Finite Group Databasebeta

← #24912876

Subgroups — #24912876

Order 10624.

412 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127632C211yesmaximal, characteristic
2#19127621C211yesmaximal, characteristic
3#19127621C211yesmaximal, characteristic
4#19127621C211yesmaximal, characteristic
5#19127606C211yesmaximal, characteristic
6#19127605C211yesmaximal, characteristic
7#19127605C211yesmaximal, characteristic
8#19127596C211yesmaximal, characteristic
9#19127585C211yesmaximal, characteristic
10#19127583C211yesmaximal, characteristic
11#19127582C211yesmaximal, characteristic
12#19127582C211yesmaximal, characteristic
13C4×Dic83⋊C4C211yesmaximal, characteristic
14#19127552C211yesmaximal, characteristic
15#389×C83C211yesmaximal, characteristic
16C22×Dic166C2211yescharacteristic
17C22×Dic166C2211yescharacteristic
18C2×Dic83⋊C4C2211yescharacteristic
19C2×Dic83⋊C4C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×C4×Dic83C2211yescharacteristic
27C2×C4×Dic83C2211yescharacteristic
28C2×C4×Dic83C2211yescharacteristic
29C2×C4×Dic83C2211yescharacteristic
30C83⋊#95C2211yescharacteristic
31C83⋊#95C2211yescharacteristic
32C83⋊#95C2211yescharacteristic
33C83⋊#95C2211yescharacteristic
34C83⋊#95C2211yescharacteristic
35C83⋊#95C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C2×C4⋊C4×C83C2211yescharacteristic
45C2×C4⋊C4×C83C2211yescharacteristic
46C2×C4⋊C4×C83C2211yescharacteristic
47C2×C4⋊C4×C83C2211yescharacteristic
48C2×C42×C83C2211yescharacteristic
49#95×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51C2×Dic166—22no—
52C2×Dic166—22no—
53C2×Dic166—22no—
54C2×Dic166—41no—
55C2×Dic166—41no—
56C2×Dic166—41no—
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C22×Dic83C2311yescharacteristic
65Dic83⋊C4—22no—
66Dic83⋊C4—22no—
67Dic83⋊C4—22no—
68Dic83⋊C4—41no—
69Dic83⋊C4—41no—
70Dic83⋊C4—41no—
71Dic83⋊C4Q814yescomplemented
72Dic83⋊C4Q814yescomplemented
73C4×Dic83—22no—
74C4×Dic83—22no—
75C4×Dic83—41no—
76C4×Dic83—41no—
77C22×C4×C83C2311yescharacteristic
78C22×C4×C83C2311yescharacteristic
79C22×C4×C83C2311yescharacteristic
80C22×C4×C83C2311yescharacteristic
81C22×C4×C83C2311yescharacteristic
82C22×C4×C83C2311yescharacteristic
83C22×C4×C83C2311yescharacteristic
84C4⋊C4×C83—22no—
85C4⋊C4×C83—41no—
86C4⋊C4×C83—41no—
87C4⋊C4×C83—41no—
88C42×C83—41no—
89C23×C83C2411yescharacteristic
90C2×C4×C83—21no—
91C2×C4×C83—21no—
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×C83C2×Q812yes—
109C2×C4×C83C2×Q812yes—
110C2×C4×C83#4112yes—
111C2×Dic83—21no—
112C2×Dic83—21no—
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×Dic83C2×Q812yes—
130C2×Dic83C2×Q812yes—
131C2×Dic83C2×Q812yes—
132C2×Dic83C2×Q812yes—
133C2×Dic83#4112yes—
134C2×Dic83#4112yes—
135Dic166—44no—
136Dic166—44no—
137C22×C83C22×Q811yescharacteristic
138C22×C83C22×Q811yescharacteristic
139C22×C83C2×#4111yescharacteristic
140C22×C83C2×#4111yescharacteristic
141C22×C83C2×#4111yescharacteristic
142C22×C83H(5,𝔽2)11yescharacteristic
143C22×C83H(5,𝔽2)11yescharacteristic
144C4×C83—22no—
145C4×C83—22no—
146C4×C83—22no—
147C4×C83—41no—
148C4×C83—41no—
149C4×C83—41no—
150C4×C83—41no—
151Dic83—22no—
152Dic83—22no—
153Dic83—22no—
154Dic83—22no—
155Dic83—22no—
156Dic83—22no—
157Dic83—41no—
158Dic83—41no—
159C2×C83#53311yescharacteristic
160C2×C83#53311yescharacteristic
161C2×C83#53811yescharacteristic
162C2×C83#55111yescharacteristic
163C2×C83#55411yescharacteristic
164C2×C83#55411yescharacteristic
165C2×C83Q8211yescharacteristic
166#2586—831nomaximal, Sylow
167C83#258611yescharacteristic, complemented, Sylow
168#398—831no—
169#395—831no—
170#395—831no—
171#395—831no—
172#391—831no—
173#391—831no—
174#391—831no—
175#389—831no—
176#389D8311yescharacteristic
177#387—831no—
178#387—831no—
179#387—831no—
180#387—831no—
181C4×C4⋊C4—831no—
182C4×C4⋊C4—831no—
183C22×Q8—831no—
184C22×Q8—831no—
185C2×C4⋊C4—831no—
186C2×C4⋊C4—831no—
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⋊C4C2×D8311yescharacteristic
194C2×C4⋊C4C2×D8311yescharacteristic
195C2×C4⋊C4C2×D8311yescharacteristic
196C2×C4⋊C4C2×D8311yescharacteristic
197C2×C42—831no—
198C2×C42—831no—
199C2×C42—831no—
200C2×C42—831no—
201C2×C42C2×D8311yescharacteristic
202#95—831no—
203#95—831no—
204#95—831no—
205#95—831no—
206#95—831no—
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#95C2×D8311yescharacteristic
217#95C2×D8311yescharacteristic
218C2×Q8—3321no—
219C2×Q8—3321no—
220C2×Q8—3321no—
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—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—3321no—
244C4⋊C4—3321no—
245C4⋊C4—3321no—
246C4⋊C4—834no—
247C4⋊C4—834no—
248C4⋊C4—1662no—
249C4⋊C4—1662no—
250C4⋊C4—1662no—
251C42—41no—
252C42—3321no—
253C42—3321no—
254C42—1662no—
255C42—1662no—
256C23C23×D8311yescharacteristic
257Q8—3324no—
258Q8—3324no—
259C2×C4—21no—
260C2×C4—21no—
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—832no—
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×C4Q8×D8312yes—
302C2×C4Q8×D8312yes—
303C2×C4#1305059012yes—
304C22C2×Q8×D8311yescharacteristic
305C22C2×Q8×D8311yescharacteristic
306C22#41×D8311yescharacteristic
307C22#41×D8311yescharacteristic
308C22C2×#1305059011yescharacteristic
309C22#1458183711yescharacteristic
310C22#1458183711yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—3321no—
319C4—3321no—
320C4—1662no—
321C4—1662no—
322C4—1662no—
323C4—1662no—
324C4—1662no—
325C4—1662no—
326C2#1912825511yescharacteristic
327C2#1912825711yescharacteristic
328C2#1912828311yescharacteristic
329C2#1912838011yescharacteristic
330C2#1912840511yescharacteristic
331C2#1912840611yescharacteristic
332C2#1912843111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#389×C83C2
hypercenter#389D83
hypocenterC83#2586
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
71. Dic83⋊C4Q8semidirect
72. Dic83⋊C4Q8semidirect
167. C83#2586semidirect

Maximal subgroups

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

subgroupindex
#191276322
#191276212
#191276062
#191276052
#191275962
#191275852
#191275832
#191275822
C4×Dic83⋊C42
#191275522
#389×C832
#258683