Finite Group Databasebeta

← #49093893

Subgroups — #49093893

Order 35968.

270 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 63 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#31824012C211yesmaximal, characteristic
2#31823415C212yesmaximal, complemented
3#31823203C211yesmaximal, characteristic, complemented
4#31823202C212yesmaximal, complemented
5#329×C281C211yesmaximal, characteristic, complemented
6C2×#17985139C411yescharacteristic
7C2×#17985137C411yescharacteristic
8C2×#17985121—22no—
9#22582877C411yescharacteristic
10#22582875C411yescharacteristic
11#22582867C2211yescharacteristic
12#22582852—22no—
13#22582839—22no—
14C42×D281C2211yescharacteristic
15#22582790C2212yes—
16C8×Dic281—22no—
17#124×C281C2211yescharacteristic
18#97×C281C2212yes—
19#17985139—42no—
20#17985137—42no—
21C2×Dic562C2×C411yescharacteristic
22C2×D1124—21no—
23C2×D1124C2×C411yescharacteristic
24C2×C22⋊D281—21no—
25C2×C22⋊D281—22no—
26C22×Dic281—21no—
27C2×C4×D281—21no—
28C2×C4×D281C2×C411yescharacteristic
29C2×C4×D281D412yes—
30#17985121—28no—
31C2×#14555886—22no—
32#17985117—22no—
33#17985115—22no—
34C4×Dic281C2×C411yescharacteristic
35C4×Dic281D412yes—
36C2×Q8×C281C2×C411yescharacteristic
37C2×D4×C281C2×C411yescharacteristic
38C2×C8×C281—22no—
39C22⋊C4×C281—22no—
40C42×C281C2311yescharacteristic
41C22×D281—21no—
42C22×D281C22⋊C411yescharacteristic
43Dic562—41no—
44D1124—41no—
45D1124—42no—
46C22⋊D281—42no—
47C22⋊D281—44no—
48C2×Dic281—21no—
49C2×Dic281—42no—
50C2×Dic281C22⋊C411yescharacteristic
51C2×Dic281C22⋊C412yes—
52C4×D281—22no—
53C4×D281—24no—
54C4×D281—42no—
55#14555886—24no—
56C23×C281—21no—
57Q8×C281—41no—
58D4×C281—41no—
59C2×C4×C281—21no—
60C2×C4×C281C22×C411yescharacteristic
61C2×C4×C281C2×D412yes—
62C8×C281—24no—
63C22×C281—41no—
64C22×C281—42no—
65C22×C281C2×C22⋊C411yescharacteristic
66C2×D281—21no—
67C2×D281—22no—
68C2×D281—41no—
69C2×D281—42no—
70C4×C281—21no—
71C4×C281—22no—
72C4×C281—41no—
73Dic281—41no—
74Dic281#10012yes—
75Dic281#10414yes—
76C2×C281—81no—
77C2×C281C2×#10011yescharacteristic
78C2×C281C2×#10412yes—
79D281—41no—
80D281—81no—
81C281#152511yescharacteristic, complemented, Sylow
82#1525—2811nomaximal, Sylow
83#532—2811no—
84C4×M16—2812no—
85#329—2811no—
86#329—2812no—
87#329D28111yescharacteristic, complemented
88C2×#41—2811no—
89C2×#41—2811no—
90C2×M16—5622no—
91C4⋊Q8—2811no—
92#127—2811no—
93#124—2811no—
94#124C2×D28111yescharacteristic
95#121—5622no—
96C4×D4—5622no—
97C2×C42—2811no—
98#97—2812no—
99#97C2×D28112yes—
100C4×C8—5622no—
101#41—11242no—
102#41—11242no—
103C2×Q8—2811no—
104C2×Q8C4×D28111yescharacteristic
105C2×D4—2811no—
106C2×D4—5621no—
107C2×D4—5622no—
108C2×D4—5621no—
109C2×D4C4×D28111yescharacteristic
110C22×C4—2811no—
111C22×C4—2812no—
112C22×C4—5621no—
113C22×C4—5621no—
114M16—5628no—
115C2×C8—22no—
116C2×C8—5622no—
117C4⋊C4—5622no—
118C22⋊C4—22no—
119C22⋊C4—5622no—
120C42—2811no—
121C42—2812no—
122C42C22×D28111yescharacteristic
123C23—21no—
124C23—2811no—
125C23—5621no—
126Q8—41no—
127Q8—11241no—
128D4—41no—
129D4—11241no—
130D4—11242no—
131D4—11244no—
132D4—11242no—
133C2×C4—21no—
134C2×C4—2812no—
135C2×C4—2811no—
136C2×C4—5624no—
137C2×C4—5622no—
138C2×C4—5621no—
139C2×C4—11242no—
140C2×C4—11242no—
141C2×C4C2×C4×D28111yescharacteristic
142C2×C4D4×D28112yes—
143C8—24no—
144C8—5624no—
145C22—41no—
146C22—42no—
147C22—5621no—
148C22—5622no—
149C22—11241no—
150C22—11242no—
151C22C22⋊C4×D28111yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—2812no—
156C4—2814no—
157C4—11241no—
158C2—81no—
159C2—11241no—
160C2—22481no—
161C2#100×D28111yescharacteristic
162C2#104×D28112yes—
subgroupG/H
centerC22C22⋊C4×D281
commutatorC2×C4×C281C22×C4
FrattiniC42C22×D281
Fitting#329×C281C2
socleC22×C281C2×C22⋊C4
prime radical#31824012C2
cosocleC42×C281C23
hypercenter#329D281
hypocenterC281#1525
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31823415C2semidirect
3. #31823203C2semidirect
4. #31823202C2semidirect
5. #329×C281C2semidirect
81. C281#1525semidirect
87. #329D281semidirect

Maximal subgroups

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

subgroupindex
#318240122
#318234152
#318232032
#318232022
#329×C2812
#1525281