Finite Group Databasebeta

← #49131827

Subgroups — #49131827

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#31827002C211yesmaximal, characteristic, complemented
2#31826997C211yesmaximal, characteristic, complemented
3#31826865C211yesmaximal, characteristic, complemented
4#31826846C211yesmaximal, characteristic, complemented
5#31826821C211yesmaximal, characteristic, complemented
6#31826818C211yesmaximal, characteristic, complemented
7#31826705C211yesmaximal, characteristic, complemented
8#31826700C211yesmaximal, characteristic
9#31826695C211yesmaximal, characteristic, complemented
10#31826691C211yesmaximal, characteristic, complemented
11C4×#17985382C211yesmaximal, characteristic, complemented
12C4×#17985381C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14C4×C8×D283C211yesmaximal, characteristic, complemented
15C4×SD16×C283C211yesmaximal, characteristic, complemented
16C2×#17985382C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985377C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic
21#22583605—21no—
22#22583603—21no—
23#22583601C2211yescharacteristic
24#22583601C2211yescharacteristic
25#22583599C2211yescharacteristic
26#22583597C2211yescharacteristic
27#22583595—21no—
28#22583592—21no—
29#22583590C2211yescharacteristic
30#22583586C2211yescharacteristic
31#22583585C2211yescharacteristic
32#22583581C2211yescharacteristic
33C4×Dic566C2211yescharacteristic
34C4×D1132—21no—
35C4×D1132C2211yescharacteristic
36C4×C22⋊D283—21no—
37#22583569—21no—
38#22583567—21no—
39C42×D283C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583543C2211yescharacteristic
42#22583542C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49C4×C283⋊C8C2211yescharacteristic
50C8×Dic283C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59C2×Dic566C2311yescharacteristic
60C2×D1132—21no—
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C4×D283—21no—
64C2×C4×D283D411yescharacteristic
65C2×C4×D283D411yescharacteristic
66C2×C4×D283C2311yescharacteristic
67#17985382—22no—
68#17985381—22no—
69#17985377—22no—
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C8×D283—22no—
73C8×D283—22no—
74C4⋊Dic283—21no—
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92C4×Dic283—21no—
93C4×Dic283D411yescharacteristic
94C4×Dic283D411yescharacteristic
95C4×Dic283C2311yescharacteristic
96C2×Q8×C283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98C22×C4×C283—21no—
99SD16×C283—22no—
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C42×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283C2×D411yescharacteristic
110Dic566—21no—
111Dic566—21no—
112D1132—21no—
113D1132—21no—
114D1132—42no—
115C22⋊D283—42no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283C2×D411yescharacteristic
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C4×D283—22no—
123C4×D283—22no—
124C4×D283—21no—
125C4×D283—21no—
126C4×D283—42no—
127C283⋊C8—21no—
128C283⋊C8#4112yes—
129C23×C283—21no—
130Q8×C283—21no—
131Q8×C283—21no—
132D4×C283—21no—
133D4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—42no—
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2411yescharacteristic
141C8×C283—21no—
142C8×C283#4112yes—
143C22×C283—41no—
144C22×C283—41no—
145C22×C283—41no—
146C22×C283C22×D411yescharacteristic
147C2×D283—21no—
148C2×D283—21no—
149C2×D283—41no—
150C2×D283—41no—
151C2×D283—41no—
152C2×D283#13512yes—
153C4×C283—21no—
154C4×C283—41no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283#13512yes—
158C4×C283C2×#4111yescharacteristic
159C4×C283C2×#4111yescharacteristic
160Dic283—21no—
161Dic283—21no—
162Dic283—21no—
163Dic283—41no—
164Dic283—41no—
165Dic283—41no—
166C2×C283—81no—
167C2×C283#53211yescharacteristic
168C2×C283C2×#13511yescharacteristic
169C2×C283C2×#13511yescharacteristic
170D283—22no—
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#465—2831no—
184C4×Q16—2831no—
185C4×SD16—2831no—
186C4×SD16D28311yescharacteristic, complemented
187C4×D8—2831no—
188C2×C4×C8—2831no—
189C2×Q16—2831no—
190C2×SD16—2831no—
191C2×SD16C2×D28311yescharacteristic
192C2×D8—2831no—
193C22×C8—2831no—
194C22×C8—2831no—
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⋊Q8—2831no—
205#121—2831no—
206#121—2831no—
207C4×Q8—2831no—
208C4×Q8C2×D28311yescharacteristic
209C4×D4—2831no—
210C4×D4—5661no—
211C4×D4—5661no—
212C4×D4C2×D28311yescharacteristic
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×C8C2×D28311yescharacteristic
232C2×Q8—2831no—
233C2×Q8C22×D28311yescharacteristic
234C2×D4—2831no—
235C2×D4—5661no—
236C2×D4—5661no—
237C2×D4C22×D28311yescharacteristic
238C22×C4—21no—
239C22×C4—2831no—
240C22×C4—2831no—
241C22×C4—2831no—
242C22×C4—5661no—
243Q16—5662no—
244SD16—22no—
245SD16—5662no—
246D8—5662no—
247C2×C8—2831no—
248C2×C8—2831no—
249C2×C8—5662no—
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—5661no—
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—21no—
276C42—2831no—
277C42—2831no—
278C42—2831no—
279C42—5661no—
280C42C22×D28311yescharacteristic
281C23—21no—
282C23—2831no—
283C23—5661no—
284Q8—21no—
285Q8—21no—
286Q8—5661no—
287Q8—5661no—
288D4—21no—
289D4—21no—
290D4—5661no—
291D4—5661no—
292D4—11322no—
293D4—11322no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—2831no—
299C2×C4—2831no—
300C2×C4—2831no—
301C2×C4—5662no—
302C2×C4—5662no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—11322no—
309C2×C4D4×D28311yescharacteristic
310C2×C4D4×D28311yescharacteristic
311C2×C4C23×D28311yescharacteristic
312C8—21no—
313C8—2832no—
314C8—5661no—
315C8#1798539212yes—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—2832no—
320C22—5661no—
321C22—5661no—
322C22—11321no—
323C22—11321no—
324C22—11321no—
325C22C2×D4×D28311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—5661no—
331C4—5661no—
332C4—5661no—
333C4—11321no—
334C4—11321no—
335C4—11321no—
336C4#2258363112yes—
337C4#41×D28311yescharacteristic
338C4C2×#1798539211yescharacteristic
339C2—81no—
340C2—5662no—
341C2—22641no—
342C2#3182701211yescharacteristic
343C2#135×D28311yescharacteristic
344C2C2×#2258363111yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×SD16×C283C2
socleC22×C283C22×D4
prime radical#31826700C2
hypercenterC4×SD16D283
hypocenterC283#3168
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #31827002C2semidirect
2. #31826997C2semidirect
3. #31826865C2semidirect
4. #31826846C2semidirect
5. #31826821C2semidirect
6. #31826818C2semidirect
7. #31826705C2semidirect
9. #31826695C2semidirect
10. #31826691C2semidirect
11. C4×#17985382C2semidirect
12. C4×#17985381C2semidirect
13. C4×#17985377C2semidirect
14. C4×C8×D283C2semidirect
15. C4×SD16×C283C2semidirect
172. C283#3168semidirect
186. C4×SD16D283semidirect

Maximal subgroups

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

subgroupindex
#318270022
#318269972
#318268652
#318268462
#318268212
#318268182
#318267052
#318267002
#318266952
#318266912
C4×#179853822
C4×#179853812
C4×#179853772
C4×C8×D2832
C4×SD16×C2832
#3168283