Finite Group Databasebeta

← #49098622

Subgroups — #49098622

Order 35968.

1056 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C22×#17985138C211yesmaximal, characteristic, complemented
2C2×#22582848C212yesmaximal, complemented
3#31823375C212yesmaximal, complemented
4#31823372C212yesmaximal, complemented
5#31823342C212yesmaximal, complemented
6#31823339C214yesmaximal, complemented
7#31823326C211yesmaximal, characteristic, complemented
8C22×C22⋊C4×C281C211yesmaximal, characteristic, complemented
9C2×#17985138—28no—
10C2×#17985138—24no—
11C22×Dic562C2211yescharacteristic, complemented
12C22×D1124C2211yescharacteristic, complemented
13C22×C22⋊D281C2214yes—
14C22×C22⋊D281C2212yes—
15C22×C4×D281C2212yescomplemented
16#22582848—28no—
17C2×C22⋊Dic281C2214yes—
18C2×C22⋊Dic281C2212yes—
19C2×#17985115C2214yescomplemented
20#22582786C2212yescomplemented
21#22582786C2214yescomplemented
22#22582786C2212yescomplemented
23C25×C281C2211yescharacteristic
24C23×C4×C281C2211yescharacteristic
25C23×C4×C281C2211yescharacteristic
26C2×C22⋊C4×C281—24no—
27C2×C22⋊C4×C281C2212yes—
28C2×C22⋊C4×C281C2212yes—
29C23×D281C2312yes—
30#17985138—232no—
31C2×Dic562—24no—
32C2×Dic562—22no—
33C2×D1124—24no—
34C2×D1124—22no—
35C2×C22⋊D281—28no—
36C2×C22⋊D281—24no—
37C2×C22⋊D281—24no—
38C2×C22⋊D281—28no—
39C2×C22⋊D281—44no—
40C2×C22⋊D281D418yescomplemented
41C22×Dic281C2314yes—
42C22×Dic281C2312yes—
43C2×C4×D281—24no—
44C2×C4×D281—24no—
45C2×C4×D281—24no—
46C22⋊Dic281—28no—
47C22⋊Dic281—24no—
48#17985115—44no—
49C24×C281—22no—
50C24×C281—24no—
51C24×C281—24no—
52C24×C281—42no—
53C24×C281C2312yes—
54C24×C281C2311yescharacteristic
55C22×C4×C281—24no—
56C22×C4×C281—22no—
57C22×C4×C281—42no—
58C22×C4×C281D414yescomplemented
59C22×C4×C281C2312yes—
60C22×C4×C281C2311yescharacteristic
61C22×C4×C281C2311yescharacteristic
62C22⋊C4×C281—24no—
63C22⋊C4×C281—24no—
64C22×D281—22no—
65C22×D281—22no—
66C22×D281—24no—
67C22×D281—24no—
68C22×D281C2×D414yes—
69Dic562—28no—
70D1124—28no—
71C22⋊D281—216no—
72C22⋊D281—416no—
73C2×Dic281—22no—
74C2×Dic281—22no—
75C2×Dic281—24no—
76C2×Dic281—24no—
77C2×Dic281—24no—
78C2×Dic281C2×D414yes—
79C4×D281—216no—
80C23×C281—22no—
81C23×C281—22no—
82C23×C281—28no—
83C23×C281—22no—
84C23×C281—24no—
85C23×C281—22no—
86C23×C281—24no—
87C23×C281—416no—
88C23×C281—44no—
89C23×C281—44no—
90C23×C281C2×D414yes—
91C23×C281C2×D412yes—
92C23×C281#4114yescomplemented
93C23×C281C2411yescharacteristic
94C2×C4×C281—28no—
95C2×C4×C281—22no—
96C2×C4×C281—22no—
97C2×C4×C281—22no—
98C2×C4×C281—24no—
99C2×C4×C281—44no—
100C2×C4×C281C2×D412yes—
101C2×C4×C281C2×D412yes—
102C22×C281—22no—
103C22×C281—22no—
104C22×C281—28no—
105C22×C281—24no—
106C22×C281—28no—
107C22×C281—416no—
108C22×C281—42no—
109C22×C281—42no—
110C22×C281—44no—
111C22×C281#12014yes—
112C22×C281C22×D412yes—
113C22×C281C22×D411yescharacteristic
114C22×C281C2×#4112yes—
115C22×C281H(5,𝔽2)12yes—
116C2×D281—24no—
117C2×D281—28no—
118C2×D281—42no—
119C2×D281—42no—
120C2×D281—44no—
121C4×C281—22no—
122C4×C281—22no—
123C4×C281—42no—
124Dic281—24no—
125Dic281—44no—
126C2×C281—24no—
127C2×C281—44no—
128C2×C281C2×#12011yescharacteristic
129C2×C281#52511yescharacteristic
130C2×C281#53511yescharacteristic
131C2×C281#54614yes—
132D281—44no—
133C281#240411yescharacteristic, complemented, Sylow
134#2404—2811nomaximal, Sylow
135C22×#41—2811no—
136C2×#120—2812no—
137C22×C22⋊C4D28111yescharacteristic, complemented
138#393—2812no—
139#392—2812no—
140#386—2812no—
141#386—2814no—
142#381—2811no—
143C25C2×D28111yescharacteristic
144C2×#41—5628no—
145C2×#41—5624no—
146C22×Q8—2811no—
147C22×D4—2812no—
148C22×D4—2814no—
149C22×D4—2811no—
150C23×C4—2812no—
151C23×C4C2×D28111yescharacteristic
152C23×C4C2×D28111yescharacteristic
153#120—5628no—
154C2×C22⋊C4—24no—
155C2×C22⋊C4—2812no—
156C2×C22⋊C4—2814no—
157C2×C22⋊C4—2814no—
158C2×C22⋊C4C2×D28112yes—
159C2×C22⋊C4C2×D28112yes—
160#95—2812no—
161#95—2812no—
162#95—2814no—
163C24—22no—
164C24—24no—
165C24—24no—
166C24—42no—
167C24—2812no—
168C24C22×D28112yes—
169C24C22×D28111yescharacteristic
170#41—56232no—
171C2×Q8—5624no—
172C2×Q8—5622no—
173C2×D4—2818no—
174C2×D4—5624no—
175C2×D4—5624no—
176C2×D4—5624no—
177C2×D4—5628no—
178C2×D4—5628no—
179C2×D4—5622no—
180C2×D4—11244no—
181C22×C4—24no—
182C22×C4—22no—
183C22×C4—42no—
184C22×C4—2812no—
185C22×C4—2814no—
186C22×C4—5624no—
187C22×C4—5624no—
188C22×C4—5624no—
189C22×C4C22⋊D28114yescomplemented
190C22×C4C22×D28112yes—
191C22×C4C22×D28111yescharacteristic
192C22×C4C22×D28111yescharacteristic
193C22⋊C4—24no—
194C22⋊C4—24no—
195C22⋊C4—5628no—
196C22⋊C4—5624no—
197C22⋊C4—11244no—
198C23—22no—
199C23—22no—
200C23—28no—
201C23—24no—
202C23—22no—
203C23—22no—
204C23—24no—
205C23—416no—
206C23—44no—
207C23—44no—
208C23—2814no—
209C23—5622no—
210C23—5622no—
211C23—5624no—
212C23—5624no—
213C23D4×D28114yes—
214C23C2×C22⋊D28112yes—
215C23#1798513814yescomplemented
216C23C23×D28111yescharacteristic
217Q8—5628no—
218D4—5628no—
219D4—56216no—
220D4—112416no—
221C2×C4—28no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—24no—
226C2×C4—44no—
227C2×C4—2814no—
228C2×C4—56216no—
229C2×C4—5622no—
230C2×C4—5622no—
231C2×C4—5624no—
232C2×C4—5624no—
233C2×C4—5624no—
234C2×C4C2×C22⋊D28112yes—
235C2×C4C2×C22⋊D28112yes—
236C22—22no—
237C22—22no—
238C22—28no—
239C22—24no—
240C22—28no—
241C22—416no—
242C22—42no—
243C22—42no—
244C22—44no—
245C22—5624no—
246C22—5628no—
247C22—11242no—
248C22—11242no—
249C22—11244no—
250C22#2258284714yes—
251C22C2×D4×D28112yes—
252C22C22×C22⋊D28111yescharacteristic
253C22C2×#1798513812yes—
254C22#2258292412yes—
255C4—22no—
256C4—22no—
257C4—42no—
258C4—5624no—
259C4—11244no—
260C2—24no—
261C2—44no—
262C2—11244no—
263C2C2×#2258284711yescharacteristic
264C2#3182397411yescharacteristic
265C2#3182403011yescharacteristic
266C2#3182410314yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
FittingC22×C22⋊C4×C281C2
hypercenterC22×C22⋊C4D281
hypocenterC281#2404
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#17985138C2semidirect
2. C2×#22582848C2semidirect
3. #31823375C2semidirect
4. #31823372C2semidirect
5. #31823342C2semidirect
6. #31823339C2semidirect
7. #31823326C2semidirect
8. C22×C22⋊C4×C281C2semidirect
11. C22×Dic562C22semidirect
12. C22×D1124C22semidirect
15. C22×C4×D281C22semidirect
19. C2×#17985115C22semidirect
20. #22582786C22semidirect
21. #22582786C22semidirect
22. #22582786C22semidirect
40. C2×C22⋊D281D4semidirect
58. C22×C4×C281D4semidirect
92. C23×C281#41semidirect
133. C281#2404semidirect
137. C22×C22⋊C4D281semidirect
189. C22×C4C22⋊D281semidirect
215. C23#17985138semidirect

Maximal subgroups

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

subgroupindex
C22×#179851382
C2×#225828482
#318233752
#318233722
#318233422
#318233392
#318233262
C22×C22⋊C4×C2812
#2404281