Finite Group Databasebeta

← #49131259

Subgroups — #49131259

Order 36224.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827012C211yesmaximal, characteristic, complemented
2C4×D4×D283C211yesmaximal, characteristic, complemented
3#31826780C211yesmaximal, characteristic, complemented
4#31826777C211yesmaximal, characteristic, complemented
5#31826744C211yesmaximal, characteristic, complemented
6#31826743C211yesmaximal, characteristic, complemented
7#31826659C211yesmaximal, characteristic, complemented
8#31826658C211yesmaximal, characteristic, complemented
9#31826600C211yesmaximal, characteristic, complemented
10#31826597C211yesmaximal, characteristic, complemented
11C4×D2264C211yesmaximal, characteristic, complemented
12C4×#17985377C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826516C211yesmaximal, characteristic, complemented
15C4×D8×C283C211yesmaximal, characteristic, complemented
16C2×#17985392—21no—
17C2×D4×D283C2211yescharacteristic
18C22×C4×D283—21no—
19C2×D2264C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21C2×#17985377C2211yescharacteristic
22#22583609C2211yescharacteristic, complemented
23#22583606C2211yescharacteristic, complemented
24#22583596—21no—
25#22583585C2211yescharacteristic
26#22583583—21no—
27#22583581C2211yescharacteristic
28C4×D1132C2211yescharacteristic
29C4×D1132C2211yescharacteristic, complemented
30D4×Dic283C2211yescharacteristic
31#22583572C2211yescharacteristic
32C4×C22⋊D283—21no—
33C4×C22⋊D283—21no—
34(C22⋊D283)⋊C4—21no—
35C4⋊C4×D283C2211yescharacteristic
36C22⋊C4×D283—21no—
37C42×D283C2211yescharacteristic
38#22583544C2211yescharacteristic, complemented
39#22583543C2211yescharacteristic, complemented
40#22583543C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42Dic283⋊C8C2211yescharacteristic, complemented
43#22583532C2211yescharacteristic
44#22583532C2211yescharacteristic, complemented
45#22583531C2211yescharacteristic
46#22583531C2211yescharacteristic, complemented
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic, complemented
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C4×C283⋊C8C2211yescharacteristic, complemented
52C2×D8×C283C2211yescharacteristic
53C4×D4×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic, complemented
55#107×C283C2211yescharacteristic, complemented
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic, complemented
58C4×C8×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60#17985392—44no—
61C2×Dic566—21no—
62C2×D1132—21no—
63C2×D1132C2311yescharacteristic
64C2×D1132C2311yescharacteristic
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69D4×D283—22no—
70D4×D283—22no—
71C22×Dic283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75C2×C4×D283—21no—
76C2×C4×D283—44no—
77C2×C4×D283D411yescharacteristic
78C2×C4×D283D411yescharacteristic
79C2×C4×D283C2311yescharacteristic
80D2264—22no—
81#17985377—22no—
82#17985377—22no—
83C2×C283⋊C8C2311yescharacteristic
84C2×C283⋊C8C2311yescharacteristic
85C4⋊Dic283C2311yescharacteristic
86C4⋊Dic283C2311yescharacteristic
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95C4×Dic283D411yescharacteristic
96C4×Dic283D411yescharacteristic
97C4×Dic283C2311yescharacteristic
98C2×D4×C283C2311yescharacteristic
99C2×D4×C283C2311yescharacteristic
100C22×C4×C283—21no—
101C22×C4×C283—21no—
102D8×C283—22no—
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C22⋊C4×C283—21no—
108C22⋊C4×C283—21no—
109C42×C283C2311yescharacteristic
110C22×D283—24no—
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—42no—
114C22×D283—42no—
115C22×D283C2×D411yescharacteristic
116Dic566—42no—
117D1132—21no—
118D1132—21no—
119D1132—21no—
120D1132—42no—
121D1132#4112yescomplemented
122C22⋊D283—24no—
123C22⋊D283—42no—
124C22⋊D283—42no—
125C22⋊D283—42no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—42no—
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C2×Dic283C2×D411yescharacteristic
132C4×D283—21no—
133C4×D283—21no—
134C4×D283—41no—
135C4×D283—42no—
136C4×D283—42no—
137C4×D283—42no—
138C4×D283—42no—
139C4×D283D814yescomplemented
140C283⋊C8—21no—
141C283⋊C8—21no—
142C23×C283—21no—
143C23×C283—21no—
144D4×C283—21no—
145D4×C283—21no—
146D4×C283—21no—
147D4×C283#4112yescomplemented
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—42no—
151C2×C4×C283—42no—
152C2×C4×C283C2×D411yescharacteristic
153C2×C4×C283C2×D411yescharacteristic
154C2×C4×C283C2411yescharacteristic
155C8×C283—21no—
156C8×C283—21no—
157C22×C283—22no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283—41no—
161C22×C283—41no—
162C22×C283—41no—
163C22×C283C22×D411yescharacteristic
164C2×D283—21no—
165C2×D283—21no—
166C2×D283—22no—
167C2×D283—48no—
168C2×D283—41no—
169C2×D283—41no—
170C2×D283—41no—
171C2×D283—41no—
172C2×D283—41no—
173C2×D283C2×D812yes—
174C4×C283—21no—
175C4×C283—41no—
176C4×C283—41no—
177C4×C283C2×D812yes—
178C4×C283C2×#4111yescharacteristic
179C4×C283C2×#4111yescharacteristic
180Dic283—21no—
181Dic283—21no—
182Dic283—41no—
183Dic283—41no—
184Dic283C2×D812yes—
185C2×C283—42no—
186C2×C283—81no—
187C2×C283#52511yescharacteristic
188C2×C283C22×D811yescharacteristic
189C2×C283#57511yescharacteristic
190D283—22no—
191D283—42no—
192D283—81no—
193C283#310011yescharacteristic, complemented, Sylow
194#3100—2831nomaximal, Sylow
195#532—2831no—
196C2×C4×D4—2831no—
197#480—2831no—
198#480—2831no—
199#474—2831no—
200#474—2831no—
201#459—2831no—
202#459—2831no—
203#447—2831no—
204#447—2831no—
205C4×D8—2831no—
206C4×D8—2831no—
207C4×D8—2831no—
208C4×D8D28311yescharacteristic, complemented
209#431—2831no—
210C2×#41—5661no—
211C22×D4—2831no—
212C23×C4—5661no—
213C2×D8—2831no—
214C2×D8—2831no—
215C2×D8—2831no—
216C2×D8C2×D28311yescharacteristic
217C4⋊Q8—2831no—
218#127—2831no—
219#124—5661no—
220#121—2831no—
221#121—2831no—
222#121—5661no—
223C4×D4—2831no—
224C4×D4—2831no—
225C4×D4—2831no—
226C4×D4—2831no—
227C4×D4—5661no—
228C4×D4—5661no—
229C4×D4—5661no—
230C4×D4C2×D28311yescharacteristic
231C4×D4C2×D28311yescharacteristic, complemented
232C2×C4⋊C4—2831no—
233C2×C22⋊C4—5661no—
234C2×C42—2831no—
235#107—2831no—
236#107—2831no—
237#107—2831no—
238#107C2×D28311yescharacteristic, complemented
239C4⋊C8—2831no—
240C4⋊C8—2831no—
241#102—2831no—
242#102—2831no—
243#102—2831no—
244#102—2831no—
245#102—2831no—
246#102—2831no—
247#102C2×D28311yescharacteristic
248#102C2×D28311yescharacteristic, complemented
249C22⋊C8—2831no—
250C22⋊C8—2831no—
251C4×C8—2831no—
252C4×C8C2×D28311yescharacteristic, complemented
253C24—5661no—
254#41—11324no—
255C2×Q8—5661no—
256C2×D4—2831no—
257C2×D4—2831no—
258C2×D4—5661no—
259C2×D4—5661no—
260C2×D4—5661no—
261C2×D4—5661no—
262C2×D4—5662no—
263C2×D4—5662no—
264C2×D4—5661no—
265C2×D4C22×D28311yescharacteristic
266C2×D4C22×D28311yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—2831no—
270C22×C4—2831no—
271C22×C4—2831no—
272C22×C4—5661no—
273C22×C4—5661no—
274C22×C4—5661no—
275C22×C4—5661no—
276C22×C4—5661no—
277C22×C4—11324no—
278D8—22no—
279D8—5662no—
280D8—5662no—
281D8—5662no—
282C2×C8—2831no—
283C2×C8—2831no—
284C2×C8C22×D28311yescharacteristic
285C2×C8C22×D28311yescharacteristic
286C4⋊C4—2831no—
287C4⋊C4—2831no—
288C4⋊C4—5661no—
289C4⋊C4—5661no—
290C4⋊C4C22×D28311yescharacteristic
291C4⋊C4C22×D28311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C22⋊C4—5661no—
298C22⋊C4—5661no—
299C22⋊C4—5661no—
300C42—2831no—
301C42—2831no—
302C42—2831no—
303C42C22×D28311yescharacteristic
304C23—21no—
305C23—21no—
306C23—2831no—
307C23—5664no—
308C23—5661no—
309C23—5661no—
310C23—11322no—
311C23—11322no—
312Q8—11322no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—2832no—
317D4—5664no—
318D4—5661no—
319D4—5661no—
320D4—5661no—
321D4—11322no—
322D4—11322no—
323D4—11322no—
324D4—11322no—
325D4#1798539212yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—2831no—
331C2×C4—2834no—
332C2×C4—2831no—
333C2×C4—2831no—
334C2×C4—5661no—
335C2×C4—5661no—
336C2×C4—5661no—
337C2×C4—5661no—
338C2×C4—11321no—
339C2×C4—11322no—
340C2×C4—11322no—
341C2×C4—11322no—
342C2×C4—11322no—
343C2×C4—11322no—
344C2×C4D4×D28311yescharacteristic
345C2×C4D4×D28311yescharacteristic
346C2×C4C23×D28311yescharacteristic
347C8—21no—
348C8—21no—
349C8—5661no—
350C8—5661no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—2832no—
358C22—5661no—
359C22—5661no—
360C22—5662no—
361C22—11328no—
362C22—11321no—
363C22—11321no—
364C22—11321no—
365C22—11321no—
366C22—11321no—
367C22C2×D4×D28311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—2832no—
372C4—5661no—
373C4—5661no—
374C4—11321no—
375C4—11321no—
376C4D8×D28312yes—
377C4#41×D28311yescharacteristic
378C4C2×#1798539211yescharacteristic
379C2—42no—
380C2—81no—
381C2—5662no—
382C2—11322no—
383C2—22641no—
384C2#3182697411yescharacteristic
385C2C2×D8×D28311yescharacteristic
386C2#3182726211yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×D8×C283C2
socleC22×C283C22×D4
hypercenterC4×D8D283
hypocenterC283#3100
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #31827012C2semidirect
2. C4×D4×D283C2semidirect
3. #31826780C2semidirect
4. #31826777C2semidirect
5. #31826744C2semidirect
6. #31826743C2semidirect
7. #31826659C2semidirect
8. #31826658C2semidirect
9. #31826600C2semidirect
10. #31826597C2semidirect
11. C4×D2264C2semidirect
12. C4×#17985377C2semidirect
13. C4×#17985377C2semidirect
14. #31826516C2semidirect
15. C4×D8×C283C2semidirect
22. #22583609C22semidirect
23. #22583606C22semidirect
29. C4×D1132C22semidirect
38. #22583544C22semidirect
39. #22583543C22semidirect
40. #22583543C22semidirect
41. Dic283⋊C8C22semidirect
42. Dic283⋊C8C22semidirect
44. #22583532C22semidirect
46. #22583531C22semidirect
48. #22583530C22semidirect
51. C4×C283⋊C8C22semidirect
54. C4×D4×C283C22semidirect
55. #107×C283C22semidirect
57. #102×C283C22semidirect
58. C4×C8×C283C22semidirect
121. D1132#41semidirect
139. C4×D283D8semidirect
147. D4×C283#41semidirect
193. C283#3100semidirect
208. C4×D8D283semidirect
231. C4×D4C2×D283semidirect
238. #107C2×D283semidirect
248. #102C2×D283semidirect
252. C4×C8C2×D283semidirect
325. D4#17985392semidirect

Maximal subgroups

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

subgroupindex
#318270122
C4×D4×D2832
#318267802
#318267772
#318267442
#318267432
#318266592
#318266582
#318266002
#318265972
C4×D22642
C4×#179853772
#318265162
C4×D8×C2832
#3100283