Finite Group Databasebeta

← #35302807

Subgroups — #35302807

Order 21248.

386 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24908423C211yesmaximal, characteristic
2#24908386C211yesmaximal, characteristic
3#24907332C211yesmaximal, characteristic
4C2×#19127448C211yesmaximal, characteristic
5#24905346C211yesmaximal, characteristic
6#24905297C211yesmaximal, characteristic
7C83×#1947C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9C2×C4⋊(C83⋊C8)C2211yescharacteristic
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×#14581715—21no—
12C2×#14581715—21no—
13C2×#14581703—21no—
14C2×C4×C83⋊C8C2211yescharacteristic
15#19127463—21no—
16#19127463—21no—
17#19127456—21no—
18#19127448C414yescomplemented
19C2×#107×C83—21no—
20C2×C4⋊C8×C83C2211yescharacteristic
21#384×C83C2211yescharacteristic
22C4×C4⋊C4×C83C2211yescharacteristic
23#340×C83—21no—
24C22×Dic166—21no—
25C22×C83⋊C8—21no—
26C22×C83⋊C8—21no—
27C22×C83⋊C8D411yescharacteristic
28C22×C83⋊C8D411yescharacteristic
29#14581792—21no—
30#14581792—21no—
31#14581792—21no—
32#14581792C2×C412yes—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83—21no—
35C4⋊(C83⋊C8)—21no—
36C4⋊(C83⋊C8)—21no—
37C4⋊(C83⋊C8)—21no—
38C4⋊(C83⋊C8)C2×C412yes—
39#14581715—42no—
40#14581715—42no—
41#14581703—42no—
42C4×C83⋊C8—21no—
43C4×C83⋊C8—21no—
44C22×C8×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83—21no—
48C2×C4⋊C4×C83D411yescharacteristic
49C2×C4⋊C4×C83D411yescharacteristic
50C2×C42×C83—21no—
51C2×C42×C83C2311yescharacteristic
52#107×C83—42no—
53C4⋊C8×C83—21no—
54C4⋊C8×C83C2×C412yes—
55#95×C83—21no—
56C2×Dic166—22no—
57C2×Dic166—41no—
58C2×Dic166—41no—
59C2×Dic166—41no—
60C2×Dic166—41no—
61C2×Dic166—41no—
62C22×Dic83—41no—
63C2×C83⋊C8—21no—
64C2×C83⋊C8—21no—
65C2×C83⋊C8—22no—
66C2×C83⋊C8—21no—
67C2×C83⋊C8—21no—
68C2×C83⋊C8—21no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8—41no—
72C2×C83⋊C8—41no—
73C2×C83⋊C8—41no—
74C2×C83⋊C8Q1612yes—
75C4⋊Dic83—22no—
76C4⋊Dic83—22no—
77C4⋊Dic83—41no—
78C4⋊Dic83—41no—
79C22×C4×C83—21no—
80C22×C4×C83—21no—
81C22×C4×C83—41no—
82C22×C4×C83C2×D411yescharacteristic
83C22×C4×C83C2×D411yescharacteristic
84C22×C4×C83#4111yescharacteristic
85C2×C8×C83—22no—
86C2×C8×C83—41no—
87C2×C8×C83—41no—
88C4⋊C4×C83—21no—
89C4⋊C4×C83—21no—
90C4⋊C4×C83—21no—
91C4⋊C4×C83—21no—
92C4⋊C4×C83—41no—
93C4⋊C4×C83—41no—
94C4⋊C4×C83—41no—
95C4⋊C4×C83—41no—
96C4⋊C4×C83—81no—
97C42×C83—41no—
98C42×C83—41no—
99C42×C83C22×C411yescharacteristic
100C42×C83#4111yescharacteristic
101C42×C83#4111yescharacteristic
102C42×C83#4111yescharacteristic
103C23×C83#12111yescharacteristic
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—41no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—81no—
113C2×C4×C83—81no—
114C2×C4×C83—81no—
115C2×C4×C83#11711yescharacteristic
116C2×C4×C83C4×D411yescharacteristic
117C2×C4×C83C4×D411yescharacteristic
118C2×C4×C83#12311yescharacteristic
119C2×C4×C83#12411yescharacteristic
120C2×C4×C83#12611yescharacteristic
121C2×C4×C83C2×Q1611yescharacteristic
122C2×C4×C83#13511yescharacteristic
123C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C83#13711yescharacteristic
128C2×C4×C83#13711yescharacteristic
129C2×Dic83—42no—
130C2×Dic83—81no—
131C2×Dic83—81no—
132Dic166—42no—
133Dic166—42no—
134Dic166—81no—
135Dic166—81no—
136C8×C83—42no—
137C83⋊C8—22no—
138C83⋊C8—42no—
139C83⋊C8—41no—
140C83⋊C8—81no—
141C22×C83#38811yescharacteristic
142C22×C83#46211yescharacteristic
143C22×C83#46311yescharacteristic
144C22×C83#46811yescharacteristic
145C22×C83#46911yescharacteristic
146C22×C83#47111yescharacteristic
147C22×C83#47311yescharacteristic
148C4×C83—21no—
149C4×C83—21no—
150C4×C83—81no—
151C4×C83—81no—
152C4×C83—161no—
153C4×C83C4×Q1611yescharacteristic
154C4×C83#44011yescharacteristic
155C4×C83#44011yescharacteristic
156C4×C83#44211yescharacteristic
157C4×C83#48411yescharacteristic
158C4×C83#48511yescharacteristic
159C4×C83#48911yescharacteristic
160C4×C83#49011yescharacteristic
161Dic83—82no—
162#9574—831nomaximal, Sylow
163C2×C83#169211yescharacteristic
164C2×C83#169411yescharacteristic
165C2×C83#169911yescharacteristic
166C2×C83#170111yescharacteristic
167C2×C83#192811yescharacteristic
168C2×C83#193011yescharacteristic
169C2×C83#193611yescharacteristic
170#1990—831no—
171#1981—831no—
172#1947D8311yescharacteristic
173#1770—831no—
174C2×#332—831no—
175#1296—831no—
176#1277—831no—
177C83#957411yescharacteristic, complemented, Sylow
178C2×C4⋊Q8—831no—
179C2×#107—21no—
180C2×C4⋊C8—831no—
181C2×C4⋊C8—831no—
182C2×C4⋊C8C2×D8311yescharacteristic
183C2×#103—1661no—
184C2×#103—1661no—
185C2×#97—1661no—
186C2×C4×C8—831no—
187#384C2×D8311yescharacteristic
188C4×C4⋊C4C2×D8311yescharacteristic
189#340—21no—
190#340—1661no—
191#340—1661no—
192#336—1661no—
193#332—834no—
194C22×Q8—1661no—
195C22×C8—21no—
196C22×C8—831no—
197C22×C8—831no—
198C22×C8—1661no—
199C22×C8—1661no—
200C4⋊Q8—832no—
201C4⋊Q8—1661no—
202C4⋊Q8—1661no—
203C4⋊Q8—1661no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—1661no—
208C2×C4⋊C4—1661no—
209C2×C4⋊C4C22⋊D8311yescharacteristic
210C2×C4⋊C4C22⋊D8311yescharacteristic
211C2×C42—21no—
212C2×C42C22×D8311yescharacteristic
213#107—42no—
214C4⋊C8—21no—
215C4⋊C8—832no—
216C4⋊C8—1661no—
217C4⋊C8—1661no—
218C4⋊C8—1661no—
219C4⋊C8C4×D8312yes—
220#103—3322no—
221#103—3322no—
222#97—3322no—
223C4×C8—1661no—
224C4×C8—1661no—
225#95—21no—
226C2×Q8—3321no—
227C2×Q8—3321no—
228C2×Q8—3321no—
229C2×Q8—3321no—
230C2×Q8—3321no—
231C2×Q8—1662no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—41no—
235C22×C4—3321no—
236C22×C4D4×D8311yescharacteristic
237C22×C4C2×C22⋊D8311yescharacteristic
238C22×C4#1305058911yescharacteristic
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—3321no—
243C2×C8—3321no—
244C2×C8—3321no—
245C2×C8—3321no—
246C2×C8—3321no—
247C2×C8—832no—
248C2×C8—1661no—
249C2×C8—1661no—
250C2×C8—1661no—
251C2×C8—1662no—
252C2×C8—1661no—
253C2×C8—1661no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C4⋊C4—3321no—
264C4⋊C4—3321no—
265C4⋊C4—1662no—
266C4⋊C4—1662no—
267C42—41no—
268C42—41no—
269C42C2×C4×D8311yescharacteristic
270C42#1305059011yescharacteristic
271C42#1305059111yescharacteristic
272C42#1305059111yescharacteristic
273C23#1458176411yescharacteristic
274Q8—3322no—
275Q8—3322no—
276Q8—6641no—
277Q8—6641no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—3322no—
290C2×C4—6641no—
291C2×C4—6641no—
292C2×C4#1458175011yescharacteristic
293C2×C4C4×C22⋊D8311yescharacteristic
294C2×C4#1458175411yescharacteristic
295C2×C4#1458177711yescharacteristic
296C2×C4#1458178111yescharacteristic
297C2×C4#1458178711yescharacteristic
298C2×C4Q16×D8311yescharacteristic
299C2×C4#1458181111yescharacteristic
300C2×C4#1458181611yescharacteristic
301C2×C4#1458181711yescharacteristic
302C2×C4#1458181711yescharacteristic
303C2×C4#1458181811yescharacteristic
304C2×C4#1458182311yescharacteristic
305C2×C4#1458182411yescharacteristic
306C8—42no—
307C8—3321no—
308C8—3322no—
309C8—6641no—
310C8—1662no—
311C22#1912759111yescharacteristic
312C22#1912790911yescharacteristic
313C22#1912791411yescharacteristic
314C22#1912794911yescharacteristic
315C22#1912795211yescharacteristic
316C22#1912796211yescharacteristic
317C22#1912797411yescharacteristic
318C4—21no—
319C4—21no—
320C4—81no—
321C4—81no—
322C4—161no—
323C4—6642no—
324C4#1912779511yescharacteristic
325C4#1912779911yescharacteristic
326C4#1912780011yescharacteristic
327C4#1912781111yescharacteristic
328C4#1912803811yescharacteristic
329C4#1912804411yescharacteristic
330C4#1912806311yescharacteristic
331C4#1912806711yescharacteristic
332C2#2490697111yescharacteristic
333C2#2490697911yescharacteristic
334C2#2490700811yescharacteristic
335C2#2490702211yescharacteristic
336C2#2490810311yescharacteristic
337C2#2490811711yescharacteristic
338C2#2490815911yescharacteristic
subgroupG/H
centerC23#14581764
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1947C2
socle, prime radicalC23×C83#121
cosocleC2×C42×C83C23
hypercenter#1947D83
hypocenterC83#9574
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
18. #19127448C4semidirect
177. C83#9574semidirect

Maximal subgroups

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

subgroupindex
#249084232
#249083862
#249073322
C2×#191274482
#249053462
#249052972
C83×#19472
#957483