Finite Group Databasebeta

← #49095823

Subgroups — #49095823

Order 35968.

312 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 85 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#31824230C211yesmaximal, characteristic
2#31824034C211yesmaximal, characteristic
3#31823471C212yesmaximal, complemented
4#31823219C212yesmaximal, complemented
5#410×C281C211yesmaximal, characteristic
6C22×Dic562C2211yescharacteristic
7#22582886—24no—
8C2×#17985122—22no—
9C2×#17985122C2212yes—
10#22582877C412yescomplemented
11#22582866C412yescomplemented
12#22582860—22no—
13#22582858—22no—
14#22582838C2211yescharacteristic
15#22582802—24no—
16C2×#41×C281C2211yescharacteristic
17#117×C281C2212yes—
18#99×C281—22no—
19C2×Dic562—21no—
20C2×Dic562—22no—
21C2×Dic562—22no—
22C2×Dic562C2×C412yes—
23C22×Dic281—21no—
24#17985122—24no—
25#17985122—22no—
26#17985122—22no—
27C2×#14555886—24no—
28C2×#14555886D414yes—
29C4⋊Dic281—21no—
30#17985117—24no—
31C22⋊Dic281—24no—
32C22⋊Dic281—21no—
33C4×Dic281C2×C412yes—
34#41×C281—22no—
35#41×C281—22no—
36C2×Q8×C281C2×C411yescharacteristic
37C2×D4×C281C2×C411yescharacteristic
38C2×D4×C281D412yes—
39C22×C4×C281D412yes—
40C22×C4×C281C2311yescharacteristic
41C4⋊C4×C281—22no—
42C22⋊C4×C281—22no—
43C42×C281—22no—
44Dic562—24no—
45Dic562—41no—
46Dic562—41no—
47C2×Dic281—22no—
48C2×Dic281—22no—
49C2×Dic281—42no—
50#14555886—24no—
51C23×C281C22⋊C412yes—
52C23×C281C2×D411yescharacteristic
53Q8×C281—22no—
54D4×C281—24no—
55D4×C281—22no—
56C2×C4×C281—22no—
57C2×C4×C281—22no—
58C2×C4×C281—42no—
59C2×C4×C281C22⋊C412yes—
60C2×C4×C281C22×C411yescharacteristic
61C2×C4×C281C2×D412yes—
62C2×C4×C281C2×D411yescharacteristic
63C2×C4×C281#4112yes—
64C22×C281—22no—
65C22×C281—41no—
66C22×C281—42no—
67C22×C281C2×C22⋊C411yescharacteristic
68C22×C281#12112yes—
69C4×C281—22no—
70C4×C281—82no—
71C4×C281C4×D412yes—
72C4×C281#12011yescharacteristic
73C4×C281#12311yescharacteristic
74Dic281—42no—
75Dic281—42no—
76C2×C281—21no—
77C2×C281—22no—
78C2×C281—42no—
79C2×C281#38611yescharacteristic
80C281#190911yescharacteristic, complemented, Sylow
81#1909—2811nomaximal, Sylow
82#568—2811no—
83#536—2811no—
84#419—2812no—
85#410D28111yescharacteristic
86H(3,ℤ/4)—2812no—
87C2×#41C2×D28111yescharacteristic
88C22×Q8—2811no—
89#131—5624no—
90C2×M16—2812no—
91C2×M16—5622no—
92C4⋊Q8—2812no—
93#124—2812no—
94#123—5622no—
95C22⋊Q8—5622no—
96#117—2811no—
97#117C2×D28112yes—
98#103—5624no—
99#99—22no—
100#41—22no—
101#41—22no—
102C2×Q8—2812no—
103C2×Q8—5621no—
104C2×Q8—5622no—
105C2×Q8—5622no—
106C2×Q8C4×D28111yescharacteristic
107C2×D4C4×D28111yescharacteristic
108C2×D4C22⋊D28112yes—
109C22×C4—5621no—
110C22×C4D112412yes—
111C22×C4C22×D28111yescharacteristic
112M16—5624no—
113M16—5622no—
114M16—5622no—
115C2×C8—2814no—
116C2×C8—5624no—
117C4⋊C4—22no—
118C4⋊C4—5624no—
119C4⋊C4—5621no—
120C22⋊C4—22no—
121C22⋊C4—5624no—
122C22⋊C4—5621no—
123C42—22no—
124C42—2812no—
125C23#1798511512yes—
126C23C2×C22⋊D28111yescharacteristic
127Q8—22no—
128Q8—5624no—
129Q8—11241no—
130Q8—11241no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—5622no—
137C2×C4—5622no—
138C2×C4—11242no—
139C2×C4#1798511512yes—
140C2×C4C2×C4×D28111yescharacteristic
141C2×C4D4×D28112yes—
142C2×C4C2×D112411yescharacteristic
143C2×C4#1798513712yes—
144C8—5624no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×#1798511511yescharacteristic
149C22#2258285112yes—
150C4—22no—
151C4—82no—
152C4—11242no—
153C4—11242no—
154C4#2258283912yes—
155C4#2258284911yescharacteristic
156C4#2258286311yescharacteristic
157C2—22no—
158C2—21no—
159C2—42no—
160C2#3182334011yescharacteristic
subgroupG/H
centerC2#31823340
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#410×C281C2
socleC2×C281#386
prime radicalC2×#41×C281C22
cosocleC22×C4×C281C23
hypercenter#410D281
hypocenterC281#1909
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #31823471C2semidirect
4. #31823219C2semidirect
10. #22582877C4semidirect
11. #22582866C4semidirect
80. C281#1909semidirect

Maximal subgroups

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

subgroupindex
#318242302
#318240342
#318234712
#318232192
#410×C2812
#1909281