Finite Group Databasebeta

← #35321485

Subgroups — #35321485

Order 21248.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581738C211yesmaximal, characteristic
2C2×C4×Dic332C211yesmaximal, characteristic
3C2×#19127505C211yesmaximal, characteristic
4C2×#19127504C211yesmaximal, characteristic
5#24905554C211yesmaximal, characteristic
6#24905541C211yesmaximal, characteristic
7C83×#1969C211yesmaximal, characteristic
8C22×Dic332C2211yescharacteristic
9C2×C4×Dic166—21no—
10C2×#14581738—22no—
11C2×#14581738—22no—
12C2×#14581738C414yescomplemented
13C22×C83⋊C16C2211yescharacteristic
14C22×C83⋊C16C2211yescharacteristic
15C4×Dic332—22no—
16C4×Dic332—22no—
17C2×#14581726C2211yescharacteristic
18C2×#14581717—21no—
19#19127505—22no—
20#19127504—22no—
21C22×Q16×C83C2211yescharacteristic
22C2×#107×C83C2211yescharacteristic
23C2×#103×C83—21no—
24C2×C4×C8×C83C2211yescharacteristic
25#391×C83—21no—
26C22×Dic166—21no—
27C2×Dic332—21no—
28C2×Dic332—21no—
29C2×Dic332—21no—
30C2×Dic332C2×C412yes—
31C2×Dic332D412yes—
32C2×Dic332D412yes—
33C4×Dic166—24no—
34C4×Dic166—42no—
35C2×C4⋊Dic83—21no—
36C2×Dic83⋊C4—41no—
37C2×C4×Dic83—41no—
38#14581738—28no—
39C2×C83⋊C16—21no—
40C2×C83⋊C16—21no—
41C2×C83⋊C16—21no—
42C2×C83⋊C16—21no—
43C2×C83⋊C16—21no—
44C2×C83⋊C16C2×C412yes—
45#14581726—21no—
46#14581726D412yes—
47#14581717—24no—
48C22×Q8×C83—21no—
49C2×Q16×C83—21no—
50C2×Q16×C83—21no—
51C2×Q16×C83—21no—
52C2×Q16×C83—21no—
53C2×Q16×C83—21no—
54C2×Q16×C83C2×C412yes—
55C22×C8×C83D411yescharacteristic
56C22×C8×C83C2311yescharacteristic
57C2×C4⋊C4×C83—21no—
58C2×C42×C83D411yescharacteristic
59#107×C83—21no—
60#107×C83—21no—
61#103×C83—42no—
62C4×C8×C83—21no—
63C4×C8×C83—21no—
64#95×C83—41no—
65#95×C83—41no—
66C2×Dic166—22no—
67C2×Dic166—22no—
68C2×Dic166—22no—
69C2×Dic166—41no—
70C2×Dic166—41no—
71C2×Dic166—41no—
72C22×Dic83—41no—
73C22×Dic83—41no—
74Dic332—22no—
75Dic332—22no—
76Dic332—22no—
77Dic332C22⋊C414yes—
78C4⋊Dic83—22no—
79C4⋊Dic83—41no—
80Dic83⋊C4—44no—
81C4×Dic83—44no—
82C83⋊C16—22no—
83C83⋊C16—41no—
84C2×Q8×C83—22no—
85C2×Q8×C83—41no—
86C2×Q8×C83—41no—
87C2×Q8×C83—41no—
88C2×Q8×C83—41no—
89C2×Q8×C83—41no—
90C22×C4×C83—41no—
91C22×C4×C83—41no—
92C22×C4×C83D811yescharacteristic
93C22×C4×C83D811yescharacteristic
94C22×C4×C83C2×D411yescharacteristic
95Q16×C83—22no—
96Q16×C83—22no—
97Q16×C83—41no—
98Q16×C83—41no—
99C2×C8×C83—21no—
100C2×C8×C83—21no—
101C2×C8×C83—21no—
102C2×C8×C83C22×C411yescharacteristic
103C2×C8×C83C2×D411yescharacteristic
104C2×C8×C83C2×D411yescharacteristic
105C2×C8×C83C2×D411yescharacteristic
106C2×C8×C83#4111yescharacteristic
107C2×C8×C83#4111yescharacteristic
108C4⋊C4×C83—41no—
109C4⋊C4×C83—41no—
110C42×C83—21no—
111C42×C83—21no—
112C23×C83C2×D811yescharacteristic
113Q8×C83—42no—
114Q8×C83—42no—
115Q8×C83—81no—
116Q8×C83—81no—
117C2×C4×C83—21no—
118C2×C4×C83—21no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
122C2×C4×C83—42no—
123C2×C4×C83—81no—
124C2×C4×C83—81no—
125C2×C4×C83—81no—
126C2×C4×C83—81no—
127C2×C4×C83—81no—
128C2×C4×C83Q3212yescomplemented
129C2×C4×C83C4×D411yescharacteristic
130C2×C4×C83#12011yescharacteristic
131C2×C4×C83#12111yescharacteristic
132C2×C4×C83#13511yescharacteristic
133C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
135C2×Dic83—42no—
136C2×Dic83—42no—
137C2×Dic83—42no—
138C2×Dic83—42no—
139C2×Dic83—81no—
140C2×Dic83—81no—
141Dic166—24no—
142Dic166—42no—
143Dic166—42no—
144Dic166—42no—
145C8×C83—41no—
146C8×C83C2×C22⋊C411yescharacteristic
147C8×C83C4×D411yescharacteristic
148C8×C83#12111yescharacteristic
149C8×C83#12311yescharacteristic
150C22×C83C4×D811yescharacteristic
151C22×C83#44711yescharacteristic
152C22×C83#45911yescharacteristic
153C22×C83C2×Q3211yescharacteristic
154C22×C83#50811yescharacteristic
155C22×C83#51011yescharacteristic
156C22×C83#51011yescharacteristic
157C4×C83—22no—
158C4×C83—41no—
159C4×C83—82no—
160C4×C83—161no—
161C4×C83#38611yescharacteristic
162C4×C83#44211yescharacteristic
163C4×C83#44911yescharacteristic
164C4×C83#46311yescharacteristic
165Dic83—44no—
166Dic83—82no—
167#13015—831nomaximal, Sylow
168C2×C83#187911yescharacteristic
169C2×C83C4×Q3211yescharacteristic
170C2×C83#217611yescharacteristic
171C2×C83#218811yescharacteristic
172C2×C83#218911yescharacteristic
173C2×C83#220911yescharacteristic
174C2×C83#221111yescharacteristic
175C22×Q32—831no—
176C2×C4×Q16—831no—
177C2×#358—831no—
178C2×#358—831no—
179#1969D8311yescharacteristic
180#1380—831no—
181#1374—831no—
182C83#1301511yescharacteristic, complemented, Sylow
183C22×Q16—831no—
184C22×Q16C2×D8311yescharacteristic
185C2×C4×Q8—1661no—
186C2×Q32—834no—
187C2×Q32—1662no—
188C2×Q32—1662no—
189C22×C16—831no—
190C22×C16—831no—
191C4×Q16—1662no—
192C4×Q16—1662no—
193C2×#107—831no—
194C2×#107C2×D8311yescharacteristic
195C2×#103—21no—
196C2×#103—1661no—
197C2×C4×C8C2×D8311yescharacteristic
198#391—21no—
199#358—1662no—
200#358—1662no—
201C22×Q8—21no—
202C22×Q8—1661no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—832no—
209C2×Q16—832no—
210C2×Q16—832no—
211C2×Q16—1661no—
212C2×Q16—1661no—
213C2×Q16—1661no—
214C2×Q16C4×D8312yes—
215C22×C8C22⋊D8311yescharacteristic
216C22×C8C22×D8311yescharacteristic
217C4×Q8—3322no—
218C4×Q8—1664no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—3321no—
221C2×C4⋊C4—1661no—
222C2×C42—3321no—
223C2×C42C22⋊D8311yescharacteristic
224Q32—1668no—
225C2×C16—832no—
226C2×C16—1661no—
227C2×C16—1661no—
228C2×C16—1661no—
229C2×C16—1661no—
230C2×C16—1661no—
231#107—21no—
232#107—21no—
233#107—832no—
234#107—1661no—
235#103—42no—
236#103—1664no—
237C4×C8—21no—
238C4×C8—21no—
239#95—41no—
240#95—41no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—3321no—
248C2×Q8—3321no—
249C2×Q8—3321no—
250C2×Q8—1662no—
251C2×Q8—1662no—
252C2×Q8—1662no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—3321no—
256C22×C4—3321no—
257C22×C4#1305057511yescharacteristic
258C22×C4#1305057511yescharacteristic
259C22×C4C2×C22⋊D8311yescharacteristic
260Q16—22no—
261Q16—22no—
262Q16—41no—
263Q16—41no—
264Q16—834no—
265Q16—1662no—
266Q16—1662no—
267Q16—1662no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8C2×C4×D8311yescharacteristic
272C2×C8D4×D8311yescharacteristic
273C2×C8D4×D8311yescharacteristic
274C2×C8D4×D8311yescharacteristic
275C2×C8#1305058911yescharacteristic
276C2×C8#1305059011yescharacteristic
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—3324no—
280C4⋊C4—3321no—
281C4⋊C4—1662no—
282C42—21no—
283C42—21no—
284C42—3324no—
285C16—3321no—
286C16—1662no—
287C23C2×#1305057511yescharacteristic
288Q8—42no—
289Q8—42no—
290Q8—81no—
291Q8—81no—
292Q8—3322no—
293Q8—3322no—
294Q8—3322no—
295Q8—1664no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—3322no—
308C2×C4—3322no—
309C2×C4—3322no—
310C2×C4—3322no—
311C2×C4—6641no—
312C2×C4—6641no—
313C2×C4#1458173812yescomplemented
314C2×C4C4×C22⋊D8311yescharacteristic
315C2×C4#1458176011yescharacteristic
316C2×C4#1458176311yescharacteristic
317C2×C4#1458181211yescharacteristic
318C2×C4#1458181711yescharacteristic
319C2×C4#1458181811yescharacteristic
320C8—41no—
321C8C22⋊C4×D8311yescharacteristic
322C8(C22⋊D83)⋊C411yescharacteristic
323C8#1458176511yescharacteristic
324C8#1458177411yescharacteristic
325C22C4×#1305057511yescharacteristic
326C22#1912783411yescharacteristic
327C22#1912789311yescharacteristic
328C22C2×#1458173811yescharacteristic
329C22#1912813111yescharacteristic
330C22#1912814111yescharacteristic
331C22#1912814211yescharacteristic
332C4—22no—
333C4—41no—
334C4—82no—
335C4—161no—
336C4—3324no—
337C4—6642no—
338C4#1912757711yescharacteristic
339C4#1912781111yescharacteristic
340C4#1912784411yescharacteristic
341C4#1912791311yescharacteristic
342C2#2490781411yescharacteristic
343C2C4×#1458173811yescharacteristic
344C2#2490933211yescharacteristic
345C2#2490939611yescharacteristic
346C2#2490940111yescharacteristic
347C2#2490951011yescharacteristic
348C2#2490952211yescharacteristic
subgroupG/H
centerC23C2×#13050575
commutatorC2×C8×C83C22×C4
FrattiniC22×C8C22×D83
FittingC83×#1969C2
socle, prime radicalC23×C83C2×D8
cosocleC22×C8×C83C23
hypercenter#1969D83
hypocenterC83#13015
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1969

Complements

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

NH ≅ G/Ntype
12. C2×#14581738C4semidirect
128. C2×C4×C83Q32semidirect
182. C83#13015semidirect
313. C2×C4#14581738semidirect

Maximal subgroups

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

subgroupindex
C22×#145817382
C2×C4×Dic3322
C2×#191275052
C2×#191275042
#249055542
#249055412
C83×#19692
#1301583