Finite Group Databasebeta

← #35322333

Subgroups — #35322333

Order 21248.

386 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127501C211yesmaximal, characteristic
2C2×#19127501C211yesmaximal, characteristic
3C2×#19127477C211yesmaximal, characteristic, complemented
4#24908329C211yesmaximal, characteristic
5#24905554C211yesmaximal, characteristic, complemented
6#24905554C211yesmaximal, characteristic, complemented
7C83×#1942C211yesmaximal, characteristic, complemented
8C22×D664C2211yescharacteristic
9C22×C83⋊C16C2211yescharacteristic
10C22×C83⋊C16C2211yescharacteristic
11C2×#14581726C2211yescharacteristic
12C2×#14581714—21no—
13#19127603—21no—
14#19127501—22no—
15#19127501C414yescomplemented
16#19127477—22no—
17C2×#107×C83C2211yescharacteristic
18C2×#107×C83C2211yescharacteristic
19C2×C4×C8×C83C2211yescharacteristic
20#389×C83—21no—
21#340×C83—21no—
22C22×D332—21no—
23C2×D664—21no—
24C2×D664—21no—
25C2×D664—21no—
26C2×D664—21no—
27C2×D664—21no—
28C2×D664C2×C412yes—
29C2×C4⋊Dic83—21no—
30C2×(C2×D83)⋊C4—41no—
31C2×(C2×D83)⋊C4—41no—
32C2×C83⋊C16—21no—
33C2×C83⋊C16—21no—
34C2×C83⋊C16—21no—
35C2×C83⋊C16—21no—
36C2×C83⋊C16C2×C412yes—
37C2×C83⋊C16D412yes—
38#14581726—21no—
39#14581726—21no—
40#14581714—42no—
41C22×C8×C83D411yescharacteristic
42C22×C8×C83C2311yescharacteristic
43C2×C4⋊C4×C83—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—41no—
46C2×C42×C83D411yescharacteristic
47#107×C83—21no—
48#107×C83—21no—
49#107×C83—21no—
50#107×C83C2×C412yes—
51C4×C8×C83—21no—
52C4×C8×C83—21no—
53#95×C83—41no—
54C23×D83—41no—
55C2×D332—22no—
56C2×D332—41no—
57C2×D332—41no—
58C2×D332—41no—
59C2×D332—41no—
60C2×D332—41no—
61C22×Dic83—41no—
62D664—22no—
63D664—22no—
64D664—41no—
65D664—41no—
66C4⋊Dic83—41no—
67C4⋊Dic83—41no—
68(C2×D83)⋊C4—82no—
69(C2×D83)⋊C4—82no—
70C83⋊C16—22no—
71C83⋊C16—22no—
72C22×C4×C83—41no—
73C22×C4×C83—41no—
74C22×C4×C83D811yescharacteristic
75C22×C4×C83D811yescharacteristic
76C22×C4×C83C2×D411yescharacteristic
77C2×C8×C83—21no—
78C2×C8×C83—21no—
79C2×C8×C83SD1612yes—
80C2×C8×C83C22×C411yescharacteristic
81C2×C8×C83C2×D411yescharacteristic
82C2×C8×C83#4111yescharacteristic
83C2×C8×C83#4111yescharacteristic
84C2×C8×C83#4111yescharacteristic
85C2×C8×C83#4111yescharacteristic
86C4⋊C4×C83—22no—
87C4⋊C4×C83—41no—
88C4⋊C4×C83—41no—
89C4⋊C4×C83—41no—
90C4⋊C4×C83—82no—
91C42×C83—21no—
92C42×C83—21no—
93C23×C83C2×D811yescharacteristic
94C22×D83—42no—
95C22×D83—81no—
96C22×D83—81no—
97C22×D83—81no—
98C22×D83—81no—
99C22×D83—81no—
100C22×D83—81no—
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—42no—
108C2×C4×C83—81no—
109C2×C4×C83—81no—
110C2×C4×C83—81no—
111C2×C4×C83—81no—
112C2×C4×C83—81no—
113C2×C4×C83C4×D411yescharacteristic
114C2×C4×C83#12111yescharacteristic
115C2×C4×C83#12411yescharacteristic
116C2×C4×C83C2×SD1611yescharacteristic
117C2×C4×C83#13511yescharacteristic
118C2×C4×C83#13511yescharacteristic
119C2×Dic83—81no—
120C2×Dic83—81no—
121C2×Dic83—81no—
122D332—42no—
123D332—42no—
124D332—81no—
125D332—81no—
126C8×C83—22no—
127C8×C83#11711yescharacteristic
128C8×C83C4×D411yescharacteristic
129C8×C83#12311yescharacteristic
130C8×C83#12611yescharacteristic
131C22×C83C4×D811yescharacteristic
132C22×C83#46611yescharacteristic
133C22×C83#48611yescharacteristic
134C22×C83#50911yescharacteristic
135C22×C83#50911yescharacteristic
136C22×C83#50911yescharacteristic
137C22×C83#51011yescharacteristic
138C2×D83—82no—
139C2×D83—82no—
140C2×D83—82no—
141C2×D83—161no—
142C2×D83—161no—
143C2×D83—161no—
144C2×D83—161no—
145C4×C83—41no—
146C4×C83—41no—
147C4×C83—82no—
148C4×C83—161no—
149C4×C83#38811yescharacteristic
150C4×C83C4×SD1611yescharacteristic
151C4×C83#46511yescharacteristic
152C4×C83#48811yescharacteristic
153Dic83—161no—
154#13149—831nomaximal, Sylow
155C2×C83#193411yescharacteristic
156C2×C83#217511yescharacteristic
157C2×C83#217711yescharacteristic
158C2×C83#221811yescharacteristic
159C2×C83#222011yescharacteristic
160C2×C83#224311yescharacteristic
161C2×C83#224411yescharacteristic
162D83—162no—
163C2×#357—831no—
164C2×#357—831no—
165C2×#346—831no—
166#1970—831no—
167#1942D8311yescharacteristic, complemented
168#1380—831no—
169#1380—831no—
170C83#1314911yescharacteristic, complemented, Sylow
171C22×D8—831no—
172C22×C16—831no—
173C22×C16—831no—
174C2×#107—831no—
175C2×#107C2×D8311yescharacteristic
176C2×#107C2×D8311yescharacteristic
177C2×#102—1661no—
178C2×C4×C8C2×D8311yescharacteristic
179#390—1661no—
180#389—21no—
181#357—834no—
182#357—1662no—
183#346—1662no—
184#340—21no—
185C22×D4—1661no—
186C2×D8—832no—
187C2×D8—1661no—
188C2×D8—1661no—
189C2×D8—1661no—
190C2×D8—1661no—
191C2×D8—1661no—
192C22×C8C22⋊D8311yescharacteristic
193C22×C8C22×D8311yescharacteristic
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—1661no—
198C2×C22⋊C4—3321no—
199C2×C22⋊C4—3321no—
200C2×C42C22⋊D8311yescharacteristic
201C2×C16—832no—
202C2×C16—832no—
203C2×C16—1661no—
204C2×C16—1661no—
205C2×C16—1661no—
206C2×C16—1661no—
207#107—21no—
208#107—21no—
209#107—21no—
210#107—1661no—
211#107—1661no—
212#107C4×D8312yes—
213#102—3322no—
214C4×C8—21no—
215C4×C8—21no—
216#95—41no—
217C24—3321no—
218C2×D4—3321no—
219C2×D4—3321no—
220C2×D4—3321no—
221C2×D4—3321no—
222C2×D4—3321no—
223C2×D4—1662no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—3321no—
227C22×C4#1305057511yescharacteristic
228C22×C4#1305057511yescharacteristic
229C22×C4C2×C22⋊D8311yescharacteristic
230D8—3321no—
231D8—3321no—
232D8—1662no—
233D8—1662no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8#1305057712yes—
237C2×C8C2×C4×D8311yescharacteristic
238C2×C8D4×D8311yescharacteristic
239C2×C8#1305058911yescharacteristic
240C2×C8#1305059011yescharacteristic
241C2×C8#1305059111yescharacteristic
242C2×C8#1305059111yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—82no—
248C4⋊C4—3321no—
249C4⋊C4—3321no—
250C22⋊C4—6642no—
251C22⋊C4—6642no—
252C42—21no—
253C42—21no—
254C16—1662no—
255C16—1662no—
256C23—3322no—
257C23—6641no—
258C23—6641no—
259C23—6641no—
260C23—6641no—
261C23—6641no—
262C23—6641no—
263C23C2×#1305057511yescharacteristic
264D4—3322no—
265D4—3322no—
266D4—6641no—
267D4—6641no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—6641no—
281C2×C4—6641no—
282C2×C4—6641no—
283C2×C4C4×C22⋊D8311yescharacteristic
284C2×C4#1458176411yescharacteristic
285C2×C4#1458178111yescharacteristic
286C2×C4C2×#1305057711yescharacteristic
287C2×C4#1458181211yescharacteristic
288C2×C4#1458181211yescharacteristic
289C8—22no—
290C8#1458175011yescharacteristic
291C8#1458175411yescharacteristic
292C8#1458177711yescharacteristic
293C8#1458178711yescharacteristic
294C22—13281no—
295C22—13281no—
296C22—13281no—
297C22—13281no—
298C22—6642no—
299C22—6642no—
300C22—6642no—
301C22C4×#1305057511yescharacteristic
302C22#1912793511yescharacteristic
303C22#1912804911yescharacteristic
304C22#1912813611yescharacteristic
305C22#1912813611yescharacteristic
306C22#1912813711yescharacteristic
307C22#1912814211yescharacteristic
308C4—41no—
309C4—41no—
310C4—82no—
311C4—161no—
312C4—13281no—
313C4#1912759111yescharacteristic
314C4C4×#1305057711yescharacteristic
315C4#1912793211yescharacteristic
316C4#1912805811yescharacteristic
317C2—13282no—
318C2#2490814511yescharacteristic
319C2#2490932511yescharacteristic
320C2#2490933711yescharacteristic
321C2#2490956411yescharacteristic
322C2#2490957811yescharacteristic
323C2#2490970211yescharacteristic
324C2#2490970611yescharacteristic
subgroupG/H
centerC23C2×#13050575
commutatorC2×C8×C83C22×C4
FrattiniC22×C8C22×D83
FittingC83×#1942C2
socleC23×C83C2×D8
prime radicalC22×D664C22
cosocleC22×C8×C83C23
hypercenter#1942D83
hypocenterC83#13149
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1942

Complements

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

NH ≅ G/Ntype
3. C2×#19127477C2semidirect
5. #24905554C2semidirect
6. #24905554C2semidirect
7. C83×#1942C2semidirect
15. #19127501C4semidirect
167. #1942D83semidirect
170. C83#13149semidirect

Maximal subgroups

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

subgroupindex
C2×#191275012
C2×#191274772
#249083292
#249055542
C83×#19422
#1314983