Finite Group Databasebeta

← #35308813

Subgroups — #35308813

Order 21248.

560 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913577C211yesmaximal, characteristic
2#24907658C212yesmaximal
3#24905719C211yesmaximal, characteristic
4#24905343C212yesmaximal
5C83×#1280C211yesmaximal, characteristic
6C2×#14581771—21no—
7C22×C4⋊Dic83C2211yescharacteristic
8C2×#14581724—22no—
9#19127633—22no—
10#19127622—22no—
11#19127561—21no—
12#19127561C2212yes—
13C2×C83⋊#95—21no—
14C2×C83⋊#95—21no—
15C2×C83⋊#95C2211yescharacteristic
16#19127464—22no—
17C2×C22⋊C8×C83C2212yes—
18C2×#95×C83C2211yescharacteristic
19C22×Dic166—21no—
20C23×Dic83—21no—
21C23×Dic83—21no—
22#14581771—42no—
23#14581771—42no—
24C2×C4⋊Dic83—21no—
25C2×C4⋊Dic83—21no—
26C2×C4⋊Dic83—21no—
27C2×C4⋊Dic83—22no—
28C2×C4⋊Dic83—42no—
29C2×C4⋊Dic83D412yes—
30C2×C4⋊Dic83D412yes—
31C2×Dic83⋊C4—22no—
32C2×C22⋊Dic83—22no—
33#14581724—44no—
34C83⋊#95—22no—
35C83⋊#95—22no—
36C83⋊#95—21no—
37C83⋊#95—42no—
38C83⋊#95—42no—
39C83⋊#95Q812yescomplemented
40C23×C4×C83D411yescharacteristic
41C23×C4×C83D411yescharacteristic
42C23×C4×C83C2311yescharacteristic
43C22×C8×C83—22no—
44C22⋊C8×C83—22no—
45C22⋊C8×C83Q814yescomplemented
46#95×C83—22no—
47C2×Dic166—42no—
48C2×Dic166—81no—
49C2×Dic166—81no—
50C22×Dic83—22no—
51C22×Dic83—22no—
52C22×Dic83—22no—
53C22×Dic83—22no—
54C22×Dic83—41no—
55C22×Dic83—41no—
56C22×Dic83—41no—
57C22×Dic83—41no—
58C22×Dic83—41no—
59C22×Dic83—41no—
60C22×Dic83—41no—
61C22×Dic83—41no—
62C22×Dic83—41no—
63C22×Dic83—41no—
64C22×Dic83—41no—
65C22×Dic83—41no—
66C4⋊Dic83—24no—
67C4⋊Dic83—42no—
68C4⋊Dic83—42no—
69C4⋊Dic83—42no—
70C4⋊Dic83—42no—
71C4⋊Dic83—81no—
72C4⋊Dic83—81no—
73Dic83⋊C4—44no—
74C22⋊Dic83—42no—
75C22⋊Dic83—42no—
76C24×C83C2×D411yescharacteristic
77C22×C4×C83—21no—
78C22×C4×C83—21no—
79C22×C4×C83—21no—
80C22×C4×C83—21no—
81C22×C4×C83—41no—
82C22×C4×C83—41no—
83C22×C4×C83—41no—
84C22×C4×C83—41no—
85C22×C4×C83—41no—
86C22×C4×C83—41no—
87C22×C4×C83SD1612yes—
88C22×C4×C83SD1612yes—
89C22×C4×C83C2×D412yes—
90C22×C4×C83C2×Q811yescharacteristic
91C22×C4×C83C2×Q812yes—
92C22×C4×C83#4111yescharacteristic
93C2×C8×C83—24no—
94C2×C8×C83—42no—
95C2×C8×C83—42no—
96C23×C83—21no—
97C23×C83—21no—
98C23×C83—21no—
99C23×C83—21no—
100C23×C83#12011yescharacteristic
101C23×C83C22⋊Q811yescharacteristic
102C23×C83C4⋊Q811yescharacteristic
103C23×C83C2×SD1611yescharacteristic
104C23×C83C2×SD1611yescharacteristic
105C23×C83AGL(1,ℤ/8)11yescharacteristic
106C23×C83#13711yescharacteristic
107C2×C4×C83—22no—
108C2×C4×C83—22no—
109C2×C4×C83—22no—
110C2×C4×C83—22no—
111C2×C4×C83—41no—
112C2×C4×C83—42no—
113C2×C4×C83—41no—
114C2×C4×C83—41no—
115C2×C4×C83—41no—
116C2×C4×C83—41no—
117C2×C4×C83—41no—
118C2×C4×C83—42no—
119C2×C4×C83—42no—
120C2×C4×C83—81no—
121C2×C4×C83—81no—
122C2×C4×C83C22⋊Q812yes—
123C2×C4×C83C4⋊Q812yes—
124C2×Dic83—42no—
125C2×Dic83—42no—
126C2×Dic83—42no—
127C2×Dic83—42no—
128C2×Dic83—42no—
129C2×Dic83—42no—
130C2×Dic83—42no—
131C2×Dic83—42no—
132C2×Dic83—42no—
133C2×Dic83—42no—
134C2×Dic83—42no—
135C2×Dic83—42no—
136C2×Dic83—81no—
137C2×Dic83—81no—
138C2×Dic83—81no—
139C2×Dic83—81no—
140C2×Dic83—81no—
141C2×Dic83—81no—
142C2×Dic83—81no—
143C2×Dic83—81no—
144Dic166—84no—
145C8×C83—44no—
146C22×C83—21no—
147C22×C83—21no—
148C22×C83—21no—
149C22×C83—21no—
150C22×C83—21no—
151C22×C83—21no—
152C22×C83—21no—
153C22×C83—21no—
154C22×C83—21no—
155C22×C83—21no—
156C22×C83—21no—
157C22×C83—21no—
158C22×C83#39511yescharacteristic
159C22×C83#44811yescharacteristic
160C22×C83#45011yescharacteristic
161C22×C83#45411yescharacteristic
162C22×C83#45511yescharacteristic
163C22×C83B(4,𝔽2)11yescharacteristic
164C22×C83#45811yescharacteristic
165C22×C83#47511yescharacteristic
166C22×C83#47611yescharacteristic
167C22×C83#49811yescharacteristic
168C22×C83#50111yescharacteristic
169C4×C83—22no—
170C4×C83—22no—
171C4×C83—42no—
172C4×C83—42no—
173Dic83—82no—
174Dic83—82no—
175Dic83—82no—
176Dic83—82no—
177#10568—831nomaximal, Sylow
178C2×C83—21no—
179C2×C83—21no—
180C2×C83—21no—
181C2×C83—21no—
182C2×C83#159911yescharacteristic
183C2×C83#160111yescharacteristic
184C2×C83#160811yescharacteristic
185C2×C83#161611yescharacteristic
186C2×C83#205811yescharacteristic
187C2×C83#206111yescharacteristic
188C2×C83#206211yescharacteristic
189#2659—831no—
190#1853—832no—
191#1442—831no—
192#1294—832no—
193#1280D8311yescharacteristic
194C83#1056811yescharacteristic, complemented, Sylow
195C2×C22⋊Q8—1661no—
196C22×C4⋊C4—831no—
197C2×#106—1662no—
198C2×C22⋊C8C2×D8312yes—
199#398—1662no—
200#395—1662no—
201#380—832no—
202#380—1661no—
203C2×#95—831no—
204C2×#95—1661no—
205C2×#95—1661no—
206C2×#95C2×D8311yescharacteristic
207#340—1662no—
208C22×Q8—1661no—
209C23×C4—1661no—
210C23×C4—1661no—
211C23×C4D33211yescharacteristic
212C23×C4D33211yescharacteristic
213C23×C4C22×D8311yescharacteristic
214C22×C8—22no—
215C22⋊Q8—3322no—
216C22⋊Q8—3322no—
217C2×C4⋊C4—3322no—
218C2×C4⋊C4—832no—
219C2×C4⋊C4—832no—
220C2×C4⋊C4—1662no—
221C2×C4⋊C4—1661no—
222C2×C4⋊C4—1662no—
223C2×C4⋊C4—1661no—
224C2×C4⋊C4—1661no—
225C2×C22⋊C4—1662no—
226#106—3324no—
227C22⋊C8—22no—
228C22⋊C8Dic16614yescomplemented
229#95—22no—
230#95—3322no—
231#95—3322no—
232#95—832no—
233#95—1662no—
234#95—1662no—
235#95—1661no—
236C24C2×D33211yescharacteristic
237C2×Q8—3322no—
238C2×Q8—6641no—
239C2×Q8—6641no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—3321no—
251C22×C4—3321no—
252C22×C4—3321no—
253C22×C4—3321no—
254C22×C4—3321no—
255C22×C4—3321no—
256C22×C4—3321no—
257C22×C4—3321no—
258C22×C4—3321no—
259C22×C4—3321no—
260C22×C4—3321no—
261C22×C4—3321no—
262C22×C4—1662no—
263C22×C4—1662no—
264C22×C4—1662no—
265C22×C4—1662no—
266C22×C4#1305057912yes—
267C22×C4#1305057912yes—
268C22×C4D4×D8312yes—
269C22×C4Q8×D8311yescharacteristic
270C22×C4C2×Dic16612yes—
271C22×C4#1305058911yescharacteristic
272C2×C8—24no—
273C2×C8—42no—
274C2×C8—42no—
275C4⋊C4—3322no—
276C4⋊C4—3322no—
277C4⋊C4—3322no—
278C4⋊C4—3324no—
279C4⋊C4—3322no—
280C4⋊C4—6641no—
281C4⋊C4—6641no—
282C4⋊C4—1664no—
283C22⋊C4—3322no—
284C22⋊C4—3322no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23#1458176211yescharacteristic
290C23#1458177211yescharacteristic
291C23#1458179211yescharacteristic
292C23C2×#1305057911yescharacteristic
293C23C2×#1305057911yescharacteristic
294C23#1458182011yescharacteristic
295C23#1458182511yescharacteristic
296Q8—6644no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—3322no—
313C2×C4—3322no—
314C2×C4—3322no—
315C2×C4—3322no—
316C2×C4—3322no—
317C2×C4—3322no—
318C2×C4—3322no—
319C2×C4—3322no—
320C2×C4—3322no—
321C2×C4—3322no—
322C2×C4—3322no—
323C2×C4—3322no—
324C2×C4—6641no—
325C2×C4—6641no—
326C2×C4—6641no—
327C2×C4—6641no—
328C2×C4—6641no—
329C2×C4—6641no—
330C2×C4—6641no—
331C2×C4—6641no—
332C2×C4#1458176912yes—
333C2×C4#1458179112yes—
334C8—44no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22#1912762211yescharacteristic
348C22#1912784211yescharacteristic
349C22#1912785411yescharacteristic
350C22#1912787611yescharacteristic
351C22#1912788111yescharacteristic
352C22#1912788911yescharacteristic
353C22#1912789211yescharacteristic
354C22#1912798711yescharacteristic
355C22#1912799211yescharacteristic
356C22#1912809911yescharacteristic
357C22#1912811011yescharacteristic
358C4—22no—
359C4—22no—
360C4—42no—
361C4—42no—
362C4—6642no—
363C4—6642no—
364C4—6642no—
365C4—6642no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2#2490640511yescharacteristic
371C2#2490641711yescharacteristic
372C2#2490645611yescharacteristic
373C2#2490650211yescharacteristic
374C2#2490879711yescharacteristic
375C2#2490881411yescharacteristic
376C2#2490881711yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC23×C4×C83C23
FrattiniC23×C4C22×D83
FittingC83×#1280C2
socleC23×C83#120
prime radicalC24×C83C2×D4
hypercenter#1280D83
hypocenterC83#10568
LCSG ▷ C23×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
39. C83⋊#95Q8semidirect
45. C22⋊C8×C83Q8semidirect
194. C83#10568semidirect
228. C22⋊C8Dic166semidirect

Maximal subgroups

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

subgroupindex
#249135772
#249076582
#249057192
#249053432
C83×#12802
#1056883