Finite Group Databasebeta

← #49120295

Subgroups — #49120295

Order 36224.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#31827064C211yesmaximal, characteristic
2#31826798C211yesmaximal, characteristic, complemented
3#31826784C211yesmaximal, characteristic
4#31826405C211yesmaximal, characteristic, complemented
5#31826198C211yesmaximal, characteristic
6#31826190C211yesmaximal, characteristic, complemented
7#328×C283C211yesmaximal, characteristic, complemented
8#22583605—21no—
9#22583601—21no—
10#22583595—21no—
11#22583594—21no—
12#22583586—21no—
13#22583584C2211yescharacteristic
14(C22⋊D283)⋊C4—21no—
15C2×C4⋊Dic283C2211yescharacteristic
16C2×Dic283⋊C4C2211yescharacteristic
17#22583543—21no—
18#22583542—21no—
19#22583534—21no—
20#22583532—21no—
21C22⋊(C283⋊C8)C2211yescharacteristic
22C283⋊#95—21no—
23C283⋊#95—21no—
24C22⋊Q8×C283C2211yescharacteristic
25C22⋊C8×C283C2211yescharacteristic
26#95×C283C2211yescharacteristic
27C2×D1132D411yescharacteristic
28C2×C22⋊D283—21no—
29C22×Dic283—21no—
30C22×Dic283D411yescharacteristic
31C22×Dic283D411yescharacteristic
32C2×C4×D283—21no—
33C2×C283⋊C8—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283—21no—
37C4⋊Dic283—21no—
38C4⋊Dic283D411yescharacteristic
39Dic283⋊C4—21no—
40Dic283⋊C4—21no—
41Dic283⋊C4—21no—
42(C2×D283)⋊C4—21no—
43(C2×D283)⋊C4—21no—
44(C2×D283)⋊C4—21no—
45(C2×D283)⋊C4—21no—
46C4×Dic283—21no—
47C2×Q8×C283D411yescharacteristic
48C22×C4×C283—21no—
49C22×C4×C283C2311yescharacteristic
50C2×C8×C283—21no—
51C4⋊C4×C283—21no—
52C4⋊C4×C283D411yescharacteristic
53C22⋊C4×C283—21no—
54C22×D283—21no—
55D1132—41no—
56C22⋊D283—41no—
57C22⋊D283—41no—
58C2×Dic283—21no—
59C2×Dic283—21no—
60C2×Dic283—21no—
61C2×Dic283—21no—
62C2×Dic283—21no—
63C2×Dic283—41no—
64C2×Dic283—42no—
65C2×Dic283—41no—
66C4×D283—81no—
67C283⋊C8—41no—
68C23×C283C2×D411yescharacteristic
69Q8×C283—41no—
70C2×C4×C283—21no—
71C2×C4×C283—21no—
72C2×C4×C283—41no—
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×C283#13511yescharacteristic
83C22×C283#13711yescharacteristic
84C2×D283—41no—
85C2×D283—41no—
86C2×D283—41no—
87C4×C283—21no—
88C4×C283—21no—
89C4×C283—41no—
90C4×C283—41no—
91C4×C283—81no—
92Dic283—41no—
93Dic283—41no—
94Dic283—41no—
95Dic283—81no—
96C2×C283—21no—
97C2×C283—21no—
98C2×C283#45211yescharacteristic
99C2×C283#45411yescharacteristic
100C2×C283#45811yescharacteristic
101D283—81no—
102C283#161511yescharacteristic, complemented, Sylow
103#1615—2831nomaximal, Sylow
104#539—2831no—
105#484—2831no—
106#481—2831no—
107#400—2831no—
108#328D28311yescharacteristic, complemented
109#327—2831no—
110#324—2831no—
111#126—5661no—
112#125—5661no—
113#123—5661no—
114#123—5661no—
115C22⋊Q8—5661no—
116C22⋊Q8C2×D28311yescharacteristic
117#121—2831no—
118C4×D4—5661no—
119C2×C4⋊C4—2831no—
120C2×C4⋊C4—2831no—
121#107—5661no—
122#106—5661no—
123#103—5661no—
124#102—5661no—
125C22⋊C8—2831no—
126C22⋊C8C2×D28311yescharacteristic
127#95—5661no—
128#95—5661no—
129#95C2×D28311yescharacteristic
130C2×Q8D113211yescharacteristic
131C2×D4—2831no—
132C2×D4—5661no—
133C22×C4—21no—
134C22×C4—2831no—
135C22×C4—2831no—
136C22×C4—5661no—
137C22×C4—5661no—
138C22×C4C22×D28311yescharacteristic
139C2×C8—21no—
140C2×C8—5661no—
141C4⋊C4—21no—
142C4⋊C4—2831no—
143C4⋊C4—5661no—
144C4⋊C4—5661no—
145C4⋊C4—5661no—
146C4⋊C4—5661no—
147C4⋊C4—5661no—
148C4⋊C4—5661no—
149C4⋊C4—5661no—
150C4⋊C4D113211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5661no—
153C22⋊C4—5661no—
154C22⋊C4—5661no—
155C22⋊C4—5661no—
156C42—5661no—
157C23—5661no—
158C23D4×D28311yescharacteristic
159Q8—41no—
160D4—11321no—
161D4—11321no—
162D4—11321no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—5661no—
170C2×C4—5661no—
171C2×C4—5661no—
172C2×C4—5661no—
173C2×C4—5661no—
174C2×C4—11321no—
175C2×C4—11322no—
176C2×C4—11321no—
177C2×C4—22641no—
178C2×C4D4×D28311yescharacteristic
179C2×C4C2×D113211yescharacteristic
180C8—41no—
181C8—11321no—
182C22—21no—
183C22—21no—
184C22—11321no—
185C22—11321no—
186C22—11321no—
187C22#2258358011yescharacteristic
188C22#2258363111yescharacteristic
189C22#2258364211yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—11321no—
196C4—11321no—
197C4—11321no—
198C4—22641no—
199C2—21no—
200C2—21no—
201C2—22641no—
202C2#3182663011yescharacteristic
203C2#3182663911yescharacteristic
204C2#3182665611yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#328×C283C2
socleC22×C283#120
prime radical#22583584C22
hypercenter#328D283
hypocenterC283#1615
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
2. #31826798C2semidirect
4. #31826405C2semidirect
6. #31826190C2semidirect
7. #328×C283C2semidirect
102. C283#1615semidirect
108. #328D283semidirect

Maximal subgroups

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

subgroupindex
#318270642
#318267982
#318267842
#318264052
#318261982
#318261902
#328×C2832
#1615283