Finite Group Databasebeta

← #49094640

Subgroups — #49094640

Order 35968.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#31824213C211yesmaximal, characteristic
2#31823872C211yesmaximal, characteristic, complemented
3#31823832C211yesmaximal, characteristic, complemented
4#31823822C211yesmaximal, characteristic
5#31823204C211yesmaximal, characteristic, complemented
6#31823204C211yesmaximal, characteristic, complemented
7#329×C281C211yesmaximal, characteristic
8#22582879C2211yescharacteristic
9#22582877—21no—
10#22582872—21no—
11#22582872—21no—
12#22582871C2211yescharacteristic
13#22582871C2211yescharacteristic
14#22582860—21no—
15#22582856—21no—
16#22582856—21no—
17#22582813—21no—
18#22582811—21no—
19#22582804—21no—
20#22582804—21no—
21#22582803—21no—
22#22582800—21no—
23#22582790C2211yescharacteristic
24#124×C281C2211yescharacteristic
25#97×C281C2211yescharacteristic
26#97×C281C2211yescharacteristic
27C2×Dic562—21no—
28C2×Dic562—21no—
29C22×Dic281—21no—
30C2×#14555886—21no—
31C4⋊Dic281—21no—
32C4⋊Dic281—21no—
33C4⋊Dic281D411yescharacteristic
34C4⋊Dic281D411yescharacteristic
35C4⋊Dic281D411yescharacteristic
36C4⋊Dic281D411yescharacteristic
37#17985117—21no—
38#17985117—21no—
39#17985117—21no—
40#17985117—21no—
41#17985117—21no—
42#17985117—21no—
43C22⋊Dic281—21no—
44C22⋊Dic281—21no—
45C22⋊Dic281—21no—
46C4×Dic281—21no—
47C2×Q8×C281D411yescharacteristic
48C2×D4×C281D411yescharacteristic
49C2×C8×C281—21no—
50C2×C8×C281—21no—
51C22⋊C4×C281—21no—
52C22⋊C4×C281—21no—
53C42×C281C2311yescharacteristic
54Dic562—42no—
55Dic562—81no—
56C2×Dic281—21no—
57C2×Dic281—21no—
58C2×Dic281—21no—
59C2×Dic281—21no—
60C2×Dic281—41no—
61C2×Dic281—81no—
62#14555886—41no—
63C23×C281—21no—
64Q8×C281—41no—
65D4×C281—41no—
66C2×C4×C281—21no—
67C2×C4×C281C2×D411yescharacteristic
68C2×C4×C281C2×D411yescharacteristic
69C2×C4×C281C2×D411yescharacteristic
70C8×C281—22no—
71C8×C281—41no—
72C22×C281—41no—
73C22×C281—41no—
74C22×C281—41no—
75C22×C281#12011yescharacteristic
76C4×C281—21no—
77C4×C281—21no—
78C4×C281—21no—
79C4×C281—41no—
80Dic281—41no—
81Dic281—41no—
82Dic281—41no—
83Dic281—41no—
84Dic281—81no—
85C2×C281—81no—
86C2×C281#45411yescharacteristic
87C2×C281#45511yescharacteristic
88C2×C281#45611yescharacteristic
89C281#166411yescharacteristic, complemented, Sylow
90#1664—2811nomaximal, Sylow
91#563—2811no—
92#501—2811no—
93#491—2811no—
94#489—2811no—
95#330—2811no—
96#330—2811no—
97#329D28111yescharacteristic
98C4⋊Q8—2811no—
99C4⋊Q8—5621no—
100#126—5621no—
101#126—5621no—
102#125—2811no—
103#125—2811no—
104#124C2×D28111yescharacteristic
105#123—5621no—
106C22⋊Q8—5621no—
107C22⋊Q8—5621no—
108#107—5621no—
109#106—5621no—
110#103—5621no—
111#103—5621no—
112#103—5621no—
113#102—5621no—
114#97—2811no—
115#97C2×D28111yescharacteristic
116#97C2×D28111yescharacteristic
117C2×Q8—5621no—
118C2×Q8—5621no—
119C2×Q8D112411yescharacteristic
120C2×D4D112411yescharacteristic
121C22×C4—5621no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—5621no—
125C4⋊C4—2811no—
126C4⋊C4—2811no—
127C4⋊C4—2811no—
128C4⋊C4—2811no—
129C4⋊C4—5621no—
130C4⋊C4—5621no—
131C4⋊C4—5621no—
132C4⋊C4—5621no—
133C4⋊C4—5621no—
134C4⋊C4—5621no—
135C4⋊C4—5621no—
136C4⋊C4—5621no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—5621no—
140C22⋊C4—5621no—
141C22⋊C4—5621no—
142C42—5621no—
143C42C22×D28111yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—11242no—
147Q8—22481no—
148D4—41no—
149C2×C4—21no—
150C2×C4—5621no—
151C2×C4—5621no—
152C2×C4—5621no—
153C2×C4—5621no—
154C2×C4—11241no—
155C2×C4—22481no—
156C2×C4D4×D28111yescharacteristic
157C2×C4D4×D28111yescharacteristic
158C2×C4C2×D112411yescharacteristic
159C8—22no—
160C8—41no—
161C8—11241no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#2258284911yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—11241no—
171C4—11241no—
172C4—11241no—
173C4—11241no—
174C4—22481no—
175C2—81no—
176C2#3182363711yescharacteristic
177C2#3182364311yescharacteristic
178C2#3182364711yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#329×C281C2
socleC22×C281#120
prime radicalC2×D4×C281D4
hypercenter#329D281
hypocenterC281#1664
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31823872C2semidirect
3. #31823832C2semidirect
5. #31823204C2semidirect
6. #31823204C2semidirect
89. C281#1664semidirect

Maximal subgroups

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

subgroupindex
#318242132
#318238722
#318238322
#318238222
#318232042
#329×C2812
#1664281