Finite Group Databasebeta

← #16856275

Subgroups — #16856275

Order 3968.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521583C211yesmaximal, characteristic, complemented
2#14521448C211yesmaximal, characteristic, complemented
3#14521431C211yesmaximal, characteristic, complemented
4#14521406C211yesmaximal, characteristic, complemented
5#14521403C211yesmaximal, characteristic, complemented
6#14521288C211yesmaximal, characteristic, complemented
7#14521283C211yesmaximal, characteristic
8#14521280C211yesmaximal, characteristic, complemented
9#14521276C211yesmaximal, characteristic, complemented
10C4×#92482C211yesmaximal, characteristic, complemented
11C4×#92481C211yesmaximal, characteristic, complemented
12C4×#92480C211yesmaximal, characteristic, complemented
13C4×#92479C211yesmaximal, characteristic, complemented
14C2×C4×C31⋊C8C211yesmaximal, characteristic, complemented
15C31×#529C211yesmaximal, characteristic, complemented
16C31×#126—21no—
17C31×#125C2211yescharacteristic
18C31×#124C2211yescharacteristic
19C31×#123—21no—
20C31×C22⋊Q8C2211yescharacteristic
21C31×#121C2211yescharacteristic
22C4×Q8×C31C2211yescharacteristic
23C4×D4×C31—21no—
24C4×D4×C31C2211yescharacteristic
25C31×#117—21no—
26C2×C42×C31C2211yescharacteristic
27C2×#92482C2211yescharacteristic
28C2×#92481C2211yescharacteristic
29C2×#92480C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31#11758507C2211yescharacteristic
32#11758506—21no—
33C4×C22⋊D31—21no—
34#11758501C2211yescharacteristic
35C22×C31⋊C8C2211yescharacteristic
36C22×C31⋊C8C2211yescharacteristic
37#11758453—21no—
38#11758452C2211yescharacteristic
39C4×D124C2211yescharacteristic
40#11758449—21no—
41#11758447C2211yescharacteristic
42C4×Dic62C2211yescharacteristic
43#11758423C2211yescharacteristic
44#11758423C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758398C2211yescharacteristic
48#11758398C2211yescharacteristic
49#11758397C2211yescharacteristic
50#11758397C2211yescharacteristic
51#11758396C2211yescharacteristic
52#11758396C2211yescharacteristic
53#11758395C2211yescharacteristic
54#11758395C2211yescharacteristic
55C4×C31⋊C8C2211yescharacteristic
56C4×C31⋊C8C2211yescharacteristic
57C4×C31⋊C8C2211yescharacteristic
58C4×C31⋊C8C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31—21no—
61C2×D4×C31C2311yescharacteristic
62C22×C4×C31—21no—
63C22×C4×C31D411yescharacteristic
64C22×C4×C31D411yescharacteristic
65C22×C4×C31C2311yescharacteristic
66C2×C22⋊D31—21no—
67C2×D124C2311yescharacteristic
68C2×C4×D31—21no—
69C2×Dic62C2311yescharacteristic
70C4⋊C4×C31—21no—
71C4⋊C4×C31—21no—
72C4⋊C4×C31—21no—
73C4⋊C4×C31—21no—
74C4⋊C4×C31C2311yescharacteristic
75C4⋊C4×C31C2311yescharacteristic
76C22⋊C4×C31—21no—
77C22⋊C4×C31—21no—
78C22⋊C4×C31—21no—
79C22⋊C4×C31—21no—
80C22⋊C4×C31—21no—
81C42×C31—21no—
82C42×C31D411yescharacteristic
83C42×C31D411yescharacteristic
84C42×C31C2311yescharacteristic
85C42×C31C2311yescharacteristic
86C22⋊Dic31—21no—
87#92482—22no—
88#92481—22no—
89#92480—22no—
90#92479—22no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95C4⋊Dic31C2311yescharacteristic
96C4⋊Dic31C2311yescharacteristic
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101C4×Dic31—21no—
102C2×C31⋊C8—22no—
103C2×C31⋊C8—22no—
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—21no—
109C23×C31C2×D411yescharacteristic
110C22×D31—21no—
111Q8×C31—21no—
112Q8×C31—21no—
113D4×C31—21no—
114D4×C31—21no—
115D4×C31—42no—
116C2×C4×C31—22no—
117C2×C4×C31—22no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—42no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2411yescharacteristic
130C22⋊D31—42no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134D124—21no—
135D124—21no—
136C4×D31—42no—
137Dic62—21no—
138Dic62—21no—
139C31⋊C8—21no—
140C31⋊C8—21no—
141C31⋊C8#4112yes—
142C31⋊C8#4112yes—
143#3168—311nomaximal, Sylow
144C22×C31—21no—
145C22×C31—21no—
146C22×C31—41no—
147C22×C31—41no—
148C22×C31—41no—
149C22×C31#13512yes—
150C22×C31C22×D411yescharacteristic
151C2×D31—41no—
152C2×D31—41no—
153C2×D31—41no—
154C4×C31—21no—
155C4×C31—21no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—41no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31#13512yes—
162C4×C31C2×#4111yescharacteristic
163C4×C31C2×#4111yescharacteristic
164Dic31—41no—
165Dic31—41no—
166Dic31—41no—
167#529—311no—
168#529D3111yescharacteristic, complemented
169#499—311no—
170#495—311no—
171#488—311no—
172#488—311no—
173#467—311no—
174#466—311no—
175#465—311no—
176#465—311no—
177C4×Q16—311no—
178C4×SD16—311no—
179C4×SD16—311no—
180C4×D8—311no—
181C2×C4×C8—311no—
182C2×C31—22no—
183C2×C31—81no—
184C2×C31#53211yescharacteristic
185C2×C31C2×#13511yescharacteristic
186C2×C31C2×#13511yescharacteristic
187D31—81no—
188C2×Q16—311no—
189C2×SD16—311no—
190C2×SD16—311no—
191C2×D8—311no—
192C22×C8—311no—
193C22×C8—311no—
194#126—21no—
195#126—621no—
196#125—311no—
197#125C2×D3111yescharacteristic
198#124—311no—
199#124C2×D3111yescharacteristic
200#123—21no—
201#123—621no—
202C22⋊Q8—311no—
203C22⋊Q8C2×D3111yescharacteristic
204#121—311no—
205#121C2×D3111yescharacteristic
206C4×Q8—311no—
207C4×Q8C2×D3111yescharacteristic
208C4×D4—21no—
209C4×D4—311no—
210C4×D4—621no—
211C4×D4C2×D3111yescharacteristic
212#117—21no—
213#117—621no—
214C2×C42C2×D3111yescharacteristic
215#107—311no—
216#107—311no—
217#106—311no—
218#106—311no—
219#103—311no—
220#103—311no—
221#103—311no—
222#103—311no—
223#102—311no—
224#102—311no—
225#102—311no—
226#102—311no—
227C4×C8—311no—
228C4×C8—311no—
229C4×C8—311no—
230C4×C8—311no—
231C31#316811yescharacteristic, complemented, Sylow
232C2×Q8—311no—
233C2×Q8C22×D3111yescharacteristic
234C2×D4—21no—
235C2×D4—311no—
236C2×D4—621no—
237C2×D4C22×D3111yescharacteristic
238C22×C4—21no—
239C22×C4—621no—
240C22×C4C22⋊D3111yescharacteristic
241C22×C4C22⋊D3111yescharacteristic
242C22×C4C22×D3111yescharacteristic
243Q16—622no—
244SD16—622no—
245SD16—622no—
246D8—622no—
247C2×C8—311no—
248C2×C8—311no—
249C2×C8—311no—
250C2×C8—311no—
251C2×C8—622no—
252C2×C8—622no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—311no—
258C4⋊C4—311no—
259C4⋊C4—621no—
260C4⋊C4—621no—
261C4⋊C4—621no—
262C4⋊C4—621no—
263C4⋊C4C22×D3111yescharacteristic
264C4⋊C4C22×D3111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—621no—
271C22⋊C4—621no—
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C42—21no—
276C42—621no—
277C42C22⋊D3111yescharacteristic
278C42C22⋊D3111yescharacteristic
279C42C22×D3111yescharacteristic
280C42C22×D3111yescharacteristic
281C23—21no—
282C23—621no—
283C23C2×C22⋊D3111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—621no—
287Q8—621no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—621no—
292D4—621no—
293D4—1242no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—621no—
303C2×C4—621no—
304C2×C4—621no—
305C2×C4—1242no—
306C2×C4C2×C22⋊D3111yescharacteristic
307C2×C4C2×C22⋊D3111yescharacteristic
308C2×C4C2×C22⋊D3111yescharacteristic
309C2×C4C2×C22⋊D3111yescharacteristic
310C2×C4C2×C22⋊D3111yescharacteristic
311C2×C4C23×D3111yescharacteristic
312C8—312no—
313C8—312no—
314C8—621no—
315C8—621no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—1241no—
322C22—1241no—
323C22—1241no—
324C22#1175852712yes—
325C22C22×C22⋊D3111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—1241no—
334C4—1241no—
335C4—1241no—
336C4#1175852712yes—
337C4#41×D3111yescharacteristic
338C4#41×D3111yescharacteristic
339C2—22no—
340C2—81no—
341C2—2481no—
342C2#1452159511yescharacteristic
343C2C2×#1175852711yescharacteristic
344C2C2×#1175852711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#529C2
socleC22×C31C22×D4
prime radical#14521283C2
hypercenter#529D31
hypocenterC31#3168
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #14521583C2semidirect
2. #14521448C2semidirect
3. #14521431C2semidirect
4. #14521406C2semidirect
5. #14521403C2semidirect
6. #14521288C2semidirect
8. #14521280C2semidirect
9. #14521276C2semidirect
10. C4×#92482C2semidirect
11. C4×#92481C2semidirect
12. C4×#92480C2semidirect
13. C4×#92479C2semidirect
14. C2×C4×C31⋊C8C2semidirect
15. C31×#529C2semidirect
168. #529D31semidirect
231. C31#3168semidirect

Maximal subgroups

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

subgroupindex
#145215832
#145214482
#145214312
#145214062
#145214032
#145212882
#145212832
#145212802
#145212762
C4×#924822
C4×#924812
C4×#924802
C4×#924792
C2×C4×C31⋊C82
C31×#5292
#316831