Finite Group Databasebeta

← #49130723

Subgroups — #49130723

Order 36224.

548 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583637C211yesmaximal, characteristic, complemented
2C2×#22583634C211yesmaximal, characteristic, complemented
3#31827014C211yesmaximal, characteristic, complemented
4C4×D4×D283C211yesmaximal, characteristic, complemented
5#31826681C211yesmaximal, characteristic, complemented
6#31826680C211yesmaximal, characteristic, complemented
7#31826677C211yesmaximal, characteristic, complemented
8#31826669C211yesmaximal, characteristic, complemented
9#31826668C211yesmaximal, characteristic, complemented
10#31826659C211yesmaximal, characteristic, complemented
11#31826658C211yesmaximal, characteristic, complemented
12#31826487C211yesmaximal, characteristic, complemented
13#31826465C211yesmaximal, characteristic, complemented
14#31826463C211yesmaximal, characteristic, complemented
15#463×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985391C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19C22×C4×D283—21no—
20#22583637—24no—
21#22583634—24no—
22C2×#17985381C2211yescharacteristic
23C2×#17985380C2211yescharacteristic
24C2×#17985379C2211yescharacteristic
25C2×D2264C2211yescharacteristic
26C2×#17985377C2211yescharacteristic
27C2×#17985377C2211yescharacteristic
28C2×#17985375C2211yescharacteristic
29C2×#17985375C2211yescharacteristic
30#22583608C2211yescharacteristic, complemented
31#22583606C2211yescharacteristic, complemented
32#22583598C2211yescharacteristic, complemented
33#22583583—21no—
34#22583583—21no—
35C4×D1132C2211yescharacteristic
36D4×Dic283C2211yescharacteristic
37#22583572C2211yescharacteristic
38C4×C22⋊D283—21no—
39(C22⋊D283)⋊C4—21no—
40(C22⋊D283)⋊C4—21no—
41(C22⋊D283)⋊C4—21no—
42C4⋊C4×D283C2211yescharacteristic
43C22⋊C4×D283—21no—
44C42×D283C2211yescharacteristic
45C4⋊(C283⋊C8)C2211yescharacteristic, complemented
46Dic283⋊C8C2211yescharacteristic, complemented
47Dic283⋊C8C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583534C2211yescharacteristic, complemented
50#22583533C2211yescharacteristic, complemented
51#22583532C2211yescharacteristic, complemented
52#22583531C2211yescharacteristic, complemented
53#22583530C2211yescharacteristic, complemented
54C2×SD16×C283C2211yescharacteristic
55C2×D8×C283C2211yescharacteristic
56#124×C283C2211yescharacteristic, complemented
57C4×D4×C283C2211yescharacteristic
58C4⋊C8×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62#17985393—22no—
63#17985393—22no—
64#17985391—22no—
65#17985391—22no—
66C2×Dic566C2311yescharacteristic
67C2×D1132—21no—
68C2×D1132C2311yescharacteristic
69C2×D1132C2311yescharacteristic
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72C2×C22⋊D283—21no—
73C2×C22⋊D283—21no—
74D4×D283—22no—
75D4×D283D414yescomplemented
76C22×Dic283—21no—
77C22×Dic283—21no—
78C2×C4×D283—21no—
79C2×C4×D283—21no—
80C2×C4×D283—21no—
81C2×C4×D283—21no—
82C2×C4×D283—44no—
83C2×C4×D283D411yescharacteristic
84C2×C4×D283D411yescharacteristic
85C2×C4×D283C2311yescharacteristic
86#17985381—22no—
87#17985380—22no—
88#17985379—22no—
89D2264—22no—
90#17985377—22no—
91#17985377—22no—
92#17985375—22no—
93#17985375—22no—
94C2×C283⋊C8C2311yescharacteristic
95C2×C283⋊C8C2311yescharacteristic
96C4⋊Dic283C2311yescharacteristic
97Dic283⋊C4—21no—
98Dic283⋊C4—21no—
99Dic283⋊C4—21no—
100C22⋊Dic283—21no—
101(C2×D283)⋊C4—21no—
102(C2×D283)⋊C4—21no—
103(C2×D283)⋊C4—21no—
104(C2×D283)⋊C4—21no—
105C4×Dic283D411yescharacteristic
106C4×Dic283D411yescharacteristic
107C4×Dic283C2311yescharacteristic
108C2×Q8×C283C2311yescharacteristic
109C2×D4×C283C2311yescharacteristic
110C2×D4×C283C2311yescharacteristic
111C22×C4×C283—21no—
112SD16×C283—22no—
113D8×C283—22no—
114C2×C8×C283C2311yescharacteristic
115C2×C8×C283C2311yescharacteristic
116C4⋊C4×C283C2311yescharacteristic
117C22⋊C4×C283—21no—
118C22⋊C4×C283—21no—
119C22⋊C4×C283—21no—
120C42×C283C2311yescharacteristic
121C22×D283—21no—
122C22×D283—24no—
123C22×D283—21no—
124C22×D283—42no—
125C22×D283—42no—
126C22×D283C2×D411yescharacteristic
127Dic566—21no—
128Dic566—21no—
129D1132—21no—
130D1132—21no—
131D1132—21no—
132D1132—42no—
133D1132C2×D412yes—
134C22⋊D283—24no—
135C22⋊D283—42no—
136C22⋊D283—42no—
137C22⋊D283—42no—
138C2×Dic283—21no—
139C2×Dic283—21no—
140C2×Dic283—42no—
141C2×Dic283—42no—
142C2×Dic283C2×D411yescharacteristic
143C2×Dic283C2×D411yescharacteristic
144C2×Dic283C2×D411yescharacteristic
145C4×D283—22no—
146C4×D283—41no—
147C4×D283—42no—
148C4×D283—42no—
149C4×D283—42no—
150C4×D283—42no—
151C4×D283C2×D412yes—
152C4×D283#4112yes—
153C283⋊C8—21no—
154C283⋊C8—21no—
155C23×C283—21no—
156C23×C283—21no—
157Q8×C283—21no—
158Q8×C283—21no—
159D4×C283—21no—
160D4×C283—21no—
161D4×C283—21no—
162D4×C283C2×D412yes—
163C2×C4×C283—21no—
164C2×C4×C283—21no—
165C2×C4×C283—42no—
166C2×C4×C283C2×D411yescharacteristic
167C2×C4×C283C2×D411yescharacteristic
168C2×C4×C283C2411yescharacteristic
169C8×C283—21no—
170C8×C283—21no—
171C22×C283—22no—
172C22×C283—41no—
173C22×C283—41no—
174C22×C283—41no—
175C22×C283—41no—
176C22×C283—41no—
177C22×C283C22×D411yescharacteristic
178C2×D283—21no—
179C2×D283—21no—
180C2×D283—22no—
181C2×D283—48no—
182C2×D283—41no—
183C2×D283—41no—
184C2×D283—41no—
185C2×D283—41no—
186C2×D283—41no—
187C2×D283#12112yes—
188C4×C283—21no—
189C4×C283—21no—
190C4×C283—41no—
191C4×C283—41no—
192C4×C283C22×D411yescharacteristic
193C4×C283C2×#4111yescharacteristic
194Dic283—21no—
195Dic283—41no—
196Dic283—41no—
197Dic283#12112yes—
198Dic283AGL(1,ℤ/8)12yescomplemented
199C2×C283—42no—
200C2×C283—81no—
201C2×C283C2×#12111yescharacteristic
202C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
203C2×C283#57511yescharacteristic
204D283—22no—
205D283—42no—
206D283—81no—
207C283#303611yescharacteristic, complemented, Sylow
208#3036—2831nomaximal, Sylow
209C2×AGL(1,ℤ/8)—2831no—
210C2×AGL(1,ℤ/8)—2831no—
211#532—2831no—
212C2×C4×D4—2831no—
213#463—2831no—
214#463—2831no—
215#463—2831no—
216#463D28311yescharacteristic, complemented
217#461—2831no—
218#461—2831no—
219#459—2831no—
220#459—2831no—
221#423—2831no—
222#417—2831no—
223#417—2831no—
224C2×#41—2831no—
225C2×#41—2831no—
226C22×D4—2831no—
227C23×C4—5661no—
228AGL(1,ℤ/8)—5664no—
229AGL(1,ℤ/8)—5664no—
230C2×SD16—2831no—
231C2×SD16—2831no—
232C2×SD16—2831no—
233C2×SD16C2×D28311yescharacteristic
234C2×D8—2831no—
235C2×D8—2831no—
236C2×D8—2831no—
237C2×D8C2×D28311yescharacteristic
238C2×M16—2831no—
239C2×M16—2831no—
240C4⋊Q8—2831no—
241#127—2831no—
242#124—2831no—
243#124C2×D28311yescharacteristic, complemented
244#121—5661no—
245#121—5661no—
246C4×D4—2831no—
247C4×D4—2831no—
248C4×D4—2831no—
249C4×D4—5661no—
250C4×D4—5661no—
251C4×D4—5661no—
252C4×D4—5661no—
253C4×D4C2×D28311yescharacteristic
254C2×C4⋊C4—2831no—
255C2×C22⋊C4—5661no—
256C2×C42—2831no—
257C4⋊C8—2831no—
258C4⋊C8—2831no—
259C4⋊C8—2831no—
260C4⋊C8C2×D28311yescharacteristic, complemented
261#103—2831no—
262#103—2831no—
263#103—2831no—
264#103C2×D28311yescharacteristic, complemented
265#102—2831no—
266#102—2831no—
267#102—2831no—
268#102C2×D28311yescharacteristic, complemented
269C24—5661no—
270#41—5662no—
271#41—5662no—
272#41—5662no—
273#41—5662no—
274C2×Q8—2831no—
275C2×Q8C22×D28311yescharacteristic
276C2×D4—2834no—
277C2×D4—2831no—
278C2×D4—2831no—
279C2×D4—5661no—
280C2×D4—5662no—
281C2×D4—5661no—
282C2×D4—5661no—
283C2×D4—5661no—
284C2×D4—5661no—
285C2×D4C22×D28311yescharacteristic
286C2×D4C22×D28311yescharacteristic
287C22×C4—21no—
288C22×C4—2831no—
289C22×C4—2831no—
290C22×C4—2831no—
291C22×C4—5661no—
292C22×C4—5661no—
293C22×C4—5661no—
294C22×C4—5661no—
295C22×C4—5661no—
296C22×C4—5661no—
297C22×C4—11324no—
298SD16—22no—
299SD16—5662no—
300SD16—5662no—
301SD16—5662no—
302D8—22no—
303D8—5662no—
304D8—5662no—
305D8—5662no—
306M16—5662no—
307M16—5662no—
308C2×C8—2831no—
309C2×C8—2831no—
310C2×C8C22×D28311yescharacteristic
311C2×C8C22×D28311yescharacteristic
312C4⋊C4—2831no—
313C4⋊C4—5661no—
314C4⋊C4—5661no—
315C4⋊C4—5661no—
316C4⋊C4C22×D28311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—5661no—
321C22⋊C4—5661no—
322C22⋊C4—5661no—
323C22⋊C4—5661no—
324C22⋊C4—5661no—
325C42—2831no—
326C42—2831no—
327C42—2831no—
328C42C22×D28311yescharacteristic
329C23—21no—
330C23—21no—
331C23—2831no—
332C23—5664no—
333C23—5661no—
334C23—5661no—
335C23—11322no—
336C23—11322no—
337Q8—21no—
338Q8—21no—
339Q8—5661no—
340Q8—5661no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—2832no—
345D4—5664no—
346D4—5661no—
347D4—5661no—
348D4—5661no—
349D4—11322no—
350D4—11322no—
351D4—11322no—
352D4—11322no—
353D4D4×D28312yes—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—2831no—
358C2×C4—2831no—
359C2×C4—2832no—
360C2×C4—2832no—
361C2×C4—2831no—
362C2×C4—5662no—
363C2×C4—5661no—
364C2×C4—5661no—
365C2×C4—11321no—
366C2×C4—11322no—
367C2×C4—11322no—
368C2×C4—11322no—
369C2×C4—11322no—
370C2×C4—11322no—
371C2×C4—11322no—
372C2×C4D4×D28311yescharacteristic
373C2×C4D4×D28311yescharacteristic
374C2×C4C23×D28311yescharacteristic
375C8—21no—
376C8—21no—
377C8—5661no—
378C8—5661no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—2832no—
386C22—5661no—
387C22—5661no—
388C22—5662no—
389C22—11328no—
390C22—11321no—
391C22—11321no—
392C22—11321no—
393C22—11321no—
394C22—11321no—
395C22C2×D4×D28311yescharacteristic
396C4—21no—
397C4—21no—
398C4—41no—
399C4—41no—
400C4—2832no—
401C4—2832no—
402C4—5661no—
403C4—11321no—
404C4—11321no—
405C4C2×D4×D28311yescharacteristic
406C4#41×D28311yescharacteristic
407C2—42no—
408C2—81no—
409C2—5662no—
410C2—11322no—
411C2—22641no—
412C2#121×D28311yescharacteristic
413C2AGL(1,ℤ/8)×D28311yescharacteristic
414C2#3182726211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#463×C283C2
socleC22×C283C22×D4
hypercenter#463D283
hypocenterC283#3036
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#22583637C2semidirect
2. C2×#22583634C2semidirect
3. #31827014C2semidirect
4. C4×D4×D283C2semidirect
5. #31826681C2semidirect
6. #31826680C2semidirect
7. #31826677C2semidirect
8. #31826669C2semidirect
9. #31826668C2semidirect
10. #31826659C2semidirect
11. #31826658C2semidirect
12. #31826487C2semidirect
13. #31826465C2semidirect
14. #31826463C2semidirect
15. #463×C283C2semidirect
30. #22583608C22semidirect
31. #22583606C22semidirect
32. #22583598C22semidirect
45. C4⋊(C283⋊C8)C22semidirect
46. Dic283⋊C8C22semidirect
47. Dic283⋊C8C22semidirect
48. #22583535C22semidirect
49. #22583534C22semidirect
50. #22583533C22semidirect
51. #22583532C22semidirect
52. #22583531C22semidirect
53. #22583530C22semidirect
56. #124×C283C22semidirect
58. C4⋊C8×C283C22semidirect
59. #103×C283C22semidirect
60. #102×C283C22semidirect
75. D4×D283D4semidirect
198. Dic283AGL(1,ℤ/8)semidirect
207. C283#3036semidirect
216. #463D283semidirect
243. #124C2×D283semidirect
260. C4⋊C8C2×D283semidirect
264. #103C2×D283semidirect
268. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836372
C2×#225836342
#318270142
C4×D4×D2832
#318266812
#318266802
#318266772
#318266692
#318266682
#318266592
#318266582
#318264872
#318264652
#318264632
#463×C2832
#3036283