Finite Group Databasebeta

← #49098630

Subgroups — #49098630

Order 35968.

1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×C22⋊D281C211yesmaximal, characteristic
2C2×#22582862C212yesmaximal, complemented
3#31823378C214yesmaximal, complemented
4#31823342C212yesmaximal, complemented
5#31823335C212yesmaximal, complemented
6#31823319C211yesmaximal, characteristic, complemented
7#31823318C212yesmaximal, complemented
8C22×C22⋊C4×C281C211yesmaximal, characteristic, complemented
9C24×D281C2211yescharacteristic
10C22×C22⋊D281—28no—
11C22×C22⋊D281—24no—
12C22×C22⋊D281C2212yes—
13C22×C22⋊D281C2212yes—
14C23×Dic281C2211yescharacteristic
15#22582862—28no—
16C2×#17985117C2214yescomplemented
17C2×C22⋊Dic281C2212yes—
18C2×C22⋊Dic281C2212yescomplemented
19C2×C22⋊Dic281C2212yescomplemented
20C2×#17985115C2214yescomplemented
21C2×#17985115C2214yescomplemented
22#22582786C2214yescomplemented
23C25×C281C2211yescharacteristic
24C23×C4×C281C2211yescharacteristic, complemented
25C23×C4×C281C2211yescharacteristic, complemented
26C2×C22⋊C4×C281—24no—
27C2×C22⋊C4×C281C2212yes—
28C2×C22⋊C4×C281C2212yescomplemented
29C23×D281—24no—
30C23×D281—22no—
31C23×D281—24no—
32C23×D281—42no—
33C23×D281C2312yes—
34C2×C22⋊D281—232no—
35C2×C22⋊D281—24no—
36C2×C22⋊D281—24no—
37C2×C22⋊D281—24no—
38C2×C22⋊D281—24no—
39C2×C22⋊D281—24no—
40C2×C22⋊D281D418yes—
41C22×Dic281—24no—
42C22×Dic281—22no—
43C22×Dic281C2314yes—
44C22×Dic281C2312yes—
45#17985117—28no—
46C22⋊Dic281—24no—
47C22⋊Dic281—24no—
48C22⋊Dic281—42no—
49#17985115—28no—
50#17985115—44no—
51C24×C281—24no—
52C24×C281—24no—
53C24×C281—42no—
54C24×C281D414yes—
55C24×C281C2311yescharacteristic
56C24×C281C2311yescharacteristic
57C24×C281C2311yescharacteristic
58C22×C4×C281—24no—
59C22×C4×C281—22no—
60C22×C4×C281—22no—
61C22×C4×C281—42no—
62C22×C4×C281C2312yes—
63C22×C4×C281C2312yes—
64C22⋊C4×C281—24no—
65C22⋊C4×C281—24no—
66C22×D281—28no—
67C22×D281—22no—
68C22×D281—22no—
69C22×D281—24no—
70C22×D281—24no—
71C22×D281—416no—
72C22×D281—44no—
73C22×D281—44no—
74C22×D281C2×D414yes—
75C22⋊D281—216no—
76C22⋊D281—216no—
77C2×Dic281—28no—
78C2×Dic281—22no—
79C2×Dic281—22no—
80C2×Dic281—24no—
81C2×Dic281—24no—
82C2×Dic281—24no—
83C2×Dic281C2×D414yes—
84C23×C281—22no—
85C23×C281—22no—
86C23×C281—22no—
87C23×C281—22no—
88C23×C281—28no—
89C23×C281—28no—
90C23×C281—22no—
91C23×C281—22no—
92C23×C281—22no—
93C23×C281—44no—
94C23×C281—416no—
95C23×C281C2×D414yes—
96C23×C281C2×D412yes—
97C23×C281C2×D412yes—
98C23×C281C2×D412yes—
99C23×C281#4114yes—
100C23×C281C2411yescharacteristic
101C2×C4×C281—22no—
102C2×C4×C281—22no—
103C2×C4×C281—24no—
104C2×C4×C281—24no—
105C2×C4×C281—44no—
106C2×C4×C281—44no—
107C22×C281—22no—
108C22×C281—22no—
109C22×C281—22no—
110C22×C281—22no—
111C22×C281—28no—
112C22×C281—28no—
113C22×C281—22no—
114C22×C281—22no—
115C22×C281—22no—
116C22×C281—416no—
117C22×C281—44no—
118C22×C281#12014yes—
119C22×C281#12314yescomplemented
120C22×C281C22×D412yes—
121C22×C281C22×D411yescharacteristic
122C22×C281C2×#4112yes—
123C22×C281H(5,𝔽2)12yes—
124C2×D281—24no—
125C2×D281—28no—
126C2×D281—416no—
127C2×D281—42no—
128C2×D281—42no—
129C2×D281—44no—
130C4×C281—42no—
131C4×C281—42no—
132Dic281—24no—
133Dic281—44no—
134C2×C281—24no—
135C2×C281—24no—
136C2×C281—42no—
137C2×C281C2×#12011yescharacteristic
138C2×C281C2×#12311yescharacteristic
139C2×C281#53411yescharacteristic
140C2×C281#54614yes—
141D281—44no—
142C281#240511yescharacteristic, complemented, Sylow
143#2405—2811nomaximal, Sylow
144C23×D4—2811no—
145C2×#123—2812no—
146C22×C22⋊C4D28111yescharacteristic, complemented
147#394—2814no—
148#386—2812no—
149#385—2812no—
150#379—2811no—
151#379—2812no—
152C25—2811no—
153C25C2×D28111yescharacteristic
154C22×D4—2812no—
155C22×D4—2812no—
156C22×D4—5628no—
157C22×D4—5624no—
158C23×C4—2811no—
159C23×C4C2×D28111yescharacteristic, complemented
160C23×C4C2×D28111yescharacteristic, complemented
161#123—5628no—
162C2×C4⋊C4—2814no—
163C2×C22⋊C4—24no—
164C2×C22⋊C4—2812no—
165C2×C22⋊C4—2812no—
166C2×C22⋊C4—2814no—
167C2×C22⋊C4—2812no—
168C2×C22⋊C4—2814no—
169C2×C22⋊C4C2×D28112yes—
170C2×C22⋊C4C2×D28112yescomplemented
171#95—2814no—
172C24—24no—
173C24—24no—
174C24—42no—
175C24—2812no—
176C24—5624no—
177C24—5622no—
178C24—5624no—
179C24—11242no—
180C24C22⋊D28114yes—
181C24C22×D28111yescharacteristic
182C24C22×D28111yescharacteristic
183C24C22×D28111yescharacteristic
184C2×D4—2818no—
185C2×D4—5624no—
186C2×D4—5624no—
187C2×D4—56232no—
188C2×D4—5624no—
189C2×D4—5624no—
190C2×D4—5624no—
191C22×C4—24no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—42no—
195C22×C4—2812no—
196C22×C4—2814no—
197C22×C4—5624no—
198C22×C4—5622no—
199C22×C4C22×D28112yes—
200C22×C4C22×D28112yes—
201C4⋊C4—5628no—
202C22⋊C4—24no—
203C22⋊C4—24no—
204C22⋊C4—5628no—
205C22⋊C4—5624no—
206C22⋊C4—5624no—
207C22⋊C4—11244no—
208C22⋊C4—11242no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—28no—
214C23—28no—
215C23—22no—
216C23—22no—
217C23—22no—
218C23—44no—
219C23—416no—
220C23—2814no—
221C23—5628no—
222C23—5622no—
223C23—5622no—
224C23—5624no—
225C23—5624no—
226C23—112416no—
227C23—11244no—
228C23—11244no—
229C23D4×D28114yes—
230C23C2×C22⋊D28112yes—
231C23C2×C22⋊D28112yes—
232C23C2×C22⋊D28112yes—
233C23#1798513814yes—
234C23C23×D28111yescharacteristic
235D4—56216no—
236D4—56216no—
237C2×C4—24no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—24no—
241C2×C4—44no—
242C2×C4—44no—
243C2×C4—2814no—
244C2×C4—5628no—
245C2×C4—5622no—
246C2×C4—5622no—
247C2×C4—5624no—
248C2×C4—5624no—
249C2×C4—5624no—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—22no—
254C22—28no—
255C22—28no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—416no—
260C22—44no—
261C22—5624no—
262C22—5628no—
263C22—112416no—
264C22—11242no—
265C22—11242no—
266C22—11244no—
267C22#2258284714yes—
268C22#2258286214yescomplemented
269C22C2×D4×D28112yes—
270C22C22×C22⋊D28111yescharacteristic
271C22C2×#1798513812yes—
272C22#2258292412yes—
273C4—42no—
274C4—42no—
275C4—5624no—
276C4—11244no—
277C2—24no—
278C2—24no—
279C2—42no—
280C2—11244no—
281C2C2×#2258284711yescharacteristic
282C2C2×#2258286211yescharacteristic
283C2#3182402211yescharacteristic
284C2#3182410314yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
FittingC22×C22⋊C4×C281C2
prime radicalC23×C22⋊D281C2
hypercenterC22×C22⋊C4D281
hypocenterC281#2405
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#22582862C2semidirect
3. #31823378C2semidirect
4. #31823342C2semidirect
5. #31823335C2semidirect
6. #31823319C2semidirect
7. #31823318C2semidirect
8. C22×C22⋊C4×C281C2semidirect
16. C2×#17985117C22semidirect
18. C2×C22⋊Dic281C22semidirect
19. C2×C22⋊Dic281C22semidirect
20. C2×#17985115C22semidirect
21. C2×#17985115C22semidirect
22. #22582786C22semidirect
24. C23×C4×C281C22semidirect
25. C23×C4×C281C22semidirect
28. C2×C22⋊C4×C281C22semidirect
119. C22×C281#123semidirect
142. C281#2405semidirect
146. C22×C22⋊C4D281semidirect
159. C23×C4C2×D281semidirect
160. C23×C4C2×D281semidirect
170. C2×C22⋊C4C2×D281semidirect
268. C22#22582862semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D2812
C2×#225828622
#318233782
#318233422
#318233352
#318233192
#318233182
C22×C22⋊C4×C2812
#2405281