Finite Group Databasebeta

← #16857720

Subgroups — #16857720

Order 3968.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521747C211yesmaximal, characteristic, complemented
2#14521717C211yesmaximal, characteristic, complemented
3#14521412C211yesmaximal, characteristic, complemented
4#14521376C211yesmaximal, characteristic, complemented
5#14521355C211yesmaximal, characteristic, complemented
6#14521300C211yesmaximal, characteristic, complemented
7#14521286C211yesmaximal, characteristic, complemented
8#14521243C211yesmaximal, characteristic, complemented
9#14521196C211yesmaximal, characteristic, complemented
10#14521195C211yesmaximal, characteristic, complemented
11#14521148C211yesmaximal, characteristic, complemented
12#14521123C211yesmaximal, characteristic, complemented
13#14521048C211yesmaximal, characteristic, complemented
14#14521042C211yesmaximal, characteristic, complemented
15C31×#480C211yesmaximal, characteristic, complemented
16C2×#92497C2211yescharacteristic
17C2×#92495C2211yescharacteristic
18C31×#121C2211yescharacteristic
19C2×C4⋊C4×C31C2211yescharacteristic
20#11758517—21no—
21#11758517C2211yescharacteristic
22#11758516—21no—
23C2×#92479C2211yescharacteristic
24#11758507—21no—
25#11758507C2211yescharacteristic
26C4×C22⋊D31—21no—
27C4×C22⋊D31C2211yescharacteristic
28C2×#92474C2211yescharacteristic
29C2×D248C2211yescharacteristic
30C2×#92470C2211yescharacteristic
31C2×C8×D31C2211yescharacteristic
32#11758475—21no—
33#11758472C2211yescharacteristic
34#11758472C2211yescharacteristic
35#11758471—21no—
36#11758470C2211yescharacteristic
37#11758469C2211yescharacteristic
38#11758467C2211yescharacteristic
39#11758464C2211yescharacteristic
40#11758461—21no—
41(C22⋊D31)⋊C4—21no—
42C31×#107C2211yescharacteristic
43C31×#107C2211yescharacteristic
44C31×#102C2211yescharacteristic
45C31×#102C2211yescharacteristic
46C31×C22⋊C8C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758409C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758404C2211yescharacteristic
51#11758403C2211yescharacteristic
52Dic31⋊C8C2211yescharacteristic
53#11758398C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758397C2211yescharacteristic
58#11758396C2211yescharacteristic
59C2×D4×C31—21no—
60C2×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C22×C4×C31C2311yescharacteristic
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67C2×C22⋊D31—21no—
68C2×C22⋊D31D411yescharacteristic
69C22×Dic31—21no—
70#92497—22no—
71#92497—41no—
72#92495—22no—
73#92495—41no—
74C2×D124—21no—
75C2×D124—21no—
76C2×D124C2311yescharacteristic
77C2×D124C2311yescharacteristic
78C2×C4×D31—21no—
79C2×C4×D31—21no—
80C2×C4×D31C2311yescharacteristic
81C2×Dic62C2311yescharacteristic
82C2×C8×C31C2311yescharacteristic
83C2×C8×C31C2311yescharacteristic
84C4⋊C4×C31—21no—
85C4⋊C4×C31C2311yescharacteristic
86C4⋊C4×C31C2311yescharacteristic
87C4⋊C4×C31C2311yescharacteristic
88C22⋊C4×C31—21no—
89C22⋊Dic31D411yescharacteristic
90#92479—41no—
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)⋊C4D411yescharacteristic
97C4⋊Dic31—21no—
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4D411yescharacteristic
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31C2311yescharacteristic
105#92474—41no—
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108D248—41no—
109#92470—22no—
110C8×D31—41no—
111C23×C31—21no—
112C23×C31C2×D411yescharacteristic
113C22×D31—21no—
114C22×D31—21no—
115C22×D31C2×D411yescharacteristic
116D4×C31—21no—
117D4×C31—21no—
118D4×C31—81no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—81no—
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2411yescharacteristic
127C22⋊D31—41no—
128C22⋊D31—42no—
129C22⋊D31—42no—
130C22⋊D31—42no—
131C22⋊D31—42no—
132C22⋊D31—81no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31—42no—
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138C2×Dic31C2×D411yescharacteristic
139D124—21no—
140D124—21no—
141D124—21no—
142D124—21no—
143D124—81no—
144D124—81no—
145C4×D31—21no—
146C4×D31—21no—
147C4×D31—42no—
148C4×D31—81no—
149Dic62—21no—
150Dic62#4112yes—
151C8×C31—21no—
152C8×C31—21no—
153C31⋊C8—21no—
154C31⋊C8—21no—
155#3309—311nomaximal, Sylow
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—41no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31C22×D411yescharacteristic
163C2×D31—21no—
164C2×D31—21no—
165C2×D31—21no—
166C2×D31—41no—
167C2×D31—41no—
168C2×D31—41no—
169C2×D31—41no—
170C2×D31—41no—
171C2×D31—41no—
172C4×C31—21no—
173C4×C31—41no—
174C4×C31—41no—
175C4×C31—41no—
176C4×C31C2×#4111yescharacteristic
177C4×C31H(5,𝔽2)11yescharacteristic
178Dic31—22no—
179Dic31—21no—
180Dic31—21no—
181Dic31—21no—
182Dic31—41no—
183#553—311no—
184#550—311no—
185#490—311no—
186#482—311no—
187#480D3111yescharacteristic, complemented
188#479—311no—
189#469—311no—
190#466—311no—
191#459—311no—
192#449—311no—
193#449—311no—
194#440—311no—
195#435—311no—
196#417—311no—
197#416—311no—
198C2×C31—41no—
199C2×C31—81no—
200C2×C31#54611yescharacteristic
201C2×C31#57511yescharacteristic
202C2×C31#57611yescharacteristic
203D31—41no—
204D31—81no—
205D31—81no—
206C2×#41—311no—
207C2×#41—311no—
208C2×SD16—311no—
209C2×D8—311no—
210C2×D8—311no—
211C2×M16—311no—
212C22×C8—311no—
213#127—311no—
214#127—621no—
215#126—621no—
216#125—311no—
217#123—621no—
218#121—311no—
219#121—311no—
220#121—311no—
221#121—621no—
222#121—621no—
223#121—621no—
224#121C2×D3111yescharacteristic
225C4×Q8—311no—
226C4×D4—311no—
227C4×D4—311no—
228C4×D4—621no—
229C4×D4—621no—
230#117—311no—
231C2×C4⋊C4C2×D3111yescharacteristic
232#107C2×D3111yescharacteristic
233#107C2×D3111yescharacteristic
234#106—311no—
235C4⋊C8—311no—
236#103—311no—
237#103—311no—
238#103—311no—
239#102—311no—
240#102—311no—
241#102—311no—
242#102—311no—
243#102—311no—
244#102C2×D3111yescharacteristic
245#102C2×D3111yescharacteristic
246C22⋊C8—311no—
247C22⋊C8C2×D3111yescharacteristic
248#97—311no—
249C31#330911yescharacteristic, complemented, Sylow
250#41—622no—
251#41—622no—
252#41—1241no—
253#41—1241no—
254C2×Q8—311no—
255C2×D4—21no—
256C2×D4—311no—
257C2×D4—311no—
258C2×D4—311no—
259C2×D4—621no—
260C2×D4—621no—
261C2×D4—621no—
262C2×D4—621no—
263C2×D4—621no—
264C2×D4—621no—
265C2×D4—621no—
266C2×D4C22×D3111yescharacteristic
267C22×C4—21no—
268C22×C4—311no—
269C22×C4—621no—
270C22×C4—621no—
271C22×C4—621no—
272C22×C4C22×D3111yescharacteristic
273SD16—622no—
274D8—1241no—
275D8—1241no—
276M16—1241no—
277C2×C8—311no—
278C2×C8—311no—
279C2×C8—1241no—
280C2×C8C22×D3111yescharacteristic
281C2×C8C22×D3111yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—311no—
284C4⋊C4—311no—
285C4⋊C4—621no—
286C4⋊C4—621no—
287C4⋊C4—621no—
288C4⋊C4C22×D3111yescharacteristic
289C4⋊C4C22×D3111yescharacteristic
290C4⋊C4C22×D3111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—311no—
293C22⋊C4—311no—
294C22⋊C4—621no—
295C22⋊C4—621no—
296C22⋊C4—621no—
297C22⋊C4—621no—
298C22⋊C4—621no—
299C42—311no—
300C42—621no—
301C42—621no—
302C23—21no—
303C23—311no—
304C23—621no—
305C23—621no—
306C23D4×D3111yescharacteristic
307Q8—312no—
308Q8—621no—
309D4—21no—
310D4—21no—
311D4—81no—
312D4—621no—
313D4—621no—
314D4—621no—
315D4—621no—
316D4—1241no—
317D4—1242no—
318D4—1242no—
319D4—1242no—
320D4—1242no—
321D4—2481no—
322D4—2481no—
323D4—2481no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—81no—
330C2×C4—311no—
331C2×C4—311no—
332C2×C4—311no—
333C2×C4—621no—
334C2×C4—621no—
335C2×C4—621no—
336C2×C4—621no—
337C2×C4—1242no—
338C2×C4—1242no—
339C2×C4—2481no—
340C2×C4D4×D3111yescharacteristic
341C2×C4C23×D3111yescharacteristic
342C8—21no—
343C8—21no—
344C8—621no—
345C8—621no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—621no—
353C22—621no—
354C22—621no—
355C22—1241no—
356C22—1241no—
357C22—1241no—
358C22—1241no—
359C22—1241no—
360C22—1241no—
361C22C2×D4×D3111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—621no—
367C4—622no—
368C4—621no—
369C4—621no—
370C4—1241no—
371C4#41×D3111yescharacteristic
372C4#1175856611yescharacteristic
373C2—41no—
374C2—81no—
375C2—1241no—
376C2—2481no—
377C2—2481no—
378C2#1452169111yescharacteristic
379C2#1452184811yescharacteristic
380C2#1452185011yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#480C2
socleC22×C31C22×D4
hypercenter#480D31
hypocenterC31#3309
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #14521747C2semidirect
2. #14521717C2semidirect
3. #14521412C2semidirect
4. #14521376C2semidirect
5. #14521355C2semidirect
6. #14521300C2semidirect
7. #14521286C2semidirect
8. #14521243C2semidirect
9. #14521196C2semidirect
10. #14521195C2semidirect
11. #14521148C2semidirect
12. #14521123C2semidirect
13. #14521048C2semidirect
14. #14521042C2semidirect
15. C31×#480C2semidirect
187. #480D31semidirect
249. C31#3309semidirect

Maximal subgroups

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

subgroupindex
#145217472
#145217172
#145214122
#145213762
#145213552
#145213002
#145212862
#145212432
#145211962
#145211952
#145211482
#145211232
#145210482
#145210422
C31×#4802
#330931