Finite Group Databasebeta

← #49120362

Subgroups — #49120362

Order 36224.

250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×D1132C211yesmaximal, characteristic, complemented
2#31826811C211yesmaximal, characteristic, complemented
3#31826657C211yesmaximal, characteristic
4#31826212C211yesmaximal, characteristic, complemented
5Q8⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#460×C283C211yesmaximal, characteristic, complemented
8C2×Q8×D283—21no—
9C2×#17985377—21no—
10#22583610—21no—
11#22583610C2211yescharacteristic
12#22583590—22no—
13#22583590—21no—
14C4×D1132—21no—
15C4×D1132C2211yescharacteristic
16C4⋊(C283⋊C8)C2211yescharacteristic
17#22583531—22no—
18#22583531—21no—
19C4×C283⋊C8C2211yescharacteristic
20C2×SD16×C283—21no—
21#127×C283C2211yescharacteristic
22C4×Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24#102×C283—21no—
25C2×Dic566—22no—
26C2×Dic566—21no—
27Q8×D283—42no—
28Q8×D283—42no—
29C2×D1132D411yescharacteristic
30C2×C4×D283—22no—
31C2×C4×D283—21no—
32#17985377—42no—
33C2×C283⋊C8—21no—
34C2×C283⋊C8—21no—
35C4⋊Dic283—22no—
36C4⋊Dic283—21no—
37C4⋊Dic283D411yescharacteristic
38C4⋊Dic283D412yes—
39(C2×D283)⋊C4—22no—
40(C2×D283)⋊C4—21no—
41C2×Q8×C283D411yescharacteristic
42C2×D4×C283—21no—
43C2×D4×C283—21no—
44C2×D4×C283—21no—
45SD16×C283—42no—
46C2×C8×C283—21no—
47C4⋊C4×C283—21no—
48C4⋊C4×C283D411yescharacteristic
49C42×C283—21no—
50C42×C283C2311yescharacteristic
51C22×D283—21no—
52Dic566—44no—
53Dic566—41no—
54Dic566—41no—
55D1132—21no—
56D1132SD1612yescomplemented
57C2×Dic283—22no—
58C2×Dic283—21no—
59C4×D283—44no—
60C4×D283—41no—
61C4×D283—41no—
62C283⋊C8—41no—
63C283⋊C8—41no—
64C23×C283—41no—
65Q8×C283—21no—
66Q8×C283D812yescomplemented
67D4×C283—42no—
68D4×C283—41no—
69D4×C283—41no—
70D4×C283—41no—
71D4×C283—41no—
72C2×C4×C283—21no—
73C2×C4×C283—21no—
74C2×C4×C283C2×D411yescharacteristic
75C2×C4×C283C2×D411yescharacteristic
76C2×C4×C283C2×D411yescharacteristic
77C8×C283—41no—
78C22×C283—81no—
79C22×C283—81no—
80C22×C283—81no—
81C22×C283#12011yescharacteristic
82C2×D283—22no—
83C2×D283—41no—
84C2×D283—41no—
85C4×C283—22no—
86C4×C283—21no—
87C4×C283—41no—
88C4×C283C2×D811yescharacteristic
89C4×C283C2×SD1611yescharacteristic
90C4×C283AGL(1,ℤ/8)11yescharacteristic
91C4×C283#13711yescharacteristic
92Dic283—42no—
93Dic283—41no—
94C2×C283—161no—
95C2×C283#44711yescharacteristic
96C2×C283#44811yescharacteristic
97C2×C283#45411yescharacteristic
98D283—42no—
99C283#162711yescharacteristic, complemented, Sylow
100#1627—2831nomaximal, Sylow
101D4×Q8—2831no—
102#486—2831no—
103#460D28311yescharacteristic, complemented
104#459—2831no—
105#332—2831no—
106Q8⋊C8—2831no—
107D4⋊C8—2831no—
108C22×Q8—5661no—
109C2×SD16—21no—
110C2×D8—5661no—
111C4⋊Q8—2831no—
112C4⋊Q8—5661no—
113#127C2×D28311yescharacteristic
114C22⋊Q8—5662no—
115C22⋊Q8—5661no—
116C4×Q8C2×D28311yescharacteristic
117C4×D4—2831no—
118C4×D4—5661no—
119C4⋊C8—2831no—
120C4⋊C8C2×D28311yescharacteristic
121#102—21no—
122#102—5661no—
123#102—5662no—
124C4×C8—2831no—
125C2×Q8—5662no—
126C2×Q8—5661no—
127C2×Q8—11322no—
128C2×Q8—11322no—
129C2×Q8C22⋊D28311yescharacteristic
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—2831no—
134C22×C4—5662no—
135C22×C4—5661no—
136SD16—42no—
137D8—11322no—
138C2×C8—21no—
139C2×C8—5661no—
140C2×C8—5661no—
141C4⋊C4—21no—
142C4⋊C4—2831no—
143C4⋊C4—2832no—
144C4⋊C4—5662no—
145C4⋊C4—5661no—
146C4⋊C4C22⋊D28311yescharacteristic
147C22⋊C4—5662no—
148C22⋊C4—5661no—
149C42—21no—
150C42C22×D28311yescharacteristic
151C23—41no—
152C23—5661no—
153Q8—21no—
154Q8—11324no—
155Q8—11321no—
156Q8—11321no—
157Q8#1798537712yescomplemented
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—2832no—
164D4—5661no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—5662no—
168C2×C4—5661no—
169C2×C4—11324no—
170C2×C4—11321no—
171C2×C4—11321no—
172C2×C4D4×D28311yescharacteristic
173C2×C4D4×D28311yescharacteristic
174C2×C4C2×C22⋊D28311yescharacteristic
175C8—41no—
176C8—11321no—
177C8—11321no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—5662no—
182C22—11321no—
183C22—11321no—
184C22#2258357811yescharacteristic
185C4—22no—
186C4—21no—
187C4—41no—
188C4—11322no—
189C4—11321no—
190C4C2×#1798537711yescharacteristic
191C4SD16×D28311yescharacteristic
192C4#2258363511yescharacteristic
193C4#2258363911yescharacteristic
194C2—161no—
195C2—11322no—
196C2#3182659811yescharacteristic
197C2#3182660211yescharacteristic
198C2#3182663611yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#460×C283C2
socleC22×C283#120
prime radical#31826657C2
hypercenter#460D283
hypocenterC283#1627
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. Q8×D1132C2semidirect
2. #31826811C2semidirect
4. #31826212C2semidirect
5. Q8⋊(C283⋊C8)C2semidirect
6. #31826192C2semidirect
7. #460×C283C2semidirect
56. D1132SD16semidirect
66. Q8×C283D8semidirect
99. C283#1627semidirect
103. #460D283semidirect
157. Q8#17985377semidirect

Maximal subgroups

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

subgroupindex
Q8×D11322
#318268112
#318266572
#318262122
Q8⋊(C283⋊C8)2
#318261922
#460×C2832
#1627283