Finite Group Databasebeta

← #16857615

Subgroups — #16857615

Order 3968.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521745C211yesmaximal, characteristic, complemented
2#14521708C211yesmaximal, characteristic, complemented
3#14521404C211yesmaximal, characteristic, complemented
4#14521391C211yesmaximal, characteristic, complemented
5#14521368C211yesmaximal, characteristic, complemented
6#14521357C211yesmaximal, characteristic, complemented
7#14521285C211yesmaximal, characteristic, complemented
8#14521278C211yesmaximal, characteristic, complemented
9#14521265C211yesmaximal, characteristic, complemented
10#14521196C211yesmaximal, characteristic, complemented
11#14521190C211yesmaximal, characteristic, complemented
12C4×#92470C211yesmaximal, characteristic, complemented
13#14521046C211yesmaximal, characteristic, complemented
14C2×#11758404C211yesmaximal, characteristic, complemented
15C8×D4×C31C211yesmaximal, characteristic, complemented
16C2×#92495C2211yescharacteristic
17C22×Dic62C2211yescharacteristic
18C22×C8×C31C2211yescharacteristic
19C22×C8×C31C2211yescharacteristic
20C4×D4×C31C2211yescharacteristic
21#11758516—21no—
22#11758516—21no—
23#11758507C2211yescharacteristic
24#11758507C2211yescharacteristic
25#11758507C2211yescharacteristic
26#11758503C2211yescharacteristic
27C2×C4⋊Dic31C2211yescharacteristic
28#11758501C2211yescharacteristic
29C2×D248C2211yescharacteristic
30C2×#92470C2211yescharacteristic
31C2×#92470C2211yescharacteristic
32#11758475—21no—
33#11758473—21no—
34#11758462—21no—
35#11758460—21no—
36(C22⋊D31)⋊C4—21no—
37(C22⋊D31)⋊C4—21no—
38#11758452C2211yescharacteristic
39C4×D124C2211yescharacteristic
40#11758447C2211yescharacteristic
41C4×Dic62C2211yescharacteristic
42C31×C4⋊C8C2211yescharacteristic
43C31×C22⋊C8C2211yescharacteristic
44C31×C22⋊C8C2211yescharacteristic
45C4×C8×C31C2211yescharacteristic
46#11758409C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758406C2211yescharacteristic
51#11758405C2211yescharacteristic
52#11758405C2211yescharacteristic
53#11758404C2211yescharacteristic
54#11758404C2211yescharacteristic
55#11758404C2211yescharacteristic
56#11758404C2211yescharacteristic
57#11758404C2211yescharacteristic
58#11758404C2211yescharacteristic
59C2×D4×C31D411yescharacteristic
60C22×C4×C31C2311yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C2×C22⋊D31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C22×Dic31—21no—
67C22×Dic31—21no—
68#92495—22no—
69#92495—41no—
70C2×D124C2311yescharacteristic
71C2×D124C2311yescharacteristic
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×Dic62—22no—
75C2×Dic62—21no—
76C2×Dic62—41no—
77C2×Dic62C2311yescharacteristic
78C2×Dic62C2311yescharacteristic
79C2×C8×C31—41no—
80C2×C8×C31—41no—
81C2×C8×C31C2311yescharacteristic
82C2×C8×C31C2311yescharacteristic
83C2×C8×C31C2311yescharacteristic
84C2×C8×C31C2311yescharacteristic
85C4⋊C4×C31D411yescharacteristic
86C22⋊C4×C31D411yescharacteristic
87C22⋊C4×C31D411yescharacteristic
88C42×C31C2311yescharacteristic
89C22⋊Dic31—21no—
90C22⋊Dic31—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97C4⋊Dic31—21no—
98C4⋊Dic31C2311yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105Dic31⋊C4—21no—
106C4×Dic31—21no—
107C4×Dic31—21no—
108D248—41no—
109#92470—22no—
110#92470—41no—
111C23×C31C2×D411yescharacteristic
112C23×C31C2×D411yescharacteristic
113C22×D31—21no—
114C22×D31—21no—
115D4×C31—22no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2×D411yescharacteristic
122C2×C4×C31C2×D411yescharacteristic
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2411yescharacteristic
125C22⋊D31—42no—
126C22⋊D31—42no—
127C22⋊D31—42no—
128C22⋊D31—81no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31—42no—
136C2×Dic31—81no—
137D124—21no—
138D124—21no—
139D124—21no—
140D124—21no—
141C4×D31—42no—
142C4×D31—81no—
143Dic62—21no—
144Dic62—21no—
145Dic62—21no—
146Dic62—42no—
147Dic62#4112yes—
148C8×C31—21no—
149C8×C31—21no—
150C8×C31—21no—
151C8×C31—21no—
152#3301—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—21no—
158C22×C31#13512yes—
159C22×C31C22×D411yescharacteristic
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—21no—
169C4×C31—21no—
170C4×C31C2×#4111yescharacteristic
171C4×C31H(5,𝔽2)11yescharacteristic
172Dic31—22no—
173Dic31—41no—
174Dic31—41no—
175Dic31—41no—
176Dic31—41no—
177Dic31—41no—
178#553—311no—
179#548—311no—
180#488—311no—
181#485—311no—
182#481—311no—
183#479—311no—
184#466—311no—
185#465—311no—
186#463—311no—
187#449—311no—
188#448—311no—
189C4×SD16—311no—
190C8×D4D3111yescharacteristic, complemented
191#416—311no—
192C2×#103—311no—
193C2×C31—22no—
194C2×C31—41no—
195C2×C31#54611yescharacteristic
196C2×C31C2×#13511yescharacteristic
197C2×C31#57711yescharacteristic
198D31—81no—
199D31—81no—
200C2×#41—311no—
201C22×Q8—311no—
202C2×SD16—311no—
203C2×SD16—311no—
204C2×D8—311no—
205C22×C8C2×D3111yescharacteristic
206C22×C8C2×D3111yescharacteristic
207#126—621no—
208#125—311no—
209#124—311no—
210#124—621no—
211#123—621no—
212C22⋊Q8—311no—
213C22⋊Q8—621no—
214#121—311no—
215#121—311no—
216#121—311no—
217#121—621no—
218#121—621no—
219C4×Q8—311no—
220C4×D4—311no—
221C4×D4—621no—
222C4×D4—621no—
223C4×D4C2×D3111yescharacteristic
224#117—311no—
225C2×C4⋊C4—311no—
226#107—311no—
227#106—311no—
228#106—311no—
229C4⋊C8C2×D3111yescharacteristic
230#103—311no—
231#103—311no—
232#103—311no—
233#103—311no—
234#103—311no—
235#103—311no—
236#102—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240C22⋊C8C2×D3111yescharacteristic
241C22⋊C8C2×D3111yescharacteristic
242C4×C8C2×D3111yescharacteristic
243C31#330111yescharacteristic, complemented, Sylow
244#41—622no—
245#41—1241no—
246C2×Q8—311no—
247C2×Q8—311no—
248C2×Q8—622no—
249C2×Q8—621no—
250C2×Q8—1241no—
251C2×D4—311no—
252C2×D4—311no—
253C2×D4—621no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4—621no—
257C2×D4D12411yescharacteristic
258C22×C4—621no—
259C22×C4—621no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4C22×D3111yescharacteristic
263C22×C4C22×D3111yescharacteristic
264SD16—622no—
265SD16—1241no—
266D8—1241no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C22×D3111yescharacteristic
270C2×C8C22×D3111yescharacteristic
271C2×C8C22×D3111yescharacteristic
272C2×C8C22×D3111yescharacteristic
273C4⋊C4—311no—
274C4⋊C4—311no—
275C4⋊C4—311no—
276C4⋊C4—311no—
277C4⋊C4—621no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4—621no—
281C4⋊C4—621no—
282C4⋊C4D12411yescharacteristic
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C22⋊C4—621no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4D12411yescharacteristic
292C22⋊C4D12411yescharacteristic
293C42—621no—
294C42—621no—
295C42C22×D3111yescharacteristic
296C23—621no—
297C23—621no—
298C23C2×D12411yescharacteristic
299C23C2×D12411yescharacteristic
300Q8—312no—
301Q8—621no—
302Q8—621no—
303Q8—621no—
304Q8—1242no—
305D4—22no—
306D4—621no—
307D4—621no—
308D4—621no—
309D4—621no—
310D4—1242no—
311D4—1242no—
312D4—1242no—
313D4—2481no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—621no—
319C2×C4—621no—
320C2×C4—621no—
321C2×C4—621no—
322C2×C4—621no—
323C2×C4—621no—
324C2×C4—1242no—
325C2×C4—1242no—
326C2×C4—2481no—
327C2×C4—2481no—
328C2×C4C2×D12411yescharacteristic
329C2×C4C2×D12411yescharacteristic
330C2×C4C2×D12411yescharacteristic
331C2×C4C2×D12411yescharacteristic
332C2×C4C23×D3111yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—1241no—
343C22—1241no—
344C22—1241no—
345C22—1241no—
346C22—1241no—
347C22—1241no—
348C22#1175848112yes—
349C22C22×D12411yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—622no—
355C4—1241no—
356C4—1241no—
357C4—1241no—
358C4—1241no—
359C4—1241no—
360C4#1175856111yescharacteristic
361C4#41×D3111yescharacteristic
362C2—22no—
363C2—41no—
364C2—2481no—
365C2—2481no—
366C2#1452169411yescharacteristic
367C2C2×#1175848111yescharacteristic
368C2#1452186111yescharacteristic
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC8×D4×C31C2
socleC22×C31C22×D4
hypercenterC8×D4D31
hypocenterC31#3301
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #14521745C2semidirect
2. #14521708C2semidirect
3. #14521404C2semidirect
4. #14521391C2semidirect
5. #14521368C2semidirect
6. #14521357C2semidirect
7. #14521285C2semidirect
8. #14521278C2semidirect
9. #14521265C2semidirect
10. #14521196C2semidirect
11. #14521190C2semidirect
12. C4×#92470C2semidirect
13. #14521046C2semidirect
14. C2×#11758404C2semidirect
15. C8×D4×C31C2semidirect
190. C8×D4D31semidirect
243. C31#3301semidirect

Maximal subgroups

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

subgroupindex
#145217452
#145217082
#145214042
#145213912
#145213682
#145213572
#145212852
#145212782
#145212652
#145211962
#145211902
C4×#924702
#145210462
C2×#117584042
C8×D4×C312
#330131