Finite Group Databasebeta

← #49098161

Subgroups — #49098161

Order 35968.

532 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22582835C211yesmaximal, characteristic
2#31823350C211yesmaximal, characteristic, complemented
3#31823350C211yesmaximal, characteristic, complemented
4#31823344C211yesmaximal, characteristic, complemented
5#31823344C211yesmaximal, characteristic, complemented
6#31823338C211yesmaximal, characteristic
7#31823330C211yesmaximal, characteristic, complemented
8#31823328C211yesmaximal, characteristic, complemented
9#31823324C211yesmaximal, characteristic
10C4⋊C4×Dic281C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic281C211yesmaximal, characteristic
12C4×C22⋊Dic281C211yesmaximal, characteristic
13#31823308C211yesmaximal, characteristic, complemented
14C2×#22582786C211yesmaximal, characteristic
15#385×C281C211yesmaximal, characteristic
16C23×Dic281C2211yescharacteristic
17C23×Dic281C2211yescharacteristic
18#22582835C418yescomplemented
19C2×C4⋊Dic281C2211yescharacteristic
20C2×C4⋊Dic281C2211yescharacteristic
21C2×#17985117C2211yescharacteristic
22C2×#17985117C2211yescharacteristic
23C2×C22⋊Dic281C2211yescharacteristic
24C2×C22⋊Dic281C2211yescharacteristic
25C2×C4×Dic281C2211yescharacteristic
26C2×C4×Dic281C2211yescharacteristic
27C2×C4×Dic281C2211yescharacteristic
28C2×C4×Dic281C2211yescharacteristic
29C2×C4×Dic281C2211yescharacteristic
30C2×C4×Dic281C2211yescharacteristic
31#22582786C2211yescharacteristic
32#22582786C2211yescharacteristic
33#22582786C2211yescharacteristic
34#22582786C2211yescharacteristic
35#22582786C2211yescharacteristic
36#22582786C2211yescharacteristic
37#22582786C2211yescharacteristic
38#22582786C2211yescharacteristic
39#22582786C2211yescharacteristic
40#22582786C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45C23×C4×C281C2211yescharacteristic
46C2×C4⋊C4×C281C2211yescharacteristic
47C2×C4⋊C4×C281C2211yescharacteristic
48C2×C22⋊C4×C281C2211yescharacteristic
49C2×C22⋊C4×C281C2211yescharacteristic
50#95×C281C2211yescharacteristic
51#95×C281C2211yescharacteristic
52C22×Dic281—22no—
53C22×Dic281—22no—
54C22×Dic281—22no—
55C22×Dic281—22no—
56C22×Dic281—41no—
57C22×Dic281C2×C414yes—
58C22×Dic281C2311yescharacteristic
59C22×Dic281C2311yescharacteristic
60C22×Dic281C2311yescharacteristic
61C22×Dic281C2311yescharacteristic
62C22×Dic281C2311yescharacteristic
63C22×Dic281C2311yescharacteristic
64C22×Dic281C2311yescharacteristic
65C22×Dic281C2311yescharacteristic
66C4⋊Dic281—22no—
67C4⋊Dic281—41no—
68#17985117C2×C414yescomplemented
69#17985117C2×C414yescomplemented
70C22⋊Dic281—22no—
71C22⋊Dic281C2×C414yes—
72C4×Dic281—22no—
73C4×Dic281—22no—
74C4×Dic281—41no—
75C4×Dic281—41no—
76C4×Dic281C2×C414yescomplemented
77C4×Dic281C2×C414yescomplemented
78C24×C281C2311yescharacteristic
79C22×C4×C281—22no—
80C22×C4×C281—22no—
81C22×C4×C281—41no—
82C22×C4×C281C2311yescharacteristic
83C22×C4×C281C2311yescharacteristic
84C22×C4×C281C2311yescharacteristic
85C22×C4×C281C2311yescharacteristic
86C22×C4×C281C2311yescharacteristic
87C22×C4×C281C2311yescharacteristic
88C4⋊C4×C281—22no—
89C4⋊C4×C281—41no—
90C22⋊C4×C281—22no—
91C22⋊C4×C281C2×C414yes—
92C2×Dic281—28no—
93C2×Dic281—21no—
94C2×Dic281—21no—
95C2×Dic281—21no—
96C2×Dic281—21no—
97C2×Dic281—21no—
98C2×Dic281—21no—
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—44no—
113C2×Dic281C22×C412yes—
114C2×Dic281C22×C412yes—
115C2×Dic281C22×C412yes—
116C2×Dic281C22×C412yes—
117C2×Dic281#4112yes—
118C23×C281—21no—
119C23×C281—21no—
120C23×C281—21no—
121C23×C281—21no—
122C23×C281C22×C412yes—
123C23×C281#4112yes—
124C23×C281#4112yes—
125C23×C281C2411yescharacteristic
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×C281—44no—
142C2×C4×C281C22×C412yes—
143C2×C4×C281C22×C412yes—
144C2×C4×C281#4112yes—
145C22×C281—22no—
146C22×C281—22no—
147C22×C281—22no—
148C22×C281—22no—
149C22×C281—22no—
150C22×C281—22no—
151C22×C281#11714yes—
152C22×C281C23×C411yescharacteristic
153C22×C281C2×#4111yescharacteristic
154C22×C281C2×#4111yescharacteristic
155C22×C281C2×#4111yescharacteristic
156C22×C281C2×#4111yescharacteristic
157C22×C281H(5,𝔽2)11yescharacteristic
158C22×C2812−1+411yescharacteristic
159C4×C281—22no—
160C4×C281—22no—
161C4×C281—22no—
162C4×C281—41no—
163C4×C281—41no—
164C4×C281—41no—
165Dic281—22no—
166Dic281—22no—
167Dic281—22no—
168Dic281—22no—
169Dic281—22no—
170Dic281—41no—
171Dic281—41no—
172Dic281—41no—
173C2×C281—24no—
174C2×C281C2×#11711yescharacteristic
175C2×C281C4×#4111yescharacteristic
176C2×C281#52011yescharacteristic
177C2×C281#55111yescharacteristic
178C2×C281#55111yescharacteristic
179C2×C281#55211yescharacteristic
180C2×C281#55211yescharacteristic
181C281#234311yescharacteristic, complemented, Sylow
182#2343—2811nomaximal, Sylow
183C2×#117—2811no—
184#387—2811no—
185#387—2811no—
186#387—2811no—
187#387—2811no—
188#385—2811no—
189#385D28111yescharacteristic
190#383—2811no—
191#382—2811no—
192#381—2811no—
193C4×C4⋊C4—2811no—
194C4×C22⋊C4—2811no—
195C4×C22⋊C4—2811no—
196#376—2811no—
197C2×#95—2811no—
198C23×C4—2811no—
199C23×C4—2811no—
200C23×C4C2×D28111yescharacteristic
201#117—2818no—
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⋊C4C2×D28111yescharacteristic
211C2×C22⋊C4C2×D28111yescharacteristic
212C2×C42—2811no—
213C2×C42—2811no—
214C2×C42—2811no—
215C2×C42—2811no—
216C2×C42—2811no—
217C2×C42—2811no—
218#95—2811no—
219#95—2811no—
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#95—2811no—
231#95—2811no—
232#95C2×D28111yescharacteristic
233#95C2×D28111yescharacteristic
234C24C22×D28111yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—2814no—
239C22×C4—2811no—
240C22×C4—2811no—
241C22×C4—2811no—
242C22×C4—2811no—
243C22×C4—2811no—
244C22×C4—2811no—
245C22×C4—2811no—
246C22×C4—2811no—
247C22×C4—5622no—
248C22×C4—5622no—
249C22×C4—5622no—
250C22×C4—5622no—
251C22×C4—11241no—
252C22×C4C22×D28111yescharacteristic
253C22×C4C22×D28111yescharacteristic
254C22×C4C22×D28111yescharacteristic
255C22×C4C22×D28111yescharacteristic
256C22×C4C22×D28111yescharacteristic
257C22×C4C22×D28111yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—2814no—
261C4⋊C4—2814no—
262C4⋊C4—5622no—
263C4⋊C4—11241no—
264C22⋊C4—22no—
265C22⋊C4—2814no—
266C22⋊C4—5622no—
267C22⋊C4C4×D28114yes—
268C42—2814no—
269C42—2814no—
270C42—5622no—
271C42—5622no—
272C42—11241no—
273C42—11241no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D28112yes—
279C23#1798513712yes—
280C23#1798513912yes—
281C23C23×D28111yescharacteristic
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—44no—
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×C4—5621no—
321C2×C4—5621no—
322C2×C4—5621no—
323C2×C4—11244no—
324C2×C4C2×C4×D28112yes—
325C2×C4C2×C4×D28112yes—
326C2×C4#1798513712yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22#2258283714yes—
334C22C22×C4×D28111yescharacteristic
335C22#41×D28111yescharacteristic
336C22C2×#1798513711yescharacteristic
337C22C2×#1798513711yescharacteristic
338C22C2×#1798513911yescharacteristic
339C22#2258292411yescharacteristic
340C22#2258292611yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—5622no—
348C4—5622no—
349C4—5622no—
350C4—5622no—
351C4—5622no—
352C4—11241no—
353C4—11241no—
354C4—11241no—
355C2—24no—
356C2C2×#2258283711yescharacteristic
357C2C4×#1798513711yescharacteristic
358C2#3182394211yescharacteristic
359C2#3182414011yescharacteristic
360C2#3182414411yescharacteristic
361C2#3182415011yescharacteristic
362C2#3182415511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#385×C281C2
socle, cosocleC23×C281C24
prime radicalC24×C281C23
hypercenter#385D281
hypocenterC281#2343
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. #31823350C2semidirect
3. #31823350C2semidirect
4. #31823344C2semidirect
5. #31823344C2semidirect
7. #31823330C2semidirect
8. #31823328C2semidirect
10. C4⋊C4×Dic281C2semidirect
13. #31823308C2semidirect
18. #22582835C4semidirect
68. #17985117C2×C4semidirect
69. #17985117C2×C4semidirect
76. C4×Dic281C2×C4semidirect
77. C4×Dic281C2×C4semidirect
181. C281#2343semidirect

Maximal subgroups

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

subgroupindex
C2×#225828352
#318233502
#318233442
#318233382
#318233302
#318233282
#318233242
C4⋊C4×Dic2812
C22⋊C4×Dic2812
C4×C22⋊Dic2812
#318233082
C2×#225827862
#385×C2812
#2343281