Finite Group Databasebeta

← #35292790

Subgroups — #35292790

Order 21248.

438 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#24907580C211yesmaximal, characteristic, complemented
2#24907209C211yesmaximal, characteristic, complemented
3#24905286C212yesmaximal, complemented
4#24905284C212yesmaximal
5C83×#2860C211yesmaximal, characteristic
6C2×C4⋊(C83⋊C8)—21no—
7C2×C4×C83⋊C8—21no—
8#19127456—21no—
9#19127456—21no—
10#19127456C2212yes—
11#19127456C2212yes—
12C2×#126×C83—21no—
13#390×C83C411yescharacteristic
14#390×C83C411yescharacteristic
15#390×C83C2211yescharacteristic
16#389×C83C411yescharacteristic
17#389×C83C411yescharacteristic
18#389×C83C2211yescharacteristic
19#388×C83—21no—
20#388×C83—21no—
21#388×C83—21no—
22C43×C83C2211yescharacteristic
23C22×C83⋊C8—22no—
24C22×C83⋊C8—22no—
25C4⋊(C83⋊C8)—42no—
26C4×C83⋊C8—24no—
27C22×D4×C83C2×C411yescharacteristic
28#126×C83—42no—
29#126×C83—42no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83—21no—
32C2×C4⋊C4×C83—21no—
33C2×C4⋊C4×C83C2×C411yescharacteristic
34C2×C4⋊C4×C83C2×C411yescharacteristic
35C2×C4⋊C4×C83C2×C411yescharacteristic
36C2×C22⋊C4×C83—21no—
37C2×C22⋊C4×C83—21no—
38C2×C22⋊C4×C83—21no—
39C2×C22⋊C4×C83—21no—
40C2×C22⋊C4×C83—21no—
41C2×C22⋊C4×C83—21no—
42C2×C42×C83C2×C411yescharacteristic
43C2×C42×C83C2×C411yescharacteristic
44C2×C42×C83D411yescharacteristic
45C2×C42×C83D411yescharacteristic
46C2×C42×C83D411yescharacteristic
47C2×C42×C83D411yescharacteristic
48C2×C42×C83C2311yescharacteristic
49#95×C83—21no—
50#95×C83—21no—
51#95×C83—21no—
52C2×C83⋊C8—24no—
53C2×C83⋊C8—42no—
54C2×C83⋊C8—42no—
55C2×C83⋊C8—42no—
56C2×C83⋊C8—42no—
57C2×C83⋊C8—42no—
58C24×C83—21no—
59C2×D4×C83—22no—
60C2×D4×C83—41no—
61C2×D4×C83—41no—
62C22×C4×C83—21no—
63C22×C4×C83—21no—
64C22×C4×C83—21no—
65C22×C4×C83C22⋊C411yescharacteristic
66C22×C4×C83C22⋊C411yescharacteristic
67C22×C4×C83C22⋊C411yescharacteristic
68C22×C4×C83C22⋊C411yescharacteristic
69C22×C4×C83C22×C411yescharacteristic
70C22×C4×C83C2×D411yescharacteristic
71C22×C4×C83C2×D411yescharacteristic
72C4⋊C4×C83—22no—
73C4⋊C4×C83—41no—
74C4⋊C4×C83—41no—
75C4⋊C4×C83—42no—
76C4⋊C4×C83—42no—
77C4⋊C4×C83—41no—
78C4⋊C4×C83—41no—
79C22⋊C4×C83—42no—
80C22⋊C4×C83—42no—
81C22⋊C4×C83—42no—
82C22⋊C4×C83—42no—
83C22⋊C4×C83—41no—
84C22⋊C4×C83—41no—
85C22⋊C4×C83—42no—
86C42×C83—22no—
87C42×C83—22no—
88C42×C83—22no—
89C42×C83—41no—
90C42×C83—41no—
91C42×C83—41no—
92C42×C83D812yes—
93C42×C83SD1612yes—
94C23×C83—41no—
95C23×C83—41no—
96C23×C83—41no—
97C23×C83—41no—
98C23×C83—41no—
99C23×C83—41no—
100C23×C83—41no—
101C23×C83C2×C22⋊C411yescharacteristic
102D4×C83—82no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83—41no—
119C2×C4×C83—41no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83—41no—
124C2×C4×C83—41no—
125C2×C4×C83—41no—
126C2×C4×C83—41no—
127C2×C4×C83#10212yes—
128C2×C4×C83#10212yes—
129C2×C4×C83#10412yes—
130C2×C4×C83#13112yes—
131C2×C4×C83C2×D811yescharacteristic
132C2×C4×C83C2×SD1611yescharacteristic
133C2×C4×C83#13512yes—
134C83⋊C8—44no—
135C83⋊C8—82no—
136C22×C83—81no—
137C22×C83—81no—
138C22×C83—81no—
139C22×C83—81no—
140C22×C83—81no—
141C22×C83—81no—
142C22×C83—81no—
143C22×C83#40811yescharacteristic
144C22×C83#41011yescharacteristic
145C22×C83#41311yescharacteristic
146C22×C83C2×#10211yescharacteristic
147C22×C83#41611yescharacteristic
148C22×C83C2×#10411yescharacteristic
149C22×C83#42111yescharacteristic
150C4×C83—22no—
151C4×C83—22no—
152C4×C83—22no—
153C4×C83—22no—
154C4×C83—21no—
155C4×C83—21no—
156C4×C83—22no—
157C4×C83—41no—
158C4×C83—81no—
159C4×C83—81no—
160C4×C83—81no—
161#7666—831nomaximal, Sylow
162C2×C83—161no—
163C2×C83#147311yescharacteristic
164C2×C83#148211yescharacteristic
165C2×C83#149211yescharacteristic
166C2×C83#150011yescharacteristic
167C2×C83#151711yescharacteristic
168C2×C83#153211yescharacteristic
169C2×C83#154011yescharacteristic
170#2860D8311yescharacteristic
171#1831—831no—
172#1744—831no—
173#1271—832no—
174#1270—832no—
175C83#766611yescharacteristic, complemented, Sylow
176C2×#126—21no—
177C2×C4⋊C8—1661no—
178C2×C4×C8—1661no—
179#390Dic8311yescharacteristic
180#390Dic8311yescharacteristic
181#390C2×D8311yescharacteristic
182#389Dic8311yescharacteristic
183#389Dic8311yescharacteristic
184#389C2×D8311yescharacteristic
185#388—21no—
186#388—21no—
187#388—21no—
188C43C2×D8311yescharacteristic
189#336—832no—
190#336—832no—
191#336—1661no—
192#336—1661no—
193C22×D4C2×Dic8311yescharacteristic
194C22×C8—1662no—
195C22×C8—1662no—
196#126—42no—
197#126—42no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×Dic8311yescharacteristic
202C2×C4⋊C4C2×Dic8311yescharacteristic
203C2×C4⋊C4C2×Dic8311yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C42C2×Dic8311yescharacteristic
211C2×C42C2×Dic8311yescharacteristic
212C2×C42C22⋊D8311yescharacteristic
213C2×C42C22⋊D8311yescharacteristic
214C2×C42C22⋊D8311yescharacteristic
215C2×C42C22⋊D8311yescharacteristic
216C2×C42C22×D8311yescharacteristic
217C4⋊C8—3322no—
218C4×C8—1664no—
219#95—21no—
220#95—21no—
221#95—21no—
222C24—21no—
223C2×D4—22no—
224C2×D4—41no—
225C2×D4—41no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4C22⋊Dic8311yescharacteristic
230C22×C4C22⋊Dic8311yescharacteristic
231C22×C4C22⋊Dic8311yescharacteristic
232C22×C4C22⋊Dic8311yescharacteristic
233C22×C4C22×Dic8311yescharacteristic
234C22×C4C2×C22⋊D8311yescharacteristic
235C22×C4C2×C22⋊D8311yescharacteristic
236C2×C8—3322no—
237C2×C8—3322no—
238C2×C8—3322no—
239C2×C8—3322no—
240C2×C8—3322no—
241C2×C8—1664no—
242C4⋊C4—22no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42#1305057512yes—
263C42#1305057812yes—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23C2×C22⋊Dic8311yescharacteristic
272D4—82no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4#1458171312yes—
298C2×C4#1458171312yes—
299C2×C4#1458171912yes—
300C2×C4#1458179912yes—
301C2×C4C2×#1305057511yescharacteristic
302C2×C4C2×#1305057811yescharacteristic
303C2×C4#1458181212yes—
304C8—3324no—
305C8—6642no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22#1912766811yescharacteristic
314C22#1912767511yescharacteristic
315C22#1912768511yescharacteristic
316C22C2×#1458171311yescharacteristic
317C22#1912769711yescharacteristic
318C22C2×#1458171911yescharacteristic
319C22#1912771811yescharacteristic
320C4—21no—
321C4—21no—
322C4—22no—
323C4—22no—
324C4—22no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—161no—
332C2#2490583211yescharacteristic
333C2#2490587111yescharacteristic
334C2#2490591411yescharacteristic
335C2#2490594911yescharacteristic
336C2#2490602311yescharacteristic
337C2#2490608311yescharacteristic
338C2#2490611211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic83
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#2860C2
socleC23×C83C2×C22⋊C4
prime radicalC22×D4×C83C2×C4
cosocleC2×C42×C83C23
hypercenter#2860D83
hypocenterC83#7666
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C43 ◁ #2860

Complements

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

NH ≅ G/Ntype
1. #24907580C2semidirect
2. #24907209C2semidirect
3. #24905286C2semidirect
175. C83#7666semidirect

Maximal subgroups

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

subgroupindex
#249075802
#249072092
#249052862
#249052842
C83×#28602
#766683