Finite Group Databasebeta

← #49131824

Subgroups — #49131824

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#31827001C211yesmaximal, characteristic, complemented
2#31826996C211yesmaximal, characteristic, complemented
3#31826865C211yesmaximal, characteristic, complemented
4#31826846C211yesmaximal, characteristic, complemented
5#31826821C211yesmaximal, characteristic, complemented
6#31826818C211yesmaximal, characteristic, complemented
7#31826704C211yesmaximal, characteristic, complemented
8#31826699C211yesmaximal, characteristic
9#31826694C211yesmaximal, characteristic, complemented
10#31826557C211yesmaximal, characteristic, complemented
11SD16×Dic283C211yesmaximal, characteristic, complemented
12#31826552C211yesmaximal, characteristic, complemented
13#31826545C211yesmaximal, characteristic, complemented
14C2×C8×Dic283C211yesmaximal, characteristic, complemented
15#465×C283C211yesmaximal, characteristic, complemented
16C2×#17985382C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985377C2211yescharacteristic
19C22×C283⋊C8C2211yescharacteristic
20#22583605—21no—
21#22583603—21no—
22#22583601C2211yescharacteristic
23#22583601C2211yescharacteristic
24#22583599C2211yescharacteristic
25#22583597C2211yescharacteristic
26#22583594—21no—
27#22583591—21no—
28#22583589C2211yescharacteristic
29#22583584C2211yescharacteristic
30Q8×Dic283C2211yescharacteristic
31#22583575C2211yescharacteristic
32D4×Dic283—21no—
33D4×Dic283C2211yescharacteristic
34#22583572C2211yescharacteristic
35(C22⋊D283)⋊C4—21no—
36#22583568—21no—
37#22583566—21no—
38C2×C4×Dic283C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583530C2211yescharacteristic
48C8×Dic283C2211yescharacteristic
49C8×Dic283C2211yescharacteristic
50C8×Dic283C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C22⋊Q8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#106×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C2×Dic566C2311yescharacteristic
60C2×D1132C2311yescharacteristic
61C2×C22⋊D283—21no—
62C22×Dic283—21no—
63C22×Dic283D411yescharacteristic
64C22×Dic283D411yescharacteristic
65C2×C4×D283—21no—
66#17985382—22no—
67#17985381—22no—
68#17985377—22no—
69C2×C283⋊C8—22no—
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C4⋊Dic283—21no—
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81C22⋊Dic283—21no—
82C22⋊Dic283—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283D411yescharacteristic
92C4×Dic283D411yescharacteristic
93C4×Dic283C2311yescharacteristic
94C4×Dic283C2311yescharacteristic
95C2×Q8×C283C2311yescharacteristic
96C2×D4×C283—21no—
97C2×D4×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99SD16×C283—22no—
100C2×C8×C283—22no—
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C4⋊C4×C283—21no—
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C22⋊C4×C283—21no—
108C22×D283—21no—
109Dic566—21no—
110Dic566—21no—
111D1132—21no—
112D1132—21no—
113C22⋊D283—42no—
114C2×Dic283—22no—
115C2×Dic283—22no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—42no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C4×D283—42no—
125C283⋊C8—21no—
126C283⋊C8#4112yes—
127C23×C283—21no—
128C23×C283C2×D411yescharacteristic
129Q8×C283—21no—
130Q8×C283—21no—
131D4×C283—21no—
132D4×C283—21no—
133D4×C283—42no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2411yescharacteristic
141C8×C283—21no—
142C8×C283#4112yes—
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—41no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283C2×#4111yescharacteristic
158C4×C283C2×#4111yescharacteristic
159Dic283—21no—
160Dic283—21no—
161Dic283—21no—
162Dic283—41no—
163Dic283—41no—
164Dic283—41no—
165Dic283#13512yes—
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#529—2831no—
176#499—2831no—
177#495—2831no—
178#488—2831no—
179#488—2831no—
180#467—2831no—
181#466—2831no—
182#465—2831no—
183#465D28311yescharacteristic, complemented
184C4×Q16—2831no—
185C4×SD16—2831no—
186C4×SD16—2831no—
187C4×D8—2831no—
188C2×C4×C8—2831no—
189C2×Q16—2831no—
190C2×SD16—2831no—
191C2×SD16C2×D28311yescharacteristic
192C2×D8—2831no—
193C22×C8—2831no—
194C22×C8C2×D28311yescharacteristic
195#126—5661no—
196#126—5661no—
197#125—2831no—
198#125—2831no—
199#124—2831no—
200#124—2831no—
201#123—5661no—
202#123—5661no—
203C22⋊Q8—2831no—
204C22⋊Q8C2×D28311yescharacteristic
205#121—2831no—
206#121C2×D28311yescharacteristic
207C4×Q8—2831no—
208C4×Q8—2831no—
209C4×D4—2831no—
210C4×D4—2831no—
211C4×D4—5661no—
212C4×D4—5661no—
213#117—5661no—
214#117—5661no—
215C2×C42—2831no—
216#107—2831no—
217#107—2831no—
218#106—2831no—
219#106C2×D28311yescharacteristic
220#103—2831no—
221#103—2831no—
222#103—2831no—
223#103C2×D28311yescharacteristic
224#102—2831no—
225#102—2831no—
226#102—2831no—
227#102C2×D28311yescharacteristic
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—2831no—
239C22×C4—2831no—
240C22×C4—5661no—
241C22×C4—5661no—
242C22×C4C22×D28311yescharacteristic
243Q16—5662no—
244SD16—22no—
245SD16—5662no—
246D8—5662no—
247C2×C8—22no—
248C2×C8—2831no—
249C2×C8—2831no—
250C2×C8—5662no—
251C2×C8C22×D28311yescharacteristic
252C2×C8C22×D28311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—2831no—
255C4⋊C4—2831no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4—5661no—
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—5661no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C42—2831no—
276C42—2831no—
277C42—2831no—
278C42—2831no—
279C42—5661no—
280C42—5661no—
281C23—21no—
282C23—5661no—
283C23D4×D28311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—5661no—
287Q8—5661no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—5661no—
292D4—5661no—
293D4—11322no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—2831no—
300C2×C4—2831no—
301C2×C4—2831no—
302C2×C4—2831no—
303C2×C4—5662no—
304C2×C4—5662no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—11322no—
309C2×C4—11322no—
310C2×C4D4×D28311yescharacteristic
311C2×C4C23×D28311yescharacteristic
312C8—21no—
313C8—2832no—
314C8—5661no—
315C8#1798539112yes—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—11321no—
322C22—11321no—
323C22—11321no—
324C22#2258363112yes—
325C22C2×D4×D28311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—2832no—
331C4—5661no—
332C4—5661no—
333C4—5661no—
334C4—11321no—
335C4—11321no—
336C4—11321no—
337C4#41×D28311yescharacteristic
338C4C2×#1798539111yescharacteristic
339C2—22no—
340C2—81no—
341C2—22641no—
342C2#3182701011yescharacteristic
343C2#135×D28311yescharacteristic
344C2C2×#2258363111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#465×C283C2
socleC22×C283C22×D4
prime radical#31826699C2
hypercenter#465D283
hypocenterC283#3168
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #31827001C2semidirect
2. #31826996C2semidirect
3. #31826865C2semidirect
4. #31826846C2semidirect
5. #31826821C2semidirect
6. #31826818C2semidirect
7. #31826704C2semidirect
9. #31826694C2semidirect
10. #31826557C2semidirect
11. SD16×Dic283C2semidirect
12. #31826552C2semidirect
13. #31826545C2semidirect
14. C2×C8×Dic283C2semidirect
15. #465×C283C2semidirect
172. C283#3168semidirect
183. #465D283semidirect

Maximal subgroups

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

subgroupindex
#318270012
#318269962
#318268652
#318268462
#318268212
#318268182
#318267042
#318266992
#318266942
#318265572
SD16×Dic2832
#318265522
#318265452
C2×C8×Dic2832
#465×C2832
#3168283