Finite Group Databasebeta

← #49121714

Subgroups — #49121714

Order 36224.

598 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22583579C211yesmaximal, characteristic
2C2×#22583524C212yesmaximal, complemented
3#31826321C211yesmaximal, characteristic, complemented
4#31826231C212yesmaximal, complemented
5C22×C22⋊C4×C283C211yesmaximal, characteristic, complemented
6C22×C22⋊D283C412yescomplemented
7C22×C22⋊D283C2211yescharacteristic
8#22583579—21no—
9#22583579—21no—
10#22583579—22no—
11C2×C22⋊Dic283—22no—
12C2×C22⋊Dic283C412yescomplemented
13C2×C22⋊Dic283C2212yes—
14C2×C22⋊Dic283C2211yescharacteristic
15#22583524—24no—
16C25×C283C2211yescharacteristic
17C23×C4×C283—21no—
18C2×C22⋊C4×C283—21no—
19C2×C22⋊C4×C283—24no—
20C2×C22⋊C4×C283C2212yes—
21C23×D283C2×C411yescharacteristic, complemented
22C2×C22⋊D283—22no—
23C2×C22⋊D283—22no—
24C2×C22⋊D283—21no—
25C2×C22⋊D283—21no—
26C2×C22⋊D283—22no—
27C2×C22⋊D283—22no—
28C2×C22⋊D283—44no—
29C22×Dic283—22no—
30C22×Dic283C2×C411yescharacteristic, complemented
31C22×Dic283C2×C412yescomplemented
32C22⋊Dic283—22no—
33C22⋊Dic283—22no—
34C22⋊Dic283—21no—
35C22⋊Dic283—21no—
36C22⋊Dic283—22no—
37C22⋊Dic283—22no—
38C22⋊Dic283—44no—
39C24×C283—22no—
40C24×C283—22no—
41C24×C283—44no—
42C24×C283C2×C412yes—
43C24×C283D411yescharacteristic
44C24×C283D411yescharacteristic
45C24×C283D412yes—
46C24×C283C2311yescharacteristic
47C22×C4×C283—24no—
48C22×C4×C283—22no—
49C22×C4×C283—44no—
50C22⋊C4×C283—24no—
51C22⋊C4×C283—22no—
52C22⋊C4×C283D414yescomplemented
53C22×D283—21no—
54C22×D283—22no—
55C22×D283—42no—
56C22⋊D283—44no—
57C22⋊D283—44no—
58C22⋊D283—41no—
59C22⋊D283—42no—
60C22⋊D283—41no—
61C2×Dic283—21no—
62C2×Dic283—22no—
63C2×Dic283—22no—
64C2×Dic283—42no—
65C2×Dic283—44no—
66C2×Dic283—42no—
67C23×C283—24no—
68C23×C283—21no—
69C23×C283—21no—
70C23×C283—24no—
71C23×C283—24no—
72C23×C283—24no—
73C23×C283—21no—
74C23×C283—24no—
75C23×C283—21no—
76C23×C283—42no—
77C23×C283—42no—
78C23×C283—42no—
79C23×C283—42no—
80C23×C283—48no—
81C23×C283—48no—
82C23×C283C22⋊C412yes—
83C23×C283C22⋊C412yes—
84C23×C283C22×C411yescharacteristic
85C23×C283C2×D411yescharacteristic
86C23×C283C2×D412yes—
87C23×C283C2×D411yescharacteristic
88C23×C283#4112yes—
89C2×C4×C283—24no—
90C2×C4×C283—48no—
91C2×C4×C283—44no—
92C22×C283—24no—
93C22×C283—24no—
94C22×C283—22no—
95C22×C283—22no—
96C22×C283—22no—
97C22×C283—22no—
98C22×C283—22no—
99C22×C283—22no—
100C22×C283—22no—
101C22×C283—22no—
102C22×C283—42no—
103C22×C283—42no—
104C22×C283—48no—
105C22×C283—48no—
106C22×C283—42no—
107C22×C283—42no—
108C22×C283#9914yescomplemented
109C22×C283C2×C22⋊C411yescharacteristic
110C22×C283C4×D412yes—
111C22×C283#12011yescharacteristic
112C22×C283#12112yes—
113C22×C283#12311yescharacteristic
114C2×D283—41no—
115C2×D283—42no—
116C2×D283—82no—
117C4×C283—44no—
118Dic283—41no—
119Dic283—42no—
120Dic283—82no—
121C2×C283—22no—
122C2×C283—21no—
123C2×C283—22no—
124C2×C283—24no—
125C2×C283—21no—
126C2×C283—42no—
127C2×C283#38611yescharacteristic
128C2×C283C2×#9912yes—
129D283—81no—
130C283#189811yescharacteristic, complemented, Sylow
131#1898—2831nomaximal, Sylow
132C2×#120—2831no—
133C22×C22⋊C4D28311yescharacteristic, complemented
134C2×#99—2832no—
135#379—2831no—
136#342—2832no—
137C25C2×D28311yescharacteristic
138C22×D4—2831no—
139C22×D4—2832no—
140C23×C4—21no—
141#120—5661no—
142#120—5661no—
143#120—5662no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—24no—
146C2×C22⋊C4—2832no—
147C2×C22⋊C4—2831no—
148C2×C22⋊C4—2832no—
149C2×C22⋊C4—5662no—
150C2×C22⋊C4C2×D28312yes—
151#99—5664no—
152C24—22no—
153C24—22no—
154C24—44no—
155C24—2831no—
156C24C4×D28312yes—
157C24C22⋊D28311yescharacteristic
158C24C22⋊D28311yescharacteristic
159C24D113212yes—
160C24C22×D28311yescharacteristic
161C2×D4—5662no—
162C2×D4—5662no—
163C2×D4—5662no—
164C2×D4—5661no—
165C2×D4—5661no—
166C2×D4—5662no—
167C2×D4—11324no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—44no—
171C22×C4—2831no—
172C22×C4—2832no—
173C22×C4—5662no—
174C22⋊C4—24no—
175C22⋊C4—22no—
176C22⋊C4—5662no—
177C22⋊C4—5662no—
178C22⋊C4—5661no—
179C22⋊C4—5661no—
180C22⋊C4—5662no—
181C22⋊C4—5662no—
182C22⋊C4—11324no—
183C22⋊C4C22⋊D28314yescomplemented
184C23—21no—
185C23—21no—
186C23—24no—
187C23—24no—
188C23—21no—
189C23—24no—
190C23—21no—
191C23—24no—
192C23—24no—
193C23—42no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—48no—
198C23—48no—
199C23—5661no—
200C23—5662no—
201C23—11322no—
202C23(C2×D283)⋊C412yes—
203C23(C2×D283)⋊C412yes—
204C23C2×C4×D28311yescharacteristic
205C23C2×C22⋊D28311yescharacteristic
206C23C2×C22⋊D28312yes—
207C23C2×D113211yescharacteristic
208C23#1798539212yes—
209D4—11324no—
210D4—11321no—
211D4—11322no—
212D4—11321no—
213D4—11324no—
214C2×C4—24no—
215C2×C4—48no—
216C2×C4—44no—
217C2×C4—5662no—
218C2×C4—5661no—
219C2×C4—5662no—
220C2×C4—11322no—
221C2×C4—11324no—
222C2×C4—11322no—
223C22—24no—
224C22—24no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—42no—
234C22—42no—
235C22—48no—
236C22—48no—
237C22—42no—
238C22—42no—
239C22—11322no—
240C22—11321no—
241C22—22642no—
242C22#2258352414yescomplemented
243C22C2×(C2×D283)⋊C411yescharacteristic
244C22C4×C22⋊D28312yes—
245C22#2258357911yescharacteristic
246C22#2258358412yes—
247C22#2258359311yescharacteristic
248C4—44no—
249C4—11322no—
250C4—11321no—
251C4—22642no—
252C2—21no—
253C2—22no—
254C2—21no—
255C2—24no—
256C2—22no—
257C2—42no—
258C2—22641no—
259C2#3182634411yescharacteristic
260C2C2×#2258352412yes—
subgroupG/H
centerC22C2×(C2×D283)⋊C4
commutatorC23×C283C22×C4
FrattiniC24C22×D283
FittingC22×C22⋊C4×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC2×#22583579C2
cosocleC24×C283C23
hypercenterC22×C22⋊C4D283
hypocenterC283#1898
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#22583524C2semidirect
3. #31826321C2semidirect
4. #31826231C2semidirect
5. C22×C22⋊C4×C283C2semidirect
6. C22×C22⋊D283C4semidirect
12. C2×C22⋊Dic283C4semidirect
21. C23×D283C2×C4semidirect
30. C22×Dic283C2×C4semidirect
31. C22×Dic283C2×C4semidirect
52. C22⋊C4×C283D4semidirect
108. C22×C283#99semidirect
130. C283#1898semidirect
133. C22×C22⋊C4D283semidirect
183. C22⋊C4C22⋊D283semidirect
242. C22#22583524semidirect

Maximal subgroups

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

subgroupindex
C2×#225835792
C2×#225835242
#318263212
#318262312
C22×C22⋊C4×C2832
#1898283