Finite Group Databasebeta

← #49133348

Subgroups — #49133348

Order 36224.

410 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#31827173C211yesmaximal, characteristic, complemented
2#31827106C211yesmaximal, characteristic
3#31826826C211yesmaximal, characteristic, complemented
4#31826798C211yesmaximal, characteristic, complemented
5#31826780C211yesmaximal, characteristic, complemented
6#31826744C211yesmaximal, characteristic, complemented
7#31826714C211yesmaximal, characteristic, complemented
8#31826689C211yesmaximal, characteristic, complemented
9#31826626C211yesmaximal, characteristic, complemented
10#31826615C211yesmaximal, characteristic, complemented
11#31826568C211yesmaximal, characteristic, complemented
12#31826536C211yesmaximal, characteristic, complemented
13#31826465C211yesmaximal, characteristic, complemented
14C2×#22583532C211yesmaximal, characteristic, complemented
15#467×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C22×D1132C2211yescharacteristic
18C2×#17985379C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C2×#17985375C2211yescharacteristic, complemented
21#22583609C2211yescharacteristic, complemented
22#22583600—21no—
23#22583599C2211yescharacteristic
24#22583595—21no—
25#22583590—21no—
26#22583587—21no—
27#22583586C2211yescharacteristic, complemented
28#22583585—21no—
29#22583585C2211yescharacteristic
30#22583580—21no—
31Q8×Dic283C2211yescharacteristic, complemented
32#22583572C2211yescharacteristic
33C4×C22⋊D283C2211yescharacteristic
34(C22⋊D283)⋊C4—21no—
35C2×C4⋊Dic283C2211yescharacteristic
36C4⋊C4×D283C2211yescharacteristic, complemented
37C22⋊C4×D283—21no—
38#22583543C2211yescharacteristic, complemented
39#22583543C2211yescharacteristic, complemented
40Dic283⋊C8C2211yescharacteristic, complemented
41#22583534C2211yescharacteristic, complemented
42#22583534C2211yescharacteristic, complemented
43#22583532C2211yescharacteristic
44#22583532C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51#22583520C2211yescharacteristic, complemented
52C2×Q16×C283C2211yescharacteristic, complemented
53C22×C8×C283C2211yescharacteristic
54C22⋊Q8×C283C2211yescharacteristic
55C22⋊Q8×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic, complemented
57#103×C283C2211yescharacteristic, complemented
58#103×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60#17985393—22no—
61#17985393—41no—
62C2×Dic566—21no—
63C2×D1132—22no—
64C2×D1132—21no—
65C2×D1132—21no—
66C2×D1132—21no—
67C2×D1132—41no—
68C2×D1132C2311yescharacteristic
69C2×D1132C2311yescharacteristic
70C2×C22⋊D283D411yescharacteristic
71C22×Dic283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75C2×C4×D283C2311yescharacteristic
76#17985379—22no—
77#17985379—41no—
78#17985375—41no—
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C4⋊Dic283—21no—
82C4⋊Dic283—21no—
83C4⋊Dic283C2311yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4D411yescharacteristic
89C22⋊Dic283D411yescharacteristic
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—
95(C2×D283)⋊C4D411yescharacteristic
96C4×Dic283—21no—
97C4×Dic283C2311yescharacteristic
98C2×Q8×C283C2311yescharacteristic
99C2×Q8×C283C2311yescharacteristic
100C22×C4×C283C2311yescharacteristic
101Q16×C283—41no—
102C2×C8×C283—41no—
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C4⋊C4×C283—21no—
106C4⋊C4×C283—21no—
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C22⋊C4×C283—21no—
110C22⋊C4×C283—21no—
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—42no—
114C22×D283—42no—
115C22×D283—81no—
116C22×D283C2×D411yescharacteristic
117Dic566—81no—
118D1132—21no—
119D1132—21no—
120D1132—21no—
121D1132—42no—
122D1132—42no—
123D1132—81no—
124D1132#4112yes—
125C22⋊D283—22no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—81no—
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C2×Dic283C2×D411yescharacteristic
132C4×D283—21no—
133C4×D283—21no—
134C4×D283—42no—
135C4×D283—81no—
136C4×D283—81no—
137C283⋊C8—21no—
138C283⋊C8—21no—
139C23×C283C2×D411yescharacteristic
140Q8×C283—21no—
141Q8×C283—21no—
142Q8×C283—21no—
143Q8×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283C2×D411yescharacteristic
151C2×C4×C283C2411yescharacteristic
152C8×C283—21no—
153C8×C283—21no—
154C22×C283—21no—
155C22×C283—21no—
156C22×C283#13712yes—
157C22×C283C22×D411yescharacteristic
158C2×D283—21no—
159C2×D283—22no—
160C2×D283—21no—
161C2×D283—21no—
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×C283—41no—
173C4×C283C2×#4111yescharacteristic
174C4×C283H(5,𝔽2)11yescharacteristic
175Dic283—21no—
176Dic283—21no—
177Dic283—21no—
178Dic283—41no—
179Dic283—41no—
180C2×C283—22no—
181C2×C283#54611yescharacteristic
182C2×C283C2×#13711yescharacteristic
183C2×C283#57611yescharacteristic
184D283—41no—
185D283—42no—
186D283—81no—
187C283#331411yescharacteristic, complemented, Sylow
188#3314—2831nomaximal, Sylow
189#554—2831no—
190#546—2831no—
191#489—2831no—
192#484—2831no—
193#480—2831no—
194#474—2831no—
195#468—2831no—
196#467D28311yescharacteristic, complemented
197#464—2831no—
198#452—2831no—
199#450—2831no—
200#440—2831no—
201#435—2831no—
202#417—2831no—
203C2×#102—2831no—
204C2×#41—2831no—
205C22×D4—2831no—
206C2×Q16C2×D28311yescharacteristic, complemented
207C2×SD16—2831no—
208C2×SD16—2831no—
209C2×M16—2831no—
210C22×C8C2×D28311yescharacteristic
211C4⋊Q8—2831no—
212#125—5661no—
213#124—2831no—
214#123—5661no—
215C22⋊Q8—2831no—
216C22⋊Q8—5661no—
217C22⋊Q8—5661no—
218C22⋊Q8C2×D28311yescharacteristic
219C22⋊Q8C2×D28311yescharacteristic
220#121—2831no—
221#121—5661no—
222#120—5661no—
223C4×Q8—2831no—
224C4×D4—2831no—
225C4×D4—2831no—
226C4×D4—5661no—
227C2×C4⋊C4—2831no—
228C2×C4⋊C4—2831no—
229C2×C22⋊C4—5661no—
230#107—2831no—
231#107—2831no—
232#107C2×D28311yescharacteristic, complemented
233C4⋊C8—2831no—
234#103—2831no—
235#103—2831no—
236#103C2×D28311yescharacteristic, complemented
237#103C2×D28311yescharacteristic, complemented
238#102—2831no—
239#102—2831no—
240#102—2831no—
241#102—2831no—
242#102—2831no—
243#102—2831no—
244C22⋊C8—2831no—
245C22⋊C8—2831no—
246#97—2831no—
247C24—5661no—
248#41—5662no—
249#41—11321no—
250C2×Q8—5661no—
251C2×Q8C22×D28311yescharacteristic
252C2×Q8C22×D28311yescharacteristic
253C2×D4—2831no—
254C2×D4—2831no—
255C2×D4—2831no—
256C2×D4—5662no—
257C2×D4—5661no—
258C2×D4—5661no—
259C2×D4—5661no—
260C2×D4—11321no—
261C22×C4—2831no—
262C22×C4—5661no—
263C22×C4—5661no—
264C22×C4—5661no—
265C22×C4—5661no—
266C22×C4C22×D28311yescharacteristic
267Q16—41no—
268SD16—5662no—
269SD16—11321no—
270M16—11321no—
271C2×C8—41no—
272C2×C8—2831no—
273C2×C8—2831no—
274C2×C8C22×D28311yescharacteristic
275C2×C8C22×D28311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—2831no—
279C4⋊C4—2831no—
280C4⋊C4—2831no—
281C4⋊C4—5661no—
282C4⋊C4—5661no—
283C4⋊C4—5661no—
284C4⋊C4—5661no—
285C4⋊C4—5661no—
286C4⋊C4C22×D28311yescharacteristic
287C4⋊C4C22×D28311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—2831no—
291C22⋊C4—2831no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C42—2831no—
298C42—5661no—
299C23—2831no—
300C23—5661no—
301C23—5661no—
302C23—11322no—
303C23—11322no—
304C23—22641no—
305C23D4×D28311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—22641no—
311D4—2832no—
312D4—5662no—
313D4—5661no—
314D4—5661no—
315D4—5661no—
316D4—11322no—
317D4—11322no—
318D4—22641no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—2831no—
326C2×C4—2831no—
327C2×C4—2831no—
328C2×C4—5661no—
329C2×C4—5661no—
330C2×C4—5661no—
331C2×C4—5661no—
332C2×C4—11322no—
333C2×C4—22641no—
334C2×C4—22641no—
335C2×C4—22641no—
336C2×C4D4×D28311yescharacteristic
337C2×C4C23×D28311yescharacteristic
338C8—21no—
339C8—21no—
340C8—5661no—
341C8—5661no—
342C22—21no—
343C22—21no—
344C22—5661no—
345C22—5661no—
346C22—5661no—
347C22—5662no—
348C22—11321no—
349C22—11321no—
350C22—11321no—
351C22—11321no—
352C22—11321no—
353C22—22644no—
354C22#2258364212yes—
355C22C2×D4×D28311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—5661no—
362C4—5661no—
363C4—5661no—
364C4—11321no—
365C4—11321no—
366C4#41×D28311yescharacteristic
367C4#2258365511yescharacteristic
368C2—22no—
369C2—11321no—
370C2—11322no—
371C2—22641no—
372C2#3182710411yescharacteristic
373C2C2×#2258364211yescharacteristic
374C2#3182726711yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#467×C283C2
socleC22×C283C22×D4
prime radical#31827106C2
hypercenter#467D283
hypocenterC283#3314
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #31827173C2semidirect
3. #31826826C2semidirect
4. #31826798C2semidirect
5. #31826780C2semidirect
6. #31826744C2semidirect
7. #31826714C2semidirect
8. #31826689C2semidirect
9. #31826626C2semidirect
10. #31826615C2semidirect
11. #31826568C2semidirect
12. #31826536C2semidirect
13. #31826465C2semidirect
14. C2×#22583532C2semidirect
15. #467×C283C2semidirect
20. C2×#17985375C22semidirect
21. #22583609C22semidirect
27. #22583586C22semidirect
31. Q8×Dic283C22semidirect
36. C4⋊C4×D283C22semidirect
38. #22583543C22semidirect
39. #22583543C22semidirect
40. Dic283⋊C8C22semidirect
41. #22583534C22semidirect
42. #22583534C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. #22583520C22semidirect
52. C2×Q16×C283C22semidirect
56. #107×C283C22semidirect
57. #103×C283C22semidirect
58. #103×C283C22semidirect
187. C283#3314semidirect
196. #467D283semidirect
206. C2×Q16C2×D283semidirect
232. #107C2×D283semidirect
236. #103C2×D283semidirect
237. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271732
#318271062
#318268262
#318267982
#318267802
#318267442
#318267142
#318266892
#318266262
#318266152
#318265682
#318265362
#318264652
C2×#225835322
#467×C2832
#3314283