Finite Group Databasebeta

← #35302089

Subgroups — #35302089

Order 21248.

468 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 111 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#24916548C211yesmaximal, characteristic
2#24906189C212yesmaximal
3#24905807C211yesmaximal, characteristic
4#24905319C212yesmaximal
5C83×#2546C211yesmaximal, characteristic
6#19127832—24no—
7#19127758—21no—
8#19127758C2212yes—
9#19127758C2212yes—
10#19127754—21no—
11#19127450—24no—
12#19127427—21no—
13#19127427—21no—
14C2×C4⋊Q8×C83C412yes—
15C2×C4⋊Q8×C83C2211yescharacteristic
16C2×C4×Q8×C83C2211yescharacteristic
17#398×C83—21no—
18#398×C83—21no—
19#391×C83C412yes—
20#389×C83—21no—
21#389×C83—21no—
22C4×C4⋊C4×C83C2211yescharacteristic
23C4⋊(C83⋊C8)—22no—
24C4⋊(C83⋊C8)—22no—
25C4⋊(C83⋊C8)—22no—
26C4⋊(C83⋊C8)D414yes—
27C22⋊(C83⋊C8)—22no—
28C22⋊(C83⋊C8)—22no—
29#14581703—22no—
30#14581703—22no—
31#14581703—22no—
32C4×C83⋊C8—22no—
33C22×Q8×C83C2×C412yes—
34C22×Q8×C83C2×C411yescharacteristic
35C4⋊Q8×C83—22no—
36C4⋊Q8×C83—22no—
37C4⋊Q8×C83—44no—
38C4×Q8×C83—22no—
39C4×Q8×C83—22no—
40C2×C4⋊C4×C83—21no—
41C2×C4⋊C4×C83—22no—
42C2×C4⋊C4×C83—22no—
43C2×C4⋊C4×C83—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83C2×C411yescharacteristic
46C2×C4⋊C4×C83D411yescharacteristic
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C42×C83C2×C412yes—
49C2×C42×C83D411yescharacteristic
50C2×C42×C83D411yescharacteristic
51C2×C42×C83C2311yescharacteristic
52#95×C83—22no—
53#95×C83—22no—
54#95×C83—21no—
55C2×C83⋊C8—24no—
56C2×C83⋊C8—42no—
57C2×Q8×C83—22no—
58C2×Q8×C83—22no—
59C2×Q8×C83—24no—
60C2×Q8×C83—41no—
61C2×Q8×C83—42no—
62C2×Q8×C83—42no—
63C22×C4×C83—22no—
64C22×C4×C83—22no—
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—24no—
73C4⋊C4×C83—22no—
74C4⋊C4×C83—22no—
75C4⋊C4×C83—22no—
76C4⋊C4×C83—44no—
77C4⋊C4×C83—44no—
78C4⋊C4×C83—41no—
79C4⋊C4×C83—42no—
80C4⋊C4×C83—41no—
81C42×C83—21no—
82C42×C83—21no—
83C42×C83—21no—
84C42×C83—21no—
85C42×C83—42no—
86C42×C83C2×D412yes—
87C42×C83#4112yes—
88C23×C83C2×C22⋊C411yescharacteristic
89Q8×C83—44no—
90Q8×C83—84no—
91C2×C4×C83—21no—
92C2×C4×C83—21no—
93C2×C4×C83—21no—
94C2×C4×C83—21no—
95C2×C4×C83—22no—
96C2×C4×C83—24no—
97C2×C4×C83—21no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—41no—
103C2×C4×C83—42no—
104C2×C4×C83—42no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—42no—
108C2×C4×C83—42no—
109C2×C4×C83—42no—
110C2×C4×C83#10012yes—
111C2×C4×C83C4×D412yes—
112C2×C4×C83#12011yescharacteristic
113C2×C4×C83#12112yes—
114C2×C4×C83#12311yescharacteristic
115C83⋊C8—44no—
116C83⋊C8—82no—
117C22×C83—21no—
118C22×C83—21no—
119C22×C83#38611yescharacteristic
120C22×C83C2×#10011yescharacteristic
121C22×C83#41311yescharacteristic
122C4×C83—21no—
123C4×C83—22no—
124C4×C83—22no—
125C4×C83—22no—
126C4×C83—44no—
127C4×C83—41no—
128C4×C83—41no—
129C4×C83—41no—
130C4×C83—82no—
131C4×C83#45612yes—
132#9452—831nomaximal, Sylow
133C2×C83—21no—
134C2×C83—21no—
135C2×C83#188611yescharacteristic
136C2×C83#190011yescharacteristic
137C2×C83#190911yescharacteristic
138#2983—831no—
139#2546D8311yescharacteristic
140#1558—832no—
141#1467—831no—
142#1285—832no—
143C83#945211yescharacteristic, complemented, Sylow
144C2×C4⋊Q8Dic8312yes—
145C2×C4⋊Q8C2×D8311yescharacteristic
146C2×C4×Q8C2×D8311yescharacteristic
147#446—1664no—
148#432—832no—
149#432—832no—
150#432—1661no—
151#431—1661no—
152#398—21no—
153#398—21no—
154#391Dic8312yes—
155#389—21no—
156#389—21no—
157C4×C4⋊C4C2×D8311yescharacteristic
158#333—1664no—
159#324—1661no—
160#324—1661no—
161C22×Q8C2×Dic8312yes—
162C22×Q8C2×Dic8311yescharacteristic
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165C4⋊Q8—44no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C2×Dic8311yescharacteristic
174C2×C4⋊C4C22⋊D8311yescharacteristic
175C2×C4⋊C4C22⋊D8311yescharacteristic
176C2×C42C2×Dic8312yes—
177C2×C42C22⋊D8311yescharacteristic
178C2×C42C22⋊D8311yescharacteristic
179C2×C42C22×D8311yescharacteristic
180C4⋊C8—834no—
181C4⋊C8—1662no—
182C4⋊C8—1662no—
183C4⋊C8—1662no—
184C22⋊C8—1662no—
185C22⋊C8—1662no—
186#97—1662no—
187#97—1662no—
188#97—1662no—
189C4×C8—1662no—
190#95—22no—
191#95—22no—
192#95—21no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—24no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4C22⋊Dic8311yescharacteristic
202C22×C4C22⋊Dic8311yescharacteristic
203C22×C4C22⋊Dic8311yescharacteristic
204C22×C4C22⋊Dic8311yescharacteristic
205C22×C4C22×Dic8311yescharacteristic
206C22×C4C2×C22⋊D8311yescharacteristic
207C22×C4C2×C22⋊D8311yescharacteristic
208C2×C8—3322no—
209C2×C8—1664no—
210C4⋊C4—24no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—41no—
216C4⋊C4—42no—
217C4⋊C4—41no—
218C4⋊C4—44no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—42no—
224C42D4×D8312yes—
225C42#1305058912yes—
226C23C2×C22⋊Dic8311yescharacteristic
227Q8—44no—
228Q8—84no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4#1458170912yes—
249C2×C4D4×Dic8312yes—
250C2×C4#1458176011yescharacteristic
251C2×C4#1458176412yes—
252C2×C4#1458177311yescharacteristic
253C8—3324no—
254C8—6642no—
255C22—21no—
256C22—21no—
257C22#1912758111yescharacteristic
258C22C2×#1458170911yescharacteristic
259C22#1912768511yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—44no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4—82no—
269C4#1912788312yes—
270C2—21no—
271C2—21no—
272C2#2490785711yescharacteristic
273C2#2490792711yescharacteristic
274C2#2490798611yescharacteristic
subgroupG/H
centerC22#19127581
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#2546C2
socleC22×C83#386
prime radicalC23×C83C2×C22⋊C4
cosocleC2×C42×C83C23
hypercenter#2546D83
hypocenterC83#9452
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
143. C83#9452semidirect

Maximal subgroups

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

subgroupindex
#249165482
#249061892
#249058072
#249053192
C83×#25462
#945283