Finite Group Databasebeta

← #49094458

Subgroups — #49094458

Order 35968.

188 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 55 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#31824188C211yesmaximal, characteristic
2#31823755C211yesmaximal, characteristic
3#31823755C211yesmaximal, characteristic
4#31823209C211yesmaximal, characteristic
5#31823195C211yesmaximal, characteristic
6#31823195C211yesmaximal, characteristic
7#487×C281C211yesmaximal, characteristic
8#22582877—21no—
9#22582870—21no—
10#22582869—22no—
11Q8×Dic281—21no—
12C4×Dic562C2211yescharacteristic
13C4×Dic562C2211yescharacteristic
14#22582844—21no—
15#22582812—21no—
16#22582812—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582802—21no—
20#22582802—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23#103×C281—22no—
24C4×C8×C281C2211yescharacteristic
25C2×Dic562D411yescharacteristic
26C2×Dic562D411yescharacteristic
27C2×#14555886—21no—
28C2×#14555886—21no—
29C4⋊Dic281—22no—
30C4⋊Dic281D411yescharacteristic
31C4⋊Dic281D411yescharacteristic
32#17985117—22no—
33#17985117—22no—
34#17985117—21no—
35#17985117—21no—
36C4×Dic281—22no—
37C4×Dic281—21no—
38C4×Dic281—21no—
39C2×Q8×C281—21no—
40C2×Q8×C281—21no—
41C2×C8×C281—21no—
42C4⋊C4×C281—21no—
43C4⋊C4×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281D412yes—
46C42×C281C2311yescharacteristic
47Dic562—21no—
48Dic562—21no—
49Dic562—21no—
50Dic562Q1612yes—
51C2×Dic281—21no—
52C2×Dic281—21no—
53C2×Dic281—21no—
54C2×Dic281—21no—
55#14555886—41no—
56#14555886—41no—
57Q8×C281—42no—
58Q8×C281—41no—
59Q8×C281—41no—
60C2×C4×C281—22no—
61C2×C4×C281—41no—
62C2×C4×C281C2×D411yescharacteristic
63C2×C4×C281C2×D411yescharacteristic
64C2×C4×C281C2×D411yescharacteristic
65C8×C281—41no—
66C22×C281#12011yescharacteristic
67C4×C281—21no—
68C4×C281—42no—
69C4×C281—81no—
70C4×C281C2×Q1611yescharacteristic
71C4×C281#13511yescharacteristic
72C4×C281#13711yescharacteristic
73C4×C281#13711yescharacteristic
74Dic281—22no—
75Dic281—41no—
76Dic281—41no—
77Dic281—41no—
78C2×C281#45111yescharacteristic
79C2×C281#45211yescharacteristic
80C2×C281#45411yescharacteristic
81C281#163611yescharacteristic, complemented, Sylow
82#1636—2811nomaximal, Sylow
83#557—2811no—
84#487D28111yescharacteristic
85#477—2811no—
86#477—2811no—
87#332—2811no—
88Q8⋊C8—2811no—
89Q8⋊C8—2811no—
90C4⋊Q8—5621no—
91C4⋊Q8C2×D28111yescharacteristic
92C4⋊Q8C2×D28111yescharacteristic
93#125—5621no—
94#125—5622no—
95C4×Q8—2811no—
96C4×Q8—2811no—
97C4×Q8—5621no—
98C4×Q8—5621no—
99#107—5621no—
100#107—5621no—
101C4⋊C8—2811no—
102C4⋊C8—2811no—
103#103—22no—
104#103—5621no—
105#103—5621no—
106C4×C8C2×D28111yescharacteristic
107C2×Q8—21no—
108C2×Q8—21no—
109C2×Q8—2811no—
110C2×Q8—2811no—
111C2×C8—21no—
112C2×C8—5621no—
113C2×C8—5621no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—2811no—
118C4⋊C4—2811no—
119C4⋊C4—5622no—
120C4⋊C4—5622no—
121C4⋊C4—5622no—
122C4⋊C4—5621no—
123C4⋊C4—5621no—
124C4⋊C4C22⋊D28112yes—
125C42—5622no—
126C42—5621no—
127C42—5621no—
128C42C22×D28111yescharacteristic
129Q8—42no—
130Q8—41no—
131Q8—41no—
132Q8—2812no—
133Q8—5621no—
134Q8—5621no—
135Q8—5621no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—5621no—
139C2×C4—5621no—
140C2×C4—5621no—
141C2×C4—5621no—
142C2×C4D4×D28111yescharacteristic
143C2×C4D4×D28111yescharacteristic
144C2×C4C2×C22⋊D28111yescharacteristic
145C8—41no—
146C8—11241no—
147C8—11241no—
148C22#2258284711yescharacteristic
149C4—21no—
150C4—42no—
151C4—81no—
152C4—5622no—
153C4—11241no—
154C4—11241no—
155C4—11241no—
156C4Q16×D28111yescharacteristic
157C4#2258290011yescharacteristic
158C4#2258290811yescharacteristic
159C4#2258291111yescharacteristic
160C2#3182361711yescharacteristic
161C2#3182362211yescharacteristic
162C2#3182363511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#487×C281C2
socle, prime radicalC22×C281#120
hypercenter#487D281
hypocenterC281#1636
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
81. C281#1636semidirect

Maximal subgroups

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

subgroupindex
#318241882
#318237552
#318232092
#318231952
#487×C2812
#1636281