Finite Group Databasebeta

← C83×#9450 #35237274

Subgroups — C83×#9450 #35237274

Order 21248.

424 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2983C211yesmaximal, characteristic
2C83×#2565C211yesmaximal, characteristic
3C83×#1534C212yesmaximal
4C83×#1467C211yesmaximal, characteristic
5C83×#1285C212yesmaximal
6C2×#125×C83C2211yescharacteristic
7C2×C4×Q8×C83C2211yescharacteristic
8#446×C83—24no—
9#432×C83—21no—
10#432×C83C2212yes—
11#432×C83C2212yes—
12#431×C83—21no—
13#398×C83—21no—
14#398×C83—21no—
15#391×C83C411yescharacteristic
16#391×C83C411yescharacteristic
17#387×C83—21no—
18#387×C83—21no—
19#384×C83C411yescharacteristic
20#382×C83C411yescharacteristic
21C4×C4⋊C4×C83C2211yescharacteristic
22#330×C83—24no—
23#324×C83—21no—
24#324×C83—21no—
25C22×Q8×C83C2×C411yescharacteristic
26#125×C83—22no—
27#125×C83—22no—
28C4×Q8×C83—22no—
29C4×Q8×C83—22no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83—21no—
32C2×C4⋊C4×C83—21no—
33C2×C4⋊C4×C83—21no—
34C2×C4⋊C4×C83—21no—
35C2×C4⋊C4×C83C2×C411yescharacteristic
36C2×C4⋊C4×C83C2×C411yescharacteristic
37C2×C4⋊C4×C83C2×C411yescharacteristic
38C2×C4⋊C4×C83D411yescharacteristic
39C2×C4⋊C4×C83D411yescharacteristic
40C2×C42×C83C2×C411yescharacteristic
41C2×C42×C83C2×C411yescharacteristic
42C2×C42×C83D411yescharacteristic
43C2×C42×C83D411yescharacteristic
44C2×C42×C83C2311yescharacteristic
45C4⋊C8×C83—22no—
46C4⋊C8×C83—22no—
47C4⋊C8×C83—22no—
48C4⋊C8×C83—22no—
49C22⋊C8×C83—22no—
50C22⋊C8×C83—22no—
51#97×C83—22no—
52#97×C83—22no—
53#97×C83D414yes—
54C4×C8×C83—22no—
55#95×C83—21no—
56#95×C83—21no—
57#95×C83—21no—
58#95×C83—21no—
59#95×C83—21no—
60#95×C83—21no—
61#95×C83—21no—
62C2×Q8×C83—22no—
63C2×Q8×C83—22no—
64C2×Q8×C83—41no—
65C22×C4×C83—21no—
66C22×C4×C83—21no—
67C22×C4×C83—21no—
68C22×C4×C83—21no—
69C22×C4×C83C22⋊C411yescharacteristic
70C22×C4×C83C22⋊C411yescharacteristic
71C22×C4×C83C22⋊C411yescharacteristic
72C22×C4×C83C22⋊C411yescharacteristic
73C22×C4×C83C22×C411yescharacteristic
74C22×C4×C83C2×D411yescharacteristic
75C22×C4×C83C2×D411yescharacteristic
76C2×C8×C83—24no—
77C2×C8×C83—42no—
78C4⋊C4×C83—22no—
79C4⋊C4×C83—22no—
80C4⋊C4×C83—22no—
81C4⋊C4×C83—22no—
82C4⋊C4×C83—22no—
83C4⋊C4×C83—42no—
84C4⋊C4×C83—42no—
85C4⋊C4×C83—42no—
86C4⋊C4×C83—41no—
87C4⋊C4×C83—42no—
88C4⋊C4×C83—41no—
89C42×C83—21no—
90C42×C83—21no—
91C42×C83—21no—
92C42×C83—21no—
93C42×C83—41no—
94C42×C83—41no—
95C42×C83C2×D412yes—
96C42×C83#4112yes—
97C23×C83C2×C22⋊C411yescharacteristic
98Q8×C83—44no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—22no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—41no—
113C2×C4×C83—41no—
114C2×C4×C83—41no—
115C2×C4×C83—41no—
116C2×C4×C83—41no—
117C2×C4×C83—41no—
118C2×C4×C83—41no—
119C2×C4×C83—42no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83#10112yes—
124C2×C4×C83C4×D412yes—
125C2×C4×C83#12011yescharacteristic
126C2×C4×C83#12112yes—
127C2×C4×C83#12311yescharacteristic
128C8×C83—44no—
129C8×C83—82no—
130C22×C83—21no—
131C22×C83—21no—
132C22×C83#38611yescharacteristic
133C22×C83C2×#10111yescharacteristic
134C22×C83#41311yescharacteristic
135C4×C83—22no—
136C4×C83—22no—
137C4×C83—22no—
138C4×C83—21no—
139C4×C83—21no—
140C4×C83—42no—
141C4×C83—41no—
142C4×C83—41no—
143C4×C83—41no—
144C4×C83—81no—
145C4×C83—81no—
146C4×C83—81no—
147#9450C8311yesmaximal, characteristic, direct product factor, Sylow
148C2×C83—21no—
149C2×C83—21no—
150C2×C83#188411yescharacteristic
151C2×C83#190111yescharacteristic
152C2×C83#191211yescharacteristic
153#2983C2×C8311yescharacteristic
154#2565C2×C8311yescharacteristic
155#1534C2×C8312yes—
156#1467C2×C8311yescharacteristic
157#1285C2×C8312yes—
158C83#945011yescharacteristic, direct product factor, Sylow
159C2×#125C22×C8311yescharacteristic
160C2×C4×Q8C22×C8311yescharacteristic
161#446—24no—
162#432—21no—
163#432C22×C8312yes—
164#432C22×C8312yes—
165#431—21no—
166#398—21no—
167#398—21no—
168#391C4×C8311yescharacteristic
169#391C4×C8311yescharacteristic
170#387—21no—
171#387—21no—
172#384C4×C8311yescharacteristic
173#382C4×C8311yescharacteristic
174C4×C4⋊C4C22×C8311yescharacteristic
175#330—24no—
176#324—21no—
177#324—21no—
178C22×Q8C2×C4×C8311yescharacteristic
179#125—22no—
180#125—22no—
181C4×Q8—22no—
182C4×Q8—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4C2×C4×C8311yescharacteristic
189C2×C4⋊C4C2×C4×C8311yescharacteristic
190C2×C4⋊C4C2×C4×C8311yescharacteristic
191C2×C4⋊C4D4×C8311yescharacteristic
192C2×C4⋊C4D4×C8311yescharacteristic
193C2×C42C2×C4×C8311yescharacteristic
194C2×C42C2×C4×C8311yescharacteristic
195C2×C42D4×C8311yescharacteristic
196C2×C42D4×C8311yescharacteristic
197C2×C42C23×C8311yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8—22no—
201C4⋊C8—22no—
202C22⋊C8—22no—
203C22⋊C8—22no—
204#97—22no—
205#97—22no—
206#97D4×C8314yes—
207C4×C8—22no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊C4×C8311yescharacteristic
223C22×C4C22⋊C4×C8311yescharacteristic
224C22×C4C22⋊C4×C8311yescharacteristic
225C22×C4C22⋊C4×C8311yescharacteristic
226C22×C4C22×C4×C8311yescharacteristic
227C22×C4C2×D4×C8311yescharacteristic
228C22×C4C2×D4×C8311yescharacteristic
229C2×C8—24no—
230C2×C8—42no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—41no—
247C42—41no—
248C42C2×D4×C8312yes—
249C42#41×C8312yes—
250C23C2×C22⋊C4×C8311yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4#101×C8312yes—
277C2×C4C4×D4×C8312yes—
278C2×C4#120×C8311yescharacteristic
279C2×C4#121×C8312yes—
280C2×C4#123×C8311yescharacteristic
281C8—44no—
282C8—82no—
283C22—21no—
284C22—21no—
285C22#386×C8311yescharacteristic
286C22C2×#101×C8311yescharacteristic
287C22#413×C8311yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—21no—
292C4—21no—
293C4—42no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C2—21no—
301C2—21no—
302C2C83×#188411yescharacteristic
303C2C83×#190111yescharacteristic
304C2C83×#191211yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×C42C23×C83
prime radicalC23×C83C2×C22⋊C4
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
147. #9450C83direct (N × H)
158. C83#9450direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#29832
C83×#25652
C83×#15342
C83×#14672
C83×#12852
#945083