Finite Group Databasebeta

← C83×#10521 #35238345

Subgroups — C83×#10521 #35238345

Order 21248.

420 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3246C211yesmaximal, characteristic
2C83×#1994C211yesmaximal, characteristic, complemented
3C83×#1962C211yesmaximal, characteristic
4C83×#1831C211yesmaximal, characteristic, complemented
5C83×#1550C211yesmaximal, characteristic, complemented
6C83×#1547C211yesmaximal, characteristic
7C83×#1292C211yesmaximal, characteristic, complemented
8#533×C83C2211yescharacteristic
9#532×C83C2211yescharacteristic
10#476×C83—21no—
11#475×C83—21no—
12#465×C83—22no—
13#461×C83—21no—
14#460×C83—21no—
15#423×C83C2211yescharacteristic
16#423×C83C2211yescharacteristic
17C2×C4⋊C8×C83C2211yescharacteristic
18C2×C4⋊C8×C83C2211yescharacteristic
19C2×#104×C83—21no—
20C2×#104×C83—21no—
21C43×C83C2211yescharacteristic
22#339×C83—21no—
23#339×C83—21no—
24#336×C83—22no—
25#333×C83—21no—
26#332×C83—21no—
27#332×C83—21no—
28#331×C83—21no—
29C2×#41×C83—21no—
30C2×SD16×C83—22no—
31C2×M16×C83—21no—
32C2×M16×C83—21no—
33C22×C8×C83—21no—
34C22×C8×C83D412yes—
35C4⋊Q8×C83D411yescharacteristic
36C4⋊Q8×C83D411yescharacteristic
37C4⋊Q8×C83D411yescharacteristic
38#127×C83D411yescharacteristic
39#125×C83—21no—
40#124×C83—21no—
41C22⋊Q8×C83—21no—
42C22⋊Q8×C83—21no—
43#121×C83—21no—
44#121×C83—21no—
45C4×Q8×C83—21no—
46C4×Q8×C83—21no—
47C4×D4×C83—21no—
48C4×D4×C83—21no—
49#117×C83—21no—
50C2×C42×C83—21no—
51C2×C42×C83—21no—
52C2×C42×C83D411yescharacteristic
53C2×C42×C83D411yescharacteristic
54C2×C42×C83C2311yescharacteristic
55#106×C83—22no—
56C4⋊C8×C83—21no—
57C4⋊C8×C83—21no—
58C4⋊C8×C83—21no—
59C4⋊C8×C83—21no—
60C4⋊C8×C83—21no—
61C4⋊C8×C83—21no—
62C4⋊C8×C83—21no—
63C4⋊C8×C83—21no—
64#104×C83—42no—
65#104×C83—42no—
66#103×C83—22no—
67#102×C83—22no—
68#41×C83—41no—
69#41×C83—41no—
70#41×C83—41no—
71#41×C83—41no—
72C2×Q8×C83—21no—
73C2×Q8×C83—21no—
74C2×Q8×C83—21no—
75C2×D4×C83—21no—
76C2×D4×C83—21no—
77C2×D4×C83—21no—
78C2×D4×C83—41no—
79C22×C4×C83—21no—
80C22×C4×C83—21no—
81C22×C4×C83—41no—
82C22×C4×C83C2×D411yescharacteristic
83C22×C4×C83C2×D411yescharacteristic
84C22×C4×C83#4111yescharacteristic
85SD16×C83—82no—
86M16×C83—41no—
87M16×C83—41no—
88M16×C83—41no—
89M16×C83—41no—
90C2×C8×C83—22no—
91C2×C8×C83—42no—
92C2×C8×C83—42no—
93C2×C8×C83—41no—
94C2×C8×C83—41no—
95C2×C8×C83—41no—
96C4⋊C4×C83—21no—
97C4⋊C4×C83—21no—
98C4⋊C4×C83—21no—
99C4⋊C4×C83—21no—
100C4⋊C4×C83—21no—
101C4⋊C4×C83—21no—
102C4⋊C4×C83—41no—
103C4⋊C4×C83—41no—
104C22⋊C4×C83—41no—
105C22⋊C4×C83—41no—
106C22⋊C4×C83—41no—
107C42×C83—21no—
108C42×C83—21no—
109C42×C83—21no—
110C42×C83—41no—
111C42×C83—41no—
112C42×C83—42no—
113C42×C83—41no—
114C42×C83SD1612yescomplemented
115C42×C83C2×D411yescharacteristic
116C42×C83C2×D411yescharacteristic
117C42×C83#4111yescharacteristic
118C42×C83#4111yescharacteristic
119C23×C83—41no—
120C23×C83#12111yescharacteristic
121Q8×C83—41no—
122Q8×C83—41no—
123Q8×C83—41no—
124Q8×C83—41no—
125Q8×C83—81no—
126D4×C83—41no—
127D4×C83—41no—
128D4×C83—41no—
129D4×C83—41no—
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—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—81no—
146C2×C4×C83—81no—
147C2×C4×C83#12011yescharacteristic
148C2×C4×C83#12111yescharacteristic
149C2×C4×C83#12111yescharacteristic
150C2×C4×C83#12311yescharacteristic
151C2×C4×C83#12311yescharacteristic
152C2×C4×C83#12411yescharacteristic
153C2×C4×C83C2×SD1611yescharacteristic
154C2×C4×C83#13511yescharacteristic
155C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C83#13711yescharacteristic
157C8×C83—42no—
158C8×C83—81no—
159C8×C83—81no—
160C8×C83—81no—
161C22×C83—21no—
162C22×C83—21no—
163C22×C83—81no—
164C22×C83—81no—
165C22×C83—81no—
166C22×C83#39411yescharacteristic
167C22×C83#46511yescharacteristic
168C22×C83#46811yescharacteristic
169C4×C83—21no—
170C4×C83—21no—
171C4×C83—21no—
172C4×C83—42no—
173C4×C83—42no—
174C4×C83—81no—
175C4×C83—81no—
176C4×C83—81no—
177C4×C83#45411yescharacteristic
178C4×C83#45511yescharacteristic
179C4×C83#46011yescharacteristic
180C4×C83#46111yescharacteristic
181C4×C83#46311yescharacteristic
182C4×C83#46411yescharacteristic
183#10521C8311yesmaximal, characteristic, direct product factor, Sylow
184C2×C83—21no—
185C2×C83—21no—
186C2×C83—161no—
187C2×C83#204011yescharacteristic
188C2×C83#205011yescharacteristic
189C2×C83#205511yescharacteristic
190#3246C2×C8311yescharacteristic
191#1994C2×C8311yescharacteristic, complemented
192#1962C2×C8311yescharacteristic
193#1831C2×C8311yescharacteristic, complemented
194#1550C2×C8311yescharacteristic, complemented
195#1547C2×C8311yescharacteristic
196#1292C2×C8311yescharacteristic, complemented
197C83#1052111yescharacteristic, direct product factor, Sylow
198#533C22×C8311yescharacteristic
199#532C22×C8311yescharacteristic
200#476—21no—
201#475—21no—
202#465—22no—
203#461—21no—
204#460—21no—
205#423C22×C8311yescharacteristic
206#423C22×C8311yescharacteristic
207C2×C4⋊C8C22×C8311yescharacteristic
208C2×C4⋊C8C22×C8311yescharacteristic
209C2×#104—21no—
210C2×#104—21no—
211C43C22×C8311yescharacteristic
212#339—21no—
213#339—21no—
214#336—22no—
215#333—21no—
216#332—21no—
217#332—21no—
218#331—21no—
219C2×#41—21no—
220C2×SD16—22no—
221C2×M16—21no—
222C2×M16—21no—
223C22×C8—21no—
224C22×C8D4×C8312yes—
225C4⋊Q8D4×C8311yescharacteristic
226C4⋊Q8D4×C8311yescharacteristic
227C4⋊Q8D4×C8311yescharacteristic
228#127D4×C8311yescharacteristic
229#125—21no—
230#124—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233#121—21no—
234#121—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×D4—21no—
238C4×D4—21no—
239#117—21no—
240C2×C42—21no—
241C2×C42—21no—
242C2×C42D4×C8311yescharacteristic
243C2×C42D4×C8311yescharacteristic
244C2×C42C23×C8311yescharacteristic
245#106—22no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254#104—42no—
255#104—42no—
256#103—22no—
257#102—22no—
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4C2×D4×C8311yescharacteristic
273C22×C4C2×D4×C8311yescharacteristic
274C22×C4#41×C8311yescharacteristic
275SD16—82no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—41no—
280C2×C8—22no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—41no—
301C42—41no—
302C42—42no—
303C42—41no—
304C42SD16×C8312yescomplemented
305C42C2×D4×C8311yescharacteristic
306C42C2×D4×C8311yescharacteristic
307C42#41×C8311yescharacteristic
308C42#41×C8311yescharacteristic
309C23—41no—
310C23#121×C8311yescharacteristic
311Q8—41no—
312Q8—41no—
313Q8—41no—
314Q8—41no—
315Q8—81no—
316D4—41no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—81no—
321D4—81no—
322D4—81no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
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—81no—
336C2×C4—81no—
337C2×C4#120×C8311yescharacteristic
338C2×C4#121×C8311yescharacteristic
339C2×C4#121×C8311yescharacteristic
340C2×C4#123×C8311yescharacteristic
341C2×C4#123×C8311yescharacteristic
342C2×C4#124×C8311yescharacteristic
343C2×C4C2×SD16×C8311yescharacteristic
344C2×C4#135×C8311yescharacteristic
345C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
346C2×C4#137×C8311yescharacteristic
347C8—42no—
348C8—81no—
349C8—81no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#394×C8311yescharacteristic
357C22#465×C8311yescharacteristic
358C22#468×C8311yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—42no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4#454×C8311yescharacteristic
368C4#455×C8311yescharacteristic
369C4#460×C8311yescharacteristic
370C4#461×C8311yescharacteristic
371C4#463×C8311yescharacteristic
372C4#464×C8311yescharacteristic
373C2—21no—
374C2—21no—
375C2—161no—
376C2C83×#204011yescharacteristic
377C2C83×#205011yescharacteristic
378C2C83×#205511yescharacteristic
subgroupG/H
center, socleC22×C83#394
commutator, Frattini, cosocleC2×C42C23×C83
prime radical#532×C83C22
LCSG ▷ C2×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×#1994C2semidirect
4. C83×#1831C2semidirect
5. C83×#1550C2semidirect
7. C83×#1292C2semidirect
114. C42×C83SD16semidirect
183. #10521C83direct (N × H)
191. #1994C2×C83semidirect
193. #1831C2×C83semidirect
194. #1550C2×C83semidirect
196. #1292C2×C83semidirect
197. C83#10521direct (N × H)
304. C42SD16×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#32462
C83×#19942
C83×#19622
C83×#18312
C83×#15502
C83×#15472
C83×#12922
#1052183