Finite Group Databasebeta

← #49097902

Subgroups — #49097902

Order 35968.

512 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×C4⋊C4×D281C211yesmaximal, characteristic
2#31823350C211yesmaximal, characteristic, complemented
3#31823349C211yesmaximal, characteristic, complemented
4#31823348C211yesmaximal, characteristic, complemented
5#31823347C211yesmaximal, characteristic, complemented
6#31823346C211yesmaximal, characteristic, complemented
7#31823345C211yesmaximal, characteristic, complemented
8#31823344C211yesmaximal, characteristic, complemented
9#31823325C211yesmaximal, characteristic
10#31823325C211yesmaximal, characteristic
11#31823322C211yesmaximal, characteristic
12#31823320C211yesmaximal, characteristic
13C4×#17985115C211yesmaximal, characteristic
14#31823310C211yesmaximal, characteristic
15#387×C281C211yesmaximal, characteristic, complemented
16C22×C4×D281C2211yescharacteristic
17C22×C4×D281C2211yescharacteristic
18C22×C4×D281C2211yescharacteristic
19C2×C4⋊Dic281C2211yescharacteristic
20C2×C4⋊Dic281C2211yescharacteristic
21C2×#17985117C2211yescharacteristic
22C2×#17985117C2211yescharacteristic
23C2×#17985117C2211yescharacteristic
24C2×#17985117C2211yescharacteristic
25C4⋊C4×D281C418yescomplemented
26C2×#17985115C2211yescharacteristic
27C2×#17985115C2211yescharacteristic
28C2×#17985115C2211yescharacteristic
29C2×#17985115C2211yescharacteristic
30C2×C4×Dic281C2211yescharacteristic
31C2×C4×Dic281C2211yescharacteristic
32C2×C4×Dic281C2211yescharacteristic
33#22582786C2211yescharacteristic
34#22582786C2211yescharacteristic
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×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×D281—41no—
63C2×C4×D281—41no—
64C2×C4×D281—41no—
65C2×C4×D281—41no—
66C2×C4×D281C2×C414yes—
67C2×C4×D281C2×C414yes—
68C2×C4×D281C2×C414yes—
69C4⋊Dic281—41no—
70C4⋊Dic281C2×C414yes—
71#17985117—41no—
72#17985117—41no—
73#17985117C2×C414yes—
74#17985117C2×C414yes—
75#17985115—22no—
76#17985115—22no—
77#17985115—22no—
78#17985115—22no—
79C4×Dic281—41no—
80C4×Dic281—41no—
81C4×Dic281—41no—
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×D281C22×C412yes—
97C22×D281#4112yes—
98C22×D281#4112yes—
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×Dic281—21no—
116C2×Dic281—21no—
117C2×Dic281C22×C412yes—
118C2×Dic281C22×C412yes—
119C2×Dic281C22×C412yes—
120C4×D281—28no—
121C4×D281—44no—
122C4×D281—44no—
123C23×C281C2411yescharacteristic
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×C281—21no—
141C2×C4×C281—21no—
142C2×C4×C281C22×C412yes—
143C2×C4×C281C22×C412yes—
144C2×C4×C281C22×C412yes—
145C22×C281C23×C411yescharacteristic
146C22×C281C2×#4111yescharacteristic
147C22×C281C2×#4111yescharacteristic
148C22×C281H(5,𝔽2)11yescharacteristic
149C22×C281H(5,𝔽2)11yescharacteristic
150C22×C2812−1+411yescharacteristic
151C22×C2812−1+411yescharacteristic
152C2×D281—22no—
153C2×D281—22no—
154C2×D281—22no—
155C2×D281—22no—
156C2×D281—22no—
157C2×D281—22no—
158C2×D281#11714yes—
159C4×C281—22no—
160C4×C281—22no—
161C4×C281—22no—
162C4×C281—41no—
163C4×C281—41no—
164C4×C281—41no—
165C4×C281—41no—
166Dic281—22no—
167Dic281—22no—
168Dic281—22no—
169Dic281—41no—
170Dic281—41no—
171Dic281—41no—
172Dic281—41no—
173C2×C281C2×#11711yescharacteristic
174C2×C281#51811yescharacteristic
175C2×C281#51911yescharacteristic
176C2×C281#53911yescharacteristic
177C2×C281#53911yescharacteristic
178C2×C281#53911yescharacteristic
179C2×C281#53911yescharacteristic
180D281—24no—
181C281#231311yescharacteristic, complemented, Sylow
182#2313—2811nomaximal, Sylow
183C22×C4⋊C4—2811no—
184#387—2811no—
185#387—2811no—
186#387—2811no—
187#387—2811no—
188#387—2811no—
189#387—2811no—
190#387—2811no—
191#387D28111yescharacteristic, complemented
192#381—2811no—
193#381—2811no—
194#380—2811no—
195#380—2811no—
196C4×C22⋊C4—2811no—
197C4×C22⋊C4—2811no—
198C23×C4—2811no—
199C23×C4—2811no—
200C23×C4—2811no—
201C2×C4⋊C4—2811no—
202C2×C4⋊C4—2811no—
203C2×C4⋊C4—2811no—
204C2×C4⋊C4—2818no—
205C2×C4⋊C4—2811no—
206C2×C4⋊C4—2811no—
207C2×C4⋊C4—2811no—
208C2×C4⋊C4C2×D28111yescharacteristic
209C2×C4⋊C4C2×D28111yescharacteristic
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×C42C2×D28111yescharacteristic
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#95C2×D28111yescharacteristic
231#95C2×D28111yescharacteristic
232#95C2×D28111yescharacteristic
233#95C2×D28111yescharacteristic
234C24—2811no—
235C22×C4—2811no—
236C22×C4—2811no—
237C22×C4—2811no—
238C22×C4—2814no—
239C22×C4—2814no—
240C22×C4—2814no—
241C22×C4—2811no—
242C22×C4—2811no—
243C22×C4—2811no—
244C22×C4—2811no—
245C22×C4—5622no—
246C22×C4—5622no—
247C22×C4—11241no—
248C22×C4—11241no—
249C22×C4—11241no—
250C22×C4—11241no—
251C22×C4C22×D28111yescharacteristic
252C22×C4C22×D28111yescharacteristic
253C22×C4C22×D28111yescharacteristic
254C22×C4C22×D28111yescharacteristic
255C22×C4C22×D28111yescharacteristic
256C22×C4C22×D28111yescharacteristic
257C22×C4C22×D28111yescharacteristic
258C4⋊C4—41no—
259C4⋊C4—2814no—
260C4⋊C4—2814no—
261C4⋊C4—2814no—
262C4⋊C4—11241no—
263C4⋊C4—11241no—
264C4⋊C4—11241no—
265C4⋊C4C4×D28114yes—
266C22⋊C4—5622no—
267C22⋊C4—5622no—
268C22⋊C4—5622no—
269C22⋊C4—5622no—
270C42—41no—
271C42—11241no—
272C42—11241no—
273C42—11241no—
274C23—2812no—
275C23—2812no—
276C23—2812no—
277C23—5621no—
278C23—5621no—
279C23—5621no—
280C23—5621no—
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—21no—
298C2×C4—21no—
299C2×C4—21no—
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—11244no—
323C2×C4—11244no—
324C2×C4C2×C4×D28112yes—
325C2×C4C2×C4×D28112yes—
326C2×C4C2×C4×D28112yes—
327C22—2814no—
328C22—5622no—
329C22—5622no—
330C22—5622no—
331C22—5622no—
332C22—5622no—
333C22—5622no—
334C22C22×C4×D28111yescharacteristic
335C22#41×D28111yescharacteristic
336C22#41×D28111yescharacteristic
337C22#2258292411yescharacteristic
338C22#2258292511yescharacteristic
339C22#2258292611yescharacteristic
340C22#2258292711yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—5622no—
349C4—5622no—
350C4—5622no—
351C4—11241no—
352C4—11241no—
353C4—11241no—
354C4—11241no—
355C2—5624no—
356C2#117×D28111yescharacteristic
357C2#3182393511yescharacteristic
358C2#3182393911yescharacteristic
359C2#3182405411yescharacteristic
360C2#3182405611yescharacteristic
361C2#3182405911yescharacteristic
362C2#3182406111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#387×C281C2
socle, cosocleC23×C281C24
prime radicalC23×D281C23
hypercenter#387D281
hypocenterC281#2313
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #31823350C2semidirect
3. #31823349C2semidirect
4. #31823348C2semidirect
5. #31823347C2semidirect
6. #31823346C2semidirect
7. #31823345C2semidirect
8. #31823344C2semidirect
15. #387×C281C2semidirect
25. C4⋊C4×D281C4semidirect
181. C281#2313semidirect
191. #387D281semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D2812
#318233502
#318233492
#318233482
#318233472
#318233462
#318233452
#318233442
#318233252
#318233222
#318233202
C4×#179851152
#318233102
#387×C2812
#2313281