Finite Group Databasebeta

← #49131397

Subgroups — #49131397

Order 36224.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31826997C211yesmaximal, characteristic, complemented
2C4×D4×D283C211yesmaximal, characteristic, complemented
3#31826797C211yesmaximal, characteristic, complemented
4#31826777C211yesmaximal, characteristic, complemented
5#31826764C211yesmaximal, characteristic, complemented
6#31826763C211yesmaximal, characteristic, complemented
7#31826679C211yesmaximal, characteristic, complemented
8#31826678C211yesmaximal, characteristic, complemented
9#31826617C211yesmaximal, characteristic, complemented
10#31826597C211yesmaximal, characteristic
11#31826575C211yesmaximal, characteristic, complemented
12#31826567C211yesmaximal, characteristic, complemented
13#31826565C211yesmaximal, characteristic, complemented
14#31826520C211yesmaximal, characteristic, complemented
15#442×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283C2211yescharacteristic
17C22×C4×D283—21no—
18C2×#17985381C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21#22583603—21no—
22#22583601C2211yescharacteristic, complemented
23#22583597C2211yescharacteristic, complemented
24#22583592—21no—
25#22583590C2211yescharacteristic
26#22583581C2211yescharacteristic
27C4×Dic566C2211yescharacteristic, complemented
28C4×D1132C2211yescharacteristic
29D4×Dic283C2211yescharacteristic
30#22583572C2211yescharacteristic
31C4×C22⋊D283—21no—
32C4×C22⋊D283—21no—
33(C22⋊D283)⋊C4—21no—
34#22583569—21no—
35C4⋊C4×D283C2211yescharacteristic
36C22⋊C4×D283—21no—
37C42×D283C2211yescharacteristic
38#22583544C2211yescharacteristic, complemented
39#22583543C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42Dic283⋊C8C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583533C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic, complemented
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583521C2211yescharacteristic, complemented
52C2×D8×C283C2211yescharacteristic
53C4×D4×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic, complemented
55#106×C283C2211yescharacteristic, complemented
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic, complemented
58#97×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C2×Dic566C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C22⋊D283—21no—
64D4×D283—22no—
65D4×D283—22no—
66C22×Dic283—21no—
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283—44no—
71C2×C4×D283D411yescharacteristic
72C2×C4×D283D411yescharacteristic
73C2×C4×D283C2311yescharacteristic
74#17985381—22no—
75#17985380—22no—
76#17985377—22no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C4⋊Dic283—21no—
80C4⋊Dic283—21no—
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93C4×Dic283—21no—
94C4×Dic283D411yescharacteristic
95C4×Dic283D411yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283—21no—
100C22×C4×C283—21no—
101D8×C283—22no—
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C22⋊C4×C283—21no—
108C42×C283C2311yescharacteristic
109C22×D283—24no—
110C22×D283—21no—
111C22×D283—42no—
112C22×D283—42no—
113C22×D283C2×D411yescharacteristic
114Dic566—21no—
115Dic566—21no—
116D1132—21no—
117D1132#4112yes—
118C22⋊D283—24no—
119C22⋊D283—42no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—42no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—22no—
128C4×D283—21no—
129C4×D283—21no—
130C4×D283—41no—
131C4×D283—42no—
132C4×D283—42no—
133C4×D283—42no—
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283—21no—
137C23×C283—21no—
138D4×C283—21no—
139D4×C283—21no—
140D4×C283—21no—
141D4×C283#4112yes—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—42no—
145C2×C4×C283—42no—
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2411yescharacteristic
149C8×C283—21no—
150C8×C283—21no—
151C22×C283—22no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283—41no—
156C22×C283—41no—
157C22×C283C22×D411yescharacteristic
158C2×D283—21no—
159C2×D283—21no—
160C2×D283—22no—
161C2×D283—48no—
162C2×D283—41no—
163C2×D283—41no—
164C2×D283AGL(1,ℤ/8)12yes—
165C4×C283—21no—
166C4×C283—21no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283C2×#4111yescharacteristic
170C4×C283C2×#4111yescharacteristic
171Dic283—21no—
172Dic283—21no—
173Dic283—21no—
174Dic283—41no—
175Dic283—41no—
176Dic283—41no—
177C2×C283—42no—
178C2×C283—81no—
179C2×C283#52511yescharacteristic
180C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C283#57511yescharacteristic
182D283—22no—
183D283—42no—
184C283#311411yescharacteristic, complemented, Sylow
185#3114—2831nomaximal, Sylow
186#529—2831no—
187C2×C4×D4—2831no—
188#483—2831no—
189#480—2831no—
190#478—2831no—
191#478—2831no—
192#463—2831no—
193#463—2831no—
194#450—2831no—
195#447—2831no—
196#442—2831no—
197#442D28311yescharacteristic, complemented
198#440—2831no—
199#440—2831no—
200#432—2831no—
201C22×D4—2831no—
202C23×C4—5661no—
203C2×SD16—2831no—
204C2×SD16—2831no—
205C2×D8—2831no—
206C2×D8C2×D28311yescharacteristic
207#126—5661no—
208#125—2831no—
209#124—2831no—
210#123—5661no—
211C22⋊Q8—2831no—
212#121—2831no—
213C4×Q8—2831no—
214C4×D4—2831no—
215C4×D4—2831no—
216C4×D4—2831no—
217C4×D4—5661no—
218C4×D4—5661no—
219C4×D4—5661no—
220C4×D4C2×D28311yescharacteristic
221C4×D4C2×D28311yescharacteristic, complemented
222#117—5661no—
223C2×C4⋊C4—2831no—
224C2×C22⋊C4—5661no—
225C2×C42—2831no—
226#107—2831no—
227#107—2831no—
228#106—2831no—
229#106C2×D28311yescharacteristic, complemented
230C4⋊C8—2831no—
231C4⋊C8—2831no—
232#103—2831no—
233#103—2831no—
234#102—2831no—
235#102—2831no—
236#102—2831no—
237#102—2831no—
238#102C2×D28311yescharacteristic
239#102C2×D28311yescharacteristic, complemented
240C22⋊C8—2831no—
241C22⋊C8—2831no—
242#97—2831no—
243#97C2×D28311yescharacteristic, complemented
244C24—5661no—
245C2×Q8—2831no—
246C2×D4—2831no—
247C2×D4—5661no—
248C2×D4—5662no—
249C2×D4—5662no—
250C2×D4—5661no—
251C2×D4C22×D28311yescharacteristic
252C2×D4C22×D28311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2831no—
256C22×C4—2831no—
257C22×C4—2831no—
258C22×C4—5661no—
259C22×C4—5661no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4—11324no—
263SD16—5662no—
264SD16—5662no—
265D8—22no—
266D8—5662no—
267C2×C8—2831no—
268C2×C8—2831no—
269C2×C8C22×D28311yescharacteristic
270C2×C8C22×D28311yescharacteristic
271C4⋊C4—2831no—
272C4⋊C4—2831no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4C22×D28311yescharacteristic
279C4⋊C4C22×D28311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C42—2831no—
290C42—2831no—
291C42—2831no—
292C42—5661no—
293C42C22×D28311yescharacteristic
294C23—21no—
295C23—21no—
296C23—2831no—
297C23—5664no—
298C23—5661no—
299C23—11322no—
300C23—11322no—
301Q8—5661no—
302Q8—5661no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—2832no—
307D4—5664no—
308D4—5661no—
309D4—11322no—
310D4#1798539212yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—2831no—
316C2×C4—2831no—
317C2×C4—2831no—
318C2×C4—5662no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—5661no—
323C2×C4—5661no—
324C2×C4—11321no—
325C2×C4—11322no—
326C2×C4—11322no—
327C2×C4—11322no—
328C2×C4—11322no—
329C2×C4D4×D28311yescharacteristic
330C2×C4D4×D28311yescharacteristic
331C2×C4C23×D28311yescharacteristic
332C8—21no—
333C8—21no—
334C8—5661no—
335C8—5661no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—2832no—
343C22—5661no—
344C22—5661no—
345C22—5662no—
346C22—11328no—
347C22—11321no—
348C22—11321no—
349C22C2×D4×D28311yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—5661no—
355C4—5661no—
356C4—5661no—
357C4—11321no—
358C4—11321no—
359C4—11321no—
360C4#41×D28311yescharacteristic
361C4C2×#1798539211yescharacteristic
362C2—42no—
363C2—81no—
364C2—5662no—
365C2—11322no—
366C2#3182697411yescharacteristic
367C2AGL(1,ℤ/8)×D28311yescharacteristic
368C2#3182726111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#442×C283C2
socleC22×C283C22×D4
prime radical#31826597C2
hypercenter#442D283
hypocenterC283#3114
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #31826997C2semidirect
2. C4×D4×D283C2semidirect
3. #31826797C2semidirect
4. #31826777C2semidirect
5. #31826764C2semidirect
6. #31826763C2semidirect
7. #31826679C2semidirect
8. #31826678C2semidirect
9. #31826617C2semidirect
11. #31826575C2semidirect
12. #31826567C2semidirect
13. #31826565C2semidirect
14. #31826520C2semidirect
15. #442×C283C2semidirect
22. #22583601C22semidirect
23. #22583597C22semidirect
27. C4×Dic566C22semidirect
38. #22583544C22semidirect
39. #22583543C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. Dic283⋊C8C22semidirect
43. #22583535C22semidirect
44. #22583533C22semidirect
47. #22583531C22semidirect
51. #22583521C22semidirect
54. C4×D4×C283C22semidirect
55. #106×C283C22semidirect
57. #102×C283C22semidirect
58. #97×C283C22semidirect
184. C283#3114semidirect
197. #442D283semidirect
221. C4×D4C2×D283semidirect
229. #106C2×D283semidirect
239. #102C2×D283semidirect
243. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318269972
C4×D4×D2832
#318267972
#318267772
#318267642
#318267632
#318266792
#318266782
#318266172
#318265972
#318265752
#318265672
#318265652
#318265202
#442×C2832
#3114283