Finite Group Databasebeta

← #16858779

Subgroups — #16858779

Order 3968.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521784C211yesmaximal, characteristic, complemented
2#14521772C211yesmaximal, characteristic, complemented
3#14521443C211yesmaximal, characteristic, complemented
4#14521438C211yesmaximal, characteristic
5#14521433C211yesmaximal, characteristic, complemented
6#14521272C211yesmaximal, characteristic, complemented
7#14521272C211yesmaximal, characteristic, complemented
8#14521265C211yesmaximal, characteristic, complemented
9#14521265C211yesmaximal, characteristic, complemented
10#14521255C211yesmaximal, characteristic, complemented
11#14521250C211yesmaximal, characteristic, complemented
12#14521162C211yesmaximal, characteristic, complemented
13#14521157C211yesmaximal, characteristic, complemented
14C4×#92470C211yesmaximal, characteristic, complemented
15C31×#446C211yesmaximal, characteristic, complemented
16C4×Q8×C31C2211yescharacteristic
17#11758524—21no—
18#11758523—21no—
19C2×Dic124C2211yescharacteristic
20C2×Dic124C2211yescharacteristic
21C2×D248C2211yescharacteristic
22C2×D248C2211yescharacteristic
23C2×#92470C2211yescharacteristic
24C2×#92470C2211yescharacteristic
25C2×#92470C2211yescharacteristic
26C2×#92470C2211yescharacteristic
27C2×#92470C2211yescharacteristic
28#11758475—21no—
29#11758475—21no—
30#11758471—21no—
31#11758471—21no—
32#11758470—21no—
33#11758469—21no—
34#11758452C2211yescharacteristic
35#11758452C2211yescharacteristic
36#11758452C2211yescharacteristic
37#11758452C2211yescharacteristic
38#11758451C2211yescharacteristic
39C4×D124C2211yescharacteristic
40C4×D124C2211yescharacteristic
41C4×D124C2211yescharacteristic
42#11758446C2211yescharacteristic
43C4×Dic62C2211yescharacteristic
44C4×Dic62C2211yescharacteristic
45C4×Dic62C2211yescharacteristic
46C31×C4⋊C8C2211yescharacteristic
47C31×C4⋊C8C2211yescharacteristic
48C31×C4⋊C8C2211yescharacteristic
49C31×#97C2211yescharacteristic
50C31×#97C2211yescharacteristic
51C4×C8×C31C2211yescharacteristic
52#11758409C2211yescharacteristic
53#11758409C2211yescharacteristic
54#11758409C2211yescharacteristic
55#11758405C2211yescharacteristic
56#11758404C2211yescharacteristic
57#11758404C2211yescharacteristic
58#11758404C2211yescharacteristic
59C2×Q8×C31D411yescharacteristic
60C2×D124—21no—
61C2×D124—21no—
62C2×D124C2311yescharacteristic
63C2×D124C2311yescharacteristic
64C2×D124C2311yescharacteristic
65C2×C4×D31—21no—
66C2×C4×D31—21no—
67C2×C4×D31—21no—
68C2×Dic62C2311yescharacteristic
69C2×Dic62C2311yescharacteristic
70C2×Dic62C2311yescharacteristic
71C2×C8×C31C2311yescharacteristic
72C2×C8×C31C2311yescharacteristic
73C2×C8×C31C2311yescharacteristic
74C2×C8×C31C2311yescharacteristic
75C4⋊C4×C31D411yescharacteristic
76C4⋊C4×C31D411yescharacteristic
77C4⋊C4×C31D411yescharacteristic
78C42×C31C2311yescharacteristic
79C42×C31C2311yescharacteristic
80C42×C31C2311yescharacteristic
81(C2×D31)⋊C4—21no—
82(C2×D31)⋊C4—21no—
83(C2×D31)⋊C4—21no—
84(C2×D31)⋊C4—21no—
85(C2×D31)⋊C4—21no—
86(C2×D31)⋊C4—21no—
87(C2×D31)⋊C4—21no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92C4⋊Dic31—21no—
93C4⋊Dic31—21no—
94C4⋊Dic31C2311yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99C4×Dic31—21no—
100C4×Dic31—21no—
101C4×Dic31—21no—
102Dic124—22no—
103Dic124—41no—
104D248—22no—
105D248—41no—
106#92470—22no—
107#92470—41no—
108#92470—41no—
109#92470—41no—
110#92470—41no—
111C22×D31—21no—
112C22×D31—21no—
113C22×D31—21no—
114Q8×C31—41no—
115C2×C4×C31C2×D411yescharacteristic
116C2×C4×C31C2×D411yescharacteristic
117C2×C4×C31C2×D411yescharacteristic
118C2×C4×C31C2×D411yescharacteristic
119C2×C4×C31C2×D411yescharacteristic
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2411yescharacteristic
122C2×Dic31—21no—
123C2×Dic31—21no—
124C2×Dic31—21no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127D124—21no—
128D124—21no—
129D124—21no—
130D124—21no—
131D124—21no—
132D124—21no—
133D124—42no—
134D124—81no—
135C4×D31—42no—
136C4×D31—81no—
137C4×D31—81no—
138Dic62—21no—
139Dic62—21no—
140Dic62—21no—
141Dic62—21no—
142Dic62—21no—
143Dic62—21no—
144C8×C31—21no—
145C8×C31—21no—
146C8×C31—21no—
147C8×C31#4112yes—
148#3401—311nomaximal, Sylow
149C22×C31C22×D411yescharacteristic
150C2×D31—41no—
151C2×D31—41no—
152C2×D31—41no—
153C2×D31—41no—
154C2×D31—41no—
155C2×D31—41no—
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—21no—
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—21no—
165C4×C31C2×#4111yescharacteristic
166C4×C31H(5,𝔽2)11yescharacteristic
167Dic31—41no—
168Dic31—41no—
169Dic31—41no—
170Dic31—41no—
171Dic31—41no—
172#559—311no—
173#556—311no—
174#497—311no—
175#496—311no—
176#495—311no—
177#464—311no—
178#464—311no—
179#463—311no—
180#463—311no—
181#461—311no—
182#460—311no—
183#446D3111yescharacteristic, complemented
184#442—311no—
185#441—311no—
186C4×SD16—311no—
187C2×C31#55011yescharacteristic
188C2×C31#57511yescharacteristic
189C2×C31#57711yescharacteristic
190D31—81no—
191D31—81no—
192D31—81no—
193C2×Q16—311no—
194C2×Q16—311no—
195C2×SD16—311no—
196C2×SD16—311no—
197C2×SD16—311no—
198C2×SD16—311no—
199C2×SD16—311no—
200C2×D8—311no—
201C2×D8—311no—
202C4⋊Q8—311no—
203#127—311no—
204#126—621no—
205#126—621no—
206#124—311no—
207#124—311no—
208#124—311no—
209#124—311no—
210#124—621no—
211#123—621no—
212#123—621no—
213C22⋊Q8—621no—
214C4×Q8—311no—
215C4×Q8—311no—
216C4×Q8—311no—
217C4×Q8C2×D3111yescharacteristic
218C4×D4—311no—
219C4×D4—311no—
220C4×D4—311no—
221C4×D4—621no—
222#117—621no—
223#106—311no—
224C4⋊C8C2×D3111yescharacteristic
225C4⋊C8C2×D3111yescharacteristic
226C4⋊C8C2×D3111yescharacteristic
227#103—311no—
228#103—311no—
229#103—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#97C2×D3111yescharacteristic
234#97C2×D3111yescharacteristic
235C4×C8C2×D3111yescharacteristic
236C31#340111yescharacteristic, complemented, Sylow
237C2×Q8—311no—
238C2×Q8—311no—
239C2×Q8—311no—
240C2×Q8D12411yescharacteristic
241C2×D4—311no—
242C2×D4—311no—
243C2×D4—311no—
244C2×D4—621no—
245C2×D4—621no—
246C22×C4—621no—
247C22×C4—621no—
248C22×C4—621no—
249Q16—622no—
250Q16—1241no—
251SD16—622no—
252SD16—1241no—
253SD16—1241no—
254SD16—1241no—
255SD16—1241no—
256D8—622no—
257D8—1241no—
258C2×C8C22×D3111yescharacteristic
259C2×C8C22×D3111yescharacteristic
260C2×C8C22×D3111yescharacteristic
261C2×C8C22×D3111yescharacteristic
262C4⋊C4—311no—
263C4⋊C4—311no—
264C4⋊C4—621no—
265C4⋊C4—621no—
266C4⋊C4—621no—
267C4⋊C4—621no—
268C4⋊C4—621no—
269C4⋊C4D12411yescharacteristic
270C4⋊C4D12411yescharacteristic
271C4⋊C4D12411yescharacteristic
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C22⋊C4—621no—
276C22⋊C4—621no—
277C22⋊C4—621no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C42—621no—
284C42—621no—
285C42—621no—
286C42C22×D3111yescharacteristic
287C42C22×D3111yescharacteristic
288C42C22×D3111yescharacteristic
289C23—621no—
290C23—621no—
291C23—621no—
292Q8—41no—
293Q8—621no—
294Q8—621no—
295Q8—621no—
296Q8—621no—
297Q8—621no—
298Q8—621no—
299D4—621no—
300D4—621no—
301D4—621no—
302D4—621no—
303D4—621no—
304D4—621no—
305D4—1242no—
306D4—2481no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—621no—
310C2×C4—621no—
311C2×C4—621no—
312C2×C4—1242no—
313C2×C4—2481no—
314C2×C4—2481no—
315C2×C4C2×D12411yescharacteristic
316C2×C4C2×D12411yescharacteristic
317C2×C4C2×D12411yescharacteristic
318C2×C4C2×D12411yescharacteristic
319C2×C4C2×D12411yescharacteristic
320C2×C4C2×D12411yescharacteristic
321C2×C4C23×D3111yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8#9249912yes—
326C22—1241no—
327C22—1241no—
328C22—1241no—
329C22—1241no—
330C22—1241no—
331C22—1241no—
332C22—1241no—
333C22—1241no—
334C22—1241no—
335C22C22×D12411yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—1241no—
343C4—1241no—
344C4—1241no—
345C4—1241no—
346C4—1241no—
347C4C2×#9249911yescharacteristic
348C4#1175856611yescharacteristic
349C2—2481no—
350C2—2481no—
351C2—2481no—
352C2#1452172111yescharacteristic
353C2#1452184911yescharacteristic
354C2#1452186111yescharacteristic
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#446C2
socleC22×C31C22×D4
prime radical#14521438C2
hypercenter#446D31
hypocenterC31#3401
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #14521784C2semidirect
2. #14521772C2semidirect
3. #14521443C2semidirect
5. #14521433C2semidirect
6. #14521272C2semidirect
7. #14521272C2semidirect
8. #14521265C2semidirect
9. #14521265C2semidirect
10. #14521255C2semidirect
11. #14521250C2semidirect
12. #14521162C2semidirect
13. #14521157C2semidirect
14. C4×#92470C2semidirect
15. C31×#446C2semidirect
183. #446D31semidirect
236. C31#3401semidirect

Maximal subgroups

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

subgroupindex
#145217842
#145217722
#145214432
#145214382
#145214332
#145212722
#145212652
#145212552
#145212502
#145211622
#145211572
C4×#924702
C31×#4462
#340131