Finite Group Databasebeta

← #49123979

Subgroups — #49123979

Order 36224.

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×#22583608C211yesmaximal, characteristic
2C2×Q8×Dic283C211yesmaximal, characteristic
3C2×#22583575C211yesmaximal, characteristic
4#31826371C211yesmaximal, characteristic
5#31826352C214yesmaximal
6#31826347C214yesmaximal
7#31826330C211yesmaximal, characteristic
8#31826311C211yesmaximal, characteristic
9#391×C283C211yesmaximal, characteristic
10C22×Dic566C2211yescharacteristic
11#22583608C418yescomplemented
12Q8×Dic283—24no—
13#22583575—24no—
14C2×C4⋊Dic283C2211yescharacteristic
15C2×C4⋊Dic283C2212yes—
16C2×Dic283⋊C4C2212yes—
17C2×Dic283⋊C4C2214yes—
18C2×C4×Dic283C2212yes—
19C2×C4×Dic283C2212yes—
20C2×C4×Dic283C2211yescharacteristic
21C2×C4×Dic283C2211yescharacteristic
22C283⋊#95C2212yes—
23C283⋊#95C2212yes—
24C283⋊#95C2214yes—
25C283⋊#95C2214yes—
26C22×Q8×C283C2211yescharacteristic
27C2×C4⋊C4×C283C2211yescharacteristic
28C2×C42×C283C2211yescharacteristic
29#95×C283C2214yes—
30C2×Dic566—22no—
31C2×Dic566—22no—
32C2×Dic566C2×C414yes—
33C22×Dic283C2312yes—
34C22×Dic283C2312yes—
35C22×Dic283C2312yes—
36C22×Dic283C2311yescharacteristic
37C22×Dic283C2311yescharacteristic
38C4⋊Dic283—24no—
39C4⋊Dic283—22no—
40Dic283⋊C4—24no—
41Dic283⋊C4C2×C4116yes—
42C4×Dic283—24no—
43C4×Dic283—24no—
44C4×Dic283C2×C414yes—
45C4×Dic283D414yes—
46C2×Q8×C283—22no—
47C2×Q8×C283—22no—
48C2×Q8×C283C2×C414yes—
49C22×C4×C283C2312yes—
50C22×C4×C283C2312yes—
51C22×C4×C283C2312yes—
52C22×C4×C283C2311yescharacteristic
53C4⋊C4×C283—22no—
54C42×C283—22no—
55Dic566—28no—
56C2×Dic283—22no—
57C2×Dic283—22no—
58C2×Dic283—22no—
59C2×Dic283—22no—
60C2×Dic283—22no—
61C2×Dic283—22no—
62C2×Dic283—22no—
63C2×Dic283—24no—
64C2×Dic283C22×C414yes—
65C2×Dic283C22×C414yes—
66C2×Dic283C2×D412yes—
67C2×Dic283C2×D412yes—
68C23×C283C2411yescharacteristic
69Q8×C283—28no—
70C2×C4×C283—22no—
71C2×C4×C283—22no—
72C2×C4×C283—22no—
73C2×C4×C283—22no—
74C2×C4×C283—24no—
75C2×C4×C283—22no—
76C2×C4×C283—22no—
77C2×C4×C283C22×C414yes—
78C2×C4×C283C22×C412yes—
79C2×C4×C283C2×D412yes—
80C2×C4×C283#4112yes—
81C22×C283C23×C411yescharacteristic
82C22×C283C22×D411yescharacteristic
83C22×C283C2×#4111yescharacteristic
84C22×C2832−1+412yes—
85C22×C2832−1+412yes—
86C4×C283—24no—
87C4×C283—42no—
88C4×C283—42no—
89C4×C283C4×D414yes—
90Dic283—24no—
91Dic283—24no—
92Dic283—22no—
93Dic283—22no—
94Dic283—42no—
95C2×C283C2×C4×D411yescharacteristic
96C2×C283#51912yes—
97C2×C283#53611yescharacteristic
98C2×C283#53611yescharacteristic
99C2×C283#54112yes—
100C283#232711yescharacteristic, complemented, Sylow
101#2327—2831nomaximal, Sylow
102C2×C4⋊Q8—2831no—
103C2×C4×Q8—2831no—
104C2×C4×Q8—2831no—
105#391—2831no—
106#391D28311yescharacteristic
107#387—2834no—
108#387—2834no—
109#382—2831no—
110#376—2831no—
111C22×Q8—2831no—
112C22×Q8C2×D28311yescharacteristic
113C4⋊Q8—2838no—
114C4×Q8—5664no—
115C4×Q8—5664no—
116C2×C4⋊C4—2834no—
117C2×C4⋊C4—2832no—
118C2×C4⋊C4—2831no—
119C2×C4⋊C4—2832no—
120C2×C4⋊C4C2×D28311yescharacteristic
121C2×C42—2831no—
122C2×C42—2831no—
123C2×C42—2832no—
124C2×C42—2832no—
125C2×C42C2×D28311yescharacteristic
126#95—2832no—
127#95—2832no—
128#95—2834no—
129#95—2834no—
130#95C2×D28314yes—
131C2×Q8—22no—
132C2×Q8—22no—
133C2×Q8—2834no—
134C2×Q8—5662no—
135C2×Q8—5662no—
136C2×Q8C4×D28314yes—
137C22×C4—2832no—
138C22×C4—2831no—
139C22×C4—2831no—
140C22×C4—2832no—
141C22×C4—2832no—
142C22×C4C22×D28312yes—
143C22×C4C22×D28312yes—
144C22×C4C22×D28312yes—
145C22×C4C22×D28311yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—28316no—
148C4⋊C4—5664no—
149C4⋊C4—5664no—
150C4⋊C4—5662no—
151C42—22no—
152C42—2834no—
153C42—2834no—
154C42—5664no—
155C42—5664no—
156C23C23×D28311yescharacteristic
157Q8—28no—
158Q8—5668no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—2834no—
167C2×C4—2834no—
168C2×C4—2832no—
169C2×C4—2832no—
170C2×C4—5662no—
171C2×C4—5662no—
172C2×C4—5662no—
173C2×C4—5662no—
174C2×C4—5662no—
175C2×C4—5662no—
176C2×C4—5662no—
177C2×C4—5664no—
178C2×C4C2×C4×D28314yes—
179C2×C4C2×C4×D28312yes—
180C2×C4D4×D28312yes—
181C2×C4#1798539112yes—
182C22C22×C4×D28311yescharacteristic
183C22C2×D4×D28311yescharacteristic
184C22C2×#1798539111yescharacteristic
185C22#2258365712yes—
186C22#2258365812yes—
187C4—24no—
188C4—42no—
189C4—42no—
190C4—5662no—
191C4—5662no—
192C4—5664no—
193C4—5664no—
194C4—11322no—
195C4(C22⋊D283)⋊C414yes—
196C2C2×(C22⋊D283)⋊C411yescharacteristic
197C2#3182694112yes—
198C2#3182703511yescharacteristic
199C2#3182704011yescharacteristic
200C2#3182707512yes—
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#391×C283C2
socle, prime radical, cosocleC23×C283C24
hypercenter#391D283
hypocenterC283#2327
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #22583608C4semidirect
100. C283#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#225836082
C2×Q8×Dic2832
C2×#225835752
#318263712
#318263522
#318263472
#318263302
#318263112
#391×C2832
#2327283