Finite Group Databasebeta

← #49133345

Subgroups — #49133345

Order 36224.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827170C211yesmaximal, characteristic, complemented
2#31827112C211yesmaximal, characteristic
3#31826823C211yesmaximal, characteristic, complemented
4#31826802C211yesmaximal, characteristic, complemented
5#31826744C211yesmaximal, characteristic, complemented
6#31826709C211yesmaximal, characteristic, complemented
7#31826707C211yesmaximal, characteristic, complemented
8#31826686C211yesmaximal, characteristic, complemented
9#31826629C211yesmaximal, characteristic, complemented
10#31826617C211yesmaximal, characteristic, complemented
11#31826564C211yesmaximal, characteristic, complemented
12#31826539C211yesmaximal, characteristic, complemented
13#31826464C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#480×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic, complemented
19C2×#17985381C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21C2×#17985376C2211yescharacteristic, complemented
22C2×C8×D283C2211yescharacteristic
23#22583609C2211yescharacteristic, complemented
24#22583600—21no—
25#22583597C2211yescharacteristic
26#22583592—21no—
27#22583590C2211yescharacteristic
28#22583590C2211yescharacteristic
29#22583589—21no—
30#22583589C2211yescharacteristic, complemented
31#22583588—21no—
32#22583581—21no—
33#22583578—21no—
34#22583575C2211yescharacteristic, complemented
35#22583572C2211yescharacteristic
36C4×C22⋊D283—21no—
37C4×C22⋊D283C2211yescharacteristic
38C4⋊C4×D283C2211yescharacteristic
39C22⋊C4×D283—21no—
40#22583543C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42#22583535C2211yescharacteristic, complemented
43#22583533C2211yescharacteristic, complemented
44#22583533C2211yescharacteristic, complemented
45#22583533C2211yescharacteristic, complemented
46#22583532C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic, complemented
52#121×C283C2211yescharacteristic
53C2×C4⋊C4×C283C2211yescharacteristic, complemented
54#107×C283C2211yescharacteristic, complemented
55#107×C283C2211yescharacteristic, complemented
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60#17985392—22no—
61#17985392—41no—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64C2×Dic566C2311yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283D411yescharacteristic
69D4×D283—22no—
70D4×D283—41no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75Dic1132—41no—
76#17985381—22no—
77#17985380—41no—
78#17985376—41no—
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C8×D283—41no—
82C4⋊Dic283—21no—
83C4⋊Dic283—21no—
84C4⋊Dic283C2311yescharacteristic
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4D411yescharacteristic
90C22⋊Dic283—21no—
91C22⋊Dic283—21no—
92C22⋊Dic283—21no—
93C22⋊Dic283D411yescharacteristic
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4D411yescharacteristic
98C4×Dic283—21no—
99C4×Dic283C2311yescharacteristic
100C2×D4×C283—21no—
101C2×D4×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C4⋊C4×C283—21no—
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C22×D283—21no—
112C22×D283—42no—
113C22×D283—42no—
114C22×D283—81no—
115C22×D283C2×D411yescharacteristic
116Dic566—21no—
117Dic566—21no—
118Dic566—21no—
119Dic566—21no—
120Dic566—81no—
121D1132—21no—
122D1132#4112yes—
123C22⋊D283—22no—
124C22⋊D283—42no—
125C22⋊D283—42no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C2×Dic283C2×D411yescharacteristic
132C4×D283—21no—
133C4×D283—21no—
134C4×D283—42no—
135C4×D283—81no—
136C4×D283—81no—
137C283⋊C8—21no—
138C283⋊C8—21no—
139C23×C283—21no—
140C23×C283C2×D411yescharacteristic
141D4×C283—21no—
142D4×C283—21no—
143D4×C283—81no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—81no—
150C2×C4×C283C2×D411yescharacteristic
151C2×C4×C283C2411yescharacteristic
152C8×C283—21no—
153C8×C283—21no—
154C22×C283—21no—
155C22×C283—21no—
156C22×C283—21no—
157C22×C283—41no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283C22×D411yescharacteristic
161C2×D283—21no—
162C2×D283—21no—
163C2×D283—22no—
164C2×D283—41no—
165C2×D283—41no—
166C2×D283—84no—
167C2×D283#13712yes—
168C4×C283—21no—
169C4×C283—41no—
170C4×C283—41no—
171C4×C283—41no—
172C4×C283C2×#4111yescharacteristic
173C4×C283H(5,𝔽2)11yescharacteristic
174Dic283—21no—
175Dic283—21no—
176Dic283—21no—
177Dic283—41no—
178Dic283—41no—
179Dic283—41no—
180C2×C283—41no—
181C2×C283—81no—
182C2×C283#54611yescharacteristic
183C2×C283C2×#13711yescharacteristic
184C2×C283#57611yescharacteristic
185D283—22no—
186D283—42no—
187C283#331411yescharacteristic, complemented, Sylow
188#3314—2831nomaximal, Sylow
189#554—2831no—
190#546—2831no—
191#489—2831no—
192#484—2831no—
193#480D28311yescharacteristic, complemented
194#474—2831no—
195#468—2831no—
196#467—2831no—
197#464—2831no—
198#452—2831no—
199#450—2831no—
200#440—2831no—
201#435—2831no—
202#417—2831no—
203C2×#102—2831no—
204C2×#41—2831no—
205C22×D4—2831no—
206C2×Q16—2831no—
207C2×SD16—2831no—
208C2×SD16—2831no—
209C2×M16—2831no—
210C22×C8—2831no—
211C4⋊Q8—2831no—
212#125—5661no—
213#124—2831no—
214#123—5661no—
215C22⋊Q8—2831no—
216C22⋊Q8—2831no—
217C22⋊Q8—2831no—
218C22⋊Q8—5661no—
219C22⋊Q8—5661no—
220#121—5661no—
221#121C2×D28311yescharacteristic
222#120—5661no—
223C4×Q8—2831no—
224C4×D4—2831no—
225C4×D4—2831no—
226C4×D4—5661no—
227C2×C4⋊C4—2831no—
228C2×C4⋊C4C2×D28311yescharacteristic, complemented
229C2×C22⋊C4—5661no—
230#107—2831no—
231#107C2×D28311yescharacteristic, complemented
232#107C2×D28311yescharacteristic, complemented
233C4⋊C8—2831no—
234#103—2831no—
235#103—2831no—
236#103—2831no—
237#103—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241#102—2831no—
242#102C2×D28311yescharacteristic
243#102C2×D28311yescharacteristic
244C22⋊C8—2831no—
245C22⋊C8C2×D28311yescharacteristic, complemented
246#97—2831no—
247C24—5661no—
248#41—5662no—
249#41—11321no—
250C2×Q8—2831no—
251C2×Q8—2831no—
252C2×Q8—5661no—
253C2×D4—21no—
254C2×D4—2831no—
255C2×D4—2831no—
256C2×D4—5661no—
257C2×D4—5662no—
258C2×D4—5661no—
259C2×D4—11321no—
260C2×D4C22×D28311yescharacteristic
261C22×C4—21no—
262C22×C4—2831no—
263C22×C4—5661no—
264C22×C4—5661no—
265C22×C4—5661no—
266C22×C4C22×D28311yescharacteristic
267Q16—11321no—
268SD16—5662no—
269SD16—11321no—
270M16—11321no—
271C2×C8—2831no—
272C2×C8—2831no—
273C2×C8—11321no—
274C2×C8C22×D28311yescharacteristic
275C2×C8C22×D28311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—2831no—
278C4⋊C4—2831no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4—5661no—
282C4⋊C4—5661no—
283C4⋊C4—5661no—
284C4⋊C4—5661no—
285C4⋊C4C22×D28311yescharacteristic
286C4⋊C4C22×D28311yescharacteristic
287C4⋊C4C22×D28311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—2831no—
290C22⋊C4—2831no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C42—2831no—
298C42—5661no—
299C23—21no—
300C23—2831no—
301C23—5661no—
302C23—11322no—
303C23—11322no—
304C23—22641no—
305C23D4×D28311yescharacteristic
306Q8—5661no—
307Q8—5661no—
308Q8—5661no—
309Q8—5661no—
310Q8—22641no—
311D4—21no—
312D4—21no—
313D4—81no—
314D4—2832no—
315D4—5662no—
316D4—5661no—
317D4—11322no—
318D4—11322no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—81no—
325C2×C4—2831no—
326C2×C4—2831no—
327C2×C4—2831no—
328C2×C4—5661no—
329C2×C4—5661no—
330C2×C4—5661no—
331C2×C4—5661no—
332C2×C4—5661no—
333C2×C4—11322no—
334C2×C4—22641no—
335C2×C4—22641no—
336C2×C4D4×D28311yescharacteristic
337C2×C4C23×D28311yescharacteristic
338C8—21no—
339C8—21no—
340C8—5661no—
341C8—5661no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—2832no—
349C22—5661no—
350C22—5661no—
351C22—5662no—
352C22—11321no—
353C22—11321no—
354C22—22644no—
355C22C2×D4×D28311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—5661no—
361C4—5661no—
362C4—5661no—
363C4—11321no—
364C4—11321no—
365C4—11321no—
366C4#41×D28311yescharacteristic
367C4#2258365611yescharacteristic
368C2—41no—
369C2—81no—
370C2—5662no—
371C2—11322no—
372C2#3182710711yescharacteristic
373C2#137×D28311yescharacteristic
374C2#3182726611yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#480×C283C2
socleC22×C283C22×D4
prime radical#31827112C2
hypercenter#480D283
hypocenterC283#3314
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #31827170C2semidirect
3. #31826823C2semidirect
4. #31826802C2semidirect
5. #31826744C2semidirect
6. #31826709C2semidirect
7. #31826707C2semidirect
8. #31826686C2semidirect
9. #31826629C2semidirect
10. #31826617C2semidirect
11. #31826564C2semidirect
12. #31826539C2semidirect
13. #31826464C2semidirect
14. #102×D283C2semidirect
15. #480×C283C2semidirect
18. C2×Dic1132C22semidirect
21. C2×#17985376C22semidirect
23. #22583609C22semidirect
30. #22583589C22semidirect
34. #22583575C22semidirect
40. #22583543C22semidirect
41. Dic283⋊C8C22semidirect
42. #22583535C22semidirect
43. #22583533C22semidirect
44. #22583533C22semidirect
45. #22583533C22semidirect
51. #22583520C22semidirect
53. C2×C4⋊C4×C283C22semidirect
54. #107×C283C22semidirect
55. #107×C283C22semidirect
58. C22⋊C8×C283C22semidirect
187. C283#3314semidirect
193. #480D283semidirect
228. C2×C4⋊C4C2×D283semidirect
231. #107C2×D283semidirect
232. #107C2×D283semidirect
245. C22⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271702
#318271122
#318268232
#318268022
#318267442
#318267092
#318267072
#318266862
#318266292
#318266172
#318265642
#318265392
#318264642
#102×D2832
#480×C2832
#3314283