Finite Group Databasebeta

← C83×#9446 #35237270

Subgroups — C83×#9446 #35237270

Order 21248.

516 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2921C211yesmaximal, characteristic, complemented
2C83×#2500C211yesmaximal, characteristic
3C83×#1820C211yesmaximal, characteristic, complemented
4C83×#1510C212yesmaximal
5C83×#1284C212yesmaximal, complemented
6C2×#121×C83C2211yescharacteristic
7C2×#117×C83C2211yescharacteristic
8#433×C83—24no—
9#423×C83—21no—
10#407×C83C2212yes—
11C4×M16×C83—21no—
12#394×C83—21no—
13#394×C83—21no—
14#390×C83C411yescharacteristic, complemented
15#390×C83C411yescharacteristic, complemented
16#388×C83—21no—
17#388×C83—21no—
18#384×C83C411yescharacteristic, complemented
19#382×C83C411yescharacteristic, complemented
20#381×C83C2212yes—
21C4×C22⋊C4×C83C2211yescharacteristic
22#342×C83—21no—
23#342×C83—21no—
24#327×C83—24no—
25C22×D4×C83—21no—
26C22×D4×C83C2×C411yescharacteristic
27C23×C4×C83C2311yescharacteristic
28C2×M16×C83—22no—
29#121×C83—22no—
30#121×C83—22no—
31#117×C83—22no—
32#117×C83—22no—
33C2×C4⋊C4×C83—21no—
34C2×C4⋊C4×C83—21no—
35C2×C4⋊C4×C83C2×C411yescharacteristic
36C2×C4⋊C4×C83C2×C411yescharacteristic
37C2×C4⋊C4×C83C2×C411yescharacteristic
38C2×C22⋊C4×C83—21no—
39C2×C22⋊C4×C83—21no—
40C2×C22⋊C4×C83—21no—
41C2×C22⋊C4×C83—21no—
42C2×C22⋊C4×C83—22no—
43C2×C22⋊C4×C83—21no—
44C2×C22⋊C4×C83—21no—
45C2×C22⋊C4×C83D411yescharacteristic
46C2×C22⋊C4×C83D411yescharacteristic
47C2×C42×C83C2×C411yescharacteristic
48C2×C42×C83C2×C411yescharacteristic
49C2×C42×C83D411yescharacteristic
50C2×C42×C83D411yescharacteristic
51C4⋊C8×C83—24no—
52C22⋊C8×C83—22no—
53C22⋊C8×C83D414yes—
54#97×C83—22no—
55C4×C8×C83—22no—
56#95×C83—21no—
57#95×C83—21no—
58#95×C83—21no—
59#95×C83—22no—
60#95×C83—22no—
61C24×C83—21no—
62C24×C83C2×D411yescharacteristic
63C2×D4×C83—22no—
64C2×D4×C83—41no—
65C2×D4×C83—41no—
66C2×D4×C83—42no—
67C2×D4×C83—81no—
68C2×D4×C83—81no—
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83—41no—
73C22×C4×C83—41no—
74C22×C4×C83—42no—
75C22×C4×C83C22⋊C411yescharacteristic
76C22×C4×C83C22⋊C411yescharacteristic
77C22×C4×C83C22⋊C411yescharacteristic
78C22×C4×C83C22⋊C411yescharacteristic
79C22×C4×C83C22×C411yescharacteristic
80C22×C4×C83C2×D411yescharacteristic
81C22×C4×C83C2×D412yes—
82C22×C4×C83#4112yes—
83M16×C83—42no—
84M16×C83—42no—
85C2×C8×C83—24no—
86C4⋊C4×C83—22no—
87C4⋊C4×C83—22no—
88C4⋊C4×C83—22no—
89C4⋊C4×C83—81no—
90C4⋊C4×C83—81no—
91C22⋊C4×C83—22no—
92C22⋊C4×C83—22no—
93C22⋊C4×C83—42no—
94C22⋊C4×C83—42no—
95C22⋊C4×C83—42no—
96C22⋊C4×C83—41no—
97C22⋊C4×C83—41no—
98C22⋊C4×C83—42no—
99C22⋊C4×C83—42no—
100C22⋊C4×C83—81no—
101C22⋊C4×C83—81no—
102C42×C83—21no—
103C42×C83—21no—
104C42×C83—21no—
105C42×C83—21no—
106C42×C83—41no—
107C42×C83—41no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—41no—
111C23×C83—41no—
112C23×C83—41no—
113C23×C83—41no—
114C23×C83—41no—
115C23×C83—41no—
116C23×C83—41no—
117C23×C83—41no—
118C23×C83—41no—
119C23×C83C2×C22⋊C411yescharacteristic
120C23×C83#12112yes—
121D4×C83—82no—
122D4×C83—84no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—22no—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—42no—
133C2×C4×C83—42no—
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—82no—
147C2×C4×C83—82no—
148C2×C4×C83—82no—
149C2×C4×C83C4×D412yes—
150C2×C4×C83#12011yescharacteristic
151C2×C4×C83#12311yescharacteristic
152C8×C83—44no—
153C22×C83—21no—
154C22×C83—21no—
155C22×C83—22no—
156C22×C83—22no—
157C22×C83—22no—
158C22×C83—81no—
159C22×C83—81no—
160C22×C83—81no—
161C22×C83—81no—
162C22×C83—81no—
163C22×C83—81no—
164C22×C83—81no—
165C22×C83—81no—
166C22×C83—81no—
167C22×C83#38611yescharacteristic
168C22×C83#41011yescharacteristic
169C22×C83#41011yescharacteristic
170C4×C83—21no—
171C4×C83—22no—
172C4×C83—21no—
173C4×C83—42no—
174C4×C83—41no—
175C4×C83—41no—
176C4×C83—41no—
177C4×C83—41no—
178C4×C83—81no—
179C4×C83—81no—
180C4×C83—162no—
181#9446C8311yesmaximal, characteristic, direct product factor, Sylow
182C2×C83—21no—
183C2×C83—21no—
184C2×C83—42no—
185C2×C83—161no—
186C2×C83#188411yescharacteristic
187C2×C83#189911yescharacteristic
188C2×C83#191011yescharacteristic
189#2921C2×C8311yescharacteristic, complemented
190#2500C2×C8311yescharacteristic
191#1820C2×C8311yescharacteristic, complemented
192#1510C2×C8312yes—
193#1284C2×C8312yescomplemented
194C83#944611yescharacteristic, direct product factor, Sylow
195C2×#121C22×C8311yescharacteristic
196C2×#117C22×C8311yescharacteristic
197#433—24no—
198#423—21no—
199#407C22×C8312yes—
200C4×M16—21no—
201#394—21no—
202#394—21no—
203#390C4×C8311yescharacteristic, complemented
204#390C4×C8311yescharacteristic, complemented
205#388—21no—
206#388—21no—
207#384C4×C8311yescharacteristic, complemented
208#382C4×C8311yescharacteristic, complemented
209#381C22×C8312yes—
210C4×C22⋊C4C22×C8311yescharacteristic
211#342—21no—
212#342—21no—
213#327—24no—
214C22×D4—21no—
215C22×D4C2×C4×C8311yescharacteristic
216C23×C4C23×C8311yescharacteristic
217C2×M16—22no—
218#121—22no—
219#121—22no—
220#117—22no—
221#117—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C2×C4×C8311yescharacteristic
225C2×C4⋊C4C2×C4×C8311yescharacteristic
226C2×C4⋊C4C2×C4×C8311yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4D4×C8311yescharacteristic
235C2×C22⋊C4D4×C8311yescharacteristic
236C2×C42C2×C4×C8311yescharacteristic
237C2×C42C2×C4×C8311yescharacteristic
238C2×C42D4×C8311yescharacteristic
239C2×C42D4×C8311yescharacteristic
240C4⋊C8—24no—
241C22⋊C8—22no—
242C22⋊C8D4×C8314yes—
243#97—22no—
244C4×C8—22no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—22no—
249#95—22no—
250C24—21no—
251C24C2×D4×C8311yescharacteristic
252C2×D4—22no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—42no—
256C2×D4—81no—
257C2×D4—81no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—42no—
264C22×C4C22⋊C4×C8311yescharacteristic
265C22×C4C22⋊C4×C8311yescharacteristic
266C22×C4C22⋊C4×C8311yescharacteristic
267C22×C4C22⋊C4×C8311yescharacteristic
268C22×C4C22×C4×C8311yescharacteristic
269C22×C4C2×D4×C8311yescharacteristic
270C22×C4C2×D4×C8312yes—
271C22×C4#41×C8312yes—
272M16—42no—
273M16—42no—
274C2×C8—24no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—21no—
295C42—41no—
296C42—41no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23C2×C22⋊C4×C8311yescharacteristic
309C23#121×C8312yes—
310D4—82no—
311D4—84no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
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—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4C4×D4×C8312yes—
339C2×C4#120×C8311yescharacteristic
340C2×C4#123×C8311yescharacteristic
341C8—44no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#386×C8311yescharacteristic
357C22#410×C8311yescharacteristic
358C22#410×C8311yescharacteristic
359C4—21no—
360C4—22no—
361C4—21no—
362C4—42no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—162no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—161no—
374C2C83×#188411yescharacteristic
375C2C83×#189911yescharacteristic
376C2C83×#191011yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC22×C4C22×C4×C83
Frattini, cosocleC23×C4C23×C83
prime radicalC2×#121×C83C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#2921C2semidirect
3. C83×#1820C2semidirect
5. C83×#1284C2semidirect
14. #390×C83C4semidirect
15. #390×C83C4semidirect
18. #384×C83C4semidirect
19. #382×C83C4semidirect
181. #9446C83direct (N × H)
189. #2921C2×C83semidirect
191. #1820C2×C83semidirect
193. #1284C2×C83semidirect
194. C83#9446direct (N × H)
203. #390C4×C83semidirect
204. #390C4×C83semidirect
207. #384C4×C83semidirect
208. #382C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#29212
C83×#25002
C83×#18202
C83×#15102
C83×#12842
#944683