Finite Group Databasebeta

← #35302963

Subgroups — #35302963

Order 21248.

378 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
1#24908181C211yesmaximal, characteristic
2C4×#14581725C211yesmaximal, characteristic
3C2×#19127453C211yesmaximal, characteristic
4C2×#19127422C211yesmaximal, characteristic
5#24905304C211yesmaximal, characteristic
6#24905302C211yesmaximal, characteristic
7C83×#1939C211yesmaximal, characteristic
8C2×#14581725C411yescharacteristic
9C2×#14581725C411yescharacteristic
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×Dic83⋊C8—21no—
12C2×C4×C83⋊C8C2211yescharacteristic
13C2×C4×C83⋊C8C2211yescharacteristic
14C4×C4⋊Dic83C2211yescharacteristic
15#19127463C411yescharacteristic
16#19127463C411yescharacteristic
17#19127455—21no—
18#19127453—22no—
19#19127422—22no—
20C2×C4⋊C8×C83—21no—
21C2×C4⋊C8×C83C2211yescharacteristic
22C2×C4×C8×C83C2211yescharacteristic
23C4×C4⋊C4×C83C2211yescharacteristic
24#336×C83—21no—
25C22×C83⋊C8—21no—
26C22×C83⋊C8—21no—
27C22×C83⋊C8C2×C411yescharacteristic
28C22×C83⋊C8C2×C411yescharacteristic
29C2×C4⋊Dic83C2×C411yescharacteristic
30C2×C4⋊Dic83C2×C411yescharacteristic
31C2×C4×Dic83—21no—
32#14581725—22no—
33#14581725—22no—
34C4⋊(C83⋊C8)—21no—
35C4⋊(C83⋊C8)—21no—
36Dic83⋊C8—42no—
37C4×C83⋊C8—21no—
38C4×C83⋊C8D412yes—
39C4×C83⋊C8Q812yes—
40C4×C83⋊C8Q812yes—
41C83⋊#95—21no—
42C22×C8×C83—21no—
43C22×C8×C83D411yescharacteristic
44C22×C8×C83D411yescharacteristic
45C2×C4⋊C4×C83C2×C411yescharacteristic
46C2×C4⋊C4×C83C2×C411yescharacteristic
47C2×C42×C83—21no—
48C2×C42×C83C2311yescharacteristic
49C4⋊C8×C83—21no—
50C4⋊C8×C83—21no—
51C4⋊C8×C83—42no—
52C4×C8×C83—21no—
53C4×C8×C83—21no—
54#95×C83—21no—
55C22×Dic83—21no—
56C22×Dic83—21no—
57C2×C83⋊C8—21no—
58C2×C83⋊C8—21no—
59C2×C83⋊C8—21no—
60C2×C83⋊C8—21no—
61C2×C83⋊C8—22no—
62C2×C83⋊C8—41no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8C4⋊C412yes—
68C2×C83⋊C8C4⋊C412yes—
69C4⋊Dic83—21no—
70C4⋊Dic83—21no—
71C4⋊Dic83—21no—
72C4⋊Dic83M1612yes—
73C4×Dic83—41no—
74C4×Dic83—41no—
75C22×C4×C83—21no—
76C22×C4×C83—21no—
77C22×C4×C83C22×C411yescharacteristic
78C22×C4×C83C2×D411yescharacteristic
79C22×C4×C83#4111yescharacteristic
80C2×C8×C83—21no—
81C2×C8×C83—21no—
82C2×C8×C83—21no—
83C2×C8×C83—21no—
84C2×C8×C83—41no—
85C2×C8×C83—41no—
86C2×C8×C83—41no—
87C2×C8×C83D812yes—
88C2×C8×C83Q1612yes—
89C4⋊C4×C83—21no—
90C4⋊C4×C83—21no—
91C4⋊C4×C83—21no—
92C4⋊C4×C83M1612yes—
93C42×C83—41no—
94C42×C83—41no—
95C42×C83C2×D411yescharacteristic
96C42×C83C2×Q811yescharacteristic
97C42×C83C2×Q811yescharacteristic
98C42×C83#4111yescharacteristic
99C23×C83C4×D411yescharacteristic
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—22no—
103C2×C4×C83—41no—
104C2×C4×C83—41no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83C2×C4⋊C411yescharacteristic
109C2×C4×C83C4×Q811yescharacteristic
110C2×C4×C83#12111yescharacteristic
111C2×C4×C83C22⋊Q811yescharacteristic
112C2×C4×C83#12511yescharacteristic
113C2×C4×C83C4⋊Q811yescharacteristic
114C2×C4×C83C2×M1611yescharacteristic
115C2×C4×C83C2×M1611yescharacteristic
116C2×C4×C83#13111yescharacteristic
117C2×C4×C83#13111yescharacteristic
118C2×C4×C83C2×D811yescharacteristic
119C2×C4×C83C2×Q1611yescharacteristic
120C2×C4×C83#13511yescharacteristic
121C2×C4×C83#13511yescharacteristic
122C2×Dic83—22no—
123C2×Dic83—41no—
124C2×Dic83—41no—
125C2×Dic83—41no—
126C2×Dic83—41no—
127C2×Dic83—41no—
128C8×C83—22no—
129C8×C83—22no—
130C8×C83—81no—
131C83⋊C8—22no—
132C83⋊C8—22no—
133C83⋊C8—42no—
134C83⋊C8—81no—
135C22×C83#38911yescharacteristic
136C22×C83#43511yescharacteristic
137C22×C83#43511yescharacteristic
138C22×C83C4×D811yescharacteristic
139C22×C83C4×Q1611yescharacteristic
140C22×C83#44411yescharacteristic
141C22×C83#44411yescharacteristic
142C4×C83—21no—
143C4×C83—21no—
144C4×C83—42no—
145C4×C83—81no—
146C4×C83#42311yescharacteristic
147C4×C83#42411yescharacteristic
148C4×C83#44611yescharacteristic
149C4×C83#44611yescharacteristic
150C4×C83#46611yescharacteristic
151C4×C83#46711yescharacteristic
152C4×C83#49911yescharacteristic
153C4×C83#50011yescharacteristic
154Dic83—42no—
155Dic83—81no—
156#9598—831nomaximal, Sylow
157C2×C83#158111yescharacteristic
158C2×C83#158111yescharacteristic
159C2×C83#158411yescharacteristic
160C2×C83#158411yescharacteristic
161C2×C83#194011yescharacteristic
162C2×C83#194211yescharacteristic
163C2×C83#194611yescharacteristic
164#1939—831no—
165#1939D8311yescharacteristic
166C4×#107—831no—
167C2×#335—831no—
168C2×#322—831no—
169#1279—831no—
170#1279—831no—
171C83#959811yescharacteristic, complemented, Sylow
172C2×#107—831no—
173C2×#107—831no—
174C2×C4⋊C8—21no—
175C2×C4⋊C8—831no—
176C2×C4⋊C8—1661no—
177C2×C4⋊C8C2×D8311yescharacteristic
178C2×C4×C8—831no—
179C2×C4×C8—831no—
180C2×C4×C8C2×D8311yescharacteristic
181C4×C4⋊C4—831no—
182C4×C4⋊C4C2×D8311yescharacteristic
183#340—831no—
184#340—831no—
185#336—21no—
186#336—1661no—
187#335—1662no—
188#322—1662no—
189C22×C8—21no—
190C22×C8—831no—
191C22×C8—831no—
192C22×C8—1661no—
193C22×C8—1661no—
194C22×C8C22⋊D8311yescharacteristic
195C22×C8C22⋊D8311yescharacteristic
196C2×C4⋊C4—831no—
197C2×C4⋊C4—831no—
198C2×C4⋊C4C4×D8311yescharacteristic
199C2×C4⋊C4C4×D8311yescharacteristic
200C2×C42—21no—
201C2×C42—1661no—
202C2×C42C22×D8311yescharacteristic
203#107—1662no—
204#107—1662no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—42no—
208C4⋊C8—3322no—
209C4⋊C8—1661no—
210C4⋊C8—1661no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—832no—
214C4×C8—832no—
215C4×C8—832no—
216C4×C8—1661no—
217#95—21no—
218#95—1661no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—1661no—
222C22×C4—1661no—
223C22×C4C2×C4×D8311yescharacteristic
224C22×C4C2×C22⋊D8311yescharacteristic
225C22×C4#1305059011yescharacteristic
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—3321no—
234C2×C8—3321no—
235C2×C8—3321no—
236C2×C8—3321no—
237C2×C8—3321no—
238C2×C8—832no—
239C2×C8—832no—
240C2×C8—1662no—
241C2×C8—1661no—
242C2×C8—1661no—
243C2×C8—1661no—
244C2×C8—1661no—
245C2×C8#1305057512yes—
246C2×C8#1305058012yes—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—832no—
251C4⋊C4—1661no—
252C4⋊C4—1661no—
253C4⋊C4—1661no—
254C4⋊C4#1305057312yes—
255C42—41no—
256C42—41no—
257C42—3321no—
258C42—3321no—
259C42D4×D8311yescharacteristic
260C42Q8×D8311yescharacteristic
261C42Q8×D8311yescharacteristic
262C42#1305058911yescharacteristic
263C23C4×C22⋊D8311yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—3321no—
273C2×C4—3321no—
274C2×C4—3321no—
275C2×C4—3321no—
276C2×C4—3321no—
277C2×C4—1662no—
278C2×C4C4⋊C4×D8311yescharacteristic
279C2×C4#1458175711yescharacteristic
280C2×C4#1458176411yescharacteristic
281C2×C4#1458177011yescharacteristic
282C2×C4#1458178211yescharacteristic
283C2×C4#1458179011yescharacteristic
284C2×C4M16×D8311yescharacteristic
285C2×C4C2×#1305057311yescharacteristic
286C2×C4#1458179811yescharacteristic
287C2×C4#1458180011yescharacteristic
288C2×C4C2×#1305057511yescharacteristic
289C2×C4C2×#1305058011yescharacteristic
290C2×C4#1458181211yescharacteristic
291C2×C4#1458181211yescharacteristic
292C8—22no—
293C8—22no—
294C8—81no—
295C8—3322no—
296C8—6641no—
297C8—1662no—
298C8—1662no—
299C22#1912759611yescharacteristic
300C22#1912777011yescharacteristic
301C22#1912777211yescharacteristic
302C22C4×#1305057511yescharacteristic
303C22C4×#1305058011yescharacteristic
304C22#1912782111yescharacteristic
305C22#1912782111yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—3322no—
311C4—6641no—
312C4#1912772311yescharacteristic
313C4#1912772611yescharacteristic
314C4#1912782811yescharacteristic
315C4#1912783011yescharacteristic
316C4#1912793511yescharacteristic
317C4#1912794011yescharacteristic
318C4#1912810011yescharacteristic
319C4#1912810411yescharacteristic
320C2#2490629011yescharacteristic
321C2#2490629211yescharacteristic
322C2#2490631111yescharacteristic
323C2#2490631311yescharacteristic
324C2#2490818311yescharacteristic
325C2#2490819311yescharacteristic
326C2#2490821311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D83
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1939C2
socle, prime radicalC23×C83C4×D4
cosocleC2×C42×C83C23
hypercenter#1939D83
hypocenterC83#9598
LCSG ▷ C22×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
171. C83#9598semidirect

Maximal subgroups

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

subgroupindex
#249081812
C4×#145817252
C2×#191274532
C2×#191274222
#249053042
#249053022
C83×#19392
#959883