Finite Group Databasebeta

← #35302525

Subgroups — #35302525

Order 21248.

372 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14581723C211yesmaximal, characteristic
2C8×C4⋊Dic83C211yesmaximal, characteristic
3#24905304C211yesmaximal, characteristic
4#24905302C211yesmaximal, characteristic
5#24905297C211yesmaximal, characteristic
6C83⋊#1273C211yesmaximal, characteristic
7C83×#1939C211yesmaximal, characteristic
8C2×#14581723C411yescharacteristic
9C2×#14581723C411yescharacteristic
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×C4×C83⋊C8C2211yescharacteristic
12C2×C4×C83⋊C8C2211yescharacteristic
13C2×C8×Dic83—21no—
14C4×C4⋊Dic83C2211yescharacteristic
15#19127463C411yescharacteristic
16#19127463C411yescharacteristic
17#19127455—21no—
18C2×C4⋊C8×C83—21no—
19C2×C4⋊C8×C83C2211yescharacteristic
20C2×C4×C8×C83C2211yescharacteristic
21C4×C4⋊C4×C83C2211yescharacteristic
22#336×C83—21no—
23C22×C83⋊C8—21no—
24C22×C83⋊C8—21no—
25C22×C83⋊C8C2×C411yescharacteristic
26C22×C83⋊C8C2×C411yescharacteristic
27C2×C4⋊Dic83C2×C411yescharacteristic
28C2×C4⋊Dic83C2×C411yescharacteristic
29C2×C4×Dic83—21no—
30#14581723—22no—
31#14581723C814yescomplemented
32C4⋊(C83⋊C8)—21no—
33C4⋊(C83⋊C8)Q812yes—
34C4×C83⋊C8—21no—
35C4×C83⋊C8—21no—
36C4×C83⋊C8—21no—
37C4×C83⋊C8—21no—
38C8×Dic83—42no—
39C83⋊#95—21no—
40C22×C8×C83—21no—
41C22×C8×C83D411yescharacteristic
42C22×C8×C83D411yescharacteristic
43C2×C4⋊C4×C83C2×C411yescharacteristic
44C2×C4⋊C4×C83C2×C411yescharacteristic
45C2×C42×C83—21no—
46C2×C42×C83C2311yescharacteristic
47C4⋊C8×C83—21no—
48C4⋊C8×C83—21no—
49C4⋊C8×C83—42no—
50C4×C8×C83—21no—
51C4×C8×C83—21no—
52#95×C83—21no—
53C22×Dic83—21no—
54C22×Dic83—21no—
55C2×C83⋊C8—21no—
56C2×C83⋊C8—21no—
57C2×C83⋊C8—22no—
58C2×C83⋊C8—21no—
59C2×C83⋊C8—22no—
60C2×C83⋊C8—21no—
61C2×C83⋊C8—21no—
62C2×C83⋊C8—41no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8C2×C812yes—
67C4⋊Dic83—21no—
68C4⋊Dic83—21no—
69C4⋊Dic83C2×C812yes—
70C4⋊Dic83M1612yes—
71C4×Dic83—41no—
72C4×Dic83—41no—
73C22×C4×C83—21no—
74C22×C4×C83—21no—
75C22×C4×C83C22×C411yescharacteristic
76C22×C4×C83C2×D411yescharacteristic
77C22×C4×C83#4111yescharacteristic
78C2×C8×C83—21no—
79C2×C8×C83—21no—
80C2×C8×C83—21no—
81C2×C8×C83—21no—
82C2×C8×C83—21no—
83C2×C8×C83—41no—
84C2×C8×C83—41no—
85C2×C8×C83—41no—
86C2×C8×C83SD1612yes—
87C4⋊C4×C83—21no—
88C4⋊C4×C83—21no—
89C4⋊C4×C83—21no—
90C4⋊C4×C83C2×C812yes—
91C42×C83—41no—
92C42×C83—41no—
93C42×C83C2×Q811yescharacteristic
94C42×C83#4111yescharacteristic
95C42×C83#4111yescharacteristic
96C42×C83#4111yescharacteristic
97C23×C83C4×D411yescharacteristic
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—22no—
101C2×C4×C83—41no—
102C2×C4×C83—41no—
103C2×C4×C83—41no—
104C2×C4×C83—41no—
105C2×C4×C83—41no—
106C2×C4×C83#11711yescharacteristic
107C2×C4×C83C4×Q811yescharacteristic
108C2×C4×C83C22⋊Q811yescharacteristic
109C2×C4×C83#12311yescharacteristic
110C2×C4×C83#12511yescharacteristic
111C2×C4×C83#12611yescharacteristic
112C2×C4×C83C22×C811yescharacteristic
113C2×C4×C83C2×M1611yescharacteristic
114C2×C4×C83#13111yescharacteristic
115C2×C4×C83#13111yescharacteristic
116C2×C4×C83C2×SD1611yescharacteristic
117C2×C4×C83#13511yescharacteristic
118C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C83#13711yescharacteristic
120C2×Dic83—22no—
121C2×Dic83—22no—
122C2×Dic83—41no—
123C2×Dic83—41no—
124C2×Dic83—41no—
125C2×Dic83—41no—
126C8×C83—22no—
127C8×C83—41no—
128C8×C83—81no—
129C83⋊C8—22no—
130C83⋊C8—42no—
131C83⋊C8—41no—
132C83⋊C8—42no—
133C22×C83#38711yescharacteristic
134C22×C83C8×D411yescharacteristic
135C22×C83#43511yescharacteristic
136C22×C83C4×SD1611yescharacteristic
137C22×C83#44011yescharacteristic
138C22×C83#44311yescharacteristic
139C22×C83#44411yescharacteristic
140C4×C83—21no—
141C4×C83—21no—
142C4×C83—42no—
143C4×C83—81no—
144C4×C83#43111yescharacteristic
145C4×C83#43311yescharacteristic
146C4×C83C8×Q811yescharacteristic
147C4×C83#44611yescharacteristic
148C4×C83#47511yescharacteristic
149C4×C83#47811yescharacteristic
150C4×C83#48111yescharacteristic
151C4×C83#48511yescharacteristic
152Dic83—42no—
153Dic83—42no—
154#9534—831nomaximal, Sylow
155C2×C83C8×SD1611yescharacteristic
156C2×C83SD16⋊C811yescharacteristic
157C2×C83#158311yescharacteristic
158C2×C83#158511yescharacteristic
159C2×C83#191611yescharacteristic
160C2×C83#191911yescharacteristic
161C2×C83#192211yescharacteristic
162#1939D8311yescharacteristic
163C4×#106—831no—
164C8×C4⋊C4—831no—
165#1279—831no—
166#1279—831no—
167#1277—831no—
168#1273—831no—
169C83#953411yescharacteristic, complemented, Sylow
170C2×#106—831no—
171C2×#106—831no—
172C2×C4⋊C8—21no—
173C2×C4⋊C8—831no—
174C2×C4⋊C8C2×D8311yescharacteristic
175C2×C4×C8—831no—
176C2×C4×C8—831no—
177C2×C4×C8—1661no—
178C2×C4×C8C2×D8311yescharacteristic
179C4×C4⋊C4—831no—
180C4×C4⋊C4C2×D8311yescharacteristic
181#340—831no—
182#340—831no—
183#336—21no—
184#336—1661no—
185C22×C8—21no—
186C22×C8—831no—
187C22×C8—831no—
188C22×C8—1661no—
189C22×C8—1661no—
190C22×C8C22⋊D8311yescharacteristic
191C22×C8C22⋊D8311yescharacteristic
192C2×C4⋊C4—831no—
193C2×C4⋊C4—831no—
194C2×C4⋊C4C4×D8311yescharacteristic
195C2×C4⋊C4C4×D8311yescharacteristic
196C2×C42—21no—
197C2×C42—1661no—
198C2×C42C22×D8311yescharacteristic
199#106—834no—
200#106—1662no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—42no—
204C4⋊C8—832no—
205C4⋊C8—1661no—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—3322no—
209C4×C8—1661no—
210C4×C8—1661no—
211C4×C8—1661no—
212C4×C8—1661no—
213#95—21no—
214#95—1661no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—1661no—
218C22×C4—1661no—
219C22×C4C2×C4×D8311yescharacteristic
220C22×C4C2×C22⋊D8311yescharacteristic
221C22×C4#1305059011yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—3321no—
231C2×C8—3321no—
232C2×C8—3321no—
233C2×C8—3321no—
234C2×C8—832no—
235C2×C8—1662no—
236C2×C8—1662no—
237C2×C8—1661no—
238C2×C8—1661no—
239C2×C8—1661no—
240C2×C8—1661no—
241C2×C8—1661no—
242C2×C8#1305057812yes—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—832no—
247C4⋊C4—832no—
248C4⋊C4—1661no—
249C4⋊C4—1661no—
250C4⋊C4C8×D8312yes—
251C42—41no—
252C42—41no—
253C42—3321no—
254C42—3321no—
255C42Q8×D8311yescharacteristic
256C42#1305058911yescharacteristic
257C42#1305058911yescharacteristic
258C42#1305059111yescharacteristic
259C23C4×C22⋊D8311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—3321no—
269C2×C4—3321no—
270C2×C4—3321no—
271C2×C4—3321no—
272C2×C4—1662no—
273C2×C4—1662no—
274C2×C4#1458175011yescharacteristic
275C2×C4#1458175711yescharacteristic
276C2×C4#1458176811yescharacteristic
277C2×C4#1458177311yescharacteristic
278C2×C4#1458178211yescharacteristic
279C2×C4#1458178711yescharacteristic
280C2×C4C2×C8×D8311yescharacteristic
281C2×C4M16×D8311yescharacteristic
282C2×C4#1458179811yescharacteristic
283C2×C4#1458180011yescharacteristic
284C2×C4C2×#1305057811yescharacteristic
285C2×C4#1458181211yescharacteristic
286C2×C4#1458181711yescharacteristic
287C2×C4#1458182311yescharacteristic
288C8—22no—
289C8—41no—
290C8—81no—
291C8—3322no—
292C8—3322no—
293C8—3321no—
294C8—1662no—
295C22#1912758211yescharacteristic
296C22C8×C22⋊D8311yescharacteristic
297C22#1912777011yescharacteristic
298C22C4×#1305057811yescharacteristic
299C22#1912779911yescharacteristic
300C22#1912781611yescharacteristic
301C22#1912782111yescharacteristic
302C4—21no—
303C4—21no—
304C4—42no—
305C4—81no—
306C4—3322no—
307C4—3322no—
308C4#1912775311yescharacteristic
309C4#1912776111yescharacteristic
310C4#1912782511yescharacteristic
311C4#1912783011yescharacteristic
312C4#1912798311yescharacteristic
313C4#1912799811yescharacteristic
314C4#1912801711yescharacteristic
315C4#1912803911yescharacteristic
316C2C8×#1305057811yescharacteristic
317C2#2490627311yescharacteristic
318C2#2490630411yescharacteristic
319C2#2490631811yescharacteristic
320C2#2490801711yescharacteristic
321C2#2490803811yescharacteristic
322C2#2490805911yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D83
commutatorC2×C4×C83C22×C8
FrattiniC2×C42C22×D83
FittingC83×#1939C2
socle, prime radicalC23×C83C4×D4
cosocleC2×C42×C83C23
hypercenter#1939D83
hypocenterC83#9534
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1939

Complements

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

NH ≅ G/Ntype
31. #14581723C8semidirect
169. C83#9534semidirect

Maximal subgroups

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

subgroupindex
C4×#145817232
C8×C4⋊Dic832
#249053042
#249053022
#249052972
C83⋊#12732
C83×#19392
#953483