Finite Group Databasebeta

← #49120431

Subgroups — #49120431

Order 36224.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#31827185C211yesmaximal, characteristic
2#31826815C211yesmaximal, characteristic, complemented
3#31826757C211yesmaximal, characteristic, complemented
4#31826212C211yesmaximal, characteristic, complemented
5#31826195C211yesmaximal, characteristic, complemented
6D4⋊(C283⋊C8)C211yesmaximal, characteristic
7#476×C283C211yesmaximal, characteristic
8#22583610C2211yescharacteristic
9#22583603—22no—
10#22583597—21no—
11#22583589—21no—
12C4×Dic566C2211yescharacteristic
13#22583575—21no—
14#22583569—21no—
15#22583543—21no—
16C4⋊(C283⋊C8)C2211yescharacteristic
17#22583534—22no—
18#22583533—21no—
19C4×C283⋊C8C2211yescharacteristic
20C4⋊Q8×C283C2211yescharacteristic
21C4×D4×C283C2211yescharacteristic
22#106×C283—21no—
23C4⋊C8×C283C2211yescharacteristic
24#102×C283—21no—
25C2×Dic566—21no—
26C2×Dic566D411yescharacteristic
27C2×C283⋊C8—21no—
28C2×C283⋊C8—21no—
29C4⋊Dic283—21no—
30C4⋊Dic283D411yescharacteristic
31C4⋊Dic283D412yes—
32Dic283⋊C4—22no—
33Dic283⋊C4—21no—
34C22⋊Dic283—22no—
35C22⋊Dic283—22no—
36C4×Dic283—22no—
37C4×Dic283—21no—
38C2×Q8×C283—21no—
39C2×D4×C283D411yescharacteristic
40C22×C4×C283—21no—
41C2×C8×C283—21no—
42C4⋊C4×C283—21no—
43C4⋊C4×C283—21no—
44C4⋊C4×C283D411yescharacteristic
45C22⋊C4×C283—21no—
46C42×C283C2311yescharacteristic
47Dic566—21no—
48Dic566—21no—
49Dic566—41no—
50Dic566—41no—
51C2×Dic283—21no—
52C2×Dic283—21no—
53C2×Dic283—22no—
54C283⋊C8—41no—
55C283⋊C8—41no—
56C23×C283—21no—
57Q8×C283—42no—
58D4×C283—21no—
59D4×C283—21no—
60C2×C4×C283—21no—
61C2×C4×C283—41no—
62C2×C4×C283—41no—
63C2×C4×C283—41no—
64C2×C4×C283C2×D411yescharacteristic
65C2×C4×C283C2×D411yescharacteristic
66C2×C4×C283C2×D411yescharacteristic
67C8×C283—41no—
68C22×C283—41no—
69C22×C283—41no—
70C22×C283—41no—
71C22×C283#12011yescharacteristic
72C4×C283—21no—
73C4×C283—41no—
74C4×C283—81no—
75C4×C283#13511yescharacteristic
76C4×C283#13511yescharacteristic
77C4×C283#13711yescharacteristic
78C4×C283#13711yescharacteristic
79Dic283—41no—
80Dic283—42no—
81Dic283—41no—
82C2×C283—81no—
83C2×C283#45211yescharacteristic
84C2×C283#45211yescharacteristic
85C2×C283#45411yescharacteristic
86C283#163811yescharacteristic, complemented, Sylow
87#1638—2831nomaximal, Sylow
88#556—2831no—
89#487—2831no—
90#477—2831no—
91#476D28311yescharacteristic
92#332—2831no—
93Q8⋊C8—2831no—
94D4⋊C8—2831no—
95C4⋊Q8—2831no—
96C4⋊Q8C2×D28311yescharacteristic
97#126—5662no—
98#124—5661no—
99C22⋊Q8—5661no—
100C4×Q8—2831no—
101C4×Q8—5661no—
102C4×D4C2×D28311yescharacteristic
103#117—5661no—
104#107—5661no—
105#106—21no—
106C4⋊C8—2831no—
107C4⋊C8C2×D28311yescharacteristic
108#103—5661no—
109#103—5662no—
110#102—21no—
111C4×C8—2831no—
112C2×Q8—21no—
113C2×Q8—2831no—
114C2×Q8—5661no—
115C2×D4C22⋊D28311yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—5661no—
119C2×C8—5661no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—2832no—
123C4⋊C4—2831no—
124C4⋊C4—5662no—
125C4⋊C4—5661no—
126C4⋊C4—5661no—
127C4⋊C4C22⋊D28311yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—5662no—
130C22⋊C4—5662no—
131C42—5662no—
132C42—5661no—
133C42C22×D28311yescharacteristic
134C23—21no—
135Q8—42no—
136Q8—5661no—
137Q8—5661no—
138Q8—11321no—
139Q8—11321no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—5661no—
147C2×C4—5662no—
148C2×C4—5661no—
149C2×C4D4×D28311yescharacteristic
150C2×C4D4×D28311yescharacteristic
151C2×C4C2×C22⋊D28311yescharacteristic
152C8—41no—
153C8—11321no—
154C8—11321no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#2258357811yescharacteristic
159C4—21no—
160C4—41no—
161C4—81no—
162C4—11321no—
163C4—11322no—
164C4—11321no—
165C4#2258363011yescharacteristic
166C4#2258363111yescharacteristic
167C4#2258363911yescharacteristic
168C4#2258364111yescharacteristic
169C2—81no—
170C2#3182662411yescharacteristic
171C2#3182662511yescharacteristic
172C2#3182663611yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#476×C283C2
socleC22×C283#120
prime radicalC2×D4×C283D4
hypercenter#476D283
hypocenterC283#1638
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #31826815C2semidirect
3. #31826757C2semidirect
4. #31826212C2semidirect
5. #31826195C2semidirect
86. C283#1638semidirect

Maximal subgroups

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

subgroupindex
#318271852
#318268152
#318267572
#318262122
#318261952
D4⋊(C283⋊C8)2
#476×C2832
#1638283