Finite Group Databasebeta

← #35302991

Subgroups — #35302991

Order 21248.

384 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24907580C211yesmaximal, characteristic
2C4×C4⋊(C83⋊C8)C211yesmaximal, characteristic
3C2×#19127453C211yesmaximal, characteristic
4C2×#19127451C211yesmaximal, characteristic
5#24905297C211yesmaximal, characteristic
6#24905297C211yesmaximal, characteristic
7C4×C4⋊C8×C83C211yesmaximal, characteristic
8C2×C4⋊(C83⋊C8)C411yescharacteristic
9C2×C4⋊(C83⋊C8)C411yescharacteristic
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×C4⋊(C83⋊C8)C2211yescharacteristic
12C2×C4×C83⋊C8C2211yescharacteristic
13C2×C4×C83⋊C8C2211yescharacteristic
14#19127456—21no—
15#19127456—21no—
16#19127456C411yescharacteristic
17#19127456C411yescharacteristic
18#19127453—22no—
19#19127451—22no—
20C2×C4⋊C8×C83C2211yescharacteristic
21C2×C4⋊C8×C83C2211yescharacteristic
22C2×C4×C8×C83—21no—
23C43×C83C2211yescharacteristic
24#336×C83—21no—
25C22×C83⋊C8—21no—
26C22×C83⋊C8—21no—
27C22×C83⋊C8C2×C411yescharacteristic
28C22×C83⋊C8C2×C411yescharacteristic
29C22×C83⋊C8C2×C411yescharacteristic
30C22×C83⋊C8C2×C411yescharacteristic
31C4⋊(C83⋊C8)—22no—
32C4⋊(C83⋊C8)—21no—
33C4⋊(C83⋊C8)—21no—
34C4⋊(C83⋊C8)—21no—
35C4⋊(C83⋊C8)—21no—
36C4⋊(C83⋊C8)C814yescomplemented
37C4×C83⋊C8—21no—
38C4×C83⋊C8—21no—
39C4×C83⋊C8—21no—
40C4×C83⋊C8—21no—
41C22×C8×C83—21no—
42C22×C8×C83—21no—
43C2×C42×C83C2×C411yescharacteristic
44C2×C42×C83C2×C411yescharacteristic
45C2×C42×C83D411yescharacteristic
46C2×C42×C83D411yescharacteristic
47C2×C42×C83Q811yescharacteristic
48C2×C42×C83Q811yescharacteristic
49C2×C42×C83C2311yescharacteristic
50C4⋊C8×C83—21no—
51C4⋊C8×C83—21no—
52C4⋊C8×C83D412yes—
53C4⋊C8×C83Q812yes—
54C4×C8×C83—42no—
55C2×C83⋊C8—21no—
56C2×C83⋊C8—21no—
57C2×C83⋊C8—21no—
58C2×C83⋊C8—21no—
59C2×C83⋊C8—21no—
60C2×C83⋊C8—21no—
61C2×C83⋊C8—21no—
62C2×C83⋊C8—21no—
63C2×C83⋊C8—21no—
64C2×C83⋊C8—21no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8—41no—
68C2×C83⋊C8—41no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8C2×C812yes—
72C2×C83⋊C8C2×C812yes—
73C22×C4×C83C4⋊C411yescharacteristic
74C22×C4×C83C4⋊C411yescharacteristic
75C22×C4×C83C4⋊C411yescharacteristic
76C22×C4×C83C4⋊C411yescharacteristic
77C22×C4×C83C22×C411yescharacteristic
78C22×C4×C83C2×D411yescharacteristic
79C22×C4×C83C2×Q811yescharacteristic
80C2×C8×C83—22no—
81C2×C8×C83—22no—
82C2×C8×C83—41no—
83C2×C8×C83—41no—
84C2×C8×C83—41no—
85C2×C8×C83—41no—
86C42×C83—22no—
87C42×C83—21no—
88C42×C83—21no—
89C42×C83—21no—
90C42×C83—21no—
91C42×C83—21no—
92C42×C83—21no—
93C42×C83—41no—
94C42×C83C2×C812yes—
95C42×C83M1612yes—
96C42×C83C2×D411yescharacteristic
97C42×C83C2×Q811yescharacteristic
98C42×C83#4111yescharacteristic
99C42×C83#4111yescharacteristic
100C23×C83C2×C4⋊C411yescharacteristic
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83C4⋊C812yes—
113C2×C4×C83C4⋊C812yes—
114C2×C4×C83#10812yes—
115C2×C4×C83C4×D411yescharacteristic
116C2×C4×C83C4×Q811yescharacteristic
117C2×C4×C83#12111yescharacteristic
118C2×C4×C83C22⋊Q811yescharacteristic
119C2×C4×C83#12511yescharacteristic
120C2×C4×C83C4⋊Q811yescharacteristic
121C2×C4×C83C22×C811yescharacteristic
122C2×C4×C83C2×M1611yescharacteristic
123C2×C4×C83#13111yescharacteristic
124C2×C4×C83#13111yescharacteristic
125C2×C4×C83#13511yescharacteristic
126C2×C4×C83#13511yescharacteristic
127C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C83#13711yescharacteristic
129C8×C83—42no—
130C8×C83—42no—
131C83⋊C8—22no—
132C83⋊C8—22no—
133C83⋊C8—41no—
134C83⋊C8—41no—
135C83⋊C8—81no—
136C83⋊C8—81no—
137C22×C83#38911yescharacteristic
138C22×C83C2×C4⋊C811yescharacteristic
139C22×C83#42411yescharacteristic
140C22×C83#42711yescharacteristic
141C22×C83#42811yescharacteristic
142C22×C83C2×#10811yescharacteristic
143C22×C83#43011yescharacteristic
144C4×C83—22no—
145C4×C83—22no—
146C4×C83—22no—
147C4×C83—21no—
148C4×C83—21no—
149C4×C83—41no—
150C4×C83C8×D411yescharacteristic
151C4×C83#43611yescharacteristic
152C4×C83C8×Q811yescharacteristic
153C4×C83#44611yescharacteristic
154C4×C83#46311yescharacteristic
155C4×C83#46411yescharacteristic
156C4×C83#47811yescharacteristic
157C4×C83#47911yescharacteristic
158#9603—831nomaximal, Sylow
159C2×C83#156411yescharacteristic
160C2×C83#156511yescharacteristic
161C2×C83#157211yescharacteristic
162C2×C83#157311yescharacteristic
163C2×C83#193911yescharacteristic
164C2×C83#194911yescharacteristic
165C2×C83#195011yescharacteristic
166#1831—831no—
167C4×C4⋊C8—831no—
168C4×C4⋊C8D8311yescharacteristic
169C2×#335—831no—
170C2×#334—831no—
171#1277—831no—
172#1277—831no—
173C83#960311yescharacteristic, complemented, Sylow
174C2×C4⋊C8—831no—
175C2×C4⋊C8—831no—
176C2×C4⋊C8—831no—
177C2×C4⋊C8—831no—
178C2×C4⋊C8C2×D8311yescharacteristic
179C2×C4⋊C8C2×D8311yescharacteristic
180C2×C4×C8—21no—
181C2×C4×C8—831no—
182C2×C4×C8—831no—
183C43C2×D8311yescharacteristic
184#336—21no—
185#336—831no—
186#336—831no—
187#336—1661no—
188#336—1661no—
189#335—1662no—
190#334—1662no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—831no—
194C22×C8—831no—
195C22×C8—831no—
196C22×C8—831no—
197C22×C8—1661no—
198C22×C8—1661no—
199C2×C42Dic16611yescharacteristic
200C2×C42Dic16611yescharacteristic
201C2×C42C4×D8311yescharacteristic
202C2×C42C4×D8311yescharacteristic
203C2×C42C22⋊D8311yescharacteristic
204C2×C42C22⋊D8311yescharacteristic
205C2×C42C22×D8311yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—834no—
209C4⋊C8—1662no—
210C4⋊C8—1661no—
211C4⋊C8—1661no—
212C4⋊C8—1661no—
213C4⋊C8—1661no—
214C4⋊C8Dic16612yes—
215C4⋊C8D33212yes—
216C4×C8—42no—
217C4×C8—1661no—
218C4×C8—1661no—
219C4×C8—1661no—
220C4×C8—1661no—
221C22×C4Dic83⋊C411yescharacteristic
222C22×C4Dic83⋊C411yescharacteristic
223C22×C4Dic83⋊C411yescharacteristic
224C22×C4Dic83⋊C411yescharacteristic
225C22×C4C2×C4×D8311yescharacteristic
226C22×C4C2×C22⋊D8311yescharacteristic
227C22×C4C2×Dic16611yescharacteristic
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—41no—
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—3321no—
240C2×C8—832no—
241C2×C8—832no—
242C2×C8—1661no—
243C2×C8—1661no—
244C2×C8—1661no—
245C2×C8—1661no—
246C2×C8—1661no—
247C2×C8—1661no—
248C2×C8—1661no—
249C2×C8—1661no—
250C2×C8—1661no—
251C2×C8—1661no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—22no—
259C42—41no—
260C42C8×D8312yes—
261C42#1305057312yes—
262C42C2×D33211yescharacteristic
263C42C2×Dic16611yescharacteristic
264C42#1305059011yescharacteristic
265C42#1305059011yescharacteristic
266C23C2×Dic83⋊C411yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4Dic83⋊C812yes—
279C2×C4Dic83⋊C812yes—
280C2×C4#1458172712yes—
281C2×C4C4×D33211yescharacteristic
282C2×C4C4×Dic16611yescharacteristic
283C2×C4#1458176611yescharacteristic
284C2×C4#1458177111yescharacteristic
285C2×C4#1458178411yescharacteristic
286C2×C4#1458179211yescharacteristic
287C2×C4C2×C8×D8311yescharacteristic
288C2×C4C2×#1305057311yescharacteristic
289C2×C4#1458179811yescharacteristic
290C2×C4#1458179811yescharacteristic
291C2×C4#1458181211yescharacteristic
292C2×C4#1458181211yescharacteristic
293C2×C4#1458181811yescharacteristic
294C2×C4#1458182311yescharacteristic
295C8—42no—
296C8—42no—
297C8—3321no—
298C8—3321no—
299C8—6641no—
300C8—6641no—
301C8—1662no—
302C8—1662no—
303C22#1912759911yescharacteristic
304C22C2×Dic83⋊C811yescharacteristic
305C22#1912772711yescharacteristic
306C22#1912773711yescharacteristic
307C22#1912774111yescharacteristic
308C22C2×#1458172711yescharacteristic
309C22#1912774911yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4C8×D33211yescharacteristic
317C4#1912778011yescharacteristic
318C4C8×Dic16611yescharacteristic
319C4#1912783111yescharacteristic
320C4#1912791611yescharacteristic
321C4#1912792311yescharacteristic
322C4#1912800111yescharacteristic
323C4#1912800811yescharacteristic
324C2#2490620911yescharacteristic
325C2#2490621311yescharacteristic
326C2#2490624111yescharacteristic
327C2#2490624611yescharacteristic
328C2#2490818111yescharacteristic
329C2#2490823111yescharacteristic
330C2#2490823811yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D83
commutatorC2×C4×C83C22×C8
FrattiniC2×C42C22×D83
FittingC4×C4⋊C8×C83C2
socle, prime radicalC23×C83C2×C4⋊C4
cosocleC2×C42×C83C23
hypercenterC4×C4⋊C8D83
hypocenterC83#9603
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
36. C4⋊(C83⋊C8)C8semidirect
173. C83#9603semidirect

Maximal subgroups

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

subgroupindex
#249075802
C4×C4⋊(C83⋊C8)2
C2×#191274532
C2×#191274512
#249052972
C4×C4⋊C8×C832
#960383