Finite Group Databasebeta

← #49120304

Subgroups — #49120304

Order 36224.

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

normal subgroups only

This group has 202 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#31826801C211yesmaximal, characteristic
3#31826798C211yesmaximal, characteristic
4#31826405C211yesmaximal, 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⋊Dic283C2211yescharacteristic
16C2×Dic283⋊C4C2211yescharacteristic
17#22583544—21no—
18#22583543—21no—
19#22583535—21no—
20#22583534—21no—
21C22⋊(C283⋊C8)C2211yescharacteristic
22C283⋊#95—21no—
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⋊Dic283D411yescharacteristic
37Dic283⋊C4—21no—
38Dic283⋊C4—21no—
39Dic283⋊C4—21no—
40Dic283⋊C4—21no—
41Dic283⋊C4—21no—
42Dic283⋊C4—21no—
43Dic283⋊C4—21no—
44C22⋊Dic283—21no—
45C4×Dic283—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—
54Dic566—41no—
55Dic566—81no—
56C2×Dic283—21no—
57C2×Dic283—21no—
58C2×Dic283—21no—
59C2×Dic283—21no—
60C2×Dic283—21no—
61C2×Dic283—41no—
62C2×Dic283—42no—
63C2×Dic283—41no—
64C2×Dic283Q1612yes—
65C283⋊C8—41no—
66C23×C283C2×D411yescharacteristic
67Q8×C283—41no—
68C2×C4×C283—21no—
69C2×C4×C283—21no—
70C2×C4×C283—41no—
71C2×C4×C283—41no—
72C2×C4×C283—41no—
73C2×C4×C283—41no—
74C2×C4×C283C2×D411yescharacteristic
75C2×C4×C283C2×D411yescharacteristic
76C8×C283—41no—
77C22×C283—21no—
78C22×C283—21no—
79C22×C283#12011yescharacteristic
80C22×C283C2×Q1611yescharacteristic
81C22×C283#13711yescharacteristic
82C4×C283—21no—
83C4×C283—21no—
84C4×C283—41no—
85C4×C283—41no—
86C4×C283—81no—
87Dic283—22no—
88Dic283—41no—
89Dic283—41no—
90Dic283—41no—
91Dic283—81no—
92C2×C283—21no—
93C2×C283—21no—
94C2×C283#45111yescharacteristic
95C2×C283#45411yescharacteristic
96C2×C283#45811yescharacteristic
97C283#161711yescharacteristic, complemented, Sylow
98#1617—2831nomaximal, Sylow
99#544—2831no—
100#484—2831no—
101#484—2831no—
102#400—2831no—
103#328—2831no—
104#328D28311yescharacteristic
105#324—2831no—
106C4⋊Q8—5661no—
107C4⋊Q8—5661no—
108#125—5661no—
109#125—5661no—
110C22⋊Q8—2831no—
111C22⋊Q8—5661no—
112C22⋊Q8C2×D28311yescharacteristic
113#117—5661no—
114C2×C4⋊C4—2831no—
115C2×C4⋊C4—2831no—
116#107—5661no—
117#107—5661no—
118#103—5661no—
119#103—5661no—
120C22⋊C8—2831no—
121C22⋊C8C2×D28311yescharacteristic
122#95—5661no—
123#95—5661no—
124#95C2×D28311yescharacteristic
125C2×Q8—2831no—
126C2×Q8—5661no—
127C2×Q8D113211yescharacteristic
128C22×C4—21no—
129C22×C4—2831no—
130C22×C4—2831no—
131C22×C4—5661no—
132C22×C4C22×D28311yescharacteristic
133C2×C8—21no—
134C2×C8—5661no—
135C4⋊C4—21no—
136C4⋊C4—2831no—
137C4⋊C4—5661no—
138C4⋊C4—5661no—
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⋊C4D113211yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—5661no—
150C42—5661no—
151C42—5661no—
152C23D4×D28311yescharacteristic
153Q8—41no—
154Q8—11321no—
155Q8—22641no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—2832no—
163C2×C4—5661no—
164C2×C4—5661no—
165C2×C4—5661no—
166C2×C4—5661no—
167C2×C4—5661no—
168C2×C4—11321no—
169C2×C4—11322no—
170C2×C4—11321no—
171C2×C4D4×D28311yescharacteristic
172C2×C4C2×D113211yescharacteristic
173C8—41no—
174C8—11321no—
175C22—21no—
176C22—21no—
177C22#2258358011yescharacteristic
178C22Q16×D28311yescharacteristic
179C22#2258363911yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—5662no—
186C4—11321no—
187C4—11321no—
188C4—11321no—
189C4—22641no—
190C2—21no—
191C2—21no—
192C2#3182662211yescharacteristic
193C2#3182663911yescharacteristic
194C2#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#1617
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
97. C283#1617semidirect

Maximal subgroups

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

subgroupindex
#318270942
#318268012
#318267982
#318264052
#318262012
#318261902
#328×C2832
#1617283