Finite Group Databasebeta

← #49122914

Subgroups — #49122914

Order 36224.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#31827036C211yesmaximal, characteristic
2#31826449C211yesmaximal, characteristic
3#31826254C214yesmaximal, complemented
4#410×C283C211yesmaximal, characteristic
5C22×Dic566C411yescharacteristic, complemented
6C2×#17985376—21no—
7#22583608—21no—
8#22583597—21no—
9#22583591C412yescomplemented
10#22583591C2212yes—
11#22583589—21no—
12#22583589—21no—
13#22583569C411yescharacteristic, complemented
14#22583529—21no—
15#22583527C2212yes—
16C2×#41×C283C2211yescharacteristic
17#117×C283—21no—
18#99×C283—21no—
19#99×C283C2212yes—
20C2×Dic566—21no—
21C2×Dic566—21no—
22C2×Dic566—41no—
23C2×Dic566—41no—
24C22×Dic283C2×C412yes—
25#17985376—22no—
26#17985376—41no—
27C2×C283⋊C8—41no—
28C4⋊Dic283—21no—
29Dic283⋊C4—22no—
30Dic283⋊C4—22no—
31C22⋊Dic283—22no—
32C22⋊Dic283—22no—
33C22⋊Dic283C2×C412yes—
34C4×Dic283—21no—
35#41×C283—41no—
36#41×C283—41no—
37C2×Q8×C283D411yescharacteristic
38C2×D4×C283C2×C411yescharacteristic
39C2×D4×C283D411yescharacteristic
40C2×D4×C283C2311yescharacteristic
41C22×C4×C283C2×C411yescharacteristic
42C22×C4×C283D411yescharacteristic
43C22×C4×C283D411yescharacteristic
44C4⋊C4×C283—41no—
45C22⋊C4×C283—22no—
46C42×C283—41no—
47Dic566—42no—
48Dic566—41no—
49Dic566—41no—
50C2×Dic283—22no—
51C2×Dic283—22no—
52C2×Dic283—42no—
53C283⋊C8—42no—
54C23×C283C22⋊C411yescharacteristic
55C23×C283C22×C411yescharacteristic
56C23×C283C2×D411yescharacteristic
57Q8×C283—41no—
58D4×C283—41no—
59D4×C283—41no—
60D4×C283—41no—
61C2×C4×C283—21no—
62C2×C4×C283—21no—
63C2×C4×C283—21no—
64C2×C4×C283—21no—
65C2×C4×C283—21no—
66C2×C4×C283—21no—
67C2×C4×C283—42no—
68C2×C4×C283C22⋊C411yescharacteristic
69C2×C4×C283C22⋊C411yescharacteristic
70C2×C4×C283C22⋊C411yescharacteristic
71C2×C4×C283C2×D411yescharacteristic
72C22×C283—21no—
73C22×C283—21no—
74C22×C283—21no—
75C22×C283—41no—
76C22×C283—41no—
77C22×C283—41no—
78C22×C283C2×C22⋊C411yescharacteristic
79C4×C283—21no—
80C4×C283—21no—
81C4×C283—21no—
82C4×C283—82no—
83C4×C283#9911yescharacteristic
84C4×C283#9911yescharacteristic
85Dic283—42no—
86Dic283—42no—
87C2×C283—21no—
88C2×C283—41no—
89C2×C283—41no—
90C2×C283—41no—
91C2×C283C2×#9911yescharacteristic
92C283#212311yescharacteristic, complemented, Sylow
93#2123—2831nomaximal, Sylow
94#536—2831no—
95#413—2831no—
96#410D28311yescharacteristic
97#352—2834no—
98C2×#41C2×D28311yescharacteristic
99C22×Q8—2831no—
100C2×M16—5661no—
101C4⋊Q8—5661no—
102#124—5661no—
103#123—2832no—
104#123—2832no—
105C22⋊Q8—5661no—
106C22⋊Q8—5661no—
107#117—21no—
108#117—2831no—
109#101—5661no—
110#100—2832no—
111#99—21no—
112#99C2×D28312yes—
113#41—41no—
114#41—41no—
115C2×Q8—5661no—
116C2×Q8—5661no—
117C2×Q8—11321no—
118C2×Q8—11321no—
119C2×Q8D113211yescharacteristic
120C2×D4C4×D28311yescharacteristic
121C2×D4C22⋊D28311yescharacteristic
122C2×D4C22×D28311yescharacteristic
123C22×C4—2832no—
124C22×C4C4×D28311yescharacteristic
125C22×C4C22⋊D28311yescharacteristic
126C22×C4D113211yescharacteristic
127M16—5662no—
128M16—11321no—
129C2×C8—11321no—
130C4⋊C4—41no—
131C4⋊C4—5662no—
132C4⋊C4—5661no—
133C4⋊C4—5662no—
134C22⋊C4—22no—
135C22⋊C4—2832no—
136C22⋊C4—5662no—
137C22⋊C4—5662no—
138C42—41no—
139C42—5661no—
140C23(C2×D283)⋊C411yescharacteristic
141C23C2×C4×D28311yescharacteristic
142C23C2×C22⋊D28311yescharacteristic
143Q8—41no—
144Q8—11322no—
145Q8—11321no—
146Q8—11321no—
147D4—41no—
148D4—41no—
149D4—41no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—42no—
157C2×C4—5662no—
158C2×C4—5662no—
159C2×C4—11322no—
160C2×C4(C2×D283)⋊C411yescharacteristic
161C2×C4(C2×D283)⋊C411yescharacteristic
162C2×C4(C2×D283)⋊C411yescharacteristic
163C2×C4C2×D113211yescharacteristic
164C8—11322no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×(C2×D283)⋊C411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—82no—
176C4—11322no—
177C4—11322no—
178C4#2258352411yescharacteristic
179C4#2258352411yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#2258352411yescharacteristic
subgroupG/H
centerC2C2×#22583524
commutatorC23×C283C22×C4
FrattiniC2×D4C22×D283
Fitting#410×C283C2
socleC2×C283C2×#99
prime radicalC2×#41×C283C22
cosocleC2×D4×C283C23
hypercenter#410D283
hypocenterC283#2123
LCSG ▷ C23×C283 ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #31826254C2semidirect
5. C22×Dic566C4semidirect
9. #22583591C4semidirect
13. #22583569C4semidirect
92. C283#2123semidirect

Maximal subgroups

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

subgroupindex
#318270362
#318264492
#318262542
#410×C2832
#2123283