Finite Group Databasebeta

← #49131500

Subgroups — #49131500

Order 36224.

418 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#31827068C211yesmaximal, characteristic, complemented
2#31826939C211yesmaximal, characteristic, complemented
3#31826789C211yesmaximal, characteristic, complemented
4#31826768C211yesmaximal, characteristic, complemented
5#31826764C211yesmaximal, characteristic, complemented
6#31826659C211yesmaximal, characteristic, complemented
7#31826659C211yesmaximal, characteristic, complemented
8#31826601C211yesmaximal, characteristic, complemented
9#31826598C211yesmaximal, characteristic, complemented
10#31826576C211yesmaximal, characteristic, complemented
11#31826574C211yesmaximal, characteristic, complemented
12#31826547C211yesmaximal, characteristic, complemented
13#31826545C211yesmaximal, characteristic, complemented
14#31826523C211yesmaximal, characteristic, complemented
15#482×C283C211yesmaximal, characteristic, complemented
16C22×D1132C2211yescharacteristic
17C2×D2264C2211yescharacteristic
18C2×D2264C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21#22583606C2211yescharacteristic, complemented
22#22583601C2211yescharacteristic, complemented
23#22583594—21no—
24#22583592—21no—
25#22583584C2211yescharacteristic
26#22583582—21no—
27#22583581—21no—
28C4×D1132—21no—
29C4×D1132—21no—
30D4×Dic283C2211yescharacteristic, complemented
31#22583572C2211yescharacteristic
32#22583572C2211yescharacteristic
33#22583572C2211yescharacteristic
34#22583572C2211yescharacteristic
35#22583572C2211yescharacteristic, complemented
36#22583569C2211yescharacteristic
37C22⋊C4×D283—21no—
38C22⋊C4×D283—21no—
39#22583543C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42Dic283⋊C8C2211yescharacteristic, complemented
43#22583532C2211yescharacteristic
44#22583532C2211yescharacteristic
45#22583530C2211yescharacteristic
46#22583530C2211yescharacteristic
47#22583530C2211yescharacteristic, complemented
48#22583530C2211yescharacteristic, complemented
49C22⋊(C283⋊C8)C2211yescharacteristic
50#22583520C2211yescharacteristic, complemented
51C8×Dic283C2211yescharacteristic, complemented
52#121×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic, complemented
55#106×C283C2211yescharacteristic, complemented
56#102×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic
59C23×D283—21no—
60C2×D1132—22no—
61C2×D1132—22no—
62C2×D1132—21no—
63C2×D1132C2311yescharacteristic
64C2×D1132C2311yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75D2264—22no—
76D2264—22no—
77#17985377—22no—
78#17985377—22no—
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C4⋊Dic283—21no—
82C4⋊Dic283D411yescharacteristic
83C4⋊Dic283D411yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283D411yescharacteristic
88C22⋊Dic283D411yescharacteristic
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95C4×Dic283C2311yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×D4×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283—21no—
108C22×D283—21no—
109C22×D283—21no—
110C22×D283—24no—
111C22×D283—21no—
112C22×D283—81no—
113C22×D283—81no—
114D1132—24no—
115D1132—21no—
116D1132—21no—
117D1132—21no—
118D1132—21no—
119D1132#4112yes—
120D1132#4112yes—
121C22⋊D283—81no—
122C22⋊D283—81no—
123C22⋊D283—81no—
124C2×Dic283—21no—
125C2×Dic283—81no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C4×D283—81no—
131C4×D283—81no—
132C4×D283—81no—
133C4×D283—81no—
134C4×D283—81no—
135C283⋊C8—21no—
136C283⋊C8—21no—
137C23×C283—21no—
138C23×C283C2×D411yescharacteristic
139D4×C283—21no—
140D4×C283—21no—
141D4×C283—81no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2411yescharacteristic
149C8×C283—21no—
150C8×C283—21no—
151C22×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—41no—
155C22×C283—41no—
156C22×C283—41no—
157C22×C283C22×D411yescharacteristic
158C2×D283—22no—
159C2×D283—22no—
160C2×D283—41no—
161C2×D283—41no—
162C2×D283—41no—
163C2×D283—41no—
164C2×D283—41no—
165C2×D283—41no—
166C2×D283—41no—
167C2×D283—84no—
168C4×C283—21no—
169C4×C283—41no—
170C4×C283—41no—
171C4×C283—41no—
172C4×C283C2×#4111yescharacteristic
173C4×C283C2×#4111yescharacteristic
174Dic283—21no—
175Dic283—21no—
176Dic283—21no—
177Dic283—21no—
178Dic283—41no—
179C2×C283—41no—
180C2×C283—81no—
181C2×C283#52511yescharacteristic
182C2×C283#57611yescharacteristic
183C2×C283#57611yescharacteristic
184D283—42no—
185D283—42no—
186D283—81no—
187C283#312211yescharacteristic, complemented, Sylow
188#3122—2831nomaximal, Sylow
189#540—2831no—
190#518—2831no—
191#482—2831no—
192#482D28311yescharacteristic, complemented
193#478—2831no—
194#478—2831no—
195#459—2831no—
196#459—2831no—
197#447—2831no—
198#447—2831no—
199#442—2831no—
200#442—2831no—
201C4×D8—2831no—
202C4×D8—2831no—
203#433—2831no—
204C22×D4—2831no—
205C2×D8—2831no—
206C2×D8—2831no—
207C2×D8—2831no—
208C2×D8—2831no—
209#127—2831no—
210#125—2831no—
211#123—5661no—
212#123—5661no—
213#121—2831no—
214#121—5661no—
215#121—5661no—
216#121C2×D28311yescharacteristic
217C4×D4—2831no—
218C4×D4—2831no—
219C4×D4—2831no—
220C4×D4—2831no—
221C4×D4—2831no—
222C4×D4—2831no—
223C4×D4—5661no—
224C4×D4—5661no—
225#117—2831no—
226#117C2×D28311yescharacteristic
227C2×C22⋊C4—5661no—
228C2×C22⋊C4—5661no—
229#107—2831no—
230#107C2×D28311yescharacteristic, complemented
231#106—2831no—
232#106C2×D28311yescharacteristic, complemented
233C4⋊C8—2831no—
234C4⋊C8—2831no—
235#102—2831no—
236#102—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241#102C2×D28311yescharacteristic, complemented
242#102C2×D28311yescharacteristic, complemented
243C22⋊C8—2831no—
244C22⋊C8C2×D28311yescharacteristic
245#97—2831no—
246C4×C8—2831no—
247C24—5661no—
248C2×D4—21no—
249C2×D4—2831no—
250C2×D4—2831no—
251C2×D4—2831no—
252C2×D4—5662no—
253C2×D4—5662no—
254C2×D4—5661no—
255C2×D4—5661no—
256C2×D4—5661no—
257C2×D4—5661no—
258C2×D4C22×D28311yescharacteristic
259C22×C4—5661no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4—5661no—
263C22×C4—5661no—
264C22×C4—5661no—
265C22×C4C22×D28311yescharacteristic
266D8—5662no—
267D8—5662no—
268D8—5662no—
269D8—5662no—
270C2×C8—2831no—
271C2×C8—2831no—
272C2×C8C22×D28311yescharacteristic
273C2×C8C22×D28311yescharacteristic
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—2831no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4C22×D28311yescharacteristic
280C4⋊C4C22×D28311yescharacteristic
281C4⋊C4C22×D28311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2831no—
285C22⋊C4—2831no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C42—21no—
294C42—2831no—
295C42—2831no—
296C23—21no—
297C23—5664no—
298C23—5661no—
299C23—5661no—
300C23—5661no—
301C23—22641no—
302C23—22641no—
303C23D4×D28311yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—2832no—
308D4—2832no—
309D4—5664no—
310D4—5661no—
311D4—5661no—
312D4—5661no—
313D4—5661no—
314D4—22641no—
315D4—22641no—
316D4—22641no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—2831no—
323C2×C4—2831no—
324C2×C4—2831no—
325C2×C4—2831no—
326C2×C4—5661no—
327C2×C4—22641no—
328C2×C4—22641no—
329C2×C4—22641no—
330C2×C4—22641no—
331C2×C4—22641no—
332C2×C4—22641no—
333C2×C4D4×D28311yescharacteristic
334C2×C4C23×D28311yescharacteristic
335C8—21no—
336C8—21no—
337C8—5661no—
338C8—5661no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—5662no—
346C22—5662no—
347C22—11321no—
348C22—11321no—
349C22—11321no—
350C22—11321no—
351C22—11321no—
352C22—11321no—
353C22—11321no—
354C22—22644no—
355C22C2×D4×D28311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—5661no—
361C4—5661no—
362C4—5661no—
363C4—5661no—
364C4—11321no—
365C4#41×D28311yescharacteristic
366C4#41×D28311yescharacteristic
367C2—41no—
368C2—81no—
369C2—11322no—
370C2—11322no—
371C2—22641no—
372C2#3182697311yescharacteristic
373C2#3182726711yescharacteristic
374C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#482×C283C2
socleC22×C283C22×D4
hypercenter#482D283
hypocenterC283#3122
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #31827068C2semidirect
2. #31826939C2semidirect
3. #31826789C2semidirect
4. #31826768C2semidirect
5. #31826764C2semidirect
6. #31826659C2semidirect
7. #31826659C2semidirect
8. #31826601C2semidirect
9. #31826598C2semidirect
10. #31826576C2semidirect
11. #31826574C2semidirect
12. #31826547C2semidirect
13. #31826545C2semidirect
14. #31826523C2semidirect
15. #482×C283C2semidirect
21. #22583606C22semidirect
22. #22583601C22semidirect
30. D4×Dic283C22semidirect
35. #22583572C22semidirect
39. #22583543C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. Dic283⋊C8C22semidirect
47. #22583530C22semidirect
48. #22583530C22semidirect
50. #22583520C22semidirect
51. C8×Dic283C22semidirect
54. #107×C283C22semidirect
55. #106×C283C22semidirect
56. #102×C283C22semidirect
57. #102×C283C22semidirect
187. C283#3122semidirect
192. #482D283semidirect
230. #107C2×D283semidirect
232. #106C2×D283semidirect
241. #102C2×D283semidirect
242. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270682
#318269392
#318267892
#318267682
#318267642
#318266592
#318266012
#318265982
#318265762
#318265742
#318265472
#318265452
#318265232
#482×C2832
#3122283