Finite Group Databasebeta

← #49133250

Subgroups — #49133250

Order 36224.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827121C211yesmaximal, characteristic, complemented
2#31827116C211yesmaximal, characteristic, complemented
3#31826823C211yesmaximal, characteristic, complemented
4#31826802C211yesmaximal, characteristic, complemented
5#31826759C211yesmaximal, characteristic, complemented
6#31826712C211yesmaximal, characteristic, complemented
7#31826699C211yesmaximal, characteristic, complemented
8#31826679C211yesmaximal, characteristic, complemented
9#31826611C211yesmaximal, characteristic, complemented
10#31826606C211yesmaximal, characteristic, complemented
11#31826564C211yesmaximal, characteristic, complemented
12#31826533C211yesmaximal, characteristic, complemented
13#31826463C211yesmaximal, characteristic, complemented
14C2×#22583533C211yesmaximal, characteristic, complemented
15#480×C283C211yesmaximal, characteristic, complemented
16C2×#17985392—21no—
17C2×#17985391C2211yescharacteristic
18C22×Dic566C2211yescharacteristic
19C2×#17985381C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21C2×#17985377C2211yescharacteristic
22C2×#17985375C2211yescharacteristic
23C22×C283⋊C8C2211yescharacteristic
24#22583609C2211yescharacteristic
25#22583597C2211yescharacteristic
26#22583596—21no—
27#22583595—21no—
28#22583593—21no—
29#22583590C2211yescharacteristic
30#22583588—21no—
31#22583587—21no—
32#22583585C2211yescharacteristic
33#22583584C2211yescharacteristic
34#22583582—21no—
35#22583575C2211yescharacteristic
36D4×Dic283—21no—
37#22583572C2211yescharacteristic
38C4×C22⋊D283C2211yescharacteristic
39C4⋊C4×D283C2211yescharacteristic
40#22583543C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic
52#121×C283C2211yescharacteristic
53C2×C4⋊C4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59#17985392—44no—
60#17985391—22no—
61#17985391—41no—
62C2×Dic566—21no—
63C2×Dic566—22no—
64C2×Dic566—21no—
65C2×Dic566—41no—
66C2×Dic566C2311yescharacteristic
67C2×Dic566C2311yescharacteristic
68C2×D1132—21no—
69C2×D1132C2311yescharacteristic
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72C2×C22⋊D283D411yescharacteristic
73C22×Dic283—21no—
74C22×Dic283—21no—
75C2×C4×D283—21no—
76C2×C4×D283—21no—
77C2×C4×D283C2311yescharacteristic
78#17985381—22no—
79#17985381—41no—
80#17985377—41no—
81#17985375—41no—
82C2×C283⋊C8—41no—
83C2×C283⋊C8C2311yescharacteristic
84C2×C283⋊C8C2311yescharacteristic
85C4⋊Dic283—21no—
86C4⋊Dic283C2311yescharacteristic
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90Dic283⋊C4D411yescharacteristic
91C22⋊Dic283—21no—
92C22⋊Dic283—21no—
93C22⋊Dic283D411yescharacteristic
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4—21no—
98(C2×D283)⋊C4D411yescharacteristic
99C4×Dic283—21no—
100C4×Dic283C2311yescharacteristic
101C2×D4×C283—21no—
102C2×D4×C283C2311yescharacteristic
103C22×C4×C283—21no—
104C22×C4×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283—21no—
108C4⋊C4×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
111C22⋊C4×C283—21no—
112C22×D283—21no—
113C22×D283C2×D411yescharacteristic
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117Dic566—42no—
118Dic566—42no—
119Dic566#4112yescomplemented
120D1132—21no—
121D1132—21no—
122D1132—42no—
123C22⋊D283—22no—
124C22⋊D283—42no—
125C22⋊D283—42no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—42no—
130C2×Dic283—42no—
131C2×Dic283C2×D411yescharacteristic
132C2×Dic283C2×D411yescharacteristic
133C2×Dic283C2×D411yescharacteristic
134C4×D283—21no—
135C4×D283—21no—
136C4×D283—42no—
137C4×D283—42no—
138C283⋊C8—21no—
139C283⋊C8—21no—
140C23×C283—21no—
141C23×C283C2×D411yescharacteristic
142D4×C283—21no—
143D4×C283—21no—
144D4×C283—42no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—42no—
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2411yescharacteristic
153C8×C283—21no—
154C8×C283—21no—
155C22×C283—21no—
156C22×C283—21no—
157C22×C283—41no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283AGL(1,ℤ/8)12yes—
161C22×C283C22×D411yescharacteristic
162C2×D283—21no—
163C2×D283—21no—
164C2×D283—21no—
165C2×D283—41no—
166C2×D283—41no—
167C2×D283—41no—
168C4×C283—21no—
169C4×C283—41no—
170C4×C283—41no—
171C4×C283—41no—
172C4×C283C2×#4111yescharacteristic
173C4×C283H(5,𝔽2)11yescharacteristic
174Dic283—21no—
175Dic283—22no—
176Dic283—21no—
177Dic283—21no—
178Dic283—41no—
179Dic283—41no—
180C2×C283—22no—
181C2×C283—81no—
182C2×C283#54611yescharacteristic
183C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C283#57811yescharacteristic
185D283—41no—
186D283—81no—
187C283#330811yescharacteristic, complemented, Sylow
188#3308—2831nomaximal, Sylow
189#548—2831no—
190#547—2831no—
191#489—2831no—
192#484—2831no—
193#480D28311yescharacteristic, complemented
194#477—2831no—
195#468—2831no—
196#466—2831no—
197#463—2831no—
198#449—2831no—
199#448—2831no—
200#440—2831no—
201#435—2831no—
202#417—2831no—
203C2×#103—2831no—
204C2×#41—2831no—
205C2×#41—5661no—
206C22×Q8—2831no—
207C2×SD16—2831no—
208C2×SD16—2831no—
209C2×D8—2831no—
210C2×M16—2831no—
211C22×C8—2831no—
212C4⋊Q8—2831no—
213#124—2831no—
214#124—5661no—
215#123—5661no—
216#123—5661no—
217C22⋊Q8—2831no—
218C22⋊Q8—5661no—
219C22⋊Q8—5661no—
220#121—2831no—
221#121—2831no—
222#121—5661no—
223#121C2×D28311yescharacteristic
224C4×Q8—2831no—
225C4×D4—2831no—
226C4×D4—2831no—
227C4×D4—5661no—
228C2×C4⋊C4—2831no—
229C2×C4⋊C4C2×D28311yescharacteristic
230#107—2831no—
231#107C2×D28311yescharacteristic
232#107C2×D28311yescharacteristic
233C4⋊C8—2831no—
234#103—2831no—
235#103—2831no—
236#103—2831no—
237#103—2831no—
238#103—2831no—
239#103—2831no—
240#102—2831no—
241#102—2831no—
242#102C2×D28311yescharacteristic
243#102C2×D28311yescharacteristic
244C22⋊C8—2831no—
245C22⋊C8C2×D28311yescharacteristic
246#97—2831no—
247#41—5662no—
248#41—11324no—
249#41—11321no—
250C2×Q8—2831no—
251C2×Q8—2831no—
252C2×Q8—5661no—
253C2×Q8—5662no—
254C2×Q8—5661no—
255C2×Q8—11321no—
256C2×D4—21no—
257C2×D4—2831no—
258C2×D4—2831no—
259C2×D4—5661no—
260C2×D4—5661no—
261C2×D4—5661no—
262C2×D4C22×D28311yescharacteristic
263C22×C4—21no—
264C22×C4—2831no—
265C22×C4—5661no—
266C22×C4—5661no—
267C22×C4—5661no—
268C22×C4—5661no—
269C22×C4C22×D28311yescharacteristic
270SD16—5662no—
271SD16—11321no—
272D8—11321no—
273M16—11321no—
274C2×C8—2831no—
275C2×C8—2831no—
276C2×C8—11321no—
277C2×C8C22×D28311yescharacteristic
278C2×C8C22×D28311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—2831no—
281C4⋊C4—2831no—
282C4⋊C4—5661no—
283C4⋊C4—5661no—
284C4⋊C4—5661no—
285C4⋊C4—5661no—
286C4⋊C4C22×D28311yescharacteristic
287C4⋊C4C22×D28311yescharacteristic
288C4⋊C4C22×D28311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—2831no—
291C22⋊C4—2831no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C22⋊C4—5661no—
298C42—2831no—
299C42—5661no—
300C23—21no—
301C23—2831no—
302C23—5661no—
303C23D4×D28311yescharacteristic
304Q8—2832no—
305Q8—5661no—
306Q8—5661no—
307Q8—5661no—
308Q8—11322no—
309Q8—11322no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—5662no—
314D4—5661no—
315D4—5661no—
316D4—11322no—
317D4—11322no—
318D4—11322no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—2831no—
326C2×C4—2831no—
327C2×C4—2831no—
328C2×C4—5661no—
329C2×C4—5661no—
330C2×C4—5661no—
331C2×C4—5661no—
332C2×C4—5661no—
333C2×C4—11322no—
334C2×C4—11322no—
335C2×C4—11322no—
336C2×C4—11322no—
337C2×C4D4×D28311yescharacteristic
338C2×C4C23×D28311yescharacteristic
339C8—21no—
340C8—21no—
341C8—5661no—
342C8—5661no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—5661no—
349C22—5661no—
350C22—5661no—
351C22—11321no—
352C22—11321no—
353C22—11321no—
354C22#2258363412yes—
355C22C2×D4×D28311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—5661no—
361C4—5661no—
362C4—5661no—
363C4—5662no—
364C4—11321no—
365C4—11321no—
366C4#41×D28311yescharacteristic
367C4#2258365611yescharacteristic
368C2—22no—
369C2—81no—
370C2—11321no—
371C2—22641no—
372C2#3182710711yescharacteristic
373C2C2×#2258363411yescharacteristic
374C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#480×C283C2
socleC22×C283C22×D4
hypercenter#480D283
hypocenterC283#3308
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #31827121C2semidirect
2. #31827116C2semidirect
3. #31826823C2semidirect
4. #31826802C2semidirect
5. #31826759C2semidirect
6. #31826712C2semidirect
7. #31826699C2semidirect
8. #31826679C2semidirect
9. #31826611C2semidirect
10. #31826606C2semidirect
11. #31826564C2semidirect
12. #31826533C2semidirect
13. #31826463C2semidirect
14. C2×#22583533C2semidirect
15. #480×C283C2semidirect
119. Dic566#41semidirect
187. C283#3308semidirect
193. #480D283semidirect

Maximal subgroups

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

subgroupindex
#318271212
#318271162
#318268232
#318268022
#318267592
#318267122
#318266992
#318266792
#318266112
#318266062
#318265642
#318265332
#318264632
C2×#225835332
#480×C2832
#3308283