Finite Group Databasebeta

← #24910885

Subgroups — #24910885

Order 10624.

604 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581769C211yesmaximal, characteristic, complemented
2C2×#14581769C211yesmaximal, characteristic, complemented
3C2×D4×Dic83C211yesmaximal, characteristic
4C2×#14581748C211yesmaximal, characteristic, complemented
5#19127629C211yesmaximal, characteristic, complemented
6#19127626C211yesmaximal, characteristic, complemented
7#19127615C211yesmaximal, characteristic
8#19127605C211yesmaximal, characteristic, complemented
9#19127600C211yesmaximal, characteristic, complemented
10#19127598C211yesmaximal, characteristic, complemented
11#19127596C211yesmaximal, characteristic, complemented
12#19127594C211yesmaximal, characteristic, complemented
13#19127589C211yesmaximal, characteristic, complemented
14#19127559C211yesmaximal, characteristic, complemented
15#394×C83C211yesmaximal, characteristic
16C22×Dic166C2211yescharacteristic
17C23×Dic83C2211yescharacteristic
18C23×Dic83C2211yescharacteristic
19#14581769—24no—
20#14581769—24no—
21D4×Dic83—24no—
22#14581748—24no—
23C2×C4⋊Dic83C2211yescharacteristic
24C2×C4⋊Dic83C2211yescharacteristic
25C2×C4⋊Dic83C2211yescharacteristic
26C2×Dic83⋊C4C2211yescharacteristic
27C2×Dic83⋊C4C2211yescharacteristic
28C2×Dic83⋊C4C2211yescharacteristic
29C2×Dic83⋊C4C2211yescharacteristic
30C2×Dic83⋊C4C2211yescharacteristic
31C2×Dic83⋊C4C2211yescharacteristic
32C2×C22⋊Dic83C2211yescharacteristic
33C2×C22⋊Dic83C2211yescharacteristic
34C2×C22⋊Dic83C2211yescharacteristic
35C2×C22⋊Dic83C2211yescharacteristic
36C2×C22⋊Dic83C2211yescharacteristic
37C2×C22⋊Dic83C2211yescharacteristic
38C2×C4×Dic83C2211yescharacteristic
39C2×C4×Dic83C2211yescharacteristic
40C2×C4×Dic83C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C83⋊#95C2211yescharacteristic
46C83⋊#95C2211yescharacteristic
47C83⋊#95C2211yescharacteristic
48C22×D4×C83C2211yescharacteristic
49C2×C4⋊C4×C83C2211yescharacteristic
50C2×C22⋊C4×C83C2211yescharacteristic
51C2×C22⋊C4×C83C2211yescharacteristic
52C2×C22⋊C4×C83C2211yescharacteristic
53C2×C22⋊C4×C83C2211yescharacteristic
54#95×C83C2211yescharacteristic
55C2×Dic166—22no—
56C2×Dic166—22no—
57C2×Dic166—22no—
58C22×Dic83—22no—
59C22×Dic83—22no—
60C22×Dic83—22no—
61C22×Dic83—22no—
62C22×Dic83—22no—
63C22×Dic83D414yes—
64C22×Dic83C2311yescharacteristic
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C22×Dic83C2311yescharacteristic
68C22×Dic83C2311yescharacteristic
69C22×Dic83C2311yescharacteristic
70C22×Dic83C2311yescharacteristic
71C22×Dic83C2311yescharacteristic
72C4⋊Dic83—22no—
73C4⋊Dic83—22no—
74C4⋊Dic83—22no—
75Dic83⋊C4—22no—
76Dic83⋊C4—22no—
77Dic83⋊C4—22no—
78Dic83⋊C4—22no—
79Dic83⋊C4—22no—
80Dic83⋊C4D414yescomplemented
81C22⋊Dic83—22no—
82C22⋊Dic83—22no—
83C22⋊Dic83—22no—
84C22⋊Dic83—22no—
85C22⋊Dic83—22no—
86C22⋊Dic83—22no—
87C4×Dic83—22no—
88C4×Dic83—22no—
89C4×Dic83—22no—
90C24×C83C2311yescharacteristic
91C24×C83C2311yescharacteristic
92C2×D4×C83—22no—
93C2×D4×C83—22no—
94C2×D4×C83—22no—
95C22×C4×C83C2311yescharacteristic
96C22×C4×C83C2311yescharacteristic
97C22×C4×C83C2311yescharacteristic
98C22×C4×C83C2311yescharacteristic
99C22×C4×C83C2311yescharacteristic
100C4⋊C4×C83—22no—
101C22⋊C4×C83—22no—
102C22⋊C4×C83—22no—
103C22⋊C4×C83—22no—
104C22⋊C4×C83—22no—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—21no—
111C23×C83—21no—
112C23×C83—21no—
113C23×C83—21no—
114C23×C83—21no—
115C23×C83—21no—
116C23×C83—21no—
117C23×C83C2×D412yes—
118C23×C83#4112yes—
119C23×C83C2411yescharacteristic
120D4×C83—28no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—21no—
133C2×C4×C83—21no—
134C2×C4×C83C2×D412yes—
135C2×C4×C83#4112yes—
136C2×Dic83—21no—
137C2×Dic83—21no—
138C2×Dic83—21no—
139C2×Dic83—21no—
140C2×Dic83—28no—
141C2×Dic83—21no—
142C2×Dic83—21no—
143C2×Dic83—21no—
144C2×Dic83—21no—
145C2×Dic83—21no—
146C2×Dic83—21no—
147C2×Dic83—21no—
148C2×Dic83—21no—
149C2×Dic83—21no—
150C2×Dic83—21no—
151C2×Dic83—21no—
152C2×Dic83—21no—
153C2×Dic83—21no—
154C2×Dic83—21no—
155C2×Dic83—21no—
156C2×Dic83—44no—
157C2×Dic83C2×D412yes—
158C2×Dic83C2×D412yes—
159C2×Dic83C2×D412yes—
160C2×Dic83C2×D412yes—
161C2×Dic83#4112yes—
162Dic166—44no—
163C22×C83—22no—
164C22×C83—22no—
165C22×C83—22no—
166C22×C83—22no—
167C22×C83—22no—
168C22×C83—22no—
169C22×C83—41no—
170C22×C83—41no—
171C22×C83—41no—
172C22×C83—41no—
173C22×C83—41no—
174C22×C83—41no—
175C22×C83—41no—
176C22×C83—41no—
177C22×C83C22×D411yescharacteristic
178C22×C83C22×D411yescharacteristic
179C22×C83C2×#4111yescharacteristic
180C22×C83C2×#4111yescharacteristic
181C22×C83C2×#4111yescharacteristic
182C22×C832−1+411yescharacteristic
183C22×C832−1+411yescharacteristic
184C4×C83—22no—
185C4×C83—22no—
186C4×C83—41no—
187C4×C83—41no—
188C4×C83—41no—
189Dic83—22no—
190Dic83—22no—
191Dic83—41no—
192Dic83—41no—
193Dic83—41no—
194Dic83—41no—
195Dic83—41no—
196Dic83#12114yes—
197C2×C83—42no—
198C2×C83—42no—
199C2×C83C2×#12111yescharacteristic
200C2×C83#52511yescharacteristic
201C2×C83#53611yescharacteristic
202C2×C83#54711yescharacteristic
203C2×C83#54811yescharacteristic
204C2×C83#55211yescharacteristic
205C2×C83#55611yescharacteristic
206#2415—831nomaximal, Sylow
207C83#241511yescharacteristic, complemented, Sylow
208C2×C22⋊Q8—831no—
209C2×C22⋊Q8—831no—
210C2×C4×D4—831no—
211C2×#117—831no—
212#397—831no—
213#397—831no—
214#394—831no—
215#394D8311yescharacteristic
216#391—831no—
217#389—831no—
218#389—831no—
219#389—831no—
220#388—831no—
221#388—831no—
222#380—831no—
223C22×Q8—831no—
224C22×D4C2×D8311yescharacteristic
225C23×C4—831no—
226C23×C4—831no—
227C22⋊Q8—1664no—
228C22⋊Q8—1664no—
229C4×D4—1664no—
230#117—1664no—
231C2×C4⋊C4—831no—
232C2×C4⋊C4—831no—
233C2×C4⋊C4—831no—
234C2×C4⋊C4—831no—
235C2×C4⋊C4—831no—
236C2×C4⋊C4—831no—
237C2×C4⋊C4—831no—
238C2×C4⋊C4—831no—
239C2×C4⋊C4—831no—
240C2×C4⋊C4C2×D8311yescharacteristic
241C2×C22⋊C4—831no—
242C2×C22⋊C4—831no—
243C2×C22⋊C4—831no—
244C2×C22⋊C4—831no—
245C2×C22⋊C4—831no—
246C2×C22⋊C4—831no—
247C2×C22⋊C4C2×D8311yescharacteristic
248C2×C22⋊C4C2×D8311yescharacteristic
249C2×C22⋊C4C2×D8311yescharacteristic
250C2×C22⋊C4C2×D8311yescharacteristic
251C2×C42—831no—
252C2×C42—831no—
253C2×C42—831no—
254#95—831no—
255#95—831no—
256#95—831no—
257#95—831no—
258#95—831no—
259#95—831no—
260#95—831no—
261#95C2×D8311yescharacteristic
262C24C22×D8311yescharacteristic
263C24C22×D8311yescharacteristic
264C2×Q8—1662no—
265C2×Q8—1662no—
266C2×Q8—1662no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C22×C4—831no—
271C22×C4—834no—
272C22×C4—831no—
273C22×C4—831no—
274C22×C4—831no—
275C22×C4—831no—
276C22×C4—831no—
277C22×C4—831no—
278C22×C4—831no—
279C22×C4—1662no—
280C22×C4—1662no—
281C22×C4—1662no—
282C22×C4—1662no—
283C22×C4—1662no—
284C22×C4C22×D8311yescharacteristic
285C22×C4C22×D8311yescharacteristic
286C22×C4C22×D8311yescharacteristic
287C22×C4C22×D8311yescharacteristic
288C22×C4C22×D8311yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—834no—
291C4⋊C4—1662no—
292C4⋊C4—1662no—
293C4⋊C4—1662no—
294C4⋊C4—1662no—
295C4⋊C4—1662no—
296C4⋊C4—1662no—
297C4⋊C4—1662no—
298C4⋊C4—1662no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—1662no—
304C22⋊C4—1662no—
305C22⋊C4—1662no—
306C22⋊C4—1662no—
307C22⋊C4—1662no—
308C22⋊C4—1662no—
309C42—1662no—
310C42—1662no—
311C42—1662no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23D4×D8312yes—
325C23#1305058912yes—
326C23C23×D8311yescharacteristic
327Q8—3324no—
328D4—28no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3324no—
343C2×C4—832no—
344C2×C4—832no—
345C2×C4—832no—
346C2×C4—832no—
347C2×C4—832no—
348C2×C4—1661no—
349C2×C4—1661no—
350C2×C4—1661no—
351C2×C4—1661no—
352C2×C4—1661no—
353C2×C4—1661no—
354C2×C4—1661no—
355C2×C4—1661no—
356C2×C4—1661no—
357C2×C4—1661no—
358C2×C4—1661no—
359C2×C4—1661no—
360C2×C4—1661no—
361C2×C4—1661no—
362C2×C4—1661no—
363C2×C4—1668no—
364C2×C4—1661no—
365C2×C4—1661no—
366C2×C4—1661no—
367C2×C4—1661no—
368C2×C4D4×D8312yes—
369C2×C4#1305058912yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22C2×D4×D8311yescharacteristic
385C22C2×D4×D8311yescharacteristic
386C22#41×D8311yescharacteristic
387C22C2×#1305058911yescharacteristic
388C22C2×#1305058911yescharacteristic
389C22#1458183911yescharacteristic
390C22#1458183911yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—3321no—
397C4—3321no—
398C4—3321no—
399C4—3321no—
400C4—3321no—
401C4—834no—
402C4—1662no—
403C4—1662no—
404C2—42no—
405C2—42no—
406C2#121×D8311yescharacteristic
407C2#1912820711yescharacteristic
408C2#1912827311yescharacteristic
409C2#1912835111yescharacteristic
410C2#1912835711yescharacteristic
411C2#1912838811yescharacteristic
412C2#1912842011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#394×C83C2
prime radicalC22×D4×C83C22
hypercenter#394D83
hypocenterC83#2415
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14581769C2semidirect
2. C2×#14581769C2semidirect
4. C2×#14581748C2semidirect
5. #19127629C2semidirect
6. #19127626C2semidirect
8. #19127605C2semidirect
9. #19127600C2semidirect
10. #19127598C2semidirect
11. #19127596C2semidirect
12. #19127594C2semidirect
13. #19127589C2semidirect
14. #19127559C2semidirect
80. Dic83⋊C4D4semidirect
207. C83#2415semidirect

Maximal subgroups

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

subgroupindex
C2×#145817692
C2×D4×Dic832
C2×#145817482
#191276292
#191276262
#191276152
#191276052
#191276002
#191275982
#191275962
#191275942
#191275892
#191275592
#394×C832
#241583