Finite Group Databasebeta

← #49131825

Subgroups — #49131825

Order 36224.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31826999C211yesmaximal, characteristic, complemented
2#31826864C211yesmaximal, characteristic, complemented
3#31826847C211yesmaximal, characteristic, complemented
4#31826822C211yesmaximal, characteristic, complemented
5#31826819C211yesmaximal, characteristic, complemented
6#31826704C211yesmaximal, characteristic, complemented
7#31826699C211yesmaximal, characteristic
8#31826696C211yesmaximal, characteristic, complemented
9#31826692C211yesmaximal, characteristic, complemented
10C4×#17985382C211yesmaximal, characteristic, complemented
11C4×#17985379C211yesmaximal, characteristic, complemented
12C4×#17985380C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14C2×C4×C283⋊C8C211yesmaximal, characteristic, complemented
15#529×C283C211yesmaximal, characteristic, complemented
16C2×#17985382C2211yescharacteristic
17C2×#17985380C2211yescharacteristic
18C2×#17985379C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C22×C283⋊C8C2211yescharacteristic
21C22×C283⋊C8C2211yescharacteristic
22#22583604—21no—
23#22583602C2211yescharacteristic
24#22583598C2211yescharacteristic
25#22583593—21no—
26#22583589C2211yescharacteristic
27#22583584C2211yescharacteristic
28C4×Dic566C2211yescharacteristic
29C4×D1132C2211yescharacteristic
30C4×C22⋊D283—21no—
31#22583567—21no—
32#22583543C2211yescharacteristic
33#22583543C2211yescharacteristic
34#22583541C2211yescharacteristic
35#22583541C2211yescharacteristic
36#22583534C2211yescharacteristic
37#22583534C2211yescharacteristic
38#22583533C2211yescharacteristic
39#22583533C2211yescharacteristic
40#22583531C2211yescharacteristic
41#22583531C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44C4×C283⋊C8C2211yescharacteristic
45C4×C283⋊C8C2211yescharacteristic
46C4×C283⋊C8C2211yescharacteristic
47C4×C283⋊C8C2211yescharacteristic
48#126×C283—21no—
49#125×C283C2211yescharacteristic
50#124×C283C2211yescharacteristic
51#123×C283—21no—
52C22⋊Q8×C283C2211yescharacteristic
53#121×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55C4×D4×C283—21no—
56C4×D4×C283C2211yescharacteristic
57#117×C283—21no—
58C2×C42×C283C2211yescharacteristic
59C2×Dic566C2311yescharacteristic
60C2×D1132C2311yescharacteristic
61C2×C22⋊D283—21no—
62C2×C4×D283—21no—
63#17985382—22no—
64#17985380—22no—
65#17985379—22no—
66#17985377—22no—
67C2×C283⋊C8—22no—
68C2×C283⋊C8—22no—
69C2×C283⋊C8C2311yescharacteristic
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C4⋊Dic283C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79C22⋊Dic283—21no—
80(C2×D283)⋊C4—21no—
81(C2×D283)⋊C4—21no—
82(C2×D283)⋊C4—21no—
83(C2×D283)⋊C4—21no—
84C4×Dic283—21no—
85C2×Q8×C283C2311yescharacteristic
86C2×D4×C283—21no—
87C2×D4×C283C2311yescharacteristic
88C22×C4×C283—21no—
89C22×C4×C283D411yescharacteristic
90C22×C4×C283D411yescharacteristic
91C22×C4×C283C2311yescharacteristic
92C4⋊C4×C283—21no—
93C4⋊C4×C283—21no—
94C4⋊C4×C283—21no—
95C4⋊C4×C283—21no—
96C4⋊C4×C283C2311yescharacteristic
97C4⋊C4×C283C2311yescharacteristic
98C22⋊C4×C283—21no—
99C22⋊C4×C283—21no—
100C22⋊C4×C283—21no—
101C22⋊C4×C283—21no—
102C22⋊C4×C283—21no—
103C42×C283—21no—
104C42×C283D411yescharacteristic
105C42×C283D411yescharacteristic
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109Dic566—21no—
110Dic566—21no—
111D1132—21no—
112D1132—21no—
113C22⋊D283—42no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C4×D283—42no—
118C283⋊C8—21no—
119C283⋊C8—21no—
120C283⋊C8#4112yes—
121C283⋊C8#4112yes—
122C23×C283—21no—
123C23×C283C2×D411yescharacteristic
124Q8×C283—21no—
125Q8×C283—21no—
126D4×C283—21no—
127D4×C283—21no—
128D4×C283—42no—
129C2×C4×C283—22no—
130C2×C4×C283—22no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—42no—
137C2×C4×C283C2×D411yescharacteristic
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2411yescharacteristic
143C22×C283—21no—
144C22×C283—21no—
145C22×C283—41no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283#13512yes—
149C22×C283C22×D411yescharacteristic
150C2×D283—41no—
151C2×D283—41no—
152C2×D283—41no—
153C4×C283—21no—
154C4×C283—21no—
155C4×C283—21no—
156C4×C283—21no—
157C4×C283—41no—
158C4×C283—41no—
159C4×C283—41no—
160C4×C283#13512yes—
161C4×C283C2×#4111yescharacteristic
162C4×C283C2×#4111yescharacteristic
163Dic283—41no—
164Dic283—41no—
165Dic283—41no—
166C2×C283—22no—
167C2×C283—81no—
168C2×C283#53211yescharacteristic
169C2×C283C2×#13511yescharacteristic
170C2×C283C2×#13511yescharacteristic
171D283—81no—
172C283#316811yescharacteristic, complemented, Sylow
173#3168—2831nomaximal, Sylow
174#529—2831no—
175#529D28311yescharacteristic, complemented
176#499—2831no—
177#495—2831no—
178#488—2831no—
179#488—2831no—
180#467—2831no—
181#466—2831no—
182#465—2831no—
183#465—2831no—
184C4×Q16—2831no—
185C4×SD16—2831no—
186C4×SD16—2831no—
187C4×D8—2831no—
188C2×C4×C8—2831no—
189C2×Q16—2831no—
190C2×SD16—2831no—
191C2×SD16—2831no—
192C2×D8—2831no—
193C22×C8—2831no—
194C22×C8—2831no—
195#126—21no—
196#126—5661no—
197#125—2831no—
198#125C2×D28311yescharacteristic
199#124—2831no—
200#124C2×D28311yescharacteristic
201#123—21no—
202#123—5661no—
203C22⋊Q8—2831no—
204C22⋊Q8C2×D28311yescharacteristic
205#121—2831no—
206#121C2×D28311yescharacteristic
207C4×Q8—2831no—
208C4×Q8C2×D28311yescharacteristic
209C4×D4—21no—
210C4×D4—2831no—
211C4×D4—5661no—
212C4×D4C2×D28311yescharacteristic
213#117—21no—
214#117—5661no—
215C2×C42C2×D28311yescharacteristic
216#107—2831no—
217#107—2831no—
218#106—2831no—
219#106—2831no—
220#103—2831no—
221#103—2831no—
222#103—2831no—
223#103—2831no—
224#102—2831no—
225#102—2831no—
226#102—2831no—
227#102—2831no—
228C4×C8—2831no—
229C4×C8—2831no—
230C4×C8—2831no—
231C4×C8—2831no—
232C2×Q8—2831no—
233C2×Q8C22×D28311yescharacteristic
234C2×D4—21no—
235C2×D4—2831no—
236C2×D4—5661no—
237C2×D4C22×D28311yescharacteristic
238C22×C4—21no—
239C22×C4—5661no—
240C22×C4C22⋊D28311yescharacteristic
241C22×C4C22⋊D28311yescharacteristic
242C22×C4C22×D28311yescharacteristic
243Q16—5662no—
244SD16—5662no—
245SD16—5662no—
246D8—5662no—
247C2×C8—2831no—
248C2×C8—2831no—
249C2×C8—2831no—
250C2×C8—2831no—
251C2×C8—5662no—
252C2×C8—5662no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—2831no—
258C4⋊C4—2831no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4C22×D28311yescharacteristic
264C4⋊C4C22×D28311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C42—21no—
276C42—5661no—
277C42C22⋊D28311yescharacteristic
278C42C22⋊D28311yescharacteristic
279C42C22×D28311yescharacteristic
280C42C22×D28311yescharacteristic
281C23—21no—
282C23—5661no—
283C23C2×C22⋊D28311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—5661no—
287Q8—5661no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—5661no—
292D4—5661no—
293D4—11322no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—5661no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—11322no—
306C2×C4C2×C22⋊D28311yescharacteristic
307C2×C4C2×C22⋊D28311yescharacteristic
308C2×C4C2×C22⋊D28311yescharacteristic
309C2×C4C2×C22⋊D28311yescharacteristic
310C2×C4C2×C22⋊D28311yescharacteristic
311C2×C4C23×D28311yescharacteristic
312C8—2832no—
313C8—2832no—
314C8—5661no—
315C8—5661no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—11321no—
322C22—11321no—
323C22—11321no—
324C22#2258363012yes—
325C22C22×C22⋊D28311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—11321no—
334C4—11321no—
335C4—11321no—
336C4#2258363012yes—
337C4#41×D28311yescharacteristic
338C4#41×D28311yescharacteristic
339C2—22no—
340C2—81no—
341C2—22641no—
342C2#3182701111yescharacteristic
343C2C2×#2258363011yescharacteristic
344C2C2×#2258363011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#529×C283C2
socleC22×C283C22×D4
prime radical#31826699C2
hypercenter#529D283
hypocenterC283#3168
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #31826999C2semidirect
2. #31826864C2semidirect
3. #31826847C2semidirect
4. #31826822C2semidirect
5. #31826819C2semidirect
6. #31826704C2semidirect
8. #31826696C2semidirect
9. #31826692C2semidirect
10. C4×#17985382C2semidirect
11. C4×#17985379C2semidirect
12. C4×#17985380C2semidirect
13. C4×#17985377C2semidirect
14. C2×C4×C283⋊C8C2semidirect
15. #529×C283C2semidirect
172. C283#3168semidirect
175. #529D283semidirect

Maximal subgroups

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

subgroupindex
#318269992
#318268642
#318268472
#318268222
#318268192
#318267042
#318266992
#318266962
#318266922
C4×#179853822
C4×#179853792
C4×#179853802
C4×#179853772
C2×C4×C283⋊C82
#529×C2832
#3168283