Finite Group Databasebeta

← #11783537

Subgroups — #11783537

Order 1152.

465 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 465 conjugacy classes of subgroups — too many to draw. Only its 140 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
1#10592696C211yesmaximal, characteristic
2#10591057C212yesmaximal
3C3×#4531C212yesmaximal
4#10589159C211yesmaximal, characteristic
5#10589157C211yesmaximal, characteristic
6#68697—32nomaximal
7C32×#117C2211yescharacteristic
8C2×#3748C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C3×#926C2212yes—
11C2×C3×#208C2212yes—
12#63630C412yescomplemented
13C4×C3⋊(C3⋊C8)C412yescomplemented
14#63554C414yescomplemented
15Dic3×C3⋊C8C414yescomplemented
16#5122—32no—
17#4997—32no—
18#4997—32no—
19#4997—61no—
20C3×H(3,ℤ/4)—32no—
21C3⋊#338—32no—
22#4531—32no—
23#4531D312yes—
24C22×C32×C4C2311yescharacteristic
25C32×C4⋊C4—21no—
26C32×C22⋊C4—21no—
27C32×C42C2×C412yes—
28#3748—22no—
29C2×C3⋊(C3⋊C8)C2×C412yes—
30C2×C3⋊(C3⋊C8)C2×C412yes—
31C2×C3⋊(C3⋊C8)C2×C412yes—
32C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
33C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
34C3×#217—22no—
35C3×C4⋊Dic3—22no—
36C3×C4×Dic3C2×C414yes—
37C3×#208—22no—
38C3×#208—22no—
39C2×C3×C3⋊C8C2×C414yes—
40#1747—91noSylow
41C2×C3×M16—32no—
42C3×#117—21no—
43C3×#117—32no—
44C3×#117C2×D312yes—
45#926C2×D312yes—
46C2×#208—32no—
47C2×#208—61no—
48C2×#208C2×D312yes—
49C22×C3⋊C8—32no—
50C22×C3⋊C8—61no—
51#815—34no—
52C8×Dic3—34no—
53#803—34no—
54#803—34no—
55#803—62no—
56C4×C3⋊C8—34no—
57C4×C3⋊C8—34no—
58C4×C3⋊C8—62no—
59C23×C32#4111yescharacteristic
60C2×C32×C4—22no—
61C2×C32×C4C22×C412yes—
62C2×C32×C4C22×C411yescharacteristic
63C2×C32×C4#4111yescharacteristic
64C2×C32×C4#4112yes—
65C2×C3×Dic3—24no—
66C3⋊(C3⋊C8)—22no—
67C3⋊(C3⋊C8)C4211yescharacteristic
68C3⋊(C3⋊C8)C4212yes—
69C3⋊(C3⋊C8)C4211yescharacteristic
70C3×C3⋊C8—24no—
71#405—92no—
72#405—91no—
73#338—91no—
74H(3,ℤ/4)—32no—
75H(3,ℤ/4)—91no—
76C22×C3×C4—21no—
77C22×C3×C4C22×D312yes—
78C3×M16—62no—
79C3×M16—62no—
80C2×C3×C8—34no—
81C3×C4⋊C4—22no—
82C3×C4⋊C4—22no—
83C3×C4⋊C4—62no—
84C3×C22⋊C4—22no—
85C3×C22⋊C4—22no—
86C3×C22⋊C4—62no—
87C3×C42—22no—
88C3×C42—34no—
89C3×C42C4×D314yes—
90#217—22no—
91C4⋊Dic3—22no—
92C4×Dic3C4×D314yes—
93#208—22no—
94#208—22no—
95#208—64no—
96#208—62no—
97#208—62no—
98C2×C3⋊C8—32no—
99C2×C3⋊C8—32no—
100C2×C3⋊C8—32no—
101C2×C3⋊C8—32no—
102C2×C3⋊C8—32no—
103C2×C3⋊C8—32no—
104C2×C3⋊C8—34no—
105C2×C3⋊C8—61no—
106C2×C3⋊C8—62no—
107C2×C3⋊C8—61no—
108C2×C3⋊C8—62no—
109C2×C3⋊C8—62no—
110C2×C3⋊C8C4×D314yes—
111C22×C32—41no—
112C22×C32#11711yescharacteristic
113C22×C32#11712yes—
114C32×C4—42no—
115C32×C4C2×C4211yescharacteristic
116C32×C4#11712yes—
117C32×C4#11711yescharacteristic
118C3×Dic3—44no—
119C2×M16—32no—
120C2×M16—91no—
121C22×C8—91no—
122#117—32no—
123#117D3211yescharacteristic
124#97—94no—
125#97—92no—
126C4×C8—94no—
127C4×C8—92no—
128C23×C3—21no—
129C23×C3#23712yes—
130C2×C3×C4—24no—
131C2×C3×C4—24no—
132C2×C3×C4—22no—
133C2×C3×C4—22no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—64no—
137C2×C3×C4C2×C4×D312yes—
138C2×C3×C4C2×C4×D312yes—
139C2×C3×C4C2×C4×D312yes—
140C2×C3×C4#23712yes—
141C2×C3×C4#23712yes—
142C2×C3×C4#23912yes—
143C2×Dic3—24no—
144C3×C8—64no—
145C3⋊C8—24no—
146C3⋊C8—32no—
147C3⋊C8—32no—
148C3⋊C8—32no—
149C3⋊C8—32no—
150C3⋊C8—61no—
151C3⋊C8—61no—
152C3⋊C8—62no—
153C3⋊C8—64no—
154C3⋊C8—64no—
155C2×C32—21no—
156C2×C32—22no—
157C2×C32#37611yescharacteristic
158C22×C4C2×D3211yescharacteristic
159M16—62no—
160M16—62no—
161M16—182no—
162C2×C8—34no—
163C2×C8—92no—
164C2×C8—92no—
165C2×C8—91no—
166C2×C8—91no—
167C2×C8—92no—
168C4⋊C4—21no—
169C4⋊C4—62no—
170C22⋊C4—21no—
171C22⋊C4—62no—
172C42—34no—
173C42#62412yes—
174C22×C3—22no—
175C22×C3—21no—
176C22×C3—42no—
177C22×C3—42no—
178C22×C3#87712yes—
179C22×C3#87712yes—
180C22×C3#89212yes—
181C3×C4—21no—
182C3×C4—22no—
183C3×C4—21no—
184C3×C4—44no—
185C3×C4—44no—
186C3×C4—124no—
187C3×C4C42×D312yes—
188C3×C4#87712yes—
189C3×C4#89212yes—
190C3×C4#89212yes—
191Dic3—44no—
192C32#174711yescharacteristic, complemented, Sylow
193C23#380511yescharacteristic
194C2×C4—22no—
195C2×C4—64no—
196C2×C4#379612yes—
197C2×C4C4×D3212yes—
198C2×C4#380511yescharacteristic
199C2×C4C2×#62411yescharacteristic
200C8—64no—
201C8—91no—
202C8—92no—
203C8—91no—
204C8—182no—
205C2×C3—22no—
206C2×C3—22no—
207C2×C3—22no—
208C2×C3—22no—
209C2×C3—21no—
210C2×C3—42no—
211C2×C3#464812yes—
212C22—41no—
213C22#6387812yes—
214C22#6395711yescharacteristic
215C4—42no—
216C4—124no—
217C4#6384911yescharacteristic
218C4#6387812yes—
219C4C4×#62411yescharacteristic
220C3—21no—
221C3#6869712yescomplemented
222C2—21no—
223C2—22no—
224C2#1059125211yescharacteristic
subgroupG/H
centerC4C4×#624
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#376
prime radicalC23×C32#41
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1747
LCSG ▷ C32×C4 ▷ C32
UCSC1 ◁ C4 ◁ #117

Complements

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

NH ≅ G/Ntype
12. #63630C4semidirect
13. C4×C3⋊(C3⋊C8)C4semidirect
14. #63554C4semidirect
15. Dic3×C3⋊C8C4semidirect
192. C32#1747semidirect
221. C3#68697semidirect

Maximal subgroups

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

subgroupindex
#105926962
#105910572
C3×#45312
#105891592
#105891572
#686973