Finite Group Databasebeta

← #16857574

Subgroups — #16857574

Order 3968.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521712C211yesmaximal, characteristic, complemented
2#14521700C211yesmaximal, characteristic
3#14521398C211yesmaximal, characteristic, complemented
4#14521381C211yesmaximal, characteristic, complemented
5#14521333C211yesmaximal, characteristic, complemented
6#14521280C211yesmaximal, characteristic, complemented
7#14521279C211yesmaximal, characteristic, complemented
8#14521253C211yesmaximal, characteristic, complemented
9#14521190C211yesmaximal, characteristic, complemented
10#14521189C211yesmaximal, characteristic, complemented
11#14521136C211yesmaximal, characteristic, complemented
12(C22⋊D31)⋊C8C211yesmaximal, characteristic, complemented
13C2×#11758398C211yesmaximal, characteristic, complemented
14#103×D31C211yesmaximal, characteristic, complemented
15C31×#483C211yesmaximal, characteristic, complemented
16C2×Q8×D31C2211yescharacteristic
17C2×#92495—21no—
18C22×Dic62C2211yescharacteristic
19C31×C22⋊Q8C2211yescharacteristic
20C2×C4⋊C4×C31C2211yescharacteristic
21#11758521C2211yescharacteristic
22C2×#92481C2211yescharacteristic
23#11758507C2211yescharacteristic
24#11758506—21no—
25C4×C22⋊D31C2211yescharacteristic
26C22×C31⋊C8C2211yescharacteristic
27C2×#92470C2211yescharacteristic
28C2×#92470C2211yescharacteristic
29C2×C8×D31C2211yescharacteristic
30#11758474C2211yescharacteristic
31#11758473—21no—
32#11758473—21no—
33#11758472C2211yescharacteristic
34#11758471—21no—
35#11758470C2211yescharacteristic
36C4⋊C4×D31C2211yescharacteristic
37#11758465—21no—
38#11758465C2211yescharacteristic
39#11758464C2211yescharacteristic
40(C22⋊D31)⋊C4—21no—
41#11758455—21no—
42C31×#106C2211yescharacteristic
43C31×#106C2211yescharacteristic
44C31×#103C2211yescharacteristic
45C31×#103C2211yescharacteristic
46C31×C22⋊C8C2211yescharacteristic
47#11758423C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49#11758404C2211yescharacteristic
50#11758404C2211yescharacteristic
51Dic31⋊C8C2211yescharacteristic
52C8×Dic31C2211yescharacteristic
53#11758398C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758398C2211yescharacteristic
56#11758398C2211yescharacteristic
57#11758397C2211yescharacteristic
58#11758396C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C22×C4×C31—21no—
61C22×C4×C31C2311yescharacteristic
62C2×C22⋊D31—21no—
63C2×C22⋊D31D411yescharacteristic
64C22×Dic31—21no—
65Q8×D31—22no—
66Q8×D31—41no—
67#92495—44no—
68C2×D124—21no—
69C2×D124C2311yescharacteristic
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×C4×D31C2311yescharacteristic
74C2×Dic62—22no—
75C2×Dic62—21no—
76C2×Dic62—21no—
77C2×Dic62—21no—
78C2×Dic62—41no—
79C2×Dic62C2311yescharacteristic
80C2×Dic62C2311yescharacteristic
81C2×C8×C31C2311yescharacteristic
82C2×C8×C31C2311yescharacteristic
83C4⋊C4×C31—21no—
84C4⋊C4×C31—21no—
85C4⋊C4×C31C2311yescharacteristic
86C4⋊C4×C31C2311yescharacteristic
87C4⋊C4×C31C2311yescharacteristic
88C22⋊C4×C31—21no—
89C22⋊Dic31D411yescharacteristic
90#92481—41no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4D411yescharacteristic
96C4⋊Dic31—21no—
97C4⋊Dic31C2311yescharacteristic
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4D411yescharacteristic
104C4×Dic31—21no—
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8—41no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109#92470—22no—
110#92470—41no—
111C8×D31—41no—
112C23×C31C2×D411yescharacteristic
113C22×D31—21no—
114C22×D31C2×D411yescharacteristic
115Q8×C31—21no—
116Q8×C31—21no—
117C2×C4×C31—21no—
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×C31C2411yescharacteristic
126C22⋊D31—42no—
127C22⋊D31SD1614yescomplemented
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—42no—
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135D124—21no—
136D124—21no—
137D124—42no—
138C4×D31—21no—
139C4×D31—21no—
140C4×D31—42no—
141C4×D31—42no—
142C4×D31—42no—
143Dic62—21no—
144Dic62—21no—
145Dic62—21no—
146Dic62—42no—
147Dic62—42no—
148Dic62—42no—
149Dic62#4112yescomplemented
150C8×C31—21no—
151C8×C31—21no—
152C31⋊C8—21no—
153C31⋊C8—21no—
154#3298—311nomaximal, Sylow
155C22×C31—21no—
156C22×C31—21no—
157C22×C31C2×SD1612yes—
158C22×C31C22×D411yescharacteristic
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31C2×SD1612yes—
165C4×C31—21no—
166C4×C31—41no—
167C4×C31—41no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31C2×#4111yescharacteristic
171C4×C31H(5,𝔽2)11yescharacteristic
172Dic31—22no—
173Dic31—21no—
174Dic31—21no—
175Dic31—41no—
176Dic31—41no—
177Dic31C2×SD1612yes—
178D4×Q8—311no—
179#547—311no—
180#487—311no—
181#483—311no—
182#483D3111yescharacteristic, complemented
183#475—311no—
184#465—311no—
185#465—311no—
186#461—311no—
187#448—311no—
188#448—311no—
189C4×SD16—311no—
190C8×D4—311no—
191C2×#103—311no—
192C2×#103—311no—
193C2×C31—22no—
194C2×C31#54611yescharacteristic
195C2×C31C22×SD1611yescharacteristic
196C2×C31#57811yescharacteristic
197D31—22no—
198D31—81no—
199C2×#41—621no—
200C22×Q8—311no—
201C22×Q8—311no—
202C2×SD16—311no—
203C2×SD16—311no—
204C2×SD16—311no—
205C22×C8—311no—
206C22×C8—311no—
207C4⋊Q8—311no—
208C4⋊Q8—311no—
209C4⋊Q8—621no—
210#123—621no—
211#123—621no—
212C22⋊Q8—311no—
213C22⋊Q8—621no—
214C22⋊Q8—621no—
215C22⋊Q8—621no—
216C22⋊Q8C2×D3111yescharacteristic
217#121—311no—
218#121—311no—
219C4×Q8—311no—
220C4×D4—311no—
221C4×D4—311no—
222C4×D4—621no—
223C2×C4⋊C4—311no—
224C2×C4⋊C4C2×D3111yescharacteristic
225#106—311no—
226#106C2×D3111yescharacteristic
227#106C2×D3111yescharacteristic
228C4⋊C8—311no—
229#103—311no—
230#103—311no—
231#103—311no—
232#103—311no—
233#103—311no—
234#103—311no—
235#103—311no—
236#103C2×D3111yescharacteristic
237#103C2×D3111yescharacteristic
238#102—311no—
239C22⋊C8—311no—
240C22⋊C8C2×D3111yescharacteristic
241C4×C8—311no—
242C31#329811yescharacteristic, complemented, Sylow
243#41—1244no—
244C2×Q8—311no—
245C2×Q8—311no—
246C2×Q8—621no—
247C2×Q8—621no—
248C2×Q8—622no—
249C2×Q8—621no—
250C2×Q8—622no—
251C2×Q8—1241no—
252C2×Q8—1241no—
253C2×Q8C22×D3111yescharacteristic
254C2×D4—311no—
255C2×D4—311no—
256C2×D4—621no—
257C2×D4—621no—
258C22×C4—21no—
259C22×C4—311no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4—621no—
263C22×C4—621no—
264C22×C4C22×D3111yescharacteristic
265SD16—622no—
266SD16—1241no—
267SD16—1241no—
268C2×C8—311no—
269C2×C8—311no—
270C2×C8—1241no—
271C2×C8—1241no—
272C2×C8C22×D3111yescharacteristic
273C2×C8C22×D3111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—311no—
277C4⋊C4—311no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4—621no—
281C4⋊C4—621no—
282C4⋊C4—621no—
283C4⋊C4—621no—
284C4⋊C4C22×D3111yescharacteristic
285C4⋊C4C22×D3111yescharacteristic
286C4⋊C4C22×D3111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—311no—
289C22⋊C4—311no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C22⋊C4—621no—
294C42—311no—
295C42—621no—
296C23—311no—
297C23—621no—
298C23D4×D3111yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—312no—
302Q8—621no—
303Q8—621no—
304Q8—621no—
305Q8—1242no—
306Q8—1242no—
307Q8—1242no—
308D4—314no—
309D4—621no—
310D4—621no—
311D4—1242no—
312D4—1242no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—311no—
321C2×C4—311no—
322C2×C4—311no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—1242no—
329C2×C4—1242no—
330C2×C4—1242no—
331C2×C4—1242no—
332C2×C4D4×D3111yescharacteristic
333C2×C4C23×D3111yescharacteristic
334C8—21no—
335C8—21no—
336C8—621no—
337C8—621no—
338C22—21no—
339C22—21no—
340C22—312no—
341C22—621no—
342C22—621no—
343C22—1241no—
344C22—1241no—
345C22—1241no—
346C22SD16×D3112yes—
347C22C2×D4×D3111yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—312no—
354C4—621no—
355C4—621no—
356C4—622no—
357C4—1241no—
358C4—1241no—
359C4#41×D3111yescharacteristic
360C4#1175856611yescharacteristic
361C2—22no—
362C2—622no—
363C2—2481no—
364C2#1452169111yescharacteristic
365C2C2×SD16×D3111yescharacteristic
366C2#1452186511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#483C2
socleC22×C31C22×D4
prime radical#14521700C2
hypercenter#483D31
hypocenterC31#3298
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #14521712C2semidirect
3. #14521398C2semidirect
4. #14521381C2semidirect
5. #14521333C2semidirect
6. #14521280C2semidirect
7. #14521279C2semidirect
8. #14521253C2semidirect
9. #14521190C2semidirect
10. #14521189C2semidirect
11. #14521136C2semidirect
12. (C22⋊D31)⋊C8C2semidirect
13. C2×#11758398C2semidirect
14. #103×D31C2semidirect
15. C31×#483C2semidirect
127. C22⋊D31SD16semidirect
149. Dic62#41semidirect
182. #483D31semidirect
242. C31#3298semidirect

Maximal subgroups

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

subgroupindex
#145217122
#145217002
#145213982
#145213812
#145213332
#145212802
#145212792
#145212532
#145211902
#145211892
#145211362
(C22⋊D31)⋊C82
C2×#117583982
#103×D312
C31×#4832
#329831