Finite Group Databasebeta

← #24913292

Subgroups — #24913292

Order 10624.

472 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581782C211yesmaximal, characteristic, complemented
2C2×#14581748C211yesmaximal, characteristic
3#19127635C211yesmaximal, characteristic, complemented
4#19127634C211yesmaximal, characteristic, complemented
5#19127632C211yesmaximal, characteristic, complemented
6#19127631C211yesmaximal, characteristic, complemented
7#19127624C211yesmaximal, characteristic
8#19127624C211yesmaximal, characteristic
9#19127624C211yesmaximal, characteristic
10#19127598C211yesmaximal, characteristic, complemented
11#19127596C211yesmaximal, characteristic, complemented
12#19127570C211yesmaximal, characteristic, complemented
13#19127559C211yesmaximal, characteristic
14#19127559C211yesmaximal, characteristic
15#396×C83C211yesmaximal, characteristic
16C23×Dic83C2211yescharacteristic
17#14581782—24no—
18#14581748—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×Dic83⋊C4C2211yescharacteristic
31C2×Dic83⋊C4C2211yescharacteristic
32C2×Dic83⋊C4C2211yescharacteristic
33C2×Dic83⋊C4C2211yescharacteristic
34C2×C22⋊Dic83C2211yescharacteristic
35C2×C22⋊Dic83C2211yescharacteristic
36C2×C22⋊Dic83C2211yescharacteristic
37C2×C4×Dic83C2211yescharacteristic
38C2×C4×Dic83C2211yescharacteristic
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×C22⋊C4×C83C2211yescharacteristic
50C2×C22⋊C4×C83C2211yescharacteristic
51C2×C22⋊C4×C83C2211yescharacteristic
52#95×C83C2211yescharacteristic
53C22×Dic83—22no—
54C22×Dic83—22no—
55C22×Dic83Q814yes—
56C22×Dic83C2311yescharacteristic
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C4⋊Dic83—22no—
65C4⋊Dic83—41no—
66C4⋊Dic83—41no—
67Dic83⋊C4—22no—
68Dic83⋊C4—22no—
69Dic83⋊C4—22no—
70Dic83⋊C4—22no—
71Dic83⋊C4—22no—
72Dic83⋊C4—22no—
73Dic83⋊C4—22no—
74Dic83⋊C4—22no—
75Dic83⋊C4—41no—
76Dic83⋊C4—41no—
77Dic83⋊C4—41no—
78Dic83⋊C4—41no—
79C22⋊Dic83—22no—
80C22⋊Dic83—41no—
81C22⋊Dic83—41no—
82C4×Dic83—22no—
83C4×Dic83D414yes—
84C24×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C22×C4×C83C2311yescharacteristic
87C22×C4×C83C2311yescharacteristic
88C22×C4×C83C2311yescharacteristic
89C22×C4×C83C2311yescharacteristic
90C22×C4×C83C2311yescharacteristic
91C4⋊C4×C83—22no—
92C4⋊C4×C83—41no—
93C4⋊C4×C83—41no—
94C22⋊C4×C83—22no—
95C22⋊C4×C83—41no—
96C22⋊C4×C83—41no—
97C23×C83—21no—
98C23×C83—21no—
99C23×C83—21no—
100C23×C83—21no—
101C23×C83—21no—
102C23×C83—21no—
103C23×C83C2×Q812yes—
104C23×C83C2411yescharacteristic
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—21no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
122C2×C4×C83C2×D412yes—
123C2×Dic83—21no—
124C2×Dic83—21no—
125C2×Dic83—21no—
126C2×Dic83—21no—
127C2×Dic83—28no—
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—21no—
141C2×Dic83—21no—
142C2×Dic83—21no—
143C2×Dic83C2×D412yes—
144C2×Dic83C2×D412yes—
145C2×Dic83C2×Q812yes—
146C2×Dic83C2×Q812yes—
147C2×Dic83#4112yes—
148C22×C83—22no—
149C22×C83—22no—
150C22×C83—22no—
151C22×C83—41no—
152C22×C83—41no—
153C22×C83—41no—
154C22×C83—41no—
155C22×C83C22×D411yescharacteristic
156C22×C83C22×Q811yescharacteristic
157C22×C83C2×#4111yescharacteristic
158C22×C83H(5,𝔽2)11yescharacteristic
159C22×C83H(5,𝔽2)11yescharacteristic
160C22×C832−1+411yescharacteristic
161C22×C832−1+411yescharacteristic
162C4×C83—22no—
163C4×C83—41no—
164C4×C83—41no—
165C4×C83—41no—
166C4×C83—41no—
167C4×C83—41no—
168Dic83—22no—
169Dic83—22no—
170Dic83—41no—
171Dic83—41no—
172Dic83—41no—
173Dic83—41no—
174Dic83—41no—
175Dic83C22⋊Q814yes—
176C2×C83—42no—
177C2×C83C2×C22⋊Q811yescharacteristic
178C2×C83#53711yescharacteristic
179C2×C83#53711yescharacteristic
180C2×C83#54011yescharacteristic
181C2×C83#54111yescharacteristic
182C2×C83#54411yescharacteristic
183C2×C83#54411yescharacteristic
184#2629—831nomaximal, Sylow
185C83#262911yescharacteristic, complemented, Sylow
186C2×#125—831no—
187C2×#117—831no—
188#398—831no—
189#398—831no—
190#398—831no—
191#398—831no—
192#396—831no—
193#396—831no—
194#396—831no—
195#396D8311yescharacteristic
196#389—831no—
197#389—831no—
198#384—831no—
199#380—831no—
200#380—831no—
201C23×C4—831no—
202#125—1664no—
203#117—1664no—
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⋊C4—831no—
213C2×C4⋊C4—831no—
214C2×C4⋊C4—831no—
215C2×C4⋊C4—831no—
216C2×C4⋊C4—831no—
217C2×C4⋊C4—831no—
218C2×C4⋊C4—831no—
219C2×C4⋊C4C2×D8311yescharacteristic
220C2×C4⋊C4C2×D8311yescharacteristic
221C2×C4⋊C4C2×D8311yescharacteristic
222C2×C22⋊C4—831no—
223C2×C22⋊C4—831no—
224C2×C22⋊C4—831no—
225C2×C22⋊C4C2×D8311yescharacteristic
226C2×C22⋊C4C2×D8311yescharacteristic
227C2×C22⋊C4C2×D8311yescharacteristic
228C2×C42—831no—
229C2×C42—831no—
230#95—831no—
231#95—831no—
232#95—831no—
233#95—831no—
234#95—831no—
235#95—831no—
236#95—831no—
237#95C2×D8311yescharacteristic
238C24C22×D8311yescharacteristic
239C22×C4—831no—
240C22×C4—834no—
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—41no—
258C4⋊C4—41no—
259C4⋊C4—3321no—
260C4⋊C4—3321no—
261C4⋊C4—3321no—
262C4⋊C4—3321no—
263C4⋊C4—3321no—
264C4⋊C4—3321no—
265C4⋊C4—1662no—
266C4⋊C4—1662no—
267C4⋊C4—1662no—
268C4⋊C4—1662no—
269C4⋊C4—1662no—
270C4⋊C4—1662no—
271C4⋊C4—1662no—
272C4⋊C4—1662no—
273C4⋊C4—1662no—
274C22⋊C4—22no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—3321no—
278C22⋊C4—3321no—
279C22⋊C4—1662no—
280C42—834no—
281C42—1662no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23Q8×D8312yes—
289C23C23×D8311yescharacteristic
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—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—832no—
308C2×C4—832no—
309C2×C4—832no—
310C2×C4—832no—
311C2×C4—832no—
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—1661no—
327C2×C4—1668no—
328C2×C4—1661no—
329C2×C4—1661no—
330C2×C4—1661no—
331C2×C4—1661no—
332C2×C4D4×D8312yes—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22C2×D4×D8311yescharacteristic
341C22C2×Q8×D8311yescharacteristic
342C22#41×D8311yescharacteristic
343C22#1458183711yescharacteristic
344C22#1458183711yescharacteristic
345C22#1458183911yescharacteristic
346C22#1458183911yescharacteristic
347C4—22no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—3321no—
354C4—3321no—
355C4—3321no—
356C4—3321no—
357C4—3321no—
358C4—834no—
359C4—1662no—
360C4—1662no—
361C2—42no—
362C2C22⋊Q8×D8311yescharacteristic
363C2#1912827811yescharacteristic
364C2#1912828011yescharacteristic
365C2#1912830111yescharacteristic
366C2#1912830811yescharacteristic
367C2#1912833011yescharacteristic
368C2#1912833011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#396×C83C2
prime radicalC24×C83C23
hypercenter#396D83
hypocenterC83#2629
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14581782C2semidirect
3. #19127635C2semidirect
4. #19127634C2semidirect
5. #19127632C2semidirect
6. #19127631C2semidirect
10. #19127598C2semidirect
11. #19127596C2semidirect
12. #19127570C2semidirect
185. C83#2629semidirect

Maximal subgroups

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

subgroupindex
C2×#145817822
C2×#145817482
#191276352
#191276342
#191276322
#191276312
#191276242
#191275982
#191275962
#191275702
#191275592
#396×C832
#262983