Finite Group Databasebeta

← #49119573

Subgroups — #49119573

Order 36224.

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

normal subgroups only

This group has 264 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
1C2×#22583567C211yesmaximal, characteristic
2#31826518C211yesmaximal, characteristic, complemented
3#31826190C212yesmaximal, complemented
4#31826188C212yesmaximal
5#431×C283C211yesmaximal, characteristic, complemented
6C22×C4×D283C411yescharacteristic
7#22583567—21no—
8#22583567—21no—
9#22583567—21no—
10#22583567—21no—
11C2×Dic283⋊C4C411yescharacteristic
12C2×Dic283⋊C4C2211yescharacteristic
13C2×(C2×D283)⋊C4C411yescharacteristic
14C2×(C2×D283)⋊C4C2211yescharacteristic
15C2×C4×Dic283C411yescharacteristic
16C4⋊(C283⋊C8)—21no—
17C22⋊(C283⋊C8)C2212yes—
18C4×C283⋊C8—21no—
19C2×C42×C283C2211yescharacteristic
20C4⋊C8×C283—21no—
21C22⋊C8×C283C2212yes—
22C4×C8×C283—21no—
23C23×D283C2×C411yescharacteristic
24C22×Dic283C2×C411yescharacteristic
25C22×Dic283C2×C411yescharacteristic
26C22×Dic283C2×C411yescharacteristic
27C2×C4×D283—21no—
28C2×C4×D283—21no—
29C2×C4×D283—22no—
30C2×C4×D283C814yescomplemented
31C2×C283⋊C8—22no—
32Dic283⋊C4—21no—
33Dic283⋊C4—21no—
34Dic283⋊C4—21no—
35Dic283⋊C4—21no—
36(C2×D283)⋊C4—21no—
37(C2×D283)⋊C4—21no—
38(C2×D283)⋊C4—21no—
39(C2×D283)⋊C4—21no—
40C4×Dic283—21no—
41C4×Dic283—21no—
42C22×C4×C283C2×C411yescharacteristic
43C22×C4×C283C2×C411yescharacteristic
44C22×C4×C283C2311yescharacteristic
45C2×C8×C283—22no—
46C42×C283D411yescharacteristic
47C42×C283D411yescharacteristic
48C42×C283D411yescharacteristic
49C42×C283D411yescharacteristic
50C22×D283—21no—
51C22×D283—21no—
52C22×D283—41no—
53C22×D283—41no—
54C22×D283C2×C812yes—
55C2×Dic283—21no—
56C2×Dic283—21no—
57C2×Dic283—21no—
58C2×Dic283—21no—
59C2×Dic283—41no—
60C2×Dic283—41no—
61C2×Dic283C2×C812yes—
62C4×D283—24no—
63C4×D283—24no—
64C283⋊C8—42no—
65C23×C283C22×C411yescharacteristic
66C2×C4×C283—41no—
67C2×C4×C283—41no—
68C2×C4×C283C22⋊C411yescharacteristic
69C2×C4×C283C22⋊C411yescharacteristic
70C2×C4×C283C22⋊C411yescharacteristic
71C2×C4×C283C22⋊C411yescharacteristic
72C2×C4×C283C2×C812yes—
73C2×C4×C283M1612yes—
74C2×C4×C283C2×D411yescharacteristic
75C2×C4×C283C2×D411yescharacteristic
76C8×C283—42no—
77C22×C283—21no—
78C22×C283—21no—
79C22×C283C2×C22⋊C411yescharacteristic
80C22×C283C22×C811yescharacteristic
81C22×C283C2×M1611yescharacteristic
82C2×D283—22no—
83C2×D283—42no—
84C2×D283—41no—
85C2×D283—41no—
86C2×D283—42no—
87C4×C283—21no—
88C4×C283—21no—
89C4×C283—21no—
90C4×C283—21no—
91C4×C283C22⋊C812yes—
92C4×C283C22⋊C812yes—
93Dic283—22no—
94Dic283—41no—
95Dic283—41no—
96C2×C283—21no—
97C2×C283—21no—
98C2×C283C2×C22⋊C811yescharacteristic
99C2×C283#41011yescharacteristic
100C2×C283#41311yescharacteristic
101D283—42no—
102C283#145811yescharacteristic, complemented, Sylow
103#1458—2831nomaximal, Sylow
104C2×#117—2831no—
105#431—2831no—
106#431D28311yescharacteristic, complemented
107#324—2832no—
108#323—2832no—
109C23×C4—2831no—
110#117—5661no—
111#117—5661no—
112#117—5661no—
113#117—5661no—
114C2×C4⋊C4—2831no—
115C2×C4⋊C4—2831no—
116C2×C22⋊C4—2831no—
117C2×C22⋊C4—2831no—
118C2×C42—2831no—
119C2×C42C2×D28311yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—5661no—
122C22⋊C8—2832no—
123C22⋊C8C2×D28312yes—
124C4×C8—21no—
125C4×C8—5661no—
126C24—2831no—
127C22×C4—2831no—
128C22×C4—2834no—
129C22×C4—2831no—
130C22×C4—2831no—
131C22×C4—5661no—
132C22×C4—5661no—
133C22×C4—5662no—
134C22×C4C4×D28311yescharacteristic
135C22×C4C4×D28311yescharacteristic
136C22×C4C22×D28311yescharacteristic
137C2×C8—22no—
138C2×C8—5662no—
139C4⋊C4—5661no—
140C4⋊C4—5661no—
141C4⋊C4—5661no—
142C4⋊C4—5661no—
143C22⋊C4—5661no—
144C22⋊C4—5661no—
145C22⋊C4—5661no—
146C22⋊C4—5661no—
147C42—5661no—
148C42—5661no—
149C42C22⋊D28311yescharacteristic
150C42C22⋊D28311yescharacteristic
151C42D113211yescharacteristic
152C42D113211yescharacteristic
153C23—2832no—
154C23—5661no—
155C23—5661no—
156C23—11321no—
157C23—11321no—
158C23C2×C4×D28311yescharacteristic
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—2832no—
162C2×C4—5661no—
163C2×C4—5661no—
164C2×C4—5664no—
165C2×C4—5664no—
166C2×C4—5661no—
167C2×C4—5661no—
168C2×C4—11321no—
169C2×C4—11321no—
170C2×C4(C2×D283)⋊C411yescharacteristic
171C2×C4(C2×D283)⋊C411yescharacteristic
172C2×C4(C2×D283)⋊C411yescharacteristic
173C2×C4(C2×D283)⋊C411yescharacteristic
174C2×C4C8×D28312yes—
175C2×C4#1798537512yes—
176C2×C4C2×C22⋊D28311yescharacteristic
177C2×C4C2×D113211yescharacteristic
178C8—42no—
179C8—11322no—
180C22—21no—
181C22—21no—
182C22—5662no—
183C22—11322no—
184C22—11322no—
185C22—11321no—
186C22—11321no—
187C22C2×(C2×D283)⋊C411yescharacteristic
188C22C2×C8×D28311yescharacteristic
189C22C2×#1798537511yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—5662no—
195C4—11321no—
196C4—11321no—
197C4(C2×D283)⋊C812yes—
198C4(C2×D283)⋊C812yes—
199C2—21no—
200C2—21no—
201C2—11322no—
202C2C2×(C2×D283)⋊C811yescharacteristic
203C2#3182643811yescharacteristic
204C2#3182644711yescharacteristic
subgroupG/H
centerC2×C4(C2×D283)⋊C4
commutatorC22×C283C22×C8
FrattiniC22×C4C22×D283
Fitting#431×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC23×D283C2×C4
cosocleC22×C4×C283C23
hypercenter#431D283
hypocenterC283#1458
LCSG ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #31826518C2semidirect
3. #31826190C2semidirect
5. #431×C283C2semidirect
30. C2×C4×D283C8semidirect
102. C283#1458semidirect
106. #431D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835672
#318265182
#318261902
#318261882
#431×C2832
#1458283