Finite Group Databasebeta

← C83×#18374 #35246198

Subgroups — C83×#18374 #35246198

Order 21248.

838 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3502C211yesmaximal, characteristic
2C83×#3236C212yesmaximal
3C83×#2634C211yesmaximal, characteristic
4C83×#1617C214yesmaximal
5C83×#1611C214yesmaximal
6C83×#1515C212yesmaximal
7C83×#1467C211yesmaximal, characteristic
8Q82×C83—22no—
9#557×C83—22no—
10#557×C83—24no—
11#544×C83—21no—
12#544×C83C2214yes—
13#533×C83—22no—
14#533×C83C2212yes—
15C2×#125×C83C2211yescharacteristic
16#519×C83—21no—
17C2×C4×Q8×C83C2211yescharacteristic
18#501×C83—22no—
19#491×C83—22no—
20#484×C83C2214yes—
21#483×C83C2214yes—
22#479×C83—24no—
23#432×C83C2212yes—
24#400×C83—21no—
25#400×C83C2212yes—
26#398×C83C2212yes—
27#395×C83—21no—
28#387×C83—22no—
29#383×C83C2211yescharacteristic
30#328×C83C2218yes—
31#324×C83C2214yes—
32C22×Q8×C83D411yescharacteristic
33C4⋊Q8×C83—22no—
34C4⋊Q8×C83—22no—
35C4⋊Q8×C83—24no—
36C4⋊Q8×C83—28no—
37C4⋊Q8×C83D412yes—
38C4⋊Q8×C83D412yes—
39#125×C83—24no—
40#125×C83—24no—
41#125×C83—28no—
42#125×C83—22no—
43#125×C83—22no—
44#125×C83—22no—
45C22⋊Q8×C83—22no—
46C22⋊Q8×C83—24no—
47C22⋊Q8×C83C2314yes—
48C4×Q8×C83—24no—
49C4×Q8×C83—24no—
50C4×Q8×C83—24no—
51C4×Q8×C83—24no—
52C4×Q8×C83—22no—
53C4×Q8×C83—22no—
54C4×Q8×C83—22no—
55C4×Q8×C83D414yes—
56#117×C83—24no—
57#117×C83—22no—
58C2×C4⋊C4×C83—21no—
59C2×C4⋊C4×C83—21no—
60C2×C4⋊C4×C83—22no—
61C2×C4⋊C4×C83D411yescharacteristic
62C2×C4⋊C4×C83C2311yescharacteristic
63C2×C4⋊C4×C83C2311yescharacteristic
64C2×C4⋊C4×C83C2312yes—
65C2×C42×C83D412yes—
66C2×C42×C83C2311yescharacteristic
67#107×C83—24no—
68#106×C83—24no—
69C4⋊C8×C83—22no—
70#103×C83—24no—
71#103×C83—24no—
72C22⋊C8×C83C2314yes—
73#97×C83—22no—
74#95×C83—21no—
75#95×C83—21no—
76#95×C83—22no—
77#95×C83—22no—
78#95×C83—22no—
79#95×C83C2312yes—
80C2×Q8×C83—24no—
81C2×Q8×C83—22no—
82C2×Q8×C83—22no—
83C2×Q8×C83—24no—
84C2×Q8×C83C2×D414yes—
85C22×C4×C83—22no—
86C22×C4×C83—21no—
87C22×C4×C83—21no—
88C22×C4×C83C2×D411yescharacteristic
89C22×C4×C83C2×D412yes—
90C22×C4×C83C2×D412yes—
91C22×C4×C83C2×D411yescharacteristic
92C22×C4×C83C2411yescharacteristic
93C2×C8×C83—24no—
94C4⋊C4×C83—24no—
95C4⋊C4×C83—24no—
96C4⋊C4×C83—24no—
97C4⋊C4×C83—28no—
98C4⋊C4×C83—22no—
99C4⋊C4×C83—22no—
100C4⋊C4×C83—22no—
101C4⋊C4×C83—22no—
102C4⋊C4×C83—24no—
103C4⋊C4×C83—24no—
104C4⋊C4×C83—24no—
105C4⋊C4×C83—22no—
106C4⋊C4×C83—22no—
107C4⋊C4×C83—41no—
108C4⋊C4×C83—42no—
109C4⋊C4×C83—41no—
110C4⋊C4×C83—44no—
111C4⋊C4×C83C2×D414yes—
112C22⋊C4×C83—24no—
113C42×C83—28no—
114C42×C83—22no—
115C42×C83—22no—
116C42×C83—24no—
117C42×C83C2×D412yes—
118C42×C83C2×D412yes—
119C23×C83C22×D411yescharacteristic
120Q8×C83—28no—
121Q8×C83—44no—
122Q8×C83—44no—
123Q8×C83—84no—
124C2×C4×C83—22no—
125C2×C4×C83—22no—
126C2×C4×C83—22no—
127C2×C4×C83—24no—
128C2×C4×C83—24no—
129C2×C4×C83—22no—
130C2×C4×C83—41no—
131C2×C4×C83—41no—
132C2×C4×C83—42no—
133C2×C4×C83—42no—
134C2×C4×C83—42no—
135C2×C4×C83—42no—
136C2×C4×C83—41no—
137C2×C4×C83—41no—
138C2×C4×C83—42no—
139C2×C4×C83—42no—
140C2×C4×C83#12011yescharacteristic
141C2×C4×C83#12012yes—
142C2×C4×C83#12011yescharacteristic
143C2×C4×C83#13714yes—
144C2×C4×C83C22×D412yes—
145C8×C83—44no—
146C22×C83—21no—
147C22×C83—21no—
148C22×C83C2×#12011yescharacteristic
149C22×C83C2×#13712yes—
150C4×C83—22no—
151C4×C83—24no—
152C4×C83—21no—
153C4×C83—21no—
154C4×C83—22no—
155C4×C83—44no—
156C4×C83—42no—
157C4×C83—44no—
158C4×C83—82no—
159C4×C83—81no—
160C4×C83—81no—
161#18374C8311yesmaximal, characteristic, direct product factor, Sylow
162C2×C83—22no—
163C2×C83#300411yescharacteristic
164C2×C83#302011yescharacteristic
165C2×C83#302811yescharacteristic
166#3502C2×C8311yescharacteristic
167#3236C2×C8312yes—
168#2634C2×C8311yescharacteristic
169#1617C2×C8314yes—
170#1611C2×C8314yes—
171#1515C2×C8312yes—
172#1467C2×C8311yescharacteristic
173C83#1837411yescharacteristic, direct product factor, Sylow
174Q82—22no—
175#557—22no—
176#557—24no—
177#544—21no—
178#544C22×C8314yes—
179#533—22no—
180#533C22×C8312yes—
181C2×#125C22×C8311yescharacteristic
182#519—21no—
183C2×C4×Q8C22×C8311yescharacteristic
184#501—22no—
185#491—22no—
186#484C22×C8314yes—
187#483C22×C8314yes—
188#479—24no—
189#432C22×C8312yes—
190#400—21no—
191#400C22×C8312yes—
192#398C22×C8312yes—
193#395—21no—
194#387—22no—
195#383C22×C8311yescharacteristic
196#328C22×C8318yes—
197#324C22×C8314yes—
198C22×Q8D4×C8311yescharacteristic
199C4⋊Q8—22no—
200C4⋊Q8—22no—
201C4⋊Q8—24no—
202C4⋊Q8—28no—
203C4⋊Q8D4×C8312yes—
204C4⋊Q8D4×C8312yes—
205#125—24no—
206#125—24no—
207#125—28no—
208#125—22no—
209#125—22no—
210#125—22no—
211C22⋊Q8—22no—
212C22⋊Q8—24no—
213C22⋊Q8C23×C8314yes—
214C4×Q8—24no—
215C4×Q8—24no—
216C4×Q8—24no—
217C4×Q8—24no—
218C4×Q8—22no—
219C4×Q8—22no—
220C4×Q8—22no—
221C4×Q8D4×C8314yes—
222#117—24no—
223#117—22no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4D4×C8311yescharacteristic
228C2×C4⋊C4C23×C8311yescharacteristic
229C2×C4⋊C4C23×C8311yescharacteristic
230C2×C4⋊C4C23×C8312yes—
231C2×C42D4×C8312yes—
232C2×C42C23×C8311yescharacteristic
233#107—24no—
234#106—24no—
235C4⋊C8—22no—
236#103—24no—
237#103—24no—
238C22⋊C8C23×C8314yes—
239#97—22no—
240#95—21no—
241#95—21no—
242#95—22no—
243#95—22no—
244#95—22no—
245#95C23×C8312yes—
246C2×Q8—24no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—24no—
250C2×Q8C2×D4×C8314yes—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4C2×D4×C8311yescharacteristic
255C22×C4C2×D4×C8312yes—
256C22×C4C2×D4×C8312yes—
257C22×C4C2×D4×C8311yescharacteristic
258C22×C4C24×C8311yescharacteristic
259C2×C8—24no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—24no—
263C4⋊C4—28no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—41no—
274C4⋊C4—42no—
275C4⋊C4—41no—
276C4⋊C4—44no—
277C4⋊C4C2×D4×C8314yes—
278C22⋊C4—24no—
279C42—28no—
280C42—22no—
281C42—22no—
282C42—24no—
283C42C2×D4×C8312yes—
284C42C2×D4×C8312yes—
285C23C22×D4×C8311yescharacteristic
286Q8—28no—
287Q8—44no—
288Q8—44no—
289Q8—84no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4#120×C8311yescharacteristic
307C2×C4#120×C8312yes—
308C2×C4#120×C8311yescharacteristic
309C2×C4#137×C8314yes—
310C2×C4C22×D4×C8312yes—
311C8—44no—
312C22—21no—
313C22—21no—
314C22C2×#120×C8311yescharacteristic
315C22C2×#137×C8312yes—
316C4—21no—
317C4—21no—
318C4—22no—
319C4—22no—
320C4—24no—
321C4—44no—
322C4—42no—
323C4—44no—
324C4—82no—
325C4—81no—
326C4—81no—
327C2—22no—
328C2C83×#300411yescharacteristic
329C2C83×#302011yescharacteristic
330C2C83×#302811yescharacteristic
subgroupG/H
center, socleC22×C83C2×#120
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC23×C83C22×D4
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
161. #18374C83direct (N × H)
173. C83#18374direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#35022
C83×#32362
C83×#26342
C83×#16172
C83×#16112
C83×#15152
C83×#14672
#1837483