Finite Group Databasebeta

← #35322773

Subgroups — #35322773

Order 21248.

510 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581733C211yesmaximal, characteristic
2C2×#19127526C211yesmaximal, characteristic, complemented
3C2×#19127502C211yesmaximal, characteristic, complemented
4C2×#19127501C211yesmaximal, characteristic, complemented
5C2×C4×C83⋊C16C211yesmaximal, characteristic, complemented
6#24908329C211yesmaximal, characteristic, complemented
7C83×#1970C211yesmaximal, characteristic, complemented
8C22×D664C2211yescharacteristic
9C2×#14581733—22no—
10C2×#14581733—22no—
11C2×#14581733C414yescomplemented
12C22×C83⋊C16C2211yescharacteristic
13C22×C83⋊C16C2211yescharacteristic
14C2×#14581726C2211yescharacteristic
15C2×#14581714—21no—
16#19127603—21no—
17#19127526—22no—
18#19127502—22no—
19#19127501—22no—
20C4×C83⋊C16—22no—
21C22×D8×C83C2211yescharacteristic
22C2×#107×C83C2211yescharacteristic
23C2×#102×C83—21no—
24C2×C4×C8×C83C2211yescharacteristic
25#390×C83—21no—
26C22×D332—21no—
27C2×D664—21no—
28C2×D664—21no—
29C2×D664—21no—
30C2×D664—21no—
31C2×D664—21no—
32C2×D664C2×C412yes—
33C2×C4⋊Dic83—21no—
34C2×(C2×D83)⋊C4—42no—
35#14581733—28no—
36C2×C83⋊C16—21no—
37C2×C83⋊C16—21no—
38C2×C83⋊C16C2×C412yes—
39C2×C83⋊C16D412yes—
40C2×C83⋊C16D412yes—
41C2×C83⋊C16D412yes—
42#14581726—21no—
43#14581726—21no—
44#14581714—42no—
45C22×D4×C83—21no—
46C2×D8×C83—21no—
47C2×D8×C83—21no—
48C2×D8×C83—21no—
49C2×D8×C83—21no—
50C2×D8×C83—21no—
51C2×D8×C83C2×C412yes—
52C22×C8×C83D411yescharacteristic
53C22×C8×C83C2311yescharacteristic
54C2×C4⋊C4×C83—21no—
55C2×C22⋊C4×C83—42no—
56C2×C42×C83D411yescharacteristic
57#107×C83—21no—
58#107×C83—21no—
59#102×C83—42no—
60C4×C8×C83—21no—
61C4×C8×C83—21no—
62C23×D83—41no—
63C2×D332—22no—
64C2×D332—41no—
65C2×D332—41no—
66C2×D332—41no—
67C2×D332—41no—
68C2×D332—41no—
69C22×Dic83—41no—
70D664—22no—
71D664—22no—
72D664—41no—
73D664—41no—
74C4⋊Dic83—41no—
75C4⋊Dic83—41no—
76(C2×D83)⋊C4—84no—
77C83⋊C16—22no—
78C83⋊C16C22⋊C414yescomplemented
79C24×C83—41no—
80C2×D4×C83—22no—
81C2×D4×C83—41no—
82C2×D4×C83—41no—
83C2×D4×C83—41no—
84C2×D4×C83—41no—
85C2×D4×C83—41no—
86C22×C4×C83—41no—
87C22×C4×C83D812yes—
88C22×C4×C83C2×D411yescharacteristic
89D8×C83—22no—
90D8×C83—22no—
91D8×C83—41no—
92D8×C83—41no—
93C2×C8×C83—21no—
94C2×C8×C83—21no—
95C2×C8×C83D812yes—
96C2×C8×C83C22×C411yescharacteristic
97C2×C8×C83C2×D411yescharacteristic
98C2×C8×C83C2×D411yescharacteristic
99C2×C8×C83C2×D411yescharacteristic
100C2×C8×C83#4111yescharacteristic
101C2×C8×C83#4111yescharacteristic
102C4⋊C4×C83—41no—
103C4⋊C4×C83—41no—
104C22⋊C4×C83—84no—
105C42×C83—21no—
106C42×C83—21no—
107C23×C83—42no—
108C23×C83—81no—
109C23×C83—81no—
110C23×C83—82no—
111C23×C83—82no—
112C23×C83C2×D811yescharacteristic
113C22×D83—42no—
114C22×D83—81no—
115C22×D83—81no—
116C22×D83—82no—
117C22×D83—82no—
118D4×C83—42no—
119D4×C83—42no—
120D4×C83—81no—
121D4×C83—81no—
122C2×C4×C83—22no—
123C2×C4×C83—22no—
124C2×C4×C83—81no—
125C2×C4×C83—82no—
126C2×C4×C83D1614yescomplemented
127C2×C4×C83C4×D411yescharacteristic
128C2×C4×C83#12111yescharacteristic
129C2×C4×C83#12711yescharacteristic
130C2×C4×C83C2×D811yescharacteristic
131C2×C4×C83#13511yescharacteristic
132C2×C4×C83#13511yescharacteristic
133C2×Dic83—81no—
134C2×Dic83—82no—
135D332—42no—
136D332—42no—
137D332—81no—
138D332—81no—
139C8×C83—22no—
140C8×C83C2×C22⋊C411yescharacteristic
141C8×C83C4×D411yescharacteristic
142C8×C83#12111yescharacteristic
143C8×C83#12411yescharacteristic
144C22×C83—84no—
145C22×C83—82no—
146C22×C83—162no—
147C22×C83—161no—
148C22×C83—161no—
149C22×C83C4×D811yescharacteristic
150C22×C83#46611yescharacteristic
151C22×C83#49311yescharacteristic
152C22×C83C2×D1612yes—
153C22×C83#50812yes—
154C2×D83—84no—
155C2×D83—82no—
156C2×D83—162no—
157C2×D83—161no—
158C2×D83—161no—
159C4×C83—24no—
160C4×C83—161no—
161C4×C83#39011yescharacteristic
162C4×C83C4×D811yescharacteristic
163C4×C83#46611yescharacteristic
164C4×C83#49511yescharacteristic
165Dic83—161no—
166#13235—831nomaximal, Sylow
167C2×C83—162no—
168C2×C83#197011yescharacteristic
169C2×C83C4×D1612yes—
170C2×C83#221512yes—
171C2×C83#224611yescharacteristic
172C2×C83#224911yescharacteristic
173D83—162no—
174C22×D16—831no—
175C2×#366—831no—
176C2×#357—831no—
177C2×#357—831no—
178C2×C4×C16—831no—
179#1970—831no—
180#1970D8311yescharacteristic, complemented
181C83#1323511yescharacteristic, complemented, Sylow
182C22×D8—831no—
183C22×D8C2×D8311yescharacteristic
184C2×D16—834no—
185C2×D16—1662no—
186C2×D16—1662no—
187C22×C16—831no—
188C22×C16—831no—
189C2×#107—831no—
190C2×#107C2×D8311yescharacteristic
191C2×#102—21no—
192C2×#102—1661no—
193C2×C4×C8C2×D8311yescharacteristic
194#390—21no—
195#390—1661no—
196#366—1662no—
197#357—1662no—
198#357—1662no—
199C4×C16—1662no—
200C22×D4—21no—
201C22×D4—1661no—
202C2×D8—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8—21no—
206C2×D8—21no—
207C2×D8—832no—
208C2×D8—1661no—
209C2×D8—1661no—
210C2×D8—1661no—
211C2×D8—1661no—
212C2×D8—1661no—
213C2×D8C4×D8312yes—
214C22×C8C22⋊D8311yescharacteristic
215C22×C8C22×D8311yescharacteristic
216C2×C4⋊C4—21no—
217C2×C4⋊C4—1661no—
218C2×C22⋊C4—42no—
219C2×C22⋊C4—3322no—
220C2×C42C22⋊D8311yescharacteristic
221D16—1668no—
222C2×C16—832no—
223C2×C16—832no—
224C2×C16—832no—
225C2×C16—832no—
226C2×C16—1661no—
227C2×C16—1661no—
228#107—21no—
229#107—21no—
230#107—1661no—
231#107—1661no—
232#102—42no—
233#102—3322no—
234C4×C8—21no—
235C4×C8—21no—
236C24—41no—
237C24—3321no—
238C2×D4—22no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—3321no—
245C2×D4—3321no—
246C2×D4—3321no—
247C2×D4—3321no—
248C2×D4—3321no—
249C2×D4—1662no—
250C22×C4—41no—
251C22×C4—3321no—
252C22×C4#1305057512yes—
253C22×C4C2×C22⋊D8311yescharacteristic
254D8—22no—
255D8—22no—
256D8—41no—
257D8—41no—
258D8—3321no—
259D8—3321no—
260D8—1662no—
261D8—1662no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8#1305057512yes—
265C2×C8C2×C4×D8311yescharacteristic
266C2×C8D4×D8311yescharacteristic
267C2×C8D4×D8311yescharacteristic
268C2×C8D4×D8311yescharacteristic
269C2×C8#1305058911yescharacteristic
270C2×C8#1305059011yescharacteristic
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—3321no—
274C4⋊C4—3321no—
275C22⋊C4—84no—
276C22⋊C4—6644no—
277C42—21no—
278C42—21no—
279C16—834no—
280C16—1662no—
281C23—42no—
282C23—81no—
283C23—82no—
284C23—82no—
285C23—81no—
286C23—3322no—
287C23—6641no—
288C23—6642no—
289C23—6642no—
290C23—6641no—
291C23C2×#1305057511yescharacteristic
292D4—42no—
293D4—42no—
294D4—81no—
295D4—81no—
296D4—3322no—
297D4—3322no—
298D4—6641no—
299D4—6641no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—81no—
303C2×C4—82no—
304C2×C4—6641no—
305C2×C4—6642no—
306C2×C4#1458173314yescomplemented
307C2×C4C4×C22⋊D8311yescharacteristic
308C2×C4#1458176411yescharacteristic
309C2×C4#1458178811yescharacteristic
310C2×C4C2×#1305057511yescharacteristic
311C2×C4#1458181211yescharacteristic
312C2×C4#1458181211yescharacteristic
313C8—22no—
314C8C22⋊C4×D8311yescharacteristic
315C8(C22⋊D83)⋊C411yescharacteristic
316C8#1458176511yescharacteristic
317C8#1458177811yescharacteristic
318C22—82no—
319C22—84no—
320C22—161no—
321C22—161no—
322C22—162no—
323C22—13281no—
324C22—13281no—
325C22—13282no—
326C22—6642no—
327C22—6644no—
328C22C4×#1305057511yescharacteristic
329C22#1912793511yescharacteristic
330C22#1912807711yescharacteristic
331C22C2×#1458173312yes—
332C22#1912813112yes—
333C4—24no—
334C4—161no—
335C4—13281no—
336C4#1912760111yescharacteristic
337C4C4×#1305057511yescharacteristic
338C4#1912793511yescharacteristic
339C4#1912808311yescharacteristic
340C2—162no—
341C2—13282no—
342C2#2490832811yescharacteristic
343C2C4×#1458173312yes—
344C2#2490954712yes—
345C2#2490971211yescharacteristic
346C2#2490972211yescharacteristic
subgroupG/H
centerC23C2×#13050575
commutatorC2×C8×C83C22×C4
FrattiniC22×C8C22×D83
FittingC83×#1970C2
socleC23×C83C2×D8
prime radicalC22×#14581733C2
cosocleC22×C8×C83C23
hypercenter#1970D83
hypocenterC83#13235
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×#19127526C2semidirect
3. C2×#19127502C2semidirect
4. C2×#19127501C2semidirect
5. C2×C4×C83⋊C16C2semidirect
6. #24908329C2semidirect
7. C83×#1970C2semidirect
11. C2×#14581733C4semidirect
78. C83⋊C16C22⋊C4semidirect
126. C2×C4×C83D16semidirect
180. #1970D83semidirect
181. C83#13235semidirect
306. C2×C4#14581733semidirect

Maximal subgroups

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

subgroupindex
C22×#145817332
C2×#191275262
C2×#191275022
C2×#191275012
C2×C4×C83⋊C162
#249083292
C83×#19702
#1323583