Finite Group Databasebeta

← #49122411

Subgroups — #49122411

Order 36224.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#22583601C211yesmaximal, characteristic
2C2×#22583535C211yesmaximal, characteristic
3C2×#22583533C211yesmaximal, characteristic
4#31826370C211yesmaximal, characteristic
5#31826227C211yesmaximal, characteristic
6#31826219C211yesmaximal, characteristic
7#340×C283C211yesmaximal, characteristic
8C22×Dic566C2211yescharacteristic
9C22×C283⋊C8C2211yescharacteristic
10#22583601—22no—
11#22583601—22no—
12C2×C4⋊Dic283—21no—
13C2×C4⋊Dic283C2211yescharacteristic
14C2×Dic283⋊C4—21no—
15C2×C4×Dic283C2211yescharacteristic
16#22583535—22no—
17#22583533—22no—
18C283⋊#95—21no—
19C283⋊#95—21no—
20C22×C8×C283C2211yescharacteristic
21C2×C4⋊C4×C283C2211yescharacteristic
22C2×C4⋊C4×C283C2211yescharacteristic
23C2×Dic566—21no—
24C2×Dic566—21no—
25C2×Dic566—21no—
26C2×Dic566—21no—
27C2×Dic566—21no—
28C2×Dic566Q812yes—
29C22×Dic283—21no—
30C22×Dic283—21no—
31C22×Dic283D411yescharacteristic
32C22×Dic283D411yescharacteristic
33C2×C283⋊C8—21no—
34C2×C283⋊C8—21no—
35C2×C283⋊C8—21no—
36C4⋊Dic283—24no—
37C4⋊Dic283—21no—
38C4⋊Dic283D412yes—
39Dic283⋊C4—24no—
40C4×Dic283—21no—
41C4×Dic283—21no—
42C22×C4×C283—21no—
43C22×C4×C283—21no—
44C22×C4×C283C2311yescharacteristic
45C2×C8×C283—21no—
46C2×C8×C283—21no—
47C2×C8×C283—21no—
48C4⋊C4×C283—21no—
49C4⋊C4×C283—21no—
50C4⋊C4×C283—21no—
51C4⋊C4×C283D412yes—
52Dic566—22no—
53Dic566—22no—
54Dic566—41no—
55Dic566—41no—
56C2×Dic283—21no—
57C2×Dic283—21no—
58C2×Dic283—22no—
59C2×Dic283—22no—
60C2×Dic283—21no—
61C2×Dic283—21no—
62C2×Dic283—21no—
63C2×Dic283—21no—
64C2×Dic283—41no—
65C2×Dic283—41no—
66C2×Dic283—41no—
67C2×Dic283—41no—
68C283⋊C8—41no—
69C23×C283C2×D411yescharacteristic
70C2×C4×C283—22no—
71C2×C4×C283—41no—
72C2×C4×C283—41no—
73C2×C4×C283—41no—
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#12011yescharacteristic
84C22×C283C22⋊Q811yescharacteristic
85C22×C283#12411yescharacteristic
86C22×C283#13511yescharacteristic
87C22×C283#13511yescharacteristic
88C22×C283#13711yescharacteristic
89C22×C283#13711yescharacteristic
90C4×C283—42no—
91C4×C283—81no—
92C4×C283C22⋊Q811yescharacteristic
93C4×C283C22⋊Q811yescharacteristic
94C4×C283#12411yescharacteristic
95C4×C283#12411yescharacteristic
96Dic283—42no—
97Dic283—41no—
98Dic283—41no—
99Dic283—42no—
100C2×C283#39311yescharacteristic
101C2×C283#45211yescharacteristic
102C2×C283#45211yescharacteristic
103C2×C283#47911yescharacteristic
104C2×C283#47911yescharacteristic
105C2×C283#48811yescharacteristic
106C2×C283#49111yescharacteristic
107C283#202611yescharacteristic, complemented, Sylow
108#2026—2831nomaximal, Sylow
109C2×#125—2831no—
110C2×#103—2831no—
111C2×#103—2831no—
112#391—2831no—
113#340—2831no—
114#340D28311yescharacteristic
115#336—2831no—
116C22×Q8—2831no—
117C22×C8—2831no—
118C22×C8C2×D28311yescharacteristic
119#125—5662no—
120#125—5662no—
121C2×C4⋊C4—2831no—
122C2×C4⋊C4—5661no—
123C2×C4⋊C4—5661no—
124C2×C4⋊C4C2×D28311yescharacteristic
125C2×C4⋊C4C2×D28311yescharacteristic
126C2×C42—2831no—
127#103—5662no—
128#103—5662no—
129#95—5661no—
130#95—5661no—
131C2×Q8—2832no—
132C2×Q8—5661no—
133C2×Q8—5661no—
134C2×Q8—5661no—
135C2×Q8—5661no—
136C2×Q8—5661no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—2831no—
140C22×C4—2831no—
141C22×C4—5661no—
142C22×C4—5661no—
143C22×C4C22×D28311yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—5661no—
148C2×C8—5661no—
149C2×C8—5661no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—2832no—
154C4⋊C4—5664no—
155C4⋊C4—5664no—
156C4⋊C4—5661no—
157C4⋊C4D113212yes—
158C42—5661no—
159C42—5661no—
160C23D4×D28311yescharacteristic
161Q8—5662no—
162Q8—5662no—
163Q8—11321no—
164Q8—11321no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—5661no—
172C2×C4—5661no—
173C2×C4—5662no—
174C2×C4—5662no—
175C2×C4—5661no—
176C2×C4—5661no—
177C2×C4—5661no—
178C2×C4—5661no—
179C2×C4—11321no—
180C2×C4—11321no—
181C2×C4—11321no—
182C2×C4—11321no—
183C2×C4D4×D28311yescharacteristic
184C2×C4C2×D113211yescharacteristic
185C2×C4Q8×D28311yescharacteristic
186C2×C4#1798539111yescharacteristic
187C2×C4#1798539211yescharacteristic
188C2×C4#1798539211yescharacteristic
189C8—41no—
190C8—11321no—
191C22#2258358011yescharacteristic
192C22#2258358811yescharacteristic
193C22#2258359611yescharacteristic
194C22#2258362911yescharacteristic
195C22#2258363111yescharacteristic
196C22#2258363911yescharacteristic
197C22#2258364211yescharacteristic
198C4—42no—
199C4—81no—
200C4—11321no—
201C4—11321no—
202C4—11322no—
203C4—11322no—
204C4#2258358811yescharacteristic
205C4#2258359011yescharacteristic
206C4#2258359611yescharacteristic
207C4#2258359811yescharacteristic
208C2#3182637811yescharacteristic
209C2#3182662811yescharacteristic
210C2#3182663011yescharacteristic
211C2#3182677111yescharacteristic
212C2#3182677511yescharacteristic
213C2#3182681811yescharacteristic
214C2#3182683211yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#340×C283C2
socle, prime radicalC23×C283C2×D4
hypercenter#340D283
hypocenterC283#2026
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
107. C283#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#225836012
C2×#225835352
C2×#225835332
#318263702
#318262272
#318262192
#340×C2832
#2026283