Finite Group Databasebeta

← #49096461

Subgroups — #49096461

Order 35968.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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#31823471C212yesmaximal
2#31823368C211yesmaximal, characteristic
3#31823232C211yesmaximal, characteristic
4#31823222C212yesmaximal
5#544×C281C211yesmaximal, characteristic
6C22×Dic562C2211yescharacteristic
7C2×#17985122C2212yes—
8C2×C4×Dic281C2211yescharacteristic
9#22582802—22no—
10#22582802—22no—
11#22582786—22no—
12C4⋊Q8×C281—22no—
13#125×C281—22no—
14C22⋊Q8×C281—22no—
15#117×C281C2212yes—
16C2×C4⋊C4×C281C2211yescharacteristic
17C2×Dic562—22no—
18C2×Dic562—21no—
19C2×Dic562—22no—
20C2×Dic562Q812yescomplemented
21C22×Dic281—21no—
22C22×Dic281—21no—
23#17985122—22no—
24#17985122—22no—
25C2×#14555886—22no—
26C4×Dic281—22no—
27C2×Q8×C281—22no—
28C22×C4×C281D412yes—
29C22×C4×C281C2311yescharacteristic
30C4⋊C4×C281—22no—
31C4⋊C4×C281—24no—
32C4⋊C4×C281—22no—
33C4⋊C4×C281D412yes—
34C4⋊C4×C281D412yes—
35C22⋊C4×C281—22no—
36C42×C281—22no—
37Dic562—24no—
38Dic562—42no—
39C2×Dic281—22no—
40C2×Dic281—22no—
41C2×Dic281—41no—
42C2×Dic281—41no—
43C2×Dic281—41no—
44C2×Dic281—41no—
45#14555886—42no—
46C23×C281C2×D411yescharacteristic
47Q8×C281—82no—
48C2×C4×C281—22no—
49C2×C4×C281—22no—
50C2×C4×C281—22no—
51C2×C4×C281—42no—
52C2×C4×C281C2×D412yes—
53C2×C4×C281C2×Q811yescharacteristic
54C2×C4×C281#4112yes—
55C2×C4×C281#4111yescharacteristic
56C22×C281—21no—
57C22×C281—21no—
58C22×C281#12011yescharacteristic
59C22×C281C22⋊Q811yescharacteristic
60C22×C281#12411yescharacteristic
61C4×C281—42no—
62C4×C281—42no—
63C4×C281—42no—
64C4×C281C22⋊Q812yes—
65C4×C281#12412yes—
66Dic281—42no—
67Dic281—42no—
68C2×C281—21no—
69C2×C281—21no—
70C2×C281#39311yescharacteristic
71C2×C281#45511yescharacteristic
72C2×C281#45611yescharacteristic
73C281#202811yescharacteristic, complemented, Sylow
74#2028—2811nomaximal, Sylow
75#544D28111yescharacteristic
76#419—2812no—
77#391—2811no—
78#343—2811no—
79#339—2812no—
80C22×Q8—2811no—
81C2×M16—2812no—
82C4⋊Q8—22no—
83#125—22no—
84C22⋊Q8—22no—
85#117C2×D28112yes—
86C2×C4⋊C4C2×D28111yescharacteristic
87C2×C42—2811no—
88#103—5622no—
89#103—5622no—
90#95—5622no—
91C2×Q8—22no—
92C2×Q8—2812no—
93C2×Q8—5621no—
94C2×Q8—5622no—
95C2×Q8—5622no—
96C22×C4—5621no—
97C22×C4—5621no—
98C22×C4C22⋊D28112yes—
99C22×C4C22×D28111yescharacteristic
100M16—5622no—
101M16—5622no—
102C2×C8—5622no—
103C4⋊C4—22no—
104C4⋊C4—24no—
105C4⋊C4—22no—
106C4⋊C4C22⋊D28112yes—
107C4⋊C4C22⋊D28112yes—
108C22⋊C4—22no—
109C42—22no—
110C42—5622no—
111C23C2×C22⋊D28111yescharacteristic
112Q8—82no—
113Q8—5624no—
114Q8—11242no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—5622no—
120C2×C4—5622no—
121C2×C4—11241no—
122C2×C4—11241no—
123C2×C4—11241no—
124C2×C4—11241no—
125C2×C4C2×C22⋊D28112yes—
126C2×C4Q8×D28111yescharacteristic
127C2×C4#1798513912yes—
128C2×C4#1798513911yescharacteristic
129C8—11242no—
130C22—21no—
131C22—21no—
132C22#2258284811yescharacteristic
133C22#2258285511yescharacteristic
134C22#2258286811yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—11242no—
139C4—11242no—
140C4#2258285512yes—
141C4#2258286812yes—
142C2—21no—
143C2—21no—
144C2#3182337411yescharacteristic
145C2#3182364111yescharacteristic
146C2#3182364611yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#544×C281C2
socleC22×C281#120
prime radicalC23×C281C2×D4
hypercenter#544D281
hypocenterC281#2028
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
20. C2×Dic562Q8semidirect
73. C281#2028semidirect

Maximal subgroups

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

subgroupindex
#318234712
#318233682
#318232322
#318232222
#544×C2812
#2028281