Finite Group Databasebeta

← #49130768

Subgroups — #49130768

Order 36224.

494 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583637C211yesmaximal, characteristic
2C2×SD16×D283C211yesmaximal, characteristic, complemented
3#31827040C211yesmaximal, characteristic, complemented
4#31826937C211yesmaximal, characteristic, complemented
5#31826683C211yesmaximal, characteristic, complemented
6#31826682C211yesmaximal, characteristic, complemented
7#31826681C211yesmaximal, characteristic, complemented
8#31826680C211yesmaximal, characteristic, complemented
9#31826669C211yesmaximal, characteristic, complemented
10#31826668C211yesmaximal, characteristic, complemented
11#31826667C211yesmaximal, characteristic, complemented
12#31826490C211yesmaximal, characteristic, complemented
13#31826472C211yesmaximal, characteristic, complemented
14#31826460C211yesmaximal, characteristic, complemented
15#461×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19#22583637—24no—
20C2×#17985381C2211yescharacteristic
21C2×#17985380C2211yescharacteristic
22C2×#17985379C2211yescharacteristic
23C2×#17985379C2211yescharacteristic
24SD16×D283—24no—
25C2×D2264C2211yescharacteristic
26C2×#17985377C2211yescharacteristic
27C2×#17985375C2211yescharacteristic
28C2×C8×D283C2211yescharacteristic
29#22583608C2211yescharacteristic, complemented
30#22583599C2211yescharacteristic, complemented
31#22583598C2211yescharacteristic, complemented
32#22583595—21no—
33#22583595—21no—
34#22583588—21no—
35#22583588—21no—
36C4×D1132C2211yescharacteristic
37D4×Dic283C2211yescharacteristic
38#22583572C2211yescharacteristic
39C4×C22⋊D283—21no—
40(C22⋊D283)⋊C4—21no—
41#22583568C2211yescharacteristic
42#22583567C2211yescharacteristic
43C2×(C2×D283)⋊C4—21no—
44C22⋊C4×D283—21no—
45C4⋊(C283⋊C8)C2211yescharacteristic, complemented
46Dic283⋊C8C2211yescharacteristic, complemented
47Dic283⋊C8C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583534C2211yescharacteristic, complemented
50#22583534C2211yescharacteristic, complemented
51#22583533C2211yescharacteristic, complemented
52#22583532C2211yescharacteristic, complemented
53#22583530C2211yescharacteristic, complemented
54C2×SD16×C283C2211yescharacteristic
55C2×SD16×C283C2211yescharacteristic
56C4⋊Q8×C283C2211yescharacteristic, complemented
57C4×D4×C283C2211yescharacteristic
58C4⋊C8×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60#103×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62#17985393—22no—
63#17985393—22no—
64C2×Dic566—21no—
65C2×Dic566C2311yescharacteristic
66Q8×D283—22no—
67Q8×D283—22no—
68C2×D1132—21no—
69C2×D1132C2311yescharacteristic
70C2×D1132C2311yescharacteristic
71C2×C22⋊D283—21no—
72D4×D283—22no—
73D4×D283D414yes—
74C22×Dic283—21no—
75C2×C4×D283—21no—
76C2×C4×D283—21no—
77C2×C4×D283—21no—
78C2×C4×D283—21no—
79C2×C4×D283C2311yescharacteristic
80#17985381—22no—
81#17985380—22no—
82#17985379—22no—
83#17985379—22no—
84D2264—22no—
85#17985377—22no—
86#17985375—22no—
87C2×C283⋊C8C2311yescharacteristic
88C2×C283⋊C8C2311yescharacteristic
89C8×D283—22no—
90C4⋊Dic283C2311yescharacteristic
91Dic283⋊C4—21no—
92Dic283⋊C4—21no—
93Dic283⋊C4D411yescharacteristic
94Dic283⋊C4D411yescharacteristic
95C22⋊Dic283—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4—21no—
98(C2×D283)⋊C4—21no—
99(C2×D283)⋊C4—21no—
100(C2×D283)⋊C4—21no—
101(C2×D283)⋊C4—21no—
102(C2×D283)⋊C4—21no—
103(C2×D283)⋊C4D411yescharacteristic
104(C2×D283)⋊C4D411yescharacteristic
105C4×Dic283—21no—
106C4×Dic283C2311yescharacteristic
107C2×Q8×C283C2311yescharacteristic
108C2×Q8×C283C2311yescharacteristic
109C2×D4×C283C2311yescharacteristic
110C22×C4×C283—21no—
111SD16×C283—22no—
112SD16×C283—22no—
113C2×C8×C283C2311yescharacteristic
114C2×C8×C283C2311yescharacteristic
115C4⋊C4×C283—21no—
116C4⋊C4×C283—21no—
117C4⋊C4×C283C2311yescharacteristic
118C22⋊C4×C283—21no—
119C42×C283C2311yescharacteristic
120C22×D283—21no—
121C22×D283—24no—
122C22×D283—21no—
123C22×D283—81no—
124C22×D283—81no—
125C22×D283C2×D411yescharacteristic
126Dic566—21no—
127Dic566—21no—
128Dic566—42no—
129D1132—21no—
130D1132—21no—
131D1132—21no—
132D1132—42no—
133D1132C2×D412yes—
134C22⋊D283—24no—
135C2×Dic283—21no—
136C2×Dic283—21no—
137C2×Dic283—81no—
138C2×Dic283C2×D411yescharacteristic
139C2×Dic283C2×D411yescharacteristic
140C2×Dic283C2×D411yescharacteristic
141C4×D283—42no—
142C4×D283—42no—
143C4×D283—81no—
144C4×D283—81no—
145C4×D283C2×D412yes—
146C4×D283#4112yes—
147C283⋊C8—21no—
148C283⋊C8—21no—
149C23×C283—21no—
150Q8×C283—21no—
151Q8×C283—21no—
152Q8×C283—21no—
153Q8×C283—21no—
154D4×C283—21no—
155D4×C283C2×D412yes—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283—81no—
160C2×C4×C283C2×D411yescharacteristic
161C2×C4×C283C2×D411yescharacteristic
162C2×C4×C283C2411yescharacteristic
163C8×C283—21no—
164C8×C283—21no—
165C22×C283—22no—
166C22×C283—41no—
167C22×C283—41no—
168C22×C283C22×D411yescharacteristic
169C2×D283—21no—
170C2×D283—21no—
171C2×D283—22no—
172C2×D283—41no—
173C2×D283—41no—
174C2×D283—41no—
175C2×D283—41no—
176C2×D283—41no—
177C2×D283—84no—
178C2×D283#12112yes—
179C4×C283—21no—
180C4×C283—21no—
181C4×C283—41no—
182C4×C283—41no—
183C4×C283—41no—
184C4×C283C22×D411yescharacteristic
185C4×C283C2×#4111yescharacteristic
186Dic283—21no—
187Dic283—21no—
188Dic283—41no—
189Dic283—41no—
190Dic283#12112yes—
191C2×C283—42no—
192C2×C283C2×#12111yescharacteristic
193C2×C283#57711yescharacteristic
194C2×C283#57711yescharacteristic
195D283—22no—
196D283—42no—
197D283—81no—
198C283#304211yescharacteristic, complemented, Sylow
199#3042—2831nomaximal, Sylow
200C2×AGL(1,ℤ/8)—2831no—
201C22×SD16—2831no—
202#536—2831no—
203#518—2831no—
204#463—2831no—
205#463—2831no—
206#463—2831no—
207#463—2831no—
208#461—2831no—
209#461—2831no—
210#461—2831no—
211#461D28311yescharacteristic, complemented
212#424—2831no—
213#419—2831no—
214#416—2831no—
215C2×#41—2831no—
216C22×Q8—2831no—
217C22×D4—2831no—
218AGL(1,ℤ/8)—5664no—
219C2×SD16—2831no—
220C2×SD16—2831no—
221C2×SD16—2831no—
222C2×SD16—2831no—
223C2×SD16—5664no—
224C2×SD16C2×D28311yescharacteristic
225C2×SD16C2×D28311yescharacteristic
226C2×D8—2831no—
227C2×D8—2831no—
228C2×M16—2831no—
229C22×C8—2831no—
230C4⋊Q8—2831no—
231C4⋊Q8C2×D28311yescharacteristic, complemented
232#124—2831no—
233#124—2831no—
234#123—5661no—
235#123—5661no—
236C22⋊Q8—5661no—
237C22⋊Q8—5661no—
238C4×D4—2831no—
239C4×D4—2831no—
240C4×D4—2831no—
241C4×D4—5661no—
242C4×D4—5661no—
243C4×D4C2×D28311yescharacteristic
244#117—2831no—
245#117—2831no—
246C2×C22⋊C4—5661no—
247C2×C22⋊C4—5661no—
248C4⋊C8—2831no—
249C4⋊C8—2831no—
250C4⋊C8—2831no—
251C4⋊C8C2×D28311yescharacteristic, complemented
252#103—2831no—
253#103—2831no—
254#103—2831no—
255#103—2831no—
256#103C2×D28311yescharacteristic, complemented
257#103C2×D28311yescharacteristic, complemented
258#102—2831no—
259#102—2831no—
260C24—5661no—
261#41—5662no—
262#41—5662no—
263C2×Q8—2831no—
264C2×Q8—5661no—
265C2×Q8—5662no—
266C2×Q8—5662no—
267C2×Q8C22×D28311yescharacteristic
268C2×Q8C22×D28311yescharacteristic
269C2×D4—2834no—
270C2×D4—2831no—
271C2×D4—2831no—
272C2×D4—5661no—
273C2×D4—5662no—
274C2×D4—5661no—
275C2×D4C22×D28311yescharacteristic
276C22×C4—21no—
277C22×C4—2831no—
278C22×C4—5661no—
279C22×C4—5661no—
280C22×C4—5661no—
281C22×C4—5661no—
282C22×C4—5661no—
283SD16—22no—
284SD16—22no—
285SD16—5662no—
286SD16—5662no—
287SD16—5662no—
288SD16—5662no—
289D8—5662no—
290D8—5662no—
291M16—5662no—
292C2×C8—2831no—
293C2×C8—2831no—
294C2×C8—5662no—
295C2×C8C22×D28311yescharacteristic
296C2×C8C22×D28311yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—2831no—
300C4⋊C4—2831no—
301C4⋊C4—2831no—
302C4⋊C4—5661no—
303C4⋊C4—5661no—
304C4⋊C4C22×D28311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—2831no—
307C22⋊C4—2831no—
308C22⋊C4—5661no—
309C22⋊C4—5661no—
310C22⋊C4—5661no—
311C22⋊C4—5661no—
312C22⋊C4—5661no—
313C22⋊C4—5661no—
314C22⋊C4—5661no—
315C22⋊C4—5661no—
316C42—2831no—
317C42—5661no—
318C42C22×D28311yescharacteristic
319C23—21no—
320C23—2831no—
321C23—5664no—
322C23—5661no—
323C23—5661no—
324C23—22641no—
325C23—22641no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—21no—
330Q8—5661no—
331Q8—5661no—
332Q8—11322no—
333D4—21no—
334D4—2832no—
335D4—5664no—
336D4—5661no—
337D4—5661no—
338D4—5661no—
339D4—11322no—
340D4D4×D28312yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—2831no—
346C2×C4—2832no—
347C2×C4—2832no—
348C2×C4—2831no—
349C2×C4—2831no—
350C2×C4—5661no—
351C2×C4—5661no—
352C2×C4—11322no—
353C2×C4—11322no—
354C2×C4—22641no—
355C2×C4—22641no—
356C2×C4—22641no—
357C2×C4D4×D28311yescharacteristic
358C2×C4D4×D28311yescharacteristic
359C2×C4C23×D28311yescharacteristic
360C8—21no—
361C8—21no—
362C8—5661no—
363C8—5661no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—2832no—
368C22—5661no—
369C22—5661no—
370C22—5662no—
371C22—11321no—
372C22—11321no—
373C22—11321no—
374C22—11321no—
375C22—11321no—
376C22—22644no—
377C22C2×D4×D28311yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—2832no—
384C4—5661no—
385C4—5661no—
386C4—11321no—
387C4—11321no—
388C4C2×D4×D28311yescharacteristic
389C4#41×D28311yescharacteristic
390C2—42no—
391C2—5662no—
392C2—11322no—
393C2—22641no—
394C2#121×D28311yescharacteristic
395C2#3182727111yescharacteristic
396C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#461×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583637C2
hypercenter#461D283
hypocenterC283#3042
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. C2×SD16×D283C2semidirect
3. #31827040C2semidirect
4. #31826937C2semidirect
5. #31826683C2semidirect
6. #31826682C2semidirect
7. #31826681C2semidirect
8. #31826680C2semidirect
9. #31826669C2semidirect
10. #31826668C2semidirect
11. #31826667C2semidirect
12. #31826490C2semidirect
13. #31826472C2semidirect
14. #31826460C2semidirect
15. #461×C283C2semidirect
29. #22583608C22semidirect
30. #22583599C22semidirect
31. #22583598C22semidirect
45. C4⋊(C283⋊C8)C22semidirect
46. Dic283⋊C8C22semidirect
47. Dic283⋊C8C22semidirect
48. #22583535C22semidirect
49. #22583534C22semidirect
50. #22583534C22semidirect
51. #22583533C22semidirect
52. #22583532C22semidirect
53. #22583530C22semidirect
56. C4⋊Q8×C283C22semidirect
58. C4⋊C8×C283C22semidirect
59. #103×C283C22semidirect
60. #103×C283C22semidirect
198. C283#3042semidirect
211. #461D283semidirect
231. C4⋊Q8C2×D283semidirect
251. C4⋊C8C2×D283semidirect
256. #103C2×D283semidirect
257. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836372
C2×SD16×D2832
#318270402
#318269372
#318266832
#318266822
#318266812
#318266802
#318266692
#318266682
#318266672
#318264902
#318264722
#318264602
#461×C2832
#3042283