Finite Group Databasebeta

← #24912438

Subgroups — #24912438

Order 10624.

576 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581791C211yesmaximal, characteristic, complemented
2C2×#14581778C211yesmaximal, characteristic
3C2×#14581778C211yesmaximal, characteristic
4C2×#14581757C211yesmaximal, characteristic, complemented
5#19127624C211yesmaximal, characteristic, complemented
6#19127623C211yesmaximal, characteristic, complemented
7#19127623C211yesmaximal, characteristic, complemented
8#19127605C211yesmaximal, characteristic, complemented
9#19127601C211yesmaximal, characteristic
10#19127595C211yesmaximal, characteristic, complemented
11#19127594C211yesmaximal, characteristic, complemented
12#19127591C211yesmaximal, characteristic, complemented
13#19127590C211yesmaximal, characteristic, complemented
14C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
15#396×C83C211yesmaximal, characteristic, complemented
16C22×Dic166C2211yescharacteristic
17C22×Dic166C2211yescharacteristic
18C22×C22⋊D83C2211yescharacteristic
19#14581791—24no—
20#14581778—24no—
21#14581778—24no—
22#14581757—24no—
23C2×C4⋊Dic83C2211yescharacteristic
24C2×C4⋊Dic83C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×Dic83⋊C4C2211yescharacteristic
27C2×Dic83⋊C4C2211yescharacteristic
28C2×Dic83⋊C4C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic
30C2×C22⋊Dic83C2211yescharacteristic
31C2×C22⋊Dic83C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×(C2×D83)⋊C4C2211yescharacteristic
34C2×(C2×D83)⋊C4C2211yescharacteristic
35C2×(C2×D83)⋊C4C2211yescharacteristic
36C2×(C2×D83)⋊C4C2211yescharacteristic
37C2×(C2×D83)⋊C4C2211yescharacteristic
38C2×C4×Dic83C2211yescharacteristic
39C2×C4×Dic83C2211yescharacteristic
40C2×C4×Dic83C2211yescharacteristic
41C2×C4×Dic83C2211yescharacteristic
42C2×C4×Dic83C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C83⋊#95C2211yescharacteristic
46C83⋊#95C2211yescharacteristic
47C83⋊#95C2211yescharacteristic
48C2×C4⋊C4×C83C2211yescharacteristic
49C2×C4⋊C4×C83C2211yescharacteristic
50C2×C4⋊C4×C83C2211yescharacteristic
51C2×C22⋊C4×C83C2211yescharacteristic
52C2×C22⋊C4×C83C2211yescharacteristic
53C2×C22⋊C4×C83C2211yescharacteristic
54#95×C83C2211yescharacteristic
55C23×D83C2311yescharacteristic
56C2×Dic166—22no—
57C2×Dic166—22no—
58C2×Dic166—22no—
59C2×Dic166—22no—
60C2×Dic166—22no—
61C2×Dic166D414yes—
62C2×C22⋊D83—22no—
63C2×C22⋊D83—22no—
64C2×C22⋊D83—22no—
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C22×Dic83C2311yescharacteristic
68C22×Dic83C2311yescharacteristic
69C22×Dic83C2311yescharacteristic
70C22×Dic83C2311yescharacteristic
71C22×Dic83C2311yescharacteristic
72C4⋊Dic83—22no—
73C4⋊Dic83—22no—
74Dic83⋊C4—22no—
75Dic83⋊C4—22no—
76Dic83⋊C4—22no—
77Dic83⋊C4—22no—
78C22⋊Dic83—22no—
79C22⋊Dic83—22no—
80C22⋊Dic83—22no—
81(C2×D83)⋊C4—22no—
82(C2×D83)⋊C4—22no—
83(C2×D83)⋊C4—22no—
84(C2×D83)⋊C4—22no—
85(C2×D83)⋊C4—22no—
86(C2×D83)⋊C4—22no—
87C4×Dic83—22no—
88C4×Dic83—22no—
89C4×Dic83—22no—
90C4×Dic83—22no—
91C4×Dic83D414yes—
92C24×C83C2311yescharacteristic
93C22×C4×C83C2311yescharacteristic
94C22×C4×C83C2311yescharacteristic
95C22×C4×C83C2311yescharacteristic
96C22×C4×C83C2311yescharacteristic
97C22×C4×C83C2311yescharacteristic
98C22×C4×C83C2311yescharacteristic
99C4⋊C4×C83—22no—
100C4⋊C4×C83—22no—
101C4⋊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×C83C2411yescharacteristic
113C22×D83—21no—
114C22×D83—21no—
115C22×D83—21no—
116C22×D83—21no—
117C22×D83—21no—
118C22×D83—21no—
119C22×D83—21no—
120C2×C4×C83—21no—
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×C83—21no—
135C2×C4×C83C2×D412yes—
136C2×C4×C83C2×D412yes—
137C2×C4×C83#4112yes—
138C22⋊D83—44no—
139C2×Dic83—21no—
140C2×Dic83—21no—
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×Dic83C2×D412yes—
155C2×Dic83C2×D412yes—
156C2×Dic83C2×D412yes—
157C2×Dic83C2×D412yes—
158C2×Dic83#4112yes—
159C2×Dic83#4112yes—
160Dic166—28no—
161Dic166—44no—
162C22×C83—41no—
163C22×C83—41no—
164C22×C83—41no—
165C22×C83—41no—
166C22×C83—41no—
167C22×C83—41no—
168C22×C83—41no—
169C22×C83C22×D411yescharacteristic
170C22×C83C22×D411yescharacteristic
171C22×C83C2×#4111yescharacteristic
172C22×C83C2×#4111yescharacteristic
173C22×C83C2×#4111yescharacteristic
174C22×C832−1+411yescharacteristic
175C22×C832−1+411yescharacteristic
176C2×D83—41no—
177C2×D83—41no—
178C2×D83—41no—
179C2×D83—41no—
180C2×D83—41no—
181C2×D83—41no—
182C2×D83—41no—
183C4×C83—22no—
184C4×C83—22no—
185C4×C83—22no—
186C4×C83—41no—
187C4×C83—41no—
188C4×C83—41no—
189Dic83—22no—
190Dic83—22no—
191Dic83—22no—
192Dic83—41no—
193Dic83—41no—
194Dic83—41no—
195Dic83#12114yes—
196C2×C83—81no—
197C2×C83C2×#12111yescharacteristic
198C2×C83#53211yescharacteristic
199C2×C83#53611yescharacteristic
200C2×C83#54811yescharacteristic
201C2×C83#54811yescharacteristic
202C2×C83#55611yescharacteristic
203C2×C83#55611yescharacteristic
204D83—81no—
205#2545—831nomaximal, Sylow
206C83#254511yescharacteristic, complemented, Sylow
207C2×C4⋊Q8—831no—
208C2×#124—831no—
209C2×#124—831no—
210C2×C4×Q8—831no—
211#396—831no—
212#396—831no—
213#396—831no—
214#396D8311yescharacteristic, complemented
215#391—831no—
216#390—831no—
217#388—831no—
218#388—831no—
219#388—831no—
220#388—831no—
221C4×C4⋊C4—831no—
222C22×Q8—831no—
223C22×Q8—831no—
224C22×D4—831no—
225C4⋊Q8—1664no—
226#124—1664no—
227#124—1664no—
228C4×Q8—1664no—
229C2×C4⋊C4—831no—
230C2×C4⋊C4—831no—
231C2×C4⋊C4—831no—
232C2×C4⋊C4—831no—
233C2×C4⋊C4—831no—
234C2×C4⋊C4—831no—
235C2×C4⋊C4C2×D8311yescharacteristic
236C2×C4⋊C4C2×D8311yescharacteristic
237C2×C4⋊C4C2×D8311yescharacteristic
238C2×C22⋊C4—831no—
239C2×C22⋊C4—831no—
240C2×C22⋊C4—831no—
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×C42—831no—
251C2×C42—831no—
252C2×C42—831no—
253C2×C42—831no—
254C2×C42—831no—
255#95—831no—
256#95—831no—
257#95—831no—
258#95—831no—
259#95—831no—
260#95C2×D8311yescharacteristic
261C24—831no—
262C24C22×D8311yescharacteristic
263C2×Q8—834no—
264C2×Q8—1662no—
265C2×Q8—1662no—
266C2×Q8—1662no—
267C2×Q8—1662no—
268C2×Q8—1662no—
269C2×D4—1662no—
270C2×D4—1662no—
271C2×D4—1662no—
272C22×C4—831no—
273C22×C4—831no—
274C22×C4—831no—
275C22×C4—831no—
276C22×C4—831no—
277C22×C4—831no—
278C22×C4—831no—
279C22×C4C22×D8311yescharacteristic
280C22×C4C22×D8311yescharacteristic
281C22×C4C22×D8311yescharacteristic
282C22×C4C22×D8311yescharacteristic
283C22×C4C22×D8311yescharacteristic
284C22×C4C22×D8311yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—1662no—
289C4⋊C4—1662no—
290C4⋊C4—1662no—
291C4⋊C4—1662no—
292C4⋊C4—1662no—
293C4⋊C4—1662no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—1662no—
298C22⋊C4—1662no—
299C22⋊C4—1662no—
300C22⋊C4—1662no—
301C22⋊C4—1662no—
302C22⋊C4—1662no—
303C22⋊C4—1662no—
304C22⋊C4—1662no—
305C22⋊C4—1662no—
306C42—834no—
307C42—1662no—
308C42—1662no—
309C42—1662no—
310C42—1662no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—1661no—
319C23—1661no—
320C23—1661no—
321C23—1661no—
322C23—1661no—
323C23—1661no—
324C23—1661no—
325C23C23×D8311yescharacteristic
326Q8—3324no—
327Q8—1668no—
328D4—3324no—
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—21no—
343C2×C4—21no—
344C2×C4—832no—
345C2×C4—832no—
346C2×C4—832no—
347C2×C4—832no—
348C2×C4—832no—
349C2×C4—832no—
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—1661no—
364C2×C4—1661no—
365C2×C4D4×D8312yes—
366C2×C4D4×D8312yes—
367C2×C4#1305058912yes—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—3321no—
376C22—3321no—
377C22—3321no—
378C22—3321no—
379C22—3321no—
380C22—3321no—
381C22—3321no—
382C22C2×D4×D8311yescharacteristic
383C22C2×D4×D8311yescharacteristic
384C22#41×D8311yescharacteristic
385C22#41×D8311yescharacteristic
386C22C2×#1305058911yescharacteristic
387C22#1458183911yescharacteristic
388C22#1458184011yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—3321no—
396C4—3321no—
397C4—3321no—
398C4—834no—
399C4—1662no—
400C4—1662no—
401C4—1662no—
402C2—81no—
403C2—6641no—
404C2#121×D8311yescharacteristic
405C2#1912824611yescharacteristic
406C2#1912827411yescharacteristic
407C2#1912835711yescharacteristic
408C2#1912836111yescharacteristic
409C2#1912841811yescharacteristic
410C2#1912842211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#396×C83C2
prime radicalC22×C22⋊D83C22
hypercenter#396D83
hypocenterC83#2545
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14581791C2semidirect
4. C2×#14581757C2semidirect
5. #19127624C2semidirect
6. #19127623C2semidirect
7. #19127623C2semidirect
8. #19127605C2semidirect
10. #19127595C2semidirect
11. #19127594C2semidirect
12. #19127591C2semidirect
13. #19127590C2semidirect
14. C4⋊C4×Dic83C2semidirect
15. #396×C83C2semidirect
206. C83#2545semidirect
214. #396D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817912
C2×#145817782
C2×#145817572
#191276242
#191276232
#191276052
#191276012
#191275952
#191275942
#191275912
#191275902
C4⋊C4×Dic832
#396×C832
#254583