Finite Group Databasebeta

← C83×#11761 #35239585

Subgroups — C83×#11761 #35239585

Order 21248.

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

normal subgroups only

This group has 484 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×#2598C211yesmaximal, characteristic
2C83×#1742C211yesmaximal, characteristic, complemented
3C83×#1464C211yesmaximal, characteristic, complemented
4C83×#1353C212yesmaximal, complemented
5C83×#1345C212yesmaximal, complemented
6C22×M16×C83—21no—
7C2×C4×D4×C83C411yescharacteristic
8C2×#117×C83C2211yescharacteristic
9#432×C83—21no—
10#400×C83C2211yescharacteristic
11#399×C83C411yescharacteristic
12#394×C83C2211yescharacteristic
13#392×C83C411yescharacteristic
14#388×C83—21no—
15#386×C83—21no—
16#386×C83—21no—
17#385×C83—21no—
18#383×C83C411yescharacteristic
19#343×C83—21no—
20#343×C83C2212yes—
21#324×C83C2212yes—
22#323×C83—21no—
23C22×D4×C83—21no—
24C22×D4×C83C2×C411yescharacteristic
25C23×C4×C83—21no—
26C23×C4×C83D411yescharacteristic
27C2×M16×C83—24no—
28C2×M16×C83—22no—
29C2×M16×C83—41no—
30C2×M16×C83—42no—
31C22×C8×C83—41no—
32C4×D4×C83—41no—
33C4×D4×C83—41no—
34#117×C83—41no—
35#117×C83—41no—
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×C83—21no—
43C2×C22⋊C4×C83—21no—
44C2×C22⋊C4×C83—21no—
45C2×C22⋊C4×C83C2×C411yescharacteristic
46C2×C22⋊C4×C83D411yescharacteristic
47C2×C42×C83C2×C411yescharacteristic
48C2×C42×C83D411yescharacteristic
49C4⋊C8×C83—41no—
50C22⋊C8×C83—22no—
51#97×C83—41no—
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×C83—21no—
59C24×C83C22⋊C411yescharacteristic
60C2×D4×C83—41no—
61C2×D4×C83—42no—
62C2×D4×C83—42no—
63C2×D4×C83—42no—
64C2×D4×C83—81no—
65C22×C4×C83—22no—
66C22×C4×C83—21no—
67C22×C4×C83—21no—
68C22×C4×C83—21no—
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83—21no—
73C22×C4×C83—42no—
74C22×C4×C83—81no—
75C22×C4×C83—81no—
76C22×C4×C83C22⋊C411yescharacteristic
77C22×C4×C83C22⋊C411yescharacteristic
78C22×C4×C83C22⋊C411yescharacteristic
79C22×C4×C83C22×C411yescharacteristic
80C22×C4×C83C2×D411yescharacteristic
81C22×C4×C83C2×D411yescharacteristic
82M16×C83—24no—
83M16×C83—44no—
84M16×C83—42no—
85C2×C8×C83—44no—
86C2×C8×C83—42no—
87C2×C8×C83—42no—
88C4⋊C4×C83—41no—
89C4⋊C4×C83—41no—
90C4⋊C4×C83—41no—
91C4⋊C4×C83—81no—
92C22⋊C4×C83—41no—
93C22⋊C4×C83—41no—
94C22⋊C4×C83—42no—
95C22⋊C4×C83—41no—
96C22⋊C4×C83—41no—
97C22⋊C4×C83—41no—
98C22⋊C4×C83—41no—
99C22⋊C4×C83—81no—
100C22⋊C4×C83—81no—
101C42×C83—21no—
102C42×C83—21no—
103C42×C83—21no—
104C42×C83—21no—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—22no—
108C23×C83—41no—
109C23×C83—41no—
110C23×C83—41no—
111C23×C83—41no—
112C23×C83—41no—
113C23×C83—41no—
114C23×C83—41no—
115C23×C83—41no—
116C23×C83#10412yes—
117C23×C83C2×C22⋊C411yescharacteristic
118D4×C83—42no—
119D4×C83—42no—
120D4×C83—84no—
121C2×C4×C83—22no—
122C2×C4×C83—22no—
123C2×C4×C83—22no—
124C2×C4×C83—22no—
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—21no—
133C2×C4×C83—41no—
134C2×C4×C83—41no—
135C2×C4×C83—41no—
136C2×C4×C83—41no—
137C2×C4×C83—41no—
138C2×C4×C83—41no—
139C2×C4×C83—41no—
140C2×C4×C83—41no—
141C2×C4×C83—41no—
142C2×C4×C83—41no—
143C2×C4×C83—41no—
144C2×C4×C83—41no—
145C2×C4×C83—41no—
146C2×C4×C83—84no—
147C2×C4×C83#9911yescharacteristic
148C2×C4×C83#9911yescharacteristic
149C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C83#13711yescharacteristic
151C8×C83—44no—
152C8×C83—82no—
153C22×C83—21no—
154C22×C83—21no—
155C22×C83—22no—
156C22×C83—42no—
157C22×C83—42no—
158C22×C83—42no—
159C22×C83—41no—
160C22×C83—41no—
161C22×C83—42no—
162C22×C83—81no—
163C22×C83—81no—
164C22×C83—81no—
165C22×C83—81no—
166C22×C83—81no—
167C22×C83C2×#9911yescharacteristic
168C22×C83#41711yescharacteristic
169C22×C83C2×#10411yescharacteristic
170C4×C83—21no—
171C4×C83—21no—
172C4×C83—21no—
173C4×C83—21no—
174C4×C83—41no—
175C4×C83—41no—
176C4×C83—41no—
177C4×C83—41no—
178C4×C83—81no—
179C4×C83—81no—
180C4×C83—81no—
181#11761C8311yesmaximal, characteristic, direct product factor, Sylow
182C2×C83—21no—
183C2×C83—21no—
184C2×C83—42no—
185C2×C83—82no—
186C2×C83#150411yescharacteristic
187C2×C83#212011yescharacteristic
188C2×C83#213411yescharacteristic
189#2598C2×C8311yescharacteristic
190#1742C2×C8311yescharacteristic, complemented
191#1464C2×C8311yescharacteristic, complemented
192#1353C2×C8312yescomplemented
193#1345C2×C8312yescomplemented
194C83#1176111yescharacteristic, direct product factor, Sylow
195C22×M16—21no—
196C2×C4×D4C4×C8311yescharacteristic
197C2×#117C22×C8311yescharacteristic
198#432—21no—
199#400C22×C8311yescharacteristic
200#399C4×C8311yescharacteristic
201#394C22×C8311yescharacteristic
202#392C4×C8311yescharacteristic
203#388—21no—
204#386—21no—
205#386—21no—
206#385—21no—
207#383C4×C8311yescharacteristic
208#343—21no—
209#343C22×C8312yes—
210#324C22×C8312yes—
211#323—21no—
212C22×D4—21no—
213C22×D4C2×C4×C8311yescharacteristic
214C23×C4—21no—
215C23×C4D4×C8311yescharacteristic
216C2×M16—24no—
217C2×M16—22no—
218C2×M16—41no—
219C2×M16—42no—
220C22×C8—41no—
221C4×D4—41no—
222C4×D4—41no—
223#117—41no—
224#117—41no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C2×C4×C8311yescharacteristic
227C2×C4⋊C4D4×C8311yescharacteristic
228C2×C4⋊C4C23×C8311yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4C2×C4×C8311yescharacteristic
235C2×C22⋊C4D4×C8311yescharacteristic
236C2×C42C2×C4×C8311yescharacteristic
237C2×C42D4×C8311yescharacteristic
238C4⋊C8—41no—
239C22⋊C8—22no—
240#97—41no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95C2×C4×C8311yescharacteristic
246#95C2×C4×C8311yescharacteristic
247C24—21no—
248C24C22⋊C4×C8311yescharacteristic
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—81no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4C22⋊C4×C8311yescharacteristic
266C22×C4C22⋊C4×C8311yescharacteristic
267C22×C4C22⋊C4×C8311yescharacteristic
268C22×C4C22×C4×C8311yescharacteristic
269C22×C4C2×D4×C8311yescharacteristic
270C22×C4C2×D4×C8311yescharacteristic
271M16—24no—
272M16—44no—
273M16—42no—
274C2×C8—44no—
275C2×C8—42no—
276C2×C8—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—81no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—42no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—81no—
289C22⋊C4—81no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—21no—
294C23—21no—
295C23—21no—
296C23—22no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23#104×C8312yes—
306C23C2×C22⋊C4×C8311yescharacteristic
307D4—42no—
308D4—42no—
309D4—84no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—84no—
336C2×C4#99×C8311yescharacteristic
337C2×C4#99×C8311yescharacteristic
338C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
339C2×C4#137×C8311yescharacteristic
340C8—44no—
341C8—82no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—41no—
349C22—41no—
350C22—42no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C2×#99×C8311yescharacteristic
357C22#417×C8311yescharacteristic
358C22C2×#104×C8311yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—81no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—82no—
374C2C83×#150411yescharacteristic
375C2C83×#212011yescharacteristic
376C2C83×#213411yescharacteristic
subgroupG/H
center, socleC22×C83C2×#99
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×C4⋊C4C23×C83
prime radical#392×C83C4
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
2. C83×#1742C2semidirect
3. C83×#1464C2semidirect
4. C83×#1353C2semidirect
5. C83×#1345C2semidirect
181. #11761C83direct (N × H)
190. #1742C2×C83semidirect
191. #1464C2×C83semidirect
192. #1353C2×C83semidirect
193. #1345C2×C83semidirect
194. C83#11761direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#25982
C83×#17422
C83×#14642
C83×#13532
C83×#13452
#1176183