Finite Group Databasebeta

← #49131639

Subgroups — #49131639

Order 36224.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#31827018C211yesmaximal, characteristic
2C2×#22583608C211yesmaximal, characteristic
3#31826832C214yesmaximal, complemented
4#31826814C214yesmaximal, complemented
5#31826475C211yesmaximal, characteristic
6#31826474C211yesmaximal, characteristic
7#31826473C211yesmaximal, characteristic
8M16×Dic283C211yesmaximal, characteristic
9#419×C283C211yesmaximal, characteristic
10C22×Dic566C2211yescharacteristic
11C2×#17985376C2211yescharacteristic
12#22583609C2212yes—
13#22583608—22no—
14#22583608C2212yes—
15#22583608C2212yes—
16#22583601C2212yes—
17#22583587—22no—
18C4×Dic566—22no—
19#22583569C2211yescharacteristic
20C2×Dic283⋊C4—22no—
21C2×C4×Dic283C2211yescharacteristic
22#22583535C2214yes—
23#22583534C2214yes—
24#22583533C2214yes—
25#22583520C2212yes—
26C8×Dic283C2212yes—
27C22×Q8×C283C2211yescharacteristic
28C2×M16×C283C2211yescharacteristic
29#117×C283C2211yescharacteristic
30#103×C283C2214yes—
31C2×Dic566—22no—
32C2×Dic566—21no—
33C2×Dic566—22no—
34C2×Dic566—22no—
35C2×Dic566C2312yes—
36C22×Dic283—21no—
37C22×Dic283D412yes—
38#17985376—22no—
39C2×C283⋊C8C2312yes—
40C4⋊Dic283—22no—
41C4⋊Dic283C2312yes—
42Dic283⋊C4—24no—
43Dic283⋊C4—24no—
44Dic283⋊C4—22no—
45Dic283⋊C4—22no—
46C22⋊Dic283—21no—
47C4×Dic283—21no—
48C4×Dic283D412yes—
49C4×Dic283C2311yescharacteristic
50C4×Dic283C2311yescharacteristic
51C2×Q8×C283—21no—
52C2×Q8×C283—22no—
53C2×Q8×C283—22no—
54C2×Q8×C283C2312yes—
55C22×C4×C283—21no—
56C22×C4×C283C2311yescharacteristic
57M16×C283—22no—
58C2×C8×C283C2312yes—
59C4⋊C4×C283C2312yes—
60C22⋊C4×C283—21no—
61C42×C283—21no—
62Dic566—22no—
63Dic566—22no—
64Dic566—42no—
65Dic566—44no—
66C2×Dic283—24no—
67C2×Dic283—22no—
68C2×Dic283—22no—
69C2×Dic283—42no—
70C2×Dic283C2×D412yes—
71C2×Dic283C2×D412yes—
72C283⋊C8—22no—
73C23×C283C2×D411yescharacteristic
74Q8×C283—22no—
75Q8×C283—22no—
76Q8×C283—42no—
77C2×C4×C283—22no—
78C2×C4×C283—22no—
79C2×C4×C283—42no—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283#4112yes—
82C2×C4×C283#4112yes—
83C2×C4×C283C2411yescharacteristic
84C8×C283—22no—
85C22×C283—22no—
86C22×C283#12412yes—
87C22×C283C22×D411yescharacteristic
88C4×C283—42no—
89C4×C283—42no—
90C4×C283#12412yes—
91C4×C283C2×#4111yescharacteristic
92C4×C283C2×#4111yescharacteristic
93Dic283—22no—
94Dic283—42no—
95Dic283—42no—
96Dic283#13714yes—
97C2×C283—22no—
98C2×C283C2×#12411yescharacteristic
99C2×C283C2×#13712yes—
100C283#313911yescharacteristic, complemented, Sylow
101#3139—2831nomaximal, Sylow
102#533—2831no—
103C2×C4⋊Q8—2831no—
104#491—2834no—
105#487—2834no—
106#419—2831no—
107#419—2831no—
108#419—2831no—
109#419D28311yescharacteristic
110C4×M16—2831no—
111C22×Q8—2831no—
112C22×Q8C2×D28311yescharacteristic
113C2×M16—2831no—
114C2×M16C2×D28311yescharacteristic
115C4⋊Q8—2832no—
116C4⋊Q8—2832no—
117C4⋊Q8—2832no—
118C4⋊Q8—5662no—
119#125—2832no—
120C22⋊Q8—5662no—
121C4×Q8—5662no—
122#117—2831no—
123#117C2×D28311yescharacteristic
124C2×C4⋊C4—5662no—
125C2×C42—2831no—
126#103—2834no—
127#103—2834no—
128#103—2834no—
129#103C2×D28314yes—
130#97—2832no—
131C4×C8—2832no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—2832no—
136C2×Q8—5662no—
137C2×Q8—5661no—
138C2×Q8—5662no—
139C2×Q8—5662no—
140C2×Q8C22×D28312yes—
141C22×C4—21no—
142C22×C4—2832no—
143C22×C4—5661no—
144C22×C4C22×D28311yescharacteristic
145M16—22no—
146M16—5662no—
147C2×C8—2832no—
148C2×C8C22×D28312yes—
149C4⋊C4—2832no—
150C4⋊C4—5664no—
151C4⋊C4—5664no—
152C4⋊C4—5662no—
153C4⋊C4—5662no—
154C4⋊C4—5662no—
155C4⋊C4C22×D28312yes—
156C22⋊C4—21no—
157C22⋊C4—5661no—
158C42—21no—
159C42—2832no—
160C42—2831no—
161C42—2831no—
162C42—5661no—
163C23D4×D28311yescharacteristic
164Q8—22no—
165Q8—22no—
166Q8—42no—
167Q8—5662no—
168Q8—5662no—
169Q8—11324no—
170Q8—11322no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—2832no—
175C2×C4—2832no—
176C2×C4—5664no—
177C2×C4—5662no—
178C2×C4—5662no—
179C2×C4—11322no—
180C2×C4D4×D28311yescharacteristic
181C2×C4#1798539112yes—
182C2×C4#1798539212yes—
183C2×C4C23×D28311yescharacteristic
184C8—22no—
185C8—5662no—
186C22—22no—
187C22#2258359612yes—
188C22C2×D4×D28311yescharacteristic
189C4—42no—
190C4—42no—
191C4—2834no—
192C4—5662no—
193C4—11322no—
194C4—11322no—
195C4#2258359612yes—
196C4C2×#1798539111yescharacteristic
197C4C2×#1798539211yescharacteristic
198C2—22no—
199C2C2×#2258359611yescharacteristic
200C2#137×D28312yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#419×C283C2
socleC22×C283C22×D4
prime radicalC23×C283C2×D4
hypercenter#419D283
hypocenterC283#3139
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #31826832C2semidirect
4. #31826814C2semidirect
100. C283#3139semidirect

Maximal subgroups

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

subgroupindex
#318270182
C2×#225836082
#318268322
#318268142
#318264752
#318264742
#318264732
M16×Dic2832
#419×C2832
#3139283