Finite Group Databasebeta

← #49123231

Subgroups — #49123231

Order 36224.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#31827266C211yesmaximal, characteristic
2#31826906C211yesmaximal, characteristic, complemented
3#31826737C211yesmaximal, characteristic, complemented
4#31826278C211yesmaximal, characteristic, complemented
5#31826273C211yesmaximal, characteristic, complemented
6#31826248C211yesmaximal, characteristic, complemented
7C2×SD32×C283C211yesmaximal, characteristic, complemented
8#22583655—21no—
9#22583641—21no—
10#22583636—21no—
11#22583634—22no—
12#22583632C2211yescharacteristic
13#22583629—21no—
14D8×D283—21no—
15#22583616C2211yescharacteristic
16#22583556—21no—
17#22583553—21no—
18#22583550C2211yescharacteristic, complemented
19#22583546C2211yescharacteristic, complemented
20#22583529—21no—
21C2×Q16×C283C2211yescharacteristic, complemented
22C2×D8×C283C2211yescharacteristic
23SD32×C283—22no—
24C2×C16×C283C2211yescharacteristic, complemented
25#17985392—21no—
26#17985392D411yescharacteristic
27#17985391—22no—
28#17985391—41no—
29C2×C22⋊D283—42no—
30D4×D283—22no—
31D4×D283—41no—
32Dic1132D411yescharacteristic
33#17985382—41no—
34#17985381—21no—
35#17985380—22no—
36#17985379—41no—
37D2264D411yescharacteristic
38#17985377—22no—
39#17985376—21no—
40#17985376D411yescharacteristic
41#17985375—21no—
42C8×D283—21no—
43C283⋊C16—21no—
44C2×Q8×C283—21no—
45C2×D4×C283—21no—
46Q16×C283—21no—
47Q16×C283—21no—
48D8×C283—21no—
49D8×C283D412yes—
50C2×C8×C283C2311yescharacteristic
51C16×C283—21no—
52C22×D283—42no—
53Dic566—21no—
54Dic566D811yescharacteristic
55D1132—21no—
56D1132D811yescharacteristic
57C22⋊D283—21no—
58C22⋊D283—42no—
59C22⋊D283—42no—
60C22⋊D283—41no—
61C2×Dic283—42no—
62C4×D283—21no—
63C4×D283—41no—
64C283⋊C8—21no—
65C283⋊C8—41no—
66C23×C283—41no—
67Q8×C283—41no—
68Q8×C283—41no—
69D4×C283—22no—
70D4×C283—41no—
71C2×C4×C283—41no—
72C2×C4×C283C2×D411yescharacteristic
73C8×C283C2×D411yescharacteristic
74C8×C283C2×D411yescharacteristic
75C22×C283—42no—
76C22×C283—161no—
77C22×C283AGL(1,ℤ/8)11yescharacteristic
78C2×D283—21no—
79C2×D283—41no—
80C2×D283—162no—
81C4×C283—81no—
82C4×C283#12011yescharacteristic
83C4×C283C2×D811yescharacteristic
84Dic283—21no—
85Dic283—41no—
86C2×C283—21no—
87C2×C283—82no—
88C2×C283#44711yescharacteristic
89D283—41no—
90D283—81no—
91C283#219411yescharacteristic, complemented, Sylow
92#2194—2831nomaximal, Sylow
93#576—2831no—
94#510—2831no—
95C2×SD32D28311yescharacteristic, complemented
96#473—2831no—
97#361—2831no—
98#359—2831no—
99#350—2831no—
100H(5,𝔽2)—5661no—
101#137—5661no—
102AGL(1,ℤ/8)—5661no—
103AGL(1,ℤ/8)—5662no—
104#135—2831no—
105#135—5661no—
106C2×Q16C2×D28311yescharacteristic, complemented
107C2×D8—5661no—
108C2×D8C2×D28311yescharacteristic
109#131—2831no—
110Q32—5661no—
111SD32—22no—
112SD32—5661no—
113M32—2831no—
114C2×C16C2×D28311yescharacteristic, complemented
115#108—2831no—
116#101—5661no—
117#41—2831no—
118#41—5662no—
119#41—5661no—
120#41—11321no—
121C2×Q8—21no—
122C2×D4—21no—
123C2×D4—5662no—
124C2×D4—11321no—
125C2×D4—11322no—
126Q16—21no—
127Q16—21no—
128Q16—2831no—
129Q16—11321no—
130SD16—5662no—
131SD16—5661no—
132SD16—11321no—
133D8—21no—
134D8—2831no—
135D8—5662no—
136D8C22⋊D28312yes—
137M16—2831no—
138M16—5661no—
139M16—5661no—
140C2×C8—5661no—
141C2×C8C22×D28311yescharacteristic
142C16—21no—
143C16—5661no—
144C23—41no—
145C23—11322no—
146Q8—41no—
147Q8—41no—
148Q8—2831no—
149Q8—5661no—
150D4—22no—
151D4—41no—
152D4—2831no—
153D4—5661no—
154D4—5661no—
155D4—11322no—
156D4—11322no—
157D4—11321no—
158C2×C4—41no—
159C2×C4—5661no—
160C2×C4—11322no—
161C2×C4—11321no—
162C2×C4D4×D28311yescharacteristic
163C8—5661no—
164C8—11321no—
165C8D4×D28311yescharacteristic
166C8C2×C22⋊D28311yescharacteristic
167C22—42no—
168C22—161no—
169C22—5661no—
170C22—11321no—
171C22—45282no—
172C22#2258363411yescharacteristic
173C4—81no—
174C4—5661no—
175C4—11321no—
176C4#2258357811yescharacteristic
177C4D8×D28311yescharacteristic
178C2—21no—
179C2—82no—
180C2—11321no—
181C2—22641no—
182C2#3182659711yescharacteristic
subgroupG/H
centerC2#31826597
commutator, cosocleC2×C8×C283C23
FrattiniC2×C8C22×D283
FittingC2×SD32×C283C2
socleC2×C283#447
prime radical#31827266C2
hypercenterC2×SD32D283
hypocenterC283#2194
LCSG ▷ C2×C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. #31826906C2semidirect
3. #31826737C2semidirect
4. #31826278C2semidirect
5. #31826273C2semidirect
6. #31826248C2semidirect
7. C2×SD32×C283C2semidirect
18. #22583550C22semidirect
19. #22583546C22semidirect
21. C2×Q16×C283C22semidirect
24. C2×C16×C283C22semidirect
91. C283#2194semidirect
95. C2×SD32D283semidirect
106. C2×Q16C2×D283semidirect
114. C2×C16C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272662
#318269062
#318267372
#318262782
#318262732
#318262482
C2×SD32×C2832
#2194283