Finite Group Databasebeta

← #11787793

Subgroups — #11787793

Order 1152.

1080 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 191 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×#64156C211yesmaximal, characteristic
2#10595992C211yesmaximal, characteristic
3C32×#419C211yesmaximal, characteristic, complemented
4#10592924C211yesmaximal, characteristic, complemented
5C2×#63650C211yesmaximal, characteristic
6#10589421C211yesmaximal, characteristic, complemented
7#10589398C211yesmaximal, characteristic, complemented
8#70343—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64156—22no—
14#64156C414yescomplemented
15C2×#3752—22no—
16#64135C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19#64102—22no—
20C22⋊C4×C3⋊D3—22no—
21C4×C4⋊(C3⋊D3)—22no—
22C32×#103—22no—
23#63662—22no—
24#63650—22no—
25C2×#947—34no—
26#5521—34no—
27C3×#419D314yescomplemented
28#5225—34no—
29C2×#823—34no—
30#4555—34no—
31#4532—34no—
32C23×C3⋊D3D412yes—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8C2×C412yescomplemented
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)C2×C412yes—
47C2×C4⋊(C3⋊D3)D412yes—
48C2×C4×C3⋊D3—24no—
49C32×M16—21no—
50C32×M16—21no—
51C2×C32×C8—21no—
52C32×C4⋊C4D412yes—
53C32×C22⋊C4—21no—
54C32×C42—21no—
55#3757—21no—
56#3752—24no—
57#3752—28no—
58C4⋊(C3⋊Dic3)D412yes—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3C2×C412yescomplemented
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65#1885—91noSylow
66C22×C3×Q8C2×D314yes—
67C22×D12—34no—
68C2×C3×M16C2×D314yes—
69C3×#117C2×D314yes—
70#947—316no—
71#947—68no—
72C2×(C2×D3)⋊C4—68no—
73#926—34no—
74C2×C4×Dic3—34no—
75C2×#208—34no—
76#893—68no—
77D3×C22⋊C4—68no—
78C4×D12—68no—
79C3×#103—28no—
80#835—68no—
81#823—68no—
82C23×C32C2×D411yescharacteristic
83C22×C3⋊D3—22no—
84C22×C3⋊D3—22no—
85C22×C3⋊D3—44no—
86C22×C3⋊D3C22⋊C414yes—
87C32×Q8—22no—
88C32×Q8—22no—
89C32×Q8—41no—
90C32×Q8—41no—
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—42no—
104C4⋊(C3⋊D3)—22no—
105C4⋊(C3⋊D3)—22no—
106C4⋊(C3⋊D3)—22no—
107C4⋊(C3⋊D3)—22no—
108C4×C3⋊D3—84no—
109C32×C8—41no—
110C3⋊(C3⋊C8)—41no—
111C2×#124—91no—
112#518—91no—
113#419—91no—
114#419C3⋊D311yescharacteristic, complemented
115C2×#100—91no—
116#339—91no—
117#339—91no—
118C23×D3—38no—
119C2×C3×Q8—24no—
120C2×C3×Q8—24no—
121C2×C3×Q8—24no—
122C2×C3×Q8—24no—
123C2×C3×Q8—24no—
124C2×C3×Q8C4×D318yescomplemented
125C22×C3×C4—24no—
126C22×C3×C4C22×D314yes—
127C22×Dic3—64no—
128C2×D12—38no—
129C2×D12—38no—
130C2×D12—64no—
131C2×D12—64no—
132C2×D12—64no—
133C2×D12—64no—
134C2×C4×D3—616no—
135C3×M16—24no—
136C3×M16—24no—
137C2×C3×C8—24no—
138C3×C4⋊C4#6718yes—
139C3×C22⋊C4—24no—
140C3×C42—24no—
141#217—64no—
142(C2×D3)⋊C4—632no—
143(C2×D3)⋊C4—616no—
144C4⋊Dic3—38no—
145C4×Dic3—38no—
146C4×Dic3—64no—
147C4×Dic3—64no—
148#208—64no—
149#208—64no—
150C2×C3⋊C8—64no—
151C22×C32—22no—
152C22×C32C2×C22⋊C411yescharacteristic
153C22×C32#12011yescharacteristic
154C22×C32#12311yescharacteristic
155C2×C3⋊D3—24no—
156C2×C3⋊D3—44no—
157C2×C3⋊D3—44no—
158C2×C3⋊D3—82no—
159C32×C4—42no—
160C32×C4—42no—
161C32×C4C4×D411yescharacteristic
162C32×C4C4×D411yescharacteristic
163C32×C4#12111yescharacteristic
164C32×C4#12111yescharacteristic
165C3⋊Dic3—42no—
166C3⋊Dic3—42no—
167C22×Q8C2×C3⋊D311yescharacteristic
168C22×D4—91no—
169C2×M16—91no—
170C2×M16C2×C3⋊D311yescharacteristic
171#124—94no—
172#124—182no—
173C4×D4—182no—
174C4×D4—182no—
175#117—91no—
176#117C2×C3⋊D311yescharacteristic
177C2×C22⋊C4—182no—
178C2×C22⋊C4—182no—
179C2×C42—91no—
180#103—22no—
181#103—182no—
182#100—182no—
183C23×C3D3×D414yes—
184C22×D3—316no—
185C22×D3—68no—
186C22×D3—68no—
187C22×D3—1216no—
188C3×Q8—28no—
189C3×Q8—28no—
190C3×Q8—44no—
191C3×Q8—44no—
192C2×C3×C4—28no—
193C2×C3×C4—28no—
194C2×C3×C4—44no—
195C2×C3×C4—44no—
196C2×C3×C4C2×C4×D314yes—
197C2×C3×C4#23514yes—
198C2×C3×C4D3×D414yes—
199C2×C3×C4D3×D414yes—
200C2×C3×C4#23714yes—
201C2×C3×C4C2×#6714yes—
202C2×Dic3—68no—
203C2×Dic3—68no—
204C2×Dic3—128no—
205D12—68no—
206D12—68no—
207D12—68no—
208D12—68no—
209C4×D3—2416no—
210C3×C8—44no—
211C3⋊C8—124no—
212C2×C32—21no—
213C2×C32—21no—
214C2×C32#38611yescharacteristic
215C2×C32#45512yes—
216C3⋊D3—44no—
217C24—92no—
218C2×Q8—21no—
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8C4×C3⋊D312yescomplemented
224C2×D4—92no—
225C2×D4—92no—
226C2×D4—181no—
227C2×D4—181no—
228C2×D4—181no—
229C2×D4—181no—
230C22×C4—21no—
231C22×C4—184no—
232C22×C4—181no—
233C22×C4C22×C3⋊D311yescharacteristic
234M16—21no—
235M16—21no—
236M16—181no—
237M16—181no—
238C2×C8—21no—
239C2×C8—181no—
240C4⋊C4—92no—
241C4⋊C4#63812yes—
242C22⋊C4—21no—
243C22⋊C4—188no—
244C22⋊C4—184no—
245C22⋊C4—181no—
246C42—21no—
247C42—92no—
248C42—181no—
249C42—181no—
250C22×C3—28no—
251C22×C3D3×C22⋊C414yes—
252C22×C3#88314yes—
253C22×C3#93714yes—
254C2×D3—616no—
255C2×D3—1216no—
256C2×D3—1216no—
257C2×D3—248no—
258C3×C4—48no—
259C3×C4—48no—
260C3×C4#67⋊C414yes—
261C3×C4#88414yes—
262C3×C4C4×#6714yes—
263C3×C4#93814yes—
264Dic3—128no—
265Dic3—128no—
266C32#188511yescharacteristic, complemented, Sylow
267C23—94no—
268C23—182no—
269C23—182no—
270C23—364no—
271C23D4×C3⋊D311yescharacteristic
272Q8—22no—
273Q8—22no—
274Q8—41no—
275Q8—41no—
276D4—182no—
277D4—182no—
278D4—182no—
279D4—182no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—182no—
285C2×C4—182no—
286C2×C4—362no—
287C2×C4—724no—
288C2×C4C2×C4×C3⋊D311yescharacteristic
289C2×C4#382811yescharacteristic
290C2×C4D4×C3⋊D311yescharacteristic
291C2×C4D4×C3⋊D311yescharacteristic
292C2×C4#383011yescharacteristic
293C2×C4C2×#63811yescharacteristic
294C8—41no—
295C8—361no—
296C2×C3—24no—
297C2×C3—24no—
298C2×C3#495614yes—
299C2×C3#520218yes—
300D3—1216no—
301C22—22no—
302C22—184no—
303C22—364no—
304C22—364no—
305C22—722no—
306C22C22⋊C4×C3⋊D311yescharacteristic
307C22#6409211yescharacteristic
308C22#6414611yescharacteristic
309C4—42no—
310C4—42no—
311C4—362no—
312C4—362no—
313C4#6409011yescharacteristic
314C4#6409311yescharacteristic
315C4C4×#63811yescharacteristic
316C4#6414711yescharacteristic
317C3#7034314yescomplemented
318C2—21no—
319C2—21no—
320C2—364no—
321C2#1059265511yescharacteristic
322C2#1059290112yes—
subgroupG/H
centerC22#64146
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#419C2
socleC22×C32#120
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenter#419C3⋊D3
hypocenterC32#1885
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. C32×#419C2semidirect
4. #10592924C2semidirect
6. #10589421C2semidirect
7. #10589398C2semidirect
14. #64156C4semidirect
27. C3×#419D3semidirect
38. C2×C32×Q8C2×C4semidirect
61. C4×C3⋊Dic3C2×C4semidirect
114. #419C3⋊D3semidirect
124. C2×C3×Q8C4×D3semidirect
223. C2×Q8C4×C3⋊D3semidirect
266. C32#1885semidirect
317. C3#70343semidirect

Maximal subgroups

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

subgroupindex
C2×#641562
#105959922
C32×#4192
#105929242
C2×#636502
#105894212
#105893982
#703433