Finite Group Databasebeta

← #49119607

Subgroups — #49119607

Order 36224.

280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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×#22583593C211yesmaximal, characteristic
2#31826429C211yesmaximal, characteristic, complemented
3#31826190C212yesmaximal, complemented
4#31826188C212yesmaximal, complemented
5C2×C22⋊C8×C283C211yesmaximal, characteristic, complemented
6C22×C22⋊D283C411yescharacteristic
7C2×#17985376—21no—
8#22583593—21no—
9#22583593—21no—
10#22583593—21no—
11#22583593—21no—
12C2×Dic283⋊C4C411yescharacteristic
13C2×Dic283⋊C4C2211yescharacteristic
14C2×C22⋊Dic283C411yescharacteristic
15C2×(C2×D283)⋊C4C411yescharacteristic
16C2×(C2×D283)⋊C4C2211yescharacteristic
17C22⋊(C283⋊C8)—21no—
18C22⋊(C283⋊C8)C2212yes—
19C23×C4×C283C2211yescharacteristic
20C22×C8×C283—21no—
21C22⋊C8×C283—21no—
22C22⋊C8×C283C2212yes—
23C23×D283C2×C411yescharacteristic
24C2×C22⋊D283—21no—
25C2×C22⋊D283—21no—
26C2×C22⋊D283—42no—
27C22×Dic283C2×C411yescharacteristic
28C22×Dic283C2×C411yescharacteristic
29C22×Dic283C2×C411yescharacteristic
30#17985376—42no—
31C2×C283⋊C8—22no—
32Dic283⋊C4—21no—
33Dic283⋊C4—21no—
34Dic283⋊C4—21no—
35Dic283⋊C4—21no—
36C22⋊Dic283—21no—
37C22⋊Dic283—21no—
38(C2×D283)⋊C4—21no—
39(C2×D283)⋊C4—21no—
40(C2×D283)⋊C4—21no—
41(C2×D283)⋊C4—21no—
42C24×C283C2×C411yescharacteristic
43C22×C4×C283—42no—
44C22×C4×C283C2×C411yescharacteristic
45C22×C4×C283D411yescharacteristic
46C22×C4×C283D411yescharacteristic
47C22×C4×C283D411yescharacteristic
48C22×C4×C283D411yescharacteristic
49C22×C4×C283C2311yescharacteristic
50C2×C8×C283—22no—
51C2×C8×C283—42no—
52C22×D283—21no—
53C22×D283—22no—
54C22×D283—41no—
55C22×D283—41no—
56C22⋊D283—42no—
57C22⋊D283—42no—
58C2×Dic283—21no—
59C2×Dic283—21no—
60C2×Dic283—21no—
61C2×Dic283—22no—
62C2×Dic283—41no—
63C2×Dic283—41no—
64C283⋊C8—42no—
65C23×C283—22no—
66C23×C283—22no—
67C23×C283—41no—
68C23×C283C22⋊C411yescharacteristic
69C23×C283C22⋊C411yescharacteristic
70C23×C283C22×C411yescharacteristic
71C2×C4×C283—22no—
72C2×C4×C283—22no—
73C2×C4×C283—41no—
74C2×C4×C283—41no—
75C2×C4×C283—41no—
76C2×C4×C283—41no—
77C2×C4×C283C22⋊C411yescharacteristic
78C2×C4×C283C22⋊C411yescharacteristic
79C2×C4×C283C2×D411yescharacteristic
80C2×C4×C283C2×D411yescharacteristic
81C8×C283—42no—
82C22×C283—21no—
83C22×C283—21no—
84C22×C283—21no—
85C22×C283—21no—
86C22×C283—21no—
87C22×C283—21no—
88C22×C283—21no—
89C22×C283—44no—
90C22×C283#9912yes—
91C22×C283C2×C22⋊C411yescharacteristic
92C22×C283#13112yes—
93C2×D283—41no—
94C2×D283—41no—
95C2×D283—41no—
96C2×D283—82no—
97C4×C283—21no—
98C4×C283—21no—
99C4×C283—21no—
100C4×C283—21no—
101Dic283—41no—
102Dic283—41no—
103Dic283—41no—
104C2×C283—22no—
105C2×C283—22no—
106C2×C283—41no—
107C2×C283#40811yescharacteristic
108C2×C283C2×#9911yescharacteristic
109C2×C283#41311yescharacteristic
110D283—81no—
111C283#146811yescharacteristic, complemented, Sylow
112#1468—2831nomaximal, Sylow
113C2×#123—2831no—
114#407—2831no—
115C2×C22⋊C8D28311yescharacteristic, complemented
116#324—2832no—
117#323—2832no—
118C22×D4—2831no—
119C23×C4C2×D28311yescharacteristic
120C2×M16—5661no—
121C22×C8—21no—
122#123—5661no—
123#123—5661no—
124#123—5661no—
125#123—5661no—
126C2×C4⋊C4—2831no—
127C2×C4⋊C4—2831no—
128C2×C22⋊C4—2831no—
129C2×C22⋊C4—2831no—
130C2×C22⋊C4—2831no—
131C22⋊C8—21no—
132C22⋊C8—2832no—
133C22⋊C8—5661no—
134C22⋊C8C2×D28312yes—
135C24—2831no—
136C24C4×D28311yescharacteristic
137C2×D4—5661no—
138C2×D4—5661no—
139C2×D4—11322no—
140C22×C4—42no—
141C22×C4—2831no—
142C22×C4—2831no—
143C22×C4—2831no—
144C22×C4C4×D28311yescharacteristic
145C22×C4C22⋊D28311yescharacteristic
146C22×C4C22⋊D28311yescharacteristic
147C22×C4D113211yescharacteristic
148C22×C4D113211yescharacteristic
149C22×C4C22×D28311yescharacteristic
150M16—11322no—
151C2×C8—22no—
152C2×C8—42no—
153C2×C8—5662no—
154C4⋊C4—5661no—
155C4⋊C4—5661no—
156C4⋊C4—5661no—
157C4⋊C4—5661no—
158C22⋊C4—5661no—
159C22⋊C4—5661no—
160C22⋊C4—5661no—
161C22⋊C4—5661no—
162C22⋊C4—5661no—
163C22⋊C4—5661no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—5661no—
168C23—5662no—
169C23—11321no—
170C23—11321no—
171C23(C2×D283)⋊C411yescharacteristic
172C23(C2×D283)⋊C411yescharacteristic
173C23C2×C4×D28311yescharacteristic
174D4—11322no—
175D4—11322no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—5661no—
183C2×C4—5661no—
184C2×C4—5661no—
185C2×C4—5662no—
186C2×C4—11321no—
187C2×C4—11321no—
188C2×C4(C2×D283)⋊C411yescharacteristic
189C2×C4(C2×D283)⋊C411yescharacteristic
190C2×C4C2×C22⋊D28311yescharacteristic
191C2×C4C2×D113211yescharacteristic
192C8—42no—
193C8—11322no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—11321no—
203C22—11321no—
204C22—11321no—
205C22—22642no—
206C22#2258352412yes—
207C22C2×(C2×D283)⋊C411yescharacteristic
208C22#2258361612yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—11321no—
214C4—11321no—
215C4—11321no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—22641no—
220C2#3182643111yescharacteristic
221C2C2×#2258352411yescharacteristic
222C2#3182644711yescharacteristic
subgroupG/H
centerC22C2×(C2×D283)⋊C4
commutatorC23×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×C22⋊C8×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC22×C22⋊D283C4
cosocleC22×C4×C283C23
hypercenterC2×C22⋊C8D283
hypocenterC283#1468
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #31826429C2semidirect
3. #31826190C2semidirect
4. #31826188C2semidirect
5. C2×C22⋊C8×C283C2semidirect
111. C283#1468semidirect
115. C2×C22⋊C8D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835932
#318264292
#318261902
#318261882
C2×C22⋊C8×C2832
#1468283