Finite Group Databasebeta

← #49133112

Subgroups — #49133112

Order 36224.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827159C211yesmaximal, characteristic, complemented
2#31827103C211yesmaximal, characteristic, complemented
3#31826821C211yesmaximal, characteristic, complemented
4#31826799C211yesmaximal, characteristic, complemented
5#31826789C211yesmaximal, characteristic, complemented
6#31826763C211yesmaximal, characteristic, complemented
7#31826701C211yesmaximal, characteristic, complemented
8#31826697C211yesmaximal, characteristic, complemented
9#31826683C211yesmaximal, characteristic, complemented
10#31826610C211yesmaximal, characteristic, complemented
11#31826600C211yesmaximal, characteristic, complemented
12#31826545C211yesmaximal, characteristic, complemented
13C8×C22⋊D283C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#416×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283C2211yescharacteristic
17C2×#17985379C2211yescharacteristic, complemented
18C2×D2264C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic
21#22583604—21no—
22#22583601C2211yescharacteristic, complemented
23#22583599C2211yescharacteristic
24#22583593—21no—
25#22583592—21no—
26#22583586C2211yescharacteristic
27#22583585C2211yescharacteristic
28#22583584C2211yescharacteristic
29#22583584C2211yescharacteristic, complemented
30#22583583—21no—
31#22583582—21no—
32#22583578—21no—
33C4×D1132—21no—
34D4×Dic283C2211yescharacteristic
35#22583572C2211yescharacteristic, complemented
36C4×C22⋊D283C2211yescharacteristic
37C4⋊C4×D283C2211yescharacteristic
38C2×(C2×D283)⋊C4—21no—
39#22583544C2211yescharacteristic, complemented
40#22583543C2211yescharacteristic, complemented
41#22583541C2211yescharacteristic, complemented
42Dic283⋊C8C2211yescharacteristic, complemented
43#22583534C2211yescharacteristic, complemented
44#22583532C2211yescharacteristic
45#22583532C2211yescharacteristic, complemented
46#22583531C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic, complemented
52C2×#41×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic, complemented
54#117×C283C2211yescharacteristic, complemented
55#103×C283C2211yescharacteristic, complemented
56#103×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C23×D283—21no—
60C2×D1132—21no—
61C2×D1132C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283D411yescharacteristic
67D4×D283—22no—
68D4×D283—41no—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283C2311yescharacteristic
73#17985379—41no—
74D2264—41no—
75#17985377—22no—
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C8×D283—41no—
79C4⋊Dic283—21no—
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4D411yescharacteristic
86C22⋊Dic283—21no—
87C22⋊Dic283D411yescharacteristic
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4D411yescharacteristic
96C4×Dic283C2311yescharacteristic
97#41×C283—22no—
98#41×C283—41no—
99C2×Q8×C283C2311yescharacteristic
100C2×D4×C283—21no—
101C2×D4×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283C2311yescharacteristic
104C2×C8×C283—41no—
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C22⋊C4×C283—21no—
110C42×C283—21no—
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—42no—
114C22×D283—42no—
115C22×D283—81no—
116C22×D283C2×D411yescharacteristic
117D1132—21no—
118D1132—21no—
119D1132—21no—
120D1132—21no—
121D1132—42no—
122C22⋊D283—22no—
123C22⋊D283—42no—
124C22⋊D283—81no—
125C22⋊D283—81no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—81no—
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C2×Dic283C2×D411yescharacteristic
132C4×D283—21no—
133C4×D283—21no—
134C4×D283—81no—
135C4×D283—81no—
136C283⋊C8—21no—
137C283⋊C8—21no—
138C23×C283—21no—
139C23×C283C2×D411yescharacteristic
140Q8×C283—21no—
141Q8×C283—21no—
142D4×C283—21no—
143D4×C283—42no—
144D4×C283#4112yes—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—42no—
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2411yescharacteristic
153C8×C283—21no—
154C8×C283—21no—
155C22×C283—21no—
156C22×C283—22no—
157C22×C283—21no—
158C22×C283—21no—
159C22×C283—41no—
160C22×C283—41no—
161C22×C283C22×D411yescharacteristic
162C2×D283—21no—
163C2×D283—21no—
164C2×D283—41no—
165C2×D283—41no—
166C2×D283—41no—
167C2×D283—41no—
168C2×D283—41no—
169C2×D283—41no—
170C2×D283—84no—
171C2×D283#13512yes—
172C4×C283—21no—
173C4×C283—41no—
174C4×C283—41no—
175C4×C283—41no—
176C4×C283C2×#4111yescharacteristic
177C4×C283H(5,𝔽2)11yescharacteristic
178Dic283—21no—
179Dic283—21no—
180Dic283—21no—
181Dic283—41no—
182Dic283—41no—
183C2×C283—42no—
184C2×C283—41no—
185C2×C283#54611yescharacteristic
186C2×C283C2×#13511yescharacteristic
187C2×C283#57611yescharacteristic
188D283—22no—
189D283—81no—
190D283—81no—
191C283#329711yescharacteristic, complemented, Sylow
192#3297—2831nomaximal, Sylow
193#553—2831no—
194#546—2831no—
195#488—2831no—
196#484—2831no—
197#482—2831no—
198#478—2831no—
199#466—2831no—
200#465—2831no—
201#463—2831no—
202#449—2831no—
203#447—2831no—
204C4×D8—2831no—
205C8×D4—2831no—
206#416D28311yescharacteristic, complemented
207C2×#102—2831no—
208C2×#41C2×D28311yescharacteristic
209C22×D4—2831no—
210C2×SD16—2831no—
211C2×D8—2831no—
212C2×D8—2831no—
213C22×C8—2831no—
214C22×C8C2×D28311yescharacteristic, complemented
215#126—5661no—
216#125—2831no—
217#124—2831no—
218#123—5661no—
219#123—5661no—
220C22⋊Q8—2831no—
221#121—2831no—
222#121—2831no—
223#121—2831no—
224#121—5661no—
225#121—5661no—
226#120—5661no—
227C4×D4—2831no—
228C4×D4—2831no—
229C4×D4—2831no—
230C4×D4—5661no—
231#117C2×D28311yescharacteristic, complemented
232C2×C4⋊C4—2831no—
233C2×C22⋊C4—5661no—
234#107—2831no—
235#107—2831no—
236#106—2831no—
237C4⋊C8—2831no—
238#103—2831no—
239#103C2×D28311yescharacteristic, complemented
240#103C2×D28311yescharacteristic, complemented
241#102—2831no—
242#102—2831no—
243#102—2831no—
244#102—2831no—
245#102—2831no—
246#102C2×D28311yescharacteristic
247#102C2×D28311yescharacteristic
248C22⋊C8—2831no—
249C22⋊C8—2831no—
250C4×C8—2831no—
251C24—5661no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D28311yescharacteristic
255C2×D4—21no—
256C2×D4—2831no—
257C2×D4—2831no—
258C2×D4—2831no—
259C2×D4—5661no—
260C2×D4—5661no—
261C2×D4—5662no—
262C2×D4—5661no—
263C2×D4—5661no—
264C2×D4—11321no—
265C2×D4C22×D28311yescharacteristic
266C22×C4—21no—
267C22×C4—2831no—
268C22×C4—5661no—
269C22×C4—5661no—
270C22×C4—5661no—
271C22×C4C22×D28311yescharacteristic
272SD16—11321no—
273D8—5662no—
274D8—11321no—
275C2×C8—41no—
276C2×C8—2831no—
277C2×C8—2831no—
278C2×C8—11321no—
279C2×C8C22×D28311yescharacteristic
280C2×C8C22×D28311yescharacteristic
281C4⋊C4—2831no—
282C4⋊C4—2831no—
283C4⋊C4—2831no—
284C4⋊C4—5661no—
285C4⋊C4—5661no—
286C4⋊C4—5661no—
287C4⋊C4—5661no—
288C4⋊C4C22×D28311yescharacteristic
289C4⋊C4C22×D28311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2831no—
292C22⋊C4—2831no—
293C22⋊C4—5661no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C22⋊C4—5661no—
298C22⋊C4—5661no—
299C22⋊C4—5661no—
300C22⋊C4—5661no—
301C42—21no—
302C42—2831no—
303C23—21no—
304C23—2831no—
305C23—5661no—
306C23—5661no—
307C23—11322no—
308C23—11322no—
309C23—22641no—
310C23D4×D28311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—42no—
315D4—5662no—
316D4—5661no—
317D4—5661no—
318D4—5661no—
319D4—5661no—
320D4—11322no—
321D4—11322no—
322D4—22641no—
323D4—22641no—
324D4#1798539212yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—2831no—
332C2×C4—2831no—
333C2×C4—2831no—
334C2×C4—5661no—
335C2×C4—5661no—
336C2×C4—5661no—
337C2×C4—5661no—
338C2×C4—22641no—
339C2×C4—22641no—
340C2×C4—22641no—
341C2×C4D4×D28311yescharacteristic
342C2×C4C23×D28311yescharacteristic
343C8—21no—
344C8—21no—
345C8—5661no—
346C8—5661no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—2832no—
354C22—5661no—
355C22—5661no—
356C22—11321no—
357C22—11321no—
358C22—11321no—
359C22—11321no—
360C22—11321no—
361C22—11321no—
362C22—22644no—
363C22C2×D4×D28311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—5661no—
369C4—5661no—
370C4—5661no—
371C4—11321no—
372C4—11321no—
373C4C2×#1798539211yescharacteristic
374C4#2258365511yescharacteristic
375C2—41no—
376C2—42no—
377C2—5662no—
378C2—22641no—
379C2—22641no—
380C2#3182710511yescharacteristic
381C2#135×D28311yescharacteristic
382C2#3182726711yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#416×C283C2
socleC22×C283C22×D4
hypercenter#416D283
hypocenterC283#3297
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #31827159C2semidirect
2. #31827103C2semidirect
3. #31826821C2semidirect
4. #31826799C2semidirect
5. #31826789C2semidirect
6. #31826763C2semidirect
7. #31826701C2semidirect
8. #31826697C2semidirect
9. #31826683C2semidirect
10. #31826610C2semidirect
11. #31826600C2semidirect
12. #31826545C2semidirect
13. C8×C22⋊D283C2semidirect
14. #102×D283C2semidirect
15. #416×C283C2semidirect
17. C2×#17985379C22semidirect
22. #22583601C22semidirect
29. #22583584C22semidirect
35. #22583572C22semidirect
39. #22583544C22semidirect
40. #22583543C22semidirect
41. #22583541C22semidirect
42. Dic283⋊C8C22semidirect
43. #22583534C22semidirect
45. #22583532C22semidirect
49. C22⋊(C283⋊C8)C22semidirect
51. C8×Dic283C22semidirect
53. C22×C8×C283C22semidirect
54. #117×C283C22semidirect
55. #103×C283C22semidirect
56. #103×C283C22semidirect
191. C283#3297semidirect
206. #416D283semidirect
214. C22×C8C2×D283semidirect
231. #117C2×D283semidirect
239. #103C2×D283semidirect
240. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271592
#318271032
#318268212
#318267992
#318267892
#318267632
#318267012
#318266972
#318266832
#318266102
#318266002
#318265452
C8×C22⋊D2832
#102×D2832
#416×C2832
#3297283