Finite Group Databasebeta

← #24917481

Subgroups — #24917481

Order 10624.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128235C211yesmaximal, characteristic, complemented
2#19128042C211yesmaximal, characteristic, complemented
3#19128025C211yesmaximal, characteristic, complemented
4#19128008C211yesmaximal, characteristic, complemented
5#19128001C211yesmaximal, characteristic, complemented
6#19127923C211yesmaximal, characteristic, complemented
7#19127916C211yesmaximal, characteristic, complemented
8#19127863C211yesmaximal, characteristic, complemented
9#19127846C211yesmaximal, characteristic
10C4×#13050580C211yesmaximal, characteristic, complemented
11C4×#13050577C211yesmaximal, characteristic, complemented
12C4×#13050578C211yesmaximal, characteristic, complemented
13C4×#13050575C211yesmaximal, characteristic, complemented
14#19127754C211yesmaximal, characteristic, complemented
15C4×#41×C83C211yesmaximal, characteristic, complemented
16C2×#13050580C2211yescharacteristic
17C2×#13050578C2211yescharacteristic
18C2×#13050577C2211yescharacteristic
19C2×#13050575C2211yescharacteristic
20#14581786—21no—
21#14581784C2211yescharacteristic
22#14581780C2211yescharacteristic
23#14581775—21no—
24#14581771C2211yescharacteristic
25#14581766C2211yescharacteristic
26C4×Dic166C2211yescharacteristic
27C4×D332C2211yescharacteristic
28C4×C22⋊D83—21no—
29#14581749—21no—
30#14581725C2211yescharacteristic
31#14581725C2211yescharacteristic
32#14581723C2211yescharacteristic
33#14581723C2211yescharacteristic
34C4⋊(C83⋊C8)C2211yescharacteristic
35C4⋊(C83⋊C8)C2211yescharacteristic
36#14581716C2211yescharacteristic
37#14581716C2211yescharacteristic
38#14581715C2211yescharacteristic
39#14581715C2211yescharacteristic
40#14581713C2211yescharacteristic
41#14581713C2211yescharacteristic
42#14581712C2211yescharacteristic
43#14581712C2211yescharacteristic
44C22⋊(C83⋊C8)C2211yescharacteristic
45C22⋊(C83⋊C8)C2211yescharacteristic
46C4×C83⋊C8C2211yescharacteristic
47C4×C83⋊C8C2211yescharacteristic
48C2×#41×C83C2211yescharacteristic
49C4×Q8×C83C2211yescharacteristic
50C4×Q8×C83C2211yescharacteristic
51C4×D4×C83—21no—
52C4×D4×C83—21no—
53C4×D4×C83C2211yescharacteristic
54C4×D4×C83C2211yescharacteristic
55#117×C83—21no—
56#117×C83C2211yescharacteristic
57C2×C42×C83—21no—
58C2×C42×C83C2211yescharacteristic
59C2×Dic166C2311yescharacteristic
60C2×D332C2311yescharacteristic
61C2×C22⋊D83—21no—
62C2×C4×D83—21no—
63#13050580—22no—
64#13050578—22no—
65#13050577—22no—
66#13050575—22no—
67C2×C83⋊C8C2311yescharacteristic
68C2×C83⋊C8C2311yescharacteristic
69C2×C83⋊C8C2311yescharacteristic
70C2×C83⋊C8C2311yescharacteristic
71C4⋊Dic83C2311yescharacteristic
72C4⋊Dic83C2311yescharacteristic
73Dic83⋊C4—21no—
74Dic83⋊C4—21no—
75Dic83⋊C4—21no—
76Dic83⋊C4—21no—
77C22⋊Dic83—21no—
78(C2×D83)⋊C4—21no—
79(C2×D83)⋊C4—21no—
80(C2×D83)⋊C4—21no—
81(C2×D83)⋊C4—21no—
82C4×Dic83—21no—
83#41×C83—22no—
84#41×C83—22no—
85C2×Q8×C83C2311yescharacteristic
86C2×D4×C83—21no—
87C2×D4×C83C2311yescharacteristic
88C22×C4×C83—21no—
89C22×C4×C83—21no—
90C22×C4×C83—21no—
91C22×C4×C83D411yescharacteristic
92C22×C4×C83D411yescharacteristic
93C22×C4×C83C2311yescharacteristic
94C4⋊C4×C83—21no—
95C4⋊C4×C83—21no—
96C4⋊C4×C83C2311yescharacteristic
97C4⋊C4×C83C2311yescharacteristic
98C22⋊C4×C83—21no—
99C22⋊C4×C83—21no—
100C22⋊C4×C83—21no—
101C42×C83—21no—
102C42×C83—21no—
103C42×C83—21no—
104C42×C83D411yescharacteristic
105C42×C83D411yescharacteristic
106C42×C83C2311yescharacteristic
107C42×C83C2311yescharacteristic
108C23×C83—21no—
109C23×C83C2×D411yescharacteristic
110C22×D83—21no—
111Q8×C83—21no—
112Q8×C83#4112yes—
113D4×C83—24no—
114D4×C83—21no—
115D4×C83#4112yes—
116C2×C4×C83—24no—
117C2×C4×C83—21no—
118C2×C4×C83—22no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—41no—
124C2×C4×C83—42no—
125C2×C4×C83—42no—
126C2×C4×C83C2×D411yescharacteristic
127C2×C4×C83C2×D411yescharacteristic
128C2×C4×C83C2×D411yescharacteristic
129C2×C4×C83C2×D411yescharacteristic
130C2×C4×C83C2×D411yescharacteristic
131C2×C4×C83C2411yescharacteristic
132C22⋊D83—42no—
133C2×Dic83—21no—
134C2×Dic83—21no—
135C2×Dic83—21no—
136D332—21no—
137D332—21no—
138C4×D83—42no—
139Dic166—21no—
140Dic166—21no—
141C83⋊C8—21no—
142C83⋊C8—21no—
143C83⋊C8—21no—
144C83⋊C8—21no—
145C22×C83—21no—
146C22×C83—22no—
147C22×C83—21no—
148C22×C83—21no—
149C22×C83—41no—
150C22×C83—41no—
151C22×C83C22×D411yescharacteristic
152C2×D83—41no—
153C2×D83—41no—
154C2×D83—41no—
155C4×C83—21no—
156C4×C83—22no—
157C4×C83—21no—
158C4×C83—21no—
159C4×C83—21no—
160C4×C83—41no—
161C4×C83—41no—
162C4×C83#13512yes—
163C4×C83C2×#4111yescharacteristic
164C4×C83C2×#4111yescharacteristic
165Dic83—41no—
166Dic83—41no—
167Dic83—41no—
168C2×C83—41no—
169C2×C83—42no—
170C2×C83#52511yescharacteristic
171C2×C83C2×#13511yescharacteristic
172C2×C83#57511yescharacteristic
173D83—81no—
174#3102—831nomaximal, Sylow
175C83#310211yescharacteristic, complemented, Sylow
176#529—831no—
177C4×#41D8311yescharacteristic, complemented
178#485—831no—
179#482—831no—
180#479—831no—
181#478—831no—
182#464—831no—
183#463—831no—
184#452—831no—
185#449—831no—
186C4×Q16—831no—
187C4×SD16—831no—
188C4×SD16—831no—
189C4×D8—831no—
190#431—831no—
191C2×#41C2×D8311yescharacteristic
192C2×Q16—831no—
193C2×SD16—831no—
194C2×SD16—831no—
195C2×D8—831no—
196#126—1661no—
197#125—831no—
198#124—831no—
199#123—1661no—
200C22⋊Q8—831no—
201#121—831no—
202C4×Q8—831no—
203C4×Q8C2×D8311yescharacteristic
204C4×Q8C2×D8311yescharacteristic
205C4×D4—21no—
206C4×D4—21no—
207C4×D4—831no—
208C4×D4—1661no—
209C4×D4C2×D8311yescharacteristic
210C4×D4C2×D8311yescharacteristic
211#117—21no—
212#117—1661no—
213#117C2×D8311yescharacteristic
214C2×C42—21no—
215C2×C42C2×D8311yescharacteristic
216#107—831no—
217#107—831no—
218#106—831no—
219#106—831no—
220C4⋊C8—831no—
221C4⋊C8—831no—
222#103—831no—
223#103—831no—
224#103—831no—
225#103—831no—
226#102—831no—
227#102—831no—
228#102—831no—
229#102—831no—
230C22⋊C8—831no—
231C22⋊C8—831no—
232C4×C8—831no—
233C4×C8—831no—
234#41—22no—
235#41—22no—
236C2×Q8—831no—
237C2×Q8C22×D8311yescharacteristic
238C2×D4—21no—
239C2×D4—831no—
240C2×D4—1661no—
241C2×D4C22×D8311yescharacteristic
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—1661no—
246C22×C4C22⋊D8311yescharacteristic
247C22×C4C22⋊D8311yescharacteristic
248C22×C4C22×D8311yescharacteristic
249Q16—1662no—
250SD16—1662no—
251SD16—1662no—
252D8—1662no—
253C2×C8—831no—
254C2×C8—831no—
255C2×C8—831no—
256C2×C8—831no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—831no—
260C4⋊C4—831no—
261C4⋊C4—1661no—
262C4⋊C4—1661no—
263C4⋊C4—1661no—
264C4⋊C4—1661no—
265C4⋊C4C22×D8311yescharacteristic
266C4⋊C4C22×D8311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—1661no—
271C22⋊C4—1661no—
272C22⋊C4—1661no—
273C22⋊C4—1661no—
274C22⋊C4—1661no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—1661no—
279C42C22⋊D8311yescharacteristic
280C42C22⋊D8311yescharacteristic
281C42C22×D8311yescharacteristic
282C42C22×D8311yescharacteristic
283C23—21no—
284C23—1661no—
285C23C2×C22⋊D8311yescharacteristic
286Q8—21no—
287Q8—1661no—
288Q8—1661no—
289Q8#1305059012yes—
290D4—24no—
291D4—21no—
292D4—3322no—
293D4—1661no—
294D4—1661no—
295D4#1305059012yes—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—3322no—
307C2×C4—1661no—
308C2×C4—1661no—
309C2×C4—1661no—
310C2×C4C2×C22⋊D8311yescharacteristic
311C2×C4C2×C22⋊D8311yescharacteristic
312C2×C4C2×C22⋊D8311yescharacteristic
313C2×C4C2×C22⋊D8311yescharacteristic
314C2×C4C2×C22⋊D8311yescharacteristic
315C2×C4C23×D8311yescharacteristic
316C8—1661no—
317C8—1661no—
318C8—1661no—
319C8—1661no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—3321no—
327C22—3321no—
328C22—3321no—
329C22C22×C22⋊D8311yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—3321no—
338C4—3321no—
339C4—3321no—
340C4#1458181212yes—
341C4C2×#1305059011yescharacteristic
342C4C2×#1305059011yescharacteristic
343C2—41no—
344C2—42no—
345C2—6641no—
346C2#1912821211yescharacteristic
347C2C2×#1458181211yescharacteristic
348C2#1912849911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC4×#41×C83C2
socleC22×C83C22×D4
prime radical#19127846C2
hypercenterC4×#41D83
hypocenterC83#3102
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #19128235C2semidirect
2. #19128042C2semidirect
3. #19128025C2semidirect
4. #19128008C2semidirect
5. #19128001C2semidirect
6. #19127923C2semidirect
7. #19127916C2semidirect
8. #19127863C2semidirect
10. C4×#13050580C2semidirect
11. C4×#13050577C2semidirect
12. C4×#13050578C2semidirect
13. C4×#13050575C2semidirect
14. #19127754C2semidirect
15. C4×#41×C83C2semidirect
175. C83#3102semidirect
177. C4×#41D83semidirect

Maximal subgroups

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

subgroupindex
#191282352
#191280422
#191280252
#191280082
#191280012
#191279232
#191279162
#191278632
#191278462
C4×#130505802
C4×#130505772
C4×#130505782
C4×#130505752
#191277542
C4×#41×C832
#310283