Finite Group Databasebeta

← #24911451

Subgroups — #24911451

Order 10624.

452 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581782C211yesmaximal, characteristic
2C2×#14581757C211yesmaximal, characteristic
3#19127635C211yesmaximal, characteristic
4#19127632C211yesmaximal, characteristic
5#19127622C211yesmaximal, characteristic
6#19127621C211yesmaximal, characteristic
7#19127596C211yesmaximal, characteristic
8#19127587C211yesmaximal, characteristic
9#19127585C211yesmaximal, characteristic
10#19127584C211yesmaximal, characteristic
11#19127584C211yesmaximal, characteristic
12#19127582C211yesmaximal, characteristic
13#19127582C211yesmaximal, characteristic
14C4×C4⋊Dic83C211yesmaximal, characteristic
15#389×C83C211yesmaximal, characteristic
16C22×Dic166C2211yescharacteristic
17#14581782—24no—
18#14581757—24no—
19C2×C4⋊Dic83C2211yescharacteristic
20C2×C4⋊Dic83C2211yescharacteristic
21C2×C4⋊Dic83C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×Dic83⋊C4C2211yescharacteristic
27C2×Dic83⋊C4C2211yescharacteristic
28C2×Dic83⋊C4C2211yescharacteristic
29C2×Dic83⋊C4C2211yescharacteristic
30C2×C4×Dic83C2211yescharacteristic
31C2×C4×Dic83C2211yescharacteristic
32C2×C4×Dic83C2211yescharacteristic
33C2×C4×Dic83C2211yescharacteristic
34C83⋊#95C2211yescharacteristic
35C83⋊#95C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C83⋊#95C2211yescharacteristic
46C2×C4⋊C4×C83C2211yescharacteristic
47C2×C4⋊C4×C83C2211yescharacteristic
48C2×C4⋊C4×C83C2211yescharacteristic
49C2×C4⋊C4×C83C2211yescharacteristic
50C2×C42×C83C2211yescharacteristic
51#95×C83C2211yescharacteristic
52#95×C83C2211yescharacteristic
53C2×Dic166—22no—
54C2×Dic166—22no—
55C2×Dic166—22no—
56C22×Dic83C2311yescharacteristic
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C4⋊Dic83—22no—
65C4⋊Dic83—22no—
66C4⋊Dic83Q814yescomplemented
67Dic83⋊C4—22no—
68Dic83⋊C4—22no—
69Dic83⋊C4—22no—
70Dic83⋊C4—22no—
71Dic83⋊C4—22no—
72Dic83⋊C4—22no—
73Dic83⋊C4—22no—
74Dic83⋊C4D414yes—
75C4×Dic83—22no—
76C4×Dic83—22no—
77C4×Dic83—22no—
78C4×Dic83—22no—
79C22×C4×C83C2311yescharacteristic
80C22×C4×C83C2311yescharacteristic
81C22×C4×C83C2311yescharacteristic
82C22×C4×C83C2311yescharacteristic
83C22×C4×C83C2311yescharacteristic
84C22×C4×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C4⋊C4×C83—22no—
87C4⋊C4×C83—22no—
88C4⋊C4×C83—22no—
89C4⋊C4×C83—22no—
90C42×C83—22no—
91C23×C83C2411yescharacteristic
92C2×C4×C83—21no—
93C2×C4×C83—21no—
94C2×C4×C83—21no—
95C2×C4×C83—21no—
96C2×C4×C83—21no—
97C2×C4×C83—21no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83C2×D412yes—
110C2×C4×C83C2×Q812yes—
111C2×C4×C83#4112yes—
112C2×C4×C83#4112yes—
113C2×Dic83—21no—
114C2×Dic83—21no—
115C2×Dic83—21no—
116C2×Dic83—21no—
117C2×Dic83—21no—
118C2×Dic83—21no—
119C2×Dic83—21no—
120C2×Dic83—21no—
121C2×Dic83—21no—
122C2×Dic83—21no—
123C2×Dic83—21no—
124C2×Dic83—21no—
125C2×Dic83—21no—
126C2×Dic83—21no—
127C2×Dic83—21no—
128C2×Dic83—21no—
129C2×Dic83—21no—
130C2×Dic83—21no—
131C2×Dic83—21no—
132C2×Dic83C2×D412yes—
133C2×Dic83C2×D412yes—
134C2×Dic83C2×Q812yes—
135C2×Dic83C2×Q812yes—
136C2×Dic83#4112yes—
137Dic166—28no—
138C22×C83C22×D411yescharacteristic
139C22×C83C22×Q811yescharacteristic
140C22×C83C2×#4111yescharacteristic
141C22×C83C2×#4111yescharacteristic
142C22×C83C2×#4111yescharacteristic
143C22×C832−1+411yescharacteristic
144C22×C832−1+411yescharacteristic
145C4×C83—22no—
146C4×C83—22no—
147C4×C83—22no—
148C4×C83—22no—
149C4×C83—41no—
150C4×C83—41no—
151C4×C83—41no—
152Dic83—22no—
153Dic83—22no—
154Dic83—22no—
155Dic83—22no—
156Dic83—22no—
157Dic83—41no—
158Dic83—41no—
159Dic83—41no—
160C2×C83#52511yescharacteristic
161C2×C83#53311yescharacteristic
162C2×C83#54111yescharacteristic
163C2×C83#54711yescharacteristic
164C2×C83D4×Q811yescharacteristic
165C2×C83#55211yescharacteristic
166C2×C83#55711yescharacteristic
167#2462—831nomaximal, Sylow
168C83#246211yescharacteristic, complemented, Sylow
169C2×#125—831no—
170C2×C4×Q8—831no—
171#398—831no—
172#398—831no—
173#395—831no—
174#395—831no—
175#389—831no—
176#389D8311yescharacteristic
177#387—831no—
178#387—831no—
179#387—831no—
180#387—831no—
181#387—831no—
182#387—831no—
183C4×C4⋊C4—831no—
184C22×Q8—831no—
185#125—1664no—
186C4×Q8—1664no—
187C2×C4⋊C4—831no—
188C2×C4⋊C4—831no—
189C2×C4⋊C4—831no—
190C2×C4⋊C4—831no—
191C2×C4⋊C4—831no—
192C2×C4⋊C4—831no—
193C2×C4⋊C4—831no—
194C2×C4⋊C4—831no—
195C2×C4⋊C4—831no—
196C2×C4⋊C4—831no—
197C2×C4⋊C4—831no—
198C2×C4⋊C4C2×D8311yescharacteristic
199C2×C4⋊C4C2×D8311yescharacteristic
200C2×C4⋊C4C2×D8311yescharacteristic
201C2×C4⋊C4C2×D8311yescharacteristic
202C2×C42—831no—
203C2×C42—831no—
204C2×C42—831no—
205C2×C42—831no—
206C2×C42C2×D8311yescharacteristic
207#95—831no—
208#95—831no—
209#95—831no—
210#95—831no—
211#95—831no—
212#95—831no—
213#95—831no—
214#95—831no—
215#95—831no—
216#95—831no—
217#95—831no—
218#95—831no—
219#95C2×D8311yescharacteristic
220#95C2×D8311yescharacteristic
221C2×Q8—1662no—
222C2×Q8—1662no—
223C2×Q8—1662no—
224C22×C4—831no—
225C22×C4—831no—
226C22×C4—831no—
227C22×C4—831no—
228C22×C4—831no—
229C22×C4—831no—
230C22×C4—831no—
231C22×C4—831no—
232C22×C4C22×D8311yescharacteristic
233C22×C4C22×D8311yescharacteristic
234C22×C4C22×D8311yescharacteristic
235C22×C4C22×D8311yescharacteristic
236C22×C4C22×D8311yescharacteristic
237C22×C4C22×D8311yescharacteristic
238C22×C4C22×D8311yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—834no—
244C4⋊C4—834no—
245C4⋊C4—1662no—
246C4⋊C4—1662no—
247C4⋊C4—1662no—
248C4⋊C4—1662no—
249C4⋊C4—1662no—
250C4⋊C4—1662no—
251C4⋊C4—1662no—
252C4⋊C4—1662no—
253C4⋊C4—1662no—
254C42—22no—
255C42—1662no—
256C42—1662no—
257C42—1662no—
258C42—1662no—
259C23C23×D8311yescharacteristic
260Q8—1668no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—832no—
279C2×C4—832no—
280C2×C4—832no—
281C2×C4—832no—
282C2×C4—832no—
283C2×C4—1661no—
284C2×C4—1661no—
285C2×C4—1661no—
286C2×C4—1661no—
287C2×C4—1661no—
288C2×C4—1661no—
289C2×C4—1661no—
290C2×C4—1661no—
291C2×C4—1661no—
292C2×C4—1661no—
293C2×C4—1661no—
294C2×C4—1661no—
295C2×C4—1661no—
296C2×C4—1661no—
297C2×C4—1661no—
298C2×C4—1661no—
299C2×C4—1661no—
300C2×C4—1661no—
301C2×C4—1661no—
302C2×C4D4×D8312yes—
303C2×C4Q8×D8312yes—
304C2×C4#1305058912yes—
305C2×C4#1305059012yes—
306C22C2×D4×D8311yescharacteristic
307C22C2×Q8×D8311yescharacteristic
308C22#41×D8311yescharacteristic
309C22C2×#1305058911yescharacteristic
310C22C2×#1305059011yescharacteristic
311C22#1458183911yescharacteristic
312C22#1458184011yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—3321no—
321C4—3321no—
322C4—3321no—
323C4—1662no—
324C4—1662no—
325C4—1662no—
326C4—1662no—
327C4—1662no—
328C2#1912821011yescharacteristic
329C2#1912825311yescharacteristic
330C2#1912831011yescharacteristic
331C2#1912835111yescharacteristic
332C2#1912836611yescharacteristic
333C2#1912838611yescharacteristic
334C2#1912842911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#389×C83C2
hypercenter#389D83
hypocenterC83#2462
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
66. C4⋊Dic83Q8semidirect
168. C83#2462semidirect

Maximal subgroups

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

subgroupindex
C2×#145817822
C2×#145817572
#191276352
#191276322
#191276222
#191276212
#191275962
#191275872
#191275852
#191275842
#191275822
C4×C4⋊Dic832
#389×C832
#246283