Finite Group Databasebeta

← #49133227

Subgroups — #49133227

Order 36224.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827120C211yesmaximal, characteristic, complemented
2#31827110C211yesmaximal, characteristic, complemented
3#31826825C211yesmaximal, characteristic, complemented
4#31826797C211yesmaximal, characteristic, complemented
5#31826785C211yesmaximal, characteristic, complemented
6#31826755C211yesmaximal, characteristic, complemented
7#31826717C211yesmaximal, characteristic, complemented
8#31826693C211yesmaximal, characteristic, complemented
9#31826680C211yesmaximal, characteristic, complemented
10#31826607C211yesmaximal, characteristic, complemented
11#31826597C211yesmaximal, characteristic, complemented
12#31826538C211yesmaximal, characteristic, complemented
13#31826463C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#442×C283C211yesmaximal, characteristic, complemented
16C2×#17985392—21no—
17C2×#17985391C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19C2×#17985380C2211yescharacteristic, complemented
20C2×#17985377C2211yescharacteristic
21C2×#17985375C2211yescharacteristic, complemented
22C2×C8×D283C2211yescharacteristic
23#22583610C2211yescharacteristic, complemented
24#22583598C2211yescharacteristic
25#22583594—21no—
26#22583592—21no—
27#22583592—21no—
28#22583590C2211yescharacteristic
29#22583589—21no—
30#22583585C2211yescharacteristic
31#22583584—21no—
32#22583581C2211yescharacteristic
33#22583581C2211yescharacteristic, complemented
34#22583580—21no—
35C4×D1132C2211yescharacteristic
36C4⋊C4×D283C2211yescharacteristic
37C4⋊C4×D283C2211yescharacteristic, complemented
38C2×(C2×D283)⋊C4—21no—
39#22583541C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41C4⋊(C283⋊C8)C2211yescharacteristic, complemented
42#22583535C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583533C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51(C2×D283)⋊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—
60#17985392—44no—
61#17985391—22no—
62#17985391—41no—
63C2×Dic566—21no—
64C2×Dic566C2311yescharacteristic
65C2×D1132—21no—
66C2×D1132D411yescharacteristic
67C2×D1132C2311yescharacteristic
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72D4×D283—22no—
73D4×D283—41no—
74C22×Dic283—21no—
75C2×C4×D283—21no—
76C2×C4×D283—21no—
77C2×C4×D283C2311yescharacteristic
78C2×C4×D283C2311yescharacteristic
79#17985380—41no—
80#17985377—41no—
81#17985375—41no—
82C2×C283⋊C8C2311yescharacteristic
83C2×C283⋊C8C2311yescharacteristic
84C8×D283—41no—
85C4⋊Dic283—21no—
86C4⋊Dic283—21no—
87C4⋊Dic283D411yescharacteristic
88C4⋊Dic283C2311yescharacteristic
89C4⋊Dic283C2311yescharacteristic
90Dic283⋊C4—21no—
91Dic283⋊C4—21no—
92C22⋊Dic283—21no—
93C22⋊Dic283—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4—21no—
98(C2×D283)⋊C4D411yescharacteristic
99(C2×D283)⋊C4D411yescharacteristic
100C2×D4×C283C2311yescharacteristic
101C2×D4×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283—21no—
104D8×C283—22no—
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C22⋊C4×C283—21no—
110C22⋊C4×C283—21no—
111C42×C283C2311yescharacteristic
112C22×D283—21no—
113C22×D283—42no—
114C22×D283—42no—
115C22×D283—81no—
116C22×D283C2×D411yescharacteristic
117C22×D283C2×D411yescharacteristic
118Dic566—21no—
119Dic566—21no—
120Dic566—42no—
121D1132—22no—
122D1132—21no—
123D1132—21no—
124D1132—81no—
125C22⋊D283—42no—
126C22⋊D283—42no—
127C22⋊D283—42no—
128C22⋊D283—42no—
129C2×Dic283—21no—
130C2×Dic283—21no—
131C2×Dic283—21no—
132C2×Dic283—42no—
133C2×Dic283C2×D411yescharacteristic
134C2×Dic283C2×D411yescharacteristic
135C4×D283—21no—
136C4×D283—21no—
137C4×D283—21no—
138C4×D283—21no—
139C4×D283—42no—
140C4×D283—42no—
141C283⋊C8—21no—
142C283⋊C8—21no—
143C23×C283—21no—
144C23×C283—21no—
145D4×C283—21no—
146D4×C283—21no—
147D4×C283—21no—
148D4×C283#4112yescomplemented
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283—42no—
152C2×C4×C283—81no—
153C2×C4×C283C2×D411yescharacteristic
154C2×C4×C283C2×D411yescharacteristic
155C2×C4×C283C2411yescharacteristic
156C8×C283—21no—
157C8×C283—21no—
158C22×C283—22no—
159C22×C283—41no—
160C22×C283—41no—
161C22×C283—41no—
162C22×C283—41no—
163C22×C283—41no—
164C22×C283C22×D411yescharacteristic
165C2×D283—21no—
166C2×D283—21no—
167C2×D283—21no—
168C2×D283—21no—
169C2×D283—21no—
170C2×D283—41no—
171C2×D283—41no—
172C2×D283—41no—
173C2×D283—84no—
174C2×D283AGL(1,ℤ/8)12yes—
175C4×C283—21no—
176C4×C283—21no—
177C4×C283—41no—
178C4×C283—41no—
179C4×C283C2×#4111yescharacteristic
180C4×C283H(5,𝔽2)11yescharacteristic
181Dic283—21no—
182Dic283—21no—
183Dic283—41no—
184Dic283—41no—
185Dic283—41no—
186C2×C283—42no—
187C2×C283—81no—
188C2×C283#54611yescharacteristic
189C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C283#57711yescharacteristic
191D283—22no—
192D283—41no—
193D283—81no—
194C283#330611yescharacteristic, complemented, Sylow
195#3306—2831nomaximal, Sylow
196#547—2831no—
197#546—2831no—
198#489—2831no—
199#483—2831no—
200#481—2831no—
201#476—2831no—
202#469—2831no—
203#465—2831no—
204#463—2831no—
205#449—2831no—
206#447—2831no—
207#442D28311yescharacteristic, complemented
208#435—2831no—
209#417—2831no—
210C2×#102—2831no—
211C2×#41—2831no—
212C2×#41—5661no—
213C22×D4—2831no—
214C2×SD16—2831no—
215C2×D8—2831no—
216C2×D8C2×D28311yescharacteristic
217C2×M16—2831no—
218C22×C8—2831no—
219C4⋊Q8—2831no—
220#124—2831no—
221#123—5661no—
222#123—5661no—
223#123—5661no—
224C22⋊Q8—2831no—
225C22⋊Q8—5661no—
226#121—2831no—
227#121—2831no—
228#121—2831no—
229#121—5661no—
230#120—5661no—
231C4×D4—2831no—
232C4×D4C2×D28311yescharacteristic
233C4×D4C2×D28311yescharacteristic, complemented
234C2×C4⋊C4—2831no—
235C2×C4⋊C4—2831no—
236C2×C22⋊C4—5661no—
237#106—2831no—
238#106—2831no—
239#106C2×D28311yescharacteristic, complemented
240C4⋊C8—2831no—
241#103—2831no—
242#103—2831no—
243#103—2831no—
244#102—2831no—
245#102—2831no—
246#102—2831no—
247#102—2831no—
248#102—2831no—
249#102C2×D28311yescharacteristic
250#102C2×D28311yescharacteristic, complemented
251C22⋊C8—2831no—
252C22⋊C8—2831no—
253#97C2×D28311yescharacteristic, complemented
254C24—5661no—
255#41—5662no—
256#41—11324no—
257#41—11321no—
258C2×Q8—2831no—
259C2×Q8—5661no—
260C2×D4—2831no—
261C2×D4—2831no—
262C2×D4—5661no—
263C2×D4—5661no—
264C2×D4—5662no—
265C2×D4—5661no—
266C2×D4—5661no—
267C2×D4—5661no—
268C2×D4—11321no—
269C2×D4C22×D28311yescharacteristic
270C2×D4C22×D28311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—2831no—
274C22×C4—2831no—
275C22×C4—5661no—
276C22×C4—5661no—
277C22×C4—5661no—
278SD16—11321no—
279D8—22no—
280D8—11321no—
281M16—11321no—
282C2×C8—2831no—
283C2×C8—2831no—
284C2×C8—11321no—
285C2×C8C22×D28311yescharacteristic
286C2×C8C22×D28311yescharacteristic
287C4⋊C4—2831no—
288C4⋊C4—2831no—
289C4⋊C4—2831no—
290C4⋊C4—5661no—
291C4⋊C4—5661no—
292C4⋊C4—5661no—
293C4⋊C4—5661no—
294C4⋊C4C22×D28311yescharacteristic
295C4⋊C4C22×D28311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—2831no—
299C22⋊C4—2831no—
300C22⋊C4—5661no—
301C22⋊C4—5661no—
302C22⋊C4—5661no—
303C22⋊C4—5661no—
304C22⋊C4—5661no—
305C22⋊C4—5661no—
306C42C22×D28311yescharacteristic
307C23—21no—
308C23—21no—
309C23—2831no—
310C23—2831no—
311C23—5661no—
312C23—11322no—
313C23—11322no—
314C23—22641no—
315Q8—5661no—
316Q8—5661no—
317Q8—11322no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—5662no—
322D4—5661no—
323D4—5661no—
324D4—11322no—
325D4—11322no—
326D4—11322no—
327D4—11322no—
328D4—22641no—
329D4#1798539212yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—2831no—
335C2×C4—2831no—
336C2×C4—5661no—
337C2×C4—5661no—
338C2×C4—5661no—
339C2×C4—5661no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—5661no—
343C2×C4—11322no—
344C2×C4—11322no—
345C2×C4—11322no—
346C2×C4D4×D28311yescharacteristic
347C2×C4D4×D28311yescharacteristic
348C2×C4C23×D28311yescharacteristic
349C8—21no—
350C8—21no—
351C8—5661no—
352C8—5661no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—2832no—
360C22—5661no—
361C22—5661no—
362C22—5661no—
363C22—5661no—
364C22—5661no—
365C22—11321no—
366C22—11321no—
367C22—11321no—
368C22—22644no—
369C22C2×D4×D28311yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—5661no—
375C4—5661no—
376C4—11321no—
377C4—11321no—
378C4—11321no—
379C4C2×#1798539211yescharacteristic
380C4#2258365611yescharacteristic
381C2—42no—
382C2—81no—
383C2—5662no—
384C2—11321no—
385C2—22641no—
386C2#3182711111yescharacteristic
387C2AGL(1,ℤ/8)×D28311yescharacteristic
388C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#442×C283C2
socleC22×C283C22×D4
hypercenter#442D283
hypocenterC283#3306
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. #31827120C2semidirect
2. #31827110C2semidirect
3. #31826825C2semidirect
4. #31826797C2semidirect
5. #31826785C2semidirect
6. #31826755C2semidirect
7. #31826717C2semidirect
8. #31826693C2semidirect
9. #31826680C2semidirect
10. #31826607C2semidirect
11. #31826597C2semidirect
12. #31826538C2semidirect
13. #31826463C2semidirect
14. #102×D283C2semidirect
15. #442×C283C2semidirect
19. C2×#17985380C22semidirect
21. C2×#17985375C22semidirect
23. #22583610C22semidirect
33. #22583581C22semidirect
37. C4⋊C4×D283C22semidirect
39. #22583541C22semidirect
40. #22583541C22semidirect
41. C4⋊(C283⋊C8)C22semidirect
42. #22583535C22semidirect
43. #22583535C22semidirect
44. #22583533C22semidirect
51. (C2×D283)⋊C8C22semidirect
54. C4×D4×C283C22semidirect
55. #106×C283C22semidirect
57. #102×C283C22semidirect
58. #97×C283C22semidirect
148. D4×C283#41semidirect
194. C283#3306semidirect
207. #442D283semidirect
233. C4×D4C2×D283semidirect
239. #106C2×D283semidirect
250. #102C2×D283semidirect
253. #97C2×D283semidirect
329. D4#17985392semidirect

Maximal subgroups

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

subgroupindex
#318271202
#318271102
#318268252
#318267972
#318267852
#318267552
#318267172
#318266932
#318266802
#318266072
#318265972
#318265382
#318264632
#102×D2832
#442×C2832
#3306283