Finite Group Databasebeta

← #49121340

Subgroups — #49121340

Order 36224.

316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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×C4⋊C4×D283C211yesmaximal, characteristic
2#31826428C212yesmaximal
3#31826234C211yesmaximal, characteristic, complemented
4#31826233C212yesmaximal, complemented
5#343×C283C211yesmaximal, characteristic, complemented
6C22×C4×D283C412yes—
7C22×C4×D283C2211yescharacteristic
8C2×#17985376C2212yes—
9C2×C4⋊Dic283C2211yescharacteristic
10C2×Dic283⋊C4C412yes—
11C4⋊C4×D283—22no—
12C4⋊C4×D283—22no—
13(C2×D283)⋊C8—22no—
14(C2×D283)⋊C8—22no—
15C2×M16×C283C2212yes—
16C2×C4⋊C4×C283C2211yescharacteristic
17C23×D283C2×C411yescharacteristic
18C22×Dic283C2×C411yescharacteristic
19C22×Dic283C2×C412yes—
20C2×C4×D283—22no—
21C2×C4×D283—22no—
22C2×C4×D283—21no—
23C2×C4×D283—22no—
24C2×C4×D283—21no—
25C2×C4×D283—44no—
26C2×C4×D283D412yes—
27C2×C4×D283D412yes—
28#17985376—22no—
29#17985376—22no—
30C2×C283⋊C8—22no—
31C4⋊Dic283—22no—
32Dic283⋊C4—24no—
33C22×C4×C283C2×C412yes—
34C22×C4×C283C2311yescharacteristic
35M16×C283—22no—
36M16×C283—22no—
37C2×C8×C283—22no—
38C4⋊C4×C283—22no—
39C22×D283—21no—
40C22×D283—21no—
41C22×D283—22no—
42C22×D283—22no—
43C22×D283C22⋊C411yescharacteristic
44C22×D283C22⋊C411yescharacteristic
45C2×Dic283—21no—
46C2×Dic283—21no—
47C2×Dic283—22no—
48C2×Dic283—42no—
49C2×Dic283C22⋊C412yes—
50C4×D283—22no—
51C4×D283—22no—
52C4×D283—22no—
53C4×D283—22no—
54C4×D283—44no—
55C4×D283—44no—
56C283⋊C8—42no—
57C23×C283C22×C411yescharacteristic
58C2×C4×C283—22no—
59C2×C4×C283—42no—
60C2×C4×C283C2×D412yes—
61C2×C4×C283#4111yescharacteristic
62C2×C4×C283#4112yes—
63C2×C4×C283#4111yescharacteristic
64C8×C283—42no—
65C22×C283—21no—
66C22×C283—21no—
67C22×C283C2×C22⋊C411yescharacteristic
68C22×C283#11711yescharacteristic
69C22×C283#11711yescharacteristic
70C2×D283—24no—
71C2×D283—24no—
72C2×D283—21no—
73C2×D283—21no—
74C2×D283—21no—
75C2×D283—21no—
76C2×D283#10012yes—
77C2×D283#10112yes—
78C4×C283—42no—
79C4×C283#12312yes—
80C4×C283#12312yes—
81Dic283—22no—
82Dic283—42no—
83C2×C283—21no—
84C2×C283—21no—
85C2×C283#38111yescharacteristic
86C2×C283C2×#10011yescharacteristic
87C2×C283C2×#10111yescharacteristic
88D283—22no—
89D283—22no—
90C283#182111yescharacteristic, complemented, Sylow
91#1821—2831nomaximal, Sylow
92C22×C4⋊C4—2831no—
93#407—2832no—
94#343—2832no—
95#343—2831no—
96#343D28311yescharacteristic, complemented
97C23×C4—2831no—
98C23×C4—2832no—
99C2×M16—2832no—
100C2×M16C2×D28312yes—
101C2×C4⋊C4—2832no—
102C2×C4⋊C4—2831no—
103C2×C4⋊C4—5662no—
104C2×C4⋊C4—5662no—
105C2×C4⋊C4C2×D28311yescharacteristic
106C22⋊C8—5662no—
107C22⋊C8—5662no—
108C24—2831no—
109C22×C4—2831no—
110C22×C4—2832no—
111C22×C4—2832no—
112C22×C4—2832no—
113C22×C4—5662no—
114C22×C4—5662no—
115C22×C4—5661no—
116C22×C4—5662no—
117C22×C4—5661no—
118C22×C4—11324no—
119C22×C4C4×D28312yes—
120C22×C4C22×D28311yescharacteristic
121M16—22no—
122M16—22no—
123M16—5662no—
124M16—5662no—
125C2×C8—22no—
126C2×C8—5662no—
127C4⋊C4—22no—
128C4⋊C4—5664no—
129C4⋊C4—5662no—
130C23—2831no—
131C23—2831no—
132C23—5662no—
133C23—5662no—
134C23—5661no—
135C23—5661no—
136C23C2×C4×D28311yescharacteristic
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—2832no—
140C2×C4—5661no—
141C2×C4—5661no—
142C2×C4—5662no—
143C2×C4—5662no—
144C2×C4—5662no—
145C2×C4—5662no—
146C2×C4—5662no—
147C2×C4—11324no—
148C2×C4—11324no—
149C2×C4—11322no—
150C2×C4D4×D28312yes—
151C2×C4#1798539111yescharacteristic
152C2×C4#1798539212yes—
153C2×C4#1798539311yescharacteristic
154C8—42no—
155C8—11322no—
156C22—21no—
157C22—21no—
158C22—2832no—
159C22—2832no—
160C22—5664no—
161C22—5664no—
162C22—5661no—
163C22—5661no—
164C22—5661no—
165C22—5661no—
166C22C22⋊C4×D28311yescharacteristic
167C22#2258356711yescharacteristic
168C22#2258356811yescharacteristic
169C4—42no—
170C4—5662no—
171C4—11322no—
172C4#2258359212yes—
173C4#2258359512yes—
174C2—21no—
175C2—21no—
176C2—5662no—
177C2—5662no—
178C2#3182632711yescharacteristic
179C2#100×D28311yescharacteristic
180C2#101×D28311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC23×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#343×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC23×D283C2×C4
cosocleC22×C4×C283C23
hypercenter#343D283
hypocenterC283#1821
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #31826234C2semidirect
4. #31826233C2semidirect
5. #343×C283C2semidirect
90. C283#1821semidirect
96. #343D283semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D2832
#318264282
#318262342
#318262332
#343×C2832
#1821283