Finite Group Databasebeta

← #49095838

Subgroups — #49095838

Order 35968.

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

normal subgroups only

This group has 314 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#31824037C211yesmaximal, characteristic
2#31823941C211yesmaximal, characteristic, complemented
3#31823479C212yesmaximal
4#31823220C212yesmaximal, complemented
5C2×#101×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2211yescharacteristic
7#22582877C412yescomplemented
8#22582868C412yescomplemented
9#22582862—22no—
10#22582855—22no—
11Q8×Dic281—24no—
12#22582838—22no—
13#22582838C2211yescharacteristic
14#22582838C2212yes—
15#22582805—24no—
16C22×Q8×C281C2211yescharacteristic
17C2×M16×C281C2212yes—
18#101×C281—22no—
19#17985138—22no—
20#17985138—22no—
21C2×Dic562C2×C411yescharacteristic
22C2×D1124C2×C411yescharacteristic
23C2×C22⋊D281—21no—
24C2×C4×D281—21no—
25C4⋊Dic281—24no—
26C4⋊Dic281—22no—
27C4⋊Dic281—21no—
28#17985117—24no—
29C22⋊Dic281—22no—
30C22⋊Dic281—21no—
31#17985115—24no—
32C4×Dic281—24no—
33C4×Dic281C2×C412yes—
34C4×Dic281D414yes—
35C2×Q8×C281—22no—
36C2×Q8×C281—22no—
37C2×Q8×C281C2×C412yes—
38C2×Q8×C281D412yes—
39C22×C4×C281D412yes—
40C22×C4×C281C2311yescharacteristic
41M16×C281—22no—
42M16×C281—22no—
43C2×C8×C281—22no—
44C22×D281—21no—
45Dic562—22no—
46D1124—22no—
47C22⋊D281—41no—
48C22⋊D281—41no—
49C2×Dic281—22no—
50C2×Dic281—21no—
51C2×Dic281—24no—
52C4×D281—42no—
53C23×C281C2×D411yescharacteristic
54Q8×C281—24no—
55Q8×C281—24no—
56C2×C4×C281—22no—
57C2×C4×C281—22no—
58C2×C4×C281C22⋊C414yes—
59C2×C4×C281C22×C411yescharacteristic
60C2×C4×C281C2×D412yes—
61C2×C4×C281C2×D411yescharacteristic
62C2×C4×C281#4112yes—
63C8×C281—42no—
64C22×C281—41no—
65C22×C281C2×C22⋊C411yescharacteristic
66C22×C281#12011yescharacteristic
67C22×C281#12311yescharacteristic
68C2×D281—42no—
69C2×D281—41no—
70C4×C281—24no—
71C4×C281C4×D412yes—
72C4×C281#12112yes—
73Dic281—44no—
74Dic281—42no—
75Dic281—41no—
76C2×C281—21no—
77C2×C281—21no—
78C2×C281—21no—
79C2×C281#38611yescharacteristic
80D281—81no—
81C281#191211yescharacteristic, complemented, Sylow
82#1912—2811nomaximal, Sylow
83#536—2811no—
84#519—2811no—
85#421—2812no—
86C2×#101D28111yescharacteristic, complemented
87H(3,ℤ/4)—2812no—
88C2×#41—2811no—
89C22×Q8C2×D28111yescharacteristic
90C2×M16C2×D28112yes—
91C4⋊Q8—2812no—
92#124—2812no—
93#123—5622no—
94C22⋊Q8—5622no—
95C4×Q8—5624no—
96#117—2812no—
97#117—2811no—
98#117—5622no—
99#104—5624no—
100#101—22no—
101#41—5622no—
102#41—5622no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—2811no—
106C2×Q8C4×D28112yes—
107C2×Q8C22⋊D28112yes—
108C2×D4—2811no—
109C2×D4—5621no—
110C22×C4—5621no—
111C22×C4D112412yes—
112C22×C4C22×D28111yescharacteristic
113M16—22no—
114M16—22no—
115C2×C8—22no—
116C4⋊C4—5624no—
117C4⋊C4—5624no—
118C4⋊C4—5622no—
119C4⋊C4—5621no—
120C22⋊C4—5622no—
121C22⋊C4—5621no—
122C22⋊C4—5624no—
123C42—2812no—
124C42—2814no—
125C42—5624no—
126C23—5621no—
127C23C2×D112411yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—5622no—
131D4—5622no—
132D4—11241no—
133D4—11241no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—5622no—
137C2×C4—5621no—
138C2×C4—5624no—
139C2×C4—11242no—
140C2×C4#1798511514yes—
141C2×C4C2×C4×D28111yescharacteristic
142C2×C4D4×D28112yes—
143C2×C4C2×C22⋊D28111yescharacteristic
144C2×C4#1798513712yes—
145C8—42no—
146C22—41no—
147C22—11242no—
148C22—11241no—
149C22C2×#1798511511yescharacteristic
150C22#2258284911yescharacteristic
151C22#2258286311yescharacteristic
152C4—24no—
153C4—11244no—
154C4—11242no—
155C4—11241no—
156C4#2258283912yes—
157C4#2258285112yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—22481no—
162C2#3182334011yescharacteristic
subgroupG/H
centerC2#31823340
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
FittingC2×#101×C281C2
socleC2×C281#386
prime radicalC2×#17985138C22
cosocleC22×C4×C281C23
hypercenterC2×#101D281
hypocenterC281#1912
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #31823941C2semidirect
4. #31823220C2semidirect
5. C2×#101×C281C2semidirect
7. #22582877C4semidirect
8. #22582868C4semidirect
81. C281#1912semidirect
86. C2×#101D281semidirect

Maximal subgroups

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

subgroupindex
#318240372
#318239412
#318234792
#318232202
C2×#101×C2812
#1912281