Finite Group Databasebeta

← #49122421

Subgroups — #49122421

Order 36224.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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#31827093C211yesmaximal, characteristic
2#31826475C211yesmaximal, characteristic
3#31826473C211yesmaximal, characteristic
4#31826371C211yesmaximal, characteristic
5#31826233C211yesmaximal, characteristic
6#31826225C211yesmaximal, characteristic
7#339×C283C211yesmaximal, characteristic
8C22×Dic566C2211yescharacteristic
9C2×#17985376C2211yescharacteristic
10#22583610—21no—
11#22583609—21no—
12#22583602—21no—
13#22583601—21no—
14#22583587—22no—
15#22583569C2211yescharacteristic
16C2×C4⋊Dic283C2211yescharacteristic
17#22583535—21no—
18#22583535—21no—
19#22583533—21no—
20#22583533—21no—
21C283⋊#95—22no—
22C2×M16×C283C2211yescharacteristic
23#117×C283C2211yescharacteristic
24C2×C42×C283C2211yescharacteristic
25C2×Dic566—22no—
26C2×Dic566—21no—
27C2×Dic566—21no—
28C2×Dic566—21no—
29C2×Dic566—21no—
30C2×Dic566—21no—
31C2×Dic566Q812yescomplemented
32C22×Dic283—21no—
33C22×Dic283D412yes—
34#17985376—21no—
35#17985376—21no—
36C2×C283⋊C8—21no—
37C4⋊Dic283—22no—
38C4⋊Dic283—21no—
39C4⋊Dic283—21no—
40C4⋊Dic283D411yescharacteristic
41C4⋊Dic283D411yescharacteristic
42Dic283⋊C4—22no—
43Dic283⋊C4—22no—
44C22⋊Dic283—21no—
45C4×Dic283—21no—
46C22×C4×C283—21no—
47C22×C4×C283C2311yescharacteristic
48M16×C283—21no—
49M16×C283—21no—
50C2×C8×C283—21no—
51C4⋊C4×C283D411yescharacteristic
52C4⋊C4×C283D411yescharacteristic
53C22⋊C4×C283—21no—
54C42×C283—21no—
55C42×C283—21no—
56C42×C283—21no—
57Dic566—22no—
58Dic566—22no—
59Dic566—41no—
60Dic566—41no—
61Dic566—82no—
62C2×Dic283—21no—
63C2×Dic283—21no—
64C2×Dic283—22no—
65C2×Dic283—22no—
66C2×Dic283—41no—
67C2×Dic283—41no—
68C2×Dic283—42no—
69C283⋊C8—41no—
70C23×C283C2×D411yescharacteristic
71C2×C4×C283—22no—
72C2×C4×C283—21no—
73C2×C4×C283—21no—
74C2×C4×C283—41no—
75C2×C4×C283—41no—
76C2×C4×C283C2×D411yescharacteristic
77C2×C4×C283C2×D411yescharacteristic
78C2×C4×C283C2×Q811yescharacteristic
79C2×C4×C283#4111yescharacteristic
80C2×C4×C283#4111yescharacteristic
81C2×C4×C283#4111yescharacteristic
82C8×C283—41no—
83C22×C283—21no—
84C22×C283—21no—
85C22×C283#12011yescharacteristic
86C22×C283C22⋊Q811yescharacteristic
87C22×C283#12411yescharacteristic
88C4×C283—42no—
89C4×C283—41no—
90C4×C283—41no—
91C4×C283C22⋊Q811yescharacteristic
92C4×C283C22⋊Q811yescharacteristic
93C4×C283#12411yescharacteristic
94C4×C283#12411yescharacteristic
95Dic283—42no—
96Dic283—42no—
97Dic283—41no—
98Dic283—41no—
99C2×C283—21no—
100C2×C283—21no—
101C2×C283#39311yescharacteristic
102C2×C283#45511yescharacteristic
103C2×C283#45611yescharacteristic
104C283#202811yescharacteristic, complemented, Sylow
105#2028—2831nomaximal, Sylow
106#544—2831no—
107#419—2831no—
108#419—2831no—
109#391—2831no—
110#343—2831no—
111#339—2831no—
112#339D28311yescharacteristic
113C22×Q8—2831no—
114C2×M16—2831no—
115C2×M16C2×D28311yescharacteristic
116C4⋊Q8—5661no—
117C4⋊Q8—5661no—
118#125—5661no—
119#125—5661no—
120C22⋊Q8—5662no—
121#117—2831no—
122#117C2×D28311yescharacteristic
123C2×C4⋊C4—2831no—
124C2×C42C2×D28311yescharacteristic
125#103—5661no—
126#103—5661no—
127#103—5661no—
128#103—5661no—
129#95—5662no—
130C2×Q8—2832no—
131C2×Q8—5662no—
132C2×Q8—5661no—
133C2×Q8—5661no—
134C2×Q8—5661no—
135C2×Q8—5661no—
136C2×Q8—5661no—
137C22×C4—21no—
138C22×C4—2832no—
139C22×C4—5661no—
140C22×C4C22×D28311yescharacteristic
141M16—21no—
142M16—21no—
143M16—5661no—
144M16—5661no—
145C2×C8—21no—
146C2×C8—5661no—
147C4⋊C4—2831no—
148C4⋊C4—2831no—
149C4⋊C4—5662no—
150C4⋊C4—5662no—
151C4⋊C4—5662no—
152C4⋊C4—5661no—
153C4⋊C4—5661no—
154C4⋊C4D113211yescharacteristic
155C4⋊C4D113211yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—5661no—
158C42—21no—
159C42—21no—
160C42—21no—
161C42—5661no—
162C23D4×D28311yescharacteristic
163Q8—5662no—
164Q8—5662no—
165Q8—11321no—
166Q8—11321no—
167Q8—22642no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—5661no—
174C2×C4—5661no—
175C2×C4—5662no—
176C2×C4—5662no—
177C2×C4—11321no—
178C2×C4—11321no—
179C2×C4—11322no—
180C2×C4D4×D28311yescharacteristic
181C2×C4C2×D113211yescharacteristic
182C2×C4Q8×D28311yescharacteristic
183C2×C4#1798539111yescharacteristic
184C2×C4#1798539211yescharacteristic
185C2×C4#1798539211yescharacteristic
186C8—41no—
187C8—11321no—
188C22—21no—
189C22—21no—
190C22#2258358011yescharacteristic
191C22#2258358811yescharacteristic
192C22#2258359611yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—11322no—
197C4—11322no—
198C4—11321no—
199C4—11321no—
200C4#2258358811yescharacteristic
201C4#2258359011yescharacteristic
202C4#2258359611yescharacteristic
203C4#2258359811yescharacteristic
204C2—21no—
205C2—21no—
206C2#3182637811yescharacteristic
207C2#3182664411yescharacteristic
208C2#3182664911yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#339×C283C2
socleC22×C283#120
prime radicalC23×C283C2×D4
hypercenter#339D283
hypocenterC283#2028
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
31. C2×Dic566Q8semidirect
104. C283#2028semidirect

Maximal subgroups

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

subgroupindex
#318270932
#318264752
#318264732
#318263712
#318262332
#318262252
#339×C2832
#2028283