Finite Group Databasebeta

← C83×#11569 #35239393

Subgroups — C83×#11569 #35239393

Order 21248.

424 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2563C211yesmaximal, characteristic
2C83×#1465C211yesmaximal, characteristic
3C83×#1459C211yesmaximal, characteristic
4C83×#1324C214yesmaximal, complemented
5C2×C4⋊Q8×C83C411yescharacteristic
6C2×C4×D4×C83C2211yescharacteristic
7#407×C83—21no—
8C2×C22⋊C8×C83—21no—
9#393×C83—21no—
10#393×C83—21no—
11#390×C83C412yes—
12#382×C83C2212yes—
13#380×C83—21no—
14#380×C83—21no—
15C4×C4⋊C4×C83C411yescharacteristic
16#324×C83C2212yes—
17#324×C83C2212yes—
18#323×C83—21no—
19#323×C83—21no—
20C22×Q8×C83—21no—
21C22×D4×C83C2×C411yescharacteristic
22C23×C4×C83D411yescharacteristic
23C23×C4×C83D411yescharacteristic
24C2×M16×C83—41no—
25C22×C8×C83—41no—
26C4⋊Q8×C83—41no—
27C4⋊Q8×C83—41no—
28C4×D4×C83—41no—
29C4×D4×C83—41no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83—21no—
32C2×C4⋊C4×C83C2×C412yes—
33C2×C4⋊C4×C83C2311yescharacteristic
34C2×C22⋊C4×C83—22no—
35C2×C22⋊C4×C83—22no—
36C2×C22⋊C4×C83D411yescharacteristic
37C2×C22⋊C4×C83D411yescharacteristic
38C2×C42×C83C2×C412yes—
39C2×C42×C83C2×C411yescharacteristic
40C22⋊C8×C83—22no—
41C22⋊C8×C83—22no—
42C22⋊C8×C83—41no—
43C22⋊C8×C83—41no—
44#95×C83—21no—
45#95×C83—22no—
46#95×C83—22no—
47C24×C83C22⋊C411yescharacteristic
48C24×C83C22⋊C411yescharacteristic
49C2×Q8×C83—42no—
50C2×Q8×C83—82no—
51C2×D4×C83—22no—
52C2×D4×C83—22no—
53C2×D4×C83—41no—
54C22×C4×C83—21no—
55C22×C4×C83—21no—
56C22×C4×C83—21no—
57C22×C4×C83—21no—
58C22×C4×C83—22no—
59C22×C4×C83—22no—
60C22×C4×C83—42no—
61C22×C4×C83—42no—
62C22×C4×C83C22⋊C411yescharacteristic
63C22×C4×C83C22⋊C411yescharacteristic
64C22×C4×C83C22×C411yescharacteristic
65C22×C4×C83C2×D411yescharacteristic
66C22×C4×C83C2×D411yescharacteristic
67M16×C83—82no—
68C2×C8×C83—42no—
69C2×C8×C83—42no—
70C2×C8×C83—82no—
71C4⋊C4×C83—41no—
72C4⋊C4×C83—42no—
73C4⋊C4×C83—42no—
74C4⋊C4×C83—41no—
75C4⋊C4×C83—41no—
76C22⋊C4×C83—41no—
77C22⋊C4×C83—41no—
78C22⋊C4×C83—82no—
79C22⋊C4×C83—82no—
80C42×C83—21no—
81C42×C83—21no—
82C42×C83—24no—
83C23×C83—21no—
84C23×C83—21no—
85C23×C83—21no—
86C23×C83—21no—
87C23×C83—21no—
88C23×C83—41no—
89C23×C83—41no—
90C23×C83—41no—
91C23×C83—41no—
92C23×C83#10112yes—
93C23×C83C2×C22⋊C411yescharacteristic
94Q8×C83—84no—
95D4×C83—44no—
96C2×C4×C83—21no—
97C2×C4×C83—21no—
98C2×C4×C83—22no—
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—42no—
108C2×C4×C83—42no—
109C2×C4×C83—42no—
110C2×C4×C83—42no—
111C2×C4×C83—42no—
112C2×C4×C83—42no—
113C2×C4×C83—81no—
114C2×C4×C83—81no—
115C2×C4×C83#9911yescharacteristic
116C2×C4×C83#9911yescharacteristic
117C2×C4×C83#13112yes—
118C8×C83—82no—
119C8×C83—82no—
120C22×C83—21no—
121C22×C83—21no—
122C22×C83—22no—
123C22×C83—42no—
124C22×C83—42no—
125C22×C83—41no—
126C22×C83—41no—
127C22×C83—41no—
128C22×C83—41no—
129C22×C83—41no—
130C22×C83—81no—
131C22×C83—81no—
132C22×C83#40811yescharacteristic
133C22×C83C2×#9911yescharacteristic
134C22×C83C2×#10111yescharacteristic
135C4×C83—21no—
136C4×C83—22no—
137C4×C83—41no—
138C4×C83—41no—
139C4×C83—41no—
140C4×C83—82no—
141C4×C83—82no—
142C4×C83#35412yes—
143#11569C8311yesmaximal, characteristic, direct product factor, Sylow
144C2×C83—21no—
145C2×C83—21no—
146C2×C83—42no—
147C2×C83—81no—
148C2×C83#147211yescharacteristic
149C2×C83C2×#35411yescharacteristic
150C2×C83#213411yescharacteristic
151#2563C2×C8311yescharacteristic
152#1465C2×C8311yescharacteristic
153#1459C2×C8311yescharacteristic
154#1324C2×C8314yescomplemented
155C83#1156911yescharacteristic, direct product factor, Sylow
156C2×C4⋊Q8C4×C8311yescharacteristic
157C2×C4×D4C22×C8311yescharacteristic
158#407—21no—
159C2×C22⋊C8—21no—
160#393—21no—
161#393—21no—
162#390C4×C8312yes—
163#382C22×C8312yes—
164#380—21no—
165#380—21no—
166C4×C4⋊C4C4×C8311yescharacteristic
167#324C22×C8312yes—
168#324C22×C8312yes—
169#323—21no—
170#323—21no—
171C22×Q8—21no—
172C22×D4C2×C4×C8311yescharacteristic
173C23×C4D4×C8311yescharacteristic
174C23×C4D4×C8311yescharacteristic
175C2×M16—41no—
176C22×C8—41no—
177C4⋊Q8—41no—
178C4⋊Q8—41no—
179C4×D4—41no—
180C4×D4—41no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×C4×C8312yes—
184C2×C4⋊C4C23×C8311yescharacteristic
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4D4×C8311yescharacteristic
188C2×C22⋊C4D4×C8311yescharacteristic
189C2×C42C2×C4×C8312yes—
190C2×C42C2×C4×C8311yescharacteristic
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—41no—
194C22⋊C8—41no—
195#95—21no—
196#95—22no—
197#95—22no—
198C24C22⋊C4×C8311yescharacteristic
199C24C22⋊C4×C8311yescharacteristic
200C2×Q8—42no—
201C2×Q8—82no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4C22⋊C4×C8311yescharacteristic
214C22×C4C22⋊C4×C8311yescharacteristic
215C22×C4C22×C4×C8311yescharacteristic
216C22×C4C2×D4×C8311yescharacteristic
217C22×C4C2×D4×C8311yescharacteristic
218M16—82no—
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—82no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—82no—
230C22⋊C4—82no—
231C42—21no—
232C42—21no—
233C42—24no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23#101×C8312yes—
244C23C2×C22⋊C4×C8311yescharacteristic
245Q8—84no—
246D4—44no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4#99×C8311yescharacteristic
267C2×C4#99×C8311yescharacteristic
268C2×C4#131×C8312yes—
269C8—82no—
270C8—82no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—81no—
282C22—81no—
283C22#408×C8311yescharacteristic
284C22C2×#99×C8311yescharacteristic
285C22C2×#101×C8311yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—82no—
292C4—82no—
293C4#354×C8312yes—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2C83×#147211yescharacteristic
299C2C2×#354×C8311yescharacteristic
300C2C83×#213411yescharacteristic
subgroupG/H
center, socleC22×C83C2×#99
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×C4⋊C4C23×C83
prime radicalC22×D4×C83C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C22×C4×C83 ◁ C2×C4×D4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
4. C83×#1324C2semidirect
143. #11569C83direct (N × H)
154. #1324C2×C83semidirect
155. C83#11569direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#25632
C83×#14652
C83×#14592
C83×#13242
#1156983