Finite Group Databasebeta

← #49130092

Subgroups — #49130092

Order 36224.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583637C211yesmaximal, characteristic
2#31826947C211yesmaximal, characteristic, complemented
3#31826937C211yesmaximal, characteristic, complemented
4#31826578C211yesmaximal, characteristic, complemented
5#31826574C211yesmaximal, characteristic, complemented
6#31826568C211yesmaximal, characteristic, complemented
7SD16×Dic283C211yesmaximal, characteristic, complemented
8C4×#17985379C211yesmaximal, characteristic, complemented
9#31826547C211yesmaximal, characteristic, complemented
10C4×#17985377C211yesmaximal, characteristic, complemented
11#31826506C211yesmaximal, characteristic, complemented
12#31826460C211yesmaximal, characteristic, complemented
13#102×D283C211yesmaximal, characteristic, complemented
14#31826422C211yesmaximal, characteristic, complemented
15#440×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18#22583637C418yescomplemented
19C2×#17985379C2211yescharacteristic
20C2×D2264C2211yescharacteristic
21C2×#17985377C2211yescharacteristic
22C2×#17985375C2211yescharacteristic
23C2×C8×D283C2211yescharacteristic
24Q8×Dic283C2211yescharacteristic, complemented
25C4×D1132—21no—
26C4×D1132C2211yescharacteristic
27C4×D1132C2211yescharacteristic, complemented
28D4×Dic283C2211yescharacteristic
29#22583572—21no—
30#22583572C2211yescharacteristic
31#22583572C2211yescharacteristic, complemented
32C4×C22⋊D283—21no—
33(C22⋊D283)⋊C4—21no—
34#22583568C2211yescharacteristic
35#22583567—21no—
36#22583567C2211yescharacteristic
37C4⋊C4×D283—21no—
38C4⋊C4×D283C2211yescharacteristic
39C2×(C2×D283)⋊C4—21no—
40C22⋊C4×D283—21no—
41#22583543C2211yescharacteristic, complemented
42#22583542C2211yescharacteristic, complemented
43#22583541C2211yescharacteristic, complemented
44#22583534C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic
46#22583532C2211yescharacteristic, complemented
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583530C2211yescharacteristic, complemented
50#22583520C2211yescharacteristic, complemented
51C4×C283⋊C8C2211yescharacteristic, complemented
52C8×Dic283C2211yescharacteristic, complemented
53C2×SD16×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic, complemented
55C4×D4×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic, complemented
57#103×C283C2211yescharacteristic, complemented
58#102×C283C2211yescharacteristic
59#97×C283C2211yescharacteristic, complemented
60C23×D283—21no—
61#17985393—22no—
62#17985393C2×C414yescomplemented
63C2×D1132—21no—
64C2×D1132C2311yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67D4×D283—22no—
68D4×D283C2×C414yescomplemented
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75C2×C4×D283—21no—
76C2×C4×D283C2311yescharacteristic
77#17985379C2×C414yescomplemented
78D2264C2×C414yescomplemented
79#17985377C2×C414yescomplemented
80#17985375C2×C414yescomplemented
81C2×C283⋊C8C2311yescharacteristic
82C2×C283⋊C8C2311yescharacteristic
83C8×D283—22no—
84C4⋊Dic283—21no—
85C4⋊Dic283C2311yescharacteristic
86C4⋊Dic283C2311yescharacteristic
87Dic283⋊C4—21no—
88Dic283⋊C4D411yescharacteristic
89Dic283⋊C4D411yescharacteristic
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—
99C4×Dic283—21no—
100C4×Dic283C2311yescharacteristic
101C2×Q8×C283C2311yescharacteristic
102C2×D4×C283C2311yescharacteristic
103C22×C4×C283—21no—
104SD16×C283C2×C414yescomplemented
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283—21no—
108C4⋊C4×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C42×C283—21no—
112C42×C283C2311yescharacteristic
113C22×D283—21no—
114C22×D283—21no—
115C22×D283—24no—
116C22×D283—81no—
117C22×D283—81no—
118C22×D283C2×D411yescharacteristic
119D1132—24no—
120D1132—21no—
121D1132—21no—
122D1132C22×C412yes—
123D1132C22×C412yes—
124C22⋊D283—24no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—81no—
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C4×D283—24no—
132C4×D283—81no—
133C4×D283—81no—
134C4×D283—81no—
135C4×D283—81no—
136C4×D283—81no—
137C4×D283C22×C412yes—
138C4×D283#4112yes—
139C283⋊C8—21no—
140C283⋊C8C22×C412yes—
141C23×C283—21no—
142Q8×C283—21no—
143Q8×C283C22×C412yes—
144D4×C283—21no—
145D4×C283C22×C412yes—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—81no—
150C2×C4×C283C2×D411yescharacteristic
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2411yescharacteristic
153C8×C283—21no—
154C8×C283C22×C412yes—
155C22×C283—22no—
156C22×C283—41no—
157C22×C283—41no—
158C22×C283C22×D411yescharacteristic
159C2×D283—21no—
160C2×D283—21no—
161C2×D283—22no—
162C2×D283—22no—
163C2×D283—41no—
164C2×D283—41no—
165C2×D283—41no—
166C2×D283—41no—
167C2×D283—84no—
168C2×D283C4×D412yes—
169C4×C283—22no—
170C4×C283—21no—
171C4×C283—21no—
172C4×C283—41no—
173C4×C283—41no—
174C4×C283C23×C411yescharacteristic
175C4×C283C2×#4111yescharacteristic
176Dic283—21no—
177Dic283—21no—
178Dic283—41no—
179Dic283—41no—
180Dic283C4×D412yes—
181C2×C283—42no—
182C2×C283C2×C4×D411yescharacteristic
183C2×C283#57611yescharacteristic
184C2×C283#57711yescharacteristic
185D283—22no—
186D283—42no—
187D283—42no—
188C283#294611yescharacteristic, complemented, Sylow
189#2946—2831nomaximal, Sylow
190C2×AGL(1,ℤ/8)—2831no—
191#520—2831no—
192#518—2831no—
193#442—2831no—
194#442—2831no—
195#440—2831no—
196#440D28311yescharacteristic, complemented
197C4×SD16—2831no—
198C4×SD16—2831no—
199C4×D8—2831no—
200C4×D8—2831no—
201#428—2831no—
202#416—2831no—
203C2×#102—2831no—
204#405—2831no—
205C2×#41—2831no—
206C22×D4—2831no—
207AGL(1,ℤ/8)—2838no—
208C2×SD16—2831no—
209C2×SD16C2×D28311yescharacteristic
210C2×D8—2831no—
211C2×D8—2831no—
212C2×M16—2831no—
213C22×C8—2831no—
214C4×Q8—2831no—
215C4×Q8C2×D28311yescharacteristic, complemented
216C4×D4—2831no—
217C4×D4—2831no—
218C4×D4—2831no—
219C4×D4—2831no—
220C4×D4—2831no—
221C4×D4—5661no—
222C4×D4—5661no—
223C4×D4—5661no—
224C4×D4—5661no—
225C4×D4C2×D28311yescharacteristic
226#117—2831no—
227#117—2831no—
228#117—5661no—
229C2×C4⋊C4—2831no—
230C2×C4⋊C4—5661no—
231C2×C22⋊C4—5661no—
232C2×C22⋊C4—5661no—
233#107—2831no—
234#107C2×D28311yescharacteristic, complemented
235#106—2831no—
236#106—2831no—
237#103—2831no—
238#103C2×D28311yescharacteristic, complemented
239#102—2831no—
240#102—2831no—
241#102—2831no—
242#102—2831no—
243#102—2831no—
244#102C2×D28311yescharacteristic
245#97—2831no—
246#97C2×D28311yescharacteristic, complemented
247C4×C8—2831no—
248C4×C8—2831no—
249C24—5661no—
250#41—2834no—
251#41—5662no—
252C2×Q8C22×D28311yescharacteristic
253C2×D4—2834no—
254C2×D4—2831no—
255C2×D4—2831no—
256C2×D4—5661no—
257C2×D4—5662no—
258C2×D4—5661no—
259C2×D4C22×D28311yescharacteristic
260C22×C4—21no—
261C22×C4—2831no—
262C22×C4—5661no—
263C22×C4—5661no—
264C22×C4—5661no—
265C22×C4—5661no—
266C22×C4—5661no—
267C22×C4—5661no—
268C22×C4—5661no—
269SD16—2834no—
270SD16C4×D28314yescomplemented
271D8—2834no—
272D8—2834no—
273M16—2834no—
274C2×C8—2831no—
275C2×C8—2831no—
276C2×C8—5662no—
277C2×C8C22×D28311yescharacteristic
278C2×C8C22×D28311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—2831no—
281C4⋊C4—2831no—
282C4⋊C4—2831no—
283C4⋊C4—2831no—
284C4⋊C4—5661no—
285C4⋊C4—5661no—
286C4⋊C4C22×D28311yescharacteristic
287C4⋊C4C22×D28311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—2831no—
290C22⋊C4—2831no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C42—21no—
298C42—2831no—
299C42—5661no—
300C42—5661no—
301C42C22×D28311yescharacteristic
302C23—21no—
303C23—2831no—
304C23—5664no—
305C23—5661no—
306C23—5661no—
307C23—22641no—
308C23—22641no—
309Q8—21no—
310Q8C2×C4×D28312yes—
311D4—21no—
312D4—2832no—
313D4—2832no—
314D4—5664no—
315D4—5664no—
316D4—5661no—
317D4—5661no—
318D4C2×C4×D28312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—2831no—
324C2×C4—2832no—
325C2×C4—2832no—
326C2×C4—2831no—
327C2×C4—2831no—
328C2×C4—5664no—
329C2×C4—5661no—
330C2×C4—5661no—
331C2×C4—22641no—
332C2×C4—22641no—
333C2×C4—22641no—
334C2×C4—22641no—
335C2×C4—22641no—
336C2×C4—22641no—
337C2×C4D4×D28311yescharacteristic
338C2×C4D4×D28311yescharacteristic
339C2×C4C23×D28311yescharacteristic
340C8—21no—
341C8—2832no—
342C8—5661no—
343C8C2×C4×D28312yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—2832no—
348C22—5661no—
349C22—5661no—
350C22—5662no—
351C22—5662no—
352C22—11321no—
353C22—11321no—
354C22—11321no—
355C22—11321no—
356C22—22644no—
357C22C2×D4×D28311yescharacteristic
358C4—21no—
359C4—21no—
360C4—22no—
361C4—41no—
362C4—41no—
363C4—2832no—
364C4—5661no—
365C4—5661no—
366C4—11321no—
367C4—11321no—
368C4C22×C4×D28311yescharacteristic
369C4#41×D28311yescharacteristic
370C2—42no—
371C2—5662no—
372C2—11322no—
373C2—11322no—
374C2C4×D4×D28311yescharacteristic
375C2#3182726911yescharacteristic
376C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
Fitting#440×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583637C2
cosocleC2×C4×C283C24
hypercenter#440D283
hypocenterC283#2946
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #31826947C2semidirect
3. #31826937C2semidirect
4. #31826578C2semidirect
5. #31826574C2semidirect
6. #31826568C2semidirect
7. SD16×Dic283C2semidirect
8. C4×#17985379C2semidirect
9. #31826547C2semidirect
10. C4×#17985377C2semidirect
11. #31826506C2semidirect
12. #31826460C2semidirect
13. #102×D283C2semidirect
14. #31826422C2semidirect
15. #440×C283C2semidirect
18. #22583637C4semidirect
24. Q8×Dic283C22semidirect
27. C4×D1132C22semidirect
31. #22583572C22semidirect
41. #22583543C22semidirect
42. #22583542C22semidirect
43. #22583541C22semidirect
44. #22583534C22semidirect
46. #22583532C22semidirect
49. #22583530C22semidirect
50. #22583520C22semidirect
51. C4×C283⋊C8C22semidirect
52. C8×Dic283C22semidirect
54. C4×Q8×C283C22semidirect
56. #107×C283C22semidirect
57. #103×C283C22semidirect
59. #97×C283C22semidirect
62. #17985393C2×C4semidirect
68. D4×D283C2×C4semidirect
77. #17985379C2×C4semidirect
78. D2264C2×C4semidirect
79. #17985377C2×C4semidirect
80. #17985375C2×C4semidirect
104. SD16×C283C2×C4semidirect
188. C283#2946semidirect
196. #440D283semidirect
215. C4×Q8C2×D283semidirect
234. #107C2×D283semidirect
238. #103C2×D283semidirect
246. #97C2×D283semidirect
270. SD16C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836372
#318269472
#318269372
#318265782
#318265742
#318265682
SD16×Dic2832
C4×#179853792
#318265472
C4×#179853772
#318265062
#318264602
#102×D2832
#318264222
#440×C2832
#2946283