Finite Group Databasebeta

← #49131854

Subgroups — #49131854

Order 36224.

408 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
1#31827012C211yesmaximal, characteristic, complemented
2#31826997C211yesmaximal, characteristic, complemented
3#31826873C211yesmaximal, characteristic, complemented
4#31826853C211yesmaximal, characteristic, complemented
5#31826828C211yesmaximal, characteristic, complemented
6#31826823C211yesmaximal, characteristic, complemented
7#31826717C211yesmaximal, characteristic, complemented
8#31826715C211yesmaximal, characteristic, complemented
9#31826712C211yesmaximal, characteristic, complemented
10#31826710C211yesmaximal, characteristic, complemented
11C4×#17985381C211yesmaximal, characteristic, complemented
12C4×#17985380C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14C4×#17985375C211yesmaximal, characteristic, complemented
15C4×D8×C283C211yesmaximal, characteristic, complemented
16C2×#17985392—21no—
17C2×#17985381C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×#17985375C2211yescharacteristic
21C2×#17985375C2211yescharacteristic
22#22583609C2211yescharacteristic
23#22583606C2211yescharacteristic
24#22583603—21no—
25#22583601C2211yescharacteristic
26#22583597C2211yescharacteristic
27#22583596—21no—
28#22583592—21no—
29#22583590C2211yescharacteristic
30#22583585C2211yescharacteristic
31#22583583—21no—
32#22583581C2211yescharacteristic
33#22583581C2211yescharacteristic
34C4×Dic566C2211yescharacteristic
35C4×D1132C2211yescharacteristic
36C4×C22⋊D283—21no—
37C4×C22⋊D283—21no—
38#22583569—21no—
39C42×D283C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583541C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583520C2211yescharacteristic
50#22583520C2211yescharacteristic
51C4×C283⋊C8C2211yescharacteristic
52C2×D8×C283C2211yescharacteristic
53C4×D4×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59#17985392—44no—
60C2×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62C2×D1132—21no—
63C2×D1132C2311yescharacteristic
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283D411yescharacteristic
70C2×C4×D283D411yescharacteristic
71C2×C4×D283C2311yescharacteristic
72#17985381—22no—
73#17985380—22no—
74#17985377—22no—
75#17985375—22no—
76#17985375—22no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C4⋊Dic283—21no—
80C4⋊Dic283—21no—
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93C4×Dic283—21no—
94C4×Dic283D411yescharacteristic
95C4×Dic283D411yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283—21no—
100C22×C4×C283—21no—
101D8×C283—22no—
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C22⋊C4×C283—21no—
108C42×C283C2311yescharacteristic
109C22×D283—21no—
110C22×D283C2×D411yescharacteristic
111Dic566—21no—
112Dic566—21no—
113Dic566—42no—
114D1132—21no—
115D1132—21no—
116D1132—42no—
117C22⋊D283—42no—
118C22⋊D283—42no—
119C22⋊D283—42no—
120C22⋊D283—42no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—22no—
128C4×D283—21no—
129C4×D283—21no—
130C4×D283—41no—
131C4×D283—42no—
132C283⋊C8—21no—
133C283⋊C8#4112yescomplemented
134C23×C283—21no—
135C23×C283—21no—
136D4×C283—21no—
137D4×C283—21no—
138D4×C283—21no—
139D4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—42no—
143C2×C4×C283—42no—
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283#4112yescomplemented
149C22×C283—41no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283C22×D411yescharacteristic
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—21no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—41no—
162C4×C283—21no—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283AGL(1,ℤ/8)12yes—
166C4×C283C2×#4111yescharacteristic
167C4×C283C2×#4111yescharacteristic
168Dic283—21no—
169Dic283—21no—
170Dic283—21no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174C2×C283—81no—
175C2×C283—81no—
176C2×C283#53211yescharacteristic
177C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C283#57511yescharacteristic
179D283—41no—
180D283—81no—
181C283#317111yescharacteristic, complemented, Sylow
182#3171—2831nomaximal, Sylow
183#532—2831no—
184#529—2831no—
185#501—2831no—
186#496—2831no—
187#490—2831no—
188#489—2831no—
189#469—2831no—
190#469—2831no—
191#468—2831no—
192#468—2831no—
193C4×SD16—2831no—
194C4×SD16—2831no—
195C4×D8—2831no—
196C4×D8D28311yescharacteristic, complemented
197C4×M16—2831no—
198C2×#41—5661no—
199C2×SD16—2831no—
200C2×SD16—2831no—
201C2×D8—2831no—
202C2×D8C2×D28311yescharacteristic
203C2×M16—2831no—
204C2×M16—2831no—
205C4⋊Q8—2831no—
206#127—2831no—
207#126—5661no—
208#125—2831no—
209#124—2831no—
210#124—5661no—
211#123—5661no—
212C22⋊Q8—2831no—
213#121—2831no—
214#121—2831no—
215#121—2831no—
216#121—5661no—
217C4×Q8—2831no—
218C4×D4—2831no—
219C4×D4—5661no—
220C4×D4—5661no—
221C4×D4C2×D28311yescharacteristic
222C4×D4C2×D28311yescharacteristic
223#117—5661no—
224C2×C42—2831no—
225#107—2831no—
226#107C2×D28311yescharacteristic
227#106—2831no—
228#106—2831no—
229#103—2831no—
230#103—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102C2×D28311yescharacteristic
236#102C2×D28311yescharacteristic
237#97—2831no—
238#97—2831no—
239C4×C8—2831no—
240C4×C8C2×D28311yescharacteristic
241#41—11324no—
242C2×Q8—2831no—
243C2×Q8—5661no—
244C2×D4—2831no—
245C2×D4—5661no—
246C2×D4—5661no—
247C2×D4—5661no—
248C2×D4—5661no—
249C2×D4—5661no—
250C2×D4C22×D28311yescharacteristic
251C2×D4C22×D28311yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—2831no—
255C22×C4—2831no—
256C22×C4—2831no—
257C22×C4—5661no—
258SD16—5662no—
259SD16—5662no—
260D8—22no—
261D8—5662no—
262M16—5662no—
263M16—5662no—
264C2×C8—2831no—
265C2×C8—2831no—
266C2×C8C22×D28311yescharacteristic
267C2×C8C22×D28311yescharacteristic
268C4⋊C4—2831no—
269C4⋊C4—2831no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—2831no—
287C42—2831no—
288C42—2831no—
289C42—5661no—
290C42C22×D28311yescharacteristic
291C23—21no—
292C23—21no—
293C23—2831no—
294C23—5661no—
295Q8—5661no—
296Q8—5661no—
297Q8—11322no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—5661no—
303D4—5661no—
304D4—11322no—
305D4—11322no—
306D4—11322no—
307D4—11322no—
308D4—11322no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—2831no—
314C2×C4—2831no—
315C2×C4—2831no—
316C2×C4—5662no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—11321no—
323C2×C4—11322no—
324C2×C4D4×D28311yescharacteristic
325C2×C4D4×D28311yescharacteristic
326C2×C4C23×D28311yescharacteristic
327C8—21no—
328C8—2832no—
329C8—5661no—
330C8#1798539212yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—5661no—
338C22—5661no—
339C22—5661no—
340C22—11321no—
341C22—11321no—
342C22—11321no—
343C22C2×D4×D28311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—5661no—
348C4—5661no—
349C4—5661no—
350C4—11321no—
351C4—11321no—
352C4—11321no—
353C4#2258363412yes—
354C4#41×D28311yescharacteristic
355C4C2×#1798539211yescharacteristic
356C2—81no—
357C2—81no—
358C2—11321no—
359C2—22641no—
360C2#3182701211yescharacteristic
361C2C2×#2258363411yescharacteristic
362C2#3182726211yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×D8×C283C2
socleC22×C283C22×D4
hypercenterC4×D8D283
hypocenterC283#3171
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #31827012C2semidirect
2. #31826997C2semidirect
3. #31826873C2semidirect
4. #31826853C2semidirect
5. #31826828C2semidirect
6. #31826823C2semidirect
7. #31826717C2semidirect
8. #31826715C2semidirect
9. #31826712C2semidirect
10. #31826710C2semidirect
11. C4×#17985381C2semidirect
12. C4×#17985380C2semidirect
13. C4×#17985377C2semidirect
14. C4×#17985375C2semidirect
15. C4×D8×C283C2semidirect
133. C283⋊C8#41semidirect
148. C8×C283#41semidirect
181. C283#3171semidirect
196. C4×D8D283semidirect
330. C8#17985392semidirect

Maximal subgroups

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

subgroupindex
#318270122
#318269972
#318268732
#318268532
#318268282
#318268232
#318267172
#318267152
#318267122
#318267102
C4×#179853812
C4×#179853802
C4×#179853772
C4×#179853752
C4×D8×C2832
#3171283