Finite Group Databasebeta

← #10595399

Subgroups — #10595399

Order 576.

574 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 144 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×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C2×#3795C211yesmaximal, characteristic
3#64153C211yesmaximal, characteristic, complemented
4C3×#947C211yesmaximal, characteristic, complemented
5#63905C214yesmaximal, complemented
6#63887C214yesmaximal, complemented
7#63866C211yesmaximal, characteristic, complemented
8#63863C211yesmaximal, characteristic, complemented
9#63855C211yesmaximal, characteristic, complemented
10#5816—31nomaximal
11#5675—31nomaximal
12C2×C32×Q8C2211yescharacteristic
13C2×#634C2211yescharacteristic
14C3×D3×Q8—24no—
15C2×C3×D12C2211yescharacteristic
16C2×C3×C4×D3C2212yes—
17C2×C3×C4×D3C2211yescharacteristic
18C2×C3×Dic6C2211yescharacteristic
19C2×C3×Dic6C2212yes—
20C2×#625C2212yes—
21C2×D3×Dic3C2212yes—
22#3795—24no—
23#3750C2214yes—
24C4×C3⋊Dic3C2211yescharacteristic
25C3×(C2×D3)⋊C4C2214yes—
26C3×C4×Dic3C2211yescharacteristic
27Dic3⋊Dic3C2212yes—
28Dic3⋊Dic3C2214yes—
29(C2×D3)⋊Dic3C2212yes—
30(C2×D3)⋊Dic3C2214yes—
31C22×C3×Q8—31no—
32C2×D3×Q8D311yescharacteristic, complemented
33C2×#237—31no—
34C2×#235—31no—
35C3×#124—31no—
36#947—31no—
37#947D311yescharacteristic, complemented
38#946—34no—
39#944—31no—
40#944—31no—
41#944—31no—
42#944—61no—
43#936—31no—
44#929—34no—
45#926—31no—
46#883—34no—
47#878—34no—
48#872—31no—
49#869—31no—
50C22×C3×D3C2312yes—
51C22×C3×D3C2311yescharacteristic
52C32×Q8—22no—
53C2×C32×C4C2312yes—
54C2×C32×C4C2311yescharacteristic
55C2×C3⋊Dic3C2312yes—
56C2×C3⋊Dic3C2312yes—
57#634—22no—
58C2×C3×Dic3C2312yes—
59C2×C3×Dic3C2312yes—
60C2×C3×Dic3C2311yescharacteristic
61C3×D12—22no—
62C3×C4×D3—24no—
63C3×C4×D3D414yes—
64C3×Dic6—22no—
65C3×Dic6—24no—
66#625—24no—
67D3×Dic3—24no—
68#536—91noSylow
69C2×C3×Q8—21no—
70C2×C3×Q8—31no—
71C2×C3×Q8—32no—
72C2×C3×Q8—64no—
73C2×C3×Q8C2×D311yescharacteristic
74C2×C3×Q8C2×D311yescharacteristic
75C2×C3×D4—31no—
76C22×C3×C4—31no—
77C22×C3×C4—32no—
78C2×#67—32no—
79C2×#67—32no—
80C22×Dic3—32no—
81D3×Q8—24no—
82#237—64no—
83#235—64no—
84C2×D12C2×D311yescharacteristic
85C2×C4×D3—32no—
86C2×C4×D3C2×D312yes—
87C2×C4×D3C2×D311yescharacteristic
88C2×Dic6—31no—
89C2×Dic6—31no—
90C2×Dic6—61no—
91C2×Dic6C2×D311yescharacteristic
92C2×Dic6C2×D312yes—
93C3×C22⋊C4—34no—
94C3×C42—31no—
95#217—34no—
96#217—32no—
97(C2×D3)⋊C4—32no—
98(C2×D3)⋊C4—34no—
99(C2×D3)⋊C4C2×D314yes—
100C4⋊Dic3—34no—
101C4⋊Dic3—32no—
102Dic3⋊C4—34no—
103Dic3⋊C4—34no—
104Dic3⋊C4—32no—
105Dic3⋊C4—34no—
106Dic3⋊C4—64no—
107C4×Dic3—31no—
108C4×Dic3—31no—
109C4×Dic3—61no—
110C4×Dic3C2×D311yescharacteristic
111C22×C32C2411yescharacteristic
112C2×C3×D3—22no—
113C2×C3×D3—22no—
114C2×C3×D3—24no—
115C2×C3×D3C2×D412yes—
116C32×C4—22no—
117C32×C4C2×D412yes—
118C3⋊Dic3—22no—
119C3⋊Dic3—22no—
120C3×Dic3—22no—
121C3×Dic3—22no—
122C3×Dic3C2×D412yes—
123C2×#41—91no—
124C22×Q8—31no—
125C4⋊Q8—91no—
126C4⋊Q8—91no—
127#124—31no—
128#124—91no—
129#123—94no—
130C22⋊Q8—94no—
131#117—91no—
132C23×C3—31no—
133C23×C3—32no—
134C22×D3C22×D312yes—
135C22×D3C22×D311yescharacteristic
136C3×Q8—22no—
137C3×Q8—22no—
138C3×Q8—42no—
139C3×Q8—64no—
140C3×Q8—62no—
141C3×D4—62no—
142C2×C3×C4—21no—
143C2×C3×C4—22no—
144C2×C3×C4—31no—
145C2×C3×C4—34no—
146C2×C3×C4—32no—
147C2×C3×C4—32no—
148C2×C3×C4—64no—
149C2×C3×C4C22×D312yes—
150C2×C3×C4C22×D312yes—
151C2×C3×C4C22×D311yescharacteristic
152C2×C3×C4C22×D311yescharacteristic
153#67—64no—
154#67—64no—
155C2×Dic3—32no—
156C2×Dic3—32no—
157C2×Dic3—32no—
158C2×Dic3—32no—
159C2×Dic3—62no—
160C2×Dic3—62no—
161C2×Dic3—64no—
162C2×Dic3C22×D312yes—
163C2×Dic3C22×D312yes—
164C2×Dic3C22×D311yescharacteristic
165D12—22no—
166C4×D3—24no—
167C4×D3—64no—
168C4×D3#6714yes—
169Dic6—22no—
170Dic6—24no—
171Dic6—62no—
172Dic6—62no—
173Dic6—122no—
174C2×C32C22×D411yescharacteristic
175C2×C322−1+412yes—
176C3×D3—22no—
177C3×D3—42no—
178#41—184no—
179C2×Q8—32no—
180C2×Q8—31no—
181C2×Q8—64no—
182C2×Q8—91no—
183C2×Q8D3211yescharacteristic
184C2×D4—31no—
185C2×D4—92no—
186C22×C4—31no—
187C22×C4—32no—
188C22×C4—92no—
189C4⋊C4—92no—
190C4⋊C4—94no—
191C4⋊C4—94no—
192C22⋊C4—34no—
193C22⋊C4—92no—
194C22⋊C4—94no—
195C42—31no—
196C42—91no—
197C22×C3—21no—
198C22×C3—32no—
199C22×C3—62no—
200C22×C3—64no—
201C22×C3—62no—
202C22×C3C23×D311yescharacteristic
203C22×C3C23×D311yescharacteristic
204C2×D3—22no—
205C2×D3—22no—
206C2×D3—24no—
207C2×D3C2×#6712yes—
208C3×C4—22no—
209C3×C4—22no—
210C3×C4—22no—
211C3×C4—32no—
212C3×C4—42no—
213C3×C4—62no—
214C3×C4—62no—
215C3×C4D3×D412yes—
216C3×C4C2×#6712yes—
217Dic3—22no—
218Dic3—22no—
219Dic3—64no—
220Dic3—62no—
221Dic3—62no—
222Dic3—62no—
223Dic3—62no—
224Dic3—122no—
225Dic3C2×#6712yes—
226C32#53611yescharacteristic, complemented, Sylow
227C23—31no—
228C23—32no—
229Q8—22no—
230Q8—64no—
231Q8—62no—
232Q8—182no—
233D4—62no—
234D4—184no—
235C2×C4—31no—
236C2×C4—34no—
237C2×C4—32no—
238C2×C4—32no—
239C2×C4—64no—
240C2×C4—92no—
241C2×C4—92no—
242C2×C4—184no—
243C2×C4C2×D3212yes—
244C2×C4C2×D3211yescharacteristic
245C2×C3—22no—
246C2×C3—21no—
247C2×C3—62no—
248C2×C3—122no—
249C2×C3C2×D3×D411yescharacteristic
250C2×C3#100712yes—
251C2×C3#101012yes—
252C2×C3C22×#6711yescharacteristic
253D3—22no—
254D3—42no—
255C22—32no—
256C22—62no—
257C22—64no—
258C22—62no—
259C22C22×D3211yescharacteristic
260C4—22no—
261C4—32no—
262C4—62no—
263C4—62no—
264C4—182no—
265C4—182no—
266C4D3×#6712yes—
267C3—21no—
268C3#567511yescharacteristic, complemented
269C3#581611yescharacteristic, complemented
270C2—62no—
271C2—122no—
272C2#6431512yes—
273C2C2×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC2×C32×Q8C22
prime radicalC2×#3795C2
hypercenterC2×Q8D32
hypocenterC32#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×Q8C2semidirect
3. #64153C2semidirect
4. C3×#947C2semidirect
5. #63905C2semidirect
6. #63887C2semidirect
7. #63866C2semidirect
8. #63863C2semidirect
9. #63855C2semidirect
32. C2×D3×Q8D3semidirect
37. #947D3semidirect
226. C32#536semidirect
268. C3#5675semidirect
269. C3#5816semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q82
C2×#37952
#641532
C3×#9472
#639052
#638872
#638662
#638632
#638552
#58163
#56753