Finite Group Databasebeta

← #16846438

Subgroups — #16846438

Order 3968.

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

normal subgroups only

This group has 248 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×#11758396C211yesmaximal, characteristic
2C2×#11758396C211yesmaximal, characteristic
3C2×C8×Dic31C211yesmaximal, characteristic
4#14520948C211yesmaximal, characteristic
5#14520945C211yesmaximal, characteristic
6#14520812C211yesmaximal, characteristic
7C31×#340C211yesmaximal, characteristic
8C22×C8×C31C2211yescharacteristic
9C2×C4⋊C4×C31C2211yescharacteristic
10C2×C4⋊C4×C31C2211yescharacteristic
11C2×C4⋊Dic31—21no—
12C2×C4⋊Dic31C2211yescharacteristic
13C2×C4⋊Dic31C2211yescharacteristic
14C2×Dic31⋊C4—21no—
15C2×C4×Dic31C2211yescharacteristic
16C22×C31⋊C8C2211yescharacteristic
17C31⋊#95—21no—
18C31⋊#95—21no—
19C8×Dic31—22no—
20#11758396—22no—
21#11758396C414yescomplemented
22C22×C4×C31—21no—
23C22×C4×C31—21no—
24C22×C4×C31C2311yescharacteristic
25C22×Dic31—21no—
26C22×Dic31—21no—
27C22×Dic31D411yescharacteristic
28C22×Dic31D411yescharacteristic
29C2×C8×C31—21no—
30C2×C8×C31—21no—
31C2×C8×C31Q812yes—
32C4⋊C4×C31—21no—
33C4⋊C4×C31—21no—
34C4⋊C4×C31—21no—
35C4⋊C4×C31C2×C412yes—
36C4⋊Dic31—21no—
37C4⋊Dic31—21no—
38C4⋊Dic31—21no—
39C4⋊Dic31—42no—
40C4⋊Dic31C2×C412yes—
41Dic31⋊C4—42no—
42C4×Dic31—21no—
43C4×Dic31—21no—
44C2×C31⋊C8C2×C412yes—
45C2×C31⋊C8D412yes—
46C2×C31⋊C8Q812yes—
47C23×C31C2×D411yescharacteristic
48C2×C4×C31—22no—
49C2×C4×C31—41no—
50C2×C4×C31—41no—
51C2×C4×C31—41no—
52C2×C4×C31—41no—
53C2×C4×C31—41no—
54C2×C4×C31C22×C411yescharacteristic
55C2×C4×C31C2×D411yescharacteristic
56C2×C4×C31C2×Q811yescharacteristic
57C2×C4×C31C2×Q811yescharacteristic
58C2×C4×C31#4111yescharacteristic
59C2×C4×C31#4111yescharacteristic
60C2×Dic31—21no—
61C2×Dic31—21no—
62C2×Dic31—21no—
63C2×Dic31—21no—
64C2×Dic31—22no—
65C2×Dic31—41no—
66C2×Dic31—41no—
67C2×Dic31—41no—
68C2×Dic31—41no—
69C2×Dic31—41no—
70C2×Dic31SD1612yes—
71C2×Dic31SD1612yes—
72C8×C31—22no—
73C31⋊C8C4⋊C414yescomplemented
74#1941—311nomaximal, Sylow
75C22×C31C4×D411yescharacteristic
76C22×C31#12111yescharacteristic
77C22×C31C4⋊Q811yescharacteristic
78C22×C31C2×SD1611yescharacteristic
79C22×C31C2×SD1611yescharacteristic
80C22×C31#13511yescharacteristic
81C22×C31#13511yescharacteristic
82C4×C31—42no—
83C4×C31—81no—
84C4×C31C2×C4⋊C411yescharacteristic
85C4×C31C4×Q811yescharacteristic
86C4×C31C22⋊Q811yescharacteristic
87C4×C31#12511yescharacteristic
88Dic31—22no—
89Dic31—22no—
90Dic31—42no—
91Dic31—81no—
92C2×#106—311no—
93C2×#106—311no—
94C2×C4×C8—311no—
95#389—311no—
96#389—311no—
97#340—311no—
98#340D3111yescharacteristic
99C2×C31#38911yescharacteristic
100C2×C31C4×SD1611yescharacteristic
101C2×C31C4×SD1611yescharacteristic
102C2×C31#46511yescharacteristic
103C2×C31#46511yescharacteristic
104C2×C31#49811yescharacteristic
105C2×C31#49911yescharacteristic
106C22×C8—311no—
107C22×C8C2×D3111yescharacteristic
108C2×C4⋊C4—311no—
109C2×C4⋊C4—311no—
110C2×C4⋊C4—621no—
111C2×C4⋊C4—621no—
112C2×C4⋊C4C2×D3111yescharacteristic
113C2×C4⋊C4C2×D3111yescharacteristic
114C2×C42—311no—
115#106—314no—
116#106—622no—
117C4×C8—622no—
118#95—621no—
119#95—621no—
120C31#194111yescharacteristic, complemented, Sylow
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—311no—
124C22×C4—311no—
125C22×C4—621no—
126C22×C4—621no—
127C22×C4C22×D3111yescharacteristic
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—312no—
131C2×C8—312no—
132C2×C8—312no—
133C2×C8Dic6212yes—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—312no—
138C4⋊C4—621no—
139C4⋊C4—621no—
140C4⋊C4—621no—
141C4⋊C4—1242no—
142C4⋊C4—1242no—
143C4⋊C4C4×D3112yes—
144C42—621no—
145C42—621no—
146C23D4×D3111yescharacteristic
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—312no—
154C2×C4—312no—
155C2×C4—621no—
156C2×C4—621no—
157C2×C4—621no—
158C2×C4—621no—
159C2×C4—622no—
160C2×C4—1241no—
161C2×C4—1241no—
162C2×C4—1241no—
163C2×C4—1241no—
164C2×C4—1241no—
165C2×C4C2×Dic6211yescharacteristic
166C2×C4C2×C4×D3111yescharacteristic
167C2×C4#9249511yescharacteristic
168C2×C4D4×D3111yescharacteristic
169C2×C4#9249711yescharacteristic
170C2×C4Q8×D3111yescharacteristic
171C8—22no—
172C8—314no—
173C22(C22⋊D31)⋊C411yescharacteristic
174C22#1175846111yescharacteristic
175C22#1175846511yescharacteristic
176C22#1175848911yescharacteristic
177C22SD16×D3111yescharacteristic
178C22SD16×D3111yescharacteristic
179C22#1175849611yescharacteristic
180C4—42no—
181C4—81no—
182C4—622no—
183C4—622no—
184C4—1242no—
185C4—2481no—
186C4C4×Dic6211yescharacteristic
187C4#1175845511yescharacteristic
188C4#1175846611yescharacteristic
189C4C4⋊C4×D3111yescharacteristic
190C2#1452094611yescharacteristic
191C2#1452113411yescharacteristic
192C2#1452114011yescharacteristic
193C2#1452127711yescharacteristic
194C2#1452128111yescharacteristic
195C2#1452144611yescharacteristic
196C2#1452145011yescharacteristic
subgroupG/H
centerC23D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#340C2
socle, prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenter#340D31
hypocenterC31#1941
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
21. #11758396C4semidirect
73. C31⋊C8C4⋊C4semidirect
120. C31#1941semidirect

Maximal subgroups

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

subgroupindex
C2×#117583962
C2×C8×Dic312
#145209482
#145209452
#145208122
C31×#3402
#194131