Finite Group Databasebeta

← C83×#12980 #35240804

Subgroups — C83×#12980 #35240804

Order 21248.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#504×C83C211yesmaximal, characteristic, complemented
2C2×#443×C83C211yesmaximal, characteristic
3C2×#350×C83C211yesmaximal, characteristic, complemented
4C2×#350×C83C211yesmaximal, characteristic, complemented
5C83×#2113C211yesmaximal, characteristic, complemented
6C83×#1376C211yesmaximal, characteristic, complemented
7C83×#1374C211yesmaximal, characteristic, complemented
8C2×#135×C83C411yescharacteristic
9C2×#131×C83C2211yescharacteristic
10C2×#131×C83C2211yescharacteristic
11#504×C83—22no—
12#504×C83—22no—
13C2×M32×C83—21no—
14C2×M32×C83C2211yescharacteristic
15C2×M32×C83C2211yescharacteristic
16C22×C16×C83—21no—
17C22×C16×C83C2211yescharacteristic
18C22×C16×C83C2211yescharacteristic
19#443×C83—22no—
20#443×C83—22no—
21C2×#108×C83C411yescharacteristic
22C2×#104×C83C411yescharacteristic
23C2×#104×C83C411yescharacteristic
24C2×C4×C8×C83C2211yescharacteristic
25#350×C83—22no—
26#350×C83—22no—
27C22⋊C16×C83—21no—
28C22⋊C16×C83—21no—
29C2×#41×C83C2×C411yescharacteristic
30C2×#41×C83C2×C411yescharacteristic
31#135×C83—22no—
32#135×C83—22no—
33C2×Q16×C83C811yescharacteristic
34C2×SD16×C83C811yescharacteristic
35C2×SD16×C83C811yescharacteristic
36C2×D8×C83C811yescharacteristic
37#131×C83—21no—
38#131×C83—21no—
39#131×C83—21no—
40#131×C83—21no—
41#131×C83—21no—
42#131×C83—21no—
43#131×C83D412yes—
44#131×C83D412yes—
45C2×M16×C83—21no—
46C2×M16×C83—21no—
47C2×M16×C83C2×C411yescharacteristic
48C2×M16×C83C2×C411yescharacteristic
49C22×C8×C83—21no—
50C22×C8×C83—21no—
51C22×C8×C83C2×C411yescharacteristic
52C22×C8×C83C2311yescharacteristic
53C2×C42×C83C2×C411yescharacteristic
54M32×C83—24no—
55M32×C83—21no—
56M32×C83—21no—
57M32×C83—21no—
58M32×C83D412yes—
59C2×C16×C83—24no—
60C2×C16×C83—21no—
61C2×C16×C83—21no—
62C2×C16×C83—21no—
63C2×C16×C83—21no—
64C2×C16×C83—21no—
65C2×C16×C83—21no—
66C2×C16×C83—21no—
67C2×C16×C83D411yescharacteristic
68C2×C16×C83D411yescharacteristic
69#108×C83—22no—
70#104×C83—22no—
71#104×C83—22no—
72C4×C8×C83—21no—
73C4×C8×C83—21no—
74#41×C83—21no—
75#41×C83—21no—
76#41×C83—21no—
77#41×C83—21no—
78#41×C83—21no—
79#41×C83—21no—
80#41×C83C22⋊C412yes—
81#41×C83M1612yes—
82C2×Q8×C83C2×C811yescharacteristic
83C2×Q8×C83C2×C811yescharacteristic
84C2×D4×C83—21no—
85C2×D4×C83—21no—
86C2×D4×C83C2×C811yescharacteristic
87C2×D4×C83C2×C811yescharacteristic
88C22×C4×C83—21no—
89C22×C4×C83—21no—
90C22×C4×C83—21no—
91C22×C4×C83C22×C411yescharacteristic
92Q16×C83—22no—
93SD16×C83—22no—
94SD16×C83—22no—
95D8×C83—22no—
96M16×C83—21no—
97M16×C83—22no—
98M16×C83—22no—
99M16×C83—21no—
100M16×C83—21no—
101M16×C83—41no—
102M16×C83—41no—
103M16×C83C22⋊C412yes—
104C2×C8×C83—21no—
105C2×C8×C83—21no—
106C2×C8×C83—21no—
107C2×C8×C83—22no—
108C2×C8×C83—22no—
109C2×C8×C83—21no—
110C2×C8×C83—41no—
111C2×C8×C83—41no—
112C2×C8×C83C2×C811yescharacteristic
113C2×C8×C83C2×C811yescharacteristic
114C2×C8×C83C2×D411yescharacteristic
115C2×C8×C83C2×D411yescharacteristic
116C2×C8×C83C2×D411yescharacteristic
117C2×C8×C83C2×D411yescharacteristic
118C2×C8×C83#4111yescharacteristic
119C2×C8×C83#4111yescharacteristic
120C42×C83—21no—
121C42×C83—21no—
122C16×C83—21no—
123C16×C83—22no—
124C16×C83—21no—
125C16×C83—41no—
126C16×C83—41no—
127C23×C83—21no—
128C23×C83—21no—
129C23×C83#13111yescharacteristic
130Q8×C83—21no—
131Q8×C83—21no—
132Q8×C83—21no—
133Q8×C83C22⋊C812yes—
134D4×C83—22no—
135D4×C83—22no—
136D4×C83—21no—
137D4×C83—21no—
138D4×C83—21no—
139D4×C83—41no—
140D4×C83—41no—
141D4×C83C22⋊C812yes—
142C2×C4×C83—21no—
143C2×C4×C83—22no—
144C2×C4×C83—22no—
145C2×C4×C83—22no—
146C2×C4×C83—21no—
147C2×C4×C83—41no—
148C2×C4×C83—41no—
149C2×C4×C83—41no—
150C2×C4×C83—41no—
151C2×C4×C83C2×C22⋊C411yescharacteristic
152C2×C4×C83C4×D411yescharacteristic
153C2×C4×C83C4×D411yescharacteristic
154C2×C4×C83C22×C811yescharacteristic
155C2×C4×C83C2×M1611yescharacteristic
156C2×C4×C83#13111yescharacteristic
157C8×C83—22no—
158C8×C83—21no—
159C8×C83—21no—
160C8×C83—41no—
161C8×C83#12011yescharacteristic
162C8×C83#12111yescharacteristic
163C8×C83#12111yescharacteristic
164C8×C83#12311yescharacteristic
165C22×C83—21no—
166C22×C83—21no—
167C22×C83—22no—
168C22×C83—41no—
169C22×C83—41no—
170C22×C83—41no—
171C22×C83—41no—
172C22×C83—41no—
173C22×C83#40811yescharacteristic
174C22×C83C8×D411yescharacteristic
175C22×C83#43511yescharacteristic
176C4×C83—22no—
177C4×C83—42no—
178C4×C83—41no—
179C4×C83#38611yescharacteristic
180C4×C83C2×C22⋊C811yescharacteristic
181C4×C83C8×D411yescharacteristic
182C4×C83#43511yescharacteristic
183#12980C8311yesmaximal, characteristic, direct product factor, Sylow
184C2×C83—21no—
185C2×C83—21no—
186C2×C83—42no—
187C2×C83—81no—
188C2×C83#186911yescharacteristic
189C2×C83#217011yescharacteristic
190C2×C83#217111yescharacteristic
191C2×#504C2×C8311yescharacteristic, complemented
192C2×#443C2×C8311yescharacteristic
193C2×#350C2×C8311yescharacteristic, complemented
194C2×#350C2×C8311yescharacteristic, complemented
195#2113C2×C8311yescharacteristic, complemented
196#1376C2×C8311yescharacteristic, complemented
197#1374C2×C8311yescharacteristic, complemented
198C83#1298011yescharacteristic, direct product factor, Sylow
199C2×#135C4×C8311yescharacteristic
200C2×#131C22×C8311yescharacteristic
201C2×#131C22×C8311yescharacteristic
202#504—22no—
203#504—22no—
204C2×M32—21no—
205C2×M32C22×C8311yescharacteristic
206C2×M32C22×C8311yescharacteristic
207C22×C16—21no—
208C22×C16C22×C8311yescharacteristic
209C22×C16C22×C8311yescharacteristic
210#443—22no—
211#443—22no—
212C2×#108C4×C8311yescharacteristic
213C2×#104C4×C8311yescharacteristic
214C2×#104C4×C8311yescharacteristic
215C2×C4×C8C22×C8311yescharacteristic
216#350—22no—
217#350—22no—
218C22⋊C16—21no—
219C22⋊C16—21no—
220C2×#41C2×C4×C8311yescharacteristic
221C2×#41C2×C4×C8311yescharacteristic
222#135—22no—
223#135—22no—
224C2×Q16C8×C8311yescharacteristic
225C2×SD16C8×C8311yescharacteristic
226C2×SD16C8×C8311yescharacteristic
227C2×D8C8×C8311yescharacteristic
228#131—21no—
229#131—21no—
230#131—21no—
231#131—21no—
232#131—21no—
233#131—21no—
234#131D4×C8312yes—
235#131D4×C8312yes—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16C2×C4×C8311yescharacteristic
239C2×M16C2×C4×C8311yescharacteristic
240C22×C8—21no—
241C22×C8—21no—
242C22×C8C2×C4×C8311yescharacteristic
243C22×C8C23×C8311yescharacteristic
244C2×C42C2×C4×C8311yescharacteristic
245M32—24no—
246M32—21no—
247M32—21no—
248M32—21no—
249M32D4×C8312yes—
250C2×C16—24no—
251C2×C16—21no—
252C2×C16—21no—
253C2×C16—21no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16D4×C8311yescharacteristic
259C2×C16D4×C8311yescharacteristic
260#108—22no—
261#104—22no—
262#104—22no—
263C4×C8—21no—
264C4×C8—21no—
265#41—21no—
266#41—21no—
267#41—21no—
268#41—21no—
269#41—21no—
270#41—21no—
271#41C22⋊C4×C8312yes—
272#41M16×C8312yes—
273C2×Q8C2×C8×C8311yescharacteristic
274C2×Q8C2×C8×C8311yescharacteristic
275C2×D4—21no—
276C2×D4—21no—
277C2×D4C2×C8×C8311yescharacteristic
278C2×D4C2×C8×C8311yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4C22×C4×C8311yescharacteristic
283Q16—22no—
284SD16—22no—
285SD16—22no—
286D8—22no—
287M16—21no—
288M16—22no—
289M16—22no—
290M16—21no—
291M16—21no—
292M16—41no—
293M16—41no—
294M16C22⋊C4×C8312yes—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—21no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8C2×C8×C8311yescharacteristic
304C2×C8C2×C8×C8311yescharacteristic
305C2×C8C2×D4×C8311yescharacteristic
306C2×C8C2×D4×C8311yescharacteristic
307C2×C8C2×D4×C8311yescharacteristic
308C2×C8C2×D4×C8311yescharacteristic
309C2×C8#41×C8311yescharacteristic
310C2×C8#41×C8311yescharacteristic
311C42—21no—
312C42—21no—
313C16—21no—
314C16—22no—
315C16—21no—
316C16—41no—
317C16—41no—
318C23—21no—
319C23—21no—
320C23#131×C8311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8C22⋊C8×C8312yes—
325D4—22no—
326D4—22no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—41no—
331D4—41no—
332D4C22⋊C8×C8312yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4C2×C22⋊C4×C8311yescharacteristic
343C2×C4C4×D4×C8311yescharacteristic
344C2×C4C4×D4×C8311yescharacteristic
345C2×C4C22×C8×C8311yescharacteristic
346C2×C4C2×M16×C8311yescharacteristic
347C2×C4#131×C8311yescharacteristic
348C8—22no—
349C8—21no—
350C8—21no—
351C8—41no—
352C8#120×C8311yescharacteristic
353C8#121×C8311yescharacteristic
354C8#121×C8311yescharacteristic
355C8#123×C8311yescharacteristic
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22#408×C8311yescharacteristic
365C22C8×D4×C8311yescharacteristic
366C22#435×C8311yescharacteristic
367C4—22no—
368C4—42no—
369C4—41no—
370C4#386×C8311yescharacteristic
371C4C2×C22⋊C8×C8311yescharacteristic
372C4C8×D4×C8311yescharacteristic
373C4#435×C8311yescharacteristic
374C2—21no—
375C2—21no—
376C2—42no—
377C2—81no—
378C2C83×#186911yescharacteristic
379C2C83×#217011yescharacteristic
380C2C83×#217111yescharacteristic
subgroupG/H
centerC2×C8×C83C2×D4
commutatorC2×C4C22×C8×C83
Frattini, cosocleC22×C8C23×C83
socleC22×C83C8×D4
prime radicalC2×#135×C83C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8×C83 ◁ C22×C16×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#504×C83C2semidirect
3. C2×#350×C83C2semidirect
4. C2×#350×C83C2semidirect
5. C83×#2113C2semidirect
6. C83×#1376C2semidirect
7. C83×#1374C2semidirect
183. #12980C83direct (N × H)
191. C2×#504C2×C83semidirect
193. C2×#350C2×C83semidirect
194. C2×#350C2×C83semidirect
195. #2113C2×C83semidirect
196. #1376C2×C83semidirect
197. #1374C2×C83semidirect
198. C83#12980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#504×C832
C2×#443×C832
C2×#350×C832
C83×#21132
C83×#13762
C83×#13742
#1298083