Finite Group Databasebeta

← #35314764

Subgroups — #35314764

Order 21248.

442 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913331C211yesmaximal, characteristic
2C4×#14581707C211yesmaximal, characteristic
3#24905488C212yesmaximal, complemented
4#24905464C212yesmaximal, complemented
5C83×#1459C211yesmaximal, characteristic
6C2×#14581784C411yescharacteristic, complemented
7C2×#14581707—21no—
8#19127637C411yescharacteristic, complemented
9#19127637C2211yescharacteristic
10#19127632—21no—
11#19127626C411yescharacteristic, complemented
12#19127626C2211yescharacteristic
13#19127615—21no—
14#19127574—21no—
15#19127574—21no—
16#19127569C411yescharacteristic, complemented
17C4×C22⋊Dic83—21no—
18#19127468C2212yes—
19C2×C4×D4×C83C2211yescharacteristic
20C2×C22⋊C8×C83—21no—
21#324×C83—21no—
22#323×C83C2212yes—
23#14581784—41no—
24#14581784—41no—
25C2×C4⋊Dic83C2×C411yescharacteristic
26C2×C4⋊Dic83C2×C411yescharacteristic
27C2×Dic83⋊C4—21no—
28C2×Dic83⋊C4—21no—
29C2×Dic83⋊C4—21no—
30C2×Dic83⋊C4—21no—
31C2×C22⋊Dic83—21no—
32C2×C22⋊Dic83—21no—
33C2×C22⋊Dic83—22no—
34C2×C22⋊Dic83—21no—
35C2×C22⋊Dic83—21no—
36C2×C4×Dic83—41no—
37#14581707—24no—
38C83⋊#95—21no—
39C83⋊#95—21no—
40C83⋊#95—21no—
41C83⋊#95—21no—
42C83⋊#95—41no—
43C83⋊#95C2×C411yescharacteristic
44C83⋊#95C2×C411yescharacteristic
45C22×D4×C83D411yescharacteristic
46C23×C4×C83D411yescharacteristic
47C23×C4×C83D411yescharacteristic
48C22×C8×C83—41no—
49C4×D4×C83—41no—
50C4×D4×C83—41no—
51C2×C4⋊C4×C83D411yescharacteristic
52C2×C22⋊C4×C83C2×C411yescharacteristic
53C2×C22⋊C4×C83C2311yescharacteristic
54C2×C42×C83C2×C411yescharacteristic
55C22⋊C8×C83—22no—
56C22⋊C8×C83—41no—
57C22×Dic83—21no—
58C22×Dic83—21no—
59C22×Dic83—21no—
60C22×Dic83—21no—
61C22×Dic83—42no—
62C4⋊Dic83—41no—
63C4⋊Dic83—41no—
64Dic83⋊C4—42no—
65Dic83⋊C4—41no—
66Dic83⋊C4—41no—
67Dic83⋊C4—81no—
68Dic83⋊C4—81no—
69C22⋊Dic83—24no—
70C22⋊Dic83—42no—
71C22⋊Dic83—42no—
72C22⋊Dic83—42no—
73C22⋊Dic83—81no—
74C22⋊Dic83—81no—
75C4×Dic83—82no—
76C24×C83C22⋊C411yescharacteristic
77C24×C83C2×D411yescharacteristic
78C2×D4×C83—22no—
79C2×D4×C83—22no—
80C2×D4×C83—41no—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—81no—
86C22×C4×C83—81no—
87C22×C4×C83C22⋊C411yescharacteristic
88C22×C4×C83C22⋊C411yescharacteristic
89C22×C4×C83C22⋊C411yescharacteristic
90C22×C4×C83C22×C411yescharacteristic
91C22×C4×C83C2×D411yescharacteristic
92C2×C8×C83—42no—
93C2×C8×C83—82no—
94C4⋊C4×C83—41no—
95C22⋊C4×C83—41no—
96C22⋊C4×C83—41no—
97C42×C83—21no—
98C42×C83—21no—
99C23×C83—21no—
100C23×C83—21no—
101C23×C83—21no—
102C23×C83—21no—
103C23×C83—41no—
104C23×C83—41no—
105C23×C83—41no—
106C23×C83—41no—
107C23×C83#10412yes—
108C23×C83C2×C22⋊C411yescharacteristic
109C23×C83#13512yes—
110D4×C83—44no—
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—41no—
118C2×C4×C83—42no—
119C2×C4×C83—42no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83—81no—
124C2×C4×C83—81no—
125C2×C4×C83#9911yescharacteristic
126C2×C4×C83#9911yescharacteristic
127C2×Dic83—44no—
128C2×Dic83—41no—
129C2×Dic83—41no—
130C2×Dic83—41no—
131C2×Dic83—41no—
132C2×Dic83—41no—
133C2×Dic83—41no—
134C2×Dic83—41no—
135C2×Dic83—41no—
136C2×Dic83—41no—
137C2×Dic83—41no—
138C2×Dic83—41no—
139C2×Dic83—41no—
140C2×Dic83—82no—
141C2×Dic83—82no—
142C8×C83—82no—
143C22×C83—21no—
144C22×C83—21no—
145C22×C83—22no—
146C22×C83—22no—
147C22×C83—42no—
148C22×C83—42no—
149C22×C83—41no—
150C22×C83—41no—
151C22×C83—41no—
152C22×C83—41no—
153C22×C83—81no—
154C22×C83—81no—
155C22×C83C2×#9911yescharacteristic
156C22×C83#41611yescharacteristic
157C22×C83C2×#10411yescharacteristic
158C4×C83—21no—
159C4×C83—21no—
160C4×C83—41no—
161C4×C83—41no—
162C4×C83—41no—
163C4×C83—41no—
164Dic83—81no—
165Dic83—81no—
166Dic83—84no—
167Dic83—81no—
168Dic83—81no—
169#11732—831nomaximal, Sylow
170C2×C83—21no—
171C2×C83—21no—
172C2×C83—42no—
173C2×C83—42no—
174C2×C83#150111yescharacteristic
175C2×C83#212311yescharacteristic
176C2×C83#212711yescharacteristic
177#2633—831no—
178C4×#99—831no—
179#1459D8311yescharacteristic
180#1352—832no—
181#1344—832no—
182C83#1173211yescharacteristic, complemented, Sylow
183C2×#125—831no—
184C2×C4×D4C2×D8311yescharacteristic
185C2×#99—1661no—
186C2×C22⋊C8—21no—
187#399—831no—
188#399—831no—
189#398—1661no—
190#397—831no—
191#397—831no—
192#394—1661no—
193#385—1661no—
194#385—1661no—
195#383—831no—
196C4×C22⋊C4—1661no—
197#342—832no—
198#324—21no—
199#323C2×D8312yes—
200C22×D4D33211yescharacteristic
201C23×C4D33211yescharacteristic
202C23×C4C22⋊D8311yescharacteristic
203C22×C8—41no—
204#125—3321no—
205#125—3321no—
206C4×D4—41no—
207C4×D4—41no—
208C2×C4⋊C4—831no—
209C2×C4⋊C4—831no—
210C2×C4⋊C4—1661no—
211C2×C4⋊C4—1661no—
212C2×C4⋊C4—1661no—
213C2×C4⋊C4—1661no—
214C2×C4⋊C4C22⋊D8311yescharacteristic
215C2×C22⋊C4—1661no—
216C2×C22⋊C4—1661no—
217C2×C22⋊C4—1662no—
218C2×C22⋊C4—1661no—
219C2×C22⋊C4—1661no—
220C2×C22⋊C4C4×D8311yescharacteristic
221C2×C22⋊C4C22×D8311yescharacteristic
222C2×C42—3321no—
223C2×C42C4×D8311yescharacteristic
224#99—1664no—
225C22⋊C8—22no—
226C22⋊C8—41no—
227#95—3321no—
228#95—831no—
229#95—831no—
230#95—1661no—
231#95—1661no—
232#95—1661no—
233#95—1661no—
234C24(C2×D83)⋊C411yescharacteristic
235C24C2×D33211yescharacteristic
236C2×D4—22no—
237C2×D4—22no—
238C2×D4—41no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—81no—
244C22×C4—81no—
245C22×C4—3322no—
246C22×C4—1661no—
247C22×C4—1661no—
248C22×C4—1661no—
249C22×C4—1661no—
250C22×C4(C2×D83)⋊C411yescharacteristic
251C22×C4(C2×D83)⋊C411yescharacteristic
252C22×C4(C2×D83)⋊C411yescharacteristic
253C22×C4C2×C4×D8311yescharacteristic
254C22×C4C2×C22⋊D8311yescharacteristic
255C2×C8—42no—
256C2×C8—82no—
257C4⋊C4—41no—
258C4⋊C4—3321no—
259C4⋊C4—3321no—
260C4⋊C4—3322no—
261C4⋊C4—3321no—
262C4⋊C4—3321no—
263C4⋊C4—6641no—
264C4⋊C4—6641no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—3322no—
268C22⋊C4—3322no—
269C22⋊C4—3322no—
270C22⋊C4—6641no—
271C22⋊C4—6641no—
272C22⋊C4—1664no—
273C42—21no—
274C42—21no—
275C42—6642no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23#1458171812yes—
285C23C2×(C2×D83)⋊C411yescharacteristic
286C23#1458181412yes—
287D4—44no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—3324no—
303C2×C4—3321no—
304C2×C4—3321no—
305C2×C4—3321no—
306C2×C4—3321no—
307C2×C4—3321no—
308C2×C4—3321no—
309C2×C4—3321no—
310C2×C4—3321no—
311C2×C4—3321no—
312C2×C4—3321no—
313C2×C4—3321no—
314C2×C4—3321no—
315C2×C4—6642no—
316C2×C4—6642no—
317C2×C4#1458170611yescharacteristic
318C2×C4#1458170611yescharacteristic
319C8—82no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22—81no—
332C22C2×#1458170611yescharacteristic
333C22#1912769811yescharacteristic
334C22C2×#1458171811yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—6641no—
342C4—6641no—
343C4—6644no—
344C4—6641no—
345C4—6641no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—42no—
350C2#2490595511yescharacteristic
351C2#2490911811yescharacteristic
352C2#2490913011yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC22×C4×C83C22×C4
FrattiniC2×C22⋊C4C22×D83
FittingC83×#1459C2
socleC22×C83C2×#99
prime radicalC22×D4×C83D4
cosocleC2×C22⋊C4×C83C23
hypercenter#1459D83
hypocenterC83#11732
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #24905488C2semidirect
4. #24905464C2semidirect
6. C2×#14581784C4semidirect
8. #19127637C4semidirect
11. #19127626C4semidirect
16. #19127569C4semidirect
182. C83#11732semidirect

Maximal subgroups

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

subgroupindex
#249133312
C4×#145817072
#249054882
#249054642
C83×#14592
#1173283