Finite Group Databasebeta

← #49133985

Subgroups — #49133985

Order 36224.

382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827191C211yesmaximal, characteristic, complemented
2#31827135C211yesmaximal, characteristic
3#31826829C211yesmaximal, characteristic, complemented
4#31826828C211yesmaximal, characteristic, complemented
5#31826810C211yesmaximal, characteristic, complemented
6#31826767C211yesmaximal, characteristic, complemented
7#31826766C211yesmaximal, characteristic, complemented
8#31826743C211yesmaximal, characteristic, complemented
9#31826663C211yesmaximal, characteristic, complemented
10#31826663C211yesmaximal, characteristic, complemented
11#31826594C211yesmaximal, characteristic, complemented
12#31826566C211yesmaximal, characteristic, complemented
13#31826563C211yesmaximal, characteristic, complemented
14SD16×Dic283C211yesmaximal, characteristic, complemented
15#460×C283C211yesmaximal, characteristic, complemented
16C2×#17985391—21no—
17C2×#17985379C2211yescharacteristic
18#22583609—21no—
19#22583609C2211yescharacteristic
20#22583606C2211yescharacteristic
21#22583606C2211yescharacteristic
22#22583602—21no—
23#22583602C2211yescharacteristic
24#22583601—21no—
25#22583601C2211yescharacteristic
26#22583582—21no—
27#22583582—21no—
28#22583581—21no—
29Q8×Dic283C2211yescharacteristic
30Q8×Dic283C2211yescharacteristic
31C4×Dic566—21no—
32C4×Dic566C2211yescharacteristic
33C4×D1132C2211yescharacteristic
34D4×Dic283C2211yescharacteristic
35D4×Dic283C2211yescharacteristic
36#22583544C2211yescharacteristic
37#22583543C2211yescharacteristic
38#22583542C2211yescharacteristic
39Dic283⋊C8C2211yescharacteristic
40Dic283⋊C8C2211yescharacteristic
41#22583534C2211yescharacteristic
42#22583532C2211yescharacteristic
43#22583532C2211yescharacteristic
44#22583531C2211yescharacteristic
45#22583531C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583521C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C2×SD16×C283C2211yescharacteristic
54#127×C283C2211yescharacteristic
55C4×Q8×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59#17985391—44no—
60C2×Dic566—21no—
61C2×Dic566D411yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C22×Dic283—21no—
68C22×Dic283—21no—
69C2×C4×D283—21no—
70#17985379—22no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283—21no—
76C4⋊Dic283D411yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4D411yescharacteristic
85Dic283⋊C4D411yescharacteristic
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88(C2×D283)⋊C4—21no—
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283C2311yescharacteristic
92C4×Dic283C2311yescharacteristic
93C2×Q8×C283C2311yescharacteristic
94C2×D4×C283—21no—
95C2×D4×C283—21no—
96C2×D4×C283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98SD16×C283—22no—
99SD16×C283—22no—
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C42×C283—21no—
105C42×C283C2311yescharacteristic
106C22×D283—21no—
107Dic566—22no—
108Dic566—42no—
109D1132—21no—
110D1132—21no—
111C22⋊D283—42no—
112C22⋊D283—42no—
113C22⋊D283—81no—
114C22⋊D283—81no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—42no—
119C2×Dic283—42no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C4×D283—42no—
125C283⋊C8—21no—
126C283⋊C8—21no—
127C23×C283—21no—
128C23×C283—21no—
129Q8×C283—21no—
130Q8×C283#4112yescomplemented
131D4×C283—21no—
132D4×C283—21no—
133D4×C283—21no—
134D4×C283—21no—
135D4×C283—42no—
136D4×C283—81no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2411yescharacteristic
142C8×C283—21no—
143C8×C283—21no—
144C22×C283—41no—
145C22×C283—41no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283—41no—
149C22×C283—41no—
150C22×C283C22×D411yescharacteristic
151C2×D283—41no—
152C2×D283—41no—
153C2×D283—41no—
154C4×C283—22no—
155C4×C283—21no—
156C4×C283—21no—
157C4×C283—41no—
158C4×C283C2×#4111yescharacteristic
159C4×C2832−1+411yescharacteristic
160Dic283—21no—
161Dic283—21no—
162Dic283—21no—
163Dic283—41no—
164Dic283—41no—
165Dic283—41no—
166Dic283AGL(1,ℤ/8)12yes—
167C2×C283—81no—
168C2×C283—81no—
169C2×C283#54811yescharacteristic
170C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C283#57711yescharacteristic
172D283—81no—
173C283#336811yescharacteristic, complemented, Sylow
174#3368—2831nomaximal, Sylow
175#557—2831no—
176#550—2831no—
177#490—2831no—
178#490—2831no—
179#486—2831no—
180#478—2831no—
181#478—2831no—
182#474—2831no—
183#460—2831no—
184#460—2831no—
185#460D28311yescharacteristic, complemented
186#446—2831no—
187#440—2831no—
188#440—2831no—
189C4×SD16—2831no—
190C2×#41—5661no—
191C2×SD16—2831no—
192C2×SD16C2×D28311yescharacteristic
193C2×SD16C2×D28311yescharacteristic
194C4⋊Q8—2831no—
195C4⋊Q8—5661no—
196#127—2831no—
197#127—2831no—
198#127C2×D28311yescharacteristic
199#125—2831no—
200#125—2831no—
201#125—5661no—
202#125—5661no—
203#121—5661no—
204#121—5661no—
205#121—5661no—
206C4×Q8—2831no—
207C4×Q8—2831no—
208C4×Q8—2831no—
209C4×Q8—5661no—
210C4×Q8C2×D28311yescharacteristic
211C4×D4—2831no—
212C4×D4—2831no—
213C4×D4—2831no—
214#107—2831no—
215#107—2831no—
216#106—2831no—
217C4⋊C8—2831no—
218C4⋊C8—2831no—
219C4⋊C8C2×D28311yescharacteristic
220#103—2831no—
221#102—2831no—
222#102—2831no—
223#102—2831no—
224#102—2831no—
225#102—2831no—
226#102—2831no—
227#102—2831no—
228#102C2×D28311yescharacteristic
229#102C2×D28311yescharacteristic
230#97—2831no—
231#97—2831no—
232C4×C8—2831no—
233#41—11324no—
234C2×Q8—2831no—
235C2×Q8—5661no—
236C2×Q8C22×D28311yescharacteristic
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—2831no—
240C2×D4—5661no—
241C2×D4—5661no—
242C2×D4—5661no—
243C2×D4—5661no—
244C2×D4C22×D28311yescharacteristic
245C2×D4C22×D28311yescharacteristic
246C22×C4—5661no—
247C22×C4—5661no—
248C22×C4—5661no—
249SD16—22no—
250SD16—22no—
251SD16—5662no—
252C2×C8—2831no—
253C2×C8—2831no—
254C2×C8C22×D28311yescharacteristic
255C2×C8C22×D28311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—2831no—
258C4⋊C4—2831no—
259C4⋊C4—2831no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—2831no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4C22×D28311yescharacteristic
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C42—21no—
275C42—2831no—
276C42—2831no—
277C42—5661no—
278C42—5661no—
279C42C22×D28311yescharacteristic
280C23—21no—
281C23—21no—
282C23—5661no—
283Q8—21no—
284Q8—5662no—
285Q8—11322no—
286Q8#1798539112yescomplemented
287D4—21no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—5661no—
294D4—5661no—
295D4—11322no—
296D4—11322no—
297D4—22641no—
298D4—22641no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—2831no—
302C2×C4—2831no—
303C2×C4—2831no—
304C2×C4—2831no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—11322no—
309C2×C4—11322no—
310C2×C4—11322no—
311C2×C4D4×D28311yescharacteristic
312C2×C4D4×D28311yescharacteristic
313C2×C4C23×D28311yescharacteristic
314C8—21no—
315C8—21no—
316C8—5661no—
317C8—5661no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—11321no—
325C22—11321no—
326C22—11321no—
327C22C2×D4×D28311yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—41no—
332C4—2832no—
333C4—5661no—
334C4—5661no—
335C4—5661no—
336C4—11321no—
337C4—11321no—
338C4—11321no—
339C4C2×#1798539111yescharacteristic
340C4#2258365711yescharacteristic
341C2—81no—
342C2—81no—
343C2—22641no—
344C2#3182712111yescharacteristic
345C2AGL(1,ℤ/8)×D28311yescharacteristic
346C2#3182727111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#460×C283C2
socleC22×C283C22×D4
prime radical#31827135C2
hypercenter#460D283
hypocenterC283#3368
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #31827191C2semidirect
3. #31826829C2semidirect
4. #31826828C2semidirect
5. #31826810C2semidirect
6. #31826767C2semidirect
7. #31826766C2semidirect
8. #31826743C2semidirect
9. #31826663C2semidirect
10. #31826663C2semidirect
11. #31826594C2semidirect
12. #31826566C2semidirect
13. #31826563C2semidirect
14. SD16×Dic283C2semidirect
15. #460×C283C2semidirect
130. Q8×C283#41semidirect
173. C283#3368semidirect
185. #460D283semidirect
286. Q8#17985391semidirect

Maximal subgroups

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

subgroupindex
#318271912
#318271352
#318268292
#318268282
#318268102
#318267672
#318267662
#318267432
#318266632
#318265942
#318265662
#318265632
SD16×Dic2832
#460×C2832
#3368283