Finite Group Databasebeta

← #10591623

Subgroups — #10591623

Order 576.

217 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 217 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3×#944C211yesmaximal, characteristic
2#63918C211yesmaximal, characteristic
3#63662C211yesmaximal, characteristic
4C3×#835C211yesmaximal, characteristic
5#63566C211yesmaximal, characteristic
6#63565C211yesmaximal, characteristic
7Dic3×C3⋊C8C211yesmaximal, characteristic
8#5079—31nomaximal
9#4792—31nomaximal
10C2×C32×Q8C2211yescharacteristic
11C2×C3×Dic6C2211yescharacteristic
12C2×#627—21no—
13C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×C4⋊Dic3C2211yescharacteristic
16C3×Dic3⋊C4—21no—
17C3×Dic3⋊C4—21no—
18C3×C4×Dic3C2211yescharacteristic
19C2×C3×C3⋊C8C2211yescharacteristic
20Dic3⋊Dic3—21no—
21C3×C4⋊Q8—31no—
22#944D311yescharacteristic
23#888—31no—
24#869—31no—
25C3×#103—31no—
26#835—31no—
27#835—31no—
28#835—31no—
29#835—31no—
30#835—61no—
31#835D311yescharacteristic
32#816—31no—
33C8×Dic3—31no—
34#810—31no—
35C4×C3⋊C8—31no—
36C32×Q8—21no—
37C32×Q8—21no—
38C2×C32×C4—21no—
39C2×C32×C4C2311yescharacteristic
40C2×C3⋊Dic3—21no—
41C2×C3×Dic3—21no—
42C2×C3×Dic3—21no—
43C2×C3×Dic3D411yescharacteristic
44C2×C3×Dic3D411yescharacteristic
45C3×Dic6—21no—
46C3×Dic6—21no—
47#627—42no—
48C3⋊(C3⋊C8)—21no—
49C3×C3⋊C8—21no—
50#487—91noSylow
51C2×C3×Q8—21no—
52C2×C3×Q8—31no—
53C2×C3×Q8C2×D311yescharacteristic
54C2×C3×Q8C2×D311yescharacteristic
55C2×Dic6—61no—
56C2×Dic6—61no—
57C2×Dic6C2×D311yescharacteristic
58C2×C3×C8—31no—
59C3×C4⋊C4—31no—
60C3×C4⋊C4—61no—
61C3×C4⋊C4—61no—
62C3×C42—31no—
63C4⋊Dic3—31no—
64C4⋊Dic3—31no—
65C4⋊Dic3—61no—
66C4⋊Dic3—61no—
67C4⋊Dic3C2×D311yescharacteristic
68Dic3⋊C4—21no—
69Dic3⋊C4—21no—
70Dic3⋊C4—61no—
71C4×Dic3C2×D311yescharacteristic
72C2×C3⋊C8—31no—
73C2×C3⋊C8—31no—
74C2×C3⋊C8—61no—
75C2×C3⋊C8C2×D311yescharacteristic
76C22×C32C2×D411yescharacteristic
77C32×C4—41no—
78C32×C4#4111yescharacteristic
79C32×C4#4111yescharacteristic
80C3⋊Dic3—41no—
81C3×Dic3—41no—
82C3×Dic3—41no—
83C3×Dic3SD1612yes—
84C3×Dic3Q1612yes—
85C4⋊Q8—31no—
86C4⋊Q8—91no—
87#103—31no—
88#103—91no—
89#103—91no—
90#103—91no—
91C4×C8—91no—
92C3×Q8—22no—
93C3×Q8—21no—
94C3×Q8—21no—
95C3×Q8—21no—
96C3×Q8—21no—
97C3×Q8—41no—
98C3×Q8—61no—
99C3×Q8—61no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—31no—
104C2×C3×C4—31no—
105C2×C3×C4—41no—
106C2×C3×C4—61no—
107C2×C3×C4—61no—
108C2×C3×C4C22×D311yescharacteristic
109C2×C3×C4C22×D311yescharacteristic
110C2×Dic3—21no—
111C2×Dic3—21no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—121no—
115C2×Dic3#6711yescharacteristic
116C2×Dic3#6711yescharacteristic
117Dic6—21no—
118Dic6—21no—
119Dic6—122no—
120Dic6—122no—
121C3×C8—61no—
122C3⋊C8—21no—
123C3⋊C8—61no—
124C3⋊C8—61no—
125C3⋊C8—121no—
126C2×C32#12411yescharacteristic
127C2×C32C2×SD1611yescharacteristic
128C2×C32C2×Q1611yescharacteristic
129C2×Q8—31no—
130C2×Q8—181no—
131C2×Q8D3211yescharacteristic
132C2×C8—31no—
133C2×C8—91no—
134C4⋊C4—31no—
135C4⋊C4—61no—
136C4⋊C4—61no—
137C4⋊C4—91no—
138C4⋊C4—181no—
139C42—31no—
140C22×C3—21no—
141C22×C3D3×D411yescharacteristic
142C22×C3C2×#6711yescharacteristic
143C3×C4—21no—
144C3×C4—21no—
145C3×C4—32no—
146C3×C4—32no—
147C3×C4—42no—
148C3×C4—41no—
149C3×C4—41no—
150C3×C4—121no—
151C3×C4—121no—
152C3×C4#23511yescharacteristic
153C3×C4#23711yescharacteristic
154C3×C4#23711yescharacteristic
155C3×C4#23711yescharacteristic
156Dic3—41no—
157Dic3—41no—
158Dic3—121no—
159Dic3—121no—
160Dic3—241no—
161Dic3#21512yes—
162Dic3#21612yes—
163C32#48711yescharacteristic, complemented, Sylow
164Q8—21no—
165Q8—21no—
166Q8—61no—
167Q8—61no—
168Q8—362no—
169C2×C4—21no—
170C2×C4—31no—
171C2×C4—31no—
172C2×C4—61no—
173C2×C4—61no—
174C2×C4—181no—
175C2×C4C2×D3211yescharacteristic
176C8—61no—
177C8—181no—
178C2×C3—21no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3#88511yescharacteristic
182C2×C3D3×SD1611yescharacteristic
183C2×C3D3×Q1611yescharacteristic
184C2×C3#93611yescharacteristic
185C2×C3C2×#21511yescharacteristic
186C2×C3C2×#21611yescharacteristic
187C22D3×#6711yescharacteristic
188C4—32no—
189C4—32no—
190C4—41no—
191C4—121no—
192C4—121no—
193C4—361no—
194C4#380411yescharacteristic
195C4#380511yescharacteristic
196C3—21no—
197C3#479211yescharacteristic, complemented
198C3#507911yescharacteristic, complemented
199C2D3×#21511yescharacteristic
200C2D3×#21611yescharacteristic
201C2#6395911yescharacteristic
subgroupG/H
centerC22D3×#67
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×Q8C22
socle, prime radicalC22×C32C2×D4
hypercenterC2×Q8D32
hypocenterC32#487
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
163. C32#487semidirect
197. C3#4792semidirect
198. C3#5079semidirect

Maximal subgroups

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

subgroupindex
C3×#9442
#639182
#636622
C3×#8352
#635662
#635652
Dic3×C3⋊C82
#50793
#47923