Finite Group Databasebeta

← #35422109

Subgroups — #35422109

Order 21248.

810 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D83C211yesmaximal, characteristic
2#24910339C212yesmaximal
3#24908202C211yesmaximal, characteristic, complemented
4#24908037C212yesmaximal, complemented
5#24908031C212yesmaximal, complemented
6#24907552C212yesmaximal
7#24907485C211yesmaximal, characteristic
8#24907363C211yesmaximal, characteristic, complemented
9#24907360C211yesmaximal, characteristic, complemented
10#24907240C211yesmaximal, characteristic
11C83×#1943C211yesmaximal, characteristic, complemented
12C22×C8×D83C2211yescharacteristic
13C2×C4⋊C4×D83C2212yes—
14C2×#14581726C2211yescharacteristic
15C2×#14581725C2212yes—
16#107×D83C418yescomplemented
17C2×#14581724C2211yescharacteristic
18C2×(C2×D83)⋊C8C2211yescharacteristic
19C2×#14581702C2211yescharacteristic
20#19127600C2212yes—
21#19127588—22no—
22#19127582—22no—
23#19127558—22no—
24#19127558C2212yes—
25C4⋊C4×Dic83C2212yes—
26C4×C4⋊Dic83C2212yes—
27C4×(C2×D83)⋊C4C2211yescharacteristic
28#19127548—22no—
29#19127464C2212yes—
30#19127463C2212yes—
31#19127463C2212yes—
32#19127463C2212yes—
33#19127456C2211yescharacteristic
34#19127455C2211yescharacteristic
35C2×#107×C83C2211yescharacteristic
36C2×#106×C83C2211yescharacteristic
37C2×#97×C83C2211yescharacteristic
38#389×C83C2212yes—
39#340×C83C2212yes—
40C22×C4×D83—22no—
41C22×C4×D83C2311yescharacteristic
42C22×C83⋊C8C2311yescharacteristic
43C22×C83⋊C8C2311yescharacteristic
44C2×C8×D83—22no—
45C2×C8×D83—22no—
46C2×C8×D83C2×C414yes—
47C2×C4⋊Dic83—22no—
48C2×C4⋊Dic83C2312yes—
49C2×C4⋊Dic83C2312yes—
50C2×Dic83⋊C4—22no—
51C4⋊C4×D83—24no—
52C4⋊C4×D83C2×C418yes—
53C2×(C2×D83)⋊C4—22no—
54C2×(C2×D83)⋊C4D412yes—
55C2×C4×Dic83—22no—
56C2×C4×Dic83—22no—
57C2×C4×Dic83C2311yescharacteristic
58#14581726C2×C414yes—
59#14581725C2×C418yes—
60#14581724—22no—
61(C2×D83)⋊C8—22no—
62#14581702—22no—
63C83⋊#95—22no—
64C83⋊#95—22no—
65C83⋊#95—22no—
66C83⋊#95—22no—
67C83⋊#95D412yes—
68C22×C8×C83C2311yescharacteristic
69C22×C8×C83C2311yescharacteristic
70C2×C4⋊C4×C83—22no—
71C2×C4⋊C4×C83C2312yes—
72C2×C4⋊C4×C83C2312yes—
73C2×C42×C83C2311yescharacteristic
74#107×C83C2×C414yes—
75#106×C83—22no—
76#97×C83—22no—
77#95×C83—22no—
78C23×D83C2×D411yescharacteristic
79C22×Dic83—22no—
80C22×Dic83—22no—
81C22×Dic83C2×D412yes—
82C22×Dic83C2×D411yescharacteristic
83C2×C4×D83—21no—
84C2×C4×D83—21no—
85C2×C4×D83—21no—
86C2×C4×D83—21no—
87C2×C4×D83—28no—
88C2×C4×D83—82no—
89C2×C4×D83—82no—
90C2×C4×D83C22×C412yes—
91C2×C4×D83#4112yes—
92C2×C83⋊C8—21no—
93C2×C83⋊C8—21no—
94C2×C83⋊C8—21no—
95C2×C83⋊C8—21no—
96C2×C83⋊C8—21no—
97C2×C83⋊C8C22×C412yes—
98C8×D83—28no—
99C4⋊Dic83—22no—
100C4⋊Dic83—22no—
101C4⋊Dic83—22no—
102C4⋊Dic83—82no—
103C4⋊Dic83C22×C414yes—
104Dic83⋊C4—28no—
105(C2×D83)⋊C4—24no—
106(C2×D83)⋊C4—44no—
107C4×Dic83—21no—
108C4×Dic83—21no—
109C4×Dic83—82no—
110C4×Dic83—82no—
111C22×C4×C83—22no—
112C22×C4×C83—22no—
113C22×C4×C83C2×D412yes—
114C22×C4×C83C2411yescharacteristic
115C2×C8×C83—21no—
116C2×C8×C83—21no—
117C2×C8×C83—21no—
118C2×C8×C83C22×C412yes—
119C2×C8×C83#4112yes—
120C2×C8×C83#4112yes—
121C4⋊C4×C83—22no—
122C4⋊C4×C83—22no—
123C4⋊C4×C83—22no—
124C4⋊C4×C83—82no—
125C4⋊C4×C83C22×C414yes—
126C42×C83—21no—
127C42×C83—21no—
128C23×C83C22×D411yescharacteristic
129C22×D83—21no—
130C22×D83—21no—
131C22×D83—22no—
132C22×D83C4×D412yes—
133C22×D83#13714yes—
134C2×C4×C83—24no—
135C2×C4×C83—22no—
136C2×C4×C83—22no—
137C2×C4×C83—22no—
138C2×C4×C83—42no—
139C2×C4×C83—42no—
140C2×C4×C83—42no—
141C2×C4×C83—42no—
142C2×C4×C83—42no—
143C2×C4×C83C23×C411yescharacteristic
144C2×C4×C83C2×#4111yescharacteristic
145C2×C4×C83C2×#4111yescharacteristic
146C2×C4×C83C2×#4111yescharacteristic
147C2×C4×C832−1+411yescharacteristic
148C2×C4×C832−1+411yescharacteristic
149C2×Dic83—21no—
150C2×Dic83—21no—
151C2×Dic83—24no—
152C2×Dic83—22no—
153C2×Dic83—22no—
154C2×Dic83—22no—
155C2×Dic83—42no—
156C2×Dic83—42no—
157C2×Dic83—42no—
158C2×Dic83—42no—
159C2×Dic83—42no—
160C2×Dic83C4×D412yes—
161C4×D83—22no—
162C4×D83—22no—
163C4×D83—22no—
164C4×D83—22no—
165C4×D83—88no—
166C8×C83—41no—
167C8×C83#11714yes—
168C83⋊C8—22no—
169C83⋊C8—41no—
170C22×C83C2×C4×D411yescharacteristic
171C22×C83#54711yescharacteristic
172C22×C83#54711yescharacteristic
173C22×C83C2×#13712yes—
174C22×C83#57612yes—
175C2×D83—24no—
176C2×D83—24no—
177C2×D83—22no—
178C2×D83—22no—
179C2×D83#44114yes—
180C4×C83—42no—
181C4×C83—44no—
182C4×C83—82no—
183C4×C83C2×#11711yescharacteristic
184C4×C83#51911yescharacteristic
185C4×C83#55211yescharacteristic
186C4×C83#55211yescharacteristic
187Dic83—22no—
188Dic83—42no—
189Dic83—44no—
190Dic83—82no—
191#22618—831nomaximal, Sylow
192C2×C83#234411yescharacteristic
193C2×C83C2×#44111yescharacteristic
194C2×C83#294811yescharacteristic
195C2×C83#334612yes—
196C2×C83#334612yes—
197D83—24no—
198C22×#107—831no—
199#2345—832no—
200#1943—831no—
201#1943D8311yescharacteristic, complemented
202#1918—832no—
203#1918—832no—
204#1824—832no—
205#1807—831no—
206#1776—831no—
207#1776—831no—
208#1752—831no—
209C83#2261811yescharacteristic, complemented, Sylow
210C23×C8—831no—
211C22×C4⋊C4—832no—
212C2×#107—831no—
213C2×#107—832no—
214C2×#107—838no—
215C2×#107C2×D8311yescharacteristic
216C2×#106—831no—
217C2×#106C2×D8311yescharacteristic
218C2×C22⋊C8—831no—
219C2×#97—831no—
220C2×#97C2×D8311yescharacteristic
221#389—832no—
222#389C2×D8312yes—
223#387—1662no—
224#387—1662no—
225#380—832no—
226#380—1662no—
227C4×C4⋊C4—832no—
228C4×C4⋊C4—832no—
229C4×C22⋊C4—831no—
230C4×C22⋊C4—1662no—
231#340—832no—
232#340—832no—
233#340—832no—
234#340—832no—
235#340C2×D8312yes—
236#336—831no—
237#336—831no—
238C23×C4—831no—
239C23×C4—1662no—
240C22×C8—831no—
241C22×C8—834no—
242C22×C8—831no—
243C22×C8—1662no—
244C22×C8—1662no—
245C22×C8C22×D8311yescharacteristic
246C22×C8C22×D8311yescharacteristic
247C2×C4⋊C4—22no—
248C2×C4⋊C4—832no—
249C2×C4⋊C4—838no—
250C2×C4⋊C4—832no—
251C2×C4⋊C4—1664no—
252C2×C4⋊C4—1662no—
253C2×C4⋊C4—1662no—
254C2×C4⋊C4C22×D8312yes—
255C2×C4⋊C4C22×D8312yes—
256C2×C22⋊C4—832no—
257C2×C22⋊C4—1662no—
258C2×C42—831no—
259C2×C42—1662no—
260C2×C42—1662no—
261C2×C42C22×D8311yescharacteristic
262#107—834no—
263#107—838no—
264#107C4×D8314yes—
265#106—22no—
266#106—1662no—
267C22⋊C8—1662no—
268#97—22no—
269#97—1662no—
270#95—22no—
271#95—832no—
272#95—1662no—
273#95—1662no—
274#95—1662no—
275#95—1662no—
276C24—831no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—831no—
280C22×C4—832no—
281C22×C4—832no—
282C22×C4—832no—
283C22×C4—6642no—
284C22×C4—6642no—
285C22×C4—1668no—
286C22×C4—1662no—
287C22×C4—1662no—
288C22×C4—1661no—
289C22×C4—1661no—
290C22×C4—1661no—
291C22×C4—1661no—
292C22×C4D4×D8312yes—
293C22×C4C23×D8311yescharacteristic
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—832no—
298C2×C8—1661no—
299C2×C8—1661no—
300C2×C8—1661no—
301C2×C8—1661no—
302C2×C8—1661no—
303C2×C8—1668no—
304C2×C8C2×C4×D8312yes—
305C2×C8#1305058912yes—
306C2×C8#1305059112yes—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—82no—
311C4⋊C4—834no—
312C4⋊C4—6642no—
313C4⋊C4—1668no—
314C4⋊C4—1662no—
315C4⋊C4—1662no—
316C4⋊C4—1662no—
317C4⋊C4C2×C4×D8314yes—
318C22⋊C4—3324no—
319C22⋊C4—1664no—
320C42—21no—
321C42—21no—
322C42—6642no—
323C42—6642no—
324C42—1661no—
325C42—1661no—
326C23—832no—
327C23—834no—
328C23—1661no—
329C23—1661no—
330C23—1662no—
331C23C2×D4×D8311yescharacteristic
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—3322no—
342C2×C4—3322no—
343C2×C4—3322no—
344C2×C4—3322no—
345C2×C4—3322no—
346C2×C4—832no—
347C2×C4—6648no—
348C2×C4—1662no—
349C2×C4—1664no—
350C2×C4—1662no—
351C2×C4—1662no—
352C2×C4—1661no—
353C2×C4—1661no—
354C2×C4—1662no—
355C2×C4—1662no—
356C2×C4—1662no—
357C2×C4—1662no—
358C2×C4C22×C4×D8311yescharacteristic
359C2×C4#41×D8311yescharacteristic
360C2×C4C2×#1305058911yescharacteristic
361C2×C4C2×#1305059111yescharacteristic
362C2×C4#1458183911yescharacteristic
363C2×C4#1458184011yescharacteristic
364C8—41no—
365C8—3321no—
366C8—1662no—
367C8#1458175014yes—
368C22—834no—
369C22—1662no—
370C22—1664no—
371C22—1664no—
372C22—1662no—
373C22C4×D4×D8311yescharacteristic
374C22#1912835111yescharacteristic
375C22#1912835411yescharacteristic
376C22#137×D8312yes—
377C22#1912850512yes—
378C4—44no—
379C4—42no—
380C4—82no—
381C4—3324no—
382C4—3322no—
383C4—6642no—
384C4—1662no—
385C4C2×#1458175011yescharacteristic
386C4#1912817711yescharacteristic
387C4#1912838511yescharacteristic
388C4#1912838911yescharacteristic
389C2—1664no—
390C2#2491033111yescharacteristic
391C2#441×D8311yescharacteristic
392C2#2491631211yescharacteristic
393C2#2491994312yes—
394C2#2491994712yes—
subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1943C2
socleC23×C83C22×D4
prime radicalC23×D83C2×D4
cosocleC22×C4×C83C24
hypercenter#1943D83
hypocenterC83#22618
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
3. #24908202C2semidirect
4. #24908037C2semidirect
5. #24908031C2semidirect
8. #24907363C2semidirect
9. #24907360C2semidirect
11. C83×#1943C2semidirect
16. #107×D83C4semidirect
201. #1943D83semidirect
209. C83#22618semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D832
#249103392
#249082022
#249080372
#249080312
#249075522
#249074852
#249073632
#249073602
#249072402
C83×#19432
#2261883