Finite Group Databasebeta

← #11872800

Subgroups — #11872800

Order 1152.

1182 conjugacy classes of subgroups.

The subgroup lattice has 309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#518C211yesmaximal, characteristic
2#10595989C211yesmaximal, characteristic, complemented
3#10592917C212yesmaximal
4#10592718C212yesmaximal, complemented
5#10592717C212yesmaximal, complemented
6C4×#3754C212yesmaximal, complemented
7#10592708C212yesmaximal, complemented
8#10592699C211yesmaximal, characteristic, complemented
9#10592695C212yesmaximal, complemented
10#82545—34nomaximal
11C22×C32×D4C2211yescharacteristic
12C32×C4×D4—22no—
13C32×C4×D4C2212yes—
14C32×C4×D4C2212yes—
15C32×#117C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C32×C22⋊C4—22no—
18C2×#3754C2212yes—
19C2×#3754C2212yes—
20#64133C2212yes—
21#64098—22no—
22#64088—22no—
23#64079C2211yescharacteristic, complemented
24#64078C2211yescharacteristic, complemented
25C4×#634C2212yescomplemented
26#63659C2212yes—
27#63659C2212yes—
28#63657C2212yes—
29#63637C2212yescomplemented
30#63637C2212yescomplemented
31#63635C2212yescomplemented
32#63634C2212yescomplemented
33C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
34#63630C2211yescharacteristic, complemented
35C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
36C3×#518D314yes—
37#5518—34no—
38#5218—38no—
39#5019—38no—
40#5018—38no—
41C4×#214—38no—
42#5009—38no—
43#5000—34no—
44#4996—38no—
45C24×C32—21no—
46C2×C32×D4—24no—
47C2×C32×D4—21no—
48C2×C32×D4C2312yes—
49C22×C32×C4—22no—
50C22×C32×C4—22no—
51C22×C32×C4C2311yescharacteristic
52C2×#634C2312yes—
53C32×C4⋊C4D412yes—
54C32×C4⋊C4C2312yes—
55C32×C22⋊C4—21no—
56C32×C22⋊C4—22no—
57C32×C22⋊C4—22no—
58C32×C22⋊C4D412yes—
59C32×C42—21no—
60C32×C42C2311yescharacteristic
61C32×C42C2311yescharacteristic
62#3757—22no—
63#3754—24no—
64#3754—24no—
65C4⋊(C3⋊Dic3)—22no—
66C4⋊(C3⋊Dic3)C2312yes—
67#3750—22no—
68#3750—22no—
69#3750—22no—
70C4×C3⋊Dic3—22no—
71C2×C3⋊(C3⋊C8)C2312yes—
72C2×C3⋊(C3⋊C8)C2312yes—
73#3123—91noSylow
74C22×C3×D4C2×D314yes—
75C3×C4×D4—28no—
76C3×C4×D4C2×D318yes—
77C3×C4×D4C2×D318yes—
78C3×#117C2×D314yes—
79C3×#117C2×D314yes—
80C2×C3×C22⋊C4—28no—
81C2×#214—38no—
82C2×#214—38no—
83#924—38no—
84#889—68no—
85#879—68no—
86#870—34no—
87#869—34no—
88C4×Dic6—38no—
89#832—38no—
90#832—38no—
91#830—38no—
92#810—38no—
93#810—38no—
94#808—38no—
95#807—38no—
96C4⋊(C3⋊C8)—38no—
97#803—34no—
98C4×C3⋊C8—34no—
99C23×C32—24no—
100C23×C32—22no—
101C23×C32—82no—
102C23×C32C2×D411yescharacteristic
103C32×D4—24no—
104C32×D4—22no—
105C32×D4#4114yes—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—82no—
109C2×C32×C4—82no—
110C2×C32×C4C2×D412yes—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D412yes—
113C2×C32×C4C2411yescharacteristic
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—22no—
116#634—22no—
117#634—22no—
118C3⋊(C3⋊C8)—22no—
119C3⋊(C3⋊C8)—22no—
120#541—91no—
121#518C3⋊D311yescharacteristic
122#485—92no—
123#478—92no—
124#461—92no—
125#450—92no—
126#440—92no—
127C4×SD16—92no—
128#433—91no—
129C24×C3—24no—
130C2×C3×D4—216no—
131C2×C3×D4—24no—
132C2×C3×D4C22×D318yes—
133C22×C3×C4—28no—
134C22×C3×C4—28no—
135C22×C3×C4C22×D314yes—
136C2×Dic6—38no—
137C3×C4⋊C4#6718yes—
138C3×C4⋊C4C22×D318yes—
139C3×C22⋊C4—24no—
140C3×C22⋊C4—28no—
141C3×C22⋊C4—28no—
142C3×C22⋊C4#6718yes—
143C3×C42—24no—
144C3×C42C22×D314yes—
145C3×C42C22×D314yes—
146#217—68no—
147#214—616no—
148#214—616no—
149C4⋊Dic3—38no—
150C4⋊Dic3—68no—
151Dic3⋊C4—68no—
152Dic3⋊C4—68no—
153Dic3⋊C4—68no—
154C4×Dic3—68no—
155C2×C3⋊C8—38no—
156C2×C3⋊C8—38no—
157C22×C32—21no—
158C22×C32—24no—
159C22×C32—22no—
160C22×C32—42no—
161C22×C32—42no—
162C22×C32—84no—
163C22×C32C22×D411yescharacteristic
164C32×C4—21no—
165C32×C4—22no—
166C32×C4—22no—
167C32×C4—42no—
168C32×C4C2×#4112yes—
169C3⋊Dic3—42no—
170C3⋊Dic3—42no—
171C22×D4C2×C3⋊D311yescharacteristic
172C2×SD16—92no—
173C2×SD16—92no—
174C4⋊Q8—91no—
175#126—182no—
176#125—91no—
177#125—182no—
178C22⋊Q8—92no—
179C4×Q8—92no—
180C4×D4—22no—
181C4×D4C2×C3⋊D312yes—
182C4×D4C2×C3⋊D312yes—
183#117C2×C3⋊D311yescharacteristic
184#117C2×C3⋊D311yescharacteristic
185C2×C22⋊C4—22no—
186#107—92no—
187#106—92no—
188C4⋊C8—92no—
189#103—92no—
190#103—92no—
191#102—92no—
192#102—92no—
193C22⋊C8—92no—
194#97—91no—
195C4×C8—91no—
196C23×C3—216no—
197C23×C3—28no—
198C23×C3—88no—
199C23×C3C2×#6714yes—
200C3×D4—216no—
201C3×D4—28no—
202C3×D4#235116yes—
203C2×C3×C4—28no—
204C2×C3×C4—28no—
205C2×C3×C4—88no—
206C2×C3×C4—88no—
207C2×C3×C4C2×#6718yes—
208C2×C3×C4C2×#6714yes—
209C2×C3×C4C2×#6718yes—
210C2×C3×C4C23×D314yes—
211C2×Dic3—68no—
212C2×Dic3—68no—
213Dic6—68no—
214Dic6—68no—
215C3⋊C8—68no—
216C3⋊C8—68no—
217C2×C32—41no—
218C2×C32—44no—
219C2×C32#52511yescharacteristic
220C2×C32#57712yes—
221C24—21no—
222C2×Q8—92no—
223C2×D4—24no—
224C2×D4—21no—
225C2×D4C22×C3⋊D312yes—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4C22×C3⋊D311yescharacteristic
229SD16—184no—
230SD16—184no—
231C2×C8—92no—
232C2×C8—92no—
233C4⋊C4—92no—
234C4⋊C4—182no—
235C4⋊C4—182no—
236C4⋊C4—182no—
237C4⋊C4—182no—
238C4⋊C4#63812yes—
239C4⋊C4C22×C3⋊D312yes—
240C22⋊C4—21no—
241C22⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—182no—
244C22⋊C4#63812yes—
245C42—21no—
246C42—182no—
247C42C22×C3⋊D311yescharacteristic
248C42C22×C3⋊D311yescharacteristic
249C22×C3—24no—
250C22×C3—216no—
251C22×C3—28no—
252C22×C3—48no—
253C22×C3—48no—
254C22×C3—816no—
255C22×C3C22×#6714yes—
256C3×C4—24no—
257C3×C4—28no—
258C3×C4—28no—
259C3×C4—48no—
260C3×C4C2×#23518yes—
261Dic3—128no—
262Dic3—128no—
263C32#312311yescharacteristic, complemented, Sylow
264C23—24no—
265C23—22no—
266C23—82no—
267C23C2×#63811yescharacteristic
268Q8—182no—
269Q8—182no—
270D4—24no—
271D4—22no—
272D4#382814yes—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—182no—
278C2×C4—182no—
279C2×C4C2×#63811yescharacteristic
280C2×C4C2×#63812yes—
281C2×C4C2×#63812yes—
282C2×C4C23×C3⋊D311yescharacteristic
283C8—182no—
284C8—182no—
285C2×C3—44no—
286C2×C3—416no—
287C2×C3#579114yes—
288C2×C3#583618yes—
289C22—21no—
290C22—24no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—84no—
295C22C22×#63811yescharacteristic
296C4—21no—
297C4—22no—
298C4—22no—
299C4—42no—
300C4—362no—
301C4—362no—
302C4C2×#382812yes—
303C3#8254514yescomplemented
304C2—41no—
305C2—44no—
306C2#1059626211yescharacteristic
307C2#1059630712yes—
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#518C2
socleC22×C32C22×D4
prime radicalC22×C32×D4C22
hypercenter#518C3⋊D3
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #10595989C2semidirect
4. #10592718C2semidirect
5. #10592717C2semidirect
6. C4×#3754C2semidirect
7. #10592708C2semidirect
8. #10592699C2semidirect
9. #10592695C2semidirect
23. #64079C22semidirect
24. #64078C22semidirect
25. C4×#634C22semidirect
29. #63637C22semidirect
30. #63637C22semidirect
31. #63635C22semidirect
32. #63634C22semidirect
33. C4⋊(C3⋊(C3⋊C8))C22semidirect
34. #63630C22semidirect
35. C4×C3⋊(C3⋊C8)C22semidirect
263. C32#3123semidirect
303. C3#82545semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
#105959892
#105929172
#105927182
#105927172
C4×#37542
#105927082
#105926992
#105926952
#825453