Finite Group Databasebeta

← #35302083

Subgroups — #35302083

Order 21248.

518 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 107 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#24912455C211yesmaximal, characteristic
2#24906188C212yesmaximal, complemented
3#24905804C211yesmaximal, characteristic
4#24905320C212yesmaximal, complemented
5C83×#2973C211yesmaximal, characteristic
6C2×#14581792C2211yescharacteristic
7C2×#14581779C412yes—
8#19127758C2212yes—
9#19127626—21no—
10#19127626—21no—
11#19127606C412yes—
12#19127561—21no—
13#19127561—21no—
14C4×C4⋊Dic83C2211yescharacteristic
15#19127449—24no—
16#19127425—21no—
17#19127425—21no—
18C2×C4×D4×C83C2211yescharacteristic
19#435×C83—24no—
20#432×C83C2212yes—
21#407×C83—21no—
22C2×C22⋊C8×C83—21no—
23C22×Dic166C2×C412yes—
24#14581792—22no—
25#14581792—22no—
26#14581779—44no—
27C2×C4⋊Dic83—21no—
28C2×C4⋊Dic83—21no—
29C2×C4⋊Dic83—21no—
30C2×C22⋊Dic83—22no—
31C2×C22⋊Dic83—22no—
32C2×C4×Dic83C2×C412yes—
33C4⋊(C83⋊C8)—22no—
34C22⋊(C83⋊C8)—22no—
35#14581703—22no—
36C83⋊#95—22no—
37C83⋊#95—22no—
38C83⋊#95—21no—
39C22×D4×C83C2×C411yescharacteristic
40C23×C4×C83D411yescharacteristic
41C23×C4×C83D411yescharacteristic
42C2×M16×C83—22no—
43C22×C8×C83—22no—
44C4×D4×C83—22no—
45C4×D4×C83—22no—
46C2×C4⋊C4×C83C2×C411yescharacteristic
47C2×C22⋊C4×C83D411yescharacteristic
48C2×C22⋊C4×C83D411yescharacteristic
49C2×C42×C83C2311yescharacteristic
50C4⋊C8×C83D414yes—
51C22⋊C8×C83—22no—
52C22⋊C8×C83—22no—
53C22⋊C8×C83—22no—
54#97×C83—22no—
55C2×Dic166—24no—
56C2×Dic166—42no—
57C2×Dic166—42no—
58C22×Dic83—22no—
59C22×Dic83—22no—
60C2×C83⋊C8—42no—
61C4⋊Dic83—42no—
62C4⋊Dic83—41no—
63C4⋊Dic83—42no—
64C4⋊Dic83—41no—
65C22⋊Dic83—44no—
66C22⋊Dic83—44no—
67C4×Dic83—42no—
68C24×C83C22⋊C411yescharacteristic
69C24×C83C22⋊C411yescharacteristic
70C2×D4×C83—22no—
71C2×D4×C83—22no—
72C2×D4×C83—41no—
73C22×C4×C83—21no—
74C22×C4×C83—21no—
75C22×C4×C83—21no—
76C22×C4×C83—21no—
77C22×C4×C83—42no—
78C22×C4×C83—42no—
79C22×C4×C83C22⋊C411yescharacteristic
80C22×C4×C83C22⋊C411yescharacteristic
81C22×C4×C83C22×C411yescharacteristic
82C22×C4×C83C2×D411yescharacteristic
83C22×C4×C83C2×D411yescharacteristic
84M16×C83—82no—
85C2×C8×C83—24no—
86C2×C8×C83—82no—
87C4⋊C4×C83—22no—
88C22⋊C4×C83—22no—
89C22⋊C4×C83—22no—
90C42×C83C2×D412yes—
91C42×C83#4112yes—
92C23×C83—21no—
93C23×C83—21no—
94C23×C83—21no—
95C23×C83—21no—
96C23×C83—21no—
97C23×C83—41no—
98C23×C83—41no—
99C23×C83—41no—
100C23×C83—41no—
101C23×C83#10012yes—
102C23×C83C2×C22⋊C411yescharacteristic
103D4×C83—44no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—22no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—41no—
110C2×C4×C83—42no—
111C2×C4×C83—42no—
112C2×C4×C83—41no—
113C2×C4×C83—41no—
114C2×C4×C83—81no—
115C2×C4×C83—81no—
116C2×C4×C83C4×D412yes—
117C2×C4×C83#12011yescharacteristic
118C2×C4×C83#12112yes—
119C2×C4×C83#12311yescharacteristic
120C2×Dic83—42no—
121C2×Dic83—42no—
122C2×Dic83—42no—
123C2×Dic83—42no—
124C2×Dic83—42no—
125C2×Dic83—42no—
126Dic166—84no—
127C8×C83—44no—
128C83⋊C8—82no—
129C22×C83—21no—
130C22×C83—21no—
131C22×C83—22no—
132C22×C83—42no—
133C22×C83—42no—
134C22×C83—41no—
135C22×C83—41no—
136C22×C83—41no—
137C22×C83—41no—
138C22×C83—41no—
139C22×C83—81no—
140C22×C83—81no—
141C22×C83#38611yescharacteristic
142C22×C83C2×#10011yescharacteristic
143C22×C83#41311yescharacteristic
144C4×C83—21no—
145C4×C83—22no—
146C4×C83—22no—
147C4×C83—41no—
148C4×C83—41no—
149C4×C83#45512yes—
150Dic83—82no—
151Dic83—82no—
152#9451—831nomaximal, Sylow
153C2×C83—21no—
154C2×C83—21no—
155C2×C83—42no—
156C2×C83—81no—
157C2×C83#188511yescharacteristic
158C2×C83#190011yescharacteristic
159C2×C83#190911yescharacteristic
160#2973D8311yescharacteristic
161#2547—831no—
162#1558—832no—
163#1466—831no—
164#1285—832no—
165C83#945111yescharacteristic, complemented, Sylow
166C2×C4⋊Q8—831no—
167C2×#124—832no—
168C2×C4×D4C2×D8311yescharacteristic
169#435—24no—
170#432—832no—
171#432C2×D8312yes—
172#407—21no—
173C2×C22⋊C8—21no—
174#397—1661no—
175#397—1661no—
176#391—832no—
177#380—1661no—
178#380—1661no—
179C4×C4⋊C4—831no—
180#333—1664no—
181#323—1661no—
182#323—1661no—
183C22×Q8—832no—
184C22×D4C4×D8311yescharacteristic
185C23×C4C22⋊D8311yescharacteristic
186C23×C4C22⋊D8311yescharacteristic
187C2×M16—22no—
188C22×C8—22no—
189C4⋊Q8—1662no—
190C4⋊Q8—1662no—
191#124—3324no—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—1661no—
195C2×C4⋊C4—1661no—
196C2×C4⋊C4—1661no—
197C2×C4⋊C4C4×D8311yescharacteristic
198C2×C22⋊C4—1662no—
199C2×C22⋊C4—1662no—
200C2×C22⋊C4D33211yescharacteristic
201C2×C22⋊C4D33211yescharacteristic
202C2×C42—832no—
203C2×C42C22×D8311yescharacteristic
204C4⋊C8—1662no—
205C4⋊C8C22⋊D8314yes—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—1662no—
210#97—22no—
211#97—1662no—
212#95—1662no—
213#95—1662no—
214#95—1661no—
215C24(C2×D83)⋊C411yescharacteristic
216C24(C2×D83)⋊C411yescharacteristic
217C2×Q8—3322no—
218C2×Q8—3322no—
219C2×Q8—1664no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—1662no—
230C22×C4—1662no—
231C22×C4(C2×D83)⋊C411yescharacteristic
232C22×C4(C2×D83)⋊C411yescharacteristic
233C22×C4C2×C4×D8311yescharacteristic
234C22×C4C2×C22⋊D8311yescharacteristic
235C22×C4C2×D33211yescharacteristic
236M16—82no—
237C2×C8—24no—
238C2×C8—82no—
239C2×C8—3322no—
240C4⋊C4—22no—
241C4⋊C4—3322no—
242C4⋊C4—3321no—
243C4⋊C4—3322no—
244C4⋊C4—3321no—
245C22⋊C4—22no—
246C22⋊C4—22no—
247C22⋊C4—3324no—
248C22⋊C4—3324no—
249C42—3322no—
250C42C2×C22⋊D8312yes—
251C42#1305059012yes—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23#1458170812yes—
262C23C2×(C2×D83)⋊C411yescharacteristic
263Q8—6644no—
264D4—44no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—3322no—
278C2×C4—3322no—
279C2×C4—3322no—
280C2×C4—3322no—
281C2×C4—3322no—
282C2×C4—3322no—
283C2×C4C4×C22⋊D8312yes—
284C2×C4#1458176111yescharacteristic
285C2×C4#1458176612yes—
286C2×C4#1458177511yescharacteristic
287C8—44no—
288C8—6642no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22—81no—
301C22#1912758011yescharacteristic
302C22C2×#1458170811yescharacteristic
303C22#1912768311yescharacteristic
304C4—21no—
305C4—22no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—6642no—
310C4—6642no—
311C4#1912787912yes—
312C2—21no—
313C2—21no—
314C2—42no—
315C2—81no—
316C2#2490785111yescharacteristic
317C2#2490792611yescharacteristic
318C2#2490798511yescharacteristic
subgroupG/H
centerC22#19127580
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#2973C2
socleC22×C83#386
prime radicalC22×D4×C83C2×C4
cosocleC2×C42×C83C23
hypercenter#2973D83
hypocenterC83#9451
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #24906188C2semidirect
4. #24905320C2semidirect
165. C83#9451semidirect

Maximal subgroups

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

subgroupindex
#249124552
#249061882
#249058042
#249053202
C83×#29732
#945183