Finite Group Databasebeta

← #49098540

Subgroups — #49098540

Order 35968.

696 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 151 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×#22582841C211yesmaximal, characteristic, complemented
2C2×#22582839C212yesmaximal, complemented
3C2×#22582835C211yesmaximal, characteristic, complemented
4#31823394C211yesmaximal, characteristic, complemented
5#31823387C212yesmaximal, complemented
6#31823381C211yesmaximal, characteristic, complemented
7#31823378C212yesmaximal, complemented
8#31823372C211yesmaximal, characteristic
9#31823314C211yesmaximal, characteristic, complemented
10#31823310C212yesmaximal, complemented
11#397×C281C211yesmaximal, characteristic, complemented
12C22×D1124C2211yescharacteristic
13C22×C22⋊D281C2212yes—
14C23×Dic281C2211yescharacteristic
15C22×C4×D281C2212yes—
16#22582841—24no—
17#22582839—28no—
18#22582835—24no—
19C2×#17985117C2212yes—
20C2×#17985117C2211yescharacteristic
21C2×#17985117C2211yescharacteristic
22C2×#17985117C2212yes—
23C2×C22⋊Dic281C2211yescharacteristic
24C2×#17985115C2212yes—
25C2×#17985115C2212yes—
26C2×#17985115C2212yes—
27C2×#17985115C2212yes—
28C2×C4×Dic281C2211yescharacteristic
29C2×C4×Dic281C2212yes—
30C2×C4×Dic281C2211yescharacteristic
31#22582786C2211yescharacteristic
32#22582786C2212yes—
33C2×C4⋊C4×C281C2211yescharacteristic
34C2×C22⋊C4×C281C2211yescharacteristic
35C2×C22⋊C4×C281C2212yes—
36#95×C281C2211yescharacteristic
37#95×C281C2212yes—
38C23×D281C2312yes—
39C2×D1124—24no—
40C2×D1124—22no—
41C2×C22⋊D281—24no—
42C2×C22⋊D281—24no—
43C2×C22⋊D281—24no—
44C22×Dic281—22no—
45C22×Dic281—22no—
46C22×Dic281D414yescomplemented
47C22×Dic281C2311yescharacteristic
48C22×Dic281C2311yescharacteristic
49C22×Dic281C2311yescharacteristic
50C22×Dic281C2312yes—
51C22×Dic281C2311yescharacteristic
52C2×C4×D281—24no—
53C2×C4×D281—24no—
54C2×C4×D281—24no—
55#17985117—22no—
56#17985117—24no—
57#17985117—24no—
58#17985117—22no—
59C22⋊Dic281—22no—
60#17985115—24no—
61#17985115—24no—
62#17985115—24no—
63#17985115—24no—
64C4×Dic281—22no—
65C4×Dic281—24no—
66C4×Dic281D414yescomplemented
67C24×C281C2311yescharacteristic
68C22×C4×C281C2312yes—
69C22×C4×C281C2312yes—
70C22×C4×C281C2311yescharacteristic
71C22×C4×C281C2311yescharacteristic
72C4⋊C4×C281—22no—
73C22⋊C4×C281—24no—
74C22⋊C4×C281—22no—
75C22×D281—22no—
76C22×D281—22no—
77C22×D281—22no—
78C22×D281—22no—
79C22×D281—22no—
80C22×D281—22no—
81C22×D281#4114yes—
82D1124—28no—
83C22⋊D281—216no—
84C2×Dic281—22no—
85C2×Dic281—21no—
86C2×Dic281—22no—
87C2×Dic281—21no—
88C2×Dic281—22no—
89C2×Dic281—28no—
90C2×Dic281—21no—
91C2×Dic281—22no—
92C2×Dic281C2×D412yes—
93C2×Dic281C2×D412yes—
94C2×Dic281C2×D412yes—
95C2×Dic281C2×D412yes—
96C2×Dic281#4114yes—
97C2×Dic281#4112yes—
98C4×D281—48no—
99C23×C281—21no—
100C23×C281—21no—
101C23×C281—22no—
102C23×C281—22no—
103C23×C281C2×D412yes—
104C23×C281C2411yescharacteristic
105C2×C4×C281—22no—
106C2×C4×C281—22no—
107C2×C4×C281—21no—
108C2×C4×C281—22no—
109C2×C4×C281—22no—
110C2×C4×C281—22no—
111C2×C4×C281—22no—
112C2×C4×C281—22no—
113C2×C4×C281—22no—
114C2×C4×C281C2×D412yes—
115C22×C281—22no—
116C22×C281—24no—
117C22×C281—41no—
118C22×C281—42no—
119C22×C281—41no—
120C22×C281C22×D411yescharacteristic
121C22×C281C22×D411yescharacteristic
122C22×C281C2×#4111yescharacteristic
123C22×C281C2×#4112yes—
124C22×C281C2×#4112yes—
125C2×D281—24no—
126C2×D281—24no—
127C2×D281—24no—
128C2×D281—42no—
129C2×D281—42no—
130C2×D281—42no—
131C2×D281—42no—
132C4×C281—22no—
133C4×C281—42no—
134C4×C281—42no—
135C4×C281—41no—
136Dic281—22no—
137Dic281—24no—
138Dic281—22no—
139Dic281—41no—
140Dic281#12114yes—
141C2×C281—42no—
142C2×C281C2×#12111yescharacteristic
143C2×C281#52512yes—
144C2×C281#52511yescharacteristic
145C2×C281#52912yes—
146C2×C281#53211yescharacteristic
147D281—44no—
148C281#239211yescharacteristic, complemented, Sylow
149#2392—2811nomaximal, Sylow
150C2×C4×D4—2811no—
151C2×C4×D4—2812no—
152C2×#117—2811no—
153#398—2811no—
154#397D28111yescharacteristic, complemented
155#396—2812no—
156#394—2812no—
157#394—2811no—
158#392—2811no—
159C4×C4⋊C4—2811no—
160C4×C22⋊C4—2812no—
161C22×D4—2812no—
162C22×D4—2811no—
163C23×C4—2811no—
164C23×C4—2812no—
165C4×D4—5624no—
166C4×D4—5628no—
167#117—5624no—
168C2×C4⋊C4—2811no—
169C2×C4⋊C4—2811no—
170C2×C4⋊C4—2812no—
171C2×C4⋊C4—2812no—
172C2×C4⋊C4C2×D28111yescharacteristic
173C2×C22⋊C4—2811no—
174C2×C22⋊C4—2812no—
175C2×C22⋊C4—2812no—
176C2×C22⋊C4—2812no—
177C2×C22⋊C4—2812no—
178C2×C22⋊C4C2×D28111yescharacteristic
179C2×C22⋊C4C2×D28112yes—
180C2×C42—2811no—
181C2×C42—2811no—
182C2×C42—2812no—
183#95—2812no—
184#95—2811no—
185#95C2×D28112yes—
186#95C2×D28111yescharacteristic
187C24—2812no—
188C24C22×D28111yescharacteristic
189C2×D4—5624no—
190C2×D4—5624no—
191C2×D4—5624no—
192C2×D4—5624no—
193C2×D4—5622no—
194C22×C4—2811no—
195C22×C4—2814no—
196C22×C4—2812no—
197C22×C4—2811no—
198C22×C4—2811no—
199C22×C4—2811no—
200C22×C4—5624no—
201C22×C4—5624no—
202C22×C4—5624no—
203C22×C4—5622no—
204C22×C4—5622no—
205C22×C4C22×D28112yes—
206C22×C4C22×D28112yes—
207C22×C4C22×D28111yescharacteristic
208C22×C4C22×D28111yescharacteristic
209C4⋊C4—22no—
210C4⋊C4—5624no—
211C4⋊C4—5622no—
212C4⋊C4—5624no—
213C4⋊C4—5622no—
214C22⋊C4—24no—
215C22⋊C4—22no—
216C22⋊C4—5624no—
217C22⋊C4—5624no—
218C22⋊C4—5624no—
219C22⋊C4—5624no—
220C22⋊C4—5622no—
221C42—2814no—
222C42—5622no—
223C42—5624no—
224C23—21no—
225C23—21no—
226C23—22no—
227C23—22no—
228C23—2814no—
229C23—5622no—
230C23—5622no—
231C23—5622no—
232C23—5622no—
233C23—5622no—
234C23—5622no—
235C23D4×D28112yes—
236C23C23×D28111yescharacteristic
237D4—5628no—
238D4—56216no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—2812no—
249C2×C4—2812no—
250C2×C4—2812no—
251C2×C4—2812no—
252C2×C4—2812no—
253C2×C4—2814no—
254C2×C4—5628no—
255C2×C4—5622no—
256C2×C4—5621no—
257C2×C4—5622no—
258C2×C4—5621no—
259C2×C4—5622no—
260C2×C4—5621no—
261C2×C4—5622no—
262C2×C4—11248no—
263C2×C4D4×D28112yes—
264C22—22no—
265C22—24no—
266C22—41no—
267C22—42no—
268C22—41no—
269C22—5624no—
270C22—5624no—
271C22—5624no—
272C22—11242no—
273C22—11242no—
274C22—11242no—
275C22—11242no—
276C22C2×D4×D28111yescharacteristic
277C22C2×D4×D28111yescharacteristic
278C22#41×D28111yescharacteristic
279C22#41×D28112yes—
280C22#41×D28112yes—
281C4—22no—
282C4—42no—
283C4—42no—
284C4—41no—
285C4—2814no—
286C4—5622no—
287C4—5624no—
288C4—5622no—
289C4—11241no—
290C2—42no—
291C2—11244no—
292C2#121×D28111yescharacteristic
293C2#3182397111yescharacteristic
294C2#3182397112yes—
295C2#3182399612yes—
296C2#3182401211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#397×C281C2
prime radical#31823372C2
hypercenter#397D281
hypocenterC281#2392
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#22582841C2semidirect
2. C2×#22582839C2semidirect
3. C2×#22582835C2semidirect
4. #31823394C2semidirect
5. #31823387C2semidirect
6. #31823381C2semidirect
7. #31823378C2semidirect
9. #31823314C2semidirect
10. #31823310C2semidirect
11. #397×C281C2semidirect
46. C22×Dic281D4semidirect
66. C4×Dic281D4semidirect
148. C281#2392semidirect
154. #397D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828412
C2×#225828392
C2×#225828352
#318233942
#318233872
#318233812
#318233782
#318233722
#318233142
#318233102
#397×C2812
#2392281