Finite Group Databasebeta

← #49095751

Subgroups — #49095751

Order 35968.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#31823974C211yesmaximal, characteristic
2C2×#22582807C212yesmaximal, complemented
3#31823427C211yesmaximal, characteristic, complemented
4#31823223C212yesmaximal, complemented
5C2×#117×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2211yescharacteristic
7C2×#17985122C2212yes—
8#22582862—21no—
9#22582858C412yescomplemented
10#22582853C412yescomplemented
11#22582848—21no—
12C4×C22⋊D281—22no—
13#22582838C2211yescharacteristic
14#22582807—24no—
15C22⋊#14555886—22no—
16C23×C4×C281C2211yescharacteristic
17#117×C281—24no—
18C2×C4⋊C4×C281—21no—
19C2×C22⋊C4×C281—21no—
20C2×C42×C281C2212yes—
21#17985138—22no—
22#17985138—22no—
23C2×Dic562C2×C411yescharacteristic
24C2×D1124C2×C411yescharacteristic
25C2×C22⋊D281—22no—
26C2×C22⋊D281—21no—
27C2×C4×D281—21no—
28#17985122—22no—
29#17985122—22no—
30C2×#14555886—22no—
31C4⋊Dic281C2×C412yes—
32#17985117—22no—
33C22⋊Dic281—22no—
34C22⋊Dic281—21no—
35#17985115—22no—
36C4×Dic281—21no—
37C24×C281D411yescharacteristic
38C22×C4×C281—22no—
39C22×C4×C281—22no—
40C22×C4×C281—22no—
41C22×C4×C281C2×C412yes—
42C22×C4×C281D411yescharacteristic
43C22×C4×C281D412yes—
44C22×C4×C281C2311yescharacteristic
45C4⋊C4×C281—24no—
46C22⋊C4×C281—24no—
47C42×C281—22no—
48C42×C281D414yescomplemented
49C22×D281—21no—
50Dic562—22no—
51D1124—22no—
52C22⋊D281—44no—
53C22⋊D281—41no—
54C22⋊D281—41no—
55C2×Dic281—22no—
56C2×Dic281—21no—
57C4×D281—42no—
58#14555886—42no—
59C23×C281—21no—
60C23×C281—21no—
61C23×C281—42no—
62C23×C281C22⋊C412yes—
63C23×C281C2×D411yescharacteristic
64C2×C4×C281—21no—
65C2×C4×C281—21no—
66C2×C4×C281—24no—
67C2×C4×C281—24no—
68C2×C4×C281—24no—
69C2×C4×C281—44no—
70C2×C4×C281C22⋊C412yes—
71C2×C4×C281C22×C411yescharacteristic
72C2×C4×C281C2×D412yes—
73C2×C4×C281C2×D411yescharacteristic
74C2×C4×C281#4112yes—
75C22×C281—22no—
76C22×C281—22no—
77C22×C281—22no—
78C22×C281—22no—
79C22×C281—42no—
80C22×C281—42no—
81C22×C281C2×C22⋊C411yescharacteristic
82C22×C281#12011yescharacteristic
83C22×C281#12311yescharacteristic
84C2×D281—41no—
85C2×D281—42no—
86C4×C281—22no—
87C4×C281—44no—
88C4×C281C4×D412yes—
89C4×C281#12112yes—
90Dic281—41no—
91Dic281—42no—
92C2×C281—21no—
93C2×C281—21no—
94C2×C281—42no—
95C2×C281#38611yescharacteristic
96C2×C281#42112yes—
97D281—81no—
98C281#189711yescharacteristic, complemented, Sylow
99#1897—2811nomaximal, Sylow
100#525—2811no—
101C2×#117D28111yescharacteristic, complemented
102C2×#104—2812no—
103#407—2811no—
104#339—2812no—
105C2×#41—2811no—
106C23×C4C2×D28111yescharacteristic
107C2×M16—2812no—
108#123—5621no—
109C22⋊Q8—2812no—
110#121—2812no—
111#120—5621no—
112C4×D4—5622no—
113#117—24no—
114#117—2811no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D28112yes—
118#104—5624no—
119C22⋊C8—5622no—
120C24C22⋊D28111yescharacteristic
121#41—5622no—
122#41—5622no—
123C2×Q8—2811no—
124C2×D4—2811no—
125C2×D4—5622no—
126C2×D4—5621no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—5621no—
131C22×C4C4×D28112yes—
132C22×C4C22⋊D28111yescharacteristic
133C22×C4D112412yes—
134C22×C4C22×D28111yescharacteristic
135M16—5622no—
136M16—5622no—
137C2×C8—5622no—
138C4⋊C4—24no—
139C4⋊C4—2812no—
140C4⋊C4—5622no—
141C22⋊C4—24no—
142C22⋊C4—5622no—
143C22⋊C4—5621no—
144C22⋊C4—5622no—
145C42—22no—
146C42—5621no—
147C42C22⋊D28114yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—5621no—
152C23#1798511512yes—
153C23C2×C22⋊D28111yescharacteristic
154Q8—5622no—
155D4—5622no—
156D4—11244no—
157D4—11241no—
158D4—11241no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—5622no—
166C2×C4—5621no—
167C2×C4—11242no—
168C2×C4#1798511512yes—
169C2×C4C2×C4×D28111yescharacteristic
170C2×C4C2×C22⋊D28112yes—
171C2×C4C2×D112411yescharacteristic
172C2×C4#1798513812yes—
173C8—11242no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—11242no—
181C22—11241no—
182C22C2×#1798511511yescharacteristic
183C22#2258284811yescharacteristic
184C22#2258286211yescharacteristic
185C4—22no—
186C4—44no—
187C4—11242no—
188C4—11241no—
189C4C4×C22⋊D28112yes—
190C4#2258285312yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—22481no—
195C2#3182334211yescharacteristic
196C2#3182348112yes—
subgroupG/H
centerC2×C4C2×D1124
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
FittingC2×#117×C281C2
socleC22×C281C2×C22⋊C4
prime radical#31823974C2
cosocleC22×C4×C281C23
hypercenterC2×#117D281
hypocenterC281#1897
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#22582807C2semidirect
3. #31823427C2semidirect
4. #31823223C2semidirect
5. C2×#117×C281C2semidirect
9. #22582858C4semidirect
10. #22582853C4semidirect
48. C42×C281D4semidirect
98. C281#1897semidirect
101. C2×#117D281semidirect
147. C42C22⋊D281semidirect

Maximal subgroups

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

subgroupindex
#318239742
C2×#225828072
#318234272
#318232232
C2×#117×C2812
#1897281