Finite Group Databasebeta

← #49098652

Subgroups — #49098652

Order 35968.

1232 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 171 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×D4×D281C211yesmaximal, characteristic, complemented
2C2×#22582851C212yesmaximal, complemented
3C2×#22582847C212yesmaximal, complemented
4C2×#22582839C211yesmaximal, characteristic, complemented
5#31823381C211yesmaximal, characteristic, complemented
6#31823377C211yesmaximal, characteristic, complemented
7#31823372C211yesmaximal, characteristic, complemented
8#31823363C212yesmaximal, complemented
9#31823322C211yesmaximal, characteristic, complemented
10#31823318C212yesmaximal, complemented
11#392×C281C211yesmaximal, characteristic, complemented
12C24×D281C2212yes—
13C22×D1124C2211yescharacteristic
14C22×C22⋊D281C2212yes—
15C22×C22⋊D281C2211yescharacteristic
16C22×C22⋊D281C2212yescomplemented
17C2×D4×D281—28no—
18C2×D4×D281—24no—
19C23×Dic281C2211yescharacteristic, complemented
20C22×C4×D281C2211yescharacteristic
21#22582851—28no—
22#22582847—28no—
23#22582839—24no—
24C2×#17985117C2212yescomplemented
25C2×#17985117C2211yescharacteristic, complemented
26C2×C22⋊Dic281C2212yescomplemented
27C2×C22⋊Dic281C2212yescomplemented
28C2×#17985115C2211yescharacteristic
29C2×#17985115C2212yes—
30C2×#17985115C2212yescomplemented
31C2×#17985115C2212yescomplemented
32C2×#17985115C2212yescomplemented
33C2×C4×Dic281C2211yescharacteristic, complemented
34#22582786C2211yescharacteristic, complemented
35C22×D4×C281C2211yescharacteristic
36C22×D4×C281C2212yescomplemented
37C2×C22⋊C4×C281C2211yescharacteristic, complemented
38C2×C22⋊C4×C281C2212yescomplemented
39#95×C281C2211yescharacteristic, complemented
40C23×D281—24no—
41C23×D281—24no—
42C23×D281—24no—
43C23×D281—24no—
44C23×D281—24no—
45C23×D281—42no—
46C23×D281—42no—
47C23×D281C2312yes—
48C23×D281C2311yescharacteristic
49C2×D1124—24no—
50C2×D1124—22no—
51C2×C22⋊D281—22no—
52C2×C22⋊D281—22no—
53C2×C22⋊D281—24no—
54C2×C22⋊D281—24no—
55C2×C22⋊D281—24no—
56C2×C22⋊D281—24no—
57C2×C22⋊D281—42no—
58C2×C22⋊D281D418yescomplemented
59C2×C22⋊D281D414yescomplemented
60D4×D281—232no—
61C22×Dic281—22no—
62C22×Dic281—24no—
63C22×Dic281C2312yes—
64C22×Dic281C2311yescharacteristic
65C22×Dic281C2311yescharacteristic
66C22×Dic281C2311yescharacteristic
67C2×C4×D281—24no—
68C2×C4×D281D414yescomplemented
69#17985117—24no—
70#17985117—22no—
71C22⋊Dic281—24no—
72C22⋊Dic281—24no—
73#17985115—22no—
74#17985115—24no—
75#17985115—24no—
76#17985115—24no—
77#17985115—42no—
78C4×Dic281—22no—
79C24×C281C2312yes—
80C24×C281C2311yescharacteristic
81C2×D4×C281—24no—
82C2×D4×C281—24no—
83C2×D4×C281—24no—
84C2×D4×C281—22no—
85C2×D4×C281—42no—
86C22×C4×C281C2311yescharacteristic
87C22×C4×C281C2312yes—
88C22×C4×C281C2311yescharacteristic
89C22⋊C4×C281—22no—
90C22⋊C4×C281—42no—
91C22×D281—22no—
92C22×D281—22no—
93C22×D281—216no—
94C22×D281—22no—
95C22×D281—22no—
96C22×D281—22no—
97C22×D281—22no—
98C22×D281—22no—
99C22×D281—22no—
100C22×D281—48no—
101C22×D281—48no—
102C22×D281—48no—
103C22×D281—48no—
104C22×D281—48no—
105C22×D281—48no—
106C22×D281C2×D414yes—
107C22×D281C2×D412yes—
108C22×D281C2×D412yes—
109C22×D281#4112yes—
110D1124—28no—
111C22⋊D281—28no—
112C22⋊D281—216no—
113C22⋊D281—48no—
114C2×Dic281—21no—
115C2×Dic281—21no—
116C2×Dic281—22no—
117C2×Dic281—22no—
118C2×Dic281—21no—
119C2×Dic281—22no—
120C2×Dic281—22no—
121C2×Dic281—44no—
122C2×Dic281C2×D412yes—
123C2×Dic281C2×D414yes—
124C2×Dic281C2×D412yescomplemented
125C4×D281—28no—
126C23×C281—21no—
127C23×C281—22no—
128C23×C281—22no—
129C23×C281—22no—
130C23×C281—22no—
131C23×C281—21no—
132C23×C281—22no—
133C23×C281—22no—
134C23×C281—22no—
135C23×C281—22no—
136C23×C281C2×D414yes—
137C23×C281C2×D412yescomplemented
138C23×C281C2411yescharacteristic
139D4×C281—28no—
140D4×C281—48no—
141C2×C4×C281—22no—
142C2×C4×C281—21no—
143C2×C4×C281—22no—
144C2×C4×C281—22no—
145C2×C4×C281—22no—
146C2×C4×C281—22no—
147C2×C4×C281C2×D412yes—
148C22×C281—24no—
149C22×C281—22no—
150C22×C281—24no—
151C22×C281—24no—
152C22×C281—24no—
153C22×C281—41no—
154C22×C281—42no—
155C22×C281—41no—
156C22×C281—42no—
157C22×C281—42no—
158C22×C281—42no—
159C22×C281—42no—
160C22×C281C22×D411yescharacteristic
161C22×C281C22×D412yes—
162C22×C281C22×D411yescharacteristic
163C22×C281C2×#4111yescharacteristic
164C22×C281H(5,𝔽2)12yes—
165C2×D281—22no—
166C2×D281—22no—
167C2×D281—24no—
168C2×D281—24no—
169C2×D281—24no—
170C2×D281—24no—
171C2×D281—24no—
172C2×D281—432no—
173C2×D281—42no—
174C2×D281—42no—
175C2×D281—42no—
176C2×D281—42no—
177C2×D281#12114yescomplemented
178C4×C281—22no—
179C4×C281—41no—
180C4×C281—42no—
181Dic281—22no—
182Dic281—41no—
183Dic281—42no—
184Dic281#12014yescomplemented
185C2×C281—44no—
186C2×C281—42no—
187C2×C281C2×#12011yescharacteristic
188C2×C281C2×#12111yescharacteristic
189C2×C281#53511yescharacteristic
190C2×C281D4212yes—
191C2×C281#54612yes—
192D281—24no—
193D281—44no—
194C281#240811yescharacteristic, complemented, Sylow
195#2408—2811nomaximal, Sylow
196C23×D4—2811no—
197C2×#121—2812no—
198C2×#120—2812no—
199C2×C4×D4—2811no—
200#394—2811no—
201#394—2811no—
202#392—2811no—
203#392D28111yescharacteristic, complemented
204#390—2812no—
205#380—2811no—
206#379—2812no—
207C25—2812no—
208C22×D4—2811no—
209C22×D4—2812no—
210C22×D4—2812no—
211C22×D4—2811no—
212C22×D4—5624no—
213C22×D4—5628no—
214C22×D4C2×D28111yescharacteristic
215C22×D4C2×D28112yescomplemented
216C23×C4—2811no—
217C23×C4—2811no—
218#121—5628no—
219#120—5628no—
220C4×D4—5624no—
221C2×C4⋊C4—2811no—
222C2×C4⋊C4—2812no—
223C2×C22⋊C4—2812no—
224C2×C22⋊C4—2812no—
225C2×C22⋊C4—2811no—
226C2×C22⋊C4—2812no—
227C2×C22⋊C4—2812no—
228C2×C22⋊C4—2812no—
229C2×C22⋊C4—2812no—
230C2×C22⋊C4C2×D28111yescharacteristic, complemented
231C2×C22⋊C4C2×D28112yescomplemented
232C2×C42—2811no—
233#95—2811no—
234#95C2×D28111yescharacteristic, complemented
235C24—2811no—
236C24—2812no—
237C24—5624no—
238C24—5624no—
239C24—5624no—
240C24—5624no—
241C24—5624no—
242C24—11242no—
243C24—11242no—
244C24C22×D28112yes—
245C24C22×D28111yescharacteristic
246C2×D4—24no—
247C2×D4—24no—
248C2×D4—24no—
249C2×D4—22no—
250C2×D4—42no—
251C2×D4—2818no—
252C2×D4—2814no—
253C2×D4—5624no—
254C2×D4—5624no—
255C2×D4—5624no—
256C2×D4—56232no—
257C2×D4—5622no—
258C2×D4—5622no—
259C2×D4—5624no—
260C2×D4—5624no—
261C2×D4—5622no—
262C2×D4—11242no—
263C22×C4—2811no—
264C22×C4—2811no—
265C22×C4—2814no—
266C22×C4—2812no—
267C22×C4—2811no—
268C22×C4—5624no—
269C22×C4—5622no—
270C22×C4—5624no—
271C22×C4C22×D28112yes—
272C22×C4C22×D28111yescharacteristic
273C22×C4C22×D28111yescharacteristic
274C4⋊C4—5624no—
275C4⋊C4—5622no—
276C22⋊C4—22no—
277C22⋊C4—42no—
278C22⋊C4—5624no—
279C22⋊C4—5622no—
280C22⋊C4—5624no—
281C22⋊C4—5624no—
282C22⋊C4—5624no—
283C22⋊C4—5624no—
284C22⋊C4—11242no—
285C42—5622no—
286C23—21no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—21no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—2812no—
297C23—2812no—
298C23—2812no—
299C23—2814no—
300C23—56216no—
301C23—5622no—
302C23—5622no—
303C23—5622no—
304C23—5622no—
305C23—5622no—
306C23—5622no—
307C23—5622no—
308C23—5622no—
309C23—11248no—
310C23—11248no—
311C23—11248no—
312C23—11248no—
313C23—11248no—
314C23—11248no—
315C23D4×D28114yes—
316C23D4×D28112yescomplemented
317C23C23×D28111yescharacteristic
318D4—28no—
319D4—48no—
320D4—5628no—
321D4—56216no—
322D4—5628no—
323D4—11248no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—2812no—
331C2×C4—2814no—
332C2×C4—2812no—
333C2×C4—5628no—
334C2×C4—5621no—
335C2×C4—5621no—
336C2×C4—5622no—
337C2×C4—5622no—
338C2×C4—5621no—
339C2×C4—5622no—
340C2×C4—5622no—
341C2×C4—11244no—
342C2×C4D4×D28112yes—
343C22—24no—
344C22—22no—
345C22—24no—
346C22—24no—
347C22—24no—
348C22—41no—
349C22—42no—
350C22—42no—
351C22—41no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22—2814no—
356C22—5622no—
357C22—5622no—
358C22—5624no—
359C22—5624no—
360C22—5624no—
361C22—5624no—
362C22—5624no—
363C22—112432no—
364C22—11242no—
365C22—11242no—
366C22—11242no—
367C22—11242no—
368C22C2×D4×D28111yescharacteristic
369C22C2×D4×D28112yes—
370C22C2×D4×D28111yescharacteristic
371C22#41×D28111yescharacteristic
372C22#2258292412yes—
373C4—22no—
374C4—41no—
375C4—42no—
376C4—2814no—
377C4—5622no—
378C4—11241no—
379C4—11242no—
380C2—44no—
381C2—42no—
382C2—5624no—
383C2—11244no—
384C2#120×D28111yescharacteristic
385C2#121×D28111yescharacteristic
386C2#3182402611yescharacteristic
387C2#3182409512yes—
388C2#3182410212yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#392×C281C2
hypercenter#392D281
hypocenterC281#2408
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D281C2semidirect
2. C2×#22582851C2semidirect
3. C2×#22582847C2semidirect
4. C2×#22582839C2semidirect
5. #31823381C2semidirect
6. #31823377C2semidirect
7. #31823372C2semidirect
8. #31823363C2semidirect
9. #31823322C2semidirect
10. #31823318C2semidirect
11. #392×C281C2semidirect
16. C22×C22⋊D281C22semidirect
19. C23×Dic281C22semidirect
24. C2×#17985117C22semidirect
25. C2×#17985117C22semidirect
26. C2×C22⋊Dic281C22semidirect
27. C2×C22⋊Dic281C22semidirect
30. C2×#17985115C22semidirect
31. C2×#17985115C22semidirect
32. C2×#17985115C22semidirect
33. C2×C4×Dic281C22semidirect
34. #22582786C22semidirect
36. C22×D4×C281C22semidirect
37. C2×C22⋊C4×C281C22semidirect
38. C2×C22⋊C4×C281C22semidirect
39. #95×C281C22semidirect
58. C2×C22⋊D281D4semidirect
59. C2×C22⋊D281D4semidirect
68. C2×C4×D281D4semidirect
124. C2×Dic281C2×D4semidirect
137. C23×C281C2×D4semidirect
177. C2×D281#121semidirect
184. Dic281#120semidirect
194. C281#2408semidirect
203. #392D281semidirect
215. C22×D4C2×D281semidirect
230. C2×C22⋊C4C2×D281semidirect
231. C2×C22⋊C4C2×D281semidirect
234. #95C2×D281semidirect
316. C23D4×D281semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D2812
C2×#225828512
C2×#225828472
C2×#225828392
#318233812
#318233772
#318233722
#318233632
#318233222
#318233182
#392×C2812
#2408281