Finite Group Databasebeta

← #49098617

Subgroups — #49098617

Order 35968.

1056 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 159 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×#17985137C211yesmaximal, characteristic, complemented
2C2×#22582847C212yesmaximal, complemented
3C2×C22⋊C4×D281C211yesmaximal, characteristic, complemented
4#31823376C211yesmaximal, characteristic, complemented
5#31823375C211yesmaximal, characteristic, complemented
6#31823371C211yesmaximal, characteristic, complemented
7#31823343C212yesmaximal, complemented
8#31823340C212yesmaximal, complemented
9#31823339C212yesmaximal, complemented
10#31823325C211yesmaximal, characteristic, complemented
11#392×C281C211yesmaximal, characteristic, complemented
12C24×D281C2211yescharacteristic
13C2×#17985137—28no—
14C2×#17985137—24no—
15C22×Dic562C2211yescharacteristic, complemented
16C22×C22⋊D281C2212yes—
17C22×C22⋊D281C2212yes—
18C23×Dic281C2212yescomplemented
19C22×C4×D281C2211yescharacteristic
20C22×C4×D281C2211yescharacteristic
21#22582847—28no—
22C2×C22⋊Dic281C2212yes—
23C2×C22⋊Dic281C2211yescharacteristic
24C2×C22⋊Dic281C2212yescomplemented
25C2×#17985115C2211yescharacteristic
26C2×#17985115C2212yes—
27C2×#17985115C2211yescharacteristic
28C2×#17985115C2212yes—
29C22⋊C4×D281—24no—
30#22582786C2211yescharacteristic, complemented
31#22582786C2212yescomplemented
32#22582786C2212yescomplemented
33#22582786C2212yescomplemented
34C22×D4×C281C2212yes—
35C22×D4×C281C2211yescharacteristic, complemented
36C2×C22⋊C4×C281C2211yescharacteristic
37C2×C22⋊C4×C281C2212yescomplemented
38#95×C281C2211yescharacteristic, complemented
39C23×D281—22no—
40C23×D281—22no—
41C23×D281—24no—
42C23×D281—22no—
43C23×D281—42no—
44C23×D281C2311yescharacteristic
45C23×D281C2311yescharacteristic
46#17985137—232no—
47C2×Dic562—24no—
48C2×Dic562—22no—
49C2×C22⋊D281—24no—
50C2×C22⋊D281—24no—
51C2×C22⋊D281—24no—
52C2×C22⋊D281—24no—
53C2×C22⋊D281—42no—
54C2×C22⋊D281D418yescomplemented
55C22×Dic281—24no—
56C22×Dic281—24no—
57C22×Dic281—24no—
58C22×Dic281C2312yes—
59C22×Dic281C2311yescharacteristic
60C22×Dic281C2311yescharacteristic
61C22×Dic281C2312yes—
62C2×C4×D281—24no—
63C2×C4×D281—22no—
64C2×C4×D281—42no—
65C2×C4×D281D414yescomplemented
66C22⋊Dic281—22no—
67C22⋊Dic281—24no—
68C22⋊Dic281—42no—
69#17985115—24no—
70#17985115—22no—
71#17985115—24no—
72#17985115—22no—
73C24×C281C2312yes—
74C24×C281C2311yescharacteristic
75C2×D4×C281—24no—
76C2×D4×C281—24no—
77C2×D4×C281—24no—
78C2×D4×C281—22no—
79C2×D4×C281—42no—
80C22×C4×C281C2312yes—
81C22×C4×C281C2311yescharacteristic
82C22×C4×C281C2311yescharacteristic
83C22⋊C4×C281—22no—
84C22⋊C4×C281—42no—
85C22×D281—21no—
86C22×D281—21no—
87C22×D281—22no—
88C22×D281—28no—
89C22×D281—21no—
90C22×D281—22no—
91C22×D281—21no—
92C22×D281—22no—
93C22×D281—48no—
94C22×D281—48no—
95C22×D281—44no—
96C22×D281—44no—
97C22×D281C2×D414yes—
98C22×D281C2×D412yes—
99C22×D281#4112yescomplemented
100Dic562—28no—
101C22⋊D281—216no—
102C22⋊D281—48no—
103C2×Dic281—216no—
104C2×Dic281—22no—
105C2×Dic281—22no—
106C2×Dic281—22no—
107C2×Dic281—21no—
108C2×Dic281—22no—
109C2×Dic281—22no—
110C2×Dic281—22no—
111C2×Dic281—22no—
112C2×Dic281C2×D412yes—
113C2×Dic281C2×D414yes—
114C4×D281—28no—
115C4×D281—44no—
116C23×C281—21no—
117C23×C281—22no—
118C23×C281—22no—
119C23×C281—22no—
120C23×C281—22no—
121C23×C281—22no—
122C23×C281—21no—
123C23×C281—22no—
124C23×C281—22no—
125C23×C281—22no—
126C23×C281C2×D414yes—
127C23×C281#4112yescomplemented
128C23×C281C2411yescharacteristic
129D4×C281—28no—
130D4×C281—48no—
131C2×C4×C281—22no—
132C2×C4×C281—21no—
133C2×C4×C281—22no—
134C2×C4×C281—22no—
135C2×C4×C281—22no—
136C2×C4×C281—22no—
137C2×C4×C281C2×D412yes—
138C22×C281—24no—
139C22×C281—22no—
140C22×C281—24no—
141C22×C281—24no—
142C22×C281—24no—
143C22×C281—41no—
144C22×C281—42no—
145C22×C281—42no—
146C22×C281—41no—
147C22×C281—42no—
148C22×C281—42no—
149C22×C281—42no—
150C22×C281C22×D411yescharacteristic
151C22×C281C22×D412yes—
152C22×C281C2×#4111yescharacteristic
153C22×C281C2×#4111yescharacteristic
154C22×C281H(5,𝔽2)12yes—
155C2×D281—22no—
156C2×D281—22no—
157C2×D281—24no—
158C2×D281—24no—
159C2×D281—22no—
160C2×D281—24no—
161C2×D281—416no—
162C2×D281—41no—
163C2×D281—41no—
164C2×D281—42no—
165C2×D281#12014yes—
166C4×C281—22no—
167C4×C281—41no—
168C4×C281—42no—
169Dic281—22no—
170Dic281—24no—
171Dic281—41no—
172Dic281—42no—
173C2×C281—42no—
174C2×C281—44no—
175C2×C281C2×#12011yescharacteristic
176C2×C281#52511yescharacteristic
177C2×C281#53511yescharacteristic
178C2×C281#54612yes—
179C2×C281#54612yes—
180D281—24no—
181D281—42no—
182C281#240411yescharacteristic, complemented, Sylow
183#2404—2811nomaximal, Sylow
184C22×#41—2811no—
185C2×#120—2812no—
186C22×C22⋊C4—2811no—
187#393—2811no—
188#393—2811no—
189#392—2811no—
190#392D28111yescharacteristic, complemented
191#386—2812no—
192#386—2812no—
193#386—2812no—
194#381—2811no—
195C25—2811no—
196C2×#41—5624no—
197C2×#41—5628no—
198C22×Q8—2811no—
199C22×D4—2812no—
200C22×D4—2812no—
201C22×D4C2×D28112yes—
202C22×D4C2×D28111yescharacteristic, complemented
203C23×C4—2811no—
204C23×C4—2812no—
205C23×C4—2811no—
206#120—5628no—
207C2×C22⋊C4—2811no—
208C2×C22⋊C4—2812no—
209C2×C22⋊C4—2811no—
210C2×C22⋊C4—2811no—
211C2×C22⋊C4—2812no—
212C2×C22⋊C4—2812no—
213C2×C22⋊C4—2812no—
214C2×C22⋊C4—5624no—
215C2×C22⋊C4C2×D28111yescharacteristic
216C2×C22⋊C4C2×D28112yescomplemented
217#95—2812no—
218#95—2811no—
219#95—2812no—
220#95—2812no—
221#95C2×D28111yescharacteristic, complemented
222C24—2811no—
223C24—2811no—
224C24—5622no—
225C24—5622no—
226C24—5624no—
227C24—5622no—
228C24—11242no—
229C24C22×D28112yes—
230C24C22×D28111yescharacteristic
231#41—56232no—
232C2×Q8—5624no—
233C2×Q8—5622no—
234C2×D4—24no—
235C2×D4—24no—
236C2×D4—24no—
237C2×D4—22no—
238C2×D4—42no—
239C2×D4—2818no—
240C2×D4—5624no—
241C2×D4—5624no—
242C2×D4—5624no—
243C2×D4—5624no—
244C2×D4—11242no—
245C22×C4—2811no—
246C22×C4—2812no—
247C22×C4—2814no—
248C22×C4—2812no—
249C22×C4—2811no—
250C22×C4—5624no—
251C22×C4—5622no—
252C22×C4—5624no—
253C22×C4—5624no—
254C22×C4—5624no—
255C22×C4—11242no—
256C22×C4C22×D28112yes—
257C22×C4C22×D28111yescharacteristic
258C22×C4C22×D28111yescharacteristic
259C22⋊C4—22no—
260C22⋊C4—42no—
261C22⋊C4—5622no—
262C22⋊C4—5624no—
263C22⋊C4—5624no—
264C22⋊C4—5622no—
265C22⋊C4—5624no—
266C22⋊C4—5622no—
267C22⋊C4—11242no—
268C23—21no—
269C23—22no—
270C23—22no—
271C23—22no—
272C23—22no—
273C23—21no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—2814no—
279C23—2812no—
280C23—2812no—
281C23—5628no—
282C23—5621no—
283C23—5621no—
284C23—5622no—
285C23—5621no—
286C23—5622no—
287C23—5621no—
288C23—5622no—
289C23—11248no—
290C23—11244no—
291C23—11248no—
292C23—11244no—
293C23D4×D28114yes—
294C23#1798513712yescomplemented
295C23C23×D28111yescharacteristic
296Q8—5628no—
297D4—28no—
298D4—48no—
299D4—56216no—
300D4—11248no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—2812no—
308C2×C4—2814no—
309C2×C4—5628no—
310C2×C4—56216no—
311C2×C4—5622no—
312C2×C4—5622no—
313C2×C4—5622no—
314C2×C4—5621no—
315C2×C4—5622no—
316C2×C4—5622no—
317C2×C4—5622no—
318C2×C4—5622no—
319C2×C4—11244no—
320C2×C4D4×D28112yes—
321C22—24no—
322C22—22no—
323C22—24no—
324C22—24no—
325C22—24no—
326C22—41no—
327C22—42no—
328C22—41no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—2814no—
334C22—5622no—
335C22—5622no—
336C22—5624no—
337C22—5624no—
338C22—5622no—
339C22—5624no—
340C22—112416no—
341C22—11241no—
342C22—11241no—
343C22—11242no—
344C22C2×D4×D28111yescharacteristic
345C22C2×D4×D28112yes—
346C22#41×D28111yescharacteristic
347C22C2×#1798513711yescharacteristic
348C22#2258292412yes—
349C4—22no—
350C4—41no—
351C4—42no—
352C4—5622no—
353C4—5624no—
354C4—11241no—
355C4—11242no—
356C2—42no—
357C2—44no—
358C2—5624no—
359C2—11242no—
360C2#120×D28111yescharacteristic
361C2#3182397311yescharacteristic
362C2#3182402611yescharacteristic
363C2#3182410012yes—
364C2#3182410212yes—
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#392×C281C2
hypercenter#392D281
hypocenterC281#2404
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#17985137C2semidirect
2. C2×#22582847C2semidirect
3. C2×C22⋊C4×D281C2semidirect
4. #31823376C2semidirect
5. #31823375C2semidirect
6. #31823371C2semidirect
7. #31823343C2semidirect
8. #31823340C2semidirect
9. #31823339C2semidirect
10. #31823325C2semidirect
11. #392×C281C2semidirect
15. C22×Dic562C22semidirect
18. C23×Dic281C22semidirect
24. C2×C22⋊Dic281C22semidirect
30. #22582786C22semidirect
31. #22582786C22semidirect
32. #22582786C22semidirect
33. #22582786C22semidirect
35. C22×D4×C281C22semidirect
37. C2×C22⋊C4×C281C22semidirect
38. #95×C281C22semidirect
54. C2×C22⋊D281D4semidirect
65. C2×C4×D281D4semidirect
99. C22×D281#41semidirect
127. C23×C281#41semidirect
182. C281#2404semidirect
190. #392D281semidirect
202. C22×D4C2×D281semidirect
216. C2×C22⋊C4C2×D281semidirect
221. #95C2×D281semidirect
294. C23#17985137semidirect

Maximal subgroups

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

subgroupindex
C22×#179851372
C2×#225828472
C2×C22⋊C4×D2812
#318233762
#318233752
#318233712
#318233432
#318233402
#318233392
#318233252
#392×C2812
#2404281