Finite Group Databasebeta

← #49120508

Subgroups — #49120508

Order 36224.

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

normal subgroups only

This group has 234 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
2#31826868C211yesmaximal, characteristic, complemented
3#31826742C211yesmaximal, characteristic
4#31826212C211yesmaximal, characteristic, complemented
5Q8⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic
7#462×C283C211yesmaximal, characteristic, complemented
8C2×Q8×D283—21no—
9#22583610—21no—
10#22583610C2211yescharacteristic
11#22583590—22no—
12#22583590—21no—
13C4×D1132—21no—
14C4×D1132C2211yescharacteristic
15#22583543—21no—
16#22583543—22no—
17C4⋊(C283⋊C8)C2211yescharacteristic
18#22583530—21no—
19C4×C283⋊C8C2211yescharacteristic
20C2×Q16×C283—21no—
21C4⋊Q8×C283C2211yescharacteristic
22C4×Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24#103×C283—21no—
25C2×Dic566—22no—
26C2×Dic566—21no—
27Q8×D283—42no—
28Q8×D283—42no—
29C2×D1132D411yescharacteristic
30C2×C4×D283—22no—
31C2×C4×D283—21no—
32C2×C283⋊C8—21no—
33C2×C283⋊C8—21no—
34C4⋊Dic283—22no—
35C4⋊Dic283—21no—
36C4⋊Dic283D411yescharacteristic
37C4⋊Dic283D412yes—
38(C2×D283)⋊C4—22no—
39(C2×D283)⋊C4—21no—
40C2×Q8×C283—21no—
41C2×Q8×C283D411yescharacteristic
42Q16×C283—42no—
43C2×C8×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283—21no—
46C4⋊C4×C283—21no—
47C4⋊C4×C283D411yescharacteristic
48C42×C283—21no—
49C42×C283C2311yescharacteristic
50C22×D283—21no—
51Dic566—44no—
52Dic566—41no—
53Dic566—41no—
54D1132—21no—
55D1132Q1612yescomplemented
56C2×Dic283—22no—
57C2×Dic283—21no—
58C4×D283—44no—
59C4×D283—41no—
60C4×D283—41no—
61C283⋊C8—22no—
62C283⋊C8—41no—
63Q8×C283—21no—
64Q8×C283—41no—
65Q8×C283—41no—
66Q8×C283D812yes—
67C2×C4×C283—21no—
68C2×C4×C283—21no—
69C2×C4×C283—41no—
70C2×C4×C283C2×D411yescharacteristic
71C2×C4×C283C2×D411yescharacteristic
72C2×C4×C283C2×D411yescharacteristic
73C8×C283—41no—
74C22×C283#12011yescharacteristic
75C2×D283—22no—
76C2×D283—41no—
77C2×D283—41no—
78C4×C283—22no—
79C4×C283—21no—
80C4×C283—41no—
81C4×C283—81no—
82C4×C283C2×D811yescharacteristic
83C4×C283C2×Q1611yescharacteristic
84C4×C283AGL(1,ℤ/8)11yescharacteristic
85C4×C283#13711yescharacteristic
86Dic283—42no—
87Dic283—41no—
88C2×C283#44711yescharacteristic
89C2×C283#45111yescharacteristic
90C2×C283#45611yescharacteristic
91D283—42no—
92C283#164911yescharacteristic, complemented, Sylow
93#1649—2831nomaximal, Sylow
94D4×Q8—2831no—
95#500—2831no—
96#474—2831no—
97#462D28311yescharacteristic, complemented
98#332—2831no—
99Q8⋊C8—2831no—
100D4⋊C8—2831no—
101C22×Q8—5661no—
102C2×Q16—21no—
103C4⋊Q8—2831no—
104C4⋊Q8—5661no—
105C4⋊Q8C2×D28311yescharacteristic
106C22⋊Q8—5662no—
107C22⋊Q8—5661no—
108C4×Q8C2×D28311yescharacteristic
109C4×D4—2831no—
110C4×D4—5661no—
111#107—5661no—
112#107—5662no—
113C4⋊C8—2831no—
114C4⋊C8C2×D28311yescharacteristic
115#103—21no—
116#102—5661no—
117C4×C8—2831no—
118C2×Q8—21no—
119C2×Q8—5662no—
120C2×Q8—5661no—
121C2×Q8—11322no—
122C2×Q8—11322no—
123C2×Q8C22⋊D28311yescharacteristic
124C2×D4—2831no—
125C22×C4—5662no—
126C22×C4—5661no—
127Q16—42no—
128C2×C8—21no—
129C2×C8—5661no—
130C2×C8—5661no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—2831no—
135C4⋊C4—2832no—
136C4⋊C4—5662no—
137C4⋊C4—5661no—
138C4⋊C4C22⋊D28311yescharacteristic
139C22⋊C4—5662no—
140C22⋊C4—5661no—
141C42—21no—
142C42C22×D28311yescharacteristic
143C23—5661no—
144Q8—21no—
145Q8—41no—
146Q8—41no—
147Q8—11324no—
148Q8—11321no—
149Q8—11321no—
150Q8#1798537712yes—
151D4—2832no—
152D4—5661no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—5662no—
157C2×C4—5661no—
158C2×C4—11324no—
159C2×C4—11321no—
160C2×C4—11321no—
161C2×C4D4×D28311yescharacteristic
162C2×C4D4×D28311yescharacteristic
163C2×C4C2×C22⋊D28311yescharacteristic
164C8—41no—
165C8—5662no—
166C8—11321no—
167C22—5662no—
168C22—11321no—
169C22—11321no—
170C22#2258357811yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—81no—
175C4—11322no—
176C4—11321no—
177C4C2×#1798537711yescharacteristic
178C4Q16×D28311yescharacteristic
179C4#2258363511yescharacteristic
180C4#2258364211yescharacteristic
181C2—11322no—
182C2#3182659811yescharacteristic
183C2#3182661911yescharacteristic
184C2#3182664611yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#462×C283C2
socleC22×C283#120
prime radicalC2×D1132D4
hypercenter#462D283
hypocenterC283#1649
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #31826868C2semidirect
4. #31826212C2semidirect
5. Q8⋊(C283⋊C8)C2semidirect
7. #462×C283C2semidirect
55. D1132Q16semidirect
92. C283#1649semidirect
97. #462D283semidirect

Maximal subgroups

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

subgroupindex
Q8×D11322
#318268682
#318267422
#318262122
Q8⋊(C283⋊C8)2
#318261922
#462×C2832
#1649283