Finite Group Databasebeta

← #24919170

Subgroups — #24919170

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×#14581813C211yesmaximal, characteristic, complemented
2#19128362C211yesmaximal, characteristic, complemented
3#19128345C211yesmaximal, characteristic, complemented
4#19128082C211yesmaximal, characteristic, complemented
5#19127930C211yesmaximal, characteristic, complemented
6#19127927C211yesmaximal, characteristic, complemented
7#19127921C211yesmaximal, characteristic, complemented
8#19127918C211yesmaximal, characteristic, complemented
9#19127860C211yesmaximal, characteristic, complemented
10#19127857C211yesmaximal, characteristic, complemented
11#19127845C211yesmaximal, characteristic, complemented
12#19127835C211yesmaximal, characteristic, complemented
13SD16×Dic83C211yesmaximal, characteristic, complemented
14C8×C22⋊D83C211yesmaximal, characteristic, complemented
15C22×SD16×C83C211yesmaximal, characteristic, complemented
16C2×#13050591C2211yescharacteristic, complemented
17C2×#13050589C2211yescharacteristic
18#14581813—24no—
19C2×#13050580C2211yescharacteristic, complemented
20C2×#13050580C2211yescharacteristic, complemented
21C2×#13050579C2211yescharacteristic, complemented
22C2×#13050575C2211yescharacteristic
23C2×#13050575C2211yescharacteristic
24C2×C8×D83C2211yescharacteristic, complemented
25#14581781—21no—
26#14581781C2211yescharacteristic, complemented
27#14581779C2211yescharacteristic
28#14581773—21no—
29#14581771C2211yescharacteristic
30#14581768—21no—
31#14581768C2211yescharacteristic, complemented
32#14581766—21no—
33#14581766C2211yescharacteristic
34#14581764—21no—
35#14581763C2211yescharacteristic
36#14581761—21no—
37Q8×Dic83C2211yescharacteristic, complemented
38D4×Dic83C2211yescharacteristic
39C4×C22⋊D83—21no—
40C4×C22⋊D83C2211yescharacteristic
41C2×C22⋊Dic83—21no—
42#14581724C2211yescharacteristic, complemented
43Dic83⋊C8C2211yescharacteristic, complemented
44#14581717C2211yescharacteristic, complemented
45#14581716C2211yescharacteristic, complemented
46#14581716C2211yescharacteristic, complemented
47#14581714C2211yescharacteristic, complemented
48#14581713C2211yescharacteristic
49#14581713C2211yescharacteristic
50C22⋊(C83⋊C8)C2211yescharacteristic
51(C2×D83)⋊C8C2211yescharacteristic, complemented
52C8×Dic83C2211yescharacteristic, complemented
53C22×Q8×C83C2211yescharacteristic
54C22×D4×C83C2211yescharacteristic
55C2×SD16×C83—24no—
56C2×SD16×C83C2211yescharacteristic
57C2×SD16×C83C2211yescharacteristic
58C2×SD16×C83C2211yescharacteristic
59C2×SD16×C83C2211yescharacteristic
60C22×C8×C83C2211yescharacteristic
61#13050591—22no—
62#13050591—41no—
63#13050589—22no—
64#13050589—41no—
65C2×Dic166C2311yescharacteristic
66C2×D332—21no—
67C2×D332C2311yescharacteristic
68C2×C22⋊D83—21no—
69C2×C22⋊D83—21no—
70C2×C22⋊D83—21no—
71C2×C22⋊D83D411yescharacteristic
72C22×Dic83—21no—
73C22×Dic83—21no—
74C2×C4×D83—21no—
75C2×C4×D83C2311yescharacteristic
76#13050580—22no—
77#13050580—41no—
78#13050579—22no—
79#13050575—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
103C24×C83—21no—
104C2×Q8×C83—21no—
105C2×Q8×C83—22no—
106C2×Q8×C83—41no—
107C2×Q8×C83C2311yescharacteristic
108C2×Q8×C83C2311yescharacteristic
109C2×D4×C83—22no—
110C2×D4×C83—21no—
111C2×D4×C83—41no—
112C2×D4×C83C2311yescharacteristic
113C2×D4×C83C2311yescharacteristic
114C22×C4×C83—21no—
115C22×C4×C83C2311yescharacteristic
116SD16×C83—22no—
117SD16×C83—22no—
118SD16×C83—22no—
119SD16×C83D414yescomplemented
120C2×C8×C83—22no—
121C2×C8×C83C2311yescharacteristic
122C2×C8×C83C2311yescharacteristic
123C23×C83—21no—
124C23×C83—21no—
125C23×C83—42no—
126C23×C83—42no—
127C23×C83—81no—
128C23×C83C2×D411yescharacteristic
129C22×D83—21no—
130C22×D83C2×D411yescharacteristic
131Q8×C83—21no—
132Q8×C83—21no—
133Q8×C83—21no—
134Q8×C83—42no—
135Q8×C83C2×D412yes—
136D4×C83—21no—
137D4×C83—21no—
138D4×C83—21no—
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×C83C2×D411yescharacteristic
147C2×C4×C83C2411yescharacteristic
148C22⋊D83—22no—
149C22⋊D83—42no—
150C22⋊D83—42no—
151C22⋊D83—81no—
152C2×Dic83—21no—
153C2×Dic83—21no—
154C2×Dic83—21no—
155C2×Dic83—42no—
156C2×Dic83—81no—
157C2×Dic83C2×D411yescharacteristic
158C2×Dic83C2×D411yescharacteristic
159C2×Dic83C2×D411yescharacteristic
160D332—21no—
161D332—21no—
162D332—42no—
163C4×D83—21no—
164C4×D83—21no—
165C4×D83—42no—
166Dic166—21no—
167Dic166—21no—
168C8×C83—21no—
169C8×C83C2×D412yes—
170C83⋊C8—21no—
171C83⋊C8—21no—
172C22×C83—21no—
173C22×C83—21no—
174C22×C83—22no—
175C22×C83—41no—
176C22×C83—41no—
177C22×C83—41no—
178C22×C83—41no—
179C22×C83—41no—
180C22×C83—84no—
181C22×C83#13512yescomplemented
182C22×C83C22×D411yescharacteristic
183C2×D83—21no—
184C2×D83—21no—
185C2×D83—21no—
186C2×D83—41no—
187C2×D83—41no—
188C2×D83—41no—
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—22no—
201C2×C83—42no—
202C2×C83—81no—
203C2×C83D4211yescharacteristic
204C2×C83C2×#13511yescharacteristic
205C2×C83#57711yescharacteristic
206D83—41no—
207D83—81no—
208#3282—831nomaximal, Sylow
209C83#328211yescharacteristic, complemented, Sylow
210C2×#135—831no—
211C22×SD16D8311yescharacteristic, complemented
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×#41—831no—
226C2×#41—831no—
227C22×Q8C2×D8311yescharacteristic
228C22×D4C2×D8311yescharacteristic
229#135—1664no—
230C2×Q16—831no—
231C2×Q16—831no—
232C2×SD16—24no—
233C2×SD16—831no—
234C2×SD16C2×D8311yescharacteristic
235C2×SD16C2×D8311yescharacteristic
236C2×SD16C2×D8311yescharacteristic
237C2×SD16C2×D8311yescharacteristic
238C2×D8—831no—
239C2×D8—831no—
240C22×C8—831no—
241C22×C8C2×D8311yescharacteristic
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—21no—
271#41—3321no—
272#41—3321no—
273#41—1662no—
274#41—1662no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—831no—
279C2×Q8C22×D8311yescharacteristic
280C2×Q8C22×D8311yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—831no—
285C2×D4—831no—
286C2×D4—1661no—
287C2×D4—1661no—
288C2×D4—1661no—
289C2×D4—1661no—
290C2×D4C22×D8311yescharacteristic
291C2×D4C22×D8311yescharacteristic
292C22×C4—21no—
293C22×C4—831no—
294C22×C4—1661no—
295C22×C4—1661no—
296C22×C4—1661no—
297C22×C4C22×D8311yescharacteristic
298Q16—3321no—
299Q16—1662no—
300SD16—22no—
301SD16—22no—
302SD16—22no—
303SD16—1662no—
304SD16C22⋊D8314yescomplemented
305D8—3321no—
306D8—1662no—
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—42no—
335C23—42no—
336C23—81no—
337C23—831no—
338C23—1661no—
339C23D4×D8311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—1661no—
345Q8—1661no—
346Q8C2×C22⋊D8312yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—3322no—
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—3322no—
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—21no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—84no—
390C22—3321no—
391C22—3321no—
392C22—3321no—
393C22—1661no—
394C22—1661no—
395C22—1661no—
396C22#1458181312yescomplemented
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—22no—
410C2—42no—
411C2—81no—
412C2—3321no—
413C2—6641no—
414C2D4×C22⋊D8311yescharacteristic
415C2C2×#1458181311yescharacteristic
416C2#1912850711yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC22×SD16×C83C2
socleC22×C83C22×D4
hypercenterC22×SD16D83
hypocenterC83#3282
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14581813C2semidirect
2. #19128362C2semidirect
3. #19128345C2semidirect
4. #19128082C2semidirect
5. #19127930C2semidirect
6. #19127927C2semidirect
7. #19127921C2semidirect
8. #19127918C2semidirect
9. #19127860C2semidirect
10. #19127857C2semidirect
11. #19127845C2semidirect
12. #19127835C2semidirect
13. SD16×Dic83C2semidirect
14. C8×C22⋊D83C2semidirect
15. C22×SD16×C83C2semidirect
16. C2×#13050591C22semidirect
19. C2×#13050580C22semidirect
20. C2×#13050580C22semidirect
21. C2×#13050579C22semidirect
24. C2×C8×D83C22semidirect
26. #14581781C22semidirect
31. #14581768C22semidirect
37. Q8×Dic83C22semidirect
42. #14581724C22semidirect
43. Dic83⋊C8C22semidirect
44. #14581717C22semidirect
45. #14581716C22semidirect
46. #14581716C22semidirect
47. #14581714C22semidirect
51. (C2×D83)⋊C8C22semidirect
52. C8×Dic83C22semidirect
119. SD16×C83D4semidirect
181. C22×C83#135semidirect
209. C83#3282semidirect
211. C22×SD16D83semidirect
304. SD16C22⋊D83semidirect
396. C22#14581813semidirect

Maximal subgroups

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

subgroupindex
C2×#145818132
#191283622
#191283452
#191280822
#191279302
#191279272
#191279212
#191279182
#191278602
#191278572
#191278452
#191278352
SD16×Dic832
C8×C22⋊D832
C22×SD16×C832
#328283