Finite Group Databasebeta

← #35304512

Subgroups — #35304512

Order 21248.

424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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#24915826C211yesmaximal, characteristic
2#24907212C211yesmaximal, characteristic
3#24905345C214yesmaximal
4C83×#1767C211yesmaximal, characteristic
5C2×#14581784C412yes—
6C2×#14581703C2212yes—
7#19127599—21no—
8#19127599—21no—
9#19127599—21no—
10#19127599—21no—
11#19127571C411yescharacteristic
12#19127571C411yescharacteristic
13#19127567C2212yes—
14#19127456—21no—
15#19127456—21no—
16C2×C4⋊C8×C83—21no—
17C2×#97×C83C2212yes—
18C43×C83C2211yescharacteristic
19#336×C83—21no—
20C22×C83⋊C8—22no—
21#14581784—44no—
22C2×C4⋊Dic83—21no—
23C2×C4⋊Dic83—21no—
24C2×C4⋊Dic83—21no—
25C2×C4⋊Dic83—21no—
26C2×C4⋊Dic83C2×C412yes—
27C2×C4⋊Dic83C2×C412yes—
28C2×Dic83⋊C4—22no—
29C2×Dic83⋊C4—22no—
30#14581703—22no—
31#14581703Q814yes—
32C83⋊#95—22no—
33C83⋊#95—22no—
34C22×C8×C83—22no—
35C2×C42×C83C2×C411yescharacteristic
36C2×C42×C83C2×C411yescharacteristic
37C2×C42×C83D411yescharacteristic
38C2×C42×C83D411yescharacteristic
39C2×C42×C83D411yescharacteristic
40C2×C42×C83D411yescharacteristic
41C2×C42×C83C2311yescharacteristic
42C4⋊C8×C83—24no—
43#97×C83—24no—
44C22×Dic83—22no—
45C22×Dic83—22no—
46C2×C83⋊C8—24no—
47C2×C83⋊C8—42no—
48C2×C83⋊C8—42no—
49C4⋊Dic83—42no—
50C4⋊Dic83—42no—
51C4⋊Dic83—42no—
52C4⋊Dic83—42no—
53C4⋊Dic83—42no—
54C4⋊Dic83—42no—
55Dic83⋊C4—44no—
56Dic83⋊C4—44no—
57C22×C4×C83C22⋊C411yescharacteristic
58C22×C4×C83C22⋊C411yescharacteristic
59C22×C4×C83C22⋊C411yescharacteristic
60C22×C4×C83C22⋊C411yescharacteristic
61C22×C4×C83C22×C411yescharacteristic
62C22×C4×C83C2×D411yescharacteristic
63C22×C4×C83C2×D411yescharacteristic
64C2×C8×C83—24no—
65C2×C8×C83—42no—
66C2×C8×C83—42no—
67C42×C83—22no—
68C42×C83—22no—
69C42×C83—22no—
70C42×C83—41no—
71C42×C83—41no—
72C42×C83—41no—
73C42×C83C2×Q812yes—
74C42×C83#4112yes—
75C23×C83C2×C22⋊C411yescharacteristic
76C2×C4×C83—21no—
77C2×C4×C83—21no—
78C2×C4×C83—21no—
79C2×C4×C83—21no—
80C2×C4×C83—21no—
81C2×C4×C83—21no—
82C2×C4×C83—21no—
83C2×C4×C83—21no—
84C2×C4×C83—21no—
85C2×C4×C83—21no—
86C2×C4×C83—21no—
87C2×C4×C83—21no—
88C2×C4×C83—21no—
89C2×C4×C83—21no—
90C2×C4×C83—21no—
91C2×C4×C83#10012yes—
92C2×C4×C83#10112yes—
93C2×C4×C83#10412yes—
94C2×C4×C83C4×Q812yes—
95C2×C4×C83C22⋊Q812yes—
96C2×C4×C83#12411yescharacteristic
97C2×C4×C83C4⋊Q811yescharacteristic
98C2×Dic83—42no—
99C2×Dic83—42no—
100C2×Dic83—42no—
101C2×Dic83—42no—
102C2×Dic83—42no—
103C2×Dic83—42no—
104C8×C83—44no—
105C83⋊C8—44no—
106C22×C83#39111yescharacteristic
107C22×C83C2×#10011yescharacteristic
108C22×C83C2×#10111yescharacteristic
109C22×C83C2×#10411yescharacteristic
110C22×C83#42111yescharacteristic
111C22×C83#42111yescharacteristic
112C22×C83#42111yescharacteristic
113C4×C83—21no—
114C4×C83—21no—
115C4×C83—22no—
116C4×C83—22no—
117C4×C83—22no—
118C4×C83—22no—
119C4×C83—22no—
120C4×C83—41no—
121Dic83—82no—
122Dic83—82no—
123#9894—831nomaximal, Sylow
124C2×C83#152811yescharacteristic
125C2×C83#153011yescharacteristic
126C2×C83#153411yescharacteristic
127C2×C83#153611yescharacteristic
128C2×C83#198611yescharacteristic
129C2×C83#199511yescharacteristic
130C2×C83#199711yescharacteristic
131#2859—831no—
132#1767D8311yescharacteristic
133#1745—831no—
134#1295—834no—
135C83#989411yescharacteristic, complemented, Sylow
136C2×#125—832no—
137C2×C4⋊C8—21no—
138C2×#97—832no—
139C2×#97C2×D8312yes—
140#389—1661no—
141#389—1661no—
142#389—1661no—
143#389—1661no—
144#384—831no—
145#384—831no—
146#382—832no—
147C43C2×D8311yescharacteristic
148#336—21no—
149#336—1661no—
150#336—1661no—
151C22×C8—22no—
152C22×C8—1662no—
153#125—3324no—
154C2×C4⋊C4—832no—
155C2×C4⋊C4—832no—
156C2×C4⋊C4—1662no—
157C2×C4⋊C4—1662no—
158C2×C4⋊C4—1661no—
159C2×C4⋊C4—1661no—
160C2×C4⋊C4—1661no—
161C2×C4⋊C4—1661no—
162C2×C42C4×D8311yescharacteristic
163C2×C42C4×D8311yescharacteristic
164C2×C42D33211yescharacteristic
165C2×C42D33211yescharacteristic
166C2×C42C22⋊D8311yescharacteristic
167C2×C42C22⋊D8311yescharacteristic
168C2×C42C22×D8311yescharacteristic
169C4⋊C8—24no—
170#97—24no—
171#97—834no—
172#97—1662no—
173#95—1662no—
174#95—1662no—
175C22×C4—1662no—
176C22×C4—1662no—
177C22×C4(C2×D83)⋊C411yescharacteristic
178C22×C4(C2×D83)⋊C411yescharacteristic
179C22×C4(C2×D83)⋊C411yescharacteristic
180C22×C4(C2×D83)⋊C411yescharacteristic
181C22×C4C2×C4×D8311yescharacteristic
182C22×C4C2×C22⋊D8311yescharacteristic
183C22×C4C2×D33211yescharacteristic
184C2×C8—24no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—3322no—
188C2×C8—3322no—
189C2×C8—1664no—
190C4⋊C4—3322no—
191C4⋊C4—3322no—
192C4⋊C4—3324no—
193C4⋊C4—3322no—
194C4⋊C4—3322no—
195C4⋊C4—3322no—
196C4⋊C4—3324no—
197C4⋊C4—3322no—
198C42—22no—
199C42—22no—
200C42—22no—
201C42—41no—
202C42—41no—
203C42—41no—
204C42Q8×D8312yes—
205C42#1305058912yes—
206C23C2×(C2×D83)⋊C411yescharacteristic
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—3322no—
223C2×C4—3322no—
224C2×C4—3322no—
225C2×C4—3322no—
226C2×C4—3322no—
227C2×C4—3322no—
228C2×C4#1458170812yes—
229C2×C4#1458171012yes—
230C2×C4#1458172012yes—
231C2×C4#1458175712yes—
232C2×C4#1458177212yes—
233C2×C4#1458177911yescharacteristic
234C2×C4#1458179011yescharacteristic
235C8—44no—
236C8—3324no—
237C22#1912760611yescharacteristic
238C22C2×#1458170811yescharacteristic
239C22C2×#1458171011yescharacteristic
240C22C2×#1458172011yescharacteristic
241C22#1912771711yescharacteristic
242C22#1912771711yescharacteristic
243C22#1912771911yescharacteristic
244C4—22no—
245C4—22no—
246C4—22no—
247C4—21no—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—41no—
252C4—6642no—
253C4—6642no—
254C2#2490606411yescharacteristic
255C2#2490607311yescharacteristic
256C2#2490608911yescharacteristic
257C2#2490609711yescharacteristic
258C2#2490840611yescharacteristic
259C2#2490844311yescharacteristic
260C2#2490845111yescharacteristic
subgroupG/H
centerC23C2×(C2×D83)⋊C4
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1767C2
socle, prime radicalC23×C83C2×C22⋊C4
cosocleC2×C42×C83C23
hypercenter#1767D83
hypocenterC83#9894
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
135. C83#9894semidirect

Maximal subgroups

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

subgroupindex
#249158262
#249072122
#249053452
C83×#17672
#989483