Finite Group Databasebeta

← #10591605

Subgroups — #10591605

Order 576.

278 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 66 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×#3756C211yesmaximal, characteristic, complemented
2C3×#944C211yesmaximal, characteristic, complemented
3C2×C3×#215C211yesmaximal, characteristic
4#63860C211yesmaximal, characteristic
5C2×#3719C211yesmaximal, characteristic, complemented
6C2×#3715C211yesmaximal, characteristic
7#63554C211yesmaximal, characteristic, complemented
8#5167—31nomaximal
9#5086—31nomaximal
10C2×C32×Q8C2211yescharacteristic
11C2×#634C2211yescharacteristic
12C2×C3×D12C2211yescharacteristic
13C2×C3×Dic6C2211yescharacteristic
14#3756—22no—
15C2×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#215—22no—
17C3×Dic3⋊C4—22no—
18C3×C4×Dic3C2211yescharacteristic
19C2×C3×C3⋊C8C2211yescharacteristic
20(C2×D3)⋊Dic3—22no—
21#3719—22no—
22#3715—22no—
23C2×C3×SD16—31no—
24C3×C4⋊Q8—31no—
25#944D311yescharacteristic, complemented
26C2×#216—31no—
27C2×#216—31no—
28C2×#216—31no—
29C2×#216—61no—
30C2×#215—31no—
31C2×#215D311yescharacteristic
32#936—31no—
33C2×#214—31no—
34C2×Dic12—31no—
35#875—31no—
36#815—31no—
37#803—31no—
38C22×C3×D3—21no—
39C32×Q8—21no—
40C32×Q8—21no—
41C2×C32×C4—21no—
42C2×C32×C4C2311yescharacteristic
43C2×C3⋊Dic3—21no—
44#634—21no—
45#634—21no—
46C2×C3×Dic3—21no—
47C2×C3×Dic3D412yes—
48C3×D12—21no—
49C3×D12—21no—
50C3×Dic6—21no—
51C3×Dic6—21no—
52C3⋊(C3⋊C8)D412yes—
53C3×C3⋊C8D412yes—
54#497—91noSylow
55C2×C3×Q8—21no—
56C2×C3×Q8—31no—
57C2×C3×Q8C2×D311yescharacteristic
58C2×C3×Q8C2×D311yescharacteristic
59C2×C3×D4—31no—
60C2×D12C2×D311yescharacteristic
61C2×Dic6—31no—
62C2×Dic6—31no—
63C2×Dic6—61no—
64C2×Dic6C2×D311yescharacteristic
65C3×SD16—62no—
66C2×C3×C8—31no—
67C3×C4⋊C4—62no—
68C3×C42—31no—
69#217—62no—
70#216—62no—
71#216—62no—
72#216—64no—
73#216—62no—
74#215—22no—
75#215—62no—
76#214—62no—
77(C2×D3)⋊C4—62no—
78Dic3⋊C4—22no—
79C4×Dic3C2×D311yescharacteristic
80C2×C3⋊C8—31no—
81C2×C3⋊C8—31no—
82C2×C3⋊C8—61no—
83C2×C3⋊C8C2×D311yescharacteristic
84Dic12—62no—
85C22×C32C2×D411yescharacteristic
86C2×C3×D3—41no—
87C2×C3×D3—42no—
88C32×C4—41no—
89C32×C4C2×D411yescharacteristic
90C32×C4C2×D411yescharacteristic
91C3⋊Dic3—41no—
92C3×Dic3—22no—
93C3×Dic3—41no—
94C2×Q16—91no—
95C2×Q16—91no—
96C2×SD16—31no—
97C2×SD16—91no—
98C4⋊Q8—31no—
99#124—91no—
100#97—91no—
101C23×C3—61no—
102C22×D3—21no—
103C3×Q8—22no—
104C3×Q8—21no—
105C3×Q8—21no—
106C3×Q8—21no—
107C3×Q8—21no—
108C3×Q8—41no—
109C3×Q8—61no—
110C3×Q8—61no—
111C3×D4—61no—
112C3×D4—61no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—32no—
117C2×C3×C4—41no—
118C2×C3×C4—61no—
119C2×C3×C4C22×D311yescharacteristic
120C2×C3×C4C22×D311yescharacteristic
121C2×Dic3—21no—
122C2×Dic3—61no—
123C2×Dic3—61no—
124C2×Dic3—121no—
125C2×Dic3#6712yes—
126D12—21no—
127D12—21no—
128Dic6—21no—
129Dic6—21no—
130Dic6—62no—
131Dic6—61no—
132Dic6—61no—
133Dic6—61no—
134Dic6—61no—
135Dic6—121no—
136C3×C8—32no—
137C3⋊C8—32no—
138C3⋊C8—32no—
139C3⋊C8—62no—
140C3⋊C8#6712yes—
141C2×C32#12711yescharacteristic
142C2×C32#13712yes—
143C3×D3—81no—
144C2×Q8—31no—
145C2×Q8—91no—
146C2×Q8D3211yescharacteristic
147C2×D4—31no—
148Q16—182no—
149Q16—182no—
150SD16—62no—
151SD16—182no—
152C2×C8—31no—
153C2×C8—91no—
154C4⋊C4—62no—
155C22⋊C4—182no—
156C42—31no—
157C22×C3—21no—
158C22×C3—121no—
159C22×C3—122no—
160C22×C3D3×D411yescharacteristic
161C22×C3C2×#6711yescharacteristic
162C2×D3—42no—
163C2×D3—41no—
164C3×C4—21no—
165C3×C4—21no—
166C3×C4—42no—
167C3×C4—41no—
168C3×C4—41no—
169C3×C4—62no—
170C3×C4—121no—
171C3×C4D3×D411yescharacteristic
172C3×C4D3×D411yescharacteristic
173C3×C4D3×D411yescharacteristic
174C3×C4C2×#6711yescharacteristic
175Dic3—22no—
176Dic3—41no—
177Dic3—122no—
178Dic3—121no—
179Dic3—121no—
180C32#49711yescharacteristic, complemented, Sylow
181C23—61no—
182Q8—21no—
183Q8—21no—
184Q8—61no—
185Q8—61no—
186Q8—181no—
187Q8—181no—
188D4—61no—
189D4—61no—
190C2×C4—21no—
191C2×C4—32no—
192C2×C4—61no—
193C2×C4—181no—
194C2×C4C2×D3211yescharacteristic
195C8—32no—
196C8—92no—
197C2×C3—22no—
198C2×C3—21no—
199C2×C3—241no—
200C2×C3#91512yes—
201C2×C3#94011yescharacteristic
202C2×C3#94011yescharacteristic
203C2×C3#94212yes—
204D3—81no—
205C22—122no—
206C22—121no—
207C22D3×#6711yescharacteristic
208C4—41no—
209C4—62no—
210C4—121no—
211C4—361no—
212C4D3×#6711yescharacteristic
213C4#381111yescharacteristic
214C3—21no—
215C3#508611yescharacteristic, complemented
216C3#516711yescharacteristic, complemented
217C2—241no—
218C2#6394612yes—
219C2#6397911yescharacteristic
subgroupG/H
centerC22D3×#67
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×Q8C22
socleC22×C32C2×D4
prime radicalC2×C3×D12C22
hypercenterC2×Q8D32
hypocenterC32#497
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
1. C2×#3756C2semidirect
2. C3×#944C2semidirect
5. C2×#3719C2semidirect
7. #63554C2semidirect
25. #944D3semidirect
180. C32#497semidirect
215. C3#5086semidirect
216. C3#5167semidirect

Maximal subgroups

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

subgroupindex
C2×#37562
C3×#9442
C2×C3×#2152
#638602
C2×#37192
C2×#37152
#635542
#51673
#50863