Finite Group Databasebeta

← #11773840

Subgroups — #11773840

Order 1152.

645 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 645 conjugacy classes of subgroups — too many to draw. Only its 164 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×C4×#634C211yesmaximal, characteristic
2C3×#4925C212yesmaximal
3#10589148C214yesmaximal
4#70786—32nomaximal
5C22×#634C411yescharacteristic
6C2×C32×C42C2211yescharacteristic
7C2×C4⋊(C3⋊Dic3)C411yescharacteristic
8C2×#3750C2212yes—
9C2×C4×C3⋊Dic3C412yes—
10C4×#634—22no—
11C4×#634—22no—
12C3×#830C2214yes—
13C3×C4⋊(C3⋊C8)—22no—
14C3×C4×C3⋊C8—22no—
15C2×C4×Dic6—32no—
16C2×C4×Dic6—61no—
17C3×#431—32no—
18#4925D312yes—
19#4469—38no—
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4C2311yescharacteristic
23C22×C3⋊Dic3C2×C412yes—
24C22×C3⋊Dic3C2×C412yes—
25C2×#634—22no—
26C2×#634—22no—
27C2×#634C814yescomplemented
28C32×C42D412yes—
29C32×C42D412yes—
30C4⋊(C3⋊Dic3)—22no—
31#3750—24no—
32C4×C3⋊Dic3—22no—
33C4×C3⋊Dic3—22no—
34C2×C3×C3⋊C8—24no—
35#1461—91noSylow
36C22×Dic6—32no—
37C22×Dic6—61no—
38C2×C3×C42—21no—
39C2×C3×C42C2×D312yes—
40C2×C4⋊Dic3—32no—
41C2×C4⋊Dic3—61no—
42C2×Dic3⋊C4—34no—
43C2×Dic3⋊C4—62no—
44C2×C4×Dic3—34no—
45C2×C4×Dic3—62no—
46C4×Dic6—64no—
47C4×Dic6—64no—
48C4×Dic6—62no—
49C4×Dic6—62no—
50C4×Dic6—62no—
51C4×Dic6—62no—
52C3×C4⋊C8—62no—
53C3×C22⋊C8—34no—
54C3×C4×C8—62no—
55#830C2×D314yes—
56C4⋊(C3⋊C8)—22no—
57C4×C3⋊C8—22no—
58C23×C32C22×C411yescharacteristic
59C2×C32×C4—22no—
60C2×C32×C4—41no—
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C22⋊C412yes—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C2×C812yes—
65C2×C32×C4M1612yes—
66C2×C32×C4C2×D412yes—
67C2×C3⋊Dic3—22no—
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3—22no—
70C2×C3⋊Dic3—42no—
71C2×C3⋊Dic3C2×C814yes—
72#634—28no—
73C3×C3⋊C8—44no—
74C2×C4×Q8—91no—
75#431—32no—
76#324—94no—
77C22×C3×C4—21no—
78C22×C3×C4—21no—
79C22×C3×C4—21no—
80C22×C3×C4C4×D312yes—
81C22×C3×C4C4×D312yes—
82C22×C3×C4C22×D312yes—
83C22×Dic3—34no—
84C22×Dic3—34no—
85C22×Dic3—62no—
86C22×Dic3—62no—
87C2×Dic6—38no—
88C2×Dic6—64no—
89C2×Dic6—64no—
90C2×Dic6—64no—
91C2×Dic6—64no—
92C2×Dic6—62no—
93C2×Dic6—62no—
94C2×C3×C8—64no—
95C3×C42—22no—
96C3×C42—22no—
97C3×C42D1212yes—
98C3×C42D1212yes—
99C3×C42#6712yes—
100C3×C42#6712yes—
101C4⋊Dic3—64no—
102C4⋊Dic3—62no—
103C4⋊Dic3—62no—
104Dic3⋊C4—68no—
105Dic3⋊C4—64no—
106Dic3⋊C4—64no—
107C4×Dic3—64no—
108C4×Dic3—64no—
109C4×Dic3—64no—
110C4×Dic3—64no—
111C2×C3⋊C8—24no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32C2×C22⋊C411yescharacteristic
115C22×C32C22×C811yescharacteristic
116C22×C32C2×M1611yescharacteristic
117C32×C4—21no—
118C32×C4—22no—
119C32×C4C22⋊C814yes—
120C32×C4#10112yes—
121C3⋊Dic3—24no—
122C3⋊Dic3—42no—
123C22×Q8—91no—
124C4×Q8—182no—
125C4×Q8—182no—
126C2×C4⋊C4—91no—
127C2×C4⋊C4—92no—
128C2×C42—92no—
129C2×C42D3211yescharacteristic
130C4⋊C8—62no—
131C22⋊C8—34no—
132C4×C8—62no—
133C23×C3—21no—
134C23×C3C2×C4×D312yes—
135C2×C3×C4—24no—
136C2×C3×C4—24no—
137C2×C3×C4—22no—
138C2×C3×C4—22no—
139C2×C3×C4—21no—
140C2×C3×C4—22no—
141C2×C3×C4—21no—
142C2×C3×C4—22no—
143C2×C3×C4—42no—
144C2×C3×C4—42no—
145C2×C3×C4D3×C814yes—
146C2×C3×C4ΓL(1,𝔽25)14yes—
147C2×C3×C4(C2×D3)⋊C412yes—
148C2×C3×C4(C2×D3)⋊C412yes—
149C2×C3×C4(C2×D3)⋊C412yes—
150C2×C3×C4(C2×D3)⋊C412yes—
151C2×C3×C4C2×D1212yes—
152C2×C3×C4C2×#6712yes—
153C2×Dic3—38no—
154C2×Dic3—64no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—64no—
158C2×Dic3—64no—
159C2×Dic3—64no—
160C2×Dic3—64no—
161C2×Dic3—124no—
162C2×Dic3—124no—
163Dic6—616no—
164Dic6—68no—
165Dic6—68no—
166C3×C8—124no—
167C3⋊C8—44no—
168C2×C32—21no—
169C2×C32—21no—
170C2×C32C2×C22⋊C811yescharacteristic
171C2×C32#41011yescharacteristic
172C2×C32C2×#10111yescharacteristic
173C2×Q8—94no—
174C2×Q8—182no—
175C2×Q8—182no—
176C22×C4—92no—
177C22×C4—92no—
178C22×C4#62411yescharacteristic
179C22×C4#62411yescharacteristic
180C22×C4C2×D3211yescharacteristic
181C2×C8—64no—
182C4⋊C4—182no—
183C4⋊C4—184no—
184C42—182no—
185C42—182no—
186C42#62612yes—
187C42#62612yes—
188C22×C3—22no—
189C22×C3—22no—
190C22×C3—22no—
191C22×C3—22no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3—21no—
195C22×C3C2×D3×C812yes—
196C22×C3C2×ΓL(1,𝔽25)12yes—
197C22×C3C2×(C2×D3)⋊C412yes—
198C3×C4—22no—
199C3×C4—22no—
200C3×C4—22no—
201C3×C4—22no—
202C3×C4—24no—
203C3×C4—22no—
204C3×C4—42no—
205C3×C4(C2×D3)⋊C814yes—
206C3×C4(C2×D3)⋊C814yes—
207C3×C4#82414yes—
208Dic3—68no—
209Dic3—68no—
210Dic3—124no—
211Dic3—124no—
212C32#146111yescharacteristic, complemented, Sylow
213C23C2×#62411yescharacteristic
214Q8—188no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—94no—
218C2×C4—182no—
219C2×C4—182no—
220C2×C4—182no—
221C2×C4—362no—
222C2×C4#371012yes—
223C2×C4#371212yes—
224C2×C4#372211yescharacteristic
225C2×C4#372212yes—
226C2×C4#372211yescharacteristic
227C2×C4C2×#62612yes—
228C8—124no—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—22no—
232C2×C3—22no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3#500612yes—
237C2×C3C2×(C2×D3)⋊C812yes—
238C2×C3C2×#82412yes—
239C22—21no—
240C22—21no—
241C22C2×#371011yescharacteristic
242C22C2×#371211yescharacteristic
243C22C2×#372211yescharacteristic
244C4—22no—
245C4—21no—
246C4—184no—
247C4—362no—
248C4#6355714yes—
249C4#6356112yes—
250C3—21no—
251C3#7078612yescomplemented
252C2—21no—
253C2—21no—
254C2C2×#6355711yescharacteristic
255C2C2×#6356111yescharacteristic
256C2#1059123211yescharacteristic
subgroupG/H
centerC2×C4#3722
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1461
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
27. C2×#634C8semidirect
212. C32#1461semidirect
251. C3#70786semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C3×#49252
#105891482
#707863