Finite Group Databasebeta

← #49133116

Subgroups — #49133116

Order 36224.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827165C211yesmaximal, characteristic, complemented
2#31827110C211yesmaximal, characteristic, complemented
3#31826820C211yesmaximal, characteristic, complemented
4#31826802C211yesmaximal, characteristic, complemented
5#31826792C211yesmaximal, characteristic, complemented
6#31826765C211yesmaximal, characteristic, complemented
7#31826700C211yesmaximal, characteristic, complemented
8#31826693C211yesmaximal, characteristic, complemented
9#31826680C211yesmaximal, characteristic, complemented
10#31826607C211yesmaximal, characteristic, complemented
11#31826597C211yesmaximal, characteristic, complemented
12C8×D1132C211yesmaximal, characteristic, complemented
13#31826458C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15C4×D8×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×#17985380C2211yescharacteristic, complemented
19C2×#17985377C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic
21C2×C8×D283C2211yescharacteristic, complemented
22#22583603—21no—
23#22583602C2211yescharacteristic, complemented
24#22583598C2211yescharacteristic
25#22583594—21no—
26#22583593—21no—
27#22583590C2211yescharacteristic
28#22583585C2211yescharacteristic
29#22583584—21no—
30#22583583—21no—
31#22583581C2211yescharacteristic
32#22583581C2211yescharacteristic, complemented
33#22583580—21no—
34C4×D1132C2211yescharacteristic
35C4×C22⋊D283—21no—
36#22583568C2211yescharacteristic, complemented
37C4⋊C4×D283C2211yescharacteristic
38C2×(C2×D283)⋊C4—21no—
39#22583543C2211yescharacteristic, 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#107×C283C2211yescharacteristic, complemented
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic, complemented
58C4×C8×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60#17985391—22no—
61#17985391—41no—
62C2×Dic566C2311yescharacteristic
63C2×D1132—21no—
64C2×D1132D411yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70D4×D283—22no—
71D4×D283—41no—
72C22×Dic283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75C2×C4×D283C2311yescharacteristic
76#17985380—41no—
77#17985377—41no—
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C8×D283—41no—
81C8×D283—41no—
82C4⋊Dic283—21no—
83C4⋊Dic283D411yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85C4⋊Dic283C2311yescharacteristic
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4D411yescharacteristic
97(C2×D283)⋊C4D411yescharacteristic
98C4×Dic283—21no—
99C2×D4×C283C2311yescharacteristic
100C2×D4×C283C2311yescharacteristic
101C22×C4×C283—21no—
102C22×C4×C283—21no—
103D8×C283—22no—
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C22⋊C4×C283—21no—
109C22⋊C4×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112C22×D283—42no—
113C22×D283—42no—
114C22×D283—81no—
115C22×D283C2×D411yescharacteristic
116C22×D283C2×D411yescharacteristic
117Dic566—21no—
118Dic566—21no—
119D1132—22no—
120D1132—21no—
121D1132—21no—
122D1132—81no—
123C22⋊D283—42no—
124C22⋊D283—42no—
125C22⋊D283—42no—
126C22⋊D283—81no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283—42no—
131C2×Dic283C2×D411yescharacteristic
132C2×Dic283C2×D411yescharacteristic
133C4×D283—21no—
134C4×D283—21no—
135C4×D283—21no—
136C4×D283—21no—
137C4×D283—81no—
138C283⋊C8—21no—
139C283⋊C8—21no—
140C23×C283—21no—
141C23×C283—21no—
142D4×C283—21no—
143D4×C283—21no—
144D4×C283—21no—
145D4×C283#4112yes—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—81no—
149C2×C4×C283—81no—
150C2×C4×C283C2×D411yescharacteristic
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2411yescharacteristic
153C8×C283—21no—
154C8×C283—21no—
155C22×C283—22no—
156C22×C283—41no—
157C22×C283—41no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283—41no—
161C22×C283C22×D411yescharacteristic
162C2×D283—21no—
163C2×D283—21no—
164C2×D283—21no—
165C2×D283—21no—
166C2×D283—21no—
167C2×D283—41no—
168C2×D283—41no—
169C2×D283—41no—
170C2×D283—84no—
171C2×D283#13512yes—
172C4×C283—21no—
173C4×C283—21no—
174C4×C283—41no—
175C4×C283—41no—
176C4×C283C2×#4111yescharacteristic
177C4×C283H(5,𝔽2)11yescharacteristic
178Dic283—21no—
179Dic283—21no—
180Dic283—41no—
181Dic283—41no—
182Dic283—41no—
183C2×C283—42no—
184C2×C283—81no—
185C2×C283#54611yescharacteristic
186C2×C283C2×#13511yescharacteristic
187C2×C283#57611yescharacteristic
188D283—22no—
189D283—41no—
190D283—81no—
191C283#329711yescharacteristic, complemented, Sylow
192#3297—2831nomaximal, Sylow
193#553—2831no—
194#546—2831no—
195#488—2831no—
196#484—2831no—
197#482—2831no—
198#478—2831no—
199#466—2831no—
200#465—2831no—
201#463—2831no—
202#449—2831no—
203#447—2831no—
204C4×D8D28311yescharacteristic, complemented
205C8×D4—2831no—
206#416—2831no—
207C2×#102—2831no—
208C2×#41—2831no—
209C22×D4—2831no—
210C2×SD16—2831no—
211C2×D8—2831no—
212C2×D8C2×D28311yescharacteristic
213C22×C8—2831no—
214C22×C8—2831no—
215#126—5661no—
216#125—2831no—
217#124—2831no—
218#123—5661no—
219#123—5661no—
220C22⋊Q8—2831no—
221#121—2831no—
222#121—2831no—
223#121—2831no—
224#121—5661no—
225#121—5661no—
226#120—5661no—
227C4×D4—2831no—
228C4×D4—5661no—
229C4×D4C2×D28311yescharacteristic
230C4×D4C2×D28311yescharacteristic, complemented
231#117—2831no—
232C2×C4⋊C4—2831no—
233C2×C22⋊C4—5661no—
234#107—2831no—
235#107C2×D28311yescharacteristic, complemented
236#106—2831no—
237C4⋊C8—2831no—
238#103—2831no—
239#103—2831no—
240#103—2831no—
241#102—2831no—
242#102—2831no—
243#102—2831no—
244#102—2831no—
245#102—2831no—
246#102C2×D28311yescharacteristic
247#102C2×D28311yescharacteristic, complemented
248C22⋊C8—2831no—
249C22⋊C8—2831no—
250C4×C8C2×D28311yescharacteristic, complemented
251C24—5661no—
252#41—5662no—
253#41—11321no—
254C2×Q8—2831no—
255C2×D4—2831no—
256C2×D4—2831no—
257C2×D4—5661no—
258C2×D4—5661no—
259C2×D4—5662no—
260C2×D4—5661no—
261C2×D4—5661no—
262C2×D4—5661no—
263C2×D4—11321no—
264C2×D4C22×D28311yescharacteristic
265C2×D4C22×D28311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—2831no—
269C22×C4—2831no—
270C22×C4—5661no—
271C22×C4—5661no—
272SD16—11321no—
273D8—22no—
274D8—11321no—
275C2×C8—2831no—
276C2×C8—2831no—
277C2×C8—11321no—
278C2×C8—11321no—
279C2×C8C22×D28311yescharacteristic
280C2×C8C22×D28311yescharacteristic
281C4⋊C4—2831no—
282C4⋊C4—2831no—
283C4⋊C4—2831no—
284C4⋊C4—5661no—
285C4⋊C4—5661no—
286C4⋊C4—5661no—
287C4⋊C4—5661no—
288C4⋊C4C22×D28311yescharacteristic
289C4⋊C4C22×D28311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—2831no—
293C22⋊C4—2831no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C22⋊C4—5661no—
298C22⋊C4—5661no—
299C22⋊C4—5661no—
300C22⋊C4—5661no—
301C42—5661no—
302C42C22×D28311yescharacteristic
303C23—21no—
304C23—21no—
305C23—2831no—
306C23—2831no—
307C23—5661no—
308C23—11322no—
309C23—11322no—
310C23—22641no—
311Q8—5661no—
312Q8—5661no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—5662no—
317D4—5661no—
318D4—5661no—
319D4—11322no—
320D4—11322no—
321D4—11322no—
322D4—22641no—
323D4—22641no—
324D4#1798539212yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—2831no—
330C2×C4—2831no—
331C2×C4—5661no—
332C2×C4—5661no—
333C2×C4—5661no—
334C2×C4—5661no—
335C2×C4—5661no—
336C2×C4—5661no—
337C2×C4—5661no—
338C2×C4—11322no—
339C2×C4—22641no—
340C2×C4D4×D28311yescharacteristic
341C2×C4D4×D28311yescharacteristic
342C2×C4C23×D28311yescharacteristic
343C8—21no—
344C8—21no—
345C8—5661no—
346C8—5661no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—2832no—
354C22—5661no—
355C22—5661no—
356C22—5661no—
357C22—5661no—
358C22—5661no—
359C22—11321no—
360C22—11321no—
361C22—11321no—
362C22—22644no—
363C22C2×D4×D28311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—5661no—
369C4—5661no—
370C4—11321no—
371C4—11321no—
372C4—11321no—
373C4C2×#1798539211yescharacteristic
374C4#2258365611yescharacteristic
375C2—42no—
376C2—81no—
377C2—5662no—
378C2—11321no—
379C2—22641no—
380C2#3182711111yescharacteristic
381C2#135×D28311yescharacteristic
382C2#3182726611yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×D8×C283C2
socleC22×C283C22×D4
hypercenterC4×D8D283
hypocenterC283#3297
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #31827165C2semidirect
2. #31827110C2semidirect
3. #31826820C2semidirect
4. #31826802C2semidirect
5. #31826792C2semidirect
6. #31826765C2semidirect
7. #31826700C2semidirect
8. #31826693C2semidirect
9. #31826680C2semidirect
10. #31826607C2semidirect
11. #31826597C2semidirect
12. C8×D1132C2semidirect
13. #31826458C2semidirect
14. #102×D283C2semidirect
15. C4×D8×C283C2semidirect
18. C2×#17985380C22semidirect
21. C2×C8×D283C22semidirect
23. #22583602C22semidirect
32. #22583581C22semidirect
36. #22583568C22semidirect
39. #22583543C22semidirect
40. #22583541C22semidirect
41. C4⋊(C283⋊C8)C22semidirect
42. #22583535C22semidirect
43. #22583535C22semidirect
44. #22583533C22semidirect
51. (C2×D283)⋊C8C22semidirect
54. C4×D4×C283C22semidirect
55. #107×C283C22semidirect
57. #102×C283C22semidirect
58. C4×C8×C283C22semidirect
191. C283#3297semidirect
204. C4×D8D283semidirect
230. C4×D4C2×D283semidirect
235. #107C2×D283semidirect
247. #102C2×D283semidirect
250. C4×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271652
#318271102
#318268202
#318268022
#318267922
#318267652
#318267002
#318266932
#318266802
#318266072
#318265972
C8×D11322
#318264582
#102×D2832
C4×D8×C2832
#3297283