D3—124no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—92no—
282C22—91no—
283C22—91no—
284C22—92no—
285C22—181no—
286C22—181no—
287C22—181no—
288C22—362no—
289C22—362no—
290C22C2×C22⋊#15711yescharacteristic
291C4—21no—
292C4—41no—
293C4—41no—
294C4—92no—
295C4—181no—
296C4—361no—
297C4—361no—
298C4—722no—
299C4#6428612yes—
300C3—22no—
301C2—41no—
302C2—92no—
303C2—92no—
304C2—361no—
305C2#1059381111yescharacteristic
306C2#1059384011yescharacteristic
307C2#1059384111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#117C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenter#117#157
hypocenterC32#1825
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10590163C2semidirect
5. #10590163C2semidirect
10. C32×#117C4semidirect
11. #64135C4semidirect
12. #64101C4semidirect
13. #64101C4semidirect
151. #117#157semidirect
242. C32#1825semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
#105938122
#105938002
#105901632
#18259