Finite Group Databasebeta

← #49098021

Subgroups — #49098021

Order 35968.

516 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 197 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
1C2×#22582877C211yesmaximal, characteristic
2C2×Q8×Dic281C211yesmaximal, characteristic
3C2×#22582844C211yesmaximal, characteristic
4#31823369C211yesmaximal, characteristic
5#31823350C214yesmaximal
6#31823345C214yesmaximal
7#31823328C211yesmaximal, characteristic
8#31823309C211yesmaximal, characteristic
9#391×C281C211yesmaximal, characteristic
10C22×Dic562C2211yescharacteristic
11#22582877C418yescomplemented
12Q8×Dic281—24no—
13#22582844—24no—
14C2×C4⋊Dic281C2211yescharacteristic
15C2×C4⋊Dic281C2212yes—
16C2×#17985117C2212yes—
17C2×#17985117C2214yes—
18C2×C4×Dic281C2212yes—
19C2×C4×Dic281C2212yes—
20C2×C4×Dic281C2211yescharacteristic
21C2×C4×Dic281C2211yescharacteristic
22#22582786C2214yes—
23#22582786C2212yes—
24#22582786C2212yes—
25#22582786C2214yes—
26C22×Q8×C281C2211yescharacteristic
27C2×C4⋊C4×C281C2211yescharacteristic
28C2×C42×C281C2211yescharacteristic
29#95×C281C2214yes—
30C2×Dic562—22no—
31C2×Dic562—22no—
32C2×Dic562C2×C414yes—
33C22×Dic281C2312yes—
34C22×Dic281C2312yes—
35C22×Dic281C2312yes—
36C22×Dic281C2311yescharacteristic
37C22×Dic281C2311yescharacteristic
38C4⋊Dic281—24no—
39C4⋊Dic281—22no—
40#17985117—24no—
41#17985117C2×C4116yes—
42C4×Dic281—24no—
43C4×Dic281—24no—
44C4×Dic281C2×C414yes—
45C4×Dic281D414yes—
46C2×Q8×C281—22no—
47C2×Q8×C281—22no—
48C2×Q8×C281C2×C414yes—
49C22×C4×C281C2312yes—
50C22×C4×C281C2312yes—
51C22×C4×C281C2312yes—
52C22×C4×C281C2311yescharacteristic
53C4⋊C4×C281—22no—
54C42×C281—22no—
55Dic562—28no—
56C2×Dic281—22no—
57C2×Dic281—22no—
58C2×Dic281—22no—
59C2×Dic281—22no—
60C2×Dic281—22no—
61C2×Dic281—22no—
62C2×Dic281—22no—
63C2×Dic281—24no—
64C2×Dic281C22×C414yes—
65C2×Dic281C22×C414yes—
66C2×Dic281C2×D412yes—
67C2×Dic281C2×D412yes—
68C23×C281C2411yescharacteristic
69Q8×C281—28no—
70C2×C4×C281—22no—
71C2×C4×C281—22no—
72C2×C4×C281—22no—
73C2×C4×C281—22no—
74C2×C4×C281—24no—
75C2×C4×C281—22no—
76C2×C4×C281—22no—
77C2×C4×C281C22×C414yes—
78C2×C4×C281C22×C412yes—
79C2×C4×C281C2×D412yes—
80C2×C4×C281#4112yes—
81C22×C281C23×C411yescharacteristic
82C22×C281C22×D411yescharacteristic
83C22×C281C2×#4111yescharacteristic
84C22×C2812−1+412yes—
85C22×C2812−1+412yes—
86C4×C281—24no—
87C4×C281—42no—
88C4×C281—42no—
89C4×C281C4×D414yes—
90Dic281—24no—
91Dic281—24no—
92Dic281—22no—
93Dic281—22no—
94Dic281—42no—
95C2×C281C2×C4×D411yescharacteristic
96C2×C281#51912yes—
97C2×C281#53611yescharacteristic
98C2×C281#53611yescharacteristic
99C2×C281#54112yes—
100C281#232711yescharacteristic, complemented, Sylow
101#2327—2811nomaximal, Sylow
102C2×C4⋊Q8—2811no—
103C2×C4×Q8—2811no—
104C2×C4×Q8—2811no—
105#391—2811no—
106#391D28111yescharacteristic
107#387—2814no—
108#387—2814no—
109#382—2811no—
110#376—2811no—
111C22×Q8—2811no—
112C22×Q8C2×D28111yescharacteristic
113C4⋊Q8—2818no—
114C4×Q8—5624no—
115C4×Q8—5624no—
116C2×C4⋊C4—2814no—
117C2×C4⋊C4—2812no—
118C2×C4⋊C4—2811no—
119C2×C4⋊C4—2812no—
120C2×C4⋊C4C2×D28111yescharacteristic
121C2×C42—2811no—
122C2×C42—2811no—
123C2×C42—2812no—
124C2×C42—2812no—
125C2×C42C2×D28111yescharacteristic
126#95—2812no—
127#95—2812no—
128#95—2814no—
129#95—2814no—
130#95C2×D28114yes—
131C2×Q8—22no—
132C2×Q8—22no—
133C2×Q8—2814no—
134C2×Q8—5622no—
135C2×Q8—5622no—
136C2×Q8C4×D28114yes—
137C22×C4—2812no—
138C22×C4—2811no—
139C22×C4—2811no—
140C22×C4—2812no—
141C22×C4—2812no—
142C22×C4C22×D28112yes—
143C22×C4C22×D28112yes—
144C22×C4C22×D28112yes—
145C22×C4C22×D28111yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—28116no—
148C4⋊C4—5624no—
149C4⋊C4—5624no—
150C4⋊C4—5622no—
151C42—22no—
152C42—2814no—
153C42—2814no—
154C42—5624no—
155C42—5624no—
156C23C23×D28111yescharacteristic
157Q8—28no—
158Q8—5628no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—2814no—
167C2×C4—2814no—
168C2×C4—2812no—
169C2×C4—2812no—
170C2×C4—5622no—
171C2×C4—5622no—
172C2×C4—5622no—
173C2×C4—5622no—
174C2×C4—5622no—
175C2×C4—5622no—
176C2×C4—5622no—
177C2×C4—5624no—
178C2×C4C2×C4×D28114yes—
179C2×C4C2×C4×D28112yes—
180C2×C4D4×D28112yes—
181C2×C4#1798513712yes—
182C22C22×C4×D28111yescharacteristic
183C22C2×D4×D28111yescharacteristic
184C22C2×#1798513711yescharacteristic
185C22#2258292612yes—
186C22#2258292712yes—
187C4—24no—
188C4—42no—
189C4—42no—
190C4—5624no—
191C4—5624no—
192C4—5622no—
193C4—5622no—
194C4—11242no—
195C4#2258283914yes—
196C2C2×#2258283911yescharacteristic
197C2#3182393912yes—
198C2#3182403311yescharacteristic
199C2#3182403811yescharacteristic
200C2#3182407312yes—
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#391×C281C2
socle, prime radical, cosocleC23×C281C24
hypercenter#391D281
hypocenterC281#2327
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #22582877C4semidirect
100. C281#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#225828772
C2×Q8×Dic2812
C2×#225828442
#318233692
#318233502
#318233452
#318233282
#318233092
#391×C2812
#2327281