Finite Group Databasebeta

← #11873478

Subgroups — #11873478

Order 1152.

1200 conjugacy classes of subgroups; only the 241 normal subgroups are shown.

normal subgroups only

This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 241 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
1#10596199C211yesmaximal, characteristic, complemented
2#10596196C211yesmaximal, characteristic
3C32×#487C211yesmaximal, characteristic, complemented
4#10592787C211yesmaximal, characteristic, complemented
5#10592778C211yesmaximal, characteristic, complemented
6#10592503C214yesmaximal, complemented
7#10592499C214yesmaximal, complemented
8#10592393C211yesmaximal, characteristic, complemented
9C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
10#81598—34nomaximal
11C2×#3832C2212yes—
12C32×C4⋊Q8C2211yescharacteristic
13C32×C4⋊Q8C2211yescharacteristic
14#64156C2212yes—
15#64155—21no—
16Q8×C3⋊Dic3—21no—
17C2×C8×C3⋊D3C2212yes—
18#64106—21no—
19#64104—21no—
20#64104—21no—
21#64102—21no—
22#64102—21no—
23#64101C2212yes—
24#64099C2212yes—
25#64096—21no—
26#64083C2211yescharacteristic
27C42×C3⋊D3C2211yescharacteristic
28#64078C2211yescharacteristic
29C32×#103C2214yes—
30C32×C4×C8C2211yescharacteristic
31#63662C2214yes—
32#63648C2214yes—
33C8×C3⋊Dic3C2212yes—
34#63636C2214yes—
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36#5728—34no—
37#5725—34no—
38C3×#487D314yescomplemented
39#5088—34no—
40#5079—34no—
41#4804—316no—
42#4800—316no—
43#4694—34no—
44C4×D3×C8—34no—
45C2×C32×Q8—21no—
46C2×C32×Q8C2312yes—
47#3832—28no—
48C2×C4⋊(C3⋊D3)—22no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)C2312yes—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3C2311yescharacteristic
56C2×#634—21no—
57C2×C32×C8C2312yes—
58C32×C4⋊C4—21no—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2312yes—
62C32×C42C2311yescharacteristic
63#3752—22no—
64#3752—22no—
65#3752—22no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—22no—
68C4⋊(C3⋊Dic3)C2312yes—
69#3750—22no—
70C4×C3⋊Dic3—22no—
71C4×C3⋊Dic3D411yescharacteristic
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2312yes—
75C8×C3⋊D3—24no—
76#3131—91noSylow
77C2×#239—38no—
78C3×C4⋊Q8C2×D314yes—
79C3×C4⋊Q8C2×D314yes—
80#947—38no—
81#946—64no—
82Q8×Dic3—64no—
83C2×D3×C8—38no—
84#897—64no—
85#895—64no—
86#895—64no—
87#893—64no—
88#893—64no—
89#892—38no—
90#890—38no—
91#887—64no—
92#874—34no—
93C42×D3—34no—
94#869—34no—
95C3×#103C2×D3116yes—
96C3×C4×C8C2×D314yes—
97#835—316no—
98#821—316no—
99C8×Dic3—38no—
100#809—316no—
101C4×C3⋊C8—34no—
102C22×C3⋊D3—22no—
103C22×C3⋊D3C2×D411yescharacteristic
104C32×Q8—24no—
105C32×Q8—42no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2411yescharacteristic
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3C2×D411yescharacteristic
113C2×C3⋊Dic3C2×D411yescharacteristic
114C2×C3⋊Dic3C2×D411yescharacteristic
115C4⋊(C3⋊D3)—24no—
116C4⋊(C3⋊D3)—44no—
117C4⋊(C3⋊D3)—42no—
118C4⋊(C3⋊D3)—42no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3—44no—
122C4×C3⋊D3#4114yes—
123#634—42no—
124C32×C8—22no—
125C3⋊(C3⋊C8)—22no—
126#533—91no—
127#532—91no—
128#488—94no—
129#487—91no—
130#487C3⋊D311yescharacteristic, complemented
131#486—91no—
132#486—91no—
133#416—94no—
134C2×C4×C8—91no—
135C2×C3×Q8—24no—
136C2×C3×Q8C22×D318yes—
137#239—632no—
138C2×D12—38no—
139C2×D12—68no—
140C2×D12—64no—
141C2×D12—64no—
142C2×C4×D3—34no—
143C2×C4×D3—34no—
144C2×C4×D3—34no—
145C2×C4×D3—68no—
146C2×Dic6—64no—
147C2×C3×C8C22×D318yes—
148C3×C4⋊C4—24no—
149C3×C4⋊C4—24no—
150C3×C4⋊C4—24no—
151C3×C4⋊C4C22×D318yes—
152C3×C42C22×D314yes—
153(C2×D3)⋊C4—68no—
154(C2×D3)⋊C4—68no—
155(C2×D3)⋊C4—68no—
156C4⋊Dic3—38no—
157C4⋊Dic3—68no—
158C4⋊Dic3—64no—
159Dic3⋊C4—68no—
160C4×Dic3—34no—
161C4×Dic3—34no—
162C4×Dic3—34no—
163C4×Dic3—68no—
164C2×C3⋊C8—38no—
165D3×C8—616no—
166C22×C32C22×D411yescharacteristic
167C2×C3⋊D3—21no—
168C2×C3⋊D3—21no—
169C2×C3⋊D3—42no—
170C2×C3⋊D3—42no—
171C2×C3⋊D3—42no—
172C2×C3⋊D3#12412yes—
173C32×C4—42no—
174C32×C4—42no—
175C32×C4#13512yes—
176C32×C4#13512yes—
177C32×C4C2×#4112yes—
178C3⋊Dic3—21no—
179C3⋊Dic3—21no—
180C3⋊Dic3—42no—
181C3⋊Dic3#12412yes—
182C2×#41—92no—
183C22×C8—92no—
184C4⋊Q8—91no—
185C4⋊Q8C2×C3⋊D311yescharacteristic
186C4⋊Q8C2×C3⋊D311yescharacteristic
187#127—91no—
188#125—92no—
189#124—92no—
190C22⋊Q8—181no—
191C22⋊Q8—181no—
192#121—181no—
193#121—181no—
194C4×Q8—181no—
195C4×Q8—181no—
196C4×D4—181no—
197C4×D4—181no—
198#117—92no—
199C2×C42—91no—
200#103—94no—
201#103C2×C3⋊D314yes—
202#102—94no—
203#102—94no—
204C4×C8—92no—
205C4×C8—91no—
206C4×C8C2×C3⋊D311yescharacteristic
207C22×D3—34no—
208C22×D3—68no—
209C3×Q8—216no—
210C3×Q8—48no—
211C2×C3×C4—28no—
212C2×C3×C4—28no—
213C2×C3×C4D3×D414yes—
214C2×C3×C4D3×D414yes—
215C2×C3×C4C23×D314yes—
216C2×Dic3—34no—
217C2×Dic3—34no—
218C2×Dic3—34no—
219C2×Dic3—68no—
220D12—616no—
221D12—1216no—
222D12—128no—
223D12—128no—
224C4×D3—316no—
225C4×D3—68no—
226C4×D3—68no—
227C4×D3—1216no—
228Dic6—128no—
229C3×C8—28no—
230C3⋊C8—68no—
231C2×C32C2×#12411yescharacteristic
232C2×C32C2×#13511yescharacteristic
233C2×C32C2×#13511yescharacteristic
234C3⋊D3—22no—
235C3⋊D3—82no—
236#41—188no—
237C2×Q8—21no—
238C2×Q8—181no—
239C2×Q8C22×C3⋊D312yes—
240C2×D4—92no—
241C2×D4—182no—
242C2×D4—181no—
243C2×D4—181no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—182no—
248C2×C8—92no—
249C2×C8—184no—
250C2×C8C22×C3⋊D312yes—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—92no—
255C4⋊C4—182no—
256C4⋊C4—182no—
257C4⋊C4—181no—
258C4⋊C4C22×C3⋊D312yes—
259C22⋊C4—182no—
260C22⋊C4—182no—
261C22⋊C4—182no—
262C42—91no—
263C42—91no—
264C42—91no—
265C42—182no—
266C42C22×C3⋊D311yescharacteristic
267C22×C3C2×D3×D414yes—
268C2×D3—38no—
269C2×D3—64no—
270C2×D3—64no—
271C2×D3—128no—
272C2×D3—128no—
273C2×D3—128no—
274C3×C4—48no—
275C3×C4—48no—
276C3×C4#91618yes—
277C3×C4#91918yes—
278C3×C4D3×#4118yes—
279Dic3—38no—
280Dic3—64no—
281Dic3—64no—
282Dic3—128no—
283C32#313111yescharacteristic, complemented, Sylow
284C23—91no—
285C23—182no—
286Q8—24no—
287Q8—42no—
288Q8—362no—
289D4—184no—
290D4—364no—
291D4—362no—
292D4—362no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—91no—
296C2×C4—94no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—364no—
303C2×C4D4×C3⋊D311yescharacteristic
304C2×C4D4×C3⋊D311yescharacteristic
305C2×C4C23×C3⋊D311yescharacteristic
306C8—22no—
307C8—182no—
308C2×C3D3×#12414yes—
309C2×C3C2×#91614yes—
310C2×C3C2×#91914yes—
311D3—68no—
312D3—248no—
313C22—92no—
314C22—181no—
315C22—181no—
316C22—362no—
317C22—362no—
318C22—362no—
319C22C2×D4×C3⋊D311yescharacteristic
320C4—42no—
321C4—42no—
322C4—92no—
323C4—181no—
324C4—181no—
325C4—362no—
326C4#6412512yes—
327C4#6412812yes—
328C4#41×C3⋊D312yes—
329C3#8159814yescomplemented
330C2—182no—
331C2—722no—
332C2C3⋊D3×#12411yescharacteristic
333C2C2×#6412511yescharacteristic
334C2C2×#6412811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radical#10596196C2
hypercenter#487C3⋊D3
hypocenterC32#3131
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C32×#487C2semidirect
4. #10592787C2semidirect
5. #10592778C2semidirect
6. #10592503C2semidirect
7. #10592499C2semidirect
8. #10592393C2semidirect
9. C4×C8×C3⋊D3C2semidirect
38. C3×#487D3semidirect
130. #487C3⋊D3semidirect
283. C32#3131semidirect
329. C3#81598semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105961962
C32×#4872
#105927872
#105927782
#105925032
#105924992
#105923932
C4×C8×C3⋊D32
#815983