Finite Group Databasebeta

← #24914039

Subgroups — #24914039

Order 10624.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581785C211yesmaximal, characteristic
2C2×#14581769C211yesmaximal, characteristic
3#19127642C211yesmaximal, characteristic, complemented
4#19127635C211yesmaximal, characteristic, complemented
5#19127633C211yesmaximal, characteristic, complemented
6#19127629C211yesmaximal, characteristic
7#19127622C211yesmaximal, characteristic, complemented
8#19127605C211yesmaximal, characteristic, complemented
9#19127597C211yesmaximal, characteristic, complemented
10#19127589C211yesmaximal, characteristic
11#19127587C211yesmaximal, characteristic, complemented
12#19127576C211yesmaximal, characteristic
13#19127565C211yesmaximal, characteristic, complemented
14#19127562C211yesmaximal, characteristic
15#397×C83C211yesmaximal, characteristic
16C22×Dic166C2211yescharacteristic
17C23×Dic83C2211yescharacteristic
18#14581785—24no—
19#14581769—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×C22⋊Dic83C2211yescharacteristic
31C2×C22⋊Dic83C2211yescharacteristic
32C2×C22⋊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×C22⋊C4×C83C2211yescharacteristic
48C2×C22⋊C4×C83C2211yescharacteristic
49C2×C22⋊C4×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51#95×C83C2211yescharacteristic
52#95×C83C2211yescharacteristic
53C2×Dic166—22no—
54C2×Dic166—22no—
55C2×Dic166—41no—
56C22×Dic83—22no—
57C22×Dic83—22no—
58C22×Dic83—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⋊Dic83—41no—
71Dic83⋊C4—22no—
72Dic83⋊C4—22no—
73Dic83⋊C4—22no—
74Dic83⋊C4—22no—
75Dic83⋊C4—41no—
76Dic83⋊C4—41no—
77C22⋊Dic83—22no—
78C22⋊Dic83—41no—
79C22⋊Dic83D414yes—
80C4×Dic83—22no—
81C4×Dic83—22no—
82C24×C83C2311yescharacteristic
83C22×C4×C83C2311yescharacteristic
84C22×C4×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C22×C4×C83C2311yescharacteristic
87C22×C4×C83C2311yescharacteristic
88C22×C4×C83C2311yescharacteristic
89C4⋊C4×C83—22no—
90C22⋊C4×C83—22no—
91C22⋊C4×C83—22no—
92C22⋊C4×C83—22no—
93C23×C83—21no—
94C23×C83—21no—
95C23×C83—21no—
96C23×C83—21no—
97C23×C83—21no—
98C23×C83—21no—
99C23×C83C2×D412yes—
100C23×C83C2411yescharacteristic
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×C83—21no—
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83#4112yes—
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×Dic83—21no—
133C2×Dic83—21no—
134C2×Dic83—21no—
135C2×Dic83—21no—
136C2×Dic83—21no—
137C2×Dic83—21no—
138C2×Dic83—21no—
139C2×Dic83—21no—
140C2×Dic83—44no—
141C2×Dic83C2×D412yes—
142C2×Dic83C2×D412yes—
143C2×Dic83#4112yes—
144Dic166—44no—
145C22×C83—22no—
146C22×C83—22no—
147C22×C83—22no—
148C22×C83—41no—
149C22×C83—41no—
150C22×C83—41no—
151C22×C83—41no—
152C22×C83C22×D411yescharacteristic
153C22×C83C2×#4111yescharacteristic
154C22×C83C2×#4111yescharacteristic
155C22×C83H(5,𝔽2)11yescharacteristic
156C22×C832−1+411yescharacteristic
157C22×C832−1+411yescharacteristic
158C22×C832−1+411yescharacteristic
159C4×C83—22no—
160C4×C83—41no—
161C4×C83—41no—
162C4×C83—41no—
163C4×C83—41no—
164C4×C83—41no—
165Dic83—22no—
166Dic83—22no—
167Dic83—22no—
168Dic83—41no—
169Dic83—41no—
170Dic83—41no—
171Dic83—41no—
172Dic83—41no—
173C2×C83—42no—
174C2×C83#53611yescharacteristic
175C2×C83#54111yescharacteristic
176C2×C83#54211yescharacteristic
177C2×C83#54611yescharacteristic
178C2×C83#54711yescharacteristic
179C2×C83#55211yescharacteristic
180C2×C83#56311yescharacteristic
181#2698—831nomaximal, Sylow
182C83#269811yescharacteristic, complemented, Sylow
183C2×#126—831no—
184C2×C22⋊Q8—831no—
185#400—831no—
186#398—831no—
187#398—831no—
188#397—831no—
189#397D8311yescharacteristic
190#395—831no—
191#391—831no—
192#389—831no—
193#388—831no—
194#387—831no—
195#385—831no—
196#382—831no—
197#381—831no—
198C22×Q8—831no—
199C23×C4—831no—
200#126—1664no—
201C22⋊Q8—1664no—
202C2×C4⋊C4—831no—
203C2×C4⋊C4—831no—
204C2×C4⋊C4—831no—
205C2×C4⋊C4—831no—
206C2×C4⋊C4—831no—
207C2×C4⋊C4—831no—
208C2×C4⋊C4—831no—
209C2×C4⋊C4—831no—
210C2×C4⋊C4—831no—
211C2×C4⋊C4—831no—
212C2×C4⋊C4C2×D8311yescharacteristic
213C2×C22⋊C4—831no—
214C2×C22⋊C4—831no—
215C2×C22⋊C4—831no—
216C2×C22⋊C4C2×D8311yescharacteristic
217C2×C22⋊C4C2×D8311yescharacteristic
218C2×C22⋊C4C2×D8311yescharacteristic
219C2×C42—831no—
220C2×C42—831no—
221#95—831no—
222#95—831no—
223#95—831no—
224#95—831no—
225#95—831no—
226#95—831no—
227#95—831no—
228#95—831no—
229#95—831no—
230#95—831no—
231#95—831no—
232#95C2×D8311yescharacteristic
233#95C2×D8311yescharacteristic
234#95C2×D8311yescharacteristic
235C24C22×D8311yescharacteristic
236C2×Q8—3321no—
237C2×Q8—1662no—
238C2×Q8—1662no—
239C22×C4—3321no—
240C22×C4—831no—
241C22×C4—831no—
242C22×C4—831no—
243C22×C4—831no—
244C22×C4—831no—
245C22×C4—831no—
246C22×C4—831no—
247C22×C4—831no—
248C22×C4—1662no—
249C22×C4—1662no—
250C22×C4C22×D8311yescharacteristic
251C22×C4C22×D8311yescharacteristic
252C22×C4C22×D8311yescharacteristic
253C22×C4C22×D8311yescharacteristic
254C22×C4C22×D8311yescharacteristic
255C22×C4C22×D8311yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—3321no—
258C4⋊C4—3321no—
259C4⋊C4—3321no—
260C4⋊C4—1662no—
261C4⋊C4—1662no—
262C4⋊C4—1662no—
263C4⋊C4—1662no—
264C4⋊C4—1662no—
265C4⋊C4—1662no—
266C4⋊C4—1662no—
267C22⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—3321no—
271C22⋊C4—834no—
272C22⋊C4—1662no—
273C42—1662no—
274C42—1662no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23D4×D8312yes—
282C23C23×D8311yescharacteristic
283Q8—3324no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—3324no—
302C2×C4—832no—
303C2×C4—832no—
304C2×C4—832no—
305C2×C4—1661no—
306C2×C4—1661no—
307C2×C4—1661no—
308C2×C4—1661no—
309C2×C4—1661no—
310C2×C4—1661no—
311C2×C4—1661no—
312C2×C4—1661no—
313C2×C4—1661no—
314C2×C4—1661no—
315C2×C4—1661no—
316C2×C4—1661no—
317C2×C4—1661no—
318C2×C4—1661no—
319C2×C4—1661no—
320C2×C4—1661no—
321C2×C4—1661no—
322C2×C4—1661no—
323C2×C4—1661no—
324C2×C4—1661no—
325C2×C4—1661no—
326C2×C4#1305058912yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C2×D4×D8311yescharacteristic
335C22#41×D8311yescharacteristic
336C22C2×#1305058911yescharacteristic
337C22#1458183811yescharacteristic
338C22#1458183911yescharacteristic
339C22#1458183911yescharacteristic
340C22#1458183911yescharacteristic
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—3321no—
348C4—3321no—
349C4—3321no—
350C4—3321no—
351C4—3321no—
352C4—1662no—
353C4—1662no—
354C4—1662no—
355C2—42no—
356C2#1912827311yescharacteristic
357C2#1912830811yescharacteristic
358C2#1912832011yescharacteristic
359C2#1912834311yescharacteristic
360C2#1912835111yescharacteristic
361C2#1912838811yescharacteristic
362C2#1912845311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#397×C83C2
prime radicalC24×C83C23
hypercenter#397D83
hypocenterC83#2698
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
3. #19127642C2semidirect
4. #19127635C2semidirect
5. #19127633C2semidirect
7. #19127622C2semidirect
8. #19127605C2semidirect
9. #19127597C2semidirect
11. #19127587C2semidirect
13. #19127565C2semidirect
182. C83#2698semidirect

Maximal subgroups

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

subgroupindex
C2×#145817852
C2×#145817692
#191276422
#191276352
#191276332
#191276292
#191276222
#191276052
#191275972
#191275892
#191275872
#191275762
#191275652
#191275622
#397×C832
#269883