Finite Group Databasebeta

← C83×#9293 #35237117

Subgroups — C83×#9293 #35237117

Order 21248.

558 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3205C211yesmaximal, characteristic
2C83×#2932C211yesmaximal, characteristic, complemented
3C83×#1961C211yesmaximal, characteristic, complemented
4C83×#1545C211yesmaximal, characteristic, complemented
5C83×#1517C211yesmaximal, characteristic, complemented
6C83×#1286C211yesmaximal, characteristic, complemented
7C83×#1275C211yesmaximal, characteristic, complemented
8C2×#131×C83—21no—
9#532×C83C2211yescharacteristic
10C2×#127×C83C2211yescharacteristic
11#493×C83C412yescomplemented
12#486×C83C412yescomplemented
13#459×C83—22no—
14#447×C83—22no—
15#435×C83—22no—
16#435×C83—22no—
17#431×C83C2211yescharacteristic
18#431×C83C2211yescharacteristic
19#423×C83C2211yescharacteristic
20C2×#102×C83—21no—
21C2×#102×C83—21no—
22#408×C83—21no—
23C2×#97×C83C2211yescharacteristic
24#382×C83C2211yescharacteristic
25#331×C83—22no—
26#327×C83—22no—
27C2×#41×C83—21no—
28C22×D4×C83—21no—
29C22×D4×C83—21no—
30C22×D4×C83—21no—
31C2×D8×C83—24no—
32#131×C83—42no—
33#131×C83—42no—
34C2×M16×C83—22no—
35C2×M16×C83—21no—
36C22×C8×C83—22no—
37C22×C8×C83D411yescharacteristic
38C22×C8×C83D411yescharacteristic
39C4⋊Q8×C83C2×C411yescharacteristic
40#127×C83—21no—
41#127×C83—21no—
42#127×C83—21no—
43#127×C83C2×C412yes—
44#127×C83C2×C411yescharacteristic
45#124×C83—21no—
46#121×C83—21no—
47#121×C83D412yes—
48C4×D4×C83—21no—
49C4×D4×C83D412yes—
50C2×C4⋊C4×C83—21no—
51C2×C42×C83C2311yescharacteristic
52C4⋊C8×C83—21no—
53C4⋊C8×C83—21no—
54C4⋊C8×C83—21no—
55C4⋊C8×C83D412yes—
56#102×C83—24no—
57#102×C83—42no—
58#102×C83—42no—
59C22⋊C8×C83—24no—
60C22⋊C8×C83—21no—
61C22⋊C8×C83—21no—
62#97×C83—21no—
63#97×C83—21no—
64C4×C8×C83—21no—
65C4×C8×C83C2×C412yes—
66#95×C83—21no—
67#95×C83—21no—
68C24×C83—41no—
69#41×C83—41no—
70#41×C83—41no—
71#41×C83—41no—
72#41×C83—41no—
73C2×Q8×C83—21no—
74C2×D4×C83—22no—
75C2×D4×C83—22no—
76C2×D4×C83—21no—
77C2×D4×C83—22no—
78C2×D4×C83—21no—
79C2×D4×C83—22no—
80C2×D4×C83—41no—
81C2×D4×C83—41no—
82C2×D4×C83—41no—
83C2×D4×C83—41no—
84C2×D4×C83—41no—
85C2×D4×C83—41no—
86C2×D4×C83—41no—
87C2×D4×C83—82no—
88C2×D4×C83—82no—
89C2×D4×C83C22⋊C412yes—
90C22×C4×C83—22no—
91C22×C4×C83—41no—
92C22×C4×C83C2×D411yescharacteristic
93C22×C4×C83C2×D411yescharacteristic
94C22×C4×C83#4111yescharacteristic
95D8×C83—84no—
96M16×C83—44no—
97M16×C83—41no—
98M16×C83—41no—
99C2×C8×C83—21no—
100C2×C8×C83—21no—
101C2×C8×C83—22no—
102C2×C8×C83—21no—
103C2×C8×C83—22no—
104C2×C8×C83—21no—
105C2×C8×C83—21no—
106C2×C8×C83—44no—
107C2×C8×C83—41no—
108C2×C8×C83D812yescomplemented
109C4⋊C4×C83—21no—
110C4⋊C4×C83—41no—
111C4⋊C4×C83—41no—
112C4⋊C4×C83C22⋊C412yes—
113C22⋊C4×C83—22no—
114C22⋊C4×C83—22no—
115C42×C83C22×C411yescharacteristic
116C42×C83C2×D411yescharacteristic
117C42×C83C2×D411yescharacteristic
118C42×C83#4111yescharacteristic
119C23×C83—22no—
120C23×C83—42no—
121C23×C83—82no—
122C23×C83—82no—
123C23×C83—81no—
124C23×C83—81no—
125C23×C83#12111yescharacteristic
126Q8×C83—41no—
127Q8×C83—41no—
128D4×C83—42no—
129D4×C83—44no—
130D4×C83—42no—
131D4×C83—42no—
132D4×C83—41no—
133D4×C83—42no—
134D4×C83—41no—
135D4×C83—42no—
136D4×C83—81no—
137D4×C83—82no—
138D4×C83—82no—
139D4×C83—82no—
140D4×C83—81no—
141D4×C83—81no—
142C2×C4×C83—22no—
143C2×C4×C83—41no—
144C2×C4×C83—41no—
145C2×C4×C83—42no—
146C2×C4×C83—42no—
147C2×C4×C83—81no—
148C2×C4×C83—81no—
149C2×C4×C83—81no—
150C2×C4×C83C2×C22⋊C411yescharacteristic
151C2×C4×C83C4×D411yescharacteristic
152C2×C4×C83C4×D411yescharacteristic
153C2×C4×C83#12011yescharacteristic
154C2×C4×C83#12111yescharacteristic
155C2×C4×C83#12311yescharacteristic
156C2×C4×C83C2×D811yescharacteristic
157C2×C4×C83#13511yescharacteristic
158C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
160C8×C83—22no—
161C8×C83—42no—
162C8×C83—42no—
163C8×C83—41no—
164C8×C83—81no—
165C22×C83—21no—
166C22×C83—21no—
167C22×C83—42no—
168C22×C83—42no—
169C22×C83—42no—
170C22×C83—82no—
171C22×C83—82no—
172C22×C83—82no—
173C22×C83—162no—
174C22×C83—162no—
175C22×C83#38611yescharacteristic
176C22×C83#45911yescharacteristic
177C22×C83#46311yescharacteristic
178C4×C83—21no—
179C4×C83—21no—
180C4×C83—21no—
181C4×C83—21no—
182C4×C83—42no—
183C4×C83—161no—
184C4×C83C4×D811yescharacteristic
185C4×C83#44211yescharacteristic
186C4×C83#44711yescharacteristic
187C4×C83#44911yescharacteristic
188#9293C8311yesmaximal, characteristic, direct product factor, Sylow
189C2×C83—21no—
190C2×C83—21no—
191C2×C83—82no—
192C2×C83—162no—
193C2×C83#187911yescharacteristic
194C2×C83#190311yescharacteristic
195C2×C83#191011yescharacteristic
196#3205C2×C8311yescharacteristic
197#2932C2×C8311yescharacteristic, complemented
198#1961C2×C8311yescharacteristic, complemented
199#1545C2×C8311yescharacteristic, complemented
200#1517C2×C8311yescharacteristic, complemented
201#1286C2×C8311yescharacteristic, complemented
202#1275C2×C8311yescharacteristic, complemented
203C83#929311yescharacteristic, direct product factor, Sylow
204C2×#131—21no—
205#532C22×C8311yescharacteristic
206C2×#127C22×C8311yescharacteristic
207#493C4×C8312yescomplemented
208#486C4×C8312yescomplemented
209#459—22no—
210#447—22no—
211#435—22no—
212#435—22no—
213#431C22×C8311yescharacteristic
214#431C22×C8311yescharacteristic
215#423C22×C8311yescharacteristic
216C2×#102—21no—
217C2×#102—21no—
218#408—21no—
219C2×#97C22×C8311yescharacteristic
220#382C22×C8311yescharacteristic
221#331—22no—
222#327—22no—
223C2×#41—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C2×D8—24no—
228#131—42no—
229#131—42no—
230C2×M16—22no—
231C2×M16—21no—
232C22×C8—22no—
233C22×C8D4×C8311yescharacteristic
234C22×C8D4×C8311yescharacteristic
235C4⋊Q8C2×C4×C8311yescharacteristic
236#127—21no—
237#127—21no—
238#127—21no—
239#127C2×C4×C8312yes—
240#127C2×C4×C8311yescharacteristic
241#124—21no—
242#121—21no—
243#121D4×C8312yes—
244C4×D4—21no—
245C4×D4D4×C8312yes—
246C2×C4⋊C4—21no—
247C2×C42C23×C8311yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8D4×C8312yes—
252#102—24no—
253#102—42no—
254#102—42no—
255C22⋊C8—24no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258#97—21no—
259#97—21no—
260C4×C8—21no—
261C4×C8C2×C4×C8312yes—
262#95—21no—
263#95—21no—
264C24—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268#41—41no—
269C2×Q8—21no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—21no—
273C2×D4—22no—
274C2×D4—21no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—82no—
284C2×D4—82no—
285C2×D4C22⋊C4×C8312yes—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4C2×D4×C8311yescharacteristic
289C22×C4C2×D4×C8311yescharacteristic
290C22×C4#41×C8311yescharacteristic
291D8—84no—
292M16—44no—
293M16—41no—
294M16—41no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—22no—
298C2×C8—21no—
299C2×C8—22no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—44no—
303C2×C8—41no—
304C2×C8D8×C8312yescomplemented
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4C22⋊C4×C8312yes—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C42C22×C4×C8311yescharacteristic
312C42C2×D4×C8311yescharacteristic
313C42C2×D4×C8311yescharacteristic
314C42#41×C8311yescharacteristic
315C23—22no—
316C23—42no—
317C23—82no—
318C23—82no—
319C23—81no—
320C23—81no—
321C23#121×C8311yescharacteristic
322Q8—41no—
323Q8—41no—
324D4—42no—
325D4—44no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—42no—
330D4—41no—
331D4—42no—
332D4—81no—
333D4—82no—
334D4—82no—
335D4—82no—
336D4—81no—
337D4—81no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4C2×C22⋊C4×C8311yescharacteristic
347C2×C4C4×D4×C8311yescharacteristic
348C2×C4C4×D4×C8311yescharacteristic
349C2×C4#120×C8311yescharacteristic
350C2×C4#121×C8311yescharacteristic
351C2×C4#123×C8311yescharacteristic
352C2×C4C2×D8×C8311yescharacteristic
353C2×C4#135×C8311yescharacteristic
354C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
355C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
356C8—22no—
357C8—42no—
358C8—42no—
359C8—41no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—162no—
370C22—162no—
371C22#386×C8311yescharacteristic
372C22#459×C8311yescharacteristic
373C22#463×C8311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—42no—
379C4—161no—
380C4C4×D8×C8311yescharacteristic
381C4#442×C8311yescharacteristic
382C4#447×C8311yescharacteristic
383C4#449×C8311yescharacteristic
384C2—21no—
385C2—21no—
386C2—82no—
387C2—162no—
388C2C83×#187911yescharacteristic
389C2C83×#190311yescharacteristic
390C2C83×#191011yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC42C22×C4×C83
Frattini, cosocleC2×C42C23×C83
prime radicalC83×#3205C2
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×#2932C2semidirect
3. C83×#1961C2semidirect
4. C83×#1545C2semidirect
5. C83×#1517C2semidirect
6. C83×#1286C2semidirect
7. C83×#1275C2semidirect
11. #493×C83C4semidirect
12. #486×C83C4semidirect
108. C2×C8×C83D8semidirect
188. #9293C83direct (N × H)
197. #2932C2×C83semidirect
198. #1961C2×C83semidirect
199. #1545C2×C83semidirect
200. #1517C2×C83semidirect
201. #1286C2×C83semidirect
202. #1275C2×C83semidirect
203. C83#9293direct (N × H)
207. #493C4×C83semidirect
208. #486C4×C83semidirect
304. C2×C8D8×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#32052
C83×#29322
C83×#19612
C83×#15452
C83×#15172
C83×#12862
C83×#12752
#929383