Finite Group Databasebeta

← C83×#9329 #35237153

Subgroups — C83×#9329 #35237153

Order 21248.

530 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3109C211yesmaximal, characteristic
2C83×#2319C211yesmaximal, characteristic, complemented
3C83×#1980C211yesmaximal, characteristic, complemented
4C83×#1505C211yesmaximal, characteristic, complemented
5C83×#1490C211yesmaximal, characteristic, complemented
6C83×#1300C211yesmaximal, characteristic, complemented
7C83×#1285C211yesmaximal, characteristic, complemented
8#532×C83C2211yescharacteristic
9C2×C4×D4×C83C2211yescharacteristic
10#481×C83—21no—
11#476×C83C412yescomplemented
12#459×C83C412yescomplemented
13#447×C83—21no—
14#442×C83—22no—
15#432×C83C2211yescharacteristic
16#432×C83C2211yescharacteristic
17C2×#104×C83—22no—
18C4×M16×C83C2211yescharacteristic
19#390×C83—21no—
20#389×C83—21no—
21#388×C83—22no—
22#381×C83—21no—
23#380×C83—21no—
24C4×C4⋊C4×C83C2211yescharacteristic
25#376×C83C2211yescharacteristic
26#327×C83—21no—
27#327×C83—21no—
28D4⋊C8×C83—22no—
29C2×#41×C83—21no—
30C22×D4×C83D411yescharacteristic
31C23×C4×C83—21no—
32C2×D8×C83—22no—
33C2×M16×C83—21no—
34C4⋊Q8×C83C2×C411yescharacteristic
35#127×C83C2×C411yescharacteristic
36#124×C83—21no—
37#121×C83—21no—
38#121×C83—21no—
39C4×D4×C83—21no—
40C4×D4×C83—21no—
41C4×D4×C83—21no—
42C4×D4×C83—21no—
43C4×D4×C83C2×C412yes—
44C4×D4×C83D412yes—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—22no—
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C22⋊C4×C83—21no—
49C2×C22⋊C4×C83—22no—
50C2×C22⋊C4×C83—22no—
51C2×C42×C83—21no—
52C2×C42×C83D412yes—
53C2×C42×C83C2311yescharacteristic
54#106×C83—22no—
55C4⋊C8×C83—21no—
56C4⋊C8×C83C2×C412yes—
57#104×C83—44no—
58#102×C83—22no—
59#102×C83—22no—
60C22⋊C8×C83—21no—
61C22⋊C8×C83—21no—
62#97×C83—21no—
63#97×C83—21no—
64#97×C83—21no—
65C4×C8×C83—21no—
66#95×C83—22no—
67#95×C83—21no—
68#95×C83—21no—
69#95×C83D411yescharacteristic
70#95×C83D411yescharacteristic
71C24×C83—21no—
72#41×C83—42no—
73#41×C83—42no—
74C2×Q8×C83—21no—
75C2×D4×C83—21no—
76C2×D4×C83—21no—
77C2×D4×C83—21no—
78C2×D4×C83—21no—
79C2×D4×C83—42no—
80C2×D4×C83—41no—
81C2×D4×C83C22⋊C412yes—
82C22×C4×C83—21no—
83C22×C4×C83—22no—
84C22×C4×C83—22no—
85C22×C4×C83—21no—
86C22×C4×C83—22no—
87C22×C4×C83—21no—
88C22×C4×C83—41no—
89C22×C4×C83—82no—
90C22×C4×C83C2×D411yescharacteristic
91C22×C4×C83C2×D411yescharacteristic
92C22×C4×C83C2×D411yescharacteristic
93D8×C83—44no—
94M16×C83—22no—
95M16×C83—41no—
96C2×C8×C83—22no—
97C2×C8×C83—41no—
98C2×C8×C83—41no—
99C4⋊C4×C83—21no—
100C4⋊C4×C83—21no—
101C4⋊C4×C83—21no—
102C4⋊C4×C83—42no—
103C4⋊C4×C83—82no—
104C4⋊C4×C83C22⋊C412yes—
105C22⋊C4×C83—22no—
106C22⋊C4×C83—22no—
107C22⋊C4×C83—41no—
108C22⋊C4×C83—41no—
109C22⋊C4×C83—82no—
110C22⋊C4×C83—82no—
111C42×C83—42no—
112C42×C83—42no—
113C42×C83C22×C411yescharacteristic
114C42×C83C2×D411yescharacteristic
115C42×C83#4111yescharacteristic
116C42×C83#4111yescharacteristic
117C23×C83—22no—
118C23×C83—42no—
119C23×C83—42no—
120C23×C83—41no—
121C23×C83—41no—
122C23×C83—41no—
123C23×C83#12011yescharacteristic
124Q8×C83—42no—
125D4×C83—22no—
126D4×C83—22no—
127D4×C83—42no—
128D4×C83—42no—
129D4×C83—42no—
130D4×C83—81no—
131D4×C83—81no—
132D4×C83—81no—
133C2×C4×C83—21no—
134C2×C4×C83—21no—
135C2×C4×C83—22no—
136C2×C4×C83—22no—
137C2×C4×C83—41no—
138C2×C4×C83—42no—
139C2×C4×C83—41no—
140C2×C4×C83—41no—
141C2×C4×C83—41no—
142C2×C4×C83—42no—
143C2×C4×C83—42no—
144C2×C4×C83—41no—
145C2×C4×C83—41no—
146C2×C4×C83—42no—
147C2×C4×C83—41no—
148C2×C4×C83—41no—
149C2×C4×C83—82no—
150C2×C4×C83—82no—
151C2×C4×C83—82no—
152C2×C4×C83C2×C22⋊C411yescharacteristic
153C2×C4×C83C4×D411yescharacteristic
154C2×C4×C83C4×D411yescharacteristic
155C2×C4×C83#12111yescharacteristic
156C2×C4×C83#12111yescharacteristic
157C2×C4×C83#12311yescharacteristic
158C8×C83—42no—
159C8×C83—42no—
160C8×C83—81no—
161C22×C83—21no—
162C22×C83—21no—
163C22×C83—42no—
164C22×C83—42no—
165C22×C83—42no—
166C22×C83—82no—
167C22×C83—82no—
168C22×C83—81no—
169C22×C83—81no—
170C22×C83—81no—
171C22×C83#38611yescharacteristic
172C22×C83#45311yescharacteristic
173C22×C83#45411yescharacteristic
174C4×C83—21no—
175C4×C83—21no—
176C4×C83—21no—
177C4×C83—21no—
178C4×C83—21no—
179C4×C83—42no—
180C4×C83—81no—
181C4×C83—82no—
182C4×C83—81no—
183C4×C83—81no—
184C4×C83#42112yes—
185#9329C8311yesmaximal, characteristic, direct product factor, Sylow
186C2×C83—21no—
187C2×C83—21no—
188C2×C83—82no—
189C2×C83—161no—
190C2×C83#188311yescharacteristic
191C2×C83#189711yescharacteristic
192C2×C83#190411yescharacteristic
193#3109C2×C8311yescharacteristic
194#2319C2×C8311yescharacteristic, complemented
195#1980C2×C8311yescharacteristic, complemented
196#1505C2×C8311yescharacteristic, complemented
197#1490C2×C8311yescharacteristic, complemented
198#1300C2×C8311yescharacteristic, complemented
199#1285C2×C8311yescharacteristic, complemented
200C83#932911yescharacteristic, direct product factor, Sylow
201#532C22×C8311yescharacteristic
202C2×C4×D4C22×C8311yescharacteristic
203#481—21no—
204#476C4×C8312yescomplemented
205#459C4×C8312yescomplemented
206#447—21no—
207#442—22no—
208#432C22×C8311yescharacteristic
209#432C22×C8311yescharacteristic
210C2×#104—22no—
211C4×M16C22×C8311yescharacteristic
212#390—21no—
213#389—21no—
214#388—22no—
215#381—21no—
216#380—21no—
217C4×C4⋊C4C22×C8311yescharacteristic
218#376C22×C8311yescharacteristic
219#327—21no—
220#327—21no—
221D4⋊C8—22no—
222C2×#41—21no—
223C22×D4D4×C8311yescharacteristic
224C23×C4—21no—
225C2×D8—22no—
226C2×M16—21no—
227C4⋊Q8C2×C4×C8311yescharacteristic
228#127C2×C4×C8311yescharacteristic
229#124—21no—
230#121—21no—
231#121—21no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4C2×C4×C8312yes—
237C4×D4D4×C8312yes—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4D4×C8311yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C42—21no—
245C2×C42D4×C8312yes—
246C2×C42C23×C8311yescharacteristic
247#106—22no—
248C4⋊C8—21no—
249C4⋊C8C2×C4×C8312yes—
250#104—44no—
251#102—22no—
252#102—22no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255#97—21no—
256#97—21no—
257#97—21no—
258C4×C8—21no—
259#95—22no—
260#95—21no—
261#95—21no—
262#95D4×C8311yescharacteristic
263#95D4×C8311yescharacteristic
264C24—21no—
265#41—42no—
266#41—42no—
267C2×Q8—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4C22⋊C4×C8312yes—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—82no—
283C22×C4C2×D4×C8311yescharacteristic
284C22×C4C2×D4×C8311yescharacteristic
285C22×C4C2×D4×C8311yescharacteristic
286D8—44no—
287M16—22no—
288M16—41no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—42no—
296C4⋊C4—82no—
297C4⋊C4C22⋊C4×C8312yes—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—82no—
303C22⋊C4—82no—
304C42—42no—
305C42—42no—
306C42C22×C4×C8311yescharacteristic
307C42C2×D4×C8311yescharacteristic
308C42#41×C8311yescharacteristic
309C42#41×C8311yescharacteristic
310C23—22no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23#120×C8311yescharacteristic
317Q8—42no—
318D4—22no—
319D4—22no—
320D4—42no—
321D4—42no—
322D4—42no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4C2×C22⋊C4×C8311yescharacteristic
346C2×C4C4×D4×C8311yescharacteristic
347C2×C4C4×D4×C8311yescharacteristic
348C2×C4#121×C8311yescharacteristic
349C2×C4#121×C8311yescharacteristic
350C2×C4#123×C8311yescharacteristic
351C8—42no—
352C8—42no—
353C8—81no—
354C22—21no—
355C22—21no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—82no—
360C22—82no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22#386×C8311yescharacteristic
365C22#453×C8311yescharacteristic
366C22#454×C8311yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—82no—
375C4—81no—
376C4—81no—
377C4#421×C8312yes—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—161no—
382C2C83×#188311yescharacteristic
383C2C83×#189711yescharacteristic
384C2C83×#190411yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC42C22×C4×C83
Frattini, cosocleC2×C42C23×C83
prime radicalC83×#3109C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#2319C2semidirect
3. C83×#1980C2semidirect
4. C83×#1505C2semidirect
5. C83×#1490C2semidirect
6. C83×#1300C2semidirect
7. C83×#1285C2semidirect
11. #476×C83C4semidirect
12. #459×C83C4semidirect
185. #9329C83direct (N × H)
194. #2319C2×C83semidirect
195. #1980C2×C83semidirect
196. #1505C2×C83semidirect
197. #1490C2×C83semidirect
198. #1300C2×C83semidirect
199. #1285C2×C83semidirect
200. C83#9329direct (N × H)
204. #476C4×C83semidirect
205. #459C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#31092
C83×#23192
C83×#19802
C83×#15052
C83×#14902
C83×#13002
C83×#12852
#932983