Finite Group Databasebeta

← #49096991

Subgroups — #49096991

Order 35968.

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

normal subgroups only

This group has 230 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#31824038C211yesmaximal, characteristic
2#101×D281C212yesmaximal, complemented
3#31823262C211yesmaximal, characteristic, complemented
4#31823259C212yesmaximal, complemented
5#356×C281C211yesmaximal, characteristic, complemented
6C2×#17985139C411yescharacteristic
7C2×Q8×D281C2211yescharacteristic
8M16×D281—22no—
9#22582877C411yescharacteristic
10#22582868C2211yescharacteristic
11#22582867C411yescharacteristic
12#22582864—22no—
13#22582857—22no—
14#22582836C411yescharacteristic
15#22582798C2212yes—
16#22582797—22no—
17C4⋊Q8×C281C2211yescharacteristic
18#101×C281C2212yes—
19#17985139—42no—
20C2×Dic562C2×C411yescharacteristic
21C2×Dic562D412yes—
22Q8×D281—42no—
23C2×D1124—21no—
24C2×D1124C2×C411yescharacteristic
25C2×C4×D281—21no—
26C2×C4×D281C2×C411yescharacteristic
27C2×C4×D281D412yes—
28#17985122—22no—
29#17985121—42no—
30C8×D281—42no—
31#17985117—21no—
32#17985117—22no—
33#17985115—21no—
34#17985115—22no—
35#17985115—22no—
36C4×Dic281C2×C411yescharacteristic
37C2×Q8×C281C2×C411yescharacteristic
38C2×Q8×C281C2311yescharacteristic
39M16×C281—22no—
40C4⋊C4×C281—22no—
41C42×C281C2×C411yescharacteristic
42C22×D281—21no—
43C22×D281C22⋊C411yescharacteristic
44Dic562—41no—
45Dic562—42no—
46D1124—41no—
47D1124—42no—
48C2×Dic281—21no—
49C2×Dic281C22⋊C412yes—
50C2×Dic281C22⋊C411yescharacteristic
51C4×D281—22no—
52C4×D281—22no—
53C4×D281—22no—
54C4×D281—42no—
55#14555886—42no—
56Q8×C281—41no—
57Q8×C281—41no—
58C2×C4×C281—21no—
59C2×C4×C281—21no—
60C2×C4×C281C22×C411yescharacteristic
61C2×C4×C281C2×D412yes—
62C8×C281—42no—
63C22×C281C2×C22⋊C411yescharacteristic
64C2×D281—41no—
65C2×D281—42no—
66C2×D281—41no—
67C2×D281#9912yes—
68C4×C281—22no—
69C4×C281—21no—
70C4×C281—41no—
71C4×C281—41no—
72Dic281—21no—
73Dic281—22no—
74Dic281—41no—
75C2×C281—21no—
76C2×C281C2×#9911yescharacteristic
77D281—22no—
78D281—81no—
79C281#213311yescharacteristic, complemented, Sylow
80#2133—2811nomaximal, Sylow
81#536—2811no—
82C2×#101—2812no—
83#356—2811no—
84#356D28111yescharacteristic, complemented
85#355—2812no—
86C2×#41—2811no—
87C22×Q8—2811no—
88C2×M16—5622no—
89C4⋊Q8—2811no—
90C4⋊Q8C2×D28111yescharacteristic
91#124—2811no—
92#124—2811no—
93#123—5622no—
94C22⋊Q8—5622no—
95#117—2811no—
96#101—2812no—
97#101—5622no—
98#101C2×D28112yes—
99#41—11242no—
100C2×Q8—2811no—
101C2×Q8—2812no—
102C2×Q8—11242no—
103C2×Q8C4×D28111yescharacteristic
104C2×Q8C22×D28111yescharacteristic
105C2×D4—2811no—
106C2×D4—5621no—
107C22×C4—2811no—
108C22×C4—2812no—
109C22×C4—5621no—
110M16—22no—
111M16—5622no—
112M16—11242no—
113C2×C8—11242no—
114C4⋊C4—22no—
115C4⋊C4—5621no—
116C4⋊C4—5622no—
117C22⋊C4—5622no—
118C22⋊C4—5621no—
119C22⋊C4—5622no—
120C42—2811no—
121C42C4×D28111yescharacteristic
122C23—2811no—
123C23—5621no—
124Q8—41no—
125Q8—41no—
126Q8—11242no—
127Q8—11241no—
128D4—11241no—
129D4—11242no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—2812no—
133C2×C4—2811no—
134C2×C4—5622no—
135C2×C4—5622no—
136C2×C4—5622no—
137C2×C4—5621no—
138C2×C4—11242no—
139C2×C4C2×C4×D28111yescharacteristic
140C2×C4D4×D28112yes—
141C8—42no—
142C8—11242no—
143C22—2812no—
144C22—11241no—
145C22—11242no—
146C22—11241no—
147C22C22⋊C4×D28111yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—5621no—
153C4—5622no—
154C4—11241no—
155C2—21no—
156C2—5622no—
157C2—22481no—
158C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC2×C4×C281C22×C4
FrattiniC2×Q8C22×D281
Fitting#356×C281C2
socleC2×C281C2×#99
prime radicalC2×#17985139C4
cosocleC2×Q8×C281C23
hypercenter#356D281
hypocenterC281#2133
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #101×D281C2semidirect
3. #31823262C2semidirect
4. #31823259C2semidirect
5. #356×C281C2semidirect
79. C281#2133semidirect
84. #356D281semidirect

Maximal subgroups

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

subgroupindex
#318240382
#101×D2812
#318232622
#318232592
#356×C2812
#2133281