Finite Group Databasebeta

← #16845978

Subgroups — #16845978

Order 3968.

298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×Dic62C211yesmaximal, characteristic
2C2×#11758396C211yesmaximal, characteristic
3C2×#11758398C211yesmaximal, characteristic
4C2×#11758398C211yesmaximal, characteristic
5#14520811C211yesmaximal, characteristic
6#14520804C211yesmaximal, characteristic
7C31×#389C211yesmaximal, characteristic
8C22×Dic62C2211yescharacteristic
9C2×C4⋊C4×C31—21no—
10C2×C4⋊C4×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C42×C31C2211yescharacteristic
13C2×C4⋊Dic31C2211yescharacteristic
14C2×Dic31⋊C4—21no—
15C2×C4×Dic31—21no—
16C22×C31⋊C8C2211yescharacteristic
17C22×C31⋊C8C2211yescharacteristic
18C4×Dic62—22no—
19C4×Dic62—22no—
20C31×#95—21no—
21#11758398—22no—
22#11758398C414yescomplemented
23#11758396—22no—
24C22×C4×C31—21no—
25C22×C4×C31—21no—
26C22×C4×C31D411yescharacteristic
27C22×C4×C31D411yescharacteristic
28C22×C4×C31C2311yescharacteristic
29C22×Dic31—21no—
30C22×Dic31—21no—
31C2×Dic62—21no—
32C2×Dic62—21no—
33C2×Dic62—21no—
34C2×Dic62C2×C412yes—
35C2×Dic62D412yes—
36C2×Dic62Q812yes—
37C4⋊C4×C31—21no—
38C4⋊C4×C31—21no—
39C4⋊C4×C31—21no—
40C4⋊C4×C31—42no—
41C4⋊C4×C31C2×C412yes—
42C42×C31—21no—
43C42×C31—21no—
44C4⋊Dic31—21no—
45C4⋊Dic31D412yes—
46Dic31⋊C4—24no—
47C4×Dic31—24no—
48C2×C31⋊C8—21no—
49C2×C31⋊C8—21no—
50C2×C31⋊C8—21no—
51C2×C31⋊C8—21no—
52C2×C31⋊C8—21no—
53C2×C31⋊C8C2×C412yes—
54C23×C31C2×D411yescharacteristic
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—22no—
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31—41no—
64C2×C4×C31—41no—
65C2×C4×C31—41no—
66C2×C4×C31SD1612yes—
67C2×C4×C31C22×C411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31C2×Q811yescharacteristic
71C2×C4×C31#4111yescharacteristic
72C2×C4×C31#4111yescharacteristic
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31—41no—
78C2×Dic31—41no—
79Dic62—22no—
80Dic62—22no—
81Dic62—22no—
82Dic62C4⋊C414yescomplemented
83C31⋊C8—22no—
84C31⋊C8—41no—
85#1865—311nomaximal, Sylow
86C22×C31C4×D411yescharacteristic
87C22×C31#12011yescharacteristic
88C22×C31C22⋊Q811yescharacteristic
89C22×C31C2×SD1611yescharacteristic
90C22×C31#13511yescharacteristic
91C22×C31#13711yescharacteristic
92C22×C31#13711yescharacteristic
93C4×C31—22no—
94C4×C31—42no—
95C4×C31—41no—
96C4×C31—81no—
97C4×C31C2×C4⋊C411yescharacteristic
98C4×C31C4×D411yescharacteristic
99C4×C31C22⋊Q811yescharacteristic
100C4×C31#12311yescharacteristic
101Dic31—24no—
102Dic31—42no—
103C2×C4×Q8—311no—
104C2×#106—311no—
105C2×#103—311no—
106C2×#103—311no—
107#389D3111yescharacteristic
108#340—311no—
109#336—311no—
110C2×C31#38511yescharacteristic
111C2×C31C4×SD1611yescharacteristic
112C2×C31#44111yescharacteristic
113C2×C31#44811yescharacteristic
114C2×C31#45211yescharacteristic
115C2×C31#47511yescharacteristic
116C2×C31#47911yescharacteristic
117C22×Q8—311no—
118C22×C8—311no—
119C22×C8—311no—
120C4×Q8—622no—
121C4×Q8—622no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—311no—
124C2×C4⋊C4—621no—
125C2×C4⋊C4C2×D3111yescharacteristic
126C2×C4⋊C4C2×D3111yescharacteristic
127C2×C42—621no—
128C2×C42C2×D3111yescharacteristic
129#106—622no—
130#103—314no—
131#103—622no—
132#95—21no—
133C31#186511yescharacteristic, complemented, Sylow
134C2×Q8—312no—
135C2×Q8—312no—
136C2×Q8—312no—
137C2×Q8—621no—
138C2×Q8—621no—
139C2×Q8—621no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—621no—
143C22×C4—621no—
144C22×C4C22⋊D3111yescharacteristic
145C22×C4C22⋊D3111yescharacteristic
146C22×C4C22×D3111yescharacteristic
147C2×C8—312no—
148C2×C8—621no—
149C2×C8—621no—
150C2×C8—621no—
151C2×C8—621no—
152C2×C8—621no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—42no—
157C4⋊C4—312no—
158C4⋊C4—624no—
159C4⋊C4—621no—
160C4⋊C4C4×D3112yes—
161C42—21no—
162C42—21no—
163C42—624no—
164C23C2×C22⋊D3111yescharacteristic
165Q8—314no—
166Q8—622no—
167Q8—622no—
168Q8—622no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—622no—
181C2×C4—622no—
182C2×C4—622no—
183C2×C4—622no—
184C2×C4—1241no—
185C2×C4—1241no—
186C2×C4#9248012yes—
187C2×C4C2×C4×D3111yescharacteristic
188C2×C4#9249511yescharacteristic
189C2×C4D4×D3111yescharacteristic
190C2×C4D4×D3111yescharacteristic
191C2×C4Q8×D3111yescharacteristic
192C2×C4#9249911yescharacteristic
193C8—622no—
194C8—1241no—
195C22C4×C22⋊D3111yescharacteristic
196C22C2×#9248011yescharacteristic
197C22#1175851411yescharacteristic
198C22#1175851911yescharacteristic
199C22#1175852311yescharacteristic
200C22#1175852711yescharacteristic
201C22#1175852811yescharacteristic
202C4—22no—
203C4—42no—
204C4—41no—
205C4—81no—
206C4—624no—
207C4—1242no—
208C4C4⋊C4×D3111yescharacteristic
209C4#1175847011yescharacteristic
210C4#1175847111yescharacteristic
211C4#1175847311yescharacteristic
212C2#1452092011yescharacteristic
213C2C4×#9248011yescharacteristic
214C2#1452115411yescharacteristic
215C2#1452118711yescharacteristic
216C2#1452120911yescharacteristic
217C2#1452133111yescharacteristic
218C2#1452135311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#389C2
socle, prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenter#389D31
hypocenterC31#1865
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
22. #11758398C4semidirect
82. Dic62C4⋊C4semidirect
133. C31#1865semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic622
C2×#117583962
C2×#117583982
#145208112
#145208042
C31×#3892
#186531