Finite Group Databasebeta

← #35308935

Subgroups — #35308935

Order 21248.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24908425C211yesmaximal, characteristic
2#24908221C211yesmaximal, characteristic
3#24908182C211yesmaximal, characteristic
4C2×#19127451C211yesmaximal, characteristic
5C2×#19127450C211yesmaximal, characteristic
6#24905347C211yesmaximal, characteristic
7C83×#1987C211yesmaximal, characteristic
8C2×#14581725—21no—
9C2×C4⋊(C83⋊C8)—21no—
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×C4⋊(C83⋊C8)C2211yescharacteristic
12C2×C4×C83⋊C8C2211yescharacteristic
13#19127571C2211yescharacteristic
14#19127463—21no—
15#19127463—21no—
16#19127463—21no—
17#19127456—21no—
18#19127451—22no—
19#19127450—22no—
20C2×C4⋊Q8×C83C2211yescharacteristic
21C2×C4⋊C8×C83C2211yescharacteristic
22C4×C4⋊C4×C83C2211yescharacteristic
23#340×C83—21no—
24#340×C83—21no—
25C22×C83⋊C8—21no—
26C22×C83⋊C8—21no—
27C22×C83⋊C8D411yescharacteristic
28C22×C83⋊C8D411yescharacteristic
29C2×C4⋊Dic83—21no—
30C2×C4⋊Dic83—21no—
31C2×C4⋊Dic83—21no—
32#14581725—42no—
33C4⋊(C83⋊C8)—21no—
34C4⋊(C83⋊C8)—21no—
35C4⋊(C83⋊C8)—21no—
36C4⋊(C83⋊C8)—42no—
37C4⋊(C83⋊C8)D412yes—
38C4×C83⋊C8—21no—
39C4×C83⋊C8—21no—
40C22×Q8×C83—21no—
41C22×C8×C83—21no—
42C4⋊Q8×C83—21no—
43C4⋊Q8×C83—21no—
44C4⋊Q8×C83—21no—
45C4⋊Q8×C83Q812yes—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83—21no—
48C2×C4⋊C4×C83D411yescharacteristic
49C2×C4⋊C4×C83D411yescharacteristic
50C2×C42×C83—21no—
51C2×C42×C83C2311yescharacteristic
52C4⋊C8×C83—21no—
53C4⋊C8×C83—21no—
54#95×C83—21no—
55C22×Dic83—41no—
56C2×C83⋊C8—21no—
57C2×C83⋊C8—21no—
58C2×C83⋊C8—22no—
59C2×C83⋊C8—21no—
60C2×C83⋊C8—21no—
61C2×C83⋊C8—21no—
62C2×C83⋊C8—41no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8Q1612yes—
68C4⋊Dic83—41no—
69C4⋊Dic83—41no—
70C4⋊Dic83—41no—
71C4⋊Dic83—41no—
72C4⋊Dic83—81no—
73C2×Q8×C83—22no—
74C2×Q8×C83—41no—
75C2×Q8×C83—81no—
76C2×Q8×C83—81no—
77C22×C4×C83—21no—
78C22×C4×C83—21no—
79C22×C4×C83—41no—
80C22×C4×C83C2×D411yescharacteristic
81C22×C4×C83C2×D411yescharacteristic
82C22×C4×C83#4111yescharacteristic
83C2×C8×C83—41no—
84C2×C8×C83—41no—
85C2×C8×C83—41no—
86C4⋊C4×C83—21no—
87C4⋊C4×C83—22no—
88C4⋊C4×C83—22no—
89C4⋊C4×C83—21no—
90C4⋊C4×C83—21no—
91C4⋊C4×C83—41no—
92C4⋊C4×C83—41no—
93C4⋊C4×C83SD1612yes—
94C42×C83—41no—
95C42×C83—41no—
96C42×C83C2×D411yescharacteristic
97C42×C83C2×Q811yescharacteristic
98C42×C83#4111yescharacteristic
99C42×C83#4111yescharacteristic
100C23×C83#12111yescharacteristic
101Q8×C83—82no—
102Q8×C83—82no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—22no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—42no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—81no—
113C2×C4×C83—81no—
114C2×C4×C83#12111yescharacteristic
115C2×C4×C83#12111yescharacteristic
116C2×C4×C83C22⋊Q811yescharacteristic
117C2×C4×C83C22⋊Q811yescharacteristic
118C2×C4×C83C22⋊Q811yescharacteristic
119C2×C4×C83#12611yescharacteristic
120C2×C4×C83C2×SD1611yescharacteristic
121C2×C4×C83C2×Q1611yescharacteristic
122C2×C4×C83#13511yescharacteristic
123C2×C4×C83#13511yescharacteristic
124C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C83#13711yescharacteristic
126C2×C4×C83#13711yescharacteristic
127C2×C4×C83#13711yescharacteristic
128C2×Dic83—81no—
129C2×Dic83—81no—
130C2×Dic83—81no—
131C8×C83—81no—
132C83⋊C8—22no—
133C83⋊C8—42no—
134C83⋊C8—41no—
135C83⋊C8—81no—
136C22×C83#39611yescharacteristic
137C22×C83#46211yescharacteristic
138C22×C83#46311yescharacteristic
139C22×C83#46511yescharacteristic
140C22×C83#47011yescharacteristic
141C22×C83#47111yescharacteristic
142C22×C83#47211yescharacteristic
143C4×C83—21no—
144C4×C83—21no—
145C4×C83—42no—
146C4×C83—82no—
147C4×C83—81no—
148C4×C83#46111yescharacteristic
149C4×C83#46411yescharacteristic
150C4×C83#46711yescharacteristic
151C4×C83#46811yescharacteristic
152C4×C83#47511yescharacteristic
153C4×C83#47711yescharacteristic
154C4×C83#47911yescharacteristic
155C4×C83#47911yescharacteristic
156Dic83—161no—
157#10589—831nomaximal, Sylow
158C2×C83#167211yescharacteristic
159C2×C83#167711yescharacteristic
160C2×C83#169611yescharacteristic
161C2×C83#170311yescharacteristic
162C2×C83#206311yescharacteristic
163C2×C83#206611yescharacteristic
164C2×C83#206811yescharacteristic
165#1990—831no—
166#1987D8311yescharacteristic
167#1947—831no—
168#1939—831no—
169C2×#334—831no—
170C2×#333—831no—
171#1296—831no—
172C83#1058911yescharacteristic, complemented, Sylow
173C2×C4⋊Q8C2×D8311yescharacteristic
174C2×#107—1661no—
175C2×C4⋊C8—831no—
176C2×C4⋊C8—831no—
177C2×C4⋊C8—1661no—
178C2×C4⋊C8C2×D8311yescharacteristic
179C2×C4×C8—831no—
180#384—831no—
181C4×C4⋊C4C2×D8311yescharacteristic
182#340—21no—
183#340—21no—
184#340—1661no—
185#340—1661no—
186#340—1661no—
187#336—1661no—
188#334—1662no—
189#333—1662no—
190C22×Q8—21no—
191C22×C8—21no—
192C22×C8—831no—
193C22×C8—831no—
194C22×C8—1661no—
195C22×C8—1661no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8Dic16612yes—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—1661no—
203C2×C4⋊C4—1661no—
204C2×C4⋊C4—1661no—
205C2×C4⋊C4C22⋊D8311yescharacteristic
206C2×C4⋊C4C22⋊D8311yescharacteristic
207C2×C42—21no—
208C2×C42C22×D8311yescharacteristic
209#107—3322no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—3322no—
213C4⋊C8—832no—
214C4⋊C8—1661no—
215C4⋊C8—1661no—
216C4⋊C8—1661no—
217C4×C8—1661no—
218C4×C8—1661no—
219#95—21no—
220C2×Q8—22no—
221C2×Q8—41no—
222C2×Q8—81no—
223C2×Q8—81no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—3321no—
228C22×C4D4×D8311yescharacteristic
229C22×C4C2×C22⋊D8311yescharacteristic
230C22×C4#1305058911yescharacteristic
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—3321no—
235C2×C8—3321no—
236C2×C8—3321no—
237C2×C8—3321no—
238C2×C8—3321no—
239C2×C8—832no—
240C2×C8—1662no—
241C2×C8—1661no—
242C2×C8—1661no—
243C2×C8—1661no—
244C2×C8—1661no—
245C2×C8—1661no—
246C4⋊C4—21no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—3321no—
254C4⋊C4—3321no—
255C4⋊C4—3321no—
256C4⋊C4—3321no—
257C4⋊C4—6641no—
258C4⋊C4#1305057712yes—
259C42—41no—
260C42—41no—
261C42D4×D8311yescharacteristic
262C42C2×Dic16611yescharacteristic
263C42#1305058911yescharacteristic
264C42#1305059011yescharacteristic
265C23#1458176411yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—6641no—
280C2×C4—6641no—
281C2×C4—6641no—
282C2×C4#1458176311yescharacteristic
283C2×C4#1458176511yescharacteristic
284C2×C4#1458176911yescharacteristic
285C2×C4#1458176911yescharacteristic
286C2×C4#1458177111yescharacteristic
287C2×C4#1458178511yescharacteristic
288C2×C4C2×#1305057711yescharacteristic
289C2×C4Q16×D8311yescharacteristic
290C2×C4#1458181211yescharacteristic
291C2×C4#1458181311yescharacteristic
292C2×C4#1458181911yescharacteristic
293C2×C4#1458182211yescharacteristic
294C2×C4#1458182311yescharacteristic
295C2×C4#1458182411yescharacteristic
296C8—81no—
297C8—3322no—
298C8—3321no—
299C8—6641no—
300C8—1662no—
301C22#1912762411yescharacteristic
302C22#1912790911yescharacteristic
303C22#1912791811yescharacteristic
304C22#1912793211yescharacteristic
305C22#1912795711yescharacteristic
306C22#1912796211yescharacteristic
307C22#1912796911yescharacteristic
308C4—21no—
309C4—21no—
310C4—42no—
311C4—82no—
312C4—81no—
313C4—13281no—
314C4#1912790311yescharacteristic
315C4#1912792011yescharacteristic
316C4#1912794111yescharacteristic
317C4#1912795011yescharacteristic
318C4#1912798611yescharacteristic
319C4#1912799411yescharacteristic
320C4#1912800611yescharacteristic
321C4#1912800811yescharacteristic
322C2#2490684711yescharacteristic
323C2#2490687411yescharacteristic
324C2#2490698911yescharacteristic
325C2#2490704011yescharacteristic
326C2#2490882311yescharacteristic
327C2#2490884411yescharacteristic
328C2#2490885411yescharacteristic
subgroupG/H
centerC23#14581764
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1987C2
socle, prime radicalC23×C83#121
hypercenter#1987D83
hypocenterC83#10589
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
172. C83#10589semidirect

Maximal subgroups

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

subgroupindex
#249084252
#249082212
#249081822
C2×#191274512
C2×#191274502
#249053472
C83×#19872
#1058983