Finite Group Databasebeta

← #49131506

Subgroups — #49131506

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#31827071C211yesmaximal, characteristic, complemented
2#31826937C211yesmaximal, characteristic, complemented
3#31826792C211yesmaximal, characteristic, complemented
4#31826791C211yesmaximal, characteristic, complemented
5#31826762C211yesmaximal, characteristic, complemented
6#31826661C211yesmaximal, characteristic, complemented
7#31826660C211yesmaximal, characteristic, complemented
8#31826600C211yesmaximal, characteristic, complemented
9#31826600C211yesmaximal, characteristic, complemented
10#31826576C211yesmaximal, characteristic, complemented
11#31826574C211yesmaximal, characteristic, complemented
12#31826547C211yesmaximal, characteristic, complemented
13#31826545C211yesmaximal, characteristic, complemented
14#31826525C211yesmaximal, characteristic, complemented
15#478×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283C2211yescharacteristic
17C2×D2264C2211yescharacteristic
18C2×D2264C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21#22583607C2211yescharacteristic, complemented
22#22583595—21no—
23#22583595—21no—
24#22583585—21no—
25#22583585—21no—
26#22583585C2211yescharacteristic
27#22583585C2211yescharacteristic
28C4×D1132C2211yescharacteristic
29D4×Dic283C2211yescharacteristic
30#22583572C2211yescharacteristic
31#22583572C2211yescharacteristic, complemented
32#22583572C2211yescharacteristic, complemented
33C4×C22⋊D283—21no—
34(C22⋊D283)⋊C4—21no—
35#22583568C2211yescharacteristic
36#22583567C2211yescharacteristic
37C2×(C2×D283)⋊C4—21no—
38C22⋊C4×D283—21no—
39#22583543C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41C4⋊(C283⋊C8)C2211yescharacteristic, complemented
42#22583532C2211yescharacteristic, complemented
43#22583532C2211yescharacteristic, complemented
44#22583530C2211yescharacteristic
45#22583530C2211yescharacteristic
46#22583530C2211yescharacteristic, complemented
47#22583530C2211yescharacteristic, complemented
48(C2×D283)⋊C8C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50#22583520C2211yescharacteristic, complemented
51C8×Dic283C2211yescharacteristic, complemented
52#125×C283C2211yescharacteristic, complemented
53C4×D4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic, complemented
55#106×C283C2211yescharacteristic, complemented
56C4⋊C8×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C23×D283—21no—
60C2×D1132—21no—
61C2×D1132—21no—
62C2×D1132—21no—
63C2×D1132—21no—
64C2×D1132C2311yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×D1132C2311yescharacteristic
67C2×C22⋊D283—21no—
68D4×D283—22no—
69D4×D283—22no—
70C22×Dic283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75C2×C4×D283C2311yescharacteristic
76D2264—22no—
77D2264—22no—
78#17985377—22no—
79#17985377—22no—
80C2×C283⋊C8C2311yescharacteristic
81C2×C283⋊C8C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4D411yescharacteristic
84Dic283⋊C4D411yescharacteristic
85C22⋊Dic283—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4D411yescharacteristic
94(C2×D283)⋊C4D411yescharacteristic
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98C22×C4×C283—21no—
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C4⋊C4×C283—21no—
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283—24no—
110C22×D283—21no—
111C22×D283—21no—
112C22×D283—81no—
113C22×D283—81no—
114C22×D283C2×D411yescharacteristic
115D1132—21no—
116D1132—21no—
117D1132—21no—
118D1132—21no—
119D1132—21no—
120D1132—81no—
121D1132—81no—
122D1132—81no—
123D1132—81no—
124D1132#4112yes—
125C22⋊D283—24no—
126C2×Dic283—21no—
127C2×Dic283—81no—
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C4×D283—21no—
132C4×D283—21no—
133C4×D283—81no—
134C4×D283—81no—
135C4×D283—81no—
136C4×D283—81no—
137C283⋊C8—21no—
138C283⋊C8—21no—
139C23×C283—21no—
140D4×C283—21no—
141D4×C283#4112yes—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—81no—
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×C283C22×D411yescharacteristic
155C2×D283—21no—
156C2×D283—22no—
157C2×D283—21no—
158C2×D283—21no—
159C2×D283—41no—
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—21no—
170C4×C283—41no—
171C4×C283—41no—
172C4×C283—41no—
173C4×C283C2×#4111yescharacteristic
174C4×C283C2×#4111yescharacteristic
175Dic283—21no—
176Dic283—21no—
177Dic283—21no—
178Dic283—41no—
179C2×C283—42no—
180C2×C283#52511yescharacteristic
181C2×C283#57611yescharacteristic
182C2×C283#57611yescharacteristic
183D283—41no—
184D283—42no—
185D283—81no—
186D283—81no—
187C283#312211yescharacteristic, complemented, Sylow
188#3122—2831nomaximal, Sylow
189#540—2831no—
190#518—2831no—
191#482—2831no—
192#482—2831no—
193#478—2831no—
194#478D28311yescharacteristic, complemented
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#125C2×D28311yescharacteristic, complemented
211#123—5661no—
212#123—5661no—
213#121—2831no—
214#121—2831no—
215#121—5661no—
216#121—5661no—
217C4×D4—2831no—
218C4×D4—2831no—
219C4×D4—2831no—
220C4×D4—2831no—
221C4×D4—2831no—
222C4×D4—5661no—
223C4×D4—5661no—
224C4×D4C2×D28311yescharacteristic
225#117—2831no—
226#117—2831no—
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⋊C8C2×D28311yescharacteristic, complemented
235#102—2831no—
236#102—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241#102C2×D28311yescharacteristic
242#102C2×D28311yescharacteristic
243C22⋊C8—2831no—
244C22⋊C8—2831no—
245#97—2831no—
246C4×C8—2831no—
247C24—5661no—
248C2×D4—2831no—
249C2×D4—2831no—
250C2×D4—2831no—
251C2×D4—5661no—
252C2×D4—5661no—
253C2×D4—5661no—
254C2×D4—5662no—
255C2×D4—5662no—
256C2×D4—5661no—
257C2×D4—5661no—
258C2×D4C22×D28311yescharacteristic
259C22×C4—21no—
260C22×C4—2831no—
261C22×C4—5661no—
262C22×C4—5661no—
263C22×C4—5661no—
264C22×C4—5661no—
265C22×C4—5661no—
266D8—5662no—
267D8—5662no—
268D8—5662no—
269D8—5662no—
270C2×C8—2831no—
271C2×C8—2831no—
272C2×C8C22×D28311yescharacteristic
273C2×C8C22×D28311yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—2831no—
277C4⋊C4—2831no—
278C4⋊C4—2831no—
279C4⋊C4C22×D28311yescharacteristic
280C4⋊C4C22×D28311yescharacteristic
281C4⋊C4C22×D28311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—2831no—
284C22⋊C4—2831no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C42—2831no—
294C42—5661no—
295C42C22×D28311yescharacteristic
296C23—21no—
297C23—2831no—
298C23—5664no—
299C23—5661no—
300C23—5661no—
301C23—5661no—
302C23—22641no—
303C23—22641no—
304D4—21no—
305D4—2832no—
306D4—5664no—
307D4—5661no—
308D4—5661no—
309D4—5661no—
310D4—5661no—
311D4—5661no—
312D4—22641no—
313D4—22641no—
314D4—22641no—
315D4—22641no—
316D4#1798539312yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—2831no—
322C2×C4—2831no—
323C2×C4—2831no—
324C2×C4—5661no—
325C2×C4—5661no—
326C2×C4—5661no—
327C2×C4—22641no—
328C2×C4—22641no—
329C2×C4—22641no—
330C2×C4—22641no—
331C2×C4—22641no—
332C2×C4D4×D28311yescharacteristic
333C2×C4D4×D28311yescharacteristic
334C2×C4C23×D28311yescharacteristic
335C8—21no—
336C8—21no—
337C8—5661no—
338C8—5661no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—5661no—
343C22—5662no—
344C22—5661no—
345C22—5661no—
346C22—11321no—
347C22—11321no—
348C22—11321no—
349C22—11321no—
350C22—11321no—
351C22—11321no—
352C22—11321no—
353C22—11321no—
354C22—22644no—
355C22C2×D4×D28311yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—5661no—
362C4—5661no—
363C4—5661no—
364C4—11321no—
365C4#41×D28311yescharacteristic
366C4C2×#1798539311yescharacteristic
367C2—42no—
368C2—11321no—
369C2—11322no—
370C2—22641no—
371C2—22641no—
372C2#3182697811yescharacteristic
373C2#3182726711yescharacteristic
374C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#478×C283C2
socleC22×C283C22×D4
hypercenter#478D283
hypocenterC283#3122
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #31827071C2semidirect
2. #31826937C2semidirect
3. #31826792C2semidirect
4. #31826791C2semidirect
5. #31826762C2semidirect
6. #31826661C2semidirect
7. #31826660C2semidirect
8. #31826600C2semidirect
9. #31826600C2semidirect
10. #31826576C2semidirect
11. #31826574C2semidirect
12. #31826547C2semidirect
13. #31826545C2semidirect
14. #31826525C2semidirect
15. #478×C283C2semidirect
21. #22583607C22semidirect
31. #22583572C22semidirect
32. #22583572C22semidirect
39. #22583543C22semidirect
40. #22583541C22semidirect
41. C4⋊(C283⋊C8)C22semidirect
42. #22583532C22semidirect
43. #22583532C22semidirect
46. #22583530C22semidirect
47. #22583530C22semidirect
50. #22583520C22semidirect
51. C8×Dic283C22semidirect
52. #125×C283C22semidirect
54. #107×C283C22semidirect
55. #106×C283C22semidirect
56. C4⋊C8×C283C22semidirect
187. C283#3122semidirect
194. #478D283semidirect
210. #125C2×D283semidirect
230. #107C2×D283semidirect
232. #106C2×D283semidirect
234. C4⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270712
#318269372
#318267922
#318267912
#318267622
#318266612
#318266602
#318266002
#318265762
#318265742
#318265472
#318265452
#318265252
#478×C2832
#3122283