Finite Group Databasebeta

← #16857714

Subgroups — #16857714

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#14521752C211yesmaximal, characteristic, complemented
2#14521721C211yesmaximal, characteristic, complemented
3#14521415C211yesmaximal, characteristic, complemented
4#14521375C211yesmaximal, characteristic, complemented
5#14521364C211yesmaximal, characteristic, complemented
6#14521303C211yesmaximal, characteristic, complemented
7#14521286C211yesmaximal, characteristic, complemented
8#14521245C211yesmaximal, characteristic, complemented
9#14521197C211yesmaximal, characteristic, complemented
10#14521197C211yesmaximal, characteristic, complemented
11#14521147C211yesmaximal, characteristic, complemented
12#14521119C211yesmaximal, characteristic, complemented
13#14521049C211yesmaximal, characteristic, complemented
14#14521044C211yesmaximal, characteristic, complemented
15C31×#479C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C2×#92499C2211yescharacteristic
18C31×#125C2211yescharacteristic
19C4×Q8×C31C2211yescharacteristic
20C2×#92481C2211yescharacteristic
21C2×D248C2211yescharacteristic
22C2×D248C2211yescharacteristic
23C2×#92469C2211yescharacteristic
24C2×C8×D31C2211yescharacteristic
25#11758475—21no—
26#11758472—21no—
27#11758472—21no—
28#11758472—21no—
29#11758472C2211yescharacteristic
30#11758472C2211yescharacteristic
31#11758472C2211yescharacteristic
32#11758472C2211yescharacteristic
33#11758471—21no—
34#11758470—21no—
35#11758469C2211yescharacteristic
36C4⋊C4×D31C2211yescharacteristic
37#11758451—21no—
38#11758451C2211yescharacteristic
39C4×D124—21no—
40C4×D124C2211yescharacteristic
41C4×D124C2211yescharacteristic
42C31×#107C2211yescharacteristic
43C31×#106C2211yescharacteristic
44C31×C4⋊C8C2211yescharacteristic
45C31×#103C2211yescharacteristic
46C31×#103C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51(C2×D31)⋊C8C2211yescharacteristic
52#11758397C2211yescharacteristic
53#11758397C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60#92499—22no—
61#92499—22no—
62#92499—41no—
63#92499—41no—
64C2×D124—21no—
65C2×D124—21no—
66C2×D124—21no—
67C2×D124—21no—
68C2×D124—21no—
69C2×D124—21no—
70C2×D124—21no—
71C2×D124—21no—
72C2×D124D411yescharacteristic
73C2×D124C2311yescharacteristic
74C2×D124C2311yescharacteristic
75C2×D124C2311yescharacteristic
76C2×C4×D31—21no—
77C2×C4×D31—21no—
78C2×C4×D31—21no—
79C2×C4×D31—21no—
80C2×C4×D31C2311yescharacteristic
81C2×C4×D31C2311yescharacteristic
82C2×C8×C31C2311yescharacteristic
83C2×C8×C31C2311yescharacteristic
84C4⋊C4×C31—21no—
85C4⋊C4×C31—21no—
86C4⋊C4×C31—21no—
87C4⋊C4×C31C2311yescharacteristic
88C4⋊C4×C31C2311yescharacteristic
89C4⋊C4×C31C2311yescharacteristic
90C42×C31—21no—
91C42×C31C2311yescharacteristic
92#92481—22no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98(C2×D31)⋊C4—21no—
99(C2×D31)⋊C4D411yescharacteristic
100(C2×D31)⋊C4D411yescharacteristic
101C4⋊Dic31D411yescharacteristic
102C4⋊Dic31C2311yescharacteristic
103Dic31⋊C4—21no—
104C4×Dic31—21no—
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107D248—41no—
108D248—41no—
109#92469—41no—
110C8×D31—41no—
111C22×D31—21no—
112C22×D31—21no—
113C22×D31—21no—
114C22×D31C2×D411yescharacteristic
115C22×D31C2×D411yescharacteristic
116Q8×C31—21no—
117Q8×C31#4112yes—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31C2×D411yescharacteristic
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2411yescharacteristic
125C2×Dic31—21no—
126C2×Dic31C2×D411yescharacteristic
127C2×Dic31C2×D411yescharacteristic
128D124—21no—
129D124—21no—
130D124—21no—
131D124—21no—
132D124—21no—
133D124—21no—
134D124—41no—
135D124—42no—
136D124—42no—
137D124—42no—
138D124—42no—
139D124—81no—
140D124—81no—
141D124—81no—
142D124—81no—
143C4×D31—21no—
144C4×D31—21no—
145C4×D31—21no—
146C4×D31—21no—
147C4×D31—42no—
148C4×D31—42no—
149C4×D31—81no—
150C4×D31—81no—
151C8×C31—21no—
152C8×C31—21no—
153C31⋊C8—21no—
154C31⋊C8—21no—
155#3309—311nomaximal, Sylow
156C22×C31C22×D411yescharacteristic
157C2×D31—21no—
158C2×D31—21no—
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—21no—
162C2×D31—21no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C2×D31—41no—
167C2×D31—41no—
168C2×D31—41no—
169C2×D31—41no—
170C2×D31—41no—
171C2×D31—41no—
172C4×C31—22no—
173C4×C31—21no—
174C4×C31—21no—
175C4×C31—41no—
176C4×C31—41no—
177C4×C31—41no—
178C4×C31C2×#4111yescharacteristic
179C4×C31H(5,𝔽2)11yescharacteristic
180Dic31—21no—
181Dic31—21no—
182Dic31—41no—
183#553—311no—
184#550—311no—
185#490—311no—
186#482—311no—
187#480—311no—
188#479D3111yescharacteristic, complemented
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#54611yescharacteristic
199C2×C31#57511yescharacteristic
200C2×C31#57611yescharacteristic
201D31—41no—
202D31—41no—
203D31—81no—
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#125C2×D3111yescharacteristic
217#123—621no—
218#121—311no—
219#121—311no—
220#121—311no—
221#121—311no—
222#121—621no—
223#121—621no—
224#121—621no—
225C4×Q8C2×D3111yescharacteristic
226C4×D4—311no—
227C4×D4—311no—
228C4×D4—621no—
229C4×D4—621no—
230#117—311no—
231C2×C4⋊C4—311no—
232#107—311no—
233#107C2×D3111yescharacteristic
234#106C2×D3111yescharacteristic
235C4⋊C8C2×D3111yescharacteristic
236#103—311no—
237#103C2×D3111yescharacteristic
238#103C2×D3111yescharacteristic
239#102—311no—
240#102—311no—
241#102—311no—
242#102—311no—
243#102—311no—
244#102—311no—
245#102—311no—
246C22⋊C8—311no—
247C22⋊C8—311no—
248#97—311no—
249C31#330911yescharacteristic, complemented, Sylow
250#41—622no—
251#41—622no—
252#41—1241no—
253#41—1241no—
254C2×Q8C22×D3111yescharacteristic
255C2×D4—311no—
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×D4—621no—
267C22×C4—311no—
268C22×C4—311no—
269C22×C4—621no—
270C22×C4—621no—
271C22×C4—621no—
272C22×C4—621no—
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—21no—
284C4⋊C4—21no—
285C4⋊C4—311no—
286C4⋊C4—311no—
287C4⋊C4—621no—
288C4⋊C4C22×D3111yescharacteristic
289C4⋊C4C22×D3111yescharacteristic
290C4⋊C4C22×D3111yescharacteristic
291C22⋊C4—311no—
292C22⋊C4—311no—
293C22⋊C4—621no—
294C22⋊C4—621no—
295C22⋊C4—621no—
296C22⋊C4—621no—
297C22⋊C4—621no—
298C22⋊C4—621no—
299C42—21no—
300C42—621no—
301C42C22×D3111yescharacteristic
302C23—311no—
303C23—311no—
304C23—621no—
305C23—621no—
306C23—621no—
307Q8—21no—
308Q8#9249912yes—
309D4—621no—
310D4—621no—
311D4—621no—
312D4—621no—
313D4—621no—
314D4—621no—
315D4—1241no—
316D4—1242no—
317D4—1242no—
318D4—1242no—
319D4—1242no—
320D4—2481no—
321D4—2481no—
322D4—2481no—
323D4—2481no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—311no—
329C2×C4—311no—
330C2×C4—621no—
331C2×C4—621no—
332C2×C4—621no—
333C2×C4—621no—
334C2×C4—621no—
335C2×C4—1242no—
336C2×C4—1242no—
337C2×C4—2481no—
338C2×C4—2481no—
339C2×C4D4×D3111yescharacteristic
340C2×C4D4×D3111yescharacteristic
341C2×C4C23×D3111yescharacteristic
342C8—21no—
343C8—21no—
344C8—621no—
345C8—621no—
346C22—621no—
347C22—621no—
348C22—621no—
349C22—621no—
350C22—621no—
351C22—621no—
352C22—1241no—
353C22—1241no—
354C22—1241no—
355C22—1241no—
356C22—1241no—
357C22—1241no—
358C22—1241no—
359C22—1241no—
360C22—1241no—
361C22C2×D4×D3111yescharacteristic
362C4—22no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—621no—
369C4—621no—
370C4—1241no—
371C4C2×#9249911yescharacteristic
372C4#1175856611yescharacteristic
373C2—1241no—
374C2—1241no—
375C2—2481no—
376C2—2481no—
377C2—2481no—
378C2#1452169011yescharacteristic
379C2#1452184811yescharacteristic
380C2#1452185111yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#479C2
socleC22×C31C22×D4
hypercenter#479D31
hypocenterC31#3309
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #14521752C2semidirect
2. #14521721C2semidirect
3. #14521415C2semidirect
4. #14521375C2semidirect
5. #14521364C2semidirect
6. #14521303C2semidirect
7. #14521286C2semidirect
8. #14521245C2semidirect
9. #14521197C2semidirect
10. #14521197C2semidirect
11. #14521147C2semidirect
12. #14521119C2semidirect
13. #14521049C2semidirect
14. #14521044C2semidirect
15. C31×#479C2semidirect
188. #479D31semidirect
249. C31#3309semidirect

Maximal subgroups

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

subgroupindex
#145217522
#145217212
#145214152
#145213752
#145213642
#145213032
#145212862
#145212452
#145211972
#145211472
#145211192
#145210492
#145210442
C31×#4792
#330931