Finite Group Databasebeta

← #49096993

Subgroups — #49096993

Order 35968.

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

normal subgroups only

This group has 262 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#31824031C211yesmaximal, characteristic
2#31823446C212yesmaximal, complemented
3#31823260C211yesmaximal, characteristic, complemented
4#31823259C212yesmaximal, complemented
5#355×C281C211yesmaximal, characteristic, complemented
6C2×#17985139C2211yescharacteristic
7C2×D4×D281C411yescharacteristic
8M16×D281—22no—
9#22582876C411yescharacteristic
10#22582875C411yescharacteristic
11#22582868C2211yescharacteristic
12#22582852—22no—
13#22582849—22no—
14#22582836C411yescharacteristic
15#22582798C2212yescomplemented
16#22582795—22no—
17#124×C281C2211yescharacteristic
18#101×C281C2212yescomplemented
19C23×D281—21no—
20#17985139—42no—
21C2×D1124—22no—
22C2×D1124C2×C411yescharacteristic
23C2×D1124C2×C411yescharacteristic
24C2×D1124D412yes—
25C2×C22⋊D281—22no—
26C2×C22⋊D281—21no—
27D4×D281—42no—
28C2×C4×D281C2×C411yescharacteristic
29C2×C4×D281D412yes—
30#17985122—22no—
31#17985121—42no—
32C8×D281—42no—
33#17985117—21no—
34#17985115—21no—
35#17985115—22no—
36C4×Dic281C2×C411yescharacteristic
37C2×Q8×C281C2311yescharacteristic
38C2×D4×C281C2×C411yescharacteristic
39M16×C281—22no—
40C22⋊C4×C281—22no—
41C42×C281C2×C411yescharacteristic
42C22×D281—21no—
43C22×D281—42no—
44C22×D281—82no—
45C22×D281C22⋊C411yescharacteristic
46C22×D281C22⋊C412yes—
47D1124—41no—
48D1124—42no—
49D1124—41no—
50D1124—82no—
51C22⋊D281—42no—
52C22⋊D281—82no—
53C2×Dic281—21no—
54C2×Dic281C22⋊C411yescharacteristic
55C4×D281—22no—
56C4×D281—22no—
57C4×D281—22no—
58#14555886—42no—
59C23×C281—21no—
60Q8×C281—41no—
61D4×C281—41no—
62C2×C4×C281—21no—
63C2×C4×C281C22×C411yescharacteristic
64C2×C4×C281C2×D412yes—
65C8×C281—42no—
66C22×C281—42no—
67C22×C281—41no—
68C22×C281C2×C22⋊C411yescharacteristic
69C2×D281—21no—
70C2×D281—22no—
71C2×D281—42no—
72C2×D281—41no—
73C2×D281—42no—
74C2×D281—41no—
75C2×D281—84no—
76C4×C281—22no—
77C4×C281—21no—
78C4×C281—41no—
79Dic281—41no—
80Dic281#9912yes—
81C2×C281—21no—
82C2×C281—81no—
83C2×C281C2×#9911yescharacteristic
84D281—42no—
85D281—41no—
86D281—81no—
87C281#213411yescharacteristic, complemented, Sylow
88#2134—2811nomaximal, Sylow
89#535—2811no—
90#413—2812no—
91#355—2811no—
92#355—2812no—
93#355D28111yescharacteristic, complemented
94C2×#41—2811no—
95C22×D4—2811no—
96C2×M16—5622no—
97#127—2811no—
98#127—2811no—
99#124—2811no—
100#124C2×D28111yescharacteristic
101#121—5622no—
102#120—5622no—
103#117—2811no—
104#101—2812no—
105#101C2×D28112yescomplemented
106#100—5622no—
107C24—5621no—
108#41—11242no—
109C2×Q8C22×D28111yescharacteristic
110C2×D4—2811no—
111C2×D4—2811no—
112C2×D4—2812no—
113C2×D4—5622no—
114C2×D4—5621no—
115C2×D4—5622no—
116C2×D4—11242no—
117C2×D4C4×D28111yescharacteristic
118C22×C4—2811no—
119C22×C4—2812no—
120M16—22no—
121M16—5622no—
122M16—11242no—
123C2×C8—11242no—
124C4⋊C4—5621no—
125C22⋊C4—22no—
126C22⋊C4—5621no—
127C22⋊C4—5622no—
128C42—2811no—
129C42C4×D28111yescharacteristic
130C23—21no—
131C23—2811no—
132C23—2812no—
133C23—5621no—
134C23—11242no—
135C23—22482no—
136Q8—41no—
137D4—41no—
138D4—11242no—
139D4—11241no—
140D4—11241no—
141D4—11242no—
142D4—22482no—
143D4—22482no—
144C2×C4—21no—
145C2×C4—2811no—
146C2×C4—5622no—
147C2×C4—5622no—
148C2×C4—5622no—
149C2×C4—5621no—
150C2×C4C2×C4×D28111yescharacteristic
151C2×C4D4×D28112yes—
152C8—42no—
153C8—11242no—
154C22—42no—
155C22—41no—
156C22—5621no—
157C22—5622no—
158C22—11242no—
159C22—11241no—
160C22—11242no—
161C22—11241no—
162C22—22484no—
163C22C22⋊C4×D28111yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—2812no—
168C4—11241no—
169C2—21no—
170C2—81no—
171C2—11241no—
172C2—11242no—
173C2—22481no—
174C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC2×C4×C281C22×C4
FrattiniC2×Q8C22×D281
Fitting#355×C281C2
socleC2×C281C2×#99
prime radical#31824031C2
cosocleC2×Q8×C281C23
hypercenter#355D281
hypocenterC281#2134
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #31823446C2semidirect
3. #31823260C2semidirect
4. #31823259C2semidirect
5. #355×C281C2semidirect
15. #22582798C22semidirect
18. #101×C281C22semidirect
87. C281#2134semidirect
93. #355D281semidirect
105. #101C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318240312
#318234462
#318232602
#318232592
#355×C2812
#2134281