Finite Group Databasebeta

← #16857718

Subgroups — #16857718

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#14521718C211yesmaximal, characteristic, complemented
3#14521412C211yesmaximal, characteristic, complemented
4#14521372C211yesmaximal, characteristic, complemented
5#14521362C211yesmaximal, characteristic, complemented
6#14521354C211yesmaximal, characteristic, complemented
7#14521302C211yesmaximal, characteristic, complemented
8#14521284C211yesmaximal, characteristic, complemented
9#14521243C211yesmaximal, characteristic, complemented
10#14521197C211yesmaximal, characteristic, complemented
11#14521194C211yesmaximal, characteristic, complemented
12#14521152C211yesmaximal, characteristic, complemented
13#14521118C211yesmaximal, characteristic, complemented
14#14521044C211yesmaximal, characteristic, complemented
15C31×#417C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×#92499C2211yescharacteristic
18C2×M16×C31C2211yescharacteristic
19C2×C4⋊C4×C31C2211yescharacteristic
20Q8×Dic31C2211yescharacteristic
21C2×#92481C2211yescharacteristic
22#11758517—21no—
23#11758517C2211yescharacteristic
24#11758515—21no—
25#11758515C2211yescharacteristic
26C2×#92479C2211yescharacteristic
27#11758507—21no—
28#11758507—21no—
29#11758507C2211yescharacteristic
30#11758507C2211yescharacteristic
31C4×C22⋊D31—21no—
32C4×C22⋊D31—21no—
33C4×C22⋊D31C2211yescharacteristic
34C2×D248C2211yescharacteristic
35C2×C8×D31C2211yescharacteristic
36#11758475—21no—
37#11758472C2211yescharacteristic
38#11758471—21no—
39#11758470C2211yescharacteristic
40#11758469C2211yescharacteristic
41#11758467C2211yescharacteristic
42C31×#103C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#102C2211yescharacteristic
45C31×#102C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758420C2211yescharacteristic
48C22⋊(C31⋊C8)C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758409C2211yescharacteristic
51(C2×D31)⋊C8C2211yescharacteristic
52#11758405C2211yescharacteristic
53#11758403C2211yescharacteristic
54Dic31⋊C8C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758395C2211yescharacteristic
59#41×C31—22no—
60#41×C31—41no—
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31—21no—
63C2×D4×C31C2311yescharacteristic
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31C2311yescharacteristic
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69C2×C22⋊D31—21no—
70C2×C22⋊D31—21no—
71C2×C22⋊D31—21no—
72C2×C22⋊D31D411yescharacteristic
73#92499—22no—
74#92499—41no—
75C2×D124—21no—
76C2×D124—21no—
77C2×D124C2311yescharacteristic
78C2×D124C2311yescharacteristic
79C2×C4×D31—21no—
80C2×C4×D31—21no—
81C2×C4×D31C2311yescharacteristic
82M16×C31—41no—
83C2×C8×C31C2311yescharacteristic
84C2×C8×C31C2311yescharacteristic
85C4⋊C4×C31—21no—
86C4⋊C4×C31C2311yescharacteristic
87C4⋊C4×C31C2311yescharacteristic
88C22⋊Dic31—21no—
89C22⋊Dic31D411yescharacteristic
90#92481—22no—
91#92479—41no—
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—
97(C2×D31)⋊C4D411yescharacteristic
98C4⋊Dic31—21no—
99C4⋊Dic31—21no—
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4D411yescharacteristic
104C4×Dic31—21no—
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109D248—41no—
110C8×D31—41no—
111C23×C31—21no—
112C23×C31C2×D411yescharacteristic
113C22×D31—21no—
114C22×D31—21no—
115C22×D31C2×D411yescharacteristic
116Q8×C31—21no—
117Q8×C31#4112yes—
118D4×C31—21no—
119D4×C31—21no—
120D4×C31—42no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—42no—
127C2×C4×C31—81no—
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2411yescharacteristic
130C22⋊D31—41no—
131C22⋊D31—42no—
132C22⋊D31—42no—
133C22⋊D31—81no—
134C22⋊D31—81no—
135C22⋊D31—81no—
136C2×Dic31—21no—
137C2×Dic31—21no—
138C2×Dic31C2×D411yescharacteristic
139C2×Dic31C2×D411yescharacteristic
140C2×Dic31C2×D411yescharacteristic
141D124—21no—
142D124—21no—
143D124—21no—
144D124—21no—
145D124—42no—
146D124—81no—
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×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—22no—
173C4×C31—21no—
174C4×C31—41no—
175C4×C31—41no—
176C4×C31C2×#4111yescharacteristic
177C4×C31H(5,𝔽2)11yescharacteristic
178Dic31—21no—
179Dic31—21no—
180Dic31—21no—
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#449—311no—
194#440—311no—
195#435—311no—
196#417D3111yescharacteristic, complemented
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×#41C2×D3111yescharacteristic
208C2×SD16—311no—
209C2×D8—311no—
210C2×D8—311no—
211C2×M16C2×D3111yescharacteristic
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—311no—
222#121—621no—
223#121—621no—
224#121—621no—
225C4×Q8—311no—
226C4×D4—311no—
227C4×D4—311no—
228C4×D4—621no—
229C4×D4—621no—
230#117—311no—
231C2×C4⋊C4C2×D3111yescharacteristic
232#107—311no—
233#107—311no—
234#106—311no—
235C4⋊C8—311no—
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#102C2×D3111yescharacteristic
245#102C2×D3111yescharacteristic
246C22⋊C8—311no—
247C22⋊C8—311no—
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—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—21no—
269C22×C4—311no—
270C22×C4—621no—
271C22×C4—621no—
272C22×C4C22×D3111yescharacteristic
273SD16—622no—
274D8—1241no—
275D8—1241no—
276M16—41no—
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—311no—
286C4⋊C4—621no—
287C4⋊C4—621no—
288C4⋊C4—621no—
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—311no—
300C42—621no—
301C42—621no—
302C23—21no—
303C23—311no—
304C23—621no—
305C23—621no—
306C23D4×D3111yescharacteristic
307Q8—21no—
308Q8#9249512yes—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—621no—
313D4—621no—
314D4—621no—
315D4—621no—
316D4—1242no—
317D4—1241no—
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—21no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—311no—
332C2×C4—311no—
333C2×C4—311no—
334C2×C4—621no—
335C2×C4—621no—
336C2×C4—621no—
337C2×C4—621no—
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—22no—
364C4—41no—
365C4—41no—
366C4—621no—
367C4—621no—
368C4—621no—
369C4—1241no—
370C4—1241no—
371C4C2×#9249511yescharacteristic
372C4#1175856111yescharacteristic
373C2—41no—
374C2—81no—
375C2—1241no—
376C2—2481no—
377C2—2481no—
378C2#1452168911yescharacteristic
379C2#1452184811yescharacteristic
380C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#417C2
socleC22×C31C22×D4
hypercenter#417D31
hypocenterC31#3309
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #14521747C2semidirect
2. #14521718C2semidirect
3. #14521412C2semidirect
4. #14521372C2semidirect
5. #14521362C2semidirect
6. #14521354C2semidirect
7. #14521302C2semidirect
8. #14521284C2semidirect
9. #14521243C2semidirect
10. #14521197C2semidirect
11. #14521194C2semidirect
12. #14521152C2semidirect
13. #14521118C2semidirect
14. #14521044C2semidirect
15. C31×#417C2semidirect
196. #417D31semidirect
249. C31#3309semidirect

Maximal subgroups

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

subgroupindex
#145217472
#145217182
#145214122
#145213722
#145213622
#145213542
#145213022
#145212842
#145212432
#145211972
#145211942
#145211522
#145211182
#145210442
C31×#4172
#330931