Finite Group Databasebeta

← #24914249

Subgroups — #24914249

Order 10624.

432 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581791C211yesmaximal, characteristic
2C2×#14581783C211yesmaximal, characteristic
3#19127642C211yesmaximal, characteristic
4#19127635C211yesmaximal, characteristic
5#19127632C211yesmaximal, characteristic
6#19127622C211yesmaximal, characteristic
7#19127622C211yesmaximal, characteristic
8#19127605C211yesmaximal, characteristic
9#19127605C211yesmaximal, characteristic
10#19127598C211yesmaximal, characteristic
11#19127586C211yesmaximal, characteristic
12#19127586C211yesmaximal, characteristic
13#19127583C211yesmaximal, characteristic
14#19127582C211yesmaximal, characteristic
15#400×C83C211yesmaximal, characteristic
16C22×Dic166C2211yescharacteristic
17C22×Dic166C2211yescharacteristic
18#14581791—24no—
19#14581783—24no—
20C2×C4⋊Dic83C2211yescharacteristic
21C2×C4⋊Dic83C2211yescharacteristic
22C2×C4⋊Dic83C2211yescharacteristic
23C2×C4⋊Dic83C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×Dic83⋊C4C2211yescharacteristic
27C2×Dic83⋊C4C2211yescharacteristic
28C2×Dic83⋊C4C2211yescharacteristic
29C2×Dic83⋊C4C2211yescharacteristic
30C2×Dic83⋊C4C2211yescharacteristic
31C2×Dic83⋊C4C2211yescharacteristic
32C2×C4×Dic83C2211yescharacteristic
33C2×C4×Dic83C2211yescharacteristic
34C2×C4×Dic83C2211yescharacteristic
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
48#95×C83C2211yescharacteristic
49#95×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51#95×C83C2211yescharacteristic
52#95×C83C2211yescharacteristic
53C2×Dic166—22no—
54C2×Dic166—22no—
55C2×Dic166—22no—
56C2×Dic166—22no—
57C2×Dic166—41no—
58C2×Dic166—41no—
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C22×Dic83C2311yescharacteristic
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C4⋊Dic83—22no—
68C4⋊Dic83—22no—
69C4⋊Dic83—22no—
70C4⋊Dic83D414yes—
71Dic83⋊C4—22no—
72Dic83⋊C4—22no—
73Dic83⋊C4—22no—
74Dic83⋊C4—22no—
75Dic83⋊C4—41no—
76Dic83⋊C4—41no—
77Dic83⋊C4—41no—
78Dic83⋊C4Q814yescomplemented
79C4×Dic83—22no—
80C4×Dic83—22no—
81C4×Dic83—41no—
82C22×C4×C83C2311yescharacteristic
83C22×C4×C83C2311yescharacteristic
84C22×C4×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C22×C4×C83C2311yescharacteristic
87C22×C4×C83C2311yescharacteristic
88C22×C4×C83C2311yescharacteristic
89C4⋊C4×C83—22no—
90C4⋊C4×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×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83C2×D412yes—
112C2×C4×C83C2×Q812yes—
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—44no—
138Dic166—44no—
139C22×C83C22×D411yescharacteristic
140C22×C83C22×Q811yescharacteristic
141C22×C83C2×#4111yescharacteristic
142C22×C83H(5,𝔽2)11yescharacteristic
143C22×C832−1+411yescharacteristic
144C22×C832−1+411yescharacteristic
145C22×C832−1+411yescharacteristic
146C4×C83—22no—
147C4×C83—22no—
148C4×C83—41no—
149C4×C83—41no—
150C4×C83—41no—
151C4×C83—41no—
152C4×C83—41no—
153Dic83—22no—
154Dic83—22no—
155Dic83—22no—
156Dic83—22no—
157Dic83—22no—
158Dic83—41no—
159Dic83—41no—
160Dic83—41no—
161C2×C83#53611yescharacteristic
162C2×C83#54111yescharacteristic
163C2×C83#54411yescharacteristic
164C2×C83#54611yescharacteristic
165C2×C83D4×Q811yescharacteristic
166C2×C83#55711yescharacteristic
167C2×C83#56311yescharacteristic
168#2713—831nomaximal, Sylow
169C83#271311yescharacteristic, complemented, Sylow
170C2×C4⋊Q8—831no—
171C2×#125—831no—
172#400—831no—
173#400D8311yescharacteristic
174#398—831no—
175#398—831no—
176#395—831no—
177#395—831no—
178#391—831no—
179#391—831no—
180#389—831no—
181#387—831no—
182#387—831no—
183#387—831no—
184#387—831no—
185C22×Q8—831no—
186C22×Q8—831no—
187C4⋊Q8—1664no—
188#125—1664no—
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⋊C4—831no—
199C2×C4⋊C4—831no—
200C2×C4⋊C4—831no—
201C2×C4⋊C4C2×D8311yescharacteristic
202C2×C4⋊C4C2×D8311yescharacteristic
203C2×C42—831no—
204C2×C42—831no—
205C2×C42—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#95—831no—
217#95C2×D8311yescharacteristic
218#95C2×D8311yescharacteristic
219#95C2×D8311yescharacteristic
220#95C2×D8311yescharacteristic
221#95C2×D8311yescharacteristic
222C2×Q8—3321no—
223C2×Q8—3321no—
224C2×Q8—1662no—
225C2×Q8—1662no—
226C2×Q8—1662no—
227C2×Q8—1662no—
228C22×C4—831no—
229C22×C4—831no—
230C22×C4—831no—
231C22×C4—831no—
232C22×C4—831no—
233C22×C4—831no—
234C22×C4—831no—
235C22×C4—831no—
236C22×C4C22×D8311yescharacteristic
237C22×C4C22×D8311yescharacteristic
238C22×C4C22×D8311yescharacteristic
239C22×C4C22×D8311yescharacteristic
240C22×C4C22×D8311yescharacteristic
241C22×C4C22×D8311yescharacteristic
242C22×C4C22×D8311yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—3321no—
246C4⋊C4—3321no—
247C4⋊C4—3321no—
248C4⋊C4—834no—
249C4⋊C4—834no—
250C4⋊C4—1662no—
251C4⋊C4—1662no—
252C4⋊C4—1662no—
253C4⋊C4—1662no—
254C4⋊C4—1662no—
255C4⋊C4—1662no—
256C4⋊C4—1662no—
257C42—3321no—
258C42—1662no—
259C42—1662no—
260C23C23×D8311yescharacteristic
261Q8—3324no—
262Q8—3324no—
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—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—832no—
283C2×C4—832no—
284C2×C4—832no—
285C2×C4—832no—
286C2×C4—832no—
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×C4—1661no—
303C2×C4—1661no—
304C2×C4—1661no—
305C2×C4—1661no—
306C2×C4D4×D8312yes—
307C2×C4Q8×D8312yes—
308C22C2×D4×D8311yescharacteristic
309C22C2×Q8×D8311yescharacteristic
310C22#41×D8311yescharacteristic
311C22#1458183811yescharacteristic
312C22#1458183911yescharacteristic
313C22#1458183911yescharacteristic
314C22#1458183911yescharacteristic
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—3321no—
323C4—3321no—
324C4—3321no—
325C4—1662no—
326C4—1662no—
327C4—1662no—
328C4—1662no—
329C4—1662no—
330C2#1912827311yescharacteristic
331C2#1912830811yescharacteristic
332C2#1912833111yescharacteristic
333C2#1912834411yescharacteristic
334C2#1912836411yescharacteristic
335C2#1912842811yescharacteristic
336C2#1912845311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#400×C83C2
hypercenter#400D83
hypocenterC83#2713
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
78. Dic83⋊C4Q8semidirect
169. C83#2713semidirect

Maximal subgroups

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

subgroupindex
C2×#145817912
C2×#145817832
#191276422
#191276352
#191276322
#191276222
#191276052
#191275982
#191275862
#191275832
#191275822
#400×C832
#271383