Finite Group Databasebeta

← #49131439

Subgroups — #49131439

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#31826939C211yesmaximal, characteristic, complemented
2#31826803C211yesmaximal, characteristic, complemented
3#31826786C211yesmaximal, characteristic, complemented
4#31826752C211yesmaximal, characteristic, complemented
5#31826742C211yesmaximal, characteristic, complemented
6#31826677C211yesmaximal, characteristic, complemented
7#31826677C211yesmaximal, characteristic, complemented
8#31826615C211yesmaximal, characteristic, complemented
9#31826598C211yesmaximal, characteristic
10#31826575C211yesmaximal, characteristic, complemented
11#31826563C211yesmaximal, characteristic, complemented
12C4×#17985379C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826526C211yesmaximal, characteristic, complemented
15#542×C283C211yesmaximal, characteristic, complemented
16C22×D1132C2211yescharacteristic
17C2×#17985379C2211yescharacteristic
18C2×#17985379C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21C4×D1132C2211yescharacteristic
22C4×D1132C2211yescharacteristic
23C4×D1132C2211yescharacteristic
24C4×D1132C2211yescharacteristic
25#22583572—21no—
26#22583572—21no—
27#22583569C2211yescharacteristic
28C22⋊C4×D283—21no—
29C22⋊C4×D283—21no—
30#22583543C2211yescharacteristic, complemented
31#22583543C2211yescharacteristic, complemented
32#22583541C2211yescharacteristic, complemented
33#22583541C2211yescharacteristic, complemented
34C4⋊(C283⋊C8)C2211yescharacteristic, complemented
35C4⋊(C283⋊C8)C2211yescharacteristic, complemented
36#22583534C2211yescharacteristic, complemented
37#22583534C2211yescharacteristic, complemented
38#22583531C2211yescharacteristic, complemented
39#22583531C2211yescharacteristic, complemented
40#22583530C2211yescharacteristic
41#22583530C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44C22⋊(C283⋊C8)C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46#22583521C2211yescharacteristic, complemented
47C4×C283⋊C8C2211yescharacteristic, complemented
48C4⋊Q8×C283C2211yescharacteristic, complemented
49#126×C283—21no—
50#124×C283—21no—
51#124×C283C2211yescharacteristic, complemented
52#123×C283—21no—
53C22⋊Q8×C283—21no—
54C22⋊Q8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56C4×Q8×C283C2211yescharacteristic, complemented
57C4×D4×C283C2211yescharacteristic, complemented
58#117×C283C2211yescharacteristic
59C23×D283—21no—
60C2×D1132—22no—
61C2×D1132—22no—
62C2×D1132—21no—
63C2×D1132C2311yescharacteristic
64C2×D1132C2311yescharacteristic
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69#17985379—22no—
70#17985379—22no—
71#17985377—22no—
72#17985377—22no—
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C2×C283⋊C8C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79C22⋊Dic283—21no—
80(C2×D283)⋊C4—21no—
81(C2×D283)⋊C4—21no—
82(C2×D283)⋊C4—21no—
83(C2×D283)⋊C4—21no—
84C4×Dic283—21no—
85C2×Q8×C283—21no—
86C2×Q8×C283C2311yescharacteristic
87C2×D4×C283—21no—
88C2×D4×C283C2311yescharacteristic
89C22×C4×C283—21no—
90C22×C4×C283C2311yescharacteristic
91C4⋊C4×C283—21no—
92C4⋊C4×C283—21no—
93C4⋊C4×C283—21no—
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—
109C22×D283—21no—
110C22×D283—24no—
111C22×D283—81no—
112C22×D283—81no—
113D1132—24no—
114D1132—21no—
115D1132—21no—
116D1132#4112yes—
117D1132#4112yes—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C4×D283—81no—
121C4×D283—81no—
122C4×D283—81no—
123C4×D283—81no—
124C283⋊C8—21no—
125C283⋊C8—21no—
126C283⋊C8—21no—
127C283⋊C8—21no—
128C23×C283—21no—
129C23×C283C2×D411yescharacteristic
130Q8×C283—21no—
131Q8×C283—21no—
132Q8×C283—81no—
133D4×C283—21no—
134D4×C283—21no—
135D4×C283—81no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
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—21no—
150C22×C283—21no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283C22×D411yescharacteristic
155C2×D283—22no—
156C2×D283—22no—
157C2×D283—41no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—84no—
162C4×C283—21no—
163C4×C283—21no—
164C4×C283—21no—
165C4×C283—21no—
166C4×C283—21no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283—41no—
170C4×C283C2×#4111yescharacteristic
171C4×C283C2×#4111yescharacteristic
172Dic283—41no—
173Dic283—41no—
174C2×C283—41no—
175C2×C283—81no—
176C2×C283#52511yescharacteristic
177C2×C283#57611yescharacteristic
178C2×C283#57711yescharacteristic
179D283—42no—
180D283—42no—
181C283#311811yescharacteristic, complemented, Sylow
182#3118—2831nomaximal, Sylow
183#542D28311yescharacteristic, complemented
184#518—2831no—
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×D4—2831no—
199C2×SD16—2831no—
200C2×SD16—2831no—
201C2×D8—2831no—
202C2×D8—2831no—
203C4⋊Q8C2×D28311yescharacteristic, complemented
204#126—21no—
205#124—21no—
206#124C2×D28311yescharacteristic, complemented
207#123—21no—
208C22⋊Q8—21no—
209C22⋊Q8C2×D28311yescharacteristic
210#121C2×D28311yescharacteristic
211C4×Q8C2×D28311yescharacteristic, complemented
212C4×D4—2831no—
213C4×D4—2831no—
214C4×D4—2831no—
215C4×D4—2831no—
216C4×D4—5661no—
217C4×D4—5661no—
218C4×D4C2×D28311yescharacteristic, complemented
219#117—2831no—
220#117C2×D28311yescharacteristic
221C2×C22⋊C4—5661no—
222C2×C22⋊C4—5661no—
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—5661no—
242C2×Q8—21no—
243C2×Q8C22×D28311yescharacteristic
244C2×D4—21no—
245C2×D4—2831no—
246C2×D4—2831no—
247C2×D4—5662no—
248C2×D4—5662no—
249C2×D4—5661no—
250C2×D4C22×D28311yescharacteristic
251C22×C4—21no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4—5661no—
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—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—2831no—
269C4⋊C4—2831no—
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—21no—
291C23—5664no—
292C23—5661no—
293C23—5661no—
294C23—22641no—
295C23—22641no—
296C23C2×C22⋊D28311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—2832no—
304D4—2832no—
305D4—5664no—
306D4—5661no—
307D4—5661no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—22641no—
317C2×C4—22641no—
318C2×C4—22641no—
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—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—5662no—
337C22—5662no—
338C22—11321no—
339C22—11321no—
340C22—11321no—
341C22—11321no—
342C22—22644no—
343C22C22×C22⋊D28311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—11321no—
353C4—11321no—
354C4#41×D28311yescharacteristic
355C4#41×D28311yescharacteristic
356C2—41no—
357C2—81no—
358C2—11322no—
359C2—11322no—
360C2#3182697211yescharacteristic
361C2#3182726811yescharacteristic
362C2#3182727311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#542×C283C2
socleC22×C283C22×D4
prime radical#31826598C2
hypercenter#542D283
hypocenterC283#3118
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #31826939C2semidirect
2. #31826803C2semidirect
3. #31826786C2semidirect
4. #31826752C2semidirect
5. #31826742C2semidirect
6. #31826677C2semidirect
7. #31826677C2semidirect
8. #31826615C2semidirect
10. #31826575C2semidirect
11. #31826563C2semidirect
12. C4×#17985379C2semidirect
13. C4×#17985377C2semidirect
14. #31826526C2semidirect
15. #542×C283C2semidirect
30. #22583543C22semidirect
31. #22583543C22semidirect
32. #22583541C22semidirect
33. #22583541C22semidirect
34. C4⋊(C283⋊C8)C22semidirect
35. C4⋊(C283⋊C8)C22semidirect
36. #22583534C22semidirect
37. #22583534C22semidirect
38. #22583531C22semidirect
39. #22583531C22semidirect
46. #22583521C22semidirect
47. C4×C283⋊C8C22semidirect
48. C4⋊Q8×C283C22semidirect
51. #124×C283C22semidirect
56. C4×Q8×C283C22semidirect
57. C4×D4×C283C22semidirect
181. C283#3118semidirect
183. #542D283semidirect
203. C4⋊Q8C2×D283semidirect
206. #124C2×D283semidirect
211. C4×Q8C2×D283semidirect
218. C4×D4C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318269392
#318268032
#318267862
#318267522
#318267422
#318266772
#318266152
#318265982
#318265752
#318265632
C4×#179853792
C4×#179853772
#318265262
#542×C2832
#3118283