Finite Group Databasebeta

← #35308988

Subgroups — #35308988

Order 21248.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24908423C211yesmaximal, characteristic
2#24908411C211yesmaximal, characteristic
3#24908182C211yesmaximal, characteristic
4C2×#19127451C211yesmaximal, characteristic
5C2×#19127449C211yesmaximal, characteristic
6#24905346C211yesmaximal, characteristic
7C83×#1948C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9C2×C4⋊(C83⋊C8)—21no—
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×C4⋊(C83⋊C8)C2211yescharacteristic
12C2×C4×C83⋊C8C2211yescharacteristic
13#19127463—21no—
14#19127463—21no—
15#19127463—21no—
16#19127463—21no—
17#19127456—21no—
18#19127451—22no—
19#19127449—22no—
20C2×#106×C83—21no—
21C2×C4⋊C8×C83C2211yescharacteristic
22#384×C83C2211yescharacteristic
23C4×C4⋊C4×C83C2211yescharacteristic
24#340×C83—21no—
25C22×Dic166—21no—
26C22×C83⋊C8—21no—
27C22×C83⋊C8—21no—
28C22×C83⋊C8D411yescharacteristic
29C22×C83⋊C8D411yescharacteristic
30#14581792—21no—
31#14581792—21no—
32#14581792—21no—
33#14581792Q812yes—
34C2×C4⋊Dic83—21no—
35C2×C4⋊Dic83—21no—
36C4⋊(C83⋊C8)—21no—
37C4⋊(C83⋊C8)—21no—
38C4⋊(C83⋊C8)—21no—
39C4⋊(C83⋊C8)—21no—
40C4⋊(C83⋊C8)—42no—
41C4×C83⋊C8—21no—
42C4×C83⋊C8—21no—
43C22×C8×C83—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C4⋊C4×C83D411yescharacteristic
49C2×C42×C83—21no—
50C2×C42×C83C2311yescharacteristic
51#106×C83—42no—
52C4⋊C8×C83—21no—
53C4⋊C8×C83D412yes—
54#95×C83—21no—
55C2×Dic166—22no—
56C2×Dic166—41no—
57C2×Dic166—81no—
58C2×Dic166—81no—
59C22×Dic83—41no—
60C2×C83⋊C8—21no—
61C2×C83⋊C8—21no—
62C2×C83⋊C8—21no—
63C2×C83⋊C8—21no—
64C2×C83⋊C8—21no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8—41no—
68C2×C83⋊C8—41no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8SD1612yes—
72C4⋊Dic83—22no—
73C4⋊Dic83—22no—
74C4⋊Dic83—41no—
75C4⋊Dic83—41no—
76C22×C4×C83—21no—
77C22×C4×C83—21no—
78C22×C4×C83—41no—
79C22×C4×C83C2×D411yescharacteristic
80C22×C4×C83C2×D411yescharacteristic
81C22×C4×C83#4111yescharacteristic
82C2×C8×C83—22no—
83C2×C8×C83—41no—
84C2×C8×C83—41no—
85C4⋊C4×C83—21no—
86C4⋊C4×C83—21no—
87C4⋊C4×C83—21no—
88C4⋊C4×C83—41no—
89C4⋊C4×C83—41no—
90C4⋊C4×C83—41no—
91C4⋊C4×C83—41no—
92C4⋊C4×C83—81no—
93C4⋊C4×C83SD1612yes—
94C42×C83—41no—
95C42×C83—41no—
96C42×C83C2×D411yescharacteristic
97C42×C83C2×Q811yescharacteristic
98C42×C83#4111yescharacteristic
99C42×C83#4111yescharacteristic
100C23×C83#12111yescharacteristic
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—22no—
104C2×C4×C83—41no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—41no—
109C2×C4×C83—81no—
110C2×C4×C83—81no—
111C2×C4×C83—81no—
112C2×C4×C83#12111yescharacteristic
113C2×C4×C83#12111yescharacteristic
114C2×C4×C83C22⋊Q811yescharacteristic
115C2×C4×C83C22⋊Q811yescharacteristic
116C2×C4×C83C22⋊Q811yescharacteristic
117C2×C4×C83#12611yescharacteristic
118C2×C4×C83C2×SD1611yescharacteristic
119C2×C4×C83C2×SD1611yescharacteristic
120C2×C4×C83#13511yescharacteristic
121C2×C4×C83#13511yescharacteristic
122C2×C4×C83#13711yescharacteristic
123C2×C4×C83#13711yescharacteristic
124C2×C4×C83#13711yescharacteristic
125C2×C4×C83#13711yescharacteristic
126C2×Dic83—42no—
127C2×Dic83—81no—
128C2×Dic83—81no—
129Dic166—82no—
130Dic166—82no—
131C8×C83—42no—
132C83⋊C8—22no—
133C83⋊C8—41no—
134C83⋊C8—81no—
135C83⋊C8—81no—
136C22×C83#39611yescharacteristic
137C22×C83#46111yescharacteristic
138C22×C83#46411yescharacteristic
139C22×C83#46511yescharacteristic
140C22×C83#47011yescharacteristic
141C22×C83#47111yescharacteristic
142C22×C83#47211yescharacteristic
143C4×C83—21no—
144C4×C83—21no—
145C4×C83—42no—
146C4×C83—81no—
147C4×C83—161no—
148C4×C83#46111yescharacteristic
149C4×C83#46411yescharacteristic
150C4×C83#46511yescharacteristic
151C4×C83#47011yescharacteristic
152C4×C83#47511yescharacteristic
153C4×C83#47511yescharacteristic
154C4×C83#47911yescharacteristic
155C4×C83#47911yescharacteristic
156Dic83—82no—
157#10597—831nomaximal, Sylow
158C2×C83#167111yescharacteristic
159C2×C83#167811yescharacteristic
160C2×C83#169511yescharacteristic
161C2×C83#170411yescharacteristic
162C2×C83#206311yescharacteristic
163C2×C83#206611yescharacteristic
164C2×C83#206611yescharacteristic
165#1990—831no—
166#1987—831no—
167#1948D8311yescharacteristic
168#1939—831no—
169C2×#334—831no—
170C2×#333—831no—
171#1296—831no—
172C83#1059711yescharacteristic, complemented, Sylow
173C2×C4⋊Q8—831no—
174C2×#106—21no—
175C2×C4⋊C8—831no—
176C2×C4⋊C8—831no—
177C2×C4⋊C8—1661no—
178C2×C4⋊C8C2×D8311yescharacteristic
179C2×C4×C8—831no—
180#384C2×D8311yescharacteristic
181C4×C4⋊C4C2×D8311yescharacteristic
182#340—21no—
183#340—1661no—
184#340—1661no—
185#340—1661no—
186#340—1661no—
187#336—1661no—
188#334—1662no—
189#333—1662no—
190C22×Q8—1661no—
191C22×C8—21no—
192C22×C8—831no—
193C22×C8—831no—
194C22×C8—1661no—
195C22×C8—1661no—
196C4⋊Q8—832no—
197C4⋊Q8—1661no—
198C4⋊Q8—1661no—
199C4⋊Q8—1661no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—1661no—
204C2×C4⋊C4—1661no—
205C2×C4⋊C4C22⋊D8311yescharacteristic
206C2×C4⋊C4C22⋊D8311yescharacteristic
207C2×C42—21no—
208C2×C42C22×D8311yescharacteristic
209#106—42no—
210C4⋊C8—21no—
211C4⋊C8—3322no—
212C4⋊C8—1661no—
213C4⋊C8—1661no—
214C4⋊C8—1661no—
215C4⋊C8—1661no—
216C4⋊C8D33212yes—
217C4×C8—1661no—
218C4×C8—1661no—
219#95—21no—
220C2×Q8—3321no—
221C2×Q8—6641no—
222C2×Q8—6641no—
223C2×Q8—1662no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—3321no—
228C22×C4D4×D8311yescharacteristic
229C22×C4C2×C22⋊D8311yescharacteristic
230C22×C4#1305058911yescharacteristic
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—3321no—
235C2×C8—3321no—
236C2×C8—3321no—
237C2×C8—3321no—
238C2×C8—3321no—
239C2×C8—3321no—
240C2×C8—832no—
241C2×C8—1661no—
242C2×C8—1661no—
243C2×C8—1661no—
244C2×C8—1661no—
245C2×C8—1661no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—81no—
254C4⋊C4—3321no—
255C4⋊C4—3321no—
256C4⋊C4—1662no—
257C4⋊C4—1662no—
258C4⋊C4#1305057812yes—
259C42—41no—
260C42—41no—
261C42C2×D33211yescharacteristic
262C42Q8×D8311yescharacteristic
263C42#1305059011yescharacteristic
264C42#1305059111yescharacteristic
265C23#1458176411yescharacteristic
266Q8—6642no—
267Q8—6642no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—3322no—
280C2×C4—6641no—
281C2×C4—6641no—
282C2×C4#1458176611yescharacteristic
283C2×C4#1458176711yescharacteristic
284C2×C4#1458176811yescharacteristic
285C2×C4#1458177011yescharacteristic
286C2×C4#1458177211yescharacteristic
287C2×C4#1458178711yescharacteristic
288C2×C4SD16×D8311yescharacteristic
289C2×C4C2×#1305057811yescharacteristic
290C2×C4#1458181211yescharacteristic
291C2×C4#1458181311yescharacteristic
292C2×C4#1458182111yescharacteristic
293C2×C4#1458182111yescharacteristic
294C2×C4#1458182211yescharacteristic
295C2×C4#1458182311yescharacteristic
296C8—42no—
297C8—3321no—
298C8—6641no—
299C8—6641no—
300C8—1662no—
301C22#1912762311yescharacteristic
302C22#1912790411yescharacteristic
303C22#1912792111yescharacteristic
304C22#1912792811yescharacteristic
305C22#1912795711yescharacteristic
306C22#1912796611yescharacteristic
307C22#1912796911yescharacteristic
308C4—21no—
309C4—21no—
310C4—42no—
311C4—81no—
312C4—161no—
313C4—6642no—
314C4#1912790611yescharacteristic
315C4#1912792311yescharacteristic
316C4#1912793111yescharacteristic
317C4#1912796011yescharacteristic
318C4#1912798311yescharacteristic
319C4#1912798511yescharacteristic
320C4#1912800511yescharacteristic
321C4#1912801111yescharacteristic
322C2#2490683611yescharacteristic
323C2#2490687711yescharacteristic
324C2#2490698411yescharacteristic
325C2#2490704311yescharacteristic
326C2#2490882011yescharacteristic
327C2#2490883911yescharacteristic
328C2#2490884111yescharacteristic
subgroupG/H
centerC23#14581764
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1948C2
socle, prime radicalC23×C83#121
hypercenter#1948D83
hypocenterC83#10597
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
172. C83#10597semidirect

Maximal subgroups

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

subgroupindex
#249084232
#249084112
#249081822
C2×#191274512
C2×#191274492
#249053462
C83×#19482
#1059783