Finite Group Databasebeta

← C83×#9483 #35237307

Subgroups — C83×#9483 #35237307

Order 21248.

542 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C83×#2972C211yesmaximal, characteristic
2C83×#2580C211yesmaximal, characteristic
3C83×#1800C211yesmaximal, characteristic
4C83×#1487C212yesmaximal, complemented
5C83×#1286C212yesmaximal, complemented
6C2×C4×Q8×C83C2211yescharacteristic
7C2×C4×D4×C83C2211yescharacteristic
8C8×D4×C83—24no—
9#431×C83C2212yes—
10#423×C83C2212yes—
11C2×#100×C83—21no—
12C2×C22⋊C8×C83—22no—
13#399×C83C412yes—
14#393×C83C412yes—
15#390×C83—21no—
16#389×C83—21no—
17#385×C83—22no—
18#382×C83C2211yescharacteristic
19#343×C83—21no—
20Q8⋊C8×C83—24no—
21C22×Q8×C83C2×C411yescharacteristic
22C22×D4×C83D411yescharacteristic
23C23×C4×C83D412yes—
24C2×M16×C83—22no—
25C22×C8×C83—24no—
26C4×Q8×C83—22no—
27C4×Q8×C83—22no—
28C4×D4×C83—22no—
29C4×D4×C83—22no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83—21no—
32C2×C4⋊C4×C83—22no—
33C2×C4⋊C4×C83C2×C411yescharacteristic
34C2×C4⋊C4×C83D411yescharacteristic
35C2×C22⋊C4×C83—22no—
36C2×C22⋊C4×C83—22no—
37C2×C22⋊C4×C83C2×C412yes—
38C2×C42×C83—21no—
39C2×C42×C83C2311yescharacteristic
40C4⋊C8×C83—22no—
41C4⋊C8×C83—22no—
42C4⋊C8×C83—22no—
43#100×C83—42no—
44C22⋊C8×C83—24no—
45C22⋊C8×C83—22no—
46C4×C8×C83D414yes—
47#95×C83—22no—
48#95×C83—21no—
49#95×C83C2×C412yes—
50C24×C83C22⋊C412yes—
51C2×Q8×C83—22no—
52C2×Q8×C83—42no—
53C2×D4×C83—22no—
54C2×D4×C83—22no—
55C2×D4×C83SD1612yes—
56C2×D4×C83Q1612yes—
57C22×C4×C83—21no—
58C22×C4×C83—22no—
59C22×C4×C83—22no—
60C22×C4×C83—22no—
61C22×C4×C83—21no—
62C22×C4×C83—82no—
63C22×C4×C83C22⋊C412yes—
64C22×C4×C83C22×C411yescharacteristic
65C22×C4×C83C2×D411yescharacteristic
66C22×C4×C83C2×D411yescharacteristic
67M16×C83—42no—
68M16×C83—42no—
69C2×C8×C83—24no—
70C2×C8×C83—42no—
71C2×C8×C83—84no—
72C4⋊C4×C83—22no—
73C4⋊C4×C83—22no—
74C4⋊C4×C83—41no—
75C4⋊C4×C83—41no—
76C4⋊C4×C83—42no—
77C4⋊C4×C83—82no—
78C22⋊C4×C83—24no—
79C22⋊C4×C83—44no—
80C22⋊C4×C83—82no—
81C42×C83—42no—
82C42×C83C2×D412yes—
83C42×C83#4112yes—
84C23×C83—22no—
85C23×C83—22no—
86C23×C83—42no—
87C23×C83—42no—
88C23×C83#10314yes—
89C23×C83C2×C22⋊C411yescharacteristic
90Q8×C83—24no—
91Q8×C83—42no—
92D4×C83—24no—
93D4×C83—24no—
94C2×C4×C83—22no—
95C2×C4×C83—22no—
96C2×C4×C83—41no—
97C2×C4×C83—41no—
98C2×C4×C83—44no—
99C2×C4×C83—41no—
100C2×C4×C83—41no—
101C2×C4×C83—42no—
102C2×C4×C83—42no—
103C2×C4×C83—41no—
104C2×C4×C83—42no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—42no—
108C2×C4×C83—82no—
109C2×C4×C83C4×D412yes—
110C2×C4×C83#12011yescharacteristic
111C2×C4×C83#12112yes—
112C2×C4×C83#12311yescharacteristic
113C2×C4×C83C2×SD1611yescharacteristic
114C2×C4×C83C2×Q1611yescharacteristic
115C2×C4×C83#13512yes—
116C8×C83—44no—
117C8×C83—82no—
118C22×C83—21no—
119C22×C83—21no—
120C22×C83—24no—
121C22×C83—44no—
122C22×C83—42no—
123C22×C83—42no—
124C22×C83—82no—
125C22×C83#38611yescharacteristic
126C22×C83C2×#10311yescharacteristic
127C22×C83#41611yescharacteristic
128C4×C83—22no—
129C4×C83—21no—
130C4×C83—21no—
131C4×C83—42no—
132C4×C83—42no—
133C4×C83—82no—
134C4×C83—81no—
135C4×C83#46512yes—
136C4×C83#46712yes—
137#9483C8311yesmaximal, characteristic, direct product factor, Sylow
138C2×C83—21no—
139C2×C83—21no—
140C2×C83—44no—
141C2×C83#189111yescharacteristic
142C2×C83#189211yescharacteristic
143C2×C83#191111yescharacteristic
144#2972C2×C8311yescharacteristic
145#2580C2×C8311yescharacteristic
146#1800C2×C8311yescharacteristic
147#1487C2×C8312yescomplemented
148#1286C2×C8312yescomplemented
149C83#948311yescharacteristic, direct product factor, Sylow
150C2×C4×Q8C22×C8311yescharacteristic
151C2×C4×D4C22×C8311yescharacteristic
152C8×D4—24no—
153#431C22×C8312yes—
154#423C22×C8312yes—
155C2×#100—21no—
156C2×C22⋊C8—22no—
157#399C4×C8312yes—
158#393C4×C8312yes—
159#390—21no—
160#389—21no—
161#385—22no—
162#382C22×C8311yescharacteristic
163#343—21no—
164Q8⋊C8—24no—
165C22×Q8C2×C4×C8311yescharacteristic
166C22×D4D4×C8311yescharacteristic
167C23×C4D4×C8312yes—
168C2×M16—22no—
169C22×C8—24no—
170C4×Q8—22no—
171C4×Q8—22no—
172C4×D4—22no—
173C4×D4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4C2×C4×C8311yescharacteristic
178C2×C4⋊C4D4×C8311yescharacteristic
179C2×C22⋊C4—22no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4C2×C4×C8312yes—
182C2×C42—21no—
183C2×C42C23×C8311yescharacteristic
184C4⋊C8—22no—
185C4⋊C8—22no—
186C4⋊C8—22no—
187#100—42no—
188C22⋊C8—24no—
189C22⋊C8—22no—
190C4×C8D4×C8314yes—
191#95—22no—
192#95—21no—
193#95C2×C4×C8312yes—
194C24C22⋊C4×C8312yes—
195C2×Q8—22no—
196C2×Q8—42no—
197C2×D4—22no—
198C2×D4—22no—
199C2×D4SD16×C8312yes—
200C2×D4Q16×C8312yes—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—82no—
207C22×C4C22⋊C4×C8312yes—
208C22×C4C22×C4×C8311yescharacteristic
209C22×C4C2×D4×C8311yescharacteristic
210C22×C4C2×D4×C8311yescharacteristic
211M16—42no—
212M16—42no—
213C2×C8—24no—
214C2×C8—42no—
215C2×C8—84no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—82no—
222C22⋊C4—24no—
223C22⋊C4—44no—
224C22⋊C4—82no—
225C42—42no—
226C42C2×D4×C8312yes—
227C42#41×C8312yes—
228C23—22no—
229C23—22no—
230C23—42no—
231C23—42no—
232C23#103×C8314yes—
233C23C2×C22⋊C4×C8311yescharacteristic
234Q8—24no—
235Q8—42no—
236D4—24no—
237D4—24no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—44no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4C4×D4×C8312yes—
254C2×C4#120×C8311yescharacteristic
255C2×C4#121×C8312yes—
256C2×C4#123×C8311yescharacteristic
257C2×C4C2×SD16×C8311yescharacteristic
258C2×C4C2×Q16×C8311yescharacteristic
259C2×C4#135×C8312yes—
260C8—44no—
261C8—82no—
262C22—21no—
263C22—21no—
264C22—24no—
265C22—44no—
266C22—42no—
267C22—42no—
268C22—82no—
269C22#386×C8311yescharacteristic
270C22C2×#103×C8311yescharacteristic
271C22#416×C8311yescharacteristic
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—42no—
277C4—82no—
278C4—81no—
279C4#465×C8312yes—
280C4#467×C8312yes—
281C2—21no—
282C2—21no—
283C2—44no—
284C2C83×#189111yescharacteristic
285C2C83×#189211yescharacteristic
286C2C83×#191111yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×C42C23×C83
prime radicalC22×D4×C83D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
4. C83×#1487C2semidirect
5. C83×#1286C2semidirect
137. #9483C83direct (N × H)
147. #1487C2×C83semidirect
148. #1286C2×C83semidirect
149. C83#9483direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#29722
C83×#25802
C83×#18002
C83×#14872
C83×#12862
#948383