Finite Group Databasebeta

← #24919164

Subgroups — #24919164

Order 10624.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D83C211yesmaximal, characteristic, complemented
2#19128358C211yesmaximal, characteristic, complemented
3#19128339C211yesmaximal, characteristic, complemented
4#19128082C211yesmaximal, characteristic, complemented
5#19127930C211yesmaximal, characteristic, complemented
6#19127927C211yesmaximal, characteristic, complemented
7#19127925C211yesmaximal, characteristic, complemented
8#19127914C211yesmaximal, characteristic, complemented
9#19127863C211yesmaximal, characteristic, complemented
10#19127855C211yesmaximal, characteristic, complemented
11#19127846C211yesmaximal, characteristic, complemented
12#19127833C211yesmaximal, characteristic, complemented
13SD16×Dic83C211yesmaximal, characteristic, complemented
14C8×C22⋊D83C211yesmaximal, characteristic, complemented
15C2×#135×C83C211yesmaximal, characteristic, complemented
16C2×Q8×D83C2211yescharacteristic
17C2×D4×D83C2211yescharacteristic
18C2×#13050580C2211yescharacteristic, complemented
19C2×#13050579C2211yescharacteristic
20C2×#13050578C2211yescharacteristic
21C2×#13050577C2211yescharacteristic
22SD16×D83—24no—
23C2×#13050575C2211yescharacteristic
24C2×C8×D83C2211yescharacteristic
25#14581781C2211yescharacteristic
26#14581779—21no—
27#14581779C2211yescharacteristic, complemented
28#14581775—21no—
29#14581771—21no—
30#14581771C2211yescharacteristic, complemented
31#14581768C2211yescharacteristic
32#14581766C2211yescharacteristic
33#14581764—21no—
34#14581763—21no—
35#14581763C2211yescharacteristic
36#14581760—21no—
37Q8×Dic83C2211yescharacteristic, complemented
38D4×Dic83C2211yescharacteristic
39C4×C22⋊D83—21no—
40C4×C22⋊D83C2211yescharacteristic
41C2×(C2×D83)⋊C4—21no—
42#14581724C2211yescharacteristic, complemented
43Dic83⋊C8C2211yescharacteristic, complemented
44#14581717C2211yescharacteristic, complemented
45#14581716C2211yescharacteristic, complemented
46#14581716C2211yescharacteristic, complemented
47#14581714C2211yescharacteristic
48#14581713C2211yescharacteristic
49#14581713C2211yescharacteristic, complemented
50C22⋊(C83⋊C8)C2211yescharacteristic, complemented
51(C2×D83)⋊C8C2211yescharacteristic
52C8×Dic83C2211yescharacteristic, complemented
53C2×#41×C83C2211yescharacteristic
54C2×#41×C83C2211yescharacteristic, complemented
55#135×C83—24no—
56C2×Q16×C83C2211yescharacteristic, complemented
57C2×SD16×C83C2211yescharacteristic
58C2×SD16×C83C2211yescharacteristic, complemented
59C2×D8×C83C2211yescharacteristic
60C22×C8×C83C2211yescharacteristic, complemented
61C23×D83—21no—
62C2×Dic166—21no—
63C2×Dic166C2311yescharacteristic
64Q8×D83—22no—
65Q8×D83—41no—
66C2×D332C2311yescharacteristic
67C2×C22⋊D83—21no—
68C2×C22⋊D83—21no—
69C2×C22⋊D83—21no—
70C2×C22⋊D83D411yescharacteristic
71D4×D83—22no—
72D4×D83—41no—
73C22×Dic83—21no—
74C2×C4×D83—21no—
75C2×C4×D83C2311yescharacteristic
76#13050580—41no—
77#13050579—22no—
78#13050578—22no—
79#13050577—22no—
80#13050575—41no—
81C2×C83⋊C8C2311yescharacteristic
82C2×C83⋊C8C2311yescharacteristic
83C8×D83—22no—
84C4⋊Dic83—21no—
85C4⋊Dic83C2311yescharacteristic
86C4⋊Dic83C2311yescharacteristic
87Dic83⋊C4—21no—
88Dic83⋊C4—21no—
89Dic83⋊C4D411yescharacteristic
90C22⋊Dic83—21no—
91C22⋊Dic83—21no—
92C22⋊Dic83—21no—
93C22⋊Dic83—21no—
94C22⋊Dic83—21no—
95C22⋊Dic83D411yescharacteristic
96(C2×D83)⋊C4—21no—
97(C2×D83)⋊C4—21no—
98(C2×D83)⋊C4—21no—
99(C2×D83)⋊C4—21no—
100(C2×D83)⋊C4D411yescharacteristic
101C4×Dic83—21no—
102C4×Dic83C2311yescharacteristic
103#41×C83—22no—
104#41×C83—22no—
105#41×C83—41no—
106#41×C83—41no—
107C2×Q8×C83C2311yescharacteristic
108C2×Q8×C83C2311yescharacteristic
109C2×D4×C83—21no—
110C2×D4×C83—21no—
111C2×D4×C83C2311yescharacteristic
112C2×D4×C83C2311yescharacteristic
113C22×C4×C83—21no—
114C22×C4×C83—21no—
115C22×C4×C83C2311yescharacteristic
116Q16×C83—22no—
117SD16×C83—22no—
118SD16×C83D414yescomplemented
119D8×C83—22no—
120C2×C8×C83—22no—
121C2×C8×C83C2311yescharacteristic
122C2×C8×C83C2311yescharacteristic
123C23×C83—21no—
124C23×C83—21no—
125C23×C83C2×D411yescharacteristic
126C22×D83—21no—
127C22×D83—42no—
128C22×D83—42no—
129C22×D83—81no—
130C22×D83C2×D411yescharacteristic
131Q8×C83—21no—
132Q8×C83—21no—
133Q8×C83—21no—
134Q8×C83C2×D412yes—
135D4×C83—21no—
136D4×C83—21no—
137D4×C83—21no—
138D4×C83—42no—
139D4×C83—42no—
140D4×C83C2×D412yes—
141C2×C4×C83—21no—
142C2×C4×C83—21no—
143C2×C4×C83—21no—
144C2×C4×C83—21no—
145C2×C4×C83—42no—
146C2×C4×C83—42no—
147C2×C4×C83C2×D411yescharacteristic
148C2×C4×C83C2411yescharacteristic
149C22⋊D83—22no—
150C22⋊D83—42no—
151C22⋊D83—42no—
152C22⋊D83—81no—
153C2×Dic83—21no—
154C2×Dic83—21no—
155C2×Dic83—21no—
156C2×Dic83—81no—
157C2×Dic83C2×D411yescharacteristic
158C2×Dic83C2×D411yescharacteristic
159C2×Dic83C2×D411yescharacteristic
160D332—21no—
161D332—21no—
162C4×D83—21no—
163C4×D83—21no—
164C4×D83—42no—
165Dic166—21no—
166Dic166—21no—
167Dic166—42no—
168C8×C83—21no—
169C8×C83C2×D412yes—
170C83⋊C8—21no—
171C83⋊C8—21no—
172C22×C83—22no—
173C22×C83—21no—
174C22×C83—21no—
175C22×C83—21no—
176C22×C83—41no—
177C22×C83—41no—
178C22×C83—41no—
179C22×C83—41no—
180C22×C83—41no—
181C22×C83C22×D411yescharacteristic
182C2×D83—21no—
183C2×D83—21no—
184C2×D83—41no—
185C2×D83—41no—
186C2×D83—41no—
187C2×D83—84no—
188C2×D83#13512yescomplemented
189C4×C83—22no—
190C4×C83—21no—
191C4×C83—41no—
192C4×C83C22×D411yescharacteristic
193C4×C83H(5,𝔽2)11yescharacteristic
194Dic83—21no—
195Dic83—21no—
196Dic83—21no—
197Dic83—41no—
198Dic83—41no—
199Dic83—41no—
200C2×C83—42no—
201C2×C83—41no—
202C2×C83—81no—
203C2×C83D4211yescharacteristic
204C2×C83C2×#13511yescharacteristic
205C2×C83#57711yescharacteristic
206D83—22no—
207D83—81no—
208#3282—831nomaximal, Sylow
209C83#328211yescharacteristic, complemented, Sylow
210C2×#135D8311yescharacteristic, complemented
211C22×SD16—831no—
212#548—831no—
213#546—831no—
214#495—831no—
215#465—831no—
216#465—831no—
217#464—831no—
218#463—831no—
219#452—831no—
220#451—831no—
221#449—831no—
222#447—831no—
223C4×SD16—831no—
224C8×D4—831no—
225C2×#41C2×D8311yescharacteristic
226C2×#41C2×D8311yescharacteristic, complemented
227C22×Q8—831no—
228C22×D4—831no—
229#135—24no—
230C2×Q16—831no—
231C2×Q16C2×D8311yescharacteristic, complemented
232C2×SD16—831no—
233C2×SD16—831no—
234C2×SD16—831no—
235C2×SD16—1664no—
236C2×SD16C2×D8311yescharacteristic
237C2×SD16C2×D8311yescharacteristic, complemented
238C2×D8—831no—
239C2×D8C2×D8311yescharacteristic
240C22×C8—831no—
241C22×C8C2×D8311yescharacteristic, complemented
242#124—831no—
243#124—831no—
244#124—1661no—
245#123—1661no—
246C22⋊Q8—831no—
247C22⋊Q8—831no—
248C22⋊Q8—1661no—
249#121—831no—
250#121—831no—
251#121—1661no—
252#121—1661no—
253#120—1661no—
254C4×Q8—831no—
255C4×D4—831no—
256C4×D4—831no—
257C4×D4—1661no—
258C2×C22⋊C4—1661no—
259#106—831no—
260C4⋊C8—831no—
261#103—831no—
262#103—831no—
263#103—831no—
264#102—831no—
265#102—831no—
266#102—831no—
267C22⋊C8—831no—
268C22⋊C8—831no—
269C4×C8—831no—
270C24—1661no—
271#41—22no—
272#41—22no—
273#41—41no—
274#41—41no—
275C2×Q8—3321no—
276C2×Q8—831no—
277C2×Q8—1661no—
278C2×Q8—1662no—
279C2×Q8C22×D8311yescharacteristic
280C2×Q8C22×D8311yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—3321no—
284C2×D4—831no—
285C2×D4—831no—
286C2×D4—1661no—
287C2×D4—1661no—
288C2×D4—1662no—
289C2×D4—1661no—
290C2×D4C22×D8311yescharacteristic
291C2×D4C22×D8311yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—831no—
295C22×C4—1661no—
296C22×C4—1661no—
297C22×C4C22×D8311yescharacteristic
298Q16—22no—
299Q16—3321no—
300SD16—22no—
301SD16—1662no—
302SD16—1662no—
303SD16—1662no—
304SD16C22⋊D8314yescomplemented
305D8—22no—
306D8—3321no—
307C2×C8—22no—
308C2×C8—831no—
309C2×C8—831no—
310C2×C8—1662no—
311C2×C8C22×D8311yescharacteristic
312C2×C8C22×D8311yescharacteristic
313C4⋊C4—831no—
314C4⋊C4—831no—
315C4⋊C4—831no—
316C4⋊C4—1661no—
317C4⋊C4—1661no—
318C4⋊C4—1661no—
319C22⋊C4—831no—
320C22⋊C4—831no—
321C22⋊C4—1661no—
322C22⋊C4—1661no—
323C22⋊C4—1661no—
324C22⋊C4—1661no—
325C22⋊C4—1661no—
326C22⋊C4—1661no—
327C22⋊C4—1661no—
328C22⋊C4—1661no—
329C22⋊C4—1661no—
330C42—831no—
331C42—1661no—
332C23—21no—
333C23—21no—
334C23—3322no—
335C23—3322no—
336C23—831no—
337C23—6641no—
338C23—1661no—
339C23D4×D8311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—3322no—
344Q8—1661no—
345Q8—1661no—
346Q8C2×C22⋊D8312yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—42no—
352D4—3322no—
353D4—3322no—
354D4—6641no—
355D4—1662no—
356D4—1661no—
357D4—1661no—
358D4C2×C22⋊D8312yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—3322no—
366C2×C4—831no—
367C2×C4—831no—
368C2×C4—831no—
369C2×C4—6641no—
370C2×C4—1661no—
371C2×C4—1661no—
372C2×C4—1661no—
373C2×C4—1661no—
374C2×C4—1661no—
375C2×C4D4×D8311yescharacteristic
376C2×C4C23×D8311yescharacteristic
377C8—21no—
378C8—1661no—
379C8—1661no—
380C8C2×C22⋊D8312yes—
381C22—21no—
382C22—22no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—3321no—
391C22—3321no—
392C22—3321no—
393C22—832no—
394C22—6644no—
395C22—1661no—
396C22—1661no—
397C22C2×D4×D8311yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—3321no—
402C4—3321no—
403C4—3321no—
404C4—1661no—
405C4—1661no—
406C4—1661no—
407C4C22×C22⋊D8311yescharacteristic
408C4#1458183711yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—6641no—
413C2—1662no—
414C2D4×C22⋊D8311yescharacteristic
415C2#135×D8311yescharacteristic
416C2#1912850811yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC2×#135×C83C2
socleC22×C83C22×D4
hypercenterC2×#135D83
hypocenterC83#3282
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D83C2semidirect
2. #19128358C2semidirect
3. #19128339C2semidirect
4. #19128082C2semidirect
5. #19127930C2semidirect
6. #19127927C2semidirect
7. #19127925C2semidirect
8. #19127914C2semidirect
9. #19127863C2semidirect
10. #19127855C2semidirect
11. #19127846C2semidirect
12. #19127833C2semidirect
13. SD16×Dic83C2semidirect
14. C8×C22⋊D83C2semidirect
15. C2×#135×C83C2semidirect
18. C2×#13050580C22semidirect
27. #14581779C22semidirect
30. #14581771C22semidirect
37. Q8×Dic83C22semidirect
42. #14581724C22semidirect
43. Dic83⋊C8C22semidirect
44. #14581717C22semidirect
45. #14581716C22semidirect
46. #14581716C22semidirect
49. #14581713C22semidirect
50. C22⋊(C83⋊C8)C22semidirect
52. C8×Dic83C22semidirect
54. C2×#41×C83C22semidirect
56. C2×Q16×C83C22semidirect
58. C2×SD16×C83C22semidirect
60. C22×C8×C83C22semidirect
118. SD16×C83D4semidirect
188. C2×D83#135semidirect
209. C83#3282semidirect
210. C2×#135D83semidirect
226. C2×#41C2×D83semidirect
231. C2×Q16C2×D83semidirect
237. C2×SD16C2×D83semidirect
241. C22×C8C2×D83semidirect
304. SD16C22⋊D83semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D832
#191283582
#191283392
#191280822
#191279302
#191279272
#191279252
#191279142
#191278632
#191278552
#191278462
#191278332
SD16×Dic832
C8×C22⋊D832
C2×#135×C832
#328283