Finite Group Databasebeta

← #35324170

Subgroups — #35324170

Order 21248.

382 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127529C211yesmaximal, characteristic, complemented
2C2×#19127503C211yesmaximal, characteristic
3C2×#19127503C211yesmaximal, characteristic
4#24908329C211yesmaximal, characteristic
5#24908196C211yesmaximal, characteristic, complemented
6#24905555C211yesmaximal, characteristic, complemented
7C2×C4⋊C16×C83C211yesmaximal, characteristic, complemented
8C22×D664C2211yescharacteristic
9C2×#14581726C2211yescharacteristic
10C2×#14581726C2211yescharacteristic
11C2×#14581726C2211yescharacteristic
12C2×#14581714—21no—
13#19127603—21no—
14#19127599—21no—
15#19127529—22no—
16#19127503—22no—
17#19127503—22no—
18#19127464—21no—
19C22×C16×C83C2211yescharacteristic
20C22×C16×C83C2211yescharacteristic
21C2×C4×C8×C83C2211yescharacteristic
22C4⋊C16×C83—22no—
23C22×D332—21no—
24C2×D664—21no—
25C2×D664—21no—
26C2×D664—21no—
27C2×D664—21no—
28C2×D664—21no—
29C2×D664Q812yes—
30C2×C4⋊Dic83—21no—
31C2×C4⋊Dic83—21no—
32C2×C4⋊Dic83—21no—
33C2×Dic83⋊C4—41no—
34C2×(C2×D83)⋊C4—41no—
35C2×(C2×D83)⋊C4—41no—
36#14581726—21no—
37#14581726—21no—
38#14581726—21no—
39#14581726—21no—
40#14581726—21no—
41#14581726D412yes—
42#14581714—42no—
43C83⋊#95—41no—
44C22×C8×C83D411yescharacteristic
45C22×C8×C83C2311yescharacteristic
46C2×C42×C83D411yescharacteristic
47C2×C16×C83—21no—
48C2×C16×C83—21no—
49C2×C16×C83—21no—
50C2×C16×C83—21no—
51C2×C16×C83—21no—
52C2×C16×C83D412yes—
53C4×C8×C83—21no—
54C4×C8×C83—21no—
55C23×D83—41no—
56C2×D332—22no—
57C2×D332—41no—
58C2×D332—41no—
59C2×D332—41no—
60C2×D332—41no—
61C2×D332—41no—
62C22×Dic83—41no—
63C22×Dic83—41no—
64C22×Dic83—41no—
65D664—22no—
66D664—22no—
67D664—41no—
68D664—41no—
69C4⋊Dic83—22no—
70C4⋊Dic83—41no—
71C4⋊Dic83—41no—
72C4⋊Dic83—41no—
73C4⋊Dic83—41no—
74C4⋊Dic83—41no—
75Dic83⋊C4—82no—
76(C2×D83)⋊C4—82no—
77(C2×D83)⋊C4—82no—
78C22×C4×C83D811yescharacteristic
79C22×C4×C83D811yescharacteristic
80C22×C4×C83C2×D411yescharacteristic
81C2×C8×C83—21no—
82C2×C8×C83—21no—
83C2×C8×C83—21no—
84C2×C8×C83C2×D411yescharacteristic
85C2×C8×C83C2×D411yescharacteristic
86C2×C8×C83C2×Q811yescharacteristic
87C2×C8×C83#4111yescharacteristic
88C2×C8×C83#4111yescharacteristic
89C2×C8×C83#4111yescharacteristic
90C42×C83—21no—
91C42×C83—21no—
92C16×C83—22no—
93C16×C83—41no—
94C23×C83C2×D811yescharacteristic
95C22×D83—42no—
96C22×D83—81no—
97C22×D83—81no—
98C22×D83—81no—
99C22×D83—81no—
100C22×D83—81no—
101C22×D83—81no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83SD3212yes—
108C2×C4×C83#12111yescharacteristic
109C2×C4×C83#12111yescharacteristic
110C2×C4×C83C22⋊Q811yescharacteristic
111C2×C4×C83#13511yescharacteristic
112C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
113C2×C4×C83#13711yescharacteristic
114C2×Dic83—42no—
115C2×Dic83—81no—
116C2×Dic83—81no—
117C2×Dic83—81no—
118C2×Dic83—81no—
119C2×Dic83—81no—
120C2×Dic83—81no—
121C2×Dic83—81no—
122C2×Dic83—81no—
123D332—42no—
124D332—42no—
125D332—81no—
126D332—81no—
127C8×C83—41no—
128C8×C83#12111yescharacteristic
129C8×C83C22⋊Q811yescharacteristic
130C8×C83C22⋊Q811yescharacteristic
131C8×C83#12611yescharacteristic
132C22×C83#45911yescharacteristic
133C22×C83#46611yescharacteristic
134C22×C83#47411yescharacteristic
135C22×C83C2×SD3211yescharacteristic
136C22×C83#50811yescharacteristic
137C22×C83#50911yescharacteristic
138C22×C83#50911yescharacteristic
139C2×D83—82no—
140C2×D83—82no—
141C2×D83—82no—
142C2×D83—161no—
143C2×D83—161no—
144C2×D83—161no—
145C2×D83—161no—
146C4×C83—22no—
147C4×C83—41no—
148C4×C83#39611yescharacteristic
149C4×C83#46411yescharacteristic
150C4×C83#46811yescharacteristic
151C4×C83#47811yescharacteristic
152Dic83—82no—
153Dic83—161no—
154Dic83—161no—
155#13476—831nomaximal, Sylow
156C2×C83#206711yescharacteristic
157C2×C83#220711yescharacteristic
158C2×C83#221011yescharacteristic
159C2×C83#221711yescharacteristic
160C2×C83#221811yescharacteristic
161C2×C83#222611yescharacteristic
162C2×C83#222811yescharacteristic
163D83—162no—
164C2×#367—831no—
165C2×C4⋊C16D8311yescharacteristic, complemented
166C2×#357—831no—
167C2×#357—831no—
168#1970—831no—
169#1942—831no—
170#1380—831no—
171C83#1347611yescharacteristic, complemented, Sylow
172C22×D8—831no—
173C22×C16C2×D8311yescharacteristic
174C22×C16C2×D8311yescharacteristic
175C2×#107—831no—
176C2×#107—831no—
177C2×#107—831no—
178C2×#102—1661no—
179C2×C4×C8C2×D8311yescharacteristic
180#390—1661no—
181#389—1661no—
182#367—1662no—
183C4⋊C16—22no—
184#357—1662no—
185#357—1662no—
186#340—1661no—
187C22×D4—1661no—
188C2×D8—832no—
189C2×D8—1661no—
190C2×D8—1661no—
191C2×D8—1661no—
192C2×D8—1661no—
193C2×D8—1661no—
194C22×C8D33211yescharacteristic
195C22×C8C22×D8311yescharacteristic
196C2×C4⋊C4—3321no—
197C2×C4⋊C4—1661no—
198C2×C4⋊C4—1661no—
199C2×C4⋊C4—1661no—
200C2×C22⋊C4—3321no—
201C2×C22⋊C4—3321no—
202C2×C42D33211yescharacteristic
203C2×C16—21no—
204C2×C16—21no—
205C2×C16—21no—
206C2×C16—21no—
207C2×C16—21no—
208C2×C16C22⋊D8312yes—
209#107—832no—
210#107—1661no—
211#107—1661no—
212#107—1661no—
213#107—1661no—
214#107—1661no—
215#102—3322no—
216C4×C8—21no—
217C4×C8—21no—
218#95—3321no—
219C24—3321no—
220C2×D4—3321no—
221C2×D4—3321no—
222C2×D4—3321no—
223C2×D4—3321no—
224C2×D4—3321no—
225C2×D4—1662no—
226C22×C4—3321no—
227C22×C4—3321no—
228C22×C4—3321no—
229C22×C4D66411yescharacteristic
230C22×C4D66411yescharacteristic
231C22×C4C2×D33211yescharacteristic
232D8—3321no—
233D8—3321no—
234D8—1662no—
235D8—1662no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8D4×D8311yescharacteristic
240C2×C8C2×C22⋊D8311yescharacteristic
241C2×C8Q8×D8311yescharacteristic
242C2×C8#1305058911yescharacteristic
243C2×C8#1305059011yescharacteristic
244C2×C8#1305059111yescharacteristic
245C4⋊C4—3321no—
246C4⋊C4—3321no—
247C4⋊C4—3321no—
248C4⋊C4—3321no—
249C4⋊C4—3321no—
250C4⋊C4—6642no—
251C4⋊C4—1662no—
252C22⋊C4—6642no—
253C22⋊C4—6642no—
254C42—21no—
255C42—21no—
256C16—22no—
257C16—41no—
258C23—3322no—
259C23—6641no—
260C23—6641no—
261C23—6641no—
262C23—6641no—
263C23—6641no—
264C23—6641no—
265C23C2×D66411yescharacteristic
266D4—3322no—
267D4—3322no—
268D4—6641no—
269D4—6641no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—3322no—
276C2×C4—6641no—
277C2×C4—6641no—
278C2×C4—6641no—
279C2×C4—6641no—
280C2×C4—6641no—
281C2×C4—6641no—
282C2×C4—6641no—
283C2×C4—6641no—
284C2×C4#1458173712yes—
285C2×C4#1458176611yescharacteristic
286C2×C4#1458176711yescharacteristic
287C2×C4#1458177211yescharacteristic
288C2×C4#1458181411yescharacteristic
289C2×C4#1458182011yescharacteristic
290C2×C4#1458182511yescharacteristic
291C8—41no—
292C8#1458176411yescharacteristic
293C8#1458176811yescharacteristic
294C8#1458177011yescharacteristic
295C8#1458178711yescharacteristic
296C22—13281no—
297C22—13281no—
298C22—13281no—
299C22—13281no—
300C22—6642no—
301C22—6642no—
302C22—6642no—
303C22#1912789711yescharacteristic
304C22#1912793711yescharacteristic
305C22#1912798211yescharacteristic
306C22C2×#1458173711yescharacteristic
307C22#1912813311yescharacteristic
308C22#1912813911yescharacteristic
309C22#1912813911yescharacteristic
310C4—22no—
311C4—41no—
312C4—13281no—
313C4—13281no—
314C4—6642no—
315C4#1912762311yescharacteristic
316C4#1912792411yescharacteristic
317C4#1912794711yescharacteristic
318C4#1912800211yescharacteristic
319C2—13282no—
320C2#2490885011yescharacteristic
321C2#2490950411yescharacteristic
322C2#2490951911yescharacteristic
323C2#2490955911yescharacteristic
324C2#2490956611yescharacteristic
325C2#2490961111yescharacteristic
326C2#2490962111yescharacteristic
subgroupG/H
centerC23C2×D664
commutator, cosocleC22×C8×C83C23
FrattiniC22×C8C22×D83
FittingC2×C4⋊C16×C83C2
socleC23×C83C2×D8
prime radicalC22×D664C22
hypercenterC2×C4⋊C16D83
hypocenterC83#13476
LCSG ▷ C22×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
1. C2×#19127529C2semidirect
5. #24908196C2semidirect
6. #24905555C2semidirect
7. C2×C4⋊C16×C83C2semidirect
165. C2×C4⋊C16D83semidirect
171. C83#13476semidirect

Maximal subgroups

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

subgroupindex
C2×#191275292
C2×#191275032
#249083292
#249081962
#249055552
C2×C4⋊C16×C832
#1347683