Finite Group Databasebeta

← #35297455

Subgroups — #35297455

Order 21248.

542 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D332C211yesmaximal, characteristic
2#24907460C212yesmaximal
3C2×#19127454C211yesmaximal, characteristic, complemented
4#24905346C212yesmaximal, complemented
5C83×#1845C211yesmaximal, characteristic, complemented
6C22×C8×D83—21no—
7C2×C4×D332C2211yescharacteristic
8C8×D332—22no—
9C8×D332C414yescomplemented
10C2×C4⋊(C83⋊C8)C2212yes—
11C2×C4⋊(C83⋊C8)C2211yescharacteristic
12C2×#14581712—22no—
13C2×(C2×D83)⋊C8—21no—
14#19127463—22no—
15#19127454—22no—
16C2×#107×C83—21no—
17C2×#107×C83—21no—
18C2×C4×C8×C83C2211yescharacteristic
19#384×C83C2212yes—
20C22×D332D411yescharacteristic
21C22×C4×D83—21no—
22C22×C83⋊C8—21no—
23C22×C83⋊C8—22no—
24C2×C8×D83—24no—
25C2×C8×D83—42no—
26C2×C8×D83—42no—
27C4×D332—21no—
28C4×D332—21no—
29C4×D332C2×C412yes—
30C4×D332Q812yes—
31C2×C4⋊Dic83D411yescharacteristic
32C2×(C2×D83)⋊C4—21no—
33C4⋊(C83⋊C8)—21no—
34C4⋊(C83⋊C8)—22no—
35C4⋊(C83⋊C8)—22no—
36C4⋊(C83⋊C8)C2×C412yes—
37#14581712—44no—
38(C2×D83)⋊C8—24no—
39C22×C8×C83D411yescharacteristic
40C22×C8×C83D411yescharacteristic
41C2×C4⋊C4×C83—22no—
42C2×C4⋊C4×C83—22no—
43C2×C4⋊C4×C83—22no—
44C2×C42×C83C2311yescharacteristic
45#107×C83—42no—
46#107×C83—42no—
47C4×C8×C83C2×C412yes—
48C4×C8×C83D412yes—
49C23×D83—21no—
50C2×D332—21no—
51C2×D332—21no—
52C2×D332—21no—
53C2×D332C4⋊C412yes—
54C2×D332D812yes—
55C2×D332Q1612yes—
56C22×Dic83—21no—
57C2×C4×D83—22no—
58C2×C4×D83—22no—
59C2×C4×D83—41no—
60C2×C4×D83—41no—
61C2×C4×D83—41no—
62C2×C4×D83—41no—
63C2×C83⋊C8—22no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—42no—
67C2×C83⋊C8—42no—
68C2×C83⋊C8—42no—
69C8×D83—48no—
70C4⋊Dic83—21no—
71C4⋊Dic83C4⋊C412yes—
72(C2×D83)⋊C4—22no—
73(C2×D83)⋊C4—22no—
74C22×C4×C83—42no—
75C22×C4×C83C2×D411yescharacteristic
76C22×C4×C83C2×D411yescharacteristic
77C22×C4×C83#4111yescharacteristic
78C2×C8×C83—21no—
79C2×C8×C83—21no—
80C2×C8×C83C22⋊C412yes—
81C2×C8×C83C22⋊C412yes—
82C2×C8×C83D812yes—
83C2×C8×C83SD1612yes—
84C4⋊C4×C83—42no—
85C4⋊C4×C83—42no—
86C4⋊C4×C83—42no—
87C4⋊C4×C83—42no—
88C4⋊C4×C83—82no—
89C42×C83C22×C411yescharacteristic
90C42×C83C2×D411yescharacteristic
91C42×C83C2×Q811yescharacteristic
92C42×C83#4111yescharacteristic
93C23×C83#12111yescharacteristic
94C22×D83—22no—
95C22×D83—22no—
96C22×D83—22no—
97C22×D83—41no—
98C22×D83—41no—
99C22×D83—41no—
100C22×D83—41no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—82no—
104C2×C4×C83—82no—
105C2×C4×C83—82no—
106C2×C4×C83C2×C22⋊C411yescharacteristic
107C2×C4×C83C2×C4⋊C411yescharacteristic
108C2×C4×C83#11711yescharacteristic
109C2×C4×C83#12111yescharacteristic
110C2×C4×C83C22⋊Q811yescharacteristic
111C2×C4×C83C22⋊Q811yescharacteristic
112C2×C4×C83C2×D811yescharacteristic
113C2×C4×C83C2×D811yescharacteristic
114C2×C4×C83C2×SD1611yescharacteristic
115C2×C4×C83C2×Q1611yescharacteristic
116C2×C4×C83#13511yescharacteristic
117C2×C4×C83#13511yescharacteristic
118C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C83#13711yescharacteristic
120C2×Dic83—22no—
121C2×Dic83—41no—
122C2×Dic83—41no—
123D332—22no—
124D332—22no—
125D332—22no—
126D332#10714yescomplemented
127C4×D83—42no—
128C4×D83—42no—
129C4×D83—42no—
130C4×D83—42no—
131C8×C83—22no—
132C8×C83#10214yescomplemented
133C83⋊C8—42no—
134C83⋊C8—82no—
135C22×C83#38011yescharacteristic
136C22×C83#45911yescharacteristic
137C22×C83#46111yescharacteristic
138C22×C83#46611yescharacteristic
139C22×C83#46711yescharacteristic
140C22×C83#47211yescharacteristic
141C22×C83#47311yescharacteristic
142C2×D83—24no—
143C2×D83—42no—
144C2×D83—42no—
145C2×D83—42no—
146C2×D83—42no—
147C2×D83—42no—
148C2×D83—42no—
149C4×C83—21no—
150C4×C83—21no—
151C4×C83—162no—
152C4×C83C2×#10211yescharacteristic
153C4×C83#41711yescharacteristic
154C4×C83C2×#10711yescharacteristic
155C4×C83#42711yescharacteristic
156C4×C83#46611yescharacteristic
157C4×C83#46711yescharacteristic
158C4×C83#47411yescharacteristic
159C4×C83#47611yescharacteristic
160Dic83—42no—
161#8644—831nomaximal, Sylow
162C2×C83#166711yescharacteristic
163C2×C83#166911yescharacteristic
164C2×C83#167311yescharacteristic
165C2×C83#167511yescharacteristic
166C2×C83#180211yescharacteristic
167C2×C83#180811yescharacteristic
168C2×C83#181611yescharacteristic
169D83—44no—
170C2×C8×D4—831no—
171#1845D8311yescharacteristic, complemented
172#1802—832no—
173C2×#335—831no—
174#1296—832no—
175C83#864411yescharacteristic, complemented, Sylow
176C23×C8—1661no—
177C2×C4×D4—831no—
178C8×D4—834no—
179C8×D4—1662no—
180C2×#107—21no—
181C2×#107—21no—
182C2×C4⋊C8—831no—
183C2×C4⋊C8—832no—
184C2×#102—1662no—
185C2×C22⋊C8—1661no—
186C2×C4×C8C2×D8311yescharacteristic
187#384C2×D8312yes—
188#340—1662no—
189#335—1662no—
190C22×D4—831no—
191C23×C4—1661no—
192C22×C8—3322no—
193C22×C8—3322no—
194C22×C8—1662no—
195C22×C8—1661no—
196C22×C8—1664no—
197C22×C8C22⋊D8311yescharacteristic
198C22×C8C22⋊D8311yescharacteristic
199C4×D4—832no—
200C4×D4—832no—
201C4×D4—1661no—
202C4×D4—1661no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—831no—
207C2×C22⋊C4—1661no—
208C2×C42C22×D8311yescharacteristic
209#107—42no—
210#107—42no—
211C4⋊C8—832no—
212C4⋊C8—1662no—
213C4⋊C8—1661no—
214C4⋊C8—1662no—
215#102—3324no—
216C22⋊C8—1664no—
217C4×C8C4×D8312yes—
218C4×C8D33212yes—
219C24—1661no—
220C2×D4—832no—
221C2×D4—832no—
222C2×D4—832no—
223C2×D4—1661no—
224C2×D4—1661no—
225C2×D4—1661no—
226C22×C4—42no—
227C22×C4—3321no—
228C22×C4—3321no—
229C22×C4—3321no—
230C22×C4—3321no—
231C22×C4—1661no—
232C22×C4—1662no—
233C22×C4—1662no—
234C22×C4D4×D8311yescharacteristic
235C22×C4C2×C22⋊D8311yescharacteristic
236C22×C4#1305058911yescharacteristic
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—3321no—
240C2×C8—3321no—
241C2×C8—3328no—
242C2×C8—3322no—
243C2×C8—3322no—
244C2×C8—3322no—
245C2×C8—1662no—
246C2×C8(C2×D83)⋊C412yes—
247C2×C8(C2×D83)⋊C412yes—
248C2×C8#1305057512yes—
249C2×C8#1305057712yes—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—82no—
255C4⋊C4—832no—
256C4⋊C4—1661no—
257C22⋊C4—1662no—
258C22⋊C4—1662no—
259C42C2×C4×D8311yescharacteristic
260C42C2×D33211yescharacteristic
261C42Q8×D8311yescharacteristic
262C42#1305059111yescharacteristic
263C23—3321no—
264C23—3321no—
265C23—3321no—
266C23—3321no—
267C23—1662no—
268C23—1662no—
269C23—1662no—
270C23#1458176311yescharacteristic
271D4—834no—
272D4—1662no—
273D4—1662no—
274D4—1662no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—3321no—
281C2×C4—3321no—
282C2×C4—3322no—
283C2×C4—3322no—
284C2×C4—3322no—
285C2×C4—3322no—
286C2×C4—1662no—
287C2×C4C2×(C2×D83)⋊C411yescharacteristic
288C2×C4C4⋊C4×D8311yescharacteristic
289C2×C4#1458175011yescharacteristic
290C2×C4#1458176711yescharacteristic
291C2×C4#1458176811yescharacteristic
292C2×C4#1458177211yescharacteristic
293C2×C4D8×D8311yescharacteristic
294C2×C4C2×#1305057511yescharacteristic
295C2×C4C2×#1305057711yescharacteristic
296C2×C4Q16×D8311yescharacteristic
297C2×C4#1458181111yescharacteristic
298C2×C4#1458181511yescharacteristic
299C2×C4#1458181811yescharacteristic
300C2×C4#1458182311yescharacteristic
301C8—22no—
302C8—3322no—
303C8—6642no—
304C8#1458171214yescomplemented
305C22—3322no—
306C22—3322no—
307C22—3322no—
308C22—3322no—
309C22—3322no—
310C22—3322no—
311C22—1664no—
312C22#1912755811yescharacteristic
313C22#1912789311yescharacteristic
314C22#1912790311yescharacteristic
315C22#1912793411yescharacteristic
316C22#1912793911yescharacteristic
317C22#1912796811yescharacteristic
318C22#1912797311yescharacteristic
319C4—21no—
320C4—21no—
321C4—162no—
322C4—3322no—
323C4C2×#1458171211yescharacteristic
324C4#1912770011yescharacteristic
325C4#107×D8311yescharacteristic
326C4#1912773811yescharacteristic
327C4#1912793811yescharacteristic
328C4#1912794311yescharacteristic
329C4#1912797811yescharacteristic
330C4#1912798811yescharacteristic
331C2—3324no—
332C2#2490681511yescharacteristic
333C2#2490682511yescharacteristic
334C2#2490684911yescharacteristic
335C2#2490685911yescharacteristic
336C2#2490746011yescharacteristic
337C2#2490748911yescharacteristic
338C2#2490752811yescharacteristic
subgroupG/H
centerC23#14581763
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1845C2
socleC23×C83#121
prime radicalC22×D332D4
cosocleC2×C42×C83C23
hypercenter#1845D83
hypocenterC83#8644
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1845

Complements

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

NH ≅ G/Ntype
3. C2×#19127454C2semidirect
4. #24905346C2semidirect
5. C83×#1845C2semidirect
9. C8×D332C4semidirect
126. D332#107semidirect
132. C8×C83#102semidirect
171. #1845D83semidirect
175. C83#8644semidirect
304. C8#14581712semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D3322
#249074602
C2×#191274542
#249053462
C83×#18452
#864483