Finite Group Databasebeta

← #49120270

Subgroups — #49120270

Order 36224.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#31827094C211yesmaximal, characteristic
2#31826796C211yesmaximal, characteristic
3#31826793C211yesmaximal, characteristic
4#31826397C211yesmaximal, characteristic
5#31826201C211yesmaximal, characteristic
6#31826190C211yesmaximal, characteristic
7#328×C283C211yesmaximal, characteristic
8#22583609—21no—
9#22583608—21no—
10#22583600—21no—
11#22583600—21no—
12#22583589C2211yescharacteristic
13#22583587—21no—
14#22583566—21no—
15C2×C4⋊Dic283—21no—
16C2×C4⋊Dic283C2211yescharacteristic
17C2×Dic283⋊C4C2211yescharacteristic
18#22583542—21no—
19#22583541—21no—
20#22583535—21no—
21#22583534—21no—
22C22⋊(C283⋊C8)C2211yescharacteristic
23C283⋊#95—21no—
24C22⋊Q8×C283C2211yescharacteristic
25C22⋊C8×C283C2211yescharacteristic
26#95×C283C2211yescharacteristic
27C2×Dic566—21no—
28C2×Dic566D411yescharacteristic
29C22×Dic283—21no—
30C22×Dic283D411yescharacteristic
31C22×Dic283D411yescharacteristic
32C2×C283⋊C8—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283—42no—
37C4⋊Dic283D411yescharacteristic
38Dic283⋊C4—21no—
39Dic283⋊C4—21no—
40Dic283⋊C4—21no—
41Dic283⋊C4—21no—
42Dic283⋊C4—21no—
43Dic283⋊C4—21no—
44Dic283⋊C4—21no—
45C22⋊Dic283—21no—
46C4×Dic283—21no—
47C4×Dic283—21no—
48C2×Q8×C283D411yescharacteristic
49C22×C4×C283—21no—
50C22×C4×C283C2311yescharacteristic
51C2×C8×C283—21no—
52C4⋊C4×C283—21no—
53C4⋊C4×C283D411yescharacteristic
54C22⋊C4×C283—21no—
55Dic566—41no—
56Dic566—81no—
57C2×Dic283—21no—
58C2×Dic283—21no—
59C2×Dic283—21no—
60C2×Dic283—21no—
61C2×Dic283—21no—
62C2×Dic283—41no—
63C2×Dic283—41no—
64C2×Dic283—41no—
65C2×Dic283—41no—
66C2×Dic283SD1612yes—
67C283⋊C8—41no—
68C23×C283C2×D411yescharacteristic
69Q8×C283—41no—
70C2×C4×C283—22no—
71C2×C4×C283—21no—
72C2×C4×C283—21no—
73C2×C4×C283—41no—
74C2×C4×C283—41no—
75C2×C4×C283—41no—
76C2×C4×C283C2×D411yescharacteristic
77C2×C4×C283C2×D411yescharacteristic
78C8×C283—41no—
79C22×C283—21no—
80C22×C283—21no—
81C22×C283#12011yescharacteristic
82C22×C283C2×SD1611yescharacteristic
83C22×C283#13711yescharacteristic
84C4×C283—21no—
85C4×C283—21no—
86C4×C283—42no—
87C4×C283—41no—
88C4×C283—41no—
89Dic283—22no—
90Dic283—41no—
91Dic283—41no—
92Dic283—41no—
93Dic283—81no—
94C2×C283—21no—
95C2×C283—21no—
96C2×C283#44811yescharacteristic
97C2×C283#45611yescharacteristic
98C2×C283#45811yescharacteristic
99C283#161111yescharacteristic, complemented, Sylow
100#1611—2831nomaximal, Sylow
101#544—2831no—
102#483—2831no—
103#483—2831no—
104#398—2831no—
105#328—2831no—
106#328D28311yescharacteristic
107#324—2831no—
108C4⋊Q8—5661no—
109C4⋊Q8—5661no—
110#125—5661no—
111#125—5661no—
112C22⋊Q8—2831no—
113C22⋊Q8—5661no—
114C22⋊Q8C2×D28311yescharacteristic
115#117—5661no—
116C2×C4⋊C4—2831no—
117C2×C4⋊C4—2831no—
118C2×C4⋊C4—5661no—
119#106—5661no—
120#106—5661no—
121#103—5661no—
122#103—5661no—
123C22⋊C8—2831no—
124C22⋊C8C2×D28311yescharacteristic
125#95—5661no—
126#95C2×D28311yescharacteristic
127C2×Q8—2831no—
128C2×Q8—5661no—
129C2×Q8D113211yescharacteristic
130C22×C4—21no—
131C22×C4—2831no—
132C22×C4—2831no—
133C22×C4—5661no—
134C22×C4C22×D28311yescharacteristic
135C2×C8—21no—
136C2×C8—5661no—
137C4⋊C4—21no—
138C4⋊C4—2831no—
139C4⋊C4—5661no—
140C4⋊C4—5661no—
141C4⋊C4—5661no—
142C4⋊C4—5661no—
143C4⋊C4—5661no—
144C4⋊C4—5661no—
145C4⋊C4—5661no—
146C4⋊C4—5661no—
147C4⋊C4—5661no—
148C4⋊C4—5661no—
149C4⋊C4—11322no—
150C4⋊C4D113211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5661no—
153C42—5661no—
154C42—5661no—
155C23D4×D28311yescharacteristic
156Q8—41no—
157Q8—11321no—
158Q8—22641no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—2832no—
166C2×C4—5661no—
167C2×C4—5661no—
168C2×C4—5661no—
169C2×C4—5661no—
170C2×C4—5661no—
171C2×C4—11321no—
172C2×C4—11321no—
173C2×C4—11321no—
174C2×C4—11321no—
175C2×C4D4×D28311yescharacteristic
176C2×C4C2×D113211yescharacteristic
177C8—41no—
178C8—11321no—
179C22—21no—
180C22—21no—
181C22#2258358011yescharacteristic
182C22SD16×D28311yescharacteristic
183C22#2258364211yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—5662no—
190C4—11321no—
191C4—11321no—
192C4—11321no—
193C4—22641no—
194C2—21no—
195C2—21no—
196C2#3182660511yescharacteristic
197C2#3182664911yescharacteristic
198C2#3182665611yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#328×C283C2
socleC22×C283#120
prime radicalC23×C283C2×D4
hypercenter#328D283
hypocenterC283#1611
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C283#1611semidirect

Maximal subgroups

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

subgroupindex
#318270942
#318267962
#318267932
#318263972
#318262012
#318261902
#328×C2832
#1611283