Finite Group Databasebeta

← #10594083

Subgroups — #10594083

Order 576.

631 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 631 conjugacy classes of subgroups — too many to draw. Only its 138 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×#3804C212yesmaximal, complemented
2#64090C211yesmaximal, characteristic, complemented
3C3×#886C212yesmaximal, complemented
4#63980C211yesmaximal, characteristic, complemented
5C2×#3724C211yesmaximal, characteristic, complemented
6#63919C211yesmaximal, characteristic, complemented
7#63912C211yesmaximal, characteristic, complemented
8#63902C211yesmaximal, characteristic, complemented
9#63900C211yesmaximal, characteristic, complemented
10#63899C212yesmaximal, complemented
11#63854C212yesmaximal, complemented
12#5655—32nomaximal
13C2×#638C2211yescharacteristic
14C22×C3⋊Dic3C2211yescharacteristic
15C2×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#67C2212yes—
17C22×C3×Dic3C2212yes—
18C2×#627C2212yes—
19C2×#626C2212yes—
20C2×#625C2211yescharacteristic
21C2×#624C2212yes—
22#3804—28no—
23C2×D3×Dic3C2212yes—
24C32×C22⋊C4C2211yescharacteristic
25#3752C2211yescharacteristic
26#3750C2211yescharacteristic
27C4×C3⋊Dic3C2211yescharacteristic
28C3×(C2×D3)⋊C4C2212yes—
29C3×(C2×D3)⋊C4C2212yes—
30C3×C4⋊Dic3C2212yes—
31C3×C4⋊Dic3C2212yes—
32#3724C2212yes—
33#3724C2211yescharacteristic
34#3724C2211yescharacteristic
35#3724C2211yescharacteristic
36(C2×D3)⋊Dic3C2212yes—
37C2×#237—32no—
38C2×#235—32no—
39C3×#123—32no—
40#939—32no—
41C2×Dic3⋊C4—32no—
42#896—32no—
43#894—32no—
44D3×C4⋊C4—32no—
45#888—32no—
46#886D312yescomplemented
47#884—32no—
48#883—32no—
49#67⋊C4—32no—
50#67⋊C4—32no—
51#67⋊C4—61no—
52#878—32no—
53C23×C32C2311yescharacteristic
54C22×C3⋊D3C2311yescharacteristic
55C22×C3×D3C2312yes—
56C2×C32×C4C2311yescharacteristic
57C2×C32×C4C2311yescharacteristic
58#638D414yescomplemented
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3C2311yescharacteristic
61C2×C3⋊Dic3C2311yescharacteristic
62C2×C3⋊Dic3C2311yescharacteristic
63C4×C3⋊D3—22no—
64C3×#67—24no—
65C2×C3×Dic3—24no—
66C2×C3×Dic3C2312yes—
67C2×C3×Dic3C2312yes—
68C2×C3×Dic3C2312yes—
69#627—24no—
70#626—24no—
71#625—22no—
72#624—24no—
73D3×Dic3—24no—
74#547—91noSylow
75C2×C3×D4—32no—
76C22×C3×C4—32no—
77C2×#67—32no—
78C2×#67—32no—
79C2×#67—32no—
80C2×#67—61no—
81C2×#67C2×D312yes—
82C22×Dic3—32no—
83C22×Dic3—32no—
84C22×Dic3—61no—
85C22×Dic3C2×D312yes—
86#237—68no—
87#235—68no—
88C2×D12—32no—
89C2×C4×D3—32no—
90C2×C4×D3—32no—
91C2×C4×D3—32no—
92C2×C4×D3—32no—
93C2×C4×D3—61no—
94C2×Dic6—32no—
95C2×Dic6—32no—
96C3×C4⋊C4—32no—
97C3×C4⋊C4—32no—
98C3×C22⋊C4—21no—
99C3×C22⋊C4—32no—
100C3×C22⋊C4—32no—
101C3×C22⋊C4C2×D312yes—
102#217—32no—
103(C2×D3)⋊C4—32no—
104(C2×D3)⋊C4—32no—
105(C2×D3)⋊C4—61no—
106(C2×D3)⋊C4C2×D312yes—
107(C2×D3)⋊C4C2×D312yes—
108C4⋊Dic3C2×D312yes—
109C4⋊Dic3C2×D312yes—
110Dic3⋊C4—32no—
111Dic3⋊C4—32no—
112Dic3⋊C4—32no—
113Dic3⋊C4—32no—
114Dic3⋊C4—32no—
115Dic3⋊C4—32no—
116Dic3⋊C4—61no—
117C4×Dic3—32no—
118C4×Dic3—61no—
119C22×C32—21no—
120C22×C32—21no—
121C22×C32C2×D412yes—
122C22×C32C2411yescharacteristic
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C2×C3⋊D3C2×D412yes—
126C2×C3×D3—22no—
127C2×C3×D3—22no—
128C2×C3×D3—22no—
129C32×C4—21no—
130C32×C4—21no—
131C3⋊Dic3—21no—
132C3⋊Dic3C2×D412yes—
133C3⋊Dic3#4112yescomplemented
134C3×Dic3—22no—
135C3×Dic3—22no—
136C3×Dic3—22no—
137C2×#41—92no—
138C4⋊Q8—91no—
139#123—32no—
140#123—92no—
141C22⋊Q8—92no—
142#121—91no—
143#121—91no—
144C4×D4—91no—
145C4×D4—91no—
146C2×C4⋊C4—91no—
147C2×C4⋊C4—91no—
148C23×C3—21no—
149C23×C3—32no—
150C23×C3C22×D312yes—
151C22×D3—32no—
152C22×D3—61no—
153C22×D3C22×D312yes—
154C3×D4—64no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—32no—
158C2×C3×C4—32no—
159C2×C3×C4—32no—
160C2×C3×C4—64no—
161C2×C3×C4C22×D312yes—
162C2×C3×C4C22×D312yes—
163#67—24no—
164#67—38no—
165#67—64no—
166#67—64no—
167#67—64no—
168C2×Dic3—24no—
169C2×Dic3—32no—
170C2×Dic3—32no—
171C2×Dic3—32no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—64no—
176C2×Dic3—64no—
177C2×Dic3—122no—
178C2×Dic3C22×D312yes—
179C2×Dic3C22×D312yes—
180C2×Dic3C22×D312yes—
181D12—64no—
182C4×D3—64no—
183C4×D3—64no—
184C4×D3—64no—
185C4×D3—64no—
186C4×D3—122no—
187Dic6—64no—
188Dic6—64no—
189C2×C32—22no—
190C2×C32C22×D411yescharacteristic
191C2×C32C2×#4111yescharacteristic
192C2×C322−1+411yescharacteristic
193C3⋊D3—22no—
194C3×D3—42no—
195#41—188no—
196C2×Q8—92no—
197C2×D4—32no—
198C2×D4—92no—
199C2×D4—91no—
200C2×D4—91no—
201C22×C4—32no—
202C22×C4—92no—
203C22×C4—92no—
204C22×C4—91no—
205C22×C4—91no—
206C4⋊C4—32no—
207C4⋊C4—32no—
208C4⋊C4—91no—
209C4⋊C4—91no—
210C4⋊C4—91no—
211C4⋊C4—92no—
212C4⋊C4—91no—
213C22⋊C4—32no—
214C22⋊C4—32no—
215C22⋊C4—92no—
216C22⋊C4—91no—
217C22⋊C4D3211yescharacteristic
218C42—91no—
219C22×C3—22no—
220C22×C3—22no—
221C22×C3—21no—
222C22×C3—22no—
223C22×C3—41no—
224C22×C3—41no—
225C22×C3—62no—
226C22×C3—62no—
227C22×C3—62no—
228C22×C3D3×D414yes—
229C22×C3C23×D312yes—
230C2×D3—22no—
231C2×D3—22no—
232C2×D3—22no—
233C2×D3—34no—
234C2×D3—62no—
235C2×D3—62no—
236C2×D3—62no—
237C2×D3—121no—
238C2×D3—121no—
239C3×C4—22no—
240C3×C4—22no—
241C3×C4—41no—
242C3×C4—41no—
243C3×C4—62no—
244C3×C4—62no—
245C3×C4—62no—
246Dic3—22no—
247Dic3—22no—
248Dic3—22no—
249Dic3—34no—
250Dic3—34no—
251Dic3—62no—
252Dic3—62no—
253Dic3—62no—
254Dic3—121no—
255C32#54711yescharacteristic, complemented, Sylow
256C23—32no—
257C23—91no—
258C23C2×D3211yescharacteristic
259Q8—184no—
260D4—64no—
261D4—94no—
262D4—184no—
263D4—182no—
264C2×C4—32no—
265C2×C4—32no—
266C2×C4—32no—
267C2×C4—64no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—182no—
272C2×C4—184no—
273C2×C4—184no—
274C2×C4—182no—
275C2×C4C2×D3211yescharacteristic
276C2×C4C2×D3211yescharacteristic
277C2×C3—24no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—42no—
282C2×C3—122no—
283C2×C3C2×D3×D412yes—
284C2×C3D3×#4112yes—
285C2×C3#101012yes—
286D3—42no—
287D3—64no—
288D3—122no—
289C22—21no—
290C22—21no—
291C22—62no—
292C22—62no—
293C22—62no—
294C22—92no—
295C22—181no—
296C22—181no—
297C22#380212yes—
298C22C22×D3211yescharacteristic
299C4—21no—
300C4—21no—
301C4—62no—
302C4—62no—
303C4—62no—
304C4—92no—
305C4—92no—
306C4—181no—
307C3—21no—
308C3#565512yescomplemented
309C2—22no—
310C2—122no—
311C2—182no—
312C2C2×#380211yescharacteristic
313C2#6430911yescharacteristic
314C2#6431211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
hypercenterC22⋊C4D32
hypocenterC32#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#3804C2semidirect
2. #64090C2semidirect
3. C3×#886C2semidirect
4. #63980C2semidirect
5. C2×#3724C2semidirect
6. #63919C2semidirect
7. #63912C2semidirect
8. #63902C2semidirect
9. #63900C2semidirect
10. #63899C2semidirect
11. #63854C2semidirect
46. #886D3semidirect
58. #638D4semidirect
133. C3⋊Dic3#41semidirect
255. C32#547semidirect
308. C3#5655semidirect

Maximal subgroups

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

subgroupindex
C2×#38042
#640902
C3×#8862
#639802
C2×#37242
#639192
#639122
#639022
#639002
#638992
#638542
#56553