Finite Group Databasebeta

← #24919631

Subgroups — #24919631

Order 10624.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128404C211yesmaximal, characteristic
2Q8×D332C211yesmaximal, characteristic, complemented
3#19128071C211yesmaximal, characteristic, complemented
4#19128045C211yesmaximal, characteristic, complemented
5#19128038C211yesmaximal, characteristic, complemented
6#19127948C211yesmaximal, characteristic, complemented
7#19127931C211yesmaximal, characteristic, complemented
8#19127907C211yesmaximal, characteristic, complemented
9#19127841C211yesmaximal, characteristic, complemented
10#19127841C211yesmaximal, characteristic, complemented
11#19127799C211yesmaximal, characteristic, complemented
12#19127771C211yesmaximal, characteristic, complemented
13#19127708C211yesmaximal, characteristic, complemented
14#103×D83C211yesmaximal, characteristic, complemented
15#479×C83C211yesmaximal, characteristic, complemented
16C2×Q8×D83C2211yescharacteristic
17C2×Q8×D83C2211yescharacteristic
18C2×#13050579C2211yescharacteristic
19C2×#13050579C2211yescharacteristic
20C2×#13050577C2211yescharacteristic
21C2×#13050573C2211yescharacteristic
22C2×C8×D83C2211yescharacteristic
23#14581792—21no—
24#14581792C2211yescharacteristic
25#14581787—21no—
26#14581777—21no—
27#14581772—21no—
28#14581772—21no—
29#14581772C2211yescharacteristic
30#14581772C2211yescharacteristic
31#14581767—21no—
32#14581767C2211yescharacteristic
33#14581767C2211yescharacteristic
34C4×D332—21no—
35C4×D332C2211yescharacteristic
36C4×D332C2211yescharacteristic
37#14581754—21no—
38#14581750C2211yescharacteristic
39C4⋊C4×D83C2211yescharacteristic
40#14581725C2211yescharacteristic
41#14581717C2211yescharacteristic
42#14581717C2211yescharacteristic
43#14581716C2211yescharacteristic
44#14581715C2211yescharacteristic
45#14581715C2211yescharacteristic
46#14581715C2211yescharacteristic
47#14581715C2211yescharacteristic
48#14581712C2211yescharacteristic
49(C2×D83)⋊C8C2211yescharacteristic
50(C2×D83)⋊C8C2211yescharacteristic
51#14581703C2211yescharacteristic
52#125×C83C2211yescharacteristic
53C4×Q8×C83C2211yescharacteristic
54#107×C83C2211yescharacteristic
55#106×C83C2211yescharacteristic
56C4⋊C8×C83C2211yescharacteristic
57#103×C83C2211yescharacteristic
58#103×C83C2211yescharacteristic
59C2×Dic166—21no—
60C2×Dic166—21no—
61C2×Dic166C2311yescharacteristic
62C2×Dic166C2311yescharacteristic
63Q8×D83—22no—
64Q8×D83—22no—
65Q8×D83—41no—
66Q8×D83—41no—
67C2×D332—21no—
68C2×D332—21no—
69C2×D332D411yescharacteristic
70C2×D332C2311yescharacteristic
71C2×C4×D83—21no—
72C2×C4×D83—21no—
73C2×C4×D83—21no—
74C2×C4×D83—21no—
75C2×C4×D83C2311yescharacteristic
76C2×C4×D83C2311yescharacteristic
77#13050579—41no—
78#13050579—41no—
79#13050577—22no—
80#13050573—41no—
81C2×C83⋊C8C2311yescharacteristic
82C2×C83⋊C8C2311yescharacteristic
83C8×D83—41no—
84C4⋊Dic83—21no—
85C4⋊Dic83—21no—
86C4⋊Dic83—21no—
87C4⋊Dic83—21no—
88C4⋊Dic83D411yescharacteristic
89C4⋊Dic83C2311yescharacteristic
90Dic83⋊C4—21no—
91(C2×D83)⋊C4—21no—
92(C2×D83)⋊C4—21no—
93(C2×D83)⋊C4—21no—
94(C2×D83)⋊C4—21no—
95(C2×D83)⋊C4—21no—
96(C2×D83)⋊C4—21no—
97(C2×D83)⋊C4D411yescharacteristic
98(C2×D83)⋊C4D411yescharacteristic
99C4×Dic83—21no—
100C2×Q8×C83C2311yescharacteristic
101C2×C8×C83C2311yescharacteristic
102C2×C8×C83C2311yescharacteristic
103C4⋊C4×C83—21no—
104C4⋊C4×C83—21no—
105C4⋊C4×C83—21no—
106C4⋊C4×C83C2311yescharacteristic
107C4⋊C4×C83C2311yescharacteristic
108C4⋊C4×C83C2311yescharacteristic
109C42×C83—21no—
110C42×C83C2311yescharacteristic
111C22×D83—21no—
112C22×D83C2×D411yescharacteristic
113C22×D83C2×D411yescharacteristic
114Q8×C83—21no—
115Q8×C83#4112yes—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83—21no—
119C2×C4×C83—21no—
120C2×C4×C83C2×D411yescharacteristic
121C2×C4×C83C2×D411yescharacteristic
122C2×C4×C83C2411yescharacteristic
123C2×Dic83—21no—
124C2×Dic83—21no—
125C2×Dic83—21no—
126C2×Dic83C2×D411yescharacteristic
127C2×Dic83C2×D411yescharacteristic
128D332—22no—
129D332—21no—
130D332—21no—
131D332—42no—
132D332—81no—
133C4×D83—21no—
134C4×D83—21no—
135C4×D83—21no—
136C4×D83—21no—
137C4×D83—42no—
138C4×D83—42no—
139C4×D83—81no—
140C4×D83—81no—
141Dic166—21no—
142Dic166—21no—
143Dic166—21no—
144Dic166—21no—
145Dic166—42no—
146Dic166—42no—
147C8×C83—21no—
148C8×C83—21no—
149C83⋊C8—21no—
150C83⋊C8—21no—
151C22×C83C22×D411yescharacteristic
152C2×D83—21no—
153C2×D83—21no—
154C2×D83—21no—
155C2×D83—21no—
156C2×D83—21no—
157C2×D83—41no—
158C2×D83—41no—
159C2×D83—41no—
160C2×D83#13712yes—
161C4×C83—22no—
162C4×C83—21no—
163C4×C83—21no—
164C4×C83—41no—
165C4×C83—41no—
166C4×C83—41no—
167C4×C83C2×#4111yescharacteristic
168C4×C83H(5,𝔽2)11yescharacteristic
169Dic83—21no—
170Dic83—21no—
171Dic83—41no—
172Dic83—41no—
173Dic83—41no—
174C2×C83#54611yescharacteristic
175C2×C83C2×#13711yescharacteristic
176C2×C83#57711yescharacteristic
177D83—22no—
178D83—41no—
179D83—81no—
180#3320—831nomaximal, Sylow
181C83#332011yescharacteristic, complemented, Sylow
182#553—831no—
183D4×Q8—831no—
184#491—831no—
185#485—831no—
186#484—831no—
187#479D8311yescharacteristic, complemented
188#468—831no—
189#465—831no—
190#461—831no—
191#448—831no—
192#448—831no—
193#440—831no—
194#435—831no—
195#419—831no—
196C2×#103—831no—
197C22×Q8—831no—
198C22×Q8—831no—
199C2×SD16—831no—
200C2×SD16—831no—
201C2×SD16—831no—
202C2×M16—831no—
203C22×C8—831no—
204C4⋊Q8—831no—
205C4⋊Q8—1661no—
206#126—1661no—
207#125C2×D8311yescharacteristic
208#123—1661no—
209C22⋊Q8—831no—
210C22⋊Q8—831no—
211C22⋊Q8—1661no—
212C22⋊Q8—1661no—
213#121—831no—
214#121—831no—
215#121—1661no—
216C4×Q8C2×D8311yescharacteristic
217C4×D4—831no—
218C4×D4—831no—
219C4×D4—1661no—
220C4×D4—1661no—
221#117—831no—
222C2×C4⋊C4—831no—
223#107—831no—
224#107C2×D8311yescharacteristic
225#106C2×D8311yescharacteristic
226C4⋊C8C2×D8311yescharacteristic
227#103—831no—
228#103—831no—
229#103—831no—
230#103—831no—
231#103—831no—
232#103—831no—
233#103—831no—
234#103C2×D8311yescharacteristic
235#103C2×D8311yescharacteristic
236#102—831no—
237C22⋊C8—831no—
238C22⋊C8—831no—
239#97—831no—
240C2×Q8—3321no—
241C2×Q8—3321no—
242C2×Q8—831no—
243C2×Q8—831no—
244C2×Q8—1661no—
245C2×Q8—1661no—
246C2×Q8—1662no—
247C2×Q8—1662no—
248C2×Q8C22×D8311yescharacteristic
249C2×D4—831no—
250C2×D4—831no—
251C2×D4—1661no—
252C2×D4—1661no—
253C22×C4—831no—
254C22×C4—831no—
255C22×C4—1661no—
256C22×C4—1661no—
257C22×C4—1661no—
258C22×C4—1661no—
259SD16—3321no—
260SD16—3321no—
261SD16—1662no—
262M16—3321no—
263C2×C8—3321no—
264C2×C8—831no—
265C2×C8—831no—
266C2×C8C22×D8311yescharacteristic
267C2×C8C22×D8311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—831no—
272C4⋊C4—831no—
273C4⋊C4—1661no—
274C4⋊C4—1661no—
275C4⋊C4—1661no—
276C4⋊C4—1661no—
277C4⋊C4—1661no—
278C4⋊C4C22×D8311yescharacteristic
279C4⋊C4C22×D8311yescharacteristic
280C4⋊C4C22×D8311yescharacteristic
281C22⋊C4—831no—
282C22⋊C4—831no—
283C22⋊C4—1661no—
284C22⋊C4—1661no—
285C22⋊C4—1661no—
286C22⋊C4—1661no—
287C22⋊C4—1661no—
288C22⋊C4—1661no—
289C42—21no—
290C42—1661no—
291C42C22×D8311yescharacteristic
292C23—831no—
293C23—831no—
294C23—1661no—
295Q8—21no—
296Q8—3322no—
297Q8—3322no—
298Q8—1661no—
299Q8—1661no—
300Q8—1661no—
301Q8—1661no—
302Q8#1305059112yes—
303D4—3322no—
304D4—6641no—
305D4—1662no—
306D4—1661no—
307D4—1661no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—3322no—
313C2×C4—3322no—
314C2×C4—831no—
315C2×C4—831no—
316C2×C4—6641no—
317C2×C4—6641no—
318C2×C4—1661no—
319C2×C4—1661no—
320C2×C4—1661no—
321C2×C4—1661no—
322C2×C4—1661no—
323C2×C4—1661no—
324C2×C4—1661no—
325C2×C4D4×D8311yescharacteristic
326C2×C4D4×D8311yescharacteristic
327C2×C4C23×D8311yescharacteristic
328C8—21no—
329C8—21no—
330C8—1661no—
331C8—1661no—
332C22—3321no—
333C22—3321no—
334C22—3321no—
335C22—832no—
336C22—1661no—
337C22—1661no—
338C22—1661no—
339C22—1661no—
340C22—1661no—
341C22C2×D4×D8311yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3321no—
349C4—3321no—
350C4—3321no—
351C4—1661no—
352C4—1661no—
353C4C2×#1305059111yescharacteristic
354C4#1458183811yescharacteristic
355C2—3321no—
356C2—6641no—
357C2—1662no—
358C2#1912834211yescharacteristic
359C2#137×D8311yescharacteristic
360C2#1912850811yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#479×C83C2
socleC22×C83C22×D4
prime radical#19128404C2
hypercenter#479D83
hypocenterC83#3320
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. Q8×D332C2semidirect
3. #19128071C2semidirect
4. #19128045C2semidirect
5. #19128038C2semidirect
6. #19127948C2semidirect
7. #19127931C2semidirect
8. #19127907C2semidirect
9. #19127841C2semidirect
10. #19127841C2semidirect
11. #19127799C2semidirect
12. #19127771C2semidirect
13. #19127708C2semidirect
14. #103×D83C2semidirect
15. #479×C83C2semidirect
181. C83#3320semidirect
187. #479D83semidirect

Maximal subgroups

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

subgroupindex
#191284042
Q8×D3322
#191280712
#191280452
#191280382
#191279482
#191279312
#191279072
#191278412
#191277992
#191277712
#191277082
#103×D832
#479×C832
#332083