Finite Group Databasebeta

← C4×#19127510 #35319655

Subgroups — C4×#19127510 #35319655

Order 21248.

466 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14581814C211yesmaximal, characteristic
2C2×#19127510C212yesmaximal
3C4×#14581732C211yesmaximal, characteristic, complemented
4#24905570C212yesmaximal, complemented
5C4×#106×C83C211yesmaximal, characteristic, complemented
6C2×#14581814C2211yescharacteristic
7C4×#13050590—21no—
8C2×#14581732C2212yes—
9C4×Dic332C411yescharacteristic, complemented
10C4×Dic332C411yescharacteristic, complemented
11C4×#13050579—21no—
12C4×#13050579—21no—
13C4×D664C411yescharacteristic, complemented
14C4×D664C411yescharacteristic, complemented
15#19127739C2211yescharacteristic
16#19127698—21no—
17#19127510C418yesdirect product factor
18#19127477—21no—
19C4×C83⋊C16—21no—
20C2×#106×C83C2212yes—
21C2×C4×C8×C83C2211yescharacteristic
22C4×C4⋊C4×C83—21no—
23#340×C83—21no—
24C2×#13050590—21no—
25#14581814—22no—
26#14581814C2×C414yes—
27C2×Dic332C2×C411yescharacteristic
28C2×#13050579—21no—
29C2×D664C2×C411yescharacteristic
30C4×Dic166—21no—
31C4×Dic166—21no—
32C4×D332—21no—
33C4×D332—21no—
34C4×C22⋊D83—41no—
35C4×C22⋊D83—41no—
36#14581751—21no—
37#14581749—41no—
38C42×D83—41no—
39#14581732—22no—
40#14581732C2×C414yescomplemented
41C2×C83⋊C16—22no—
42#14581726C2×C411yescharacteristic
43#14581726C2×C411yescharacteristic
44#14581724—21no—
45#14581717—21no—
46#14581717—21no—
47#14581714—21no—
48#14581714—21no—
49C22×C8×C83D411yescharacteristic
50C22×C8×C83C2311yescharacteristic
51C2×C4⋊C4×C83—22no—
52C2×C42×C83—41no—
53C2×C42×C83D411yescharacteristic
54#106×C83—22no—
55#106×C83C2×C414yescomplemented
56C4×C8×C83C2×C411yescharacteristic
57C4×C8×C83C2×C411yescharacteristic
58C4×C8×C83D411yescharacteristic
59C4×C8×C83D411yescharacteristic
60#95×C83—41no—
61#13050590—24no—
62#13050590—42no—
63C2×Dic166—21no—
64C2×D332—21no—
65C2×C22⋊D83—41no—
66C2×C4×D83—41no—
67C2×C4×D83—41no—
68C2×C4×D83—41no—
69Dic332—21no—
70Dic332C4212yescomplemented
71#13050579—24no—
72D664—21no—
73D664C4212yescomplemented
74C4⋊Dic83—21no—
75C4⋊Dic83—21no—
76Dic83⋊C4—41no—
77Dic83⋊C4—41no—
78C22⋊Dic83—41no—
79(C2×D83)⋊C4—41no—
80(C2×D83)⋊C4—41no—
81C4×Dic83—41no—
82C4×Dic83—41no—
83C4×Dic83—41no—
84C83⋊C16—24no—
85C22×C4×C83—42no—
86C22×C4×C83D811yescharacteristic
87C22×C4×C83D811yescharacteristic
88C22×C4×C83C2×D411yescharacteristic
89C2×C8×C83—22no—
90C2×C8×C83C22⋊C411yescharacteristic
91C2×C8×C83C22⋊C411yescharacteristic
92C2×C8×C83C22×C411yescharacteristic
93C2×C8×C83C22×C412yes—
94C2×C8×C83C2×D411yescharacteristic
95C2×C8×C83#4112yes—
96C4⋊C4×C83—24no—
97C4⋊C4×C83—42no—
98C42×C83—82no—
99C42×C83C22⋊C411yescharacteristic
100C42×C83C22⋊C411yescharacteristic
101C42×C83SD1611yescharacteristic
102C42×C83SD1611yescharacteristic
103C23×C83C2×D811yescharacteristic
104C22×D83—41no—
105C2×C4×C83—22no—
106C2×C4×C83—41no—
107C2×C4×C83—44no—
108C2×C4×C83—82no—
109C2×C4×C83—82no—
110C2×C4×C83#10211yescharacteristic
111C2×C4×C83#10211yescharacteristic
112C2×C4×C83#10211yescharacteristic
113C2×C4×C83#10211yescharacteristic
114C2×C4×C83C2×C22⋊C411yescharacteristic
115C2×C4×C83C4×D412yes—
116C2×C4×C83C2×SD1611yescharacteristic
117C2×C4×C83#13512yes—
118C22⋊D83—44no—
119C2×Dic83—41no—
120C2×Dic83—41no—
121C2×Dic83—41no—
122D332—22no—
123D332—41no—
124C4×D83—44no—
125C4×D83—82no—
126C4×D83—82no—
127Dic166—22no—
128Dic166—41no—
129C8×C83—21no—
130C8×C83—21no—
131C8×C83C2×C4211yescharacteristic
132C8×C83#11711yescharacteristic
133C8×C83C4×D412yes—
134C22×C83—21no—
135C22×C83—21no—
136C22×C83C2×#10211yescharacteristic
137C22×C83C4×D812yes—
138C2×D83—42no—
139C2×D83—81no—
140C2×D83—81no—
141C4×C83—21no—
142C4×C83—21no—
143C4×C83—21no—
144C4×C83—84no—
145C4×C83#36012yescomplemented
146C4×C83C4×C22⋊C411yescharacteristic
147C4×C83#41611yescharacteristic
148C4×C83C4×SD1612yes—
149Dic83—42no—
150Dic83—81no—
151Dic83—81no—
152C4×#360—831nomaximal, Sylow
153C2×C83—22no—
154C2×C83C4×#10211yescharacteristic
155C2×C83C2×#36011yescharacteristic
156C2×C83#214511yescharacteristic
157D83—82no—
158C4×#135—831no—
159C2×#360—832no—
160C4×M32—831no—
161C4×#106D8311yescharacteristic, complemented
162#1386—832no—
163C83C4×#36011yescharacteristic, complemented, Sylow
164C2×#135—831no—
165C4×#41—1661no—
166C2×M32—832no—
167C4×Q16—831no—
168C4×Q16—831no—
169C4×SD16—1661no—
170C4×SD16—1661no—
171C4×D8—831no—
172C4×D8—831no—
173#427—831no—
174C2×#106C2×D8312yes—
175#416—1661no—
176C2×C4×C8C2×D8311yescharacteristic
177C4×C4⋊C4—21no—
178#360—838no—
179#346—1661no—
180C4×C16—1661no—
181#340—21no—
182C2×#41—1661no—
183#135—834no—
184#135—1662no—
185C2×Q16—831no—
186C2×SD16—1661no—
187C2×D8—831no—
188C22×C8C22⋊D8311yescharacteristic
189C22×C8C22×D8311yescharacteristic
190C4×Q8—1661no—
191C4×Q8—1661no—
192C4×D4—3321no—
193C4×D4—3321no—
194C4×D4—1661no—
195C4×D4—1661no—
196#117—3321no—
197#117—1661no—
198C2×C4⋊C4—22no—
199C2×C42—41no—
200C2×C42—3321no—
201C2×C42C22⋊D8311yescharacteristic
202M32—834no—
203M32—1662no—
204C2×C16—1662no—
205#107—831no—
206#107—831no—
207#106—22no—
208#106—1661no—
209#106C4×D8314yescomplemented
210#103—1661no—
211#103—1661no—
212#102—1661no—
213#102—1661no—
214C4×C8C4×D8311yescharacteristic
215C4×C8C4×D8311yescharacteristic
216C4×C8D33211yescharacteristic
217C4×C8D33211yescharacteristic
218#95—41no—
219#41—3322no—
220#41—1664no—
221C2×Q8—1661no—
222C2×D4—3321no—
223C2×D4—1661no—
224C22×C4—42no—
225C22×C4—3321no—
226C22×C4—3321no—
227C22×C4—3321no—
228C22×C4#1305057511yescharacteristic
229C22×C4#1305057511yescharacteristic
230C22×C4C2×C22⋊D8311yescharacteristic
231Q16—832no—
232Q16—1661no—
233SD16—1664no—
234D8—832no—
235D8—1661no—
236C2×C8—22no—
237C2×C8(C2×D83)⋊C411yescharacteristic
238C2×C8(C2×D83)⋊C411yescharacteristic
239C2×C8C2×C4×D8311yescharacteristic
240C2×C8C2×C4×D8312yes—
241C2×C8C2×D33211yescharacteristic
242C2×C8#1305059012yes—
243C4⋊C4—24no—
244C4⋊C4—42no—
245C4⋊C4—3321no—
246C4⋊C4—3321no—
247C4⋊C4—1661no—
248C4⋊C4—1661no—
249C22⋊C4—3321no—
250C22⋊C4—3321no—
251C22⋊C4—3321no—
252C42—82no—
253C42—3321no—
254C42—3321no—
255C42—3321no—
256C42(C2×D83)⋊C411yescharacteristic
257C42(C2×D83)⋊C411yescharacteristic
258C42#1305057711yescharacteristic
259C42#1305057711yescharacteristic
260C16—1664no—
261C23—3321no—
262C23C2×#1305057511yescharacteristic
263Q8—3321no—
264Q8—1662no—
265D4—3324no—
266D4—3321no—
267D4—1662no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—44no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4—3321no—
274C2×C4—3324no—
275C2×C4—3321no—
276C2×C4—3321no—
277C2×C4—6642no—
278C2×C4—6642no—
279C2×C4#1458171211yescharacteristic
280C2×C4#1458171211yescharacteristic
281C2×C4#1458171211yescharacteristic
282C2×C4#1458171211yescharacteristic
283C2×C4C2×(C2×D83)⋊C411yescharacteristic
284C2×C4C4×C22⋊D8312yes—
285C2×C4C2×#1305057711yescharacteristic
286C2×C4#1458181212yes—
287C8—21no—
288C8—21no—
289C8C42×D8311yescharacteristic
290C8#1458174911yescharacteristic
291C8C4×D33212yes—
292C22—21no—
293C22—21no—
294C22—3322no—
295C22—6641no—
296C22—6641no—
297C22C2×#1458171211yescharacteristic
298C22C4×#1305057512yes—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—84no—
303C4—3322no—
304C4—6641no—
305C4—6641no—
306C4#1912751012yesdirect product factor
307C4C4×(C2×D83)⋊C411yescharacteristic
308C4#1912769511yescharacteristic
309C4C4×#1305057712yes—
310C2—22no—
311C2—6642no—
312C2C4×#1458171211yescharacteristic
313C2C2×#1912751011yescharacteristic
314C2#2490919811yescharacteristic
subgroupG/H
centerC2×C4#14581712
commutatorC8×C83C2×C42
FrattiniC22×C8C22×D83
FittingC4×#106×C83C2
socleC22×C83C2×#102
prime radicalC2×#14581814C22
cosocleC22×C8×C83C23
hypercenterC4×#106D83
hypocenterC83C4×#360
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
3. C4×#14581732C2semidirect
4. #24905570C2semidirect
5. C4×#106×C83C2semidirect
9. C4×Dic332C4semidirect
10. C4×Dic332C4semidirect
13. C4×D664C4semidirect
14. C4×D664C4semidirect
17. #19127510C4direct (N × H)
40. #14581732C2×C4semidirect
55. #106×C83C2×C4semidirect
70. Dic332C42semidirect
73. D664C42semidirect
145. C4×C83#360semidirect
161. C4×#106D83semidirect
163. C83C4×#360semidirect
209. #106C4×D83semidirect
306. C4#19127510direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#145818142
C2×#191275102
C4×#145817322
#249055702
C4×#106×C832
C4×#36083