Finite Group Databasebeta

← C83×#11763 #35239587

Subgroups — C83×#11763 #35239587

Order 21248.

428 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2599C211yesmaximal, characteristic
2C83×#1742C211yesmaximal, characteristic
3C83×#1464C211yesmaximal, characteristic
4C83×#1354C212yesmaximal, complemented
5C83×#1346C212yesmaximal, complemented
6C22×M16×C83—21no—
7C2×C4×Q8×C83C411yescharacteristic
8C2×#117×C83C2211yescharacteristic
9#432×C83—21no—
10#398×C83C2211yescharacteristic
11#397×C83C411yescharacteristic
12#395×C83C2211yescharacteristic
13#393×C83C411yescharacteristic
14#388×C83—21no—
15#387×C83—21no—
16#387×C83—21no—
17#385×C83—21no—
18#383×C83C411yescharacteristic
19#343×C83—21no—
20#343×C83C2212yes—
21#324×C83C2212yes—
22#323×C83—21no—
23C22×Q8×C83C2×C411yescharacteristic
24C23×C4×C83D411yescharacteristic
25C2×M16×C83—24no—
26C2×M16×C83—22no—
27C2×M16×C83—41no—
28C2×M16×C83—42no—
29C22×C8×C83—41no—
30C4×Q8×C83—41no—
31C4×Q8×C83—41no—
32#117×C83—41no—
33#117×C83—41no—
34C2×C4⋊C4×C83—21no—
35C2×C4⋊C4×C83—21no—
36C2×C4⋊C4×C83—21no—
37C2×C4⋊C4×C83C2×C411yescharacteristic
38C2×C4⋊C4×C83D411yescharacteristic
39C2×C4⋊C4×C83C2311yescharacteristic
40C2×C22⋊C4×C83—21no—
41C2×C22⋊C4×C83—21no—
42C2×C22⋊C4×C83C2×C411yescharacteristic
43C2×C22⋊C4×C83D411yescharacteristic
44C2×C42×C83—21no—
45C2×C42×C83C2×C411yescharacteristic
46C2×C42×C83D411yescharacteristic
47C4⋊C8×C83—41no—
48C22⋊C8×C83—22no—
49#97×C83—41no—
50#95×C83—21no—
51#95×C83—21no—
52#95×C83—21no—
53#95×C83—21no—
54#95×C83—21no—
55#95×C83—21no—
56#95×C83C2×C411yescharacteristic
57#95×C83C2×C411yescharacteristic
58C24×C83C22⋊C411yescharacteristic
59C2×Q8×C83—42no—
60C2×Q8×C83—41no—
61C22×C4×C83—22no—
62C22×C4×C83—21no—
63C22×C4×C83—21no—
64C22×C4×C83—21no—
65C22×C4×C83—21no—
66C22×C4×C83—21no—
67C22×C4×C83—21no—
68C22×C4×C83—21no—
69C22×C4×C83—21no—
70C22×C4×C83C22⋊C411yescharacteristic
71C22×C4×C83C22⋊C411yescharacteristic
72C22×C4×C83C22⋊C411yescharacteristic
73C22×C4×C83C22×C411yescharacteristic
74C22×C4×C83C2×D411yescharacteristic
75C22×C4×C83C2×D411yescharacteristic
76M16×C83—24no—
77M16×C83—44no—
78M16×C83—42no—
79C2×C8×C83—44no—
80C2×C8×C83—42no—
81C2×C8×C83—42no—
82C4⋊C4×C83—41no—
83C4⋊C4×C83—41no—
84C4⋊C4×C83—41no—
85C4⋊C4×C83—42no—
86C4⋊C4×C83—41no—
87C4⋊C4×C83—41no—
88C4⋊C4×C83—41no—
89C4⋊C4×C83—41no—
90C22⋊C4×C83—41no—
91C22⋊C4×C83—41no—
92C22⋊C4×C83—42no—
93C22⋊C4×C83—42no—
94C42×C83—21no—
95C42×C83—21no—
96C42×C83—21no—
97C42×C83—21no—
98C42×C83—42no—
99C23×C83—21no—
100C23×C83—21no—
101C23×C83—41no—
102C23×C83—41no—
103C23×C83#10412yes—
104C23×C83C2×C22⋊C411yescharacteristic
105Q8×C83—42no—
106Q8×C83—42no—
107C2×C4×C83—22no—
108C2×C4×C83—22no—
109C2×C4×C83—22no—
110C2×C4×C83—22no—
111C2×C4×C83—21no—
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—22no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83—21no—
119C2×C4×C83—21no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83—41no—
124C2×C4×C83—41no—
125C2×C4×C83—41no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—41no—
129C2×C4×C83—41no—
130C2×C4×C83—41no—
131C2×C4×C83—41no—
132C2×C4×C83—41no—
133C2×C4×C83—41no—
134C2×C4×C83—41no—
135C2×C4×C83#9911yescharacteristic
136C2×C4×C83#9911yescharacteristic
137C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C83#13711yescharacteristic
139C8×C83—44no—
140C8×C83—82no—
141C22×C83—21no—
142C22×C83—21no—
143C22×C83—22no—
144C22×C83—42no—
145C22×C83—41no—
146C22×C83—41no—
147C22×C83—81no—
148C22×C83C2×#9911yescharacteristic
149C22×C83#41711yescharacteristic
150C22×C83C2×#10411yescharacteristic
151C4×C83—21no—
152C4×C83—21no—
153C4×C83—21no—
154C4×C83—21no—
155C4×C83—41no—
156C4×C83—42no—
157C4×C83—41no—
158C4×C83—41no—
159C4×C83—41no—
160C4×C83—81no—
161C4×C83—81no—
162C4×C83—81no—
163#11763C8311yesmaximal, characteristic, direct product factor, Sylow
164C2×C83—21no—
165C2×C83—21no—
166C2×C83—42no—
167C2×C83#150411yescharacteristic
168C2×C83#212011yescharacteristic
169C2×C83#213511yescharacteristic
170#2599C2×C8311yescharacteristic
171#1742C2×C8311yescharacteristic
172#1464C2×C8311yescharacteristic
173#1354C2×C8312yescomplemented
174#1346C2×C8312yescomplemented
175C83#1176311yescharacteristic, direct product factor, Sylow
176C22×M16—21no—
177C2×C4×Q8C4×C8311yescharacteristic
178C2×#117C22×C8311yescharacteristic
179#432—21no—
180#398C22×C8311yescharacteristic
181#397C4×C8311yescharacteristic
182#395C22×C8311yescharacteristic
183#393C4×C8311yescharacteristic
184#388—21no—
185#387—21no—
186#387—21no—
187#385—21no—
188#383C4×C8311yescharacteristic
189#343—21no—
190#343C22×C8312yes—
191#324C22×C8312yes—
192#323—21no—
193C22×Q8C2×C4×C8311yescharacteristic
194C23×C4D4×C8311yescharacteristic
195C2×M16—24no—
196C2×M16—22no—
197C2×M16—41no—
198C2×M16—42no—
199C22×C8—41no—
200C4×Q8—41no—
201C4×Q8—41no—
202#117—41no—
203#117—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×C4×C8311yescharacteristic
208C2×C4⋊C4D4×C8311yescharacteristic
209C2×C4⋊C4C23×C8311yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4C2×C4×C8311yescharacteristic
213C2×C22⋊C4D4×C8311yescharacteristic
214C2×C42—21no—
215C2×C42C2×C4×C8311yescharacteristic
216C2×C42D4×C8311yescharacteristic
217C4⋊C8—41no—
218C22⋊C8—22no—
219#97—41no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95C2×C4×C8311yescharacteristic
227#95C2×C4×C8311yescharacteristic
228C24C22⋊C4×C8311yescharacteristic
229C2×Q8—42no—
230C2×Q8—41no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4C22⋊C4×C8311yescharacteristic
241C22×C4C22⋊C4×C8311yescharacteristic
242C22×C4C22⋊C4×C8311yescharacteristic
243C22×C4C22×C4×C8311yescharacteristic
244C22×C4C2×D4×C8311yescharacteristic
245C22×C4C2×D4×C8311yescharacteristic
246M16—24no—
247M16—44no—
248M16—42no—
249C2×C8—44no—
250C2×C8—42no—
251C2×C8—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—42no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23#104×C8312yes—
274C23C2×C22⋊C4×C8311yescharacteristic
275Q8—42no—
276Q8—42no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4#99×C8311yescharacteristic
306C2×C4#99×C8311yescharacteristic
307C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
308C2×C4#137×C8311yescharacteristic
309C8—44no—
310C8—82no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22C2×#99×C8311yescharacteristic
319C22#417×C8311yescharacteristic
320C22C2×#104×C8311yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—42no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2C83×#150411yescharacteristic
337C2C83×#212011yescharacteristic
338C2C83×#213511yescharacteristic
subgroupG/H
center, socleC22×C83C2×#99
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×C4⋊C4C23×C83
prime radicalC24×C83C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
4. C83×#1354C2semidirect
5. C83×#1346C2semidirect
163. #11763C83direct (N × H)
173. #1354C2×C83semidirect
174. #1346C2×C83semidirect
175. C83#11763direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#25992
C83×#17422
C83×#14642
C83×#13542
C83×#13462
#1176383