Finite Group Databasebeta

← #11874272

Subgroups — #11874272

Order 1152.

1716 conjugacy classes of subgroups; only the 277 normal subgroups are shown.

normal subgroups only

This group has 1716 conjugacy classes of subgroups — too many to draw. Only its 277 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×#64125C214yesmaximal, complemented
2#10596196C211yesmaximal, characteristic, complemented
3#10596187C211yesmaximal, characteristic, complemented
4C32×#492C211yesmaximal, characteristic, complemented
5#10592867C214yesmaximal, complemented
6#10592791C211yesmaximal, characteristic, complemented
7#10592772C211yesmaximal, characteristic, complemented
8#10592392C211yesmaximal, characteristic, complemented
9C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
10#81760—34nomaximal
11C2×#3832C2212yes—
12C2×#3830C2212yes—
13C2×C32×SD16C2214yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×#127C2211yescharacteristic
16#64156C2212yes—
17C2×#3756C2214yes—
18#64147—22no—
19#64145C2212yes—
20D4×C3⋊Dic3—22no—
21C2×#3753C2214yes—
22#64125—216no—
23C2×#3744C2214yes—
24C2×C8×C3⋊D3C2212yes—
25#64104—22no—
26#64102—22no—
27#64083C2211yescharacteristic
28C42×C3⋊D3C2211yescharacteristic
29#64078C2211yescharacteristic
30C32×C4×C8C2211yescharacteristic
31C8×C3⋊Dic3C2212yes—
32C4×C3⋊(C3⋊C8)C2211yescharacteristic
33C2×#916—316no—
34#5725—34no—
35#5716—34no—
36C3×#492D314yescomplemented
37#5168—316no—
38#5092—34no—
39#5073—34no—
40#4693—34no—
41C4×D3×C8—34no—
42C2×C32×Q8C2312yes—
43C2×C32×D4—22no—
44C2×C32×D4C2312yes—
45C2×#638—22no—
46C22×C3⋊Dic3—22no—
47#3832—28no—
48#3830—28no—
49C2×C4⋊(C3⋊D3)—22no—
50C2×C4⋊(C3⋊D3)—22no—
51C2×C4⋊(C3⋊D3)C2312yes—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3D412yes—
54C2×C4×C3⋊D3C2311yescharacteristic
55C2×#634C2312yes—
56C32×SD16—28no—
57C2×C32×C8C2312yes—
58C32×C4⋊C4—22no—
59C32×C42C2311yescharacteristic
60#3757—24no—
61#3756—28no—
62#3753—28no—
63#3752—24no—
64C4⋊(C3⋊Dic3)—22no—
65C4×C3⋊Dic3D412yes—
66C4×C3⋊Dic3C2311yescharacteristic
67C2×C3⋊(C3⋊C8)C2312yes—
68#3744—28no—
69C8×C3⋊D3D418yescomplemented
70#3147—91noSylow
71C2×#239—38no—
72C2×#237—38no—
73C2×C3×SD16C2×D3116yes—
74C3×C4⋊Q8C2×D314yes—
75C3×#127C2×D314yes—
76#947—38no—
77C2×#216—316no—
78#938—68no—
79#936—38no—
80D4×Dic3—68no—
81C2×#213—316no—
82#916—664no—
83C2×#204—316no—
84C2×D3×C8—38no—
85#895—68no—
86#893—68no—
87#874—34no—
88C42×D3—34no—
89#869—34no—
90C3×C4×C8C2×D314yes—
91C8×Dic3—38no—
92C4×C3⋊C8—34no—
93C23×C32—22no—
94C22×C3⋊D3—22no—
95C22×C3⋊D3C2×D411yescharacteristic
96C32×Q8—24no—
97C32×D4—24no—
98C32×D4—44no—
99C2×C32×C4—22no—
100C2×C32×C4C2×D412yes—
101C2×C32×C4C2411yescharacteristic
102#638—44no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—44no—
105C2×C3⋊Dic3C2×D412yes—
106C2×C3⋊Dic3C2×D411yescharacteristic
107C4⋊(C3⋊D3)—24no—
108C4⋊(C3⋊D3)—44no—
109C4⋊(C3⋊D3)—44no—
110C4×C3⋊D3—24no—
111C4×C3⋊D3—44no—
112C4×C3⋊D3C2×D414yes—
113#634—24no—
114C32×C8C2×D414yes—
115C3⋊(C3⋊C8)C2×D414yes—
116C2×#135—94no—
117#532—91no—
118#532—91no—
119#495—94no—
120#494—91no—
121#493—91no—
122#492—91no—
123#492C3⋊D311yescharacteristic, complemented
124C2×C4×C8—91no—
125C2×C3×Q8C22×D318yes—
126C2×C3×D4—28no—
127C2×C3×D4C22×D318yes—
128C2×#67—68no—
129C22×Dic3—68no—
130#239—632no—
131#237—632no—
132C2×D12—38no—
133C2×D12—68no—
134C2×D12—68no—
135C2×C4×D3—34no—
136C2×C4×D3—38no—
137C2×C4×D3—68no—
138C2×Dic6—38no—
139C3×SD16—232no—
140C2×C3×C8C22×D318yes—
141C3×C4⋊C4—28no—
142C3×C42C22×D314yes—
143#217—616no—
144#216—632no—
145#213—632no—
146(C2×D3)⋊C4—616no—
147C4⋊Dic3—68no—
148C4×Dic3—38no—
149C4×Dic3—34no—
150C2×C3⋊C8—38no—
151#204—632no—
152D3×C8—332no—
153C22×C32—42no—
154C22×C32—44no—
155C22×C32C22×D411yescharacteristic
156C2×C3⋊D3—22no—
157C2×C3⋊D3—42no—
158C2×C3⋊D3—44no—
159C2×C3⋊D3#12712yes—
160C32×C4—42no—
161C32×C4#13514yescomplemented
162C32×C4C22×D412yes—
163C3⋊Dic3—22no—
164C3⋊Dic3—42no—
165C3⋊Dic3#12712yes—
166C2×#41—92no—
167C2×#41—92no—
168#135—1816no—
169C2×Q16—94no—
170C2×SD16—94no—
171C2×SD16C2×C3⋊D314yes—
172C2×D8—94no—
173C22×C8—92no—
174C4⋊Q8—91no—
175C4⋊Q8C2×C3⋊D311yescharacteristic
176#127—91no—
177#127C2×C3⋊D311yescharacteristic
178#124—92no—
179#124—92no—
180#121—182no—
181#121—182no—
182C4×D4—182no—
183C4×D4—182no—
184C2×C42—91no—
185C4×C8—92no—
186C4×C8—91no—
187C4×C8C2×C3⋊D311yescharacteristic
188C23×C3—28no—
189C22×D3—34no—
190C22×D3—68no—
191C3×Q8—216no—
192C3×D4—216no—
193C3×D4—416no—
194C2×C3×C4—28no—
195C2×C3×C4D3×D418yes—
196C2×C3×C4C23×D314yes—
197#67—1216no—
198C2×Dic3—34no—
199C2×Dic3—38no—
200C2×Dic3—68no—
201C2×Dic3—1216no—
202D12—616no—
203D12—1216no—
204D12—1216no—
205C4×D3—316no—
206C4×D3—616no—
207C4×D3—1216no—
208Dic6—616no—
209C3×C8D3×D4116yes—
210C3⋊C8—316no—
211C2×C32—82no—
212C2×C32C2×#12711yescharacteristic
213C2×C32C2×#13512yes—
214C3⋊D3—22no—
215C3⋊D3—82no—
216#41—188no—
217#41—188no—
218C2×Q8—92no—
219C2×Q8C22×C3⋊D312yes—
220C2×D4—22no—
221C2×D4—92no—
222C2×D4—182no—
223C2×D4—182no—
224C2×D4—182no—
225C2×D4C22×C3⋊D312yes—
226C22×C4—91no—
227C22×C4—92no—
228C22×C4—182no—
229C22×C4—182no—
230Q16—188no—
231SD16—28no—
232SD16—188no—
233D8—188no—
234C2×C8—92no—
235C2×C8—98no—
236C2×C8C22×C3⋊D312yes—
237C4⋊C4—22no—
238C4⋊C4—182no—
239C22⋊C4—184no—
240C22⋊C4—184no—
241C42—91no—
242C42—92no—
243C42C22×C3⋊D311yescharacteristic
244C22×C3—48no—
245C22×C3—416no—
246C22×C3C2×D3×D414yes—
247C2×D3—38no—
248C2×D3—68no—
249C2×D3—128no—
250C2×D3—1216no—
251C3×C4—48no—
252C3×C4#916116yescomplemented
253C3×C4C2×D3×D418yes—
254Dic3—38no—
255Dic3—68no—
256Dic3—128no—
257C32#314711yescharacteristic, complemented, Sylow
258C23—22no—
259C23—91no—
260C23—182no—
261Q8—24no—
262Q8—184no—
263D4—24no—
264D4—44no—
265D4—184no—
266D4—364no—
267D4—364no—
268D4—364no—
269C2×C4—22no—
270C2×C4—91no—
271C2×C4—94no—
272C2×C4—92no—
273C2×C4—184no—
274C2×C4—182no—
275C2×C4—364no—
276C2×C4—364no—
277C2×C4D4×C3⋊D312yes—
278C2×C4C23×C3⋊D311yescharacteristic
279C8—94no—
280C8D4×C3⋊D314yes—
281C2×C3—88no—
282C2×C3D3×#12714yes—
283C2×C3C2×#91618yes—
284D3—68no—
285D3—248no—
286C22—42no—
287C22—44no—
288C22—92no—
289C22—182no—
290C22—362no—
291C22—364no—
292C22C2×D4×C3⋊D311yescharacteristic
293C4—42no—
294C4—92no—
295C4—182no—
296C4—362no—
297C4#6412514yescomplemented
298C4C2×D4×C3⋊D312yes—
299C3#8176014yescomplemented
300C2—82no—
301C2—182no—
302C2—722no—
303C2C3⋊D3×#12711yescharacteristic
304C2C2×#6412512yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#492C2
socleC22×C32C22×D4
hypercenter#492C3⋊D3
hypocenterC32#3147
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#64125C2semidirect
2. #10596196C2semidirect
3. #10596187C2semidirect
4. C32×#492C2semidirect
5. #10592867C2semidirect
6. #10592791C2semidirect
7. #10592772C2semidirect
8. #10592392C2semidirect
9. C4×C8×C3⋊D3C2semidirect
36. C3×#492D3semidirect
69. C8×C3⋊D3D4semidirect
123. #492C3⋊D3semidirect
161. C32×C4#135semidirect
252. C3×C4#916semidirect
257. C32#3147semidirect
297. C4#64125semidirect
299. C3#81760semidirect

Maximal subgroups

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

subgroupindex
C2×#641252
#105961962
#105961872
C32×#4922
#105928672
#105927912
#105927722
#105923922
C4×C8×C3⋊D32
#817603