Finite Group Databasebeta

← #49098618

Subgroups — #49098618

Order 35968.

1056 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 185 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×#22582847C212yesmaximal, complemented
2C22×#17985115C211yesmaximal, characteristic, complemented
3#31823374C212yesmaximal, complemented
4#31823371C212yesmaximal, complemented
5#31823343C212yesmaximal, complemented
6#31823342C214yesmaximal, complemented
7#31823326C211yesmaximal, characteristic, complemented
8C22×#41×C281C211yesmaximal, characteristic, complemented
9C24×D281C2211yescharacteristic
10C22×C22⋊D281C2214yes—
11C23×Dic281C2211yescharacteristic
12#22582847—28no—
13C2×C22⋊Dic281C2212yes—
14C2×C22⋊Dic281C2214yescomplemented
15C2×#17985115—24no—
16C2×#17985115C2212yes—
17C2×#17985115C2214yes—
18C2×#17985115C2212yes—
19#22582786C2212yescomplemented
20#22582786C2214yescomplemented
21#22582786C2212yescomplemented
22C2×#41×C281—28no—
23C2×#41×C281—24no—
24C22×Q8×C281C2211yescharacteristic, complemented
25C22×D4×C281C2212yes—
26C22×D4×C281C2211yescharacteristic, complemented
27C23×C4×C281C2211yescharacteristic
28C23×C4×C281C2212yescomplemented
29C23×D281—24no—
30C23×D281—22no—
31C23×D281—24no—
32C23×D281—42no—
33C23×D281C2312yes—
34C2×C22⋊D281—28no—
35C2×C22⋊D281—28no—
36C2×C22⋊D281—44no—
37C22×Dic281—22no—
38C22×Dic281—42no—
39C22×Dic281C2314yes—
40C22×Dic281C2312yes—
41C22⋊Dic281—24no—
42C22⋊Dic281—44no—
43#17985115—24no—
44#17985115—24no—
45#17985115—28no—
46C24×C281C2312yes—
47C24×C281C2311yescharacteristic
48#41×C281—232no—
49C2×Q8×C281—24no—
50C2×Q8×C281—22no—
51C2×D4×C281—24no—
52C2×D4×C281—24no—
53C2×D4×C281—24no—
54C2×D4×C281—22no—
55C2×D4×C281D418yescomplemented
56C22×C4×C281—24no—
57C22×C4×C281—24no—
58C22×C4×C281—24no—
59C22×C4×C281—24no—
60C22×C4×C281D414yescomplemented
61C22×C4×C281C2311yescharacteristic
62C22×C4×C281C2311yescharacteristic
63C22×C4×C281C2312yes—
64C22×D281—28no—
65C22×D281—22no—
66C22×D281—24no—
67C22×D281—22no—
68C22×D281—24no—
69C22×D281—416no—
70C22×D281—44no—
71C22×D281—44no—
72C22×D281#4114yescomplemented
73C22⋊D281—416no—
74C2×Dic281—22no—
75C2×Dic281—24no—
76C2×Dic281—24no—
77C2×Dic281—24no—
78C2×Dic281—24no—
79C2×Dic281—44no—
80C23×C281—22no—
81C23×C281—22no—
82C23×C281—22no—
83C23×C281—22no—
84C23×C281—24no—
85C23×C281—24no—
86C23×C281C2×D414yes—
87C23×C281C2×D414yes—
88C23×C281C2×D412yes—
89C23×C281C2411yescharacteristic
90Q8×C281—28no—
91D4×C281—28no—
92D4×C281—216no—
93C2×C4×C281—216no—
94C2×C4×C281—28no—
95C2×C4×C281—22no—
96C2×C4×C281—22no—
97C2×C4×C281—22no—
98C2×C4×C281—22no—
99C2×C4×C281C2×D412yes—
100C2×C4×C281C2×D414yes—
101C2×C4×C281C2×D412yes—
102C22×C281—22no—
103C22×C281—22no—
104C22×C281—28no—
105C22×C281—24no—
106C22×C281—28no—
107C22×C281—42no—
108C22×C281—42no—
109C22×C281—44no—
110C22×C281#12014yes—
111C22×C281C22×D411yescharacteristic
112C22×C281C22×D412yes—
113C22×C281C2×#4112yes—
114C22×C281H(5,𝔽2)12yes—
115C2×D281—24no—
116C2×D281—28no—
117C2×D281—416no—
118C2×D281—42no—
119C2×D281—42no—
120C2×D281—44no—
121C4×C281—22no—
122C4×C281—24no—
123C4×C281—22no—
124Dic281—42no—
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×#41D28111yescharacteristic, complemented
136C2×#120—2812no—
137C22×C22⋊C4—2811no—
138#393—2812no—
139#392—2812no—
140#386—2812no—
141#386—2814no—
142#381—2811no—
143C25—2811no—
144C2×#41—28no—
145C2×#41—24no—
146C22×Q8C2×D28111yescharacteristic, complemented
147C22×D4—2814no—
148C22×D4C2×D28112yes—
149C22×D4C2×D28111yescharacteristic, complemented
150C23×C4—2811no—
151C23×C4C2×D28111yescharacteristic
152C23×C4C2×D28112yescomplemented
153#120—5628no—
154C2×C22⋊C4—2812no—
155C2×C22⋊C4—2812no—
156C2×C22⋊C4—2812no—
157C2×C22⋊C4—2814no—
158C2×C22⋊C4—2814no—
159C2×C22⋊C4—5624no—
160#95—2812no—
161#95—2812no—
162#95—2814no—
163C24—2812no—
164C24—5624no—
165C24—5622no—
166C24—5624no—
167C24—11242no—
168C24C22×D28112yes—
169C24C22×D28111yescharacteristic
170#41—232no—
171C2×Q8—24no—
172C2×Q8—22no—
173C2×D4—24no—
174C2×D4—24no—
175C2×D4—24no—
176C2×D4—22no—
177C2×D4—5628no—
178C2×D4—5628no—
179C2×D4—11244no—
180C2×D4C22⋊D28118yescomplemented
181C22×C4—24no—
182C22×C4—24no—
183C22×C4—24no—
184C22×C4—24no—
185C22×C4—2814no—
186C22×C4—2812no—
187C22×C4—5622no—
188C22×C4—11242no—
189C22×C4C22⋊D28114yescomplemented
190C22×C4C22×D28111yescharacteristic
191C22×C4C22×D28111yescharacteristic
192C22×C4C22×D28112yes—
193C22⋊C4—5624no—
194C22⋊C4—5624no—
195C22⋊C4—5624no—
196C22⋊C4—5628no—
197C22⋊C4—11244no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—24no—
203C23—24no—
204C23—2814no—
205C23—5628no—
206C23—5622no—
207C23—5624no—
208C23—5622no—
209C23—5624no—
210C23—112416no—
211C23—11244no—
212C23—11244no—
213C23C2×C22⋊D28114yes—
214C23C2×C22⋊D28114yes—
215C23C2×C22⋊D28112yes—
216C23C23×D28111yescharacteristic
217Q8—28no—
218D4—28no—
219D4—216no—
220D4—112416no—
221C2×C4—216no—
222C2×C4—28no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—5622no—
228C2×C4—5624no—
229C2×C4—5624no—
230C2×C4—5624no—
231C2×C4—5624no—
232C2×C4—11244no—
233C2×C4C2×C22⋊D28112yes—
234C2×C4C2×C22⋊D28114yes—
235C2×C4C2×C22⋊D28112yes—
236C22—22no—
237C22—22no—
238C22—28no—
239C22—24no—
240C22—28no—
241C22—42no—
242C22—42no—
243C22—44no—
244C22—5624no—
245C22—5628no—
246C22—112416no—
247C22—11242no—
248C22—11242no—
249C22—11244no—
250C22#2258284814yes—
251C22C22×C22⋊D28111yescharacteristic
252C22C22×C22⋊D28112yes—
253C22#41×D28112yes—
254C22#2258292512yes—
255C4—22no—
256C4—24no—
257C4—22no—
258C4—11242no—
259C4—11244no—
260C2—24no—
261C2—44no—
262C2—11244no—
263C2C2×#2258284811yescharacteristic
264C2#3182397011yescharacteristic
265C2#3182402711yescharacteristic
266C2#3182410114yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
FittingC22×#41×C281C2
hypercenterC22×#41D281
hypocenterC281#2404
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#22582847C2semidirect
2. C22×#17985115C2semidirect
3. #31823374C2semidirect
4. #31823371C2semidirect
5. #31823343C2semidirect
6. #31823342C2semidirect
7. #31823326C2semidirect
8. C22×#41×C281C2semidirect
14. C2×C22⋊Dic281C22semidirect
19. #22582786C22semidirect
20. #22582786C22semidirect
21. #22582786C22semidirect
24. C22×Q8×C281C22semidirect
26. C22×D4×C281C22semidirect
28. C23×C4×C281C22semidirect
55. C2×D4×C281D4semidirect
60. C22×C4×C281D4semidirect
72. C22×D281#41semidirect
133. C281#2404semidirect
135. C22×#41D281semidirect
146. C22×Q8C2×D281semidirect
149. C22×D4C2×D281semidirect
152. C23×C4C2×D281semidirect
180. C2×D4C22⋊D281semidirect
189. C22×C4C22⋊D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828472
C22×#179851152
#318233742
#318233712
#318233432
#318233422
#318233262
C22×#41×C2812
#2404281