Finite Group Databasebeta

← #49093925

Subgroups — #49093925

Order 35968.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D281C211yesmaximal, characteristic
2#31823518C212yesmaximal, complemented
3#31823203C211yesmaximal, characteristic, complemented
4#31823202C212yesmaximal, complemented
5#329×C281C211yesmaximal, characteristic, complemented
6C2×Q8×D281C411yescharacteristic
7C2×D4×D281C411yescharacteristic
8#22582868C411yescharacteristic
9#22582867C2211yescharacteristic
10#22582866C411yescharacteristic
11#22582865—22no—
12C22⋊C4×D281—22no—
13C42×D281C2211yescharacteristic
14#22582808—22no—
15#22582791—22no—
16#22582790C2212yescomplemented
17#124×C281C2211yescharacteristic
18#97×C281C2212yescomplemented
19C23×D281—21no—
20C2×Dic562—21no—
21C2×Dic562C2×C411yescharacteristic
22Q8×D281—42no—
23C2×D1124C2×C411yescharacteristic
24C2×C22⋊D281—21no—
25D4×D281—42no—
26C2×C4×D281—21no—
27C2×C4×D281C2×C411yescharacteristic
28C2×C4×D281D412yes—
29C2×#14555886—22no—
30C22⋊Dic281—22no—
31#17985115—22no—
32#17985115—22no—
33C4×Dic281C2×C411yescharacteristic
34C4×Dic281D412yes—
35C2×Q8×C281C2×C411yescharacteristic
36C2×D4×C281C2×C411yescharacteristic
37C2×C8×C281—22no—
38C22⋊C4×C281—22no—
39C42×C281C2311yescharacteristic
40C22×D281—21no—
41C22×D281—44no—
42C22×D281—42no—
43C22×D281C22⋊C411yescharacteristic
44Dic562—42no—
45Dic562—41no—
46D1124—41no—
47C22⋊D281—42no—
48C2×Dic281—21no—
49C2×Dic281C22⋊C412yes—
50C2×Dic281C22⋊C411yescharacteristic
51C4×D281—22no—
52C4×D281—42no—
53C4×D281—42no—
54#14555886—42no—
55C23×C281—21no—
56Q8×C281—41no—
57D4×C281—41no—
58C2×C4×C281—21no—
59C2×C4×C281C22×C411yescharacteristic
60C2×C4×C281C2×D412yes—
61C8×C281—42no—
62C22×C281—41no—
63C22×C281—42no—
64C22×C281C2×C22⋊C411yescharacteristic
65C2×D281—22no—
66C2×D281—41no—
67C2×D281—42no—
68C2×D281—84no—
69C2×D281#10012yes—
70C4×C281—21no—
71C4×C281—22no—
72C4×C281—41no—
73Dic281—21no—
74Dic281—22no—
75Dic281—41no—
76C2×C281—81no—
77C2×C281C2×#10011yescharacteristic
78C2×C281#42112yes—
79D281—22no—
80D281—81no—
81C281#153311yescharacteristic, complemented, Sylow
82#1533—2811nomaximal, Sylow
83C2×#124—2811no—
84#432—2812no—
85#329—2811no—
86#329—2812no—
87#329D28111yescharacteristic, complemented
88C22×Q8—2811no—
89C22×D4—2811no—
90#124—2811no—
91#124—2811no—
92#124—2811no—
93#124—5622no—
94#124C2×D28111yescharacteristic
95C2×C22⋊C4—5622no—
96C2×C42—2811no—
97C4⋊C8—5622no—
98C22⋊C8—5622no—
99#97—2812no—
100#97C2×D28112yescomplemented
101C24—5621no—
102C2×Q8—2811no—
103C2×Q8—5621no—
104C2×Q8—11242no—
105C2×Q8C4×D28111yescharacteristic
106C2×D4—2811no—
107C2×D4—5621no—
108C2×D4—11242no—
109C2×D4C4×D28111yescharacteristic
110C22×C4—2811no—
111C22×C4—2812no—
112C22×C4—5621no—
113C2×C8—22no—
114C2×C8—5622no—
115C22⋊C4—22no—
116C22⋊C4—5622no—
117C22⋊C4—5622no—
118C22⋊C4—5622no—
119C42—2811no—
120C42—2812no—
121C42C22×D28111yescharacteristic
122C23—21no—
123C23—2811no—
124C23—5621no—
125C23—11242no—
126C23—11244no—
127Q8—41no—
128Q8—11241no—
129Q8—11242no—
130D4—41no—
131D4—11241no—
132D4—11242no—
133C2×C4—21no—
134C2×C4—2812no—
135C2×C4—2811no—
136C2×C4—5622no—
137C2×C4—5621no—
138C2×C4—11242no—
139C2×C4—11242no—
140C2×C4C2×C4×D28111yescharacteristic
141C2×C4D4×D28112yes—
142C8—42no—
143C8—11242no—
144C22—41no—
145C22—42no—
146C22—2812no—
147C22—5622no—
148C22—11241no—
149C22—11242no—
150C22—22484no—
151C22C22⋊C4×D28111yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—5621no—
156C4—5622no—
157C4—11241no—
158C2—81no—
159C2—5622no—
160C2—22481no—
161C2#100×D28111yescharacteristic
162C2#3182347812yes—
subgroupG/H
centerC22C22⋊C4×D281
commutatorC2×C4×C281C22×C4
FrattiniC42C22×D281
Fitting#329×C281C2
socleC22×C281C2×C22⋊C4
prime radicalC2×D4×D281C4
cosocleC42×C281C23
hypercenter#329D281
hypocenterC281#1533
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. #31823518C2semidirect
3. #31823203C2semidirect
4. #31823202C2semidirect
5. #329×C281C2semidirect
16. #22582790C22semidirect
18. #97×C281C22semidirect
81. C281#1533semidirect
87. #329D281semidirect
100. #97C2×D281semidirect

Maximal subgroups

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

subgroupindex
#124×D2812
#318235182
#318232032
#318232022
#329×C2812
#1533281