Finite Group Databasebeta

← #49133954

Subgroups — #49133954

Order 36224.

348 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827197C211yesmaximal, characteristic
2#31827192C211yesmaximal, characteristic, complemented
3#31826821C211yesmaximal, characteristic, complemented
4#31826810C211yesmaximal, characteristic
5#31826767C211yesmaximal, characteristic, complemented
6#31826762C211yesmaximal, characteristic, complemented
7#31826748C211yesmaximal, characteristic, complemented
8#31826690C211yesmaximal, characteristic, complemented
9#31826684C211yesmaximal, characteristic, complemented
10#31826664C211yesmaximal, characteristic
11C8×Dic566C211yesmaximal, characteristic, complemented
12#31826557C211yesmaximal, characteristic, complemented
13#31826556C211yesmaximal, characteristic, complemented
14C4×#17985381C211yesmaximal, characteristic, complemented
15#488×C283C211yesmaximal, characteristic, complemented
16C2×#17985382C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19#22583609—21no—
20#22583609C2211yescharacteristic
21#22583606C2211yescharacteristic
22#22583601C2211yescharacteristic
23#22583600—21no—
24#22583600—21no—
25#22583599C2211yescharacteristic
26#22583596—21no—
27#22583594—21no—
28#22583592—21no—
29Q8×Dic283C2211yescharacteristic
30C4×Dic566C2211yescharacteristic
31C4×Dic566C2211yescharacteristic
32#22583575—21no—
33#22583575C2211yescharacteristic
34#22583575C2211yescharacteristic
35C4×D1132C2211yescharacteristic
36D4×Dic283C2211yescharacteristic
37(C22⋊D283)⋊C4—21no—
38#22583543C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583541C2211yescharacteristic
41C4⋊(C283⋊C8)C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583530C2211yescharacteristic
50C8×Dic283C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52#125×C283C2211yescharacteristic
53#124×C283C2211yescharacteristic
54#103×C283C2211yescharacteristic
55#103×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566D411yescharacteristic
61C2×Dic566C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C22×Dic283—21no—
66C2×C4×D283—21no—
67#17985382—22no—
68#17985381—22no—
69#17985380—22no—
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C4⋊Dic283—21no—
73C4⋊Dic283—21no—
74C4⋊Dic283D411yescharacteristic
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4D411yescharacteristic
83Dic283⋊C4D411yescharacteristic
84C22⋊Dic283—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88C4×Dic283—21no—
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283C2311yescharacteristic
93C4×Dic283C2311yescharacteristic
94C2×Q8×C283C2311yescharacteristic
95C2×D4×C283C2311yescharacteristic
96C2×C8×C283C2311yescharacteristic
97C2×C8×C283C2311yescharacteristic
98C4⋊C4×C283—21no—
99C4⋊C4×C283—21no—
100C4⋊C4×C283C2311yescharacteristic
101C4⋊C4×C283C2311yescharacteristic
102C22⋊C4×C283—21no—
103C22⋊C4×C283—21no—
104C42×C283C2311yescharacteristic
105C22×D283—21no—
106Dic566—21no—
107Dic566—22no—
108Dic566—42no—
109Dic566#4112yes—
110D1132—21no—
111D1132—21no—
112C22⋊D283—42no—
113C22⋊D283—81no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—81no—
118C2×Dic283C2×D411yescharacteristic
119C2×Dic283C2×D411yescharacteristic
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C4×D283—81no—
123C283⋊C8—21no—
124C283⋊C8—21no—
125C23×C283—21no—
126Q8×C283—21no—
127Q8×C283—21no—
128D4×C283—21no—
129D4×C283—21no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283C2×D411yescharacteristic
134C2×C4×C283C2×D411yescharacteristic
135C2×C4×C283C2411yescharacteristic
136C8×C283—21no—
137C8×C283—21no—
138C22×C283—41no—
139C22×C283—41no—
140C22×C283—41no—
141C22×C283C22×D411yescharacteristic
142C2×D283—41no—
143C2×D283—41no—
144C2×D283—41no—
145C4×C283—21no—
146C4×C283—21no—
147C4×C283—41no—
148C4×C283—41no—
149C4×C283—41no—
150C4×C283C2×#4111yescharacteristic
151C4×C2832−1+411yescharacteristic
152Dic283—22no—
153Dic283—21no—
154Dic283—21no—
155Dic283—21no—
156Dic283—41no—
157Dic283—41no—
158Dic283#13512yes—
159C2×C283—81no—
160C2×C283#54811yescharacteristic
161C2×C283C2×#13511yescharacteristic
162C2×C283#57711yescharacteristic
163D283—81no—
164C283#336511yescharacteristic, complemented, Sylow
165#3365—2831nomaximal, Sylow
166#559—2831no—
167#557—2831no—
168#488—2831no—
169#488D28311yescharacteristic, complemented
170#486—2831no—
171#478—2831no—
172#478—2831no—
173#475—2831no—
174#464—2831no—
175#464—2831no—
176#460—2831no—
177C8×Q8—2831no—
178C4×Q16—2831no—
179C4×SD16—2831no—
180C4×SD16—2831no—
181C2×Q16—2831no—
182C2×SD16—2831no—
183C2×SD16—2831no—
184C4⋊Q8—2831no—
185C4⋊Q8—5661no—
186#127—2831no—
187#125—2831no—
188#125—5661no—
189#125—5661no—
190#125C2×D28311yescharacteristic
191#124—2831no—
192#124—5661no—
193#124C2×D28311yescharacteristic
194#123—5661no—
195#123—5661no—
196C4×Q8—2831no—
197C4×Q8—2831no—
198C4×Q8—2831no—
199C4×Q8—2831no—
200C4×Q8—2831no—
201C4×Q8—5661no—
202C4×D4—2831no—
203C4×D4—2831no—
204C4×D4—5661no—
205#107—2831no—
206#106—2831no—
207#106—2831no—
208C4⋊C8—2831no—
209C4⋊C8—2831no—
210C4⋊C8—2831no—
211#103—2831no—
212#103—2831no—
213#103C2×D28311yescharacteristic
214#103C2×D28311yescharacteristic
215#102—2831no—
216#102—2831no—
217#102—2831no—
218#102—2831no—
219#102C2×D28311yescharacteristic
220#102C2×D28311yescharacteristic
221C4×C8—2831no—
222C4×C8—2831no—
223C4×C8C2×D28311yescharacteristic
224C2×Q8—2831no—
225C2×Q8—2831no—
226C2×Q8—5661no—
227C2×Q8C22×D28311yescharacteristic
228C2×D4—2831no—
229C2×D4—5661no—
230C2×D4—5661no—
231C2×D4C22×D28311yescharacteristic
232C22×C4—5661no—
233C22×C4—5661no—
234Q16—5662no—
235SD16—5662no—
236SD16—5662no—
237C2×C8—2831no—
238C2×C8—2831no—
239C2×C8C22×D28311yescharacteristic
240C2×C8C22×D28311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—2831no—
244C4⋊C4—2831no—
245C4⋊C4—2831no—
246C4⋊C4—2831no—
247C4⋊C4—2831no—
248C4⋊C4—5661no—
249C4⋊C4—5661no—
250C4⋊C4—5661no—
251C4⋊C4—5661no—
252C4⋊C4—5661no—
253C4⋊C4—5661no—
254C4⋊C4—5661no—
255C4⋊C4C22×D28311yescharacteristic
256C4⋊C4C22×D28311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—5661no—
260C22⋊C4—5661no—
261C22⋊C4—5661no—
262C22⋊C4—5661no—
263C42—2831no—
264C42—2831no—
265C42—5661no—
266C42—5661no—
267C42—5661no—
268C42—5661no—
269C42C22×D28311yescharacteristic
270C23—21no—
271C23—5661no—
272Q8—21no—
273Q8—21no—
274Q8—2832no—
275Q8—5662no—
276Q8—5661no—
277Q8—11322no—
278D4—21no—
279D4—21no—
280D4—5661no—
281D4—5661no—
282D4—11322no—
283D4—22641no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—2831no—
288C2×C4—2831no—
289C2×C4—2831no—
290C2×C4—2831no—
291C2×C4—5661no—
292C2×C4—5661no—
293C2×C4—5661no—
294C2×C4—22641no—
295C2×C4—22641no—
296C2×C4D4×D28311yescharacteristic
297C2×C4D4×D28311yescharacteristic
298C2×C4C23×D28311yescharacteristic
299C8—21no—
300C8—21no—
301C8—5661no—
302C8—5661no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—11321no—
307C22—11321no—
308C22—11321no—
309C22C2×D4×D28311yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—2832no—
316C4—5661no—
317C4—5661no—
318C4—5661no—
319C4—5662no—
320C4—11321no—
321C4—11321no—
322C4#41×D28311yescharacteristic
323C4#2258365711yescharacteristic
324C2—81no—
325C2—22641no—
326C2#3182712311yescharacteristic
327C2#135×D28311yescharacteristic
328C2#3182727211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#488×C283C2
socleC22×C283C22×D4
prime radical#22583606C22
hypercenter#488D283
hypocenterC283#3365
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #31827192C2semidirect
3. #31826821C2semidirect
5. #31826767C2semidirect
6. #31826762C2semidirect
7. #31826748C2semidirect
8. #31826690C2semidirect
9. #31826684C2semidirect
11. C8×Dic566C2semidirect
12. #31826557C2semidirect
13. #31826556C2semidirect
14. C4×#17985381C2semidirect
15. #488×C283C2semidirect
164. C283#3365semidirect
169. #488D283semidirect

Maximal subgroups

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

subgroupindex
#318271972
#318271922
#318268212
#318268102
#318267672
#318267622
#318267482
#318266902
#318266842
#318266642
C8×Dic5662
#318265572
#318265562
C4×#179853812
#488×C2832
#3365283