Finite Group Databasebeta

← C83×#11454 #35239278

Subgroups — C83×#11454 #35239278

Order 21248.

434 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 142 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×#2317C211yesmaximal, characteristic
2C83×#1458C211yesmaximal, characteristic
3C83×#1458C211yesmaximal, characteristic
4C83×#1326C214yesmaximal
5C2×#117×C83C411yescharacteristic
6C2×#117×C83C2211yescharacteristic
7C22×C4⋊C4×C83C411yescharacteristic
8#431×C83—21no—
9#431×C83—21no—
10#389×C83—21no—
11#389×C83—21no—
12#385×C83C412yes—
13#385×C83C2212yes—
14#384×C83—21no—
15#382×C83—21no—
16#324×C83—21no—
17#324×C83—21no—
18#323×C83C2212yes—
19#323×C83C2212yes—
20C23×C4×C83C2×C411yescharacteristic
21C23×C4×C83C2×C412yes—
22#117×C83—22no—
23#117×C83—41no—
24#117×C83—41no—
25#117×C83C814yescomplemented
26C2×C4⋊C4×C83—21no—
27C2×C4⋊C4×C83—21no—
28C2×C4⋊C4×C83—21no—
29C2×C4⋊C4×C83—22no—
30C2×C4⋊C4×C83—22no—
31C2×C4⋊C4×C83—41no—
32C2×C4⋊C4×C83—41no—
33C2×C4⋊C4×C83D411yescharacteristic
34C2×C4⋊C4×C83D411yescharacteristic
35C2×C22⋊C4×C83C2×C412yes—
36C2×C22⋊C4×C83C2×C411yescharacteristic
37C2×C22⋊C4×C83C2311yescharacteristic
38C2×C42×C83—21no—
39C2×C42×C83D411yescharacteristic
40C2×C42×C83D411yescharacteristic
41C4⋊C8×C83—41no—
42C4⋊C8×C83—41no—
43C22⋊C8×C83—22no—
44C22⋊C8×C83—22no—
45C4×C8×C83—41no—
46C4×C8×C83—41no—
47#95×C83—22no—
48#95×C83—22no—
49C24×C83C22×C411yescharacteristic
50C22×C4×C83—21no—
51C22×C4×C83—21no—
52C22×C4×C83—22no—
53C22×C4×C83—22no—
54C22×C4×C83—22no—
55C22×C4×C83—42no—
56C22×C4×C83—82no—
57C22×C4×C83C22⋊C411yescharacteristic
58C22×C4×C83C22⋊C411yescharacteristic
59C22×C4×C83C22⋊C411yescharacteristic
60C22×C4×C83C22⋊C411yescharacteristic
61C22×C4×C83C2×C812yes—
62C22×C4×C83M1612yes—
63C22×C4×C83C2×D411yescharacteristic
64C22×C4×C83C2×D411yescharacteristic
65C2×C8×C83—42no—
66C2×C8×C83—42no—
67C4⋊C4×C83—24no—
68C4⋊C4×C83—41no—
69C4⋊C4×C83—41no—
70C4⋊C4×C83—42no—
71C4⋊C4×C83—41no—
72C4⋊C4×C83—41no—
73C4⋊C4×C83—82no—
74C4⋊C4×C83—82no—
75C22⋊C4×C83—22no—
76C22⋊C4×C83—41no—
77C22⋊C4×C83—41no—
78C22⋊C4×C83C2×C814yes—
79C42×C83—24no—
80C42×C83—21no—
81C42×C83—21no—
82C42×C83—21no—
83C42×C83—21no—
84C23×C83—21no—
85C23×C83—21no—
86C23×C83—41no—
87C23×C83—41no—
88C23×C83C2×C22⋊C411yescharacteristic
89C23×C83C22×C811yescharacteristic
90C23×C83C2×M1611yescharacteristic
91C2×C4×C83—21no—
92C2×C4×C83—21no—
93C2×C4×C83—22no—
94C2×C4×C83—22no—
95C2×C4×C83—22no—
96C2×C4×C83—22no—
97C2×C4×C83—24no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—42no—
103C2×C4×C83—42no—
104C2×C4×C83—41no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—42no—
109C2×C4×C83—42no—
110C2×C4×C83—42no—
111C2×C4×C83—84no—
112C2×C4×C83C22⋊C812yes—
113C2×C4×C83C22⋊C812yes—
114C2×C4×C83#9911yescharacteristic
115C2×C4×C83#9911yescharacteristic
116C2×C4×C83#10112yes—
117C8×C83—82no—
118C8×C83—82no—
119C22×C83—21no—
120C22×C83—21no—
121C22×C83—21no—
122C22×C83—21no—
123C22×C83—41no—
124C22×C83—41no—
125C22×C83—42no—
126C22×C83—41no—
127C22×C83—41no—
128C22×C83C2×C22⋊C811yescharacteristic
129C22×C83C2×#9911yescharacteristic
130C22×C83C2×#10111yescharacteristic
131C4×C83—22no—
132C4×C83—44no—
133C4×C83—41no—
134C4×C83—41no—
135C4×C83—41no—
136C4×C83—41no—
137C4×C83—82no—
138C4×C83#32412yes—
139C4×C83#32412yes—
140#11454C8311yesmaximal, characteristic, direct product factor, Sylow
141C2×C83—21no—
142C2×C83—21no—
143C2×C83—41no—
144C2×C83—41no—
145C2×C83C2×#32411yescharacteristic
146C2×C83#212211yescharacteristic
147C2×C83#212311yescharacteristic
148#2317C2×C8311yescharacteristic
149#1458C2×C8311yescharacteristic
150#1458C2×C8311yescharacteristic
151#1326C2×C8314yes—
152C83#1145411yescharacteristic, direct product factor, Sylow
153C2×#117C4×C8311yescharacteristic
154C2×#117C22×C8311yescharacteristic
155C22×C4⋊C4C4×C8311yescharacteristic
156#431—21no—
157#431—21no—
158#389—21no—
159#389—21no—
160#385C4×C8312yes—
161#385C22×C8312yes—
162#384—21no—
163#382—21no—
164#324—21no—
165#324—21no—
166#323C22×C8312yes—
167#323C22×C8312yes—
168C23×C4C2×C4×C8311yescharacteristic
169C23×C4C2×C4×C8312yes—
170#117—22no—
171#117—41no—
172#117—41no—
173#117C8×C8314yescomplemented
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4D4×C8311yescharacteristic
182C2×C4⋊C4D4×C8311yescharacteristic
183C2×C22⋊C4C2×C4×C8312yes—
184C2×C22⋊C4C2×C4×C8311yescharacteristic
185C2×C22⋊C4C23×C8311yescharacteristic
186C2×C42—21no—
187C2×C42D4×C8311yescharacteristic
188C2×C42D4×C8311yescharacteristic
189C4⋊C8—41no—
190C4⋊C8—41no—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C4×C8—41no—
194C4×C8—41no—
195#95—22no—
196#95—22no—
197C24C22×C4×C8311yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—82no—
205C22×C4C22⋊C4×C8311yescharacteristic
206C22×C4C22⋊C4×C8311yescharacteristic
207C22×C4C22⋊C4×C8311yescharacteristic
208C22×C4C22⋊C4×C8311yescharacteristic
209C22×C4C2×C8×C8312yes—
210C22×C4M16×C8312yes—
211C22×C4C2×D4×C8311yescharacteristic
212C22×C4C2×D4×C8311yescharacteristic
213C2×C8—42no—
214C2×C8—42no—
215C4⋊C4—24no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—42no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—82no—
222C4⋊C4—82no—
223C22⋊C4—22no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4C2×C8×C8314yes—
227C42—24no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23C2×C22⋊C4×C8311yescharacteristic
237C23C22×C8×C8311yescharacteristic
238C23C2×M16×C8311yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—24no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—84no—
260C2×C4C22⋊C8×C8312yes—
261C2×C4C22⋊C8×C8312yes—
262C2×C4#99×C8311yescharacteristic
263C2×C4#99×C8311yescharacteristic
264C2×C4#101×C8312yes—
265C8—82no—
266C8—82no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22C2×C22⋊C8×C8311yescharacteristic
277C22C2×#99×C8311yescharacteristic
278C22C2×#101×C8311yescharacteristic
279C4—22no—
280C4—44no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—41no—
285C4—82no—
286C4#324×C8312yes—
287C4#324×C8312yes—
288C2—21no—
289C2—21no—
290C2—41no—
291C2—41no—
292C2C2×#324×C8311yescharacteristic
293C2C83×#212211yescharacteristic
294C2C83×#212311yescharacteristic
subgroupG/H
center, socleC22×C83C2×#99
commutatorC23C22×C8×C83
Frattini, cosocleC2×C22⋊C4C23×C83
prime radicalC24×C83C22×C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C22×C4×C83 ◁ C2×#117×C83 ◁ G

Complements

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

NH ≅ G/Ntype
25. #117×C83C8semidirect
140. #11454C83direct (N × H)
152. C83#11454direct (N × H)
173. #117C8×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#23172
C83×#14582
C83×#13262
#1145483