Finite Group Databasebeta

← #49098626

Subgroups — #49098626

Order 35968.

1116 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 197 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×#22582860C212yesmaximal, complemented
2C22×C22⋊Dic281C211yesmaximal, characteristic, complemented
3#31823377C214yesmaximal, complemented
4#31823343C212yesmaximal, complemented
5#31823336C212yesmaximal, complemented
6#31823319C212yesmaximal, complemented
7#31823319C211yesmaximal, characteristic, complemented
8C23×D4×C281C211yesmaximal, characteristic
9C23×Dic281C2211yescharacteristic, complemented
10C23×Dic281C2211yescharacteristic, complemented
11#22582860—28no—
12C2×#17985117C2214yescomplemented
13C2×C22⋊Dic281—24no—
14C2×C22⋊Dic281C2212yes—
15C2×C22⋊Dic281C2212yes—
16C2×C22⋊Dic281C2212yescomplemented
17C2×C22⋊Dic281C2214yescomplemented
18C2×C22⋊Dic281C2212yescomplemented
19C2×C22⋊Dic281C2212yescomplemented
20C2×C22⋊Dic281C2214yescomplemented
21#22582786C2214yescomplemented
22C25×C281C2211yescharacteristic
23C25×C281C2211yescharacteristic
24C22×D4×C281—24no—
25C22×D4×C281—28no—
26C22×D4×C281C2212yes—
27C22×D4×C281C2212yes—
28C23×C4×C281C2211yescharacteristic
29C22×Dic281—22no—
30C22×Dic281—22no—
31C22×Dic281—24no—
32C22×Dic281—42no—
33C22×Dic281C2312yes—
34C22×Dic281C2314yes—
35C22×Dic281C2312yes—
36#17985117—28no—
37C22⋊Dic281—24no—
38C22⋊Dic281—24no—
39C22⋊Dic281—28no—
40C22⋊Dic281—24no—
41C22⋊Dic281—24no—
42C22⋊Dic281—42no—
43C22⋊Dic281—44no—
44C24×C281—24no—
45C24×C281—24no—
46C24×C281—22no—
47C24×C281—24no—
48C24×C281—24no—
49C24×C281—42no—
50C24×C281—42no—
51C24×C281D414yes—
52C24×C281C2311yescharacteristic
53C24×C281C2312yes—
54C24×C281C2311yescharacteristic
55C24×C281C2311yescharacteristic
56C2×D4×C281—232no—
57C2×D4×C281—24no—
58C2×D4×C281—24no—
59C2×D4×C281—24no—
60C2×D4×C281—24no—
61C2×D4×C281—24no—
62C2×D4×C281D418yes—
63C22×C4×C281—22no—
64C22×C4×C281—24no—
65C22×C4×C281C2312yes—
66C2×Dic281—24no—
67C2×Dic281—22no—
68C2×Dic281—22no—
69C2×Dic281—24no—
70C2×Dic281—24no—
71C2×Dic281—24no—
72C2×Dic281—24no—
73C2×Dic281—44no—
74C2×Dic281—44no—
75C23×C281—22no—
76C23×C281—22no—
77C23×C281—22no—
78C23×C281—22no—
79C23×C281—28no—
80C23×C281—28no—
81C23×C281—28no—
82C23×C281—22no—
83C23×C281—22no—
84C23×C281—22no—
85C23×C281—22no—
86C23×C281—24no—
87C23×C281—22no—
88C23×C281—24no—
89C23×C281—44no—
90C23×C281—416no—
91C23×C281—416no—
92C23×C281—44no—
93C23×C281—44no—
94C23×C281C2×D412yes—
95C23×C281C2×D414yes—
96C23×C281C2×D412yes—
97C23×C281C2×D414yes—
98C23×C281C2×D412yes—
99C23×C281#4114yes—
100C23×C281C2411yescharacteristic
101D4×C281—216no—
102D4×C281—216no—
103C2×C4×C281—28no—
104C2×C4×C281—22no—
105C2×C4×C281—22no—
106C2×C4×C281C2×D414yes—
107C22×C281—22no—
108C22×C281—22no—
109C22×C281—22no—
110C22×C281—22no—
111C22×C281—28no—
112C22×C281—28no—
113C22×C281—22no—
114C22×C281—24no—
115C22×C281—22no—
116C22×C281—22no—
117C22×C281—28no—
118C22×C281—416no—
119C22×C281—416no—
120C22×C281—42no—
121C22×C281—42no—
122C22×C281—44no—
123C22×C281—44no—
124C22×C281#12014yes—
125C22×C281#12314yescomplemented
126C22×C281C22×D411yescharacteristic
127C22×C281C22×D412yes—
128C22×C281C2×#4112yes—
129C22×C281H(5,𝔽2)12yes—
130C4×C281—24no—
131Dic281—42no—
132Dic281—42no—
133Dic281—44no—
134C2×C281—24no—
135C2×C281—24no—
136C2×C281—42no—
137C2×C281—44no—
138C2×C281C2×#12011yescharacteristic
139C2×C281C2×#12311yescharacteristic
140C2×C281#53411yescharacteristic
141C2×C281#54614yes—
142C281#240511yescharacteristic, complemented, Sylow
143#2405—2811nomaximal, Sylow
144C23×D4D28111yescharacteristic
145C2×#123—2812no—
146C22×C22⋊C4—2811no—
147#394—2814no—
148#386—2812no—
149#385—2812no—
150#379—2812no—
151#379—2811no—
152C25C2×D28111yescharacteristic
153C25C2×D28111yescharacteristic
154C22×D4—24no—
155C22×D4—28no—
156C22×D4C2×D28112yes—
157C22×D4C2×D28112yes—
158C23×C4—2811no—
159C23×C4—2811no—
160C23×C4C2×D28111yescharacteristic
161#123—5628no—
162C2×C4⋊C4—2814no—
163C2×C22⋊C4—2812no—
164C2×C22⋊C4—2812no—
165C2×C22⋊C4—2812no—
166C2×C22⋊C4—2814no—
167C2×C22⋊C4—2812no—
168C2×C22⋊C4—2814no—
169C2×C22⋊C4—2812no—
170C2×C22⋊C4—5624no—
171#95—2814no—
172C24—24no—
173C24—24no—
174C24—22no—
175C24—24no—
176C24—24no—
177C24—42no—
178C24—42no—
179C24C22⋊D28114yes—
180C24C22×D28111yescharacteristic
181C24C22×D28112yes—
182C24C22×D28111yescharacteristic
183C24C22×D28111yescharacteristic
184C2×D4—232no—
185C2×D4—24no—
186C2×D4—24no—
187C2×D4—24no—
188C2×D4—24no—
189C2×D4—24no—
190C2×D4C22⋊D28118yes—
191C22×C4—22no—
192C22×C4—24no—
193C22×C4—2812no—
194C22×C4—2814no—
195C22×C4—2812no—
196C22×C4—5622no—
197C22×C4—5622no—
198C22×C4—5624no—
199C22×C4—11242no—
200C22×C4C22×D28112yes—
201C4⋊C4—5628no—
202C22⋊C4—5624no—
203C22⋊C4—5624no—
204C22⋊C4—5624no—
205C22⋊C4—5628no—
206C22⋊C4—5624no—
207C22⋊C4—11242no—
208C22⋊C4—11244no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—28no—
214C23—28no—
215C23—28no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—24no—
221C23—22no—
222C23—24no—
223C23—44no—
224C23—416no—
225C23—416no—
226C23—44no—
227C23—44no—
228C23C2×C22⋊D28112yes—
229C23C2×C22⋊D28114yes—
230C23C2×C22⋊D28114yes—
231C23C2×C22⋊D28112yes—
232C23C2×C22⋊D28112yes—
233C23#1798513714yes—
234C23C23×D28111yescharacteristic
235D4—216no—
236D4—216no—
237C2×C4—28no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—5624no—
241C2×C4—5622no—
242C2×C4—5622no—
243C2×C4—5624no—
244C2×C4—5624no—
245C2×C4—5624no—
246C2×C4—5624no—
247C2×C4—11244no—
248C2×C4—11244no—
249C2×C4C2×C22⋊D28114yes—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—22no—
254C22—28no—
255C22—28no—
256C22—22no—
257C22—24no—
258C22—22no—
259C22—22no—
260C22—28no—
261C22—416no—
262C22—416no—
263C22—42no—
264C22—42no—
265C22—44no—
266C22—44no—
267C22#2258284814yes—
268C22#2258286014yescomplemented
269C22C22×C22⋊D28111yescharacteristic
270C22C22×C22⋊D28112yes—
271C22C2×#1798513712yes—
272C22#2258292412yes—
273C4—24no—
274C4—11242no—
275C4—11242no—
276C4—11244no—
277C2—24no—
278C2—24no—
279C2—42no—
280C2—44no—
281C2C2×#2258284811yescharacteristic
282C2C2×#2258286011yescharacteristic
283C2#3182402211yescharacteristic
284C2#3182410714yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting, prime radicalC23×D4×C281C2
hypercenterC23×D4D281
hypocenterC281#2405
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#22582860C2semidirect
2. C22×C22⋊Dic281C2semidirect
3. #31823377C2semidirect
4. #31823343C2semidirect
5. #31823336C2semidirect
6. #31823319C2semidirect
7. #31823319C2semidirect
9. C23×Dic281C22semidirect
10. C23×Dic281C22semidirect
12. C2×#17985117C22semidirect
16. C2×C22⋊Dic281C22semidirect
17. C2×C22⋊Dic281C22semidirect
18. C2×C22⋊Dic281C22semidirect
19. C2×C22⋊Dic281C22semidirect
20. C2×C22⋊Dic281C22semidirect
21. #22582786C22semidirect
125. C22×C281#123semidirect
142. C281#2405semidirect
268. C22#22582860semidirect

Maximal subgroups

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

subgroupindex
C2×#225828602
C22×C22⋊Dic2812
#318233772
#318233432
#318233362
#318233192
C23×D4×C2812
#2405281