Finite Group Databasebeta

← #35308987

Subgroups — #35308987

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#24908412C211yesmaximal, characteristic
3#24908227C211yesmaximal, characteristic
4#24908179C211yesmaximal, characteristic
5C2×#19127451C211yesmaximal, characteristic
6#24905347C211yesmaximal, characteristic
7C2×#333×C83C211yesmaximal, characteristic
8C2×#14581724—21no—
9C2×C4⋊(C83⋊C8)C2211yescharacteristic
10C2×Dic83⋊C8—21no—
11C2×C4×C83⋊C8C2211yescharacteristic
12#19127571C2211yescharacteristic
13C4×C4⋊Dic83C2211yescharacteristic
14#19127464—21no—
15#19127463—21no—
16#19127463—21no—
17#19127463—21no—
18#19127463—21no—
19#19127455—21no—
20#19127451—22no—
21C2×C4⋊Q8×C83C2211yescharacteristic
22C2×C4⋊C8×C83C2211yescharacteristic
23C2×C4⋊C8×C83C2211yescharacteristic
24#333×C83—22no—
25C22×C83⋊C8—21no—
26C22×C83⋊C8D411yescharacteristic
27C22×C83⋊C8D411yescharacteristic
28C2×C4⋊Dic83—21no—
29C2×C4⋊Dic83—21no—
30C2×C4⋊Dic83—21no—
31C2×C4⋊Dic83D411yescharacteristic
32C2×C4⋊Dic83D411yescharacteristic
33C2×C4×Dic83—21no—
34#14581724—42no—
35C4⋊(C83⋊C8)—21no—
36C4⋊(C83⋊C8)—21no—
37Dic83⋊C8—42no—
38C4×C83⋊C8—21no—
39C4×C83⋊C8—21no—
40C83⋊#95—21no—
41C22×Q8×C83—21no—
42C22×C8×C83—21no—
43C22×C8×C83—21no—
44C4⋊Q8×C83—21no—
45C4⋊Q8×C83—21no—
46C4⋊Q8×C83—21no—
47C4⋊Q8×C83Q812yes—
48C2×C4⋊C4×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C42×C83C2311yescharacteristic
51C4⋊C8×C83—21no—
52C4⋊C8×C83—21no—
53C4⋊C8×C83—21no—
54C4⋊C8×C83D412yes—
55C22×Dic83—21no—
56C22×Dic83—21no—
57C22×Dic83—41no—
58C2×C83⋊C8—21no—
59C2×C83⋊C8—21no—
60C2×C83⋊C8—21no—
61C2×C83⋊C8—21no—
62C2×C83⋊C8—21no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8SD1612yes—
67C4⋊Dic83—21no—
68C4⋊Dic83—21no—
69C4⋊Dic83—21no—
70C4⋊Dic83—41no—
71C4⋊Dic83—41no—
72C4⋊Dic83—41no—
73C4⋊Dic83—41no—
74C4⋊Dic83—81no—
75C4⋊Dic83SD1612yes—
76C4×Dic83—41no—
77C4×Dic83—41no—
78C2×Q8×C83—22no—
79C2×Q8×C83—41no—
80C2×Q8×C83—81no—
81C2×Q8×C83—81no—
82C22×C4×C83—41no—
83C22×C4×C83C2×D411yescharacteristic
84C22×C4×C83C2×D411yescharacteristic
85C22×C4×C83#4111yescharacteristic
86C2×C8×C83—22no—
87C2×C8×C83—41no—
88C2×C8×C83—41no—
89C2×C8×C83—41no—
90C2×C8×C83—41no—
91C2×C8×C83—41no—
92C4⋊C4×C83—22no—
93C4⋊C4×C83—22no—
94C4⋊C4×C83—41no—
95C4⋊C4×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—42no—
106C2×C4×C83—81no—
107C2×C4×C83—81no—
108C2×C4×C83#12111yescharacteristic
109C2×C4×C83#12111yescharacteristic
110C2×C4×C83C22⋊Q811yescharacteristic
111C2×C4×C83C22⋊Q811yescharacteristic
112C2×C4×C83C22⋊Q811yescharacteristic
113C2×C4×C83#12611yescharacteristic
114C2×C4×C83C2×SD1611yescharacteristic
115C2×C4×C83C2×SD1611yescharacteristic
116C2×C4×C83#13511yescharacteristic
117C2×C4×C83#13511yescharacteristic
118C2×C4×C83#13711yescharacteristic
119C2×C4×C83#13711yescharacteristic
120C2×C4×C83#13711yescharacteristic
121C2×C4×C83#13711yescharacteristic
122C2×Dic83—22no—
123C2×Dic83—41no—
124C2×Dic83—41no—
125C2×Dic83—41no—
126C2×Dic83—41no—
127C2×Dic83—41no—
128C2×Dic83—81no—
129C2×Dic83—81no—
130C2×Dic83—81no—
131C8×C83—42no—
132C8×C83—81no—
133C83⋊C8—22no—
134C83⋊C8—41no—
135C83⋊C8—81no—
136C22×C83#39611yescharacteristic
137C22×C83#46111yescharacteristic
138C22×C83#46411yescharacteristic
139C22×C83#46511yescharacteristic
140C22×C83#47011yescharacteristic
141C22×C83#47111yescharacteristic
142C22×C83#47211yescharacteristic
143C4×C83—21no—
144C4×C83—21no—
145C4×C83—82no—
146C4×C83#46111yescharacteristic
147C4×C83#46411yescharacteristic
148C4×C83#46511yescharacteristic
149C4×C83#47011yescharacteristic
150C4×C83#47511yescharacteristic
151C4×C83#47511yescharacteristic
152C4×C83#47911yescharacteristic
153C4×C83#47911yescharacteristic
154Dic83—42no—
155Dic83—81no—
156Dic83—161no—
157#10597—831nomaximal, Sylow
158C2×C83#167111yescharacteristic
159C2×C83#167811yescharacteristic
160C2×C83#169511yescharacteristic
161C2×C83#170411yescharacteristic
162C2×C83#206311yescharacteristic
163C2×C83#206611yescharacteristic
164C2×C83#206611yescharacteristic
165#1990—831no—
166#1987—831no—
167#1948—831no—
168#1939—831no—
169C2×#334—831no—
170C2×#333D8311yescharacteristic
171#1296—831no—
172C83#1059711yescharacteristic, complemented, Sylow
173C2×C4⋊Q8C2×D8311yescharacteristic
174C2×#106—1661no—
175C2×C4⋊C8—831no—
176C2×C4⋊C8—1661no—
177C2×C4⋊C8C2×D8311yescharacteristic
178C2×C4⋊C8C2×D8311yescharacteristic
179C2×C4×C8—831no—
180#384—831no—
181C4×C4⋊C4—831no—
182#340—1661no—
183#340—1661no—
184#340—1661no—
185#340—1661no—
186#340—1661no—
187#336—1661no—
188#334—1662no—
189#333—22no—
190C22×Q8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—831no—
194C22×C8—831no—
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—831no—
203C2×C4⋊C4—831no—
204C2×C4⋊C4—1661no—
205C2×C4⋊C4—1661no—
206C2×C4⋊C4—1661no—
207C2×C42—1661no—
208C2×C42C22×D8311yescharacteristic
209#106—3322no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—3322no—
214C4⋊C8—1661no—
215C4⋊C8—1661no—
216C4⋊C8C22⋊D8312yes—
217C4×C8—1661no—
218C4×C8—1661no—
219#95—1661no—
220C2×Q8—22no—
221C2×Q8—41no—
222C2×Q8—81no—
223C2×Q8—81no—
224C22×C4—41no—
225C22×C4—3321no—
226C22×C4—1661no—
227C22×C4—1661no—
228C22×C4D4×D8311yescharacteristic
229C22×C4D4×D8311yescharacteristic
230C22×C4#1305059011yescharacteristic
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—3321no—
238C2×C8—3321no—
239C2×C8—3321no—
240C2×C8—832no—
241C2×C8—1661no—
242C2×C8—1661no—
243C2×C8—1661no—
244C2×C8—1661no—
245C2×C8—1661no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—3321no—
251C4⋊C4—3321no—
252C4⋊C4—3321no—
253C4⋊C4—3321no—
254C4⋊C4—832no—
255C4⋊C4—6641no—
256C4⋊C4—1661no—
257C4⋊C4—1661no—
258C4⋊C4—1661no—
259C42—3321no—
260C42—3321no—
261C42C2×C22⋊D8311yescharacteristic
262C42C2×Dic16611yescharacteristic
263C42#1305058911yescharacteristic
264C42#1305058911yescharacteristic
265C23#1458176511yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—3321no—
274C2×C4—3321no—
275C2×C4—3321no—
276C2×C4—3321no—
277C2×C4—3321no—
278C2×C4—6641no—
279C2×C4—6641no—
280C2×C4—6641no—
281C2×C4—1662no—
282C2×C4#1458176311yescharacteristic
283C2×C4#1458176411yescharacteristic
284C2×C4#1458176911yescharacteristic
285C2×C4#1458176911yescharacteristic
286C2×C4#1458177111yescharacteristic
287C2×C4#1458178511yescharacteristic
288C2×C4SD16×D8311yescharacteristic
289C2×C4SD16×D8311yescharacteristic
290C2×C4#1458181311yescharacteristic
291C2×C4#1458181511yescharacteristic
292C2×C4#1458182111yescharacteristic
293C2×C4#1458182411yescharacteristic
294C2×C4#1458182411yescharacteristic
295C2×C4#1458182411yescharacteristic
296C8—42no—
297C8—81no—
298C8—3321no—
299C8—6641no—
300C8—1662no—
301C22#1912762411yescharacteristic
302C22#1912790511yescharacteristic
303C22#1912792611yescharacteristic
304C22#1912793311yescharacteristic
305C22#1912795811yescharacteristic
306C22#1912796311yescharacteristic
307C22#1912797011yescharacteristic
308C4—21no—
309C4—21no—
310C4—82no—
311C4—13281no—
312C4—3322no—
313C4—6641no—
314C4#1912790411yescharacteristic
315C4#1912792511yescharacteristic
316C4#1912792711yescharacteristic
317C4#1912795611yescharacteristic
318C4#1912798411yescharacteristic
319C4#1912798411yescharacteristic
320C4#1912800611yescharacteristic
321C4#1912801011yescharacteristic
322C2#2490684111yescharacteristic
323C2#2490688211yescharacteristic
324C2#2490698511yescharacteristic
325C2#2490704811yescharacteristic
326C2#2490881911yescharacteristic
327C2#2490884011yescharacteristic
328C2#2490884211yescharacteristic
subgroupG/H
centerC23#14581765
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC2×#333×C83C2
socle, prime radicalC23×C83#121
hypercenterC2×#333D83
hypocenterC83#10597
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
172. C83#10597semidirect

Maximal subgroups

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

subgroupindex
#249084252
#249084122
#249082272
#249081792
C2×#191274512
#249053472
C2×#333×C832
#1059783