Finite Group Databasebeta

← #49097907

Subgroups — #49097907

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×#22582835C211yesmaximal, characteristic
2#31823357C211yesmaximal, characteristic
3#31823356C211yesmaximal, characteristic
4#31823351C211yesmaximal, characteristic
5#31823350C211yesmaximal, characteristic, complemented
6#31823347C211yesmaximal, characteristic, complemented
7#31823345C211yesmaximal, characteristic, complemented
8#31823344C211yesmaximal, characteristic, complemented
9#31823332C211yesmaximal, characteristic, complemented
10#31823327C211yesmaximal, characteristic, complemented
11#31823321C211yesmaximal, characteristic
12#31823321C211yesmaximal, characteristic
13C4×#17985117C211yesmaximal, characteristic, complemented
14#31823314C211yesmaximal, characteristic, complemented
15#388×C281C211yesmaximal, characteristic
16C23×Dic281C2211yescharacteristic
17#22582835C418yescomplemented
18C2×C4⋊Dic281C2211yescharacteristic
19C2×#17985117C2211yescharacteristic
20C2×#17985117C2211yescharacteristic
21C2×#17985117C2211yescharacteristic
22C2×#17985117C2211yescharacteristic
23C2×#17985117C2211yescharacteristic
24C2×#17985117C2211yescharacteristic
25C2×#17985117C2211yescharacteristic
26C2×#17985117C2211yescharacteristic
27C2×C22⋊Dic281C2211yescharacteristic
28C2×C22⋊Dic281C2211yescharacteristic
29C2×C22⋊Dic281C2211yescharacteristic
30C2×C4×Dic281C2211yescharacteristic
31C2×C4×Dic281C2211yescharacteristic
32C2×C4×Dic281C2211yescharacteristic
33C2×C4×Dic281C2211yescharacteristic
34C2×C4×Dic281C2211yescharacteristic
35#22582786C2211yescharacteristic
36#22582786C2211yescharacteristic
37#22582786C2211yescharacteristic
38#22582786C2211yescharacteristic
39#22582786C2211yescharacteristic
40#22582786C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45C2×C4⋊C4×C281C2211yescharacteristic
46C2×C22⋊C4×C281C2211yescharacteristic
47C2×C22⋊C4×C281C2211yescharacteristic
48C2×C22⋊C4×C281C2211yescharacteristic
49C2×C42×C281C2211yescharacteristic
50#95×C281C2211yescharacteristic
51#95×C281C2211yescharacteristic
52C22×Dic281—22no—
53C22×Dic281—22no—
54C22×Dic281C2×C414yes—
55C22×Dic281C2311yescharacteristic
56C22×Dic281C2311yescharacteristic
57C22×Dic281C2311yescharacteristic
58C22×Dic281C2311yescharacteristic
59C22×Dic281C2311yescharacteristic
60C22×Dic281C2311yescharacteristic
61C22×Dic281C2311yescharacteristic
62C22×Dic281C2311yescharacteristic
63C4⋊Dic281—41no—
64#17985117—22no—
65#17985117—22no—
66#17985117—22no—
67#17985117—22no—
68#17985117—41no—
69#17985117—41no—
70#17985117C2×C414yes—
71#17985117C2×C414yes—
72C22⋊Dic281—41no—
73C22⋊Dic281—41no—
74C22⋊Dic281C2×C414yes—
75C4×Dic281—41no—
76C4×Dic281—41no—
77C4×Dic281—41no—
78C4×Dic281C2×C414yes—
79C4×Dic281C2×C414yes—
80C24×C281C2311yescharacteristic
81C22×C4×C281C2311yescharacteristic
82C22×C4×C281C2311yescharacteristic
83C22×C4×C281C2311yescharacteristic
84C22×C4×C281C2311yescharacteristic
85C22×C4×C281C2311yescharacteristic
86C22×C4×C281C2311yescharacteristic
87C4⋊C4×C281—41no—
88C22⋊C4×C281—41no—
89C22⋊C4×C281—41no—
90C22⋊C4×C281C2×C414yes—
91C42×C281—41no—
92C2×Dic281—21no—
93C2×Dic281—21no—
94C2×Dic281—21no—
95C2×Dic281—21no—
96C2×Dic281—21no—
97C2×Dic281—21no—
98C2×Dic281—28no—
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×Dic281C22×C412yes—
112C2×Dic281C22×C412yes—
113C2×Dic281C22×C412yes—
114C2×Dic281C22×C412yes—
115C2×Dic281#4112yes—
116C2×Dic281#4112yes—
117C23×C281—21no—
118C23×C281—21no—
119C23×C281—21no—
120C23×C281—21no—
121C23×C281—21no—
122C23×C281—21no—
123C23×C281C22×C412yes—
124C23×C281C2411yescharacteristic
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×C281—21no—
141C2×C4×C281C22×C412yes—
142C2×C4×C281C22×C412yes—
143C22×C281—22no—
144C22×C281—22no—
145C22×C281—22no—
146C22×C281—41no—
147C22×C281—41no—
148C22×C281—41no—
149C22×C281—41no—
150C22×C281C23×C411yescharacteristic
151C22×C281C2×#4111yescharacteristic
152C22×C281C2×#4111yescharacteristic
153C22×C281H(5,𝔽2)11yescharacteristic
154C22×C281H(5,𝔽2)11yescharacteristic
155C22×C2812−1+411yescharacteristic
156C22×C2812−1+411yescharacteristic
157C4×C281—22no—
158C4×C281—22no—
159C4×C281—41no—
160C4×C281—41no—
161C4×C281—41no—
162C4×C281—41no—
163Dic281—22no—
164Dic281—22no—
165Dic281—22no—
166Dic281—41no—
167Dic281—41no—
168Dic281—41no—
169Dic281—41no—
170Dic281#11714yes—
171C2×C281—42no—
172C2×C281C2×#11711yescharacteristic
173C2×C281#52011yescharacteristic
174C2×C281#52011yescharacteristic
175C2×C281#54011yescharacteristic
176C2×C281#54111yescharacteristic
177C2×C281#54211yescharacteristic
178C2×C281#54211yescharacteristic
179C281#231411yescharacteristic, complemented, Sylow
180#2314—2811nomaximal, Sylow
181C2×#117—2811no—
182#388—2811no—
183#388—2811no—
184#388—2811no—
185#388D28111yescharacteristic
186#387—2811no—
187#387—2811no—
188#387—2811no—
189#387—2811no—
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⋊C4—2811no—
207C2×C4⋊C4C2×D28111yescharacteristic
208C2×C22⋊C4—2811no—
209C2×C22⋊C4—2811no—
210C2×C22⋊C4—2811no—
211C2×C22⋊C4C2×D28111yescharacteristic
212C2×C22⋊C4C2×D28111yescharacteristic
213C2×C22⋊C4C2×D28111yescharacteristic
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#95—2811no—
229#95—2811no—
230#95C2×D28111yescharacteristic
231#95C2×D28111yescharacteristic
232C24C22×D28111yescharacteristic
233C22×C4—2811no—
234C22×C4—2814no—
235C22×C4—2811no—
236C22×C4—2811no—
237C22×C4—2811no—
238C22×C4—2811no—
239C22×C4—2811no—
240C22×C4—2811no—
241C22×C4—2811no—
242C22×C4—5622no—
243C22×C4—5622no—
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—2814no—
253C4⋊C4—5622no—
254C4⋊C4—5622no—
255C4⋊C4—5622no—
256C4⋊C4—5622no—
257C4⋊C4—11241no—
258C4⋊C4—11241no—
259C4⋊C4—11241no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—2814no—
263C22⋊C4—11241no—
264C22⋊C4—11241no—
265C22⋊C4C4×D28114yes—
266C42—41no—
267C42—2814no—
268C42—2814no—
269C42—11241no—
270C42—11241no—
271C42—11241no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D28112yes—
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—2812no—
297C2×C4—2812no—
298C2×C4—2812no—
299C2×C4—2812no—
300C2×C4—2812no—
301C2×C4—2812no—
302C2×C4—5628no—
303C2×C4—5621no—
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×C4—5621no—
321C2×C4C2×C4×D28112yes—
322C2×C4C2×C4×D28112yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D28111yescharacteristic
331C22#41×D28111yescharacteristic
332C22#41×D28111yescharacteristic
333C22#2258292411yescharacteristic
334C22#2258292411yescharacteristic
335C22#2258292611yescharacteristic
336C22#2258292611yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2814no—
344C4—5622no—
345C4—5622no—
346C4—5622no—
347C4—11241no—
348C4—11241no—
349C4—11241no—
350C4—11241no—
351C2—42no—
352C2#117×D28111yescharacteristic
353C2#3182394211yescharacteristic
354C2#3182394211yescharacteristic
355C2#3182406311yescharacteristic
356C2#3182407011yescharacteristic
357C2#3182407711yescharacteristic
358C2#3182408111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#388×C281C2
socle, cosocleC23×C281C24
prime radicalC24×C281C23
hypercenter#388D281
hypocenterC281#2314
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
5. #31823350C2semidirect
6. #31823347C2semidirect
7. #31823345C2semidirect
8. #31823344C2semidirect
9. #31823332C2semidirect
10. #31823327C2semidirect
13. C4×#17985117C2semidirect
14. #31823314C2semidirect
17. #22582835C4semidirect
179. C281#2314semidirect

Maximal subgroups

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

subgroupindex
C2×#225828352
#318233572
#318233562
#318233512
#318233502
#318233472
#318233452
#318233442
#318233322
#318233272
#318233212
C4×#179851172
#318233142
#388×C2812
#2314281