Finite Group Databasebeta

← #49131443

Subgroups — #49131443

Order 36224.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827080C211yesmaximal, characteristic, complemented
2#31826937C211yesmaximal, characteristic, complemented
3#31826809C211yesmaximal, characteristic, complemented
4#31826787C211yesmaximal, characteristic, complemented
5#31826754C211yesmaximal, characteristic, complemented
6#31826743C211yesmaximal, characteristic, complemented
7#31826679C211yesmaximal, characteristic, complemented
8#31826678C211yesmaximal, characteristic, complemented
9#31826617C211yesmaximal, characteristic, complemented
10#31826597C211yesmaximal, characteristic
11#31826567C211yesmaximal, characteristic, complemented
12C4×#17985380C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826527C211yesmaximal, characteristic, complemented
15#442×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20#22583609C2211yescharacteristic, complemented
21#22583603—21no—
22#22583597C2211yescharacteristic, complemented
23#22583596—21no—
24#22583593—21no—
25#22583590C2211yescharacteristic
26#22583589—21no—
27#22583581C2211yescharacteristic
28C4×Dic566C2211yescharacteristic, complemented
29C4×D1132C2211yescharacteristic
30D4×Dic283C2211yescharacteristic
31#22583572C2211yescharacteristic
32C4×C22⋊D283—21no—
33(C22⋊D283)⋊C4—21no—
34#22583568C2211yescharacteristic
35#22583567C2211yescharacteristic
36C2×(C2×D283)⋊C4—21no—
37C22⋊C4×D283—21no—
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
51C4×C283⋊C8C2211yescharacteristic, 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×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65D4×D283—22no—
66D4×D283—22no—
67C22×Dic283—21no—
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283C2311yescharacteristic
71#17985381—22no—
72#17985380—22no—
73#17985377—22no—
74C2×C283⋊C8C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82Dic283⋊C4D411yescharacteristic
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4D411yescharacteristic
92(C2×D283)⋊C4D411yescharacteristic
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C2×D4×C283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98C22×C4×C283—21no—
99C22×C4×C283—21no—
100D8×C283—22no—
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283—24no—
110C22×D283—81no—
111C22×D283—81no—
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115Dic566—81no—
116D1132—21no—
117D1132#4112yes—
118C22⋊D283—24no—
119C22⋊D283—81no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—81no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—21no—
128C4×D283—21no—
129C4×D283—81no—
130C4×D283—81no—
131C283⋊C8—21no—
132C283⋊C8—21no—
133C23×C283—21no—
134C23×C283—21no—
135D4×C283—21no—
136D4×C283—21no—
137D4×C283—21no—
138D4×C283#4112yes—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—81no—
142C2×C4×C283—81no—
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2411yescharacteristic
146C8×C283—21no—
147C8×C283—21no—
148C22×C283—22no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283—41no—
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—84no—
162C4×C283—21no—
163C4×C283—21no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283C2×#4111yescharacteristic
167C4×C283C2×#4111yescharacteristic
168Dic283—21no—
169Dic283—21no—
170Dic283—21no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174C2×C283—42no—
175C2×C283—81no—
176C2×C283#52511yescharacteristic
177C2×C283#57611yescharacteristic
178C2×C283#57711yescharacteristic
179D283—41no—
180D283—42no—
181C283#311811yescharacteristic, complemented, Sylow
182#3118—2831nomaximal, Sylow
183#542—2831no—
184#518—2831no—
185#485—2831no—
186#482—2831no—
187#476—2831no—
188#474—2831no—
189#463—2831no—
190#463—2831no—
191#450—2831no—
192#447—2831no—
193#442D28311yescharacteristic, complemented
194#440—2831no—
195C4×SD16—2831no—
196C4×D8—2831no—
197#433—2831no—
198C22×D4—2831no—
199C2×SD16—2831no—
200C2×SD16—2831no—
201C2×D8—2831no—
202C2×D8C2×D28311yescharacteristic
203C4⋊Q8—2831no—
204#126—5661no—
205#124—2831no—
206#124—5661no—
207#123—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—5661no—
210#121—2831no—
211C4×Q8—2831no—
212C4×D4—2831no—
213C4×D4—2831no—
214C4×D4—2831no—
215C4×D4—5661no—
216C4×D4—5661no—
217C4×D4C2×D28311yescharacteristic
218C4×D4C2×D28311yescharacteristic, complemented
219#117—2831no—
220#117—2831no—
221C2×C22⋊C4—5661no—
222C2×C22⋊C4—5661no—
223#107—2831no—
224#107—2831no—
225#106—2831no—
226#106C2×D28311yescharacteristic, complemented
227C4⋊C8—2831no—
228C4⋊C8—2831no—
229#103—2831no—
230#103—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102C2×D28311yescharacteristic
236#102C2×D28311yescharacteristic, complemented
237C22⋊C8—2831no—
238C22⋊C8—2831no—
239#97C2×D28311yescharacteristic, complemented
240C4×C8—2831no—
241C24—5661no—
242C2×Q8—2831no—
243C2×Q8—5661no—
244C2×D4—2831no—
245C2×D4—5661no—
246C2×D4—5662no—
247C2×D4—5662no—
248C2×D4—5661no—
249C2×D4C22×D28311yescharacteristic
250C2×D4C22×D28311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—2831no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4—5661no—
257SD16—5662no—
258SD16—5662no—
259D8—22no—
260D8—5662no—
261C2×C8—2831no—
262C2×C8—2831no—
263C2×C8C22×D28311yescharacteristic
264C2×C8C22×D28311yescharacteristic
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4C22×D28311yescharacteristic
273C4⋊C4C22×D28311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—2831no—
277C22⋊C4—2831no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—2831no—
287C42—5661no—
288C42—5661no—
289C42C22×D28311yescharacteristic
290C23—21no—
291C23—21no—
292C23—2831no—
293C23—5664no—
294C23—5661no—
295C23—22641no—
296C23—22641no—
297Q8—5661no—
298Q8—5661no—
299Q8—22641no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—2832no—
304D4—5664no—
305D4—5661no—
306D4—22641no—
307D4#1798539212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—2831no—
313C2×C4—2831no—
314C2×C4—2831no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—22641no—
321C2×C4—22641no—
322C2×C4—22641no—
323C2×C4D4×D28311yescharacteristic
324C2×C4D4×D28311yescharacteristic
325C2×C4C23×D28311yescharacteristic
326C8—21no—
327C8—21no—
328C8—5661no—
329C8—5661no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—5661no—
337C22—5662no—
338C22—5661no—
339C22—5661no—
340C22—11321no—
341C22—11321no—
342C22—22644no—
343C22C2×D4×D28311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—5661no—
349C4—5661no—
350C4—5661no—
351C4—11321no—
352C4—11321no—
353C4—11321no—
354C4#41×D28311yescharacteristic
355C4C2×#1798539211yescharacteristic
356C2—42no—
357C2—81no—
358C2—11321no—
359C2—11322no—
360C2#3182697411yescharacteristic
361C2#3182726911yescharacteristic
362C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#442×C283C2
socleC22×C283C22×D4
prime radical#31826597C2
hypercenter#442D283
hypocenterC283#3118
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. #31827080C2semidirect
2. #31826937C2semidirect
3. #31826809C2semidirect
4. #31826787C2semidirect
5. #31826754C2semidirect
6. #31826743C2semidirect
7. #31826679C2semidirect
8. #31826678C2semidirect
9. #31826617C2semidirect
11. #31826567C2semidirect
12. C4×#17985380C2semidirect
13. C4×#17985377C2semidirect
14. #31826527C2semidirect
15. #442×C283C2semidirect
20. #22583609C22semidirect
22. #22583597C22semidirect
28. C4×Dic566C22semidirect
38. #22583544C22semidirect
39. #22583543C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. Dic283⋊C8C22semidirect
43. #22583535C22semidirect
44. #22583533C22semidirect
47. #22583531C22semidirect
51. C4×C283⋊C8C22semidirect
54. C4×D4×C283C22semidirect
55. #106×C283C22semidirect
57. #102×C283C22semidirect
58. #97×C283C22semidirect
181. C283#3118semidirect
193. #442D283semidirect
218. C4×D4C2×D283semidirect
226. #106C2×D283semidirect
236. #102C2×D283semidirect
239. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270802
#318269372
#318268092
#318267872
#318267542
#318267432
#318266792
#318266782
#318266172
#318265972
#318265672
C4×#179853802
C4×#179853772
#318265272
#442×C2832
#3118283