Finite Group Databasebeta

← #49131509

Subgroups — #49131509

Order 36224.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827075C211yesmaximal, characteristic, complemented
2#31826939C211yesmaximal, characteristic
3#31826806C211yesmaximal, characteristic, complemented
4#31826768C211yesmaximal, characteristic, complemented
5#31826764C211yesmaximal, characteristic, complemented
6#31826669C211yesmaximal, characteristic, complemented
7#31826669C211yesmaximal, characteristic, complemented
8#31826618C211yesmaximal, characteristic
9#31826615C211yesmaximal, characteristic
10#31826568C211yesmaximal, characteristic, complemented
11#31826564C211yesmaximal, characteristic, complemented
12#31826552C211yesmaximal, characteristic, complemented
13#31826550C211yesmaximal, characteristic, complemented
14#31826523C211yesmaximal, characteristic, complemented
15#485×C283C211yesmaximal, characteristic, complemented
16C22×D1132C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C2×#17985379C2211yescharacteristic
21#22583608C2211yescharacteristic, complemented
22#22583603—21no—
23#22583603—21no—
24#22583601—21no—
25#22583601C2211yescharacteristic, complemented
26#22583600—21no—
27#22583589C2211yescharacteristic
28Q8×Dic283C2211yescharacteristic, complemented
29#22583575C2211yescharacteristic, complemented
30C4×D1132—21no—
31C4×D1132—21no—
32#22583572C2211yescharacteristic
33#22583572C2211yescharacteristic
34#22583572C2211yescharacteristic
35#22583572C2211yescharacteristic
36#22583569C2211yescharacteristic
37C22⋊C4×D283—21no—
38C22⋊C4×D283—21no—
39#22583543C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42Dic283⋊C8C2211yescharacteristic, complemented
43#22583533C2211yescharacteristic, complemented
44#22583533C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50#22583520C2211yescharacteristic, complemented
51C8×Dic283C2211yescharacteristic, complemented
52C22⋊Q8×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic, complemented
55#106×C283C2211yescharacteristic, complemented
56#103×C283C2211yescharacteristic, complemented
57#103×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic
59C23×D283—21no—
60C2×Dic566C2311yescharacteristic
61C2×D1132—22no—
62C2×D1132—22no—
63C2×D1132—21no—
64C2×D1132C2311yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70#17985381—22no—
71#17985381—22no—
72#17985379—22no—
73#17985379—22no—
74C2×C283⋊C8C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C4⋊Dic283—21no—
77C4⋊Dic283—21no—
78C4⋊Dic283D411yescharacteristic
79C4⋊Dic283D411yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283D411yescharacteristic
88C22⋊Dic283D411yescharacteristic
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×Q8×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C4⋊C4×C283—21no—
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283—21no—
108C22×D283—21no—
109C22×D283—21no—
110C22×D283—24no—
111C22×D283—81no—
112C22×D283—81no—
113Dic566—21no—
114Dic566—21no—
115D1132—24no—
116D1132—21no—
117D1132—21no—
118D1132#4112yes—
119D1132#4112yes—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C4×D283—81no—
127C4×D283—81no—
128C4×D283—81no—
129C4×D283—81no—
130C283⋊C8—21no—
131C283⋊C8—21no—
132C23×C283C2×D411yescharacteristic
133Q8×C283—21no—
134Q8×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2411yescharacteristic
143C8×C283—21no—
144C8×C283—21no—
145C22×C283—21no—
146C22×C283—21no—
147C22×C283—21no—
148C22×C283C22×D411yescharacteristic
149C2×D283—22no—
150C2×D283—22no—
151C2×D283—41no—
152C2×D283—41no—
153C2×D283—41no—
154C2×D283—41no—
155C2×D283—84no—
156C4×C283—21no—
157C4×C283—41no—
158C4×C283—41no—
159C4×C283—41no—
160C4×C283—41no—
161C4×C283C2×#4111yescharacteristic
162C4×C283C2×#4111yescharacteristic
163Dic283—21no—
164Dic283—21no—
165Dic283—21no—
166Dic283—21no—
167Dic283—41no—
168Dic283—41no—
169C2×C283—41no—
170C2×C283#52511yescharacteristic
171C2×C283#57711yescharacteristic
172C2×C283#57711yescharacteristic
173D283—42no—
174D283—42no—
175C283#312311yescharacteristic, complemented, Sylow
176#3123—2831nomaximal, Sylow
177#541—2831no—
178#518—2831no—
179#485—2831no—
180#485D28311yescharacteristic, complemented
181#478—2831no—
182#478—2831no—
183#461—2831no—
184#461—2831no—
185#450—2831no—
186#450—2831no—
187#440—2831no—
188#440—2831no—
189C4×SD16—2831no—
190C4×SD16—2831no—
191#433—2831no—
192C22×D4—2831no—
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×SD16—2831no—
196C2×SD16—2831no—
197C4⋊Q8—2831no—
198#126—5661no—
199#126—5661no—
200#125—2831no—
201#125—5661no—
202#125—5661no—
203C22⋊Q8—2831no—
204C22⋊Q8C2×D28311yescharacteristic
205C4×Q8—2831no—
206C4×Q8—2831no—
207C4×D4—2831no—
208C4×D4—2831no—
209C4×D4—2831no—
210C4×D4—2831no—
211C4×D4—5661no—
212C4×D4—5661no—
213#117—2831no—
214#117C2×D28311yescharacteristic
215C2×C22⋊C4—5661no—
216C2×C22⋊C4—5661no—
217#107—2831no—
218#107C2×D28311yescharacteristic, complemented
219#106—2831no—
220#106C2×D28311yescharacteristic, complemented
221C4⋊C8—2831no—
222C4⋊C8—2831no—
223#103—2831no—
224#103—2831no—
225#103C2×D28311yescharacteristic, complemented
226#103C2×D28311yescharacteristic, complemented
227#102—2831no—
228#102—2831no—
229#102—2831no—
230#102—2831no—
231C22⋊C8—2831no—
232C22⋊C8C2×D28311yescharacteristic
233#97—2831no—
234C4×C8—2831no—
235C24—5661no—
236C2×Q8—2831no—
237C2×Q8C22×D28311yescharacteristic
238C2×D4—2831no—
239C2×D4—2831no—
240C2×D4—5662no—
241C2×D4—5662no—
242C2×D4—5661no—
243C22×C4—5661no—
244C22×C4—5661no—
245C22×C4—5661no—
246C22×C4—5661no—
247C22×C4C22×D28311yescharacteristic
248SD16—5662no—
249SD16—5662no—
250SD16—5662no—
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—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4C22×D28311yescharacteristic
268C4⋊C4C22×D28311yescharacteristic
269C4⋊C4C22×D28311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—2831no—
273C22⋊C4—2831no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C42—21no—
280C42—2831no—
281C42—2831no—
282C42—5661no—
283C42—5661no—
284C23—5664no—
285C23—5661no—
286C23—5661no—
287C23—22641no—
288C23—22641no—
289C23D4×D28311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—5661no—
293Q8—5661no—
294D4—2832no—
295D4—2832no—
296D4—5664no—
297D4—5661no—
298D4—5661no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—2831no—
306C2×C4—2831no—
307C2×C4—2831no—
308C2×C4—2831no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—22641no—
312C2×C4—22641no—
313C2×C4—22641no—
314C2×C4—22641no—
315C2×C4D4×D28311yescharacteristic
316C2×C4C23×D28311yescharacteristic
317C8—21no—
318C8—21no—
319C8—5661no—
320C8—5661no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—5662no—
325C22—5662no—
326C22—11321no—
327C22—11321no—
328C22—11321no—
329C22—11321no—
330C22—22644no—
331C22C2×D4×D28311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—5661no—
338C4—5661no—
339C4—5661no—
340C4—5661no—
341C4—11321no—
342C4—11321no—
343C4#41×D28311yescharacteristic
344C4#41×D28311yescharacteristic
345C2—41no—
346C2—11322no—
347C2—11322no—
348C2#3182697311yescharacteristic
349C2#3182727211yescharacteristic
350C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#485×C283C2
socleC22×C283C22×D4
prime radicalC22×D1132C22
hypercenter#485D283
hypocenterC283#3123
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #31827075C2semidirect
3. #31826806C2semidirect
4. #31826768C2semidirect
5. #31826764C2semidirect
6. #31826669C2semidirect
7. #31826669C2semidirect
10. #31826568C2semidirect
11. #31826564C2semidirect
12. #31826552C2semidirect
13. #31826550C2semidirect
14. #31826523C2semidirect
15. #485×C283C2semidirect
21. #22583608C22semidirect
25. #22583601C22semidirect
28. Q8×Dic283C22semidirect
29. #22583575C22semidirect
39. #22583543C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. Dic283⋊C8C22semidirect
43. #22583533C22semidirect
44. #22583533C22semidirect
50. #22583520C22semidirect
51. C8×Dic283C22semidirect
54. #107×C283C22semidirect
55. #106×C283C22semidirect
56. #103×C283C22semidirect
57. #103×C283C22semidirect
175. C283#3123semidirect
180. #485D283semidirect
218. #107C2×D283semidirect
220. #106C2×D283semidirect
225. #103C2×D283semidirect
226. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270752
#318269392
#318268062
#318267682
#318267642
#318266692
#318266182
#318266152
#318265682
#318265642
#318265522
#318265502
#318265232
#485×C2832
#3123283