Finite Group Databasebeta

← #49131445

Subgroups — #49131445

Order 36224.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827086C211yesmaximal, characteristic, complemented
2#31826806C211yesmaximal, characteristic, complemented
3#31826789C211yesmaximal, characteristic, complemented
4#31826755C211yesmaximal, characteristic, complemented
5#31826745C211yesmaximal, characteristic, complemented
6#31826680C211yesmaximal, characteristic, complemented
7#31826680C211yesmaximal, characteristic, complemented
8#31826616C211yesmaximal, characteristic, complemented
9#31826599C211yesmaximal, characteristic
10#31826575C211yesmaximal, characteristic, complemented
11#31826565C211yesmaximal, characteristic, complemented
12C4×#17985380C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826526C211yesmaximal, characteristic, complemented
15#518×C283C211yesmaximal, characteristic, complemented
16C2×#17985380C2211yescharacteristic
17C2×#17985380C2211yescharacteristic
18C2×#17985377C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20#22583610C2211yescharacteristic, complemented
21#22583605—21no—
22#22583598C2211yescharacteristic, complemented
23#22583596—21no—
24#22583592—21no—
25#22583589C2211yescharacteristic
26#22583588—21no—
27#22583584C2211yescharacteristic
28C4×Dic566C2211yescharacteristic, complemented
29C4×D1132C2211yescharacteristic, complemented
30#22583543C2211yescharacteristic, complemented
31#22583543C2211yescharacteristic, complemented
32#22583541C2211yescharacteristic, complemented
33#22583541C2211yescharacteristic, complemented
34C4⋊(C283⋊C8)C2211yescharacteristic, complemented
35C4⋊(C283⋊C8)C2211yescharacteristic, complemented
36#22583533C2211yescharacteristic, complemented
37#22583533C2211yescharacteristic, complemented
38#22583531C2211yescharacteristic
39#22583531C2211yescharacteristic
40#22583531C2211yescharacteristic
41#22583531C2211yescharacteristic
42#22583530C2211yescharacteristic, complemented
43#22583530C2211yescharacteristic, complemented
44C22⋊(C283⋊C8)C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46#22583521C2211yescharacteristic, complemented
47C4×C283⋊C8C2211yescharacteristic, complemented
48C22×D4×C283C2211yescharacteristic
49C4×D4×C283—21no—
50C4×D4×C283—21no—
51C4×D4×C283C2211yescharacteristic
52C4×D4×C283C2211yescharacteristic
53C4×D4×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#117×C283C2211yescharacteristic
56#117×C283C2211yescharacteristic
57C2×C22⋊C4×C283—21no—
58C2×C22⋊C4×C283—21no—
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C4×D283—21no—
64#17985380—22no—
65#17985380—22no—
66#17985377—22no—
67#17985377—22no—
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C4⋊Dic283—21no—
73C4⋊Dic283C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77C22⋊Dic283—21no—
78(C2×D283)⋊C4—21no—
79(C2×D283)⋊C4—21no—
80(C2×D283)⋊C4—21no—
81(C2×D283)⋊C4—21no—
82C4×Dic283—21no—
83C24×C283—21no—
84C2×D4×C283—22no—
85C2×D4×C283—22no—
86C2×D4×C283—21no—
87C2×D4×C283C2311yescharacteristic
88C2×D4×C283C2311yescharacteristic
89C22×C4×C283—21no—
90C22×C4×C283—21no—
91C22×C4×C283—21no—
92C22×C4×C283—21no—
93C22×C4×C283C2311yescharacteristic
94C4⋊C4×C283D411yescharacteristic
95C4⋊C4×C283D411yescharacteristic
96C4⋊C4×C283C2311yescharacteristic
97C4⋊C4×C283C2311yescharacteristic
98C22⋊C4×C283—21no—
99C22⋊C4×C283—21no—
100C22⋊C4×C283—21no—
101C22⋊C4×C283—21no—
102C22⋊C4×C283—21no—
103C22⋊C4×C283D411yescharacteristic
104C22⋊C4×C283D411yescharacteristic
105C42×C283—21no—
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109Dic566—21no—
110Dic566—21no—
111Dic566—81no—
112D1132—21no—
113D1132—21no—
114C22⋊D283—81no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C4×D283—81no—
119C283⋊C8—21no—
120C283⋊C8—21no—
121C283⋊C8—21no—
122C283⋊C8—21no—
123C23×C283—24no—
124C23×C283—21no—
125C23×C283—21no—
126C23×C283—81no—
127C23×C283—81no—
128C23×C283C2×D411yescharacteristic
129D4×C283—24no—
130D4×C283—21no—
131D4×C283—21no—
132D4×C283#4112yes—
133D4×C283#4112yes—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—81no—
139C2×C4×C283—81no—
140C2×C4×C283—81no—
141C2×C4×C283—81no—
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2411yescharacteristic
148C22×C283—21no—
149C22×C283—22no—
150C22×C283—22no—
151C22×C283—21no—
152C22×C283—21no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283—41no—
156C22×C283—41no—
157C22×C283—84no—
158C22×C283C22×D411yescharacteristic
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—41no—
162C4×C283—21no—
163C4×C283—21no—
164C4×C283—21no—
165C4×C283—21no—
166C4×C283—21no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283C2×#4111yescharacteristic
170C4×C283C2×#4111yescharacteristic
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174C2×C283—41no—
175C2×C283—42no—
176C2×C283—42no—
177C2×C283#52511yescharacteristic
178C2×C283#57611yescharacteristic
179C2×C283#57711yescharacteristic
180D283—81no—
181C283#311811yescharacteristic, complemented, Sylow
182#3118—2831nomaximal, Sylow
183#542—2831no—
184#518D28311yescharacteristic, complemented
185#485—2831no—
186#482—2831no—
187#476—2831no—
188#474—2831no—
189#463—2831no—
190#463—2831no—
191#450—2831no—
192#447—2831no—
193#442—2831no—
194#440—2831no—
195C4×SD16—2831no—
196C4×D8—2831no—
197#433—2831no—
198C22×D4C2×D28311yescharacteristic
199C2×SD16—2831no—
200C2×SD16—2831no—
201C2×D8—2831no—
202C2×D8—2831no—
203C4⋊Q8—2831no—
204#126—5661no—
205#124—2831no—
206#124—5661no—
207#123—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—5661no—
210#121—2831no—
211C4×Q8—2831no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—2831no—
215C4×D4C2×D28311yescharacteristic
216C4×D4C2×D28311yescharacteristic
217C4×D4C2×D28311yescharacteristic
218C4×D4C2×D28311yescharacteristic
219#117C2×D28311yescharacteristic
220#117C2×D28311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223#107—2831no—
224#107—2831no—
225#106—2831no—
226#106—2831no—
227C4⋊C8—2831no—
228C4⋊C8—2831no—
229#103—2831no—
230#103—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236#102—2831no—
237C22⋊C8—2831no—
238C22⋊C8—2831no—
239#97—2831no—
240C4×C8—2831no—
241C24—21no—
242C2×Q8—2831no—
243C2×Q8—5661no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—2831no—
248C2×D4—5661no—
249C2×D4C22×D28311yescharacteristic
250C2×D4C22×D28311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—5661no—
256C22×C4C22×D28311yescharacteristic
257SD16—5662no—
258SD16—5662no—
259D8—5662no—
260D8—5662no—
261C2×C8—2831no—
262C2×C8—2831no—
263C2×C8—2831no—
264C2×C8—2831no—
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4C22⋊D28311yescharacteristic
271C4⋊C4C22⋊D28311yescharacteristic
272C4⋊C4C22×D28311yescharacteristic
273C4⋊C4C22×D28311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4C22⋊D28311yescharacteristic
285C22⋊C4C22⋊D28311yescharacteristic
286C42—21no—
287C42—5661no—
288C42C22×D28311yescharacteristic
289C42C22×D28311yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—5661no—
296C23C2×C22⋊D28311yescharacteristic
297Q8—5661no—
298Q8—5661no—
299Q8—22641no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—5661no—
304D4—5661no—
305D4—22641no—
306D4#1798539212yes—
307D4#1798539212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—22641no—
320C2×C4C2×C22⋊D28311yescharacteristic
321C2×C4C2×C22⋊D28311yescharacteristic
322C2×C4C2×C22⋊D28311yescharacteristic
323C2×C4C2×C22⋊D28311yescharacteristic
324C2×C4C2×C22⋊D28311yescharacteristic
325C2×C4C23×D28311yescharacteristic
326C8—5661no—
327C8—5661no—
328C8—5661no—
329C8—5661no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—11321no—
341C22—11321no—
342C22—11321no—
343C22C22×C22⋊D28311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—11321no—
352C4—11321no—
353C4—11321no—
354C4C2×#1798539211yescharacteristic
355C4C2×#1798539211yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—22641no—
360C2#3182697611yescharacteristic
361C2#3182726811yescharacteristic
362C2#3182727611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#518×C283C2
socleC22×C283C22×D4
prime radical#31826599C2
hypercenter#518D283
hypocenterC283#3118
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #31827086C2semidirect
2. #31826806C2semidirect
3. #31826789C2semidirect
4. #31826755C2semidirect
5. #31826745C2semidirect
6. #31826680C2semidirect
7. #31826680C2semidirect
8. #31826616C2semidirect
10. #31826575C2semidirect
11. #31826565C2semidirect
12. C4×#17985380C2semidirect
13. C4×#17985377C2semidirect
14. #31826526C2semidirect
15. #518×C283C2semidirect
20. #22583610C22semidirect
22. #22583598C22semidirect
28. C4×Dic566C22semidirect
29. C4×D1132C22semidirect
30. #22583543C22semidirect
31. #22583543C22semidirect
32. #22583541C22semidirect
33. #22583541C22semidirect
34. C4⋊(C283⋊C8)C22semidirect
35. C4⋊(C283⋊C8)C22semidirect
36. #22583533C22semidirect
37. #22583533C22semidirect
42. #22583530C22semidirect
43. #22583530C22semidirect
46. #22583521C22semidirect
47. C4×C283⋊C8C22semidirect
181. C283#3118semidirect
184. #518D283semidirect

Maximal subgroups

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

subgroupindex
#318270862
#318268062
#318267892
#318267552
#318267452
#318266802
#318266162
#318265992
#318265752
#318265652
C4×#179853802
C4×#179853772
#318265262
#518×C2832
#3118283