Finite Group Databasebeta

← #49130139

Subgroups — #49130139

Order 36224.

484 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
1C2×#22583631C211yesmaximal, characteristic
2#31826947C211yesmaximal, characteristic, complemented
3#31826944C211yesmaximal, characteristic, complemented
4#31826575C211yesmaximal, characteristic, complemented
5#31826574C211yesmaximal, characteristic, complemented
6#31826570C211yesmaximal, characteristic, complemented
7#31826569C211yesmaximal, characteristic, complemented
8C4×#17985381C211yesmaximal, characteristic, complemented
9SD16×Dic283C211yesmaximal, characteristic, complemented
10#31826552C211yesmaximal, characteristic, complemented
11#106×D283C211yesmaximal, characteristic, complemented
12#31826465C211yesmaximal, characteristic, complemented
13#31826463C211yesmaximal, characteristic, complemented
14#31826419C211yesmaximal, characteristic, complemented
15C4×SD16×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985391C2211yescharacteristic
18#22583631C418yescomplemented
19C2×#17985382C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21C2×#17985377C2211yescharacteristic
22C2×#17985375C2211yescharacteristic
23C2×C8×D283C2211yescharacteristic
24Q8×Dic283C2211yescharacteristic
25C4×Dic566C2211yescharacteristic
26#22583575C2211yescharacteristic
27C4×D1132—21no—
28C4×D1132C2211yescharacteristic
29D4×Dic283C2211yescharacteristic
30#22583572—21no—
31#22583572C2211yescharacteristic
32C4×C22⋊D283—21no—
33(C22⋊D283)⋊C4—21no—
34#22583567—21no—
35#22583567C2211yescharacteristic
36#22583566—21no—
37C2×Dic283⋊C4—21no—
38C4⋊C4×D283—21no—
39C4⋊C4×D283C2211yescharacteristic
40C4⋊C4×D283C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583541C2211yescharacteristic
43#22583541C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583530C2211yescharacteristic
50#22583521C2211yescharacteristic
51#22583520C2211yescharacteristic
52C8×Dic283C2211yescharacteristic
53C2×SD16×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55C4×D4×C283C2211yescharacteristic
56#106×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C4×C8×C283C2211yescharacteristic
60#17985393—22no—
61#17985393C2×C414yescomplemented
62#17985391—22no—
63#17985391C2×C414yescomplemented
64C2×Dic566C2311yescharacteristic
65C2×D1132—21no—
66C2×D1132C2311yescharacteristic
67C2×C22⋊D283—21no—
68C22×Dic283—21no—
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×D283C2311yescharacteristic
76#17985382C2×C414yescomplemented
77#17985381C2×C414yescomplemented
78#17985377C2×C414yescomplemented
79#17985375—22no—
80C2×C283⋊C8C2311yescharacteristic
81C2×C283⋊C8C2311yescharacteristic
82C8×D283C2×C414yescomplemented
83C4⋊Dic283—21no—
84C4⋊Dic283C2311yescharacteristic
85C4⋊Dic283C2311yescharacteristic
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90Dic283⋊C4D411yescharacteristic
91Dic283⋊C4D411yescharacteristic
92C22⋊Dic283—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4D411yescharacteristic
96(C2×D283)⋊C4D411yescharacteristic
97C4×Dic283—21no—
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×D283C2×D411yescharacteristic
115Dic566—21no—
116Dic566C22×C412yes—
117D1132—24no—
118D1132—21no—
119D1132C22×C412yes—
120C22⋊D283—24no—
121C2×Dic283—21no—
122C2×Dic283—24no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—81no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C4×D283—24no—
130C4×D283—81no—
131C4×D283—81no—
132C4×D283—81no—
133C4×D283—81no—
134C4×D283C22×C412yes—
135C4×D283#4112yes—
136C283⋊C8—21no—
137C283⋊C8C22×C412yes—
138C23×C283—21no—
139Q8×C283—21no—
140Q8×C283C22×C412yes—
141D4×C283—21no—
142D4×C283C22×C412yes—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—81no—
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283C22×C412yes—
152C22×C283—22no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283C22×D411yescharacteristic
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—22no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283C4×D412yes—
162C4×C283—22no—
163C4×C283—21no—
164C4×C283—21no—
165C4×C283—41no—
166C4×C283—41no—
167C4×C283C23×C411yescharacteristic
168C4×C283C2×#4111yescharacteristic
169Dic283—22no—
170Dic283—21no—
171Dic283—21no—
172Dic283—41no—
173Dic283—41no—
174Dic283C4×D412yes—
175C2×C283—42no—
176C2×C283C2×C4×D411yescharacteristic
177C2×C283#57711yescharacteristic
178C2×C283#57711yescharacteristic
179D283—22no—
180D283—42no—
181C283#295211yescharacteristic, complemented, Sylow
182#2952—2831nomaximal, Sylow
183C2×#135—2831no—
184#520—2831no—
185#520—2831no—
186#442—2831no—
187#442—2831no—
188#441—2831no—
189#441—2831no—
190C4×SD16—2831no—
191C4×SD16—2831no—
192C4×SD16—2831no—
193C4×SD16D28311yescharacteristic, complemented
194C2×#106—2831no—
195#417—2831no—
196#417—2831no—
197#405—2831no—
198C2×#41—2831no—
199C2×#41—2831no—
200#135—2838no—
201C2×Q16—2831no—
202C2×SD16—2831no—
203C2×SD16C2×D28311yescharacteristic
204C2×D8—2831no—
205C2×M16—2831no—
206C22×C8—2831no—
207C4×Q8—2831no—
208C4×Q8—2831no—
209C4×Q8—2831no—
210C4×Q8C2×D28311yescharacteristic
211C4×D4—2831no—
212C4×D4—2831no—
213C4×D4—2831no—
214C4×D4—5661no—
215C4×D4—5661no—
216C4×D4—5661no—
217C4×D4—5661no—
218C4×D4C2×D28311yescharacteristic
219#117—2831no—
220#117—5661no—
221#117—5661no—
222C2×C4⋊C4—2831no—
223C2×C4⋊C4—2831no—
224C2×C4⋊C4—5661no—
225C2×C4⋊C4—5661no—
226#106—2831no—
227#106—2831no—
228#106—2831no—
229#106C2×D28311yescharacteristic
230#103—2831no—
231#103—2831no—
232#103—2831no—
233#103C2×D28311yescharacteristic
234#102—2831no—
235#102—2831no—
236#102—2831no—
237#102C2×D28311yescharacteristic
238#97—2831no—
239#97—2831no—
240C4×C8—2831no—
241C4×C8C2×D28311yescharacteristic
242#41—2834no—
243#41—2834no—
244#41—5662no—
245#41—5662no—
246C2×Q8—2831no—
247C2×Q8C22×D28311yescharacteristic
248C2×D4—2831no—
249C2×D4—5661no—
250C2×D4—5661no—
251C2×D4C22×D28311yescharacteristic
252C22×C4—21no—
253C22×C4—2831no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4—5661no—
258C22×C4—5661no—
259C22×C4—5661no—
260C22×C4—5661no—
261Q16—2834no—
262SD16—2834no—
263SD16C4×D28314yescomplemented
264D8—2834no—
265M16—5662no—
266C2×C8—2831no—
267C2×C8—2834no—
268C2×C8—2831no—
269C2×C8C22×D28311yescharacteristic
270C2×C8C22×D28311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—2831no—
273C4⋊C4—2831no—
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4C22×D28311yescharacteristic
282C4⋊C4C22×D28311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—2831no—
285C22⋊C4—2831no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C42—21no—
290C42—2831no—
291C42—5661no—
292C42—5661no—
293C42—5661no—
294C42C22×D28311yescharacteristic
295C23—21no—
296C23—2831no—
297C23—5661no—
298Q8—21no—
299Q8—2832no—
300Q8—5661no—
301Q8C2×C4×D28312yes—
302D4—21no—
303D4—2832no—
304D4—5664no—
305D4—5664no—
306D4—5661no—
307D4C2×C4×D28312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—2831no—
313C2×C4—2832no—
314C2×C4—2832no—
315C2×C4—2831no—
316C2×C4—2831no—
317C2×C4—5664no—
318C2×C4—5664no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—22641no—
323C2×C4—22641no—
324C2×C4—22641no—
325C2×C4—22641no—
326C2×C4—22641no—
327C2×C4D4×D28311yescharacteristic
328C2×C4D4×D28311yescharacteristic
329C2×C4C23×D28311yescharacteristic
330C8—21no—
331C8—2832no—
332C8—5661no—
333C8C2×C4×D28312yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—2832no—
338C22—5661no—
339C22—5661no—
340C22—5662no—
341C22—11321no—
342C22—11321no—
343C22C2×D4×D28311yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—2832no—
350C4—5661no—
351C4—5661no—
352C4—5662no—
353C4—11321no—
354C4—11321no—
355C4C22×C4×D28311yescharacteristic
356C4#41×D28311yescharacteristic
357C2—42no—
358C2—5662no—
359C2—11322no—
360C2C4×D4×D28311yescharacteristic
361C2#3182727111yescharacteristic
362C2#3182727211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
FittingC4×SD16×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583631C2
cosocleC2×C4×C283C24
hypercenterC4×SD16D283
hypocenterC283#2952
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #31826947C2semidirect
3. #31826944C2semidirect
4. #31826575C2semidirect
5. #31826574C2semidirect
6. #31826570C2semidirect
7. #31826569C2semidirect
8. C4×#17985381C2semidirect
9. SD16×Dic283C2semidirect
10. #31826552C2semidirect
11. #106×D283C2semidirect
12. #31826465C2semidirect
13. #31826463C2semidirect
14. #31826419C2semidirect
15. C4×SD16×C283C2semidirect
18. #22583631C4semidirect
61. #17985393C2×C4semidirect
63. #17985391C2×C4semidirect
76. #17985382C2×C4semidirect
77. #17985381C2×C4semidirect
78. #17985377C2×C4semidirect
82. C8×D283C2×C4semidirect
104. SD16×C283C2×C4semidirect
181. C283#2952semidirect
193. C4×SD16D283semidirect
263. SD16C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836312
#318269472
#318269442
#318265752
#318265742
#318265702
#318265692
C4×#179853812
SD16×Dic2832
#318265522
#106×D2832
#318264652
#318264632
#318264192
C4×SD16×C2832
#2952283