Finite Group Databasebeta

← #49121574

Subgroups — #49121574

Order 36224.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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×#22583569C211yesmaximal, characteristic
2C2×#22583534C212yesmaximal, complemented
3C2×C22⋊(C283⋊C8)C211yesmaximal, characteristic
4#31826227C212yesmaximal, complemented
5C2×C22⋊Q8×C283C211yesmaximal, characteristic
6C22×C283⋊C8C2212yes—
7#22583569—24no—
8C2×C4⋊Dic283C2212yes—
9C2×C22⋊Dic283—21no—
10C2×C4×Dic283—21no—
11#22583534—24no—
12C22⋊(C283⋊C8)—22no—
13C22×Q8×C283C2211yescharacteristic
14C23×C4×C283C2211yescharacteristic
15C22⋊Q8×C283—22no—
16C22⋊Q8×C283C414yescomplemented
17C2×C4⋊C4×C283—21no—
18C2×C4⋊C4×C283C2211yescharacteristic
19C2×C22⋊C4×C283—21no—
20C22×Dic283—22no—
21C2×C283⋊C8—22no—
22C2×C283⋊C8—22no—
23C2×C283⋊C8—22no—
24C4⋊Dic283—22no—
25C4⋊Dic283D414yes—
26C22⋊Dic283—24no—
27C4×Dic283—24no—
28C24×C283D411yescharacteristic
29C2×Q8×C283—21no—
30C2×Q8×C283—22no—
31C2×Q8×C283—22no—
32C2×Q8×C283C2×C412yes—
33C22×C4×C283—22no—
34C22×C4×C283—22no—
35C22×C4×C283—21no—
36C22×C4×C283—21no—
37C22×C4×C283C2×C412yes—
38C22×C4×C283D411yescharacteristic
39C22×C4×C283D412yes—
40C22×C4×C283C2311yescharacteristic
41C4⋊C4×C283—24no—
42C4⋊C4×C283—21no—
43C4⋊C4×C283C2×C412yes—
44C22⋊C4×C283—24no—
45C2×Dic283—24no—
46C2×Dic283—42no—
47C2×Dic283—42no—
48C283⋊C8—42no—
49C23×C283—21no—
50C23×C283—21no—
51C23×C283—22no—
52C23×C283—22no—
53C23×C283C22⋊C412yes—
54C23×C283C2×D411yescharacteristic
55Q8×C283—24no—
56Q8×C283—42no—
57C2×C4×C283—21no—
58C2×C4×C283—21no—
59C2×C4×C283—24no—
60C2×C4×C283—24no—
61C2×C4×C283—22no—
62C2×C4×C283—22no—
63C2×C4×C283—41no—
64C2×C4×C283—41no—
65C2×C4×C283—42no—
66C2×C4×C283C22⋊C412yes—
67C2×C4×C283C22×C411yescharacteristic
68C2×C4×C283C2×D412yes—
69C2×C4×C283C2×D411yescharacteristic
70C2×C4×C283#4112yes—
71C22×C283—22no—
72C22×C283—22no—
73C22×C283—22no—
74C22×C283—42no—
75C22×C283—42no—
76C22×C283C2×C22⋊C411yescharacteristic
77C22×C283#12011yescharacteristic
78C22×C283#12311yescharacteristic
79C22×C283#13512yes—
80C22×C283#13712yes—
81C4×C283—22no—
82C4×C283—42no—
83C4×C283—42no—
84C4×C283C4×D412yes—
85C4×C283#12112yes—
86Dic283—44no—
87C2×C283—42no—
88C2×C283#38611yescharacteristic
89C2×C283#41611yescharacteristic
90C2×C283#41911yescharacteristic
91C2×C283#45212yes—
92C2×C283#48512yes—
93C283#187311yescharacteristic, complemented, Sylow
94#1873—2831nomaximal, Sylow
95C2×C22⋊Q8D28311yescharacteristic
96C2×#117—2831no—
97C2×#103—2832no—
98C2×C22⋊C8—2831no—
99#340—2832no—
100C22×Q8C2×D28311yescharacteristic
101C23×C4C2×D28311yescharacteristic
102C22×C8—2832no—
103C22⋊Q8—22no—
104C22⋊Q8Dic28314yescomplemented
105#117—5664no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—2832no—
108C2×C4⋊C4C2×D28311yescharacteristic
109C2×C22⋊C4—21no—
110C2×C22⋊C4—5661no—
111C2×C42—5661no—
112#103—5664no—
113C22⋊C8—5662no—
114C24C22⋊D28311yescharacteristic
115C2×Q8—21no—
116C2×Q8—22no—
117C2×Q8—22no—
118C2×Q8C2×Dic28312yes—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—5662no—
124C22×C4C2×Dic28312yes—
125C22×C4C22⋊D28311yescharacteristic
126C22×C4C22⋊D28312yes—
127C22×C4C22×D28311yescharacteristic
128C2×C8—5662no—
129C2×C8—5662no—
130C2×C8—5662no—
131C4⋊C4—24no—
132C4⋊C4—21no—
133C4⋊C4—2834no—
134C4⋊C4—5662no—
135C4⋊C4C2×Dic28312yes—
136C22⋊C4—24no—
137C22⋊C4—5664no—
138C42—5664no—
139C23—21no—
140C23—21no—
141C23—22no—
142C23—22no—
143C23C22⋊Dic28312yes—
144C23C2×C22⋊D28311yescharacteristic
145Q8—24no—
146Q8—42no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—24no—
150C2×C4—24no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—42no—
156C2×C4—5664no—
157C2×C4—11322no—
158C2×C4—11322no—
159C2×C4C22⋊Dic28312yes—
160C2×C4C22×Dic28311yescharacteristic
161C2×C4D4×D28312yes—
162C2×C4C2×C22⋊D28311yescharacteristic
163C2×C4#1798539112yes—
164C8—11322no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22C2×C22⋊Dic28311yescharacteristic
171C22#2258357811yescharacteristic
172C22#2258359111yescharacteristic
173C22#2258363012yes—
174C22#2258364112yes—
175C4—22no—
176C4—42no—
177C4—42no—
178C4—11324no—
179C4D4×Dic28312yes—
180C4#2258358212yes—
181C2—42no—
182C2#3182634511yescharacteristic
183C2#3182646111yescharacteristic
184C2#3182647411yescharacteristic
185C2#3182662512yes—
186C2#3182680312yes—
subgroupG/H
centerC23C2×C22⋊D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×C22⋊Q8×C283C2
socleC23×C283C2×D4
prime radicalC24×C283D4
cosocleC22×C4×C283C23
hypercenterC2×C22⋊Q8D283
hypocenterC283#1873
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#22583534C2semidirect
4. #31826227C2semidirect
16. C22⋊Q8×C283C4semidirect
93. C283#1873semidirect
104. C22⋊Q8Dic283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835692
C2×#225835342
C2×C22⋊(C283⋊C8)2
#318262272
C2×C22⋊Q8×C2832
#1873283