Finite Group Databasebeta

← #16857782

Subgroups — #16857782

Order 3968.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521772C211yesmaximal, characteristic, complemented
2#14521711C211yesmaximal, characteristic
3#14521409C211yesmaximal, characteristic, complemented
4#14521393C211yesmaximal, characteristic, complemented
5#14521375C211yesmaximal, characteristic, complemented
6#14521344C211yesmaximal, characteristic, complemented
7#14521298C211yesmaximal, characteristic, complemented
8#14521289C211yesmaximal, characteristic, complemented
9#14521271C211yesmaximal, characteristic, complemented
10#14521210C211yesmaximal, characteristic, complemented
11#14521203C211yesmaximal, characteristic, complemented
12#14521122C211yesmaximal, characteristic, complemented
13#14521056C211yesmaximal, characteristic, complemented
14#14521044C211yesmaximal, characteristic, complemented
15C31×#441C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C2×Q8×D31C2211yescharacteristic
18C2×Q16×C31C2211yescharacteristic
19C4×Q8×C31C2211yescharacteristic
20C4×Q8×C31C2211yescharacteristic
21#11758523C2211yescharacteristic
22#11758523C2211yescharacteristic
23C2×#92482C2211yescharacteristic
24C2×#92481C2211yescharacteristic
25C2×#92469C2211yescharacteristic
26C2×C8×D31C2211yescharacteristic
27#11758475—21no—
28#11758475—21no—
29#11758474—21no—
30#11758474C2211yescharacteristic
31#11758472—21no—
32#11758472C2211yescharacteristic
33#11758469C2211yescharacteristic
34#11758469C2211yescharacteristic
35#11758452—21no—
36#11758452—21no—
37#11758452C2211yescharacteristic
38C4×D124—21no—
39C4×D124C2211yescharacteristic
40#11758446C2211yescharacteristic
41C4×Dic62—21no—
42C31×#106C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#103C2211yescharacteristic
45C31×#97C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51(C2×D31)⋊C8C2211yescharacteristic
52#11758404C2211yescharacteristic
53#11758404C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758395C2211yescharacteristic
57#11758395C2211yescharacteristic
58C4⋊(C31⋊C8)C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×Q8×C31C2311yescharacteristic
61#92499—22no—
62#92499—41no—
63Q8×D31—22no—
64Q8×D31—41no—
65C2×D124—21no—
66C2×D124—21no—
67C2×D124D411yescharacteristic
68C2×D124C2311yescharacteristic
69C2×C4×D31—21no—
70C2×C4×D31—21no—
71C2×C4×D31C2311yescharacteristic
72C2×C4×D31C2311yescharacteristic
73C2×Dic62—21no—
74C2×Dic62—21no—
75C2×Dic62C2311yescharacteristic
76Q16×C31—22no—
77C2×C8×C31C2311yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C4⋊C4×C31—21no—
80C4⋊C4×C31—21no—
81C4⋊C4×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C42×C31—21no—
84C42×C31—21no—
85C42×C31C2311yescharacteristic
86#92482—41no—
87#92481—41no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
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
97(C2×D31)⋊C4D411yescharacteristic
98C4⋊Dic31—21no—
99C4⋊Dic31—21no—
100C4⋊Dic31D411yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102C4⋊Dic31C2311yescharacteristic
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105C4×Dic31—21no—
106C4×Dic31—21no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109#92469—41no—
110C8×D31—41no—
111C22×D31—21no—
112C22×D31C2×D411yescharacteristic
113C22×D31C2×D411yescharacteristic
114Q8×C31—21no—
115Q8×C31—21no—
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×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130D124—21no—
131D124—21no—
132D124—41no—
133D124—42no—
134D124—42no—
135C4×D31—21no—
136C4×D31—21no—
137C4×D31—21no—
138C4×D31—21no—
139C4×D31—42no—
140C4×D31—42no—
141Dic62—21no—
142Dic62—21no—
143Dic62—42no—
144Dic62—42no—
145C8×C31—21no—
146C8×C31—21no—
147C31⋊C8—21no—
148C31⋊C8—21no—
149#3313—311nomaximal, Sylow
150C22×C31C22×D411yescharacteristic
151C2×D31—21no—
152C2×D31—21no—
153C2×D31—21no—
154C2×D31—21no—
155C2×D31—21no—
156C2×D31—21no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C4×C31—22no—
161C4×C31—21no—
162C4×C31—21no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31C2×#4111yescharacteristic
167C4×C31H(5,𝔽2)11yescharacteristic
168Dic31—21no—
169Dic31—21no—
170Dic31—41no—
171Dic31—41no—
172Dic31—41no—
173#556—311no—
174#548—311no—
175#489—311no—
176#485—311no—
177#482—311no—
178#477—311no—
179#468—311no—
180#467—311no—
181#464—311no—
182#452—311no—
183#451—311no—
184#441D3111yescharacteristic, complemented
185#435—311no—
186#419—311no—
187#416—311no—
188C2×C31#54611yescharacteristic
189C2×C31#57511yescharacteristic
190C2×C31#57811yescharacteristic
191D31—41no—
192D31—41no—
193D31—81no—
194C2×#41—311no—
195C22×Q8—311no—
196C2×Q16—311no—
197C2×Q16C2×D3111yescharacteristic
198C2×SD16—311no—
199C2×M16—311no—
200C22×C8—311no—
201C4⋊Q8—311no—
202#126—621no—
203#126—621no—
204#124—311no—
205#124—621no—
206#124—621no—
207C22⋊Q8—311no—
208C22⋊Q8—311no—
209C22⋊Q8—311no—
210C22⋊Q8—621no—
211#121—311no—
212#121—621no—
213C4×Q8—621no—
214C4×Q8C2×D3111yescharacteristic
215C4×Q8C2×D3111yescharacteristic
216C4×D4—311no—
217C4×D4—621no—
218#117—311no—
219#117—311no—
220#107—311no—
221#107—311no—
222#106C2×D3111yescharacteristic
223C4⋊C8—311no—
224#103—311no—
225#103—311no—
226#103—311no—
227#103—311no—
228#103—311no—
229#103C2×D3111yescharacteristic
230#103C2×D3111yescharacteristic
231#102—311no—
232#102—311no—
233#102—311no—
234C22⋊C8—311no—
235C22⋊C8—311no—
236#97C2×D3111yescharacteristic
237C31#331311yescharacteristic, complemented, Sylow
238#41—622no—
239#41—1241no—
240C2×Q8—311no—
241C2×Q8—621no—
242C2×Q8—621no—
243C2×Q8—622no—
244C2×Q8—1241no—
245C2×Q8C22×D3111yescharacteristic
246C2×Q8C22×D3111yescharacteristic
247C2×D4—311no—
248C2×D4—311no—
249C2×D4—621no—
250C2×D4—621no—
251C22×C4—311no—
252C22×C4—311no—
253C22×C4—621no—
254C22×C4—621no—
255Q16—22no—
256Q16—1241no—
257SD16—1241no—
258M16—1241no—
259C2×C8—311no—
260C2×C8—311no—
261C2×C8—1241no—
262C2×C8C22×D3111yescharacteristic
263C2×C8C22×D3111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4C22×D3111yescharacteristic
274C4⋊C4C22×D3111yescharacteristic
275C22⋊C4—311no—
276C22⋊C4—311no—
277C22⋊C4—621no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C42—21no—
286C42—21no—
287C42—621no—
288C42—621no—
289C42C22×D3111yescharacteristic
290C23—311no—
291C23—311no—
292C23—621no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—621no—
297Q8—621no—
298Q8—1242no—
299Q8—1242no—
300Q8#9249512yes—
301D4—621no—
302D4—621no—
303D4—1241no—
304D4—1242no—
305D4—1242no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—311no—
311C2×C4—311no—
312C2×C4—621no—
313C2×C4—621no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—1242no—
320C2×C4—1242no—
321C2×C4D4×D3111yescharacteristic
322C2×C4D4×D3111yescharacteristic
323C2×C4C23×D3111yescharacteristic
324C8—21no—
325C8—21no—
326C8—621no—
327C8—621no—
328C22—621no—
329C22—621no—
330C22—621no—
331C22—621no—
332C22—621no—
333C22—621no—
334C22—1241no—
335C22—1241no—
336C22—1241no—
337C22C2×D4×D3111yescharacteristic
338C4—21no—
339C4—22no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—621no—
345C4—621no—
346C4—1241no—
347C4—1241no—
348C4—1241no—
349C4C2×#9249511yescharacteristic
350C4#1175856611yescharacteristic
351C2—1241no—
352C2—1241no—
353C2—2481no—
354C2#1452169511yescharacteristic
355C2#1452184811yescharacteristic
356C2#1452186511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#441C2
socleC22×C31C22×D4
prime radical#14521711C2
hypercenter#441D31
hypocenterC31#3313
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #14521772C2semidirect
3. #14521409C2semidirect
4. #14521393C2semidirect
5. #14521375C2semidirect
6. #14521344C2semidirect
7. #14521298C2semidirect
8. #14521289C2semidirect
9. #14521271C2semidirect
10. #14521210C2semidirect
11. #14521203C2semidirect
12. #14521122C2semidirect
13. #14521056C2semidirect
14. #14521044C2semidirect
15. C31×#441C2semidirect
184. #441D31semidirect
237. C31#3313semidirect

Maximal subgroups

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

subgroupindex
#145217722
#145217112
#145214092
#145213932
#145213752
#145213442
#145212982
#145212892
#145212712
#145212102
#145212032
#145211222
#145210562
#145210442
C31×#4412
#331331