Finite Group Databasebeta

← #11791456

Subgroups — #11791456

Order 1152.

926 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 88 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×#127C211yesmaximal, characteristic
2C2×#63782C214yesmaximal, complemented
3C4×C4⋊#157C211yesmaximal, characteristic, complemented
4#10593726C211yesmaximal, characteristic, complemented
5C2×D4×C3⋊D3—21no—
6C2×D4×C3⋊D3—21no—
7C2×D4×C3⋊D3C2212yes—
8C2×C4⋊#157C2212yes—
9C2×C4×#157—21no—
10C2×#3787C2212yes—
11C32×#127C411yescharacteristic, complemented
12#64149—21no—
13#64149—21no—
14#64149C412yescomplemented
15#64083C411yescharacteristic, complemented
16C42×C3⋊D3C2211yescharacteristic
17#63782—28no—
18#63781—21no—
19#63779—21no—
20C4⋊#622—21no—
21D3×#127—62no—
22C23×C3⋊D3—22no—
23C22×#157—22no—
24C2×C32×D4—21no—
25C2×C32×D4—21no—
26C2×C32×D4C2×C412yes—
27C2×#638—22no—
28C2×#638—22no—
29C2×#638—22no—
30D4×C3⋊D3—24no—
31D4×C3⋊D3—24no—
32D4×C3⋊D3—44no—
33D4×C3⋊D3—42no—
34D4×C3⋊D3—42no—
35C2×C4⋊(C3⋊D3)—21no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)C2×C412yes—
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3C2311yescharacteristic
41C2×#622—22no—
42C4⋊#157—22no—
43C4⋊#157D414yescomplemented
44C4×#157—42no—
45#3787—24no—
46C32×C42C2×C411yescharacteristic
47C4×C3⋊Dic3C2×C411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50#1982—91nomaximal, Sylow
51C2×D3×D4—64no—
52C2×D3×D4—64no—
53C2×D3×D4—64no—
54C3×#127—22no—
55#940—64no—
56#940—64no—
57#940—64no—
58#874—62no—
59C42×D3—62no—
60C23×C32—22no—
61C22×C3⋊D3—22no—
62C22×C3⋊D3—44no—
63C22×C3⋊D3—42no—
64C22×C3⋊D3—42no—
65C22×C3⋊D3—44no—
66C22×C3⋊D3C2×D411yescharacteristic
67C2×#157—24no—
68C2×#157—42no—
69C2×#157—42no—
70C32×D4—24no—
71C32×D4—42no—
72C32×D4—42no—
73C2×C32×C4C22⋊C411yescharacteristic
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22×C411yescharacteristic
76#638—44no—
77#638—44no—
78#638—42no—
79#638—42no—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C2×D411yescharacteristic
83C4⋊(C3⋊D3)—24no—
84C4⋊(C3⋊D3)—42no—
85C4⋊(C3⋊D3)—42no—
86C4×C3⋊D3—22no—
87C4×C3⋊D3D812yes—
88C4×C3⋊D3SD1612yes—
89C4×C3⋊D3C2×D412yes—
90C4×C3⋊D3#4112yes—
91#622—42no—
92C2×#127—91no—
93C2×C4⋊C8—91no—
94C2×#102—94no—
95C4×C4⋊C4—91no—
96C23×D3—68no—
97C2×C3×D4—24no—
98C2×C3×D4—24no—
99C2×C3×D4—24no—
100C2×#67—68no—
101C2×#67—68no—
102C2×#67—68no—
103D3×D4—128no—
104D3×D4—128no—
105D3×D4—128no—
106D3×D4—128no—
107D3×D4—1216no—
108C2×D12—64no—
109C2×D12—64no—
110C2×D12—64no—
111C2×C4×D3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C3×C42—22no—
115C4×Dic3—62no—
116C4×Dic3—62no—
117C4×Dic3—62no—
118C22×C32—42no—
119C22×C32—42no—
120C22×C32—42no—
121C22×C32C2×C22⋊C411yescharacteristic
122C2×C3⋊D3—42no—
123C2×C3⋊D3—42no—
124C2×C3⋊D3—42no—
125C2×C3⋊D3—84no—
126C2×C3⋊D3—84no—
127C2×C3⋊D3#12112yes—
128C2×C3⋊D3C2×D811yescharacteristic
129C2×C3⋊D3C2×SD1611yescharacteristic
130C2×C3⋊D3AGL(1,ℤ/8)12yes—
131#157—44no—
132C32×C4—21no—
133C32×C4#10212yescomplemented
134C32×C4C4×D412yes—
135C3⋊Dic3—21no—
136C3⋊Dic3#10212yescomplemented
137C3⋊Dic3#12411yescharacteristic
138C3⋊Dic3#12711yescharacteristic
139C22×D4—92no—
140C22×D4—181no—
141C22×D4—181no—
142C22×C8—92no—
143#127—92no—
144#127—91no—
145#127—181no—
146#127—181no—
147#127#15711yescharacteristic, complemented
148C2×C4⋊C4—92no—
149C2×C42—91no—
150C2×C42—181no—
151C4⋊C8—181no—
152C4⋊C8—181no—
153#102—188no—
154#95—181no—
155C23×C3—28no—
156C22×D3—62no—
157C22×D3—68no—
158C22×D3—1216no—
159C22×D3—128no—
160C22×D3—128no—
161C22×D3—1216no—
162C3×D4—48no—
163C3×D4—48no—
164C3×D4—48no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168#67—128no—
169#67—128no—
170#67—1216no—
171#67—1216no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175D12—128no—
176D12—128no—
177D12—128no—
178C4×D3—64no—
179C4×D3—64no—
180C4×D3—64no—
181C4×D3—64no—
182C4×D3—68no—
183C2×C32—82no—
184C2×C32#39011yescharacteristic
185C2×C32C2×#10211yescharacteristic
186C2×C32#41811yescharacteristic
187C3⋊D3—82no—
188C3⋊D3#45912yes—
189C3⋊D3#46012yes—
190C24—182no—
191C2×D4—21no—
192C2×D4—21no—
193C2×D4—92no—
194C2×D4—184no—
195C2×D4—184no—
196C2×D4—182no—
197C2×D4—182no—
198C2×D4—182no—
199C2×D4—181no—
200C2×D4—181no—
201C2×D4—362no—
202C2×D4—362no—
203C2×D4—364no—
204C2×D4C2×#15712yes—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—182no—
209C2×C8—184no—
210C2×C8—182no—
211C4⋊C4—94no—
212C4⋊C4—182no—
213C42—91no—
214C42—91no—
215C42—91no—
216C42—362no—
217C42C2×#15711yescharacteristic
218C22×C3—22no—
219C22×C3—48no—
220C22×C3—48no—
221C22×C3—48no—
222C2×D3—64no—
223C2×D3—62no—
224C2×D3—62no—
225C2×D3—64no—
226C2×D3—128no—
227C2×D3—128no—
228C2×D3—128no—
229C2×D3—2416no—
230C2×D3—2416no—
231C3×C4—24no—
232C3×C4—24no—
233C3×C4—24no—
234Dic3—64no—
235Dic3—62no—
236Dic3—62no—
237Dic3—64no—
238C32#198211yescharacteristic, complemented, Sylow
239C23—22no—
240C23—91no—
241C23—182no—
242C23—364no—
243C23—362no—
244C23—362no—
245C23—364no—
246D4—24no—
247D4—42no—
248D4—42no—
249D4—184no—
250D4—362no—
251D4—362no—
252D4—362no—
253D4—364no—
254D4—364no—
255D4—362no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—92no—
259C2×C4—92no—
260C2×C4—92no—
261C2×C4—92no—
262C2×C4—91no—
263C2×C4—182no—
264C2×C4—184no—
265C2×C4—362no—
266C2×C4—362no—
267C2×C4C22⋊#15711yescharacteristic
268C2×C4C22⋊#15711yescharacteristic
269C2×C4C22×#15711yescharacteristic
270C8—362no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—22no—
274C2×C3—88no—
275D3—64no—
276D3—64no—
277D3—248no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—91no—
282C22—91no—
283C22—92no—
284C22—92no—
285C22—362no—
286C22—362no—
287C22—362no—
288C22—724no—
289C22—724no—
290C22C2×C22⋊#15711yescharacteristic
291C4—21no—
292C4—92no—
293C4—91no—
294C4—91no—
295C4—181no—
296C4—364no—
297C4#6378212yescomplemented
298C4D4×#15712yes—
299C3—22no—
300C2—82no—
301C2—92no—
302C2—92no—
303C2—722no—
304C2C2×#6378211yescharacteristic
305C2#1059381411yescharacteristic
306C2#1059382711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#127C4
socleC22×C32C2×C22⋊C4
prime radicalC3⋊D3×#127C2
cosocleC2×C4×C3⋊D3C23
hypercenter#127#157
hypocenterC32#1982
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. C2×#63782C2semidirect
3. C4×C4⋊#157C2semidirect
4. #10593726C2semidirect
11. C32×#127C4semidirect
14. #64149C4semidirect
15. #64083C4semidirect
43. C4⋊#157D4semidirect
133. C32×C4#102semidirect
136. C3⋊Dic3#102semidirect
147. #127#157semidirect
238. C32#1982semidirect
297. C4#63782semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1272
C2×#637822
C4×C4⋊#1572
#105937262
#19829