Finite Group Databasebeta

← #35298726

Subgroups — #35298726

Order 21248.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916131C211yesmaximal, characteristic
2#24907484C211yesmaximal, characteristic
3#24906238C211yesmaximal, characteristic, complemented
4#24906218C211yesmaximal, characteristic, complemented
5#24905843C211yesmaximal, characteristic
6#24905304C211yesmaximal, characteristic, complemented
7C83×#1303C211yesmaximal, characteristic, complemented
8C4×#13050590C2211yescharacteristic
9#19127761—22no—
10#19127757—21no—
11#19127753—21no—
12#19127725C2211yescharacteristic
13C2×C4⋊(C83⋊C8)C2211yescharacteristic
14C2×#14581720—21no—
15#19127669—21no—
16#19127659—21no—
17C2×C4×C83⋊C8C2211yescharacteristic
18#19127461—21no—
19#19127454—21no—
20#19127454—21no—
21#19127451—22no—
22#19127431C411yescharacteristic, complemented
23#19127431C411yescharacteristic, complemented
24#19127428C411yescharacteristic, complemented
25#19127428C411yescharacteristic, complemented
26#431×C83C2211yescharacteristic
27#423×C83C2211yescharacteristic
28C4×C4⋊C4×C83C2211yescharacteristic
29C2×#13050590D411yescharacteristic
30C2×#13050574—21no—
31C22×C83⋊C8—21no—
32C22×C83⋊C8—21no—
33C4×Dic166C2×C411yescharacteristic
34C4×Dic166Q811yescharacteristic
35C4×D332C2×C411yescharacteristic
36C4×D332Q811yescharacteristic
37C4×C22⋊D83—21no—
38C4×C22⋊D83—21no—
39#14581751D411yescharacteristic
40#14581749—21no—
41C42×D83—21no—
42C4⋊(C83⋊C8)—21no—
43C4⋊(C83⋊C8)—21no—
44C4⋊(C83⋊C8)—21no—
45C4⋊(C83⋊C8)D411yescharacteristic
46C4⋊(C83⋊C8)D411yescharacteristic
47#14581720—42no—
48(C2×D83)⋊C8—22no—
49(C2×D83)⋊C8—22no—
50#14581702—22no—
51C4×C83⋊C8—21no—
52C4×C83⋊C8C2×C411yescharacteristic
53C4×C83⋊C8C2×C411yescharacteristic
54C8×Dic83—22no—
55C2×M16×C83—21no—
56C2×C4⋊C4×C83—21no—
57C2×C42×C83—21no—
58C2×C42×C83C2311yescharacteristic
59C4⋊C8×C83—21no—
60C4⋊C8×C83C2×C411yescharacteristic
61C4⋊C8×C83C2×C411yescharacteristic
62C4⋊C8×C83D412yes—
63C22⋊C8×C83—21no—
64C4×C8×C83—21no—
65#95×C83—21no—
66#13050590—21no—
67#13050590—21no—
68#13050590—21no—
69#13050590—21no—
70C2×Dic166C4⋊C411yescharacteristic
71C2×D332C4⋊C411yescharacteristic
72C2×C22⋊D83—21no—
73C2×C4×D83—21no—
74C2×C4×D83—21no—
75C2×C4×D83—21no—
76#13050574—41no—
77#13050574—41no—
78C2×C83⋊C8—21no—
79C2×C83⋊C8—21no—
80C2×C83⋊C8—21no—
81C2×C83⋊C8—21no—
82C2×C83⋊C8—42no—
83C2×C83⋊C8—41no—
84C2×C83⋊C8—41no—
85C2×C83⋊C8—41no—
86C4⋊Dic83C4⋊C411yescharacteristic
87C4⋊Dic83C4⋊C411yescharacteristic
88Dic83⋊C4—21no—
89Dic83⋊C4—21no—
90C22⋊Dic83—21no—
91(C2×D83)⋊C4—21no—
92(C2×D83)⋊C4—21no—
93C4×Dic83—21no—
94C4×Dic83—21no—
95C4×Dic83—21no—
96C22×C4×C83—41no—
97C22×C4×C83C2×D411yescharacteristic
98C22×C4×C83#4111yescharacteristic
99C22×C4×C83#4111yescharacteristic
100M16×C83—41no—
101M16×C83—41no—
102C2×C8×C83—21no—
103C2×C8×C83—21no—
104C2×C8×C83—22no—
105C4⋊C4×C83—22no—
106C4⋊C4×C83—41no—
107C42×C83—41no—
108C42×C83—41no—
109C42×C83C22×C411yescharacteristic
110C42×C83C2×D411yescharacteristic
111C42×C83C2×D411yescharacteristic
112C42×C83C2×Q811yescharacteristic
113C23×C83#12311yescharacteristic
114C22×D83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—41no—
118C2×C4×C83—42no—
119C2×C4×C83—81no—
120C2×C4×C83—81no—
121C2×C4×C83C2×C4⋊C411yescharacteristic
122C2×C4×C83C4×D411yescharacteristic
123C2×C4×C83C4×D411yescharacteristic
124C2×C4×C83#12011yescharacteristic
125C2×C4×C83C22⋊Q811yescharacteristic
126C2×C4×C83C22⋊Q811yescharacteristic
127C2×C4×C83#13511yescharacteristic
128C2×C4×C83#13511yescharacteristic
129C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C83#13711yescharacteristic
131C22⋊D83—41no—
132C22⋊D83—41no—
133C2×Dic83—21no—
134C2×Dic83—21no—
135C2×Dic83—21no—
136D332—21no—
137D332—21no—
138C4×D83—41no—
139C4×D83—41no—
140C4×D83—41no—
141C4×D83—41no—
142C4×D83—81no—
143Dic166—21no—
144Dic166—21no—
145C8×C83—41no—
146C8×C83—41no—
147C8×C83—42no—
148C83⋊C8—22no—
149C83⋊C8—41no—
150C83⋊C8—41no—
151C83⋊C8—41no—
152C83⋊C8—81no—
153C22×C83—21no—
154C22×C83—21no—
155C22×C83#38511yescharacteristic
156C22×C83#48211yescharacteristic
157C22×C83#48511yescharacteristic
158C2×D83—41no—
159C2×D83—41no—
160C2×D83—41no—
161C4×C83—21no—
162C4×C83—21no—
163C4×C83—21no—
164C4×C83—82no—
165C4×C83#42711yescharacteristic
166C4×C83#42811yescharacteristic
167C4×C83#44311yescharacteristic
168C4×C83#44411yescharacteristic
169C4×C83#44911yescharacteristic
170C4×C83#45211yescharacteristic
171Dic83—41no—
172Dic83—41no—
173Dic83—41no—
174#8905—831nomaximal, Sylow
175C2×C83—21no—
176C2×C83—21no—
177C2×C83#185411yescharacteristic
178C2×C83#186111yescharacteristic
179C2×C83#186611yescharacteristic
180D83—81no—
181#2925—831no—
182#1806—831no—
183#1571—831no—
184#1566—831no—
185#1476—831no—
186#1303D8311yescharacteristic, complemented
187#1279—831no—
188C83#890511yescharacteristic, complemented, Sylow
189C4×#41—831no—
190#433—1662no—
191#432—1661no—
192#431—1661no—
193#431C2×D8311yescharacteristic
194#423—831no—
195#423C2×D8311yescharacteristic
196C2×C4⋊C8—831no—
197C2×#104—1661no—
198#408—1661no—
199#405—1661no—
200C2×C4×C8—831no—
201C4×C4⋊C4C2×D8311yescharacteristic
202#339—1661no—
203#335—1661no—
204#335—1661no—
205#334—1662no—
206Q8⋊C8—831no—
207Q8⋊C8—831no—
208D4⋊C8—831no—
209D4⋊C8—831no—
210C2×#41—831no—
211C2×M16—21no—
212C2×M16—1661no—
213C22×C8—1661no—
214C22×C8—1661no—
215C4×Q8—831no—
216C4×Q8—831no—
217C4×D4—831no—
218C4×D4—831no—
219C4×D4—1661no—
220C4×D4—1661no—
221#117—831no—
222#117—1661no—
223C2×C4⋊C4—21no—
224C2×C42—21no—
225C2×C42—1661no—
226C2×C42C22×D8311yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—831no—
229C4⋊C8—831no—
230C4⋊C8—1661no—
231C4⋊C8—1661no—
232C4⋊C8—1661no—
233C4⋊C8C4×D8311yescharacteristic
234C4⋊C8C4×D8311yescharacteristic
235C4⋊C8D33212yes—
236#104—3322no—
237C22⋊C8—21no—
238C22⋊C8—1662no—
239C22⋊C8—1662no—
240#97—1662no—
241C4×C8—21no—
242C4×C8—831no—
243C4×C8—831no—
244C4×C8—1662no—
245C4×C8—1661no—
246#95—21no—
247#41—1661no—
248#41—1661no—
249#41—1661no—
250#41—1661no—
251C2×Q8—831no—
252C2×D4—831no—
253C2×D4—1661no—
254C22×C4—41no—
255C22×C4—1661no—
256C22×C4—1661no—
257C22×C4—1661no—
258C22×C4D4×D8311yescharacteristic
259C22×C4#1305058911yescharacteristic
260C22×C4#1305059011yescharacteristic
261M16—41no—
262M16—41no—
263M16—3321no—
264M16—3321no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—3321no—
269C2×C8—3321no—
270C2×C8—3322no—
271C2×C8—3321no—
272C2×C8—1661no—
273C2×C8—1661no—
274C2×C8—1661no—
275C2×C8—1661no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—831no—
279C4⋊C4—831no—
280C4⋊C4—1661no—
281C4⋊C4—1661no—
282C22⋊C4—1661no—
283C22⋊C4—1661no—
284C22⋊C4—1661no—
285C42—41no—
286C42—41no—
287C42—1661no—
288C42—1661no—
289C42—1661no—
290C42C2×C4×D8311yescharacteristic
291C42D4×D8311yescharacteristic
292C42C2×D33211yescharacteristic
293C42Q8×D8311yescharacteristic
294C23—1661no—
295C23#1458177411yescharacteristic
296Q8—1661no—
297Q8—1661no—
298D4—3321no—
299D4—3321no—
300D4—1661no—
301D4—1661no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—3321no—
309C2×C4—3321no—
310C2×C4—3321no—
311C2×C4—3321no—
312C2×C4—6641no—
313C2×C4—1661no—
314C2×C4—1661no—
315C2×C4—1661no—
316C2×C4C4⋊C4×D8311yescharacteristic
317C2×C4(C22⋊D83)⋊C411yescharacteristic
318C2×C4C4×D33211yescharacteristic
319C2×C4#1458176211yescharacteristic
320C2×C4#1458177011yescharacteristic
321C2×C4#1458177211yescharacteristic
322C2×C4#1458181111yescharacteristic
323C2×C4#1458181511yescharacteristic
324C2×C4#1458181911yescharacteristic
325C2×C4#1458182111yescharacteristic
326C8—41no—
327C8—41no—
328C8—42no—
329C8—3321no—
330C8—3321no—
331C8—3321no—
332C8—6641no—
333C8—1662no—
334C22—21no—
335C22—21no—
336C22—3321no—
337C22—3321no—
338C22—3321no—
339C22#1912757511yescharacteristic
340C22#1912802311yescharacteristic
341C22#1912804111yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—82no—
346C4—3321no—
347C4—3321no—
348C4—3321no—
349C4#1912773811yescharacteristic
350C4#1912774011yescharacteristic
351C4#1912781511yescharacteristic
352C4#1912782011yescharacteristic
353C4#1912784911yescharacteristic
354C4#1912786411yescharacteristic
355C2—21no—
356C2—21no—
357C2—6641no—
358C2#2490766511yescharacteristic
359C2#2490770611yescharacteristic
360C2#2490773911yescharacteristic
subgroupG/H
centerC2×C4#14581762
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1303C2
socleC22×C83#385
prime radicalC2×#13050590D4
cosocleC2×C42×C83C23
hypercenter#1303D83
hypocenterC83#8905
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #24906238C2semidirect
4. #24906218C2semidirect
6. #24905304C2semidirect
7. C83×#1303C2semidirect
22. #19127431C4semidirect
23. #19127431C4semidirect
24. #19127428C4semidirect
25. #19127428C4semidirect
186. #1303D83semidirect
188. C83#8905semidirect

Maximal subgroups

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

subgroupindex
#249161312
#249074842
#249062382
#249062182
#249058432
#249053042
C83×#13032
#890583