Finite Group Databasebeta

← #24918976

Subgroups — #24918976

Order 10624.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581823C211yesmaximal, characteristic, complemented
2C2×SD16×D83C211yesmaximal, characteristic, complemented
3Q8×C22⋊D83C211yesmaximal, characteristic, complemented
4#19128348C211yesmaximal, characteristic
5#19128092C211yesmaximal, characteristic, complemented
6#19127945C211yesmaximal, characteristic, complemented
7#19127941C211yesmaximal, characteristic, complemented
8#19127921C211yesmaximal, characteristic, complemented
9#19127905C211yesmaximal, characteristic, complemented
10#19127865C211yesmaximal, characteristic, complemented
11#19127858C211yesmaximal, characteristic, complemented
12#19127850C211yesmaximal, characteristic, complemented
13#19127804C211yesmaximal, characteristic, complemented
14#19127775C211yesmaximal, characteristic, complemented
15#448×C83C211yesmaximal, characteristic, complemented
16C2×#13050590C2211yescharacteristic
17C2×Q8×D83C2211yescharacteristic
18C2×D4×D83C2211yescharacteristic
19#14581823—24no—
20C2×Dic332C2211yescharacteristic, complemented
21C2×#13050580C2211yescharacteristic, complemented
22C2×#13050580C2211yescharacteristic, complemented
23C2×#13050579C2211yescharacteristic
24C2×#13050578C2211yescharacteristic
25C2×#13050577C2211yescharacteristic
26C2×#13050577C2211yescharacteristic
27SD16×D83—24no—
28C2×#13050574C2211yescharacteristic, complemented
29C2×C8×D83C2211yescharacteristic
30#14581790—21no—
31#14581790C2211yescharacteristic, complemented
32#14581779C2211yescharacteristic
33#14581774—21no—
34#14581772C2211yescharacteristic
35#14581771—21no—
36#14581771C2211yescharacteristic, complemented
37#14581768—21no—
38#14581768C2211yescharacteristic
39#14581763—21no—
40#14581760—21no—
41Q8×Dic83C2211yescharacteristic, complemented
42#14581754C2211yescharacteristic
43C4×C22⋊D83—21no—
44C4×C22⋊D83C2211yescharacteristic
45C22⋊C4×D83—21no—
46#14581725C2211yescharacteristic, complemented
47Dic83⋊C8C2211yescharacteristic, complemented
48#14581717C2211yescharacteristic, complemented
49#14581715C2211yescharacteristic, complemented
50#14581714C2211yescharacteristic
51#14581713C2211yescharacteristic
52(C2×D83)⋊C8C2211yescharacteristic
53#14581702C2211yescharacteristic, complemented
54C22×Q8×C83C2211yescharacteristic, complemented
55C2×SD16×C83C2211yescharacteristic
56C2×SD16×C83C2211yescharacteristic
57#121×C83C2211yescharacteristic
58#103×C83C2211yescharacteristic, complemented
59#103×C83C2211yescharacteristic, complemented
60C22⋊C8×C83C2211yescharacteristic, complemented
61C23×D83—21no—
62#13050590—22no—
63#13050590—41no—
64C2×Dic166—21no—
65C2×Dic166C2311yescharacteristic
66C2×Dic166C2311yescharacteristic
67Q8×D83—22no—
68Q8×D83—41no—
69C2×D332C2311yescharacteristic
70C2×C22⋊D83—21no—
71C2×C22⋊D83—21no—
72C2×C22⋊D83D411yescharacteristic
73D4×D83—22no—
74D4×D83—41no—
75C2×C4×D83—21no—
76C2×C4×D83—21no—
77C2×C4×D83—21no—
78C2×C4×D83C2311yescharacteristic
79Dic332—41no—
80#13050580—22no—
81#13050580—22no—
82#13050579—22no—
83#13050578—22no—
84#13050577—22no—
85#13050577D414yescomplemented
86#13050574—22no—
87C2×C83⋊C8C2311yescharacteristic
88C2×C83⋊C8C2311yescharacteristic
89C8×D83—22no—
90C4⋊Dic83—21no—
91C4⋊Dic83—21no—
92C4⋊Dic83C2311yescharacteristic
93Dic83⋊C4—21no—
94Dic83⋊C4—21no—
95Dic83⋊C4—21no—
96Dic83⋊C4—21no—
97Dic83⋊C4D411yescharacteristic
98C22⋊Dic83—21no—
99C22⋊Dic83—21no—
100C22⋊Dic83—21no—
101C22⋊Dic83D411yescharacteristic
102(C2×D83)⋊C4—21no—
103(C2×D83)⋊C4—21no—
104(C2×D83)⋊C4—21no—
105(C2×D83)⋊C4D411yescharacteristic
106C4×Dic83—21no—
107C4×Dic83C2311yescharacteristic
108C2×Q8×C83—21no—
109C2×Q8×C83—22no—
110C2×Q8×C83—41no—
111C2×Q8×C83C2311yescharacteristic
112C2×Q8×C83C2311yescharacteristic
113C2×D4×C83—21no—
114C2×D4×C83C2311yescharacteristic
115C22×C4×C83—21no—
116C22×C4×C83C2311yescharacteristic
117SD16×C83—22no—
118SD16×C83—41no—
119C2×C8×C83C2311yescharacteristic
120C2×C8×C83C2311yescharacteristic
121C4⋊C4×C83C2311yescharacteristic
122C22⋊C4×C83—21no—
123C23×C83—21no—
124C23×C83C2×D411yescharacteristic
125C22×D83—21no—
126C22×D83—42no—
127C22×D83—42no—
128C22×D83—81no—
129C22×D83C2×D411yescharacteristic
130Q8×C83—21no—
131Q8×C83—21no—
132Q8×C83—21no—
133Q8×C83—42no—
134Q8×C83C2×D412yes—
135D4×C83—21no—
136D4×C83—21no—
137D4×C83—81no—
138C2×C4×C83—21no—
139C2×C4×C83—21no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—21no—
143C2×C4×C83—42no—
144C2×C4×C83C2×D411yescharacteristic
145C2×C4×C83C2411yescharacteristic
146C22⋊D83—22no—
147C22⋊D83—42no—
148C22⋊D83—42no—
149C2×Dic83—21no—
150C2×Dic83—21no—
151C2×Dic83—21no—
152C2×Dic83C2×D411yescharacteristic
153C2×Dic83C2×D411yescharacteristic
154C2×Dic83C2×D411yescharacteristic
155D332—21no—
156D332C2×D412yes—
157C4×D83—21no—
158C4×D83—21no—
159C4×D83—42no—
160C4×D83—42no—
161C4×D83—81no—
162Dic166—21no—
163Dic166—21no—
164Dic166—21no—
165Dic166—21no—
166Dic166—42no—
167C8×C83—21no—
168C8×C83—21no—
169C83⋊C8—21no—
170C83⋊C8C2×D412yes—
171C22×C83—21no—
172C22×C83—21no—
173C22×C83—21no—
174C22×C83—41no—
175C22×C83—41no—
176C22×C83—41no—
177C22×C83C22×D411yescharacteristic
178C2×D83—21no—
179C2×D83—21no—
180C2×D83—22no—
181C2×D83—41no—
182C2×D83—41no—
183C2×D83—84no—
184C2×D83#13712yescomplemented
185C4×C83—22no—
186C4×C83—21no—
187C4×C83—41no—
188C4×C83—41no—
189C4×C83C22×D411yescharacteristic
190C4×C83H(5,𝔽2)11yescharacteristic
191Dic83—21no—
192Dic83—21no—
193Dic83—21no—
194Dic83—41no—
195Dic83—41no—
196Dic83—41no—
197C2×C83—41no—
198C2×C83—81no—
199C2×C83D4211yescharacteristic
200C2×C83C2×#13711yescharacteristic
201C2×C83#57711yescharacteristic
202D83—22no—
203D83—42no—
204#3266—831nomaximal, Sylow
205C83#326611yescharacteristic, complemented, Sylow
206C2×#137—831no—
207C22×SD16—831no—
208D4×Q8—831no—
209#546—831no—
210#497—831no—
211#468—831no—
212#467—831no—
213#464—831no—
214#461—831no—
215#452—831no—
216#451—831no—
217#450—831no—
218#448D8311yescharacteristic, complemented
219#440—831no—
220#435—831no—
221C2×#41—831no—
222C22×Q8—831no—
223C22×Q8C2×D8311yescharacteristic, complemented
224C22×D4—831no—
225#137—1664no—
226C2×Q16—831no—
227C2×Q16—831no—
228C2×Q16—831no—
229C2×SD16—831no—
230C2×SD16—831no—
231C2×SD16—831no—
232C2×SD16—831no—
233C2×SD16—1664no—
234C2×SD16C2×D8311yescharacteristic
235C2×SD16C2×D8311yescharacteristic
236C2×M16—831no—
237C22×C8—831no—
238C4⋊Q8—831no—
239C4⋊Q8—1661no—
240#124—831no—
241#123—1661no—
242C22⋊Q8—831no—
243C22⋊Q8—831no—
244C22⋊Q8—831no—
245C22⋊Q8—1661no—
246C22⋊Q8—1661no—
247#121—1661no—
248#121C2×D8311yescharacteristic
249#120—1661no—
250C4×Q8—831no—
251C4×D4—831no—
252C4×D4—831no—
253C4×D4—1661no—
254C2×C22⋊C4—1661no—
255#107—831no—
256C4⋊C8—831no—
257#103—831no—
258#103—831no—
259#103C2×D8311yescharacteristic, complemented
260#103C2×D8311yescharacteristic, complemented
261#102—831no—
262#102—831no—
263C22⋊C8—831no—
264C22⋊C8C2×D8311yescharacteristic, complemented
265#97—831no—
266C24—1661no—
267#41—3321no—
268#41—1662no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—3321no—
273C2×Q8—831no—
274C2×Q8—831no—
275C2×Q8—1661no—
276C2×Q8—1662no—
277C2×Q8C22×D8311yescharacteristic
278C2×Q8C22×D8311yescharacteristic
279C2×D4—21no—
280C2×D4—3321no—
281C2×D4—831no—
282C2×D4—831no—
283C2×D4—1661no—
284C2×D4—1662no—
285C2×D4—1661no—
286C2×D4C22×D8311yescharacteristic
287C22×C4—21no—
288C22×C4—831no—
289C22×C4—1661no—
290C22×C4—1661no—
291C22×C4—1661no—
292C22×C4C22×D8311yescharacteristic
293Q16—3321no—
294Q16—1662no—
295Q16—1662no—
296SD16—22no—
297SD16—41no—
298SD16—834no—
299SD16—1662no—
300SD16—1662no—
301SD16—1662no—
302M16—1662no—
303C2×C8—831no—
304C2×C8—831no—
305C2×C8—1662no—
306C2×C8C22×D8311yescharacteristic
307C2×C8C22×D8311yescharacteristic
308C4⋊C4—831no—
309C4⋊C4—831no—
310C4⋊C4—1661no—
311C4⋊C4—1661no—
312C4⋊C4—1661no—
313C4⋊C4—1661no—
314C4⋊C4—1661no—
315C4⋊C4—1661no—
316C4⋊C4C22×D8311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—831no—
319C22⋊C4—831no—
320C22⋊C4—1661no—
321C22⋊C4—1661no—
322C22⋊C4—1661no—
323C22⋊C4—1661no—
324C22⋊C4—1661no—
325C22⋊C4—1661no—
326C42—831no—
327C42—1661no—
328C23—21no—
329C23—3322no—
330C23—3322no—
331C23—831no—
332C23—6641no—
333C23—1661no—
334C23D4×D8311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—3322no—
340Q8—1661no—
341Q8—1661no—
342Q8—1661no—
343Q8—1661no—
344Q8D4×D8312yes—
345D4—21no—
346D4—21no—
347D4—81no—
348D4—3322no—
349D4—3322no—
350D4—832no—
351D4—1662no—
352D4—1661no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—3322no—
360C2×C4—3322no—
361C2×C4—831no—
362C2×C4—831no—
363C2×C4—831no—
364C2×C4—6641no—
365C2×C4—1661no—
366C2×C4—1661no—
367C2×C4—1661no—
368C2×C4—1661no—
369C2×C4—1661no—
370C2×C4D4×D8311yescharacteristic
371C2×C4C23×D8311yescharacteristic
372C8—21no—
373C8—21no—
374C8—832no—
375C8—1661no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—3321no—
383C22—3321no—
384C22—832no—
385C22—6644no—
386C22—1662no—
387C22—1661no—
388C22—1661no—
389C22C2×D4×D8311yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—3321no—
395C4—3321no—
396C4—3321no—
397C4—1661no—
398C4—1661no—
399C4—1661no—
400C4C2×D4×D8311yescharacteristic
401C4#1458183711yescharacteristic
402C2—41no—
403C2—81no—
404C2—3322no—
405C2—1662no—
406C2#1912833311yescharacteristic
407C2#137×D8311yescharacteristic
408C2#1912850711yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#448×C83C2
socleC22×C83C22×D4
prime radical#19128348C2
hypercenter#448D83
hypocenterC83#3266
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#14581823C2semidirect
2. C2×SD16×D83C2semidirect
3. Q8×C22⋊D83C2semidirect
5. #19128092C2semidirect
6. #19127945C2semidirect
7. #19127941C2semidirect
8. #19127921C2semidirect
9. #19127905C2semidirect
10. #19127865C2semidirect
11. #19127858C2semidirect
12. #19127850C2semidirect
13. #19127804C2semidirect
14. #19127775C2semidirect
15. #448×C83C2semidirect
20. C2×Dic332C22semidirect
21. C2×#13050580C22semidirect
22. C2×#13050580C22semidirect
28. C2×#13050574C22semidirect
31. #14581790C22semidirect
36. #14581771C22semidirect
41. Q8×Dic83C22semidirect
46. #14581725C22semidirect
47. Dic83⋊C8C22semidirect
48. #14581717C22semidirect
49. #14581715C22semidirect
53. #14581702C22semidirect
54. C22×Q8×C83C22semidirect
58. #103×C83C22semidirect
59. #103×C83C22semidirect
60. C22⋊C8×C83C22semidirect
85. #13050577D4semidirect
184. C2×D83#137semidirect
205. C83#3266semidirect
218. #448D83semidirect
223. C22×Q8C2×D83semidirect
259. #103C2×D83semidirect
260. #103C2×D83semidirect
264. C22⋊C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145818232
C2×SD16×D832
Q8×C22⋊D832
#191283482
#191280922
#191279452
#191279412
#191279212
#191279052
#191278652
#191278582
#191278502
#191278042
#191277752
#448×C832
#326683