Finite Group Databasebeta

← C83×#9367 #35237191

Subgroups — C83×#9367 #35237191

Order 21248.

542 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3094C211yesmaximal, characteristic
2C83×#2346C211yesmaximal, characteristic, complemented
3C83×#1964C211yesmaximal, characteristic
4C83×#1826C211yesmaximal, characteristic, complemented
5C83×#1507C211yesmaximal, characteristic
6C83×#1305C211yesmaximal, characteristic, complemented
7C83×#1297C211yesmaximal, characteristic, complemented
8C2×#121×C83C2211yescharacteristic
9C2×#117×C83C2211yescharacteristic
10#482×C83—22no—
11#481×C83—21no—
12#480×C83—21no—
13#428×C83C412yescomplemented
14#418×C83C412yescomplemented
15C2×#99×C83—22no—
16#407×C83C2211yescharacteristic
17#407×C83C2211yescharacteristic
18#389×C83—21no—
19#388×C83—22no—
20#382×C83—21no—
21#380×C83C2211yescharacteristic
22C4×C4⋊C4×C83—21no—
23C4×C22⋊C4×C83C2211yescharacteristic
24C4×C22⋊C4×C83C2211yescharacteristic
25#376×C83—21no—
26#339×C83—22no—
27#327×C83—21no—
28#327×C83—21no—
29C22×D4×C83—21no—
30C22×D4×C83C2×C411yescharacteristic
31C23×C4×C83C2311yescharacteristic
32C2×M16×C83—21no—
33C2×M16×C83C2×C412yes—
34#121×C83—21no—
35#121×C83—21no—
36#121×C83—21no—
37#121×C83—21no—
38#117×C83—21no—
39#117×C83—21no—
40#117×C83C2×C412yes—
41#117×C83D412yes—
42C2×C4⋊C4×C83—21no—
43C2×C4⋊C4×C83—22no—
44C2×C4⋊C4×C83C2×C411yescharacteristic
45C2×C4⋊C4×C83D411yescharacteristic
46C2×C4⋊C4×C83D411yescharacteristic
47C2×C22⋊C4×C83—21no—
48C2×C22⋊C4×C83—21no—
49C2×C22⋊C4×C83—21no—
50C2×C22⋊C4×C83—21no—
51C2×C22⋊C4×C83D412yes—
52C2×C42×C83—21no—
53C2×C42×C83—22no—
54C2×C42×C83—21no—
55C2×C42×C83—21no—
56#107×C83—22no—
57#106×C83—22no—
58#102×C83—22no—
59#102×C83—22no—
60#99×C83—44no—
61C22⋊C8×C83—21no—
62C22⋊C8×C83—21no—
63C22⋊C8×C83—21no—
64C22⋊C8×C83—21no—
65#95×C83—22no—
66#95×C83—22no—
67#95×C83—21no—
68#95×C83—21no—
69#95×C83D411yescharacteristic
70#95×C83D411yescharacteristic
71C24×C83—21no—
72C24×C83C2×D411yescharacteristic
73C2×D4×C83—21no—
74C2×D4×C83—21no—
75C2×D4×C83—42no—
76C2×D4×C83—42no—
77C2×D4×C83—42no—
78C2×D4×C83—41no—
79C2×D4×C83—41no—
80C22×C4×C83—21no—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—21no—
84C22×C4×C83—22no—
85C22×C4×C83—21no—
86C22×C4×C83—42no—
87C22×C4×C83—41no—
88C22×C4×C83C22×C411yescharacteristic
89C22×C4×C83C2×D411yescharacteristic
90C22×C4×C83C2×D411yescharacteristic
91C22×C4×C83C2×D411yescharacteristic
92C22×C4×C83#4111yescharacteristic
93C22×C4×C83#4111yescharacteristic
94M16×C83—42no—
95M16×C83—42no—
96C2×C8×C83—22no—
97C2×C8×C83—41no—
98C4⋊C4×C83—21no—
99C4⋊C4×C83—21no—
100C4⋊C4×C83—21no—
101C4⋊C4×C83—21no—
102C4⋊C4×C83—42no—
103C4⋊C4×C83—82no—
104C4⋊C4×C83C22⋊C412yes—
105C4⋊C4×C83C22⋊C412yes—
106C22⋊C4×C83—22no—
107C22⋊C4×C83—22no—
108C22⋊C4×C83—22no—
109C22⋊C4×C83—42no—
110C22⋊C4×C83—41no—
111C22⋊C4×C83—41no—
112C22⋊C4×C83—41no—
113C22⋊C4×C83—42no—
114C42×C83—22no—
115C42×C83—22no—
116C42×C83—42no—
117C42×C83—44no—
118C42×C83—42no—
119C23×C83—21no—
120C23×C83—21no—
121C23×C83—41no—
122C23×C83—41no—
123C23×C83—42no—
124C23×C83—41no—
125C23×C83—81no—
126C23×C83—81no—
127C23×C83C4×D411yescharacteristic
128C23×C83#12011yescharacteristic
129C23×C83#12111yescharacteristic
130D4×C83—42no—
131D4×C83—81no—
132D4×C83—82no—
133D4×C83—81no—
134D4×C83—81no—
135C2×C4×C83—22no—
136C2×C4×C83—22no—
137C2×C4×C83—22no—
138C2×C4×C83—22no—
139C2×C4×C83—22no—
140C2×C4×C83—22no—
141C2×C4×C83—41no—
142C2×C4×C83—41no—
143C2×C4×C83—41no—
144C2×C4×C83—41no—
145C2×C4×C83—42no—
146C2×C4×C83—41no—
147C2×C4×C83—41no—
148C2×C4×C83—41no—
149C2×C4×C83—41no—
150C2×C4×C83—42no—
151C2×C4×C83—42no—
152C2×C4×C83—41no—
153C2×C4×C83—42no—
154C2×C4×C83—42no—
155C2×C4×C83—41no—
156C2×C4×C83—42no—
157C2×C4×C83—41no—
158C2×C4×C83—81no—
159C2×C4×C83—81no—
160C2×C4×C83C2×C22⋊C411yescharacteristic
161C2×C4×C83C4×D411yescharacteristic
162C2×C4×C83#12111yescharacteristic
163C2×C4×C83#12311yescharacteristic
164C8×C83—42no—
165C8×C83—81no—
166C22×C83—21no—
167C22×C83—21no—
168C22×C83—21no—
169C22×C83—21no—
170C22×C83—21no—
171C22×C83—21no—
172C22×C83—21no—
173C22×C83—21no—
174C22×C83—81no—
175C22×C83—81no—
176C22×C83—81no—
177C22×C83—81no—
178C22×C83—81no—
179C22×C83—162no—
180C22×C83#38611yescharacteristic
181C22×C83#45311yescharacteristic
182C22×C83#45411yescharacteristic
183C4×C83—21no—
184C4×C83—21no—
185C4×C83—21no—
186C4×C83—42no—
187C4×C83—42no—
188C4×C83—42no—
189C4×C83—81no—
190C4×C83—82no—
191C4×C83—82no—
192C4×C83—81no—
193C4×C83#41012yes—
194#9367C8311yesmaximal, characteristic, direct product factor, Sylow
195C2×C83—21no—
196C2×C83—21no—
197C2×C83—41no—
198C2×C83—41no—
199C2×C83—161no—
200C2×C83#188311yescharacteristic
201C2×C83#189911yescharacteristic
202C2×C83#190611yescharacteristic
203#3094C2×C8311yescharacteristic
204#2346C2×C8311yescharacteristic, complemented
205#1964C2×C8311yescharacteristic
206#1826C2×C8311yescharacteristic, complemented
207#1507C2×C8311yescharacteristic
208#1305C2×C8311yescharacteristic, complemented
209#1297C2×C8311yescharacteristic, complemented
210C83#936711yescharacteristic, direct product factor, Sylow
211C2×#121C22×C8311yescharacteristic
212C2×#117C22×C8311yescharacteristic
213#482—22no—
214#481—21no—
215#480—21no—
216#428C4×C8312yescomplemented
217#418C4×C8312yescomplemented
218C2×#99—22no—
219#407C22×C8311yescharacteristic
220#407C22×C8311yescharacteristic
221#389—21no—
222#388—22no—
223#382—21no—
224#380C22×C8311yescharacteristic
225C4×C4⋊C4—21no—
226C4×C22⋊C4C22×C8311yescharacteristic
227C4×C22⋊C4C22×C8311yescharacteristic
228#376—21no—
229#339—22no—
230#327—21no—
231#327—21no—
232C22×D4—21no—
233C22×D4C2×C4×C8311yescharacteristic
234C23×C4C23×C8311yescharacteristic
235C2×M16—21no—
236C2×M16C2×C4×C8312yes—
237#121—21no—
238#121—21no—
239#121—21no—
240#121—21no—
241#117—21no—
242#117—21no—
243#117C2×C4×C8312yes—
244#117D4×C8312yes—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4C2×C4×C8311yescharacteristic
248C2×C4⋊C4D4×C8311yescharacteristic
249C2×C4⋊C4D4×C8311yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4D4×C8312yes—
255C2×C42—21no—
256C2×C42—22no—
257C2×C42—21no—
258C2×C42—21no—
259#107—22no—
260#106—22no—
261#102—22no—
262#102—22no—
263#99—44no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268#95—22no—
269#95—22no—
270#95—21no—
271#95—21no—
272#95D4×C8311yescharacteristic
273#95D4×C8311yescharacteristic
274C24—21no—
275C24C2×D4×C8311yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—41no—
282C2×D4—41no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—42no—
290C22×C4—41no—
291C22×C4C22×C4×C8311yescharacteristic
292C22×C4C2×D4×C8311yescharacteristic
293C22×C4C2×D4×C8311yescharacteristic
294C22×C4C2×D4×C8311yescharacteristic
295C22×C4#41×C8311yescharacteristic
296C22×C4#41×C8311yescharacteristic
297M16—42no—
298M16—42no—
299C2×C8—22no—
300C2×C8—41no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—42no—
306C4⋊C4—82no—
307C4⋊C4C22⋊C4×C8312yes—
308C4⋊C4C22⋊C4×C8312yes—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—42no—
317C42—22no—
318C42—22no—
319C42—42no—
320C42—44no—
321C42—42no—
322C23—21no—
323C23—21no—
324C23—41no—
325C23—41no—
326C23—42no—
327C23—41no—
328C23—81no—
329C23—81no—
330C23C4×D4×C8311yescharacteristic
331C23#120×C8311yescharacteristic
332C23#121×C8311yescharacteristic
333D4—42no—
334D4—81no—
335D4—82no—
336D4—81no—
337D4—81no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4C2×C22⋊C4×C8311yescharacteristic
364C2×C4C4×D4×C8311yescharacteristic
365C2×C4#121×C8311yescharacteristic
366C2×C4#123×C8311yescharacteristic
367C8—42no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—162no—
383C22#386×C8311yescharacteristic
384C22#453×C8311yescharacteristic
385C22#454×C8311yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—42no—
391C4—42no—
392C4—81no—
393C4—82no—
394C4—82no—
395C4—81no—
396C4#410×C8312yes—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—161no—
402C2C83×#188311yescharacteristic
403C2C83×#189911yescharacteristic
404C2C83×#190611yescharacteristic
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
2. C83×#2346C2semidirect
4. C83×#1826C2semidirect
6. C83×#1305C2semidirect
7. C83×#1297C2semidirect
13. #428×C83C4semidirect
14. #418×C83C4semidirect
194. #9367C83direct (N × H)
204. #2346C2×C83semidirect
206. #1826C2×C83semidirect
208. #1305C2×C83semidirect
209. #1297C2×C83semidirect
210. C83#9367direct (N × H)
216. #428C4×C83semidirect
217. #418C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#30942
C83×#23462
C83×#19642
C83×#18262
C83×#15072
C83×#13052
C83×#12972
#936783