Finite Group Databasebeta

← #49097909

Subgroups — #49097909

Order 35968.

484 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22582837C211yesmaximal, characteristic
2#31823355C211yesmaximal, characteristic
3#31823354C211yesmaximal, characteristic
4#31823353C211yesmaximal, characteristic
5#31823352C211yesmaximal, characteristic
6#31823349C211yesmaximal, characteristic, complemented
7#31823348C211yesmaximal, characteristic, complemented
8#31823346C211yesmaximal, characteristic, complemented
9#31823332C211yesmaximal, characteristic, complemented
10#31823327C211yesmaximal, characteristic, complemented
11#31823322C211yesmaximal, characteristic
12#31823322C211yesmaximal, characteristic
13C4×#17985117C211yesmaximal, characteristic, complemented
14#31823314C211yesmaximal, characteristic, complemented
15#387×C281C211yesmaximal, characteristic, complemented
16C22×C4×D281C2211yescharacteristic
17#22582837C418yescomplemented
18C2×C4⋊Dic281C2211yescharacteristic
19C2×C4⋊Dic281C2211yescharacteristic
20C2×#17985117C2211yescharacteristic
21C2×#17985117C2211yescharacteristic
22C2×#17985117C2211yescharacteristic
23C2×#17985117C2211yescharacteristic
24C2×#17985117C2211yescharacteristic
25C2×#17985117C2211yescharacteristic
26C2×#17985115C2211yescharacteristic
27C2×#17985115C2211yescharacteristic
28C2×#17985115C2211yescharacteristic
29C2×#17985115C2211yescharacteristic
30C2×#17985115C2211yescharacteristic
31C2×#17985115C2211yescharacteristic
32C2×C4×Dic281C2211yescharacteristic
33C2×C4×Dic281C2211yescharacteristic
34C2×C4×Dic281C2211yescharacteristic
35C2×C4×Dic281C2211yescharacteristic
36C2×C4×Dic281C2211yescharacteristic
37#22582786C2211yescharacteristic
38#22582786C2211yescharacteristic
39#22582786C2211yescharacteristic
40#22582786C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45C2×C4⋊C4×C281C2211yescharacteristic
46C2×C4⋊C4×C281C2211yescharacteristic
47C2×C42×C281C2211yescharacteristic
48#95×C281C2211yescharacteristic
49#95×C281C2211yescharacteristic
50#95×C281C2211yescharacteristic
51#95×C281C2211yescharacteristic
52C23×D281C2311yescharacteristic
53C22×Dic281C2311yescharacteristic
54C22×Dic281C2311yescharacteristic
55C22×Dic281C2311yescharacteristic
56C22×Dic281C2311yescharacteristic
57C22×Dic281C2311yescharacteristic
58C22×Dic281C2311yescharacteristic
59C22×Dic281C2311yescharacteristic
60C2×C4×D281—22no—
61C2×C4×D281—22no—
62C2×C4×D281C2×C414yes—
63C4⋊Dic281—41no—
64C4⋊Dic281C2×C414yes—
65#17985117—22no—
66#17985117—22no—
67#17985117—22no—
68#17985117—22no—
69#17985117—41no—
70#17985117—41no—
71#17985115—41no—
72#17985115—41no—
73#17985115—41no—
74#17985115—41no—
75#17985115C2×C414yes—
76#17985115C2×C414yes—
77C4×Dic281—41no—
78C4×Dic281—41no—
79C4×Dic281—41no—
80C4×Dic281C2×C414yes—
81C4×Dic281C2×C414yes—
82C22×C4×C281C2311yescharacteristic
83C22×C4×C281C2311yescharacteristic
84C22×C4×C281C2311yescharacteristic
85C22×C4×C281C2311yescharacteristic
86C22×C4×C281C2311yescharacteristic
87C22×C4×C281C2311yescharacteristic
88C22×C4×C281C2311yescharacteristic
89C4⋊C4×C281—41no—
90C4⋊C4×C281C2×C414yes—
91C42×C281—41no—
92C22×D281—21no—
93C22×D281—21no—
94C22×D281—21no—
95C22×D281—21no—
96C22×D281—21no—
97C22×D281—21no—
98C22×D281C22×C412yes—
99C2×Dic281—21no—
100C2×Dic281—21no—
101C2×Dic281—21no—
102C2×Dic281—21no—
103C2×Dic281—21no—
104C2×Dic281—21no—
105C2×Dic281—21no—
106C2×Dic281—21no—
107C2×Dic281—21no—
108C2×Dic281—21no—
109C2×Dic281—21no—
110C2×Dic281—21no—
111C2×Dic281—21no—
112C2×Dic281—21no—
113C2×Dic281—21no—
114C2×Dic281—21no—
115C2×Dic281C22×C412yes—
116C2×Dic281C22×C412yes—
117C2×Dic281C22×C412yes—
118C2×Dic281#4112yes—
119C2×Dic281#4112yes—
120C4×D281—28no—
121C23×C281C2411yescharacteristic
122C2×C4×C281—21no—
123C2×C4×C281—21no—
124C2×C4×C281—21no—
125C2×C4×C281—21no—
126C2×C4×C281—21no—
127C2×C4×C281—21no—
128C2×C4×C281—21no—
129C2×C4×C281—21no—
130C2×C4×C281—21no—
131C2×C4×C281—21no—
132C2×C4×C281—21no—
133C2×C4×C281—21no—
134C2×C4×C281—21no—
135C2×C4×C281—21no—
136C2×C4×C281—21no—
137C2×C4×C281—21no—
138C2×C4×C281—21no—
139C2×C4×C281—21no—
140C2×C4×C281C22×C412yes—
141C2×C4×C281C22×C412yes—
142C2×C4×C281C22×C412yes—
143C22×C281C23×C411yescharacteristic
144C22×C281C2×#4111yescharacteristic
145C22×C281C2×#4111yescharacteristic
146C22×C281H(5,𝔽2)11yescharacteristic
147C22×C281H(5,𝔽2)11yescharacteristic
148C22×C2812−1+411yescharacteristic
149C22×C2812−1+411yescharacteristic
150C2×D281—22no—
151C2×D281—22no—
152C2×D281—22no—
153C2×D281—41no—
154C2×D281—41no—
155C2×D281—41no—
156C2×D281—41no—
157C4×C281—22no—
158C4×C281—22no—
159C4×C281—22no—
160C4×C281—41no—
161C4×C281—41no—
162C4×C281—41no—
163C4×C281—41no—
164Dic281—22no—
165Dic281—22no—
166Dic281—41no—
167Dic281—41no—
168Dic281—41no—
169Dic281—41no—
170Dic281#11714yes—
171C2×C281C2×#11711yescharacteristic
172C2×C281#52011yescharacteristic
173C2×C281#52011yescharacteristic
174C2×C281#54011yescharacteristic
175C2×C281#54111yescharacteristic
176C2×C281#54211yescharacteristic
177C2×C281#54211yescharacteristic
178D281—42no—
179C281#231411yescharacteristic, complemented, Sylow
180#2314—2811nomaximal, Sylow
181C2×#117—2811no—
182#388—2811no—
183#388—2811no—
184#388—2811no—
185#388—2811no—
186#387—2811no—
187#387—2811no—
188#387—2811no—
189#387D28111yescharacteristic, complemented
190#384—2811no—
191#382—2811no—
192#380—2811no—
193#380—2811no—
194C4×C4⋊C4—2811no—
195C4×C4⋊C4—2811no—
196C23×C4—2811no—
197#117—2818no—
198C2×C4⋊C4—2811no—
199C2×C4⋊C4—2811no—
200C2×C4⋊C4—2811no—
201C2×C4⋊C4—2811no—
202C2×C4⋊C4—2811no—
203C2×C4⋊C4—2811no—
204C2×C4⋊C4—2811no—
205C2×C4⋊C4—2811no—
206C2×C4⋊C4C2×D28111yescharacteristic
207C2×C4⋊C4C2×D28111yescharacteristic
208C2×C22⋊C4—2811no—
209C2×C22⋊C4—2811no—
210C2×C22⋊C4—2811no—
211C2×C22⋊C4—2811no—
212C2×C22⋊C4—2811no—
213C2×C22⋊C4—2811no—
214C2×C42—2811no—
215C2×C42—2811no—
216C2×C42—2811no—
217C2×C42—2811no—
218C2×C42—2811no—
219C2×C42C2×D28111yescharacteristic
220#95—2811no—
221#95—2811no—
222#95—2811no—
223#95—2811no—
224#95—2811no—
225#95—2811no—
226#95—2811no—
227#95—2811no—
228#95C2×D28111yescharacteristic
229#95C2×D28111yescharacteristic
230#95C2×D28111yescharacteristic
231#95C2×D28111yescharacteristic
232C24—2811no—
233C22×C4—2811no—
234C22×C4—2811no—
235C22×C4—2811no—
236C22×C4—2814no—
237C22×C4—2811no—
238C22×C4—2811no—
239C22×C4—2811no—
240C22×C4—2811no—
241C22×C4—5622no—
242C22×C4—5622no—
243C22×C4C22×D28111yescharacteristic
244C22×C4C22×D28111yescharacteristic
245C22×C4C22×D28111yescharacteristic
246C22×C4C22×D28111yescharacteristic
247C22×C4C22×D28111yescharacteristic
248C22×C4C22×D28111yescharacteristic
249C22×C4C22×D28111yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—2814no—
252C4⋊C4—5622no—
253C4⋊C4—5622no—
254C4⋊C4—5622no—
255C4⋊C4—5622no—
256C4⋊C4—11241no—
257C4⋊C4—11241no—
258C4⋊C4—11241no—
259C4⋊C4C4×D28114yes—
260C22⋊C4—2814no—
261C22⋊C4—2814no—
262C22⋊C4—11241no—
263C22⋊C4—11241no—
264C22⋊C4—11241no—
265C22⋊C4—11241no—
266C42—41no—
267C42—2814no—
268C42—2814no—
269C42—11241no—
270C42—11241no—
271C42—11241no—
272C23—2812no—
273C23—5621no—
274C23—5621no—
275C23—5621no—
276C23—5621no—
277C23—5621no—
278C23—5621no—
279C23C23×D28111yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—2812no—
299C2×C4—2812no—
300C2×C4—2812no—
301C2×C4—2812no—
302C2×C4—2812no—
303C2×C4—5628no—
304C2×C4—5621no—
305C2×C4—5621no—
306C2×C4—5621no—
307C2×C4—5621no—
308C2×C4—5621no—
309C2×C4—5621no—
310C2×C4—5621no—
311C2×C4—5621no—
312C2×C4—5621no—
313C2×C4—5621no—
314C2×C4—5621no—
315C2×C4—5621no—
316C2×C4—5621no—
317C2×C4—5621no—
318C2×C4—5621no—
319C2×C4—5621no—
320C2×C4C2×C4×D28112yes—
321C2×C4C2×C4×D28112yes—
322C2×C4C2×C4×D28112yes—
323C22—5622no—
324C22—5622no—
325C22—5622no—
326C22—11241no—
327C22—11241no—
328C22—11241no—
329C22—11241no—
330C22C22×C4×D28111yescharacteristic
331C22#41×D28111yescharacteristic
332C22#41×D28111yescharacteristic
333C22#2258292411yescharacteristic
334C22#2258292511yescharacteristic
335C22#2258292611yescharacteristic
336C22#2258292711yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—2814no—
345C4—5622no—
346C4—5622no—
347C4—11241no—
348C4—11241no—
349C4—11241no—
350C4—11241no—
351C2—11242no—
352C2#117×D28111yescharacteristic
353C2#3182394211yescharacteristic
354C2#3182394511yescharacteristic
355C2#3182406511yescharacteristic
356C2#3182407211yescharacteristic
357C2#3182407911yescharacteristic
358C2#3182408311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#387×C281C2
socle, cosocleC23×C281C24
prime radicalC23×D281C23
hypercenter#387D281
hypocenterC281#2314
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
6. #31823349C2semidirect
7. #31823348C2semidirect
8. #31823346C2semidirect
9. #31823332C2semidirect
10. #31823327C2semidirect
13. C4×#17985117C2semidirect
14. #31823314C2semidirect
15. #387×C281C2semidirect
17. #22582837C4semidirect
179. C281#2314semidirect
189. #387D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828372
#318233552
#318233542
#318233532
#318233522
#318233492
#318233482
#318233462
#318233322
#318233272
#318233222
C4×#179851172
#318233142
#387×C2812
#2314281