Finite Group Databasebeta

← #49133337

Subgroups — #49133337

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#31827173C211yesmaximal, characteristic, complemented
2#31827112C211yesmaximal, characteristic
3#31826823C211yesmaximal, characteristic, complemented
4#31826802C211yesmaximal, characteristic, complemented
5#31826776C211yesmaximal, characteristic, complemented
6#31826744C211yesmaximal, characteristic, complemented
7#31826705C211yesmaximal, characteristic, complemented
8#31826685C211yesmaximal, characteristic, complemented
9#31826625C211yesmaximal, characteristic, complemented
10#31826614C211yesmaximal, characteristic, complemented
11#31826568C211yesmaximal, characteristic, complemented
12#31826534C211yesmaximal, characteristic, complemented
13#31826467C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#468×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×#17985382C2211yescharacteristic, complemented
19C2×#17985379C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic
21#22583609C2211yescharacteristic, complemented
22#22583600—21no—
23#22583597C2211yescharacteristic
24#22583592—21no—
25#22583590—21no—
26#22583590C2211yescharacteristic
27#22583587—21no—
28#22583586C2211yescharacteristic
29#22583581—21no—
30#22583578—21no—
31Q8×Dic283C2211yescharacteristic, complemented
32#22583572C2211yescharacteristic
33C4×C22⋊D283C2211yescharacteristic
34(C22⋊D283)⋊C4—21no—
35C2×C4⋊Dic283C2211yescharacteristic, complemented
36C4⋊C4×D283C2211yescharacteristic
37C22⋊C4×D283—21no—
38#22583543C2211yescharacteristic, complemented
39#22583543C2211yescharacteristic, complemented
40Dic283⋊C8C2211yescharacteristic, complemented
41#22583535C2211yescharacteristic, complemented
42#22583535C2211yescharacteristic, complemented
43#22583533C2211yescharacteristic, complemented
44#22583532C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic, complemented
52C2×SD16×C283C2211yescharacteristic
53C2×M16×C283C2211yescharacteristic, complemented
54C22⋊Q8×C283C2211yescharacteristic, complemented
55#121×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic, complemented
57#103×C283C2211yescharacteristic, complemented
58#102×C283C2211yescharacteristic
59C23×D283—21no—
60#17985392—22no—
61#17985392—41no—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64C2×D1132C2311yescharacteristic
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283D411yescharacteristic
68D4×D283—22no—
69D4×D283—41no—
70C22×Dic283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75#17985382—41no—
76#17985379—22no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C8×D283—41no—
80C4⋊Dic283—21no—
81C4⋊Dic283—21no—
82C4⋊Dic283—21no—
83C4⋊Dic283C2311yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4D411yescharacteristic
89C22⋊Dic283—21no—
90C22⋊Dic283—21no—
91C22⋊Dic283D411yescharacteristic
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4D411yescharacteristic
96C4×Dic283—21no—
97C4×Dic283C2311yescharacteristic
98C2×Q8×C283C2311yescharacteristic
99C2×D4×C283—21no—
100C2×D4×C283C2311yescharacteristic
101C22×C4×C283C2311yescharacteristic
102SD16×C283—41no—
103M16×C283—41no—
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C4⋊C4×C283—21no—
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C22⋊C4×C283—21no—
110C22⋊C4×C283—21no—
111C22×D283—21no—
112C22×D283—42no—
113C22×D283—42no—
114C22×D283—81no—
115C22×D283C2×D411yescharacteristic
116Dic566—21no—
117Dic566—21no—
118Dic566—81no—
119D1132—21no—
120D1132#4112yes—
121C22⋊D283—22no—
122C22⋊D283—42no—
123C22⋊D283—42no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—81no—
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C4×D283—21no—
132C4×D283—21no—
133C4×D283—42no—
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—21no—
144D4×C283—81no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
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#480—2831no—
194#474—2831no—
195#468D28311yescharacteristic, complemented
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×SD16C2×D28311yescharacteristic
209C2×M16C2×D28311yescharacteristic, complemented
210C22×C8—2831no—
211C4⋊Q8—2831no—
212#125—5661no—
213#124—2831no—
214#123—5661no—
215C22⋊Q8—2831no—
216C22⋊Q8—2831no—
217C22⋊Q8—5661no—
218C22⋊Q8—5661no—
219C22⋊Q8C2×D28311yescharacteristic, complemented
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⋊C4—2831no—
229C2×C22⋊C4—5661no—
230#107—2831no—
231#107—2831no—
232#107C2×D28311yescharacteristic, complemented
233C4⋊C8—2831no—
234#103—2831no—
235#103—2831no—
236#103—2831no—
237#103C2×D28311yescharacteristic, complemented
238#102—2831no—
239#102—2831no—
240#102—2831no—
241#102—2831no—
242#102—2831no—
243#102C2×D28311yescharacteristic
244C22⋊C8—2831no—
245C22⋊C8—2831no—
246#97—2831no—
247C24—5661no—
248#41—5662no—
249#41—11321no—
250C2×Q8—2831no—
251C2×Q8—5661no—
252C2×Q8C22×D28311yescharacteristic
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—2831no—
262C22×C4—5661no—
263C22×C4—5661no—
264C22×C4—5661no—
265C22×C4—5661no—
266C22×C4C22×D28311yescharacteristic
267Q16—11321no—
268SD16—41no—
269SD16—5662no—
270M16—41no—
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—2831no—
280C4⋊C4—5661no—
281C4⋊C4—5661no—
282C4⋊C4—5661no—
283C4⋊C4—5661no—
284C4⋊C4—5661no—
285C4⋊C4—5661no—
286C4⋊C4C22×D28311yescharacteristic
287C4⋊C4C22×D28311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—2831no—
291C22⋊C4—2831no—
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—21no—
307Q8—21no—
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—2831no—
325C2×C4—2831no—
326C2×C4—2831no—
327C2×C4—5661no—
328C2×C4—5661no—
329C2×C4—5661no—
330C2×C4—5661no—
331C2×C4—5661no—
332C2×C4—11322no—
333C2×C4—22641no—
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#2258365511yescharacteristic
368C2—41no—
369C2—81no—
370C2—5662no—
371C2—11322no—
372C2#3182710411yescharacteristic
373C2#137×D28311yescharacteristic
374C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#468×C283C2
socleC22×C283C22×D4
prime radical#31827112C2
hypercenter#468D283
hypocenterC283#3314
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #31827173C2semidirect
3. #31826823C2semidirect
4. #31826802C2semidirect
5. #31826776C2semidirect
6. #31826744C2semidirect
7. #31826705C2semidirect
8. #31826685C2semidirect
9. #31826625C2semidirect
10. #31826614C2semidirect
11. #31826568C2semidirect
12. #31826534C2semidirect
13. #31826467C2semidirect
14. #102×D283C2semidirect
15. #468×C283C2semidirect
18. C2×#17985382C22semidirect
21. #22583609C22semidirect
31. Q8×Dic283C22semidirect
35. C2×C4⋊Dic283C22semidirect
38. #22583543C22semidirect
39. #22583543C22semidirect
40. Dic283⋊C8C22semidirect
41. #22583535C22semidirect
42. #22583535C22semidirect
43. #22583533C22semidirect
49. C22⋊(C283⋊C8)C22semidirect
51. #22583520C22semidirect
53. C2×M16×C283C22semidirect
54. C22⋊Q8×C283C22semidirect
56. #107×C283C22semidirect
57. #103×C283C22semidirect
187. C283#3314semidirect
195. #468D283semidirect
209. C2×M16C2×D283semidirect
219. C22⋊Q8C2×D283semidirect
232. #107C2×D283semidirect
237. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271732
#318271122
#318268232
#318268022
#318267762
#318267442
#318267052
#318266852
#318266252
#318266142
#318265682
#318265342
#318264672
#102×D2832
#468×C2832
#3314283