Finite Group Databasebeta

← #16857721

Subgroups — #16857721

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#14521746C211yesmaximal, characteristic, complemented
2#14521718C211yesmaximal, characteristic, complemented
3#14521412C211yesmaximal, characteristic, complemented
4#14521374C211yesmaximal, characteristic, complemented
5#14521361C211yesmaximal, characteristic, complemented
6#14521354C211yesmaximal, characteristic, complemented
7#14521299C211yesmaximal, characteristic, complemented
8#14521283C211yesmaximal, characteristic, complemented
9#14521242C211yesmaximal, characteristic, complemented
10#14521193C211yesmaximal, characteristic, complemented
11#14521150C211yesmaximal, characteristic, complemented
12#14521117C211yesmaximal, characteristic, complemented
13#14521049C211yesmaximal, characteristic, complemented
14#14521045C211yesmaximal, characteristic, complemented
15C31×#449C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×#92499C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic
19C2×D8×C31C2211yescharacteristic
20C31×#121C2211yescharacteristic
21Q8×Dic31C2211yescharacteristic
22#11758517—21no—
23#11758517C2211yescharacteristic
24#11758515—21no—
25#11758515—21no—
26#11758515C2211yescharacteristic
27#11758515C2211yescharacteristic
28#11758512—21no—
29D4×Dic31C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31#11758507—21no—
32#11758507C2211yescharacteristic
33C4×C22⋊D31—21no—
34C4×C22⋊D31C2211yescharacteristic
35#11758503C2211yescharacteristic
36C22×C31⋊C8C2211yescharacteristic
37C2×#92469C2211yescharacteristic
38C4⋊C4×D31C2211yescharacteristic
39#11758467C2211yescharacteristic
40(C22⋊D31)⋊C4—21no—
41#11758456—21no—
42C31×#103C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C31×C22⋊C8C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic
50#11758409C2211yescharacteristic
51#11758409C2211yescharacteristic
52(C2×D31)⋊C8C2211yescharacteristic
53#11758406C2211yescharacteristic
54#11758405C2211yescharacteristic
55#11758403C2211yescharacteristic
56Dic31⋊C8C2211yescharacteristic
57#11758397C2211yescharacteristic
58#11758395C2211yescharacteristic
59#41×C31—22no—
60#41×C31—41no—
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31—21no—
63C2×D4×C31—21no—
64C2×D4×C31C2311yescharacteristic
65C2×D4×C31C2311yescharacteristic
66C22×C4×C31—21no—
67C22×C4×C31C2311yescharacteristic
68C2×C22⋊D31—21no—
69C2×C22⋊D31—21no—
70C2×C22⋊D31—21no—
71C2×C22⋊D31—21no—
72C2×C22⋊D31—21no—
73C2×C22⋊D31D411yescharacteristic
74C22×Dic31—21no—
75#92499—22no—
76#92499—41no—
77C2×D124—21no—
78C2×D124C2311yescharacteristic
79C2×C4×D31—21no—
80C2×C4×D31—21no—
81C2×C4×D31C2311yescharacteristic
82SD16×C31—22no—
83D8×C31—41no—
84C2×C8×C31C2311yescharacteristic
85C2×C8×C31C2311yescharacteristic
86C4⋊C4×C31C2311yescharacteristic
87C22⋊C4×C31—21no—
88C22⋊Dic31—21no—
89C22⋊Dic31—21no—
90C22⋊Dic31—21no—
91C22⋊Dic31—21no—
92C22⋊Dic31D411yescharacteristic
93#92479—41no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4D411yescharacteristic
96C4⋊Dic31—21no—
97C4⋊Dic31—21no—
98C4⋊Dic31C2311yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4D411yescharacteristic
104C4×Dic31—21no—
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107C2×C31⋊C8—41no—
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110#92469—41no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31C2×D411yescharacteristic
114C22×D31—21no—
115C22×D31C2×D411yescharacteristic
116Q8×C31—21no—
117Q8×C31#4112yes—
118D4×C31—21no—
119D4×C31—21no—
120D4×C31—21no—
121D4×C31—21no—
122D4×C31—42no—
123D4×C31—81no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—42no—
129C2×C4×C31C2×D411yescharacteristic
130C2×C4×C31C2411yescharacteristic
131C22⋊D31—41no—
132C22⋊D31—42no—
133C22⋊D31—42no—
134C22⋊D31—81no—
135C22⋊D31—81no—
136C22⋊D31—81no—
137C2×Dic31—21no—
138C2×Dic31—21no—
139C2×Dic31—21no—
140C2×Dic31—81no—
141C2×Dic31C2×D411yescharacteristic
142C2×Dic31C2×D411yescharacteristic
143C2×Dic31C2×D411yescharacteristic
144D124—21no—
145D124—21no—
146D124—42no—
147C4×D31—21no—
148C4×D31—21no—
149C4×D31—42no—
150C4×D31—81no—
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×C31—41no—
163C22×C31—41no—
164C22×C31—41no—
165C22×C31C22×D411yescharacteristic
166C2×D31—21no—
167C2×D31—21no—
168C2×D31—21no—
169C2×D31—41no—
170C2×D31—41no—
171C2×D31—41no—
172C4×C31—22no—
173C4×C31—21no—
174C4×C31—41no—
175C4×C31C2×#4111yescharacteristic
176C4×C31H(5,𝔽2)11yescharacteristic
177Dic31—21no—
178Dic31—21no—
179Dic31—21no—
180Dic31—41no—
181Dic31—41no—
182Dic31—41no—
183#553—311no—
184#550—311no—
185#490—311no—
186#482—311no—
187#480—311no—
188#479—311no—
189#469—311no—
190#466—311no—
191#459—311no—
192#449—311no—
193#449D3111yescharacteristic, complemented
194#440—311no—
195#435—311no—
196#417—311no—
197#416—311no—
198C2×C31—41no—
199C2×C31—81no—
200C2×C31—81no—
201C2×C31#54611yescharacteristic
202C2×C31#57511yescharacteristic
203C2×C31#57611yescharacteristic
204D31—41no—
205D31—81no—
206C2×#41—311no—
207C2×#41C2×D3111yescharacteristic
208C2×SD16C2×D3111yescharacteristic
209C2×D8—311no—
210C2×D8C2×D3111yescharacteristic
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⋊C4—311no—
232#107—311no—
233#107—311no—
234#106—311no—
235C4⋊C8—311no—
236#103—311no—
237#103—311no—
238#103C2×D3111yescharacteristic
239#102—311no—
240#102—311no—
241#102—311no—
242#102—311no—
243#102—311no—
244#102—311no—
245#102C2×D3111yescharacteristic
246C22⋊C8—311no—
247C22⋊C8C2×D3111yescharacteristic
248#97—311no—
249C31#330911yescharacteristic, complemented, Sylow
250#41—22no—
251#41—41no—
252#41—622no—
253#41—1241no—
254C2×Q8C22×D3111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
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×D4C22×D3111yescharacteristic
266C2×D4C22×D3111yescharacteristic
267C22×C4—21no—
268C22×C4—311no—
269C22×C4—621no—
270C22×C4—621no—
271C22×C4—621no—
272C22×C4C22×D3111yescharacteristic
273SD16—22no—
274D8—41no—
275D8—1241no—
276M16—1241no—
277C2×C8—311no—
278C2×C8—311no—
279C2×C8—1241no—
280C2×C8C22×D3111yescharacteristic
281C2×C8C22×D3111yescharacteristic
282C4⋊C4—311no—
283C4⋊C4—311no—
284C4⋊C4—311no—
285C4⋊C4—311no—
286C4⋊C4—621no—
287C4⋊C4—621no—
288C4⋊C4—621no—
289C4⋊C4—621no—
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—21no—
304C23—311no—
305C23—621no—
306C23D4×D3111yescharacteristic
307Q8—21no—
308Q8#9249712yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—81no—
315D4—621no—
316D4—621no—
317D4—1242no—
318D4—1241no—
319D4—1242no—
320D4—1242no—
321D4—2481no—
322D4—2481no—
323D4—2481no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—311no—
330C2×C4—311no—
331C2×C4—311no—
332C2×C4—621no—
333C2×C4—621no—
334C2×C4—621no—
335C2×C4—621no—
336C2×C4—621no—
337C2×C4—1242no—
338C2×C4—2481no—
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—41no—
353C22—41no—
354C22—41no—
355C22—621no—
356C22—621no—
357C22—621no—
358C22—1241no—
359C22—1241no—
360C22—1241no—
361C22C2×D4×D3111yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—621no—
366C4—621no—
367C4—621no—
368C4—1241no—
369C4—1241no—
370C4—1241no—
371C4C2×#9249711yescharacteristic
372C4#1175856111yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—1241no—
377C2—2481no—
378C2#1452168611yescharacteristic
379C2#1452184611yescharacteristic
380C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#449C2
socleC22×C31C22×D4
hypercenter#449D31
hypocenterC31#3309
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14521746C2semidirect
2. #14521718C2semidirect
3. #14521412C2semidirect
4. #14521374C2semidirect
5. #14521361C2semidirect
6. #14521354C2semidirect
7. #14521299C2semidirect
8. #14521283C2semidirect
9. #14521242C2semidirect
10. #14521193C2semidirect
11. #14521150C2semidirect
12. #14521117C2semidirect
13. #14521049C2semidirect
14. #14521045C2semidirect
15. C31×#449C2semidirect
193. #449D31semidirect
249. C31#3309semidirect

Maximal subgroups

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

subgroupindex
#145217462
#145217182
#145214122
#145213742
#145213612
#145213542
#145212992
#145212832
#145212422
#145211932
#145211502
#145211172
#145210492
#145210452
C31×#4492
#330931