Finite Group Databasebeta

← #49120365

Subgroups — #49120365

Order 36224.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#31827130C211yesmaximal, characteristic, complemented
2#31826813C211yesmaximal, characteristic, complemented
3#31826666C211yesmaximal, characteristic, complemented
4#31826661C211yesmaximal, characteristic
5#31826195C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#332×C283C211yesmaximal, characteristic, complemented
8C2×Q8×D283—21no—
9C2×#17985381—21no—
10C2×D2264—21no—
11#22583609—21no—
12#22583607C2211yescharacteristic
13#22583588—22no—
14#22583586—21no—
15C4×Dic566C2211yescharacteristic
16C4×D1132C2211yescharacteristic
17#22583572—21no—
18#22583532—21no—
19#22583532—21no—
20#22583530—22no—
21C4×C283⋊C8C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25C2×Dic566—22no—
26C2×Dic566D411yescharacteristic
27Q8×D283—42no—
28Q8×D283—42no—
29C2×D1132—21no—
30C2×D1132—21no—
31C2×D1132—21no—
32C2×D1132D411yescharacteristic
33C2×C4×D283—22no—
34C2×C4×D283—21no—
35#17985381—42no—
36D2264—42no—
37C2×C283⋊C8—21no—
38C4⋊Dic283D411yescharacteristic
39C4⋊Dic283D411yescharacteristic
40Dic283⋊C4—22no—
41Dic283⋊C4—21no—
42(C2×D283)⋊C4—22no—
43(C2×D283)⋊C4—21no—
44C4×Dic283—21no—
45C2×Q8×C283—21no—
46C2×C8×C283—21no—
47C2×C8×C283—21no—
48C4⋊C4×C283—21no—
49C4⋊C4×C283D412yes—
50C42×C283C2311yescharacteristic
51C22×D283—21no—
52C22×D283—41no—
53Dic566—21no—
54Dic566—44no—
55Dic566D812yescomplemented
56D1132—21no—
57D1132—42no—
58D1132—41no—
59D1132—41no—
60D1132—41no—
61D1132—41no—
62D1132SD1612yescomplemented
63C2×Dic283—21no—
64C2×Dic283—21no—
65C2×Dic283—21no—
66C4×D283—44no—
67C4×D283—41no—
68C4×D283—41no—
69C283⋊C8—41no—
70Q8×C283—41no—
71Q8×C283—41no—
72C2×C4×C283—22no—
73C2×C4×C283C2×D411yescharacteristic
74C2×C4×C283C2×D411yescharacteristic
75C2×C4×C283C2×D411yescharacteristic
76C8×C283—41no—
77C8×C283—41no—
78C22×C283#12011yescharacteristic
79C2×D283—22no—
80C2×D283—41no—
81C2×D283—41no—
82C2×D283—81no—
83C2×D283—81no—
84C2×D283—81no—
85C4×C283—21no—
86C4×C283—42no—
87C4×C283C2×D811yescharacteristic
88C4×C283C2×SD1611yescharacteristic
89C4×C283AGL(1,ℤ/8)11yescharacteristic
90C4×C283#13711yescharacteristic
91Dic283—22no—
92Dic283—41no—
93Dic283—41no—
94C2×C283#44711yescharacteristic
95C2×C283#44811yescharacteristic
96C2×C283#45411yescharacteristic
97D283—42no—
98D283—161no—
99C283#162711yescharacteristic, complemented, Sylow
100#1627—2831nomaximal, Sylow
101D4×Q8—2831no—
102#486—2831no—
103#460—2831no—
104#459—2831no—
105#332D28311yescharacteristic, complemented
106Q8⋊C8—2831no—
107D4⋊C8—2831no—
108C22×Q8—5661no—
109C2×SD16—5661no—
110C2×D8—5661no—
111C4⋊Q8—5661no—
112C4⋊Q8C2×D28311yescharacteristic
113#127—2831no—
114C22⋊Q8—5661no—
115C22⋊Q8—5662no—
116C4×Q8—2831no—
117C4×D4—2831no—
118C4×D4—5661no—
119C4⋊C8C2×D28311yescharacteristic
120C4⋊C8C2×D28311yescharacteristic
121#102—5661no—
122#102—5661no—
123#102—5662no—
124C4×C8—2831no—
125C2×Q8—21no—
126C2×Q8—2831no—
127C2×Q8—5662no—
128C2×Q8—11322no—
129C2×Q8—11322no—
130C2×D4—2831no—
131C2×D4—5661no—
132C2×D4—5661no—
133C2×D4—5661no—
134C22×C4—5662no—
135C22×C4—5661no—
136SD16—11322no—
137D8—11322no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—5661no—
141C4⋊C4—21no—
142C4⋊C4—2831no—
143C4⋊C4—2831no—
144C4⋊C4—5662no—
145C4⋊C4—5661no—
146C4⋊C4D113212yes—
147C22⋊C4—5662no—
148C22⋊C4—5661no—
149C42—5661no—
150C42C22×D28311yescharacteristic
151C23—5661no—
152C23—11321no—
153Q8—41no—
154Q8—41no—
155Q8—2832no—
156Q8—5661no—
157Q8—11324no—
158D4—2832no—
159D4—5661no—
160D4—11322no—
161D4—11321no—
162D4—11321no—
163D4—11321no—
164D4—11321no—
165C2×C4—22no—
166C2×C4—5661no—
167C2×C4—5661no—
168C2×C4—5661no—
169C2×C4—11324no—
170C2×C4—11321no—
171C2×C4—11321no—
172C2×C4D4×D28311yescharacteristic
173C2×C4D4×D28311yescharacteristic
174C2×C4C2×D113211yescharacteristic
175C8—41no—
176C8—41no—
177C8—11321no—
178C22—5662no—
179C22—11321no—
180C22—11321no—
181C22—22641no—
182C22—22641no—
183C22—22641no—
184C22#2258358011yescharacteristic
185C4—21no—
186C4—42no—
187C4—5662no—
188C4—11321no—
189C4—11321no—
190C4D8×D28311yescharacteristic
191C4SD16×D28311yescharacteristic
192C4#2258363711yescharacteristic
193C4#2258364211yescharacteristic
194C2—11322no—
195C2—45281no—
196C2#3182660011yescharacteristic
197C2#3182660511yescharacteristic
198C2#3182664011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#332×C283C2
socleC22×C283#120
prime radical#31826661C2
hypercenter#332D283
hypocenterC283#1627
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #31827130C2semidirect
2. #31826813C2semidirect
3. #31826666C2semidirect
5. #31826195C2semidirect
6. #31826192C2semidirect
7. #332×C283C2semidirect
55. Dic566D8semidirect
62. D1132SD16semidirect
99. C283#1627semidirect
105. #332D283semidirect

Maximal subgroups

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

subgroupindex
#318271302
#318268132
#318266662
#318266612
#318261952
#318261922
#332×C2832
#1627283