Finite Group Databasebeta

← #16857786

Subgroups — #16857786

Order 3968.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521695C211yesmaximal, characteristic
2#14521411C211yesmaximal, characteristic, complemented
3#14521384C211yesmaximal, characteristic, complemented
4#14521362C211yesmaximal, characteristic, complemented
5#14521326C211yesmaximal, characteristic, complemented
6#14521297C211yesmaximal, characteristic, complemented
7#14521288C211yesmaximal, characteristic, complemented
8#14521271C211yesmaximal, characteristic, complemented
9#14521209C211yesmaximal, characteristic, complemented
10#14521199C211yesmaximal, characteristic, complemented
11#14521147C211yesmaximal, characteristic, complemented
12#14521121C211yesmaximal, characteristic, complemented
13#14521048C211yesmaximal, characteristic, complemented
14C2×#11758397C211yesmaximal, characteristic, complemented
15C31×#554C211yesmaximal, characteristic, complemented
16C2×#92495C2211yescharacteristic
17C22×D124C2211yescharacteristic
18C31×C4⋊Q8C2211yescharacteristic, complemented
19C31×#125—21no—
20C31×C22⋊Q8—21no—
21C31×C22⋊Q8—21no—
22C31×C22⋊Q8C2211yescharacteristic
23C31×C22⋊Q8C2211yescharacteristic, complemented
24C4×Q8×C31C2211yescharacteristic, complemented
25C4×D4×C31—21no—
26C4×D4×C31C2211yescharacteristic
27C2×C4⋊C4×C31C2211yescharacteristic
28C2×C4⋊C4×C31C2211yescharacteristic, complemented
29C2×#92482C2211yescharacteristic, complemented
30C2×#92481C2211yescharacteristic
31C2×#92481C2211yescharacteristic
32#11758514—21no—
33#11758507C2211yescharacteristic
34#11758501C2211yescharacteristic
35C2×#92474C2211yescharacteristic, complemented
36C22×C31⋊C8C2211yescharacteristic
37#11758471—21no—
38#11758461—21no—
39C22⋊C4×D31—21no—
40#11758452C2211yescharacteristic
41C4×D124C2211yescharacteristic
42#11758423C2211yescharacteristic, complemented
43C22⋊(C31⋊C8)C2211yescharacteristic
44C22⋊(C31⋊C8)C2211yescharacteristic, complemented
45#11758398C2211yescharacteristic, complemented
46#11758398C2211yescharacteristic, complemented
47#11758398C2211yescharacteristic, complemented
48#11758397C2211yescharacteristic
49#11758397C2211yescharacteristic
50#11758397C2211yescharacteristic
51#11758397C2211yescharacteristic
52#11758397C2211yescharacteristic
53#11758397C2211yescharacteristic
54#11758395C2211yescharacteristic, complemented
55#11758395C2211yescharacteristic, complemented
56#11758395C2211yescharacteristic, complemented
57C4⋊(C31⋊C8)C2211yescharacteristic, complemented
58#11758391C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×Q8×C31—21no—
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31D411yescharacteristic
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31C2311yescharacteristic
66C22×C4×C31C2311yescharacteristic
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69#92495—22no—
70#92495—41no—
71C2×D124—22no—
72C2×D124—21no—
73C2×D124—41no—
74C2×D124C2311yescharacteristic
75C2×D124C2311yescharacteristic
76C2×C4×D31—21no—
77C2×C4×D31—21no—
78C2×Dic62C2311yescharacteristic
79C4⋊C4×C31—21no—
80C4⋊C4×C31—21no—
81C4⋊C4×C31—21no—
82C4⋊C4×C31—21no—
83C4⋊C4×C31—21no—
84C4⋊C4×C31—21no—
85C4⋊C4×C31D411yescharacteristic
86C4⋊C4×C31C2311yescharacteristic
87C4⋊C4×C31C2311yescharacteristic
88C4⋊C4×C31C2311yescharacteristic
89C22⋊C4×C31—21no—
90C22⋊C4×C31—21no—
91C22⋊C4×C31D411yescharacteristic
92C22⋊C4×C31D411yescharacteristic
93C42×C31—21no—
94C42×C31C2311yescharacteristic
95C22⋊Dic31—21no—
96#92482—41no—
97#92481—22no—
98#92481—41no—
99(C2×D31)⋊C4—21no—
100(C2×D31)⋊C4—21no—
101(C2×D31)⋊C4—21no—
102(C2×D31)⋊C4—21no—
103C4⋊Dic31C2311yescharacteristic
104Dic31⋊C4—21no—
105#92474—41no—
106C2×C31⋊C8—41no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C23×C31C2×D411yescharacteristic
112C23×C31C2×D411yescharacteristic
113C22×D31—21no—
114C22×D31—21no—
115C22×D31—42no—
116C22×D31—42no—
117C22×D31—81no—
118Q8×C31—21no—
119Q8×C31—21no—
120Q8×C31—81no—
121D4×C31—22no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—81no—
131C2×C4×C31—81no—
132C2×C4×C31C2×D411yescharacteristic
133C2×C4×C31C2×D411yescharacteristic
134C2×C4×C31C2×D411yescharacteristic
135C2×C4×C31C2×D411yescharacteristic
136C2×C4×C31C2411yescharacteristic
137C22⋊D31—42no—
138C22⋊D31—81no—
139C2×Dic31—21no—
140C2×Dic31—21no—
141D124—21no—
142D124—21no—
143D124—21no—
144D124—42no—
145D124#4112yes—
146C4×D31—42no—
147C4×D31—81no—
148Dic62—21no—
149Dic62—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152C31⋊C8—21no—
153C31⋊C8—21no—
154#3314—311nomaximal, Sylow
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31#13712yes—
161C22×C31C22×D411yescharacteristic
162C2×D31—22no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C2×D31—41no—
167C2×D31—41no—
168C2×D31—84no—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—21no—
172C4×C31—21no—
173C4×C31—41no—
174C4×C31—41no—
175C4×C31—41no—
176C4×C31—41no—
177C4×C31C2×#4111yescharacteristic
178C4×C31H(5,𝔽2)11yescharacteristic
179Dic31—41no—
180Dic31—41no—
181#554D3111yescharacteristic, complemented
182#546—311no—
183#489—311no—
184#484—311no—
185#480—311no—
186#474—311no—
187#468—311no—
188#467—311no—
189#464—311no—
190#452—311no—
191#450—311no—
192#440—311no—
193#435—311no—
194#417—311no—
195C2×#102—311no—
196C2×C31—22no—
197C2×C31—41no—
198C2×C31#54611yescharacteristic
199C2×C31C2×#13711yescharacteristic
200C2×C31#57611yescharacteristic
201D31—42no—
202D31—81no—
203C2×#41—311no—
204C22×D4—311no—
205C2×Q16—311no—
206C2×SD16—311no—
207C2×SD16—311no—
208C2×M16—311no—
209C22×C8—311no—
210C4⋊Q8C2×D3111yescharacteristic, complemented
211#125—21no—
212#124—311no—
213#123—621no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—311no—
217C22⋊Q8C2×D3111yescharacteristic
218C22⋊Q8C2×D3111yescharacteristic, complemented
219#121—311no—
220#121—621no—
221#120—621no—
222C4×Q8C2×D3111yescharacteristic, complemented
223C4×D4—21no—
224C4×D4—311no—
225C4×D4C2×D3111yescharacteristic
226C2×C4⋊C4C2×D3111yescharacteristic
227C2×C4⋊C4C2×D3111yescharacteristic, complemented
228C2×C22⋊C4—621no—
229#107—311no—
230#107—311no—
231#107—311no—
232C4⋊C8—311no—
233#103—311no—
234#103—311no—
235#103—311no—
236#103—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240#102—311no—
241#102—311no—
242#102—311no—
243C22⋊C8—311no—
244C22⋊C8—311no—
245#97—311no—
246C31#331411yescharacteristic, complemented, Sylow
247C24—621no—
248#41—622no—
249#41—1241no—
250C2×Q8—21no—
251C2×Q8—311no—
252C2×Q8C22×D3111yescharacteristic
253C2×D4—311no—
254C2×D4—311no—
255C2×D4—622no—
256C2×D4—621no—
257C2×D4—621no—
258C2×D4—621no—
259C2×D4—1241no—
260C2×D4C22⋊D3111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—621no—
264C22×C4—621no—
265C22×C4C22×D3111yescharacteristic
266C22×C4C22×D3111yescharacteristic
267Q16—1241no—
268SD16—622no—
269SD16—1241no—
270M16—1241no—
271C2×C8—311no—
272C2×C8—311no—
273C2×C8—311no—
274C2×C8—311no—
275C2×C8—1241no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—311no—
283C4⋊C4—621no—
284C4⋊C4C22⋊D3111yescharacteristic
285C4⋊C4C22×D3111yescharacteristic
286C4⋊C4C22×D3111yescharacteristic
287C4⋊C4C22×D3111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C22⋊C4—621no—
294C22⋊C4—621no—
295C22⋊C4C22⋊D3111yescharacteristic
296C22⋊C4C22⋊D3111yescharacteristic
297C42—21no—
298C42C22×D3111yescharacteristic
299C23—621no—
300C23—621no—
301C23—1242no—
302C23—1242no—
303C23—2481no—
304C23C2×C22⋊D3111yescharacteristic
305C23C2×C22⋊D3111yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—81no—
309Q8—621no—
310Q8—621no—
311D4—22no—
312D4—312no—
313D4—621no—
314D4—621no—
315D4—621no—
316D4—1242no—
317D4—1242no—
318D4—2481no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—621no—
330C2×C4—621no—
331C2×C4—1242no—
332C2×C4—2481no—
333C2×C4C2×C22⋊D3111yescharacteristic
334C2×C4C2×C22⋊D3111yescharacteristic
335C2×C4C2×C22⋊D3111yescharacteristic
336C2×C4C2×C22⋊D3111yescharacteristic
337C2×C4C23×D3111yescharacteristic
338C8—621no—
339C8—621no—
340C8—621no—
341C8—621no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—622no—
348C22—1241no—
349C22—1241no—
350C22—1241no—
351C22—1241no—
352C22—1241no—
353C22—2484no—
354C22#1175851912yes—
355C22C22×C22⋊D3111yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—1241no—
365C4—1241no—
366C4#41×D3111yescharacteristic
367C4#1175856611yescharacteristic
368C2—22no—
369C2—41no—
370C2—1242no—
371C2—2481no—
372C2#1452168711yescharacteristic
373C2C2×#1175851911yescharacteristic
374C2#1452185211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#554C2
socleC22×C31C22×D4
prime radical#14521695C2
hypercenter#554D31
hypocenterC31#3314
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #14521411C2semidirect
3. #14521384C2semidirect
4. #14521362C2semidirect
5. #14521326C2semidirect
6. #14521297C2semidirect
7. #14521288C2semidirect
8. #14521271C2semidirect
9. #14521209C2semidirect
10. #14521199C2semidirect
11. #14521147C2semidirect
12. #14521121C2semidirect
13. #14521048C2semidirect
14. C2×#11758397C2semidirect
15. C31×#554C2semidirect
18. C31×C4⋊Q8C22semidirect
23. C31×C22⋊Q8C22semidirect
24. C4×Q8×C31C22semidirect
28. C2×C4⋊C4×C31C22semidirect
29. C2×#92482C22semidirect
35. C2×#92474C22semidirect
42. #11758423C22semidirect
44. C22⋊(C31⋊C8)C22semidirect
45. #11758398C22semidirect
46. #11758398C22semidirect
47. #11758398C22semidirect
54. #11758395C22semidirect
55. #11758395C22semidirect
56. #11758395C22semidirect
57. C4⋊(C31⋊C8)C22semidirect
58. #11758391C22semidirect
181. #554D31semidirect
210. C4⋊Q8C2×D31semidirect
218. C22⋊Q8C2×D31semidirect
222. C4×Q8C2×D31semidirect
227. C2×C4⋊C4C2×D31semidirect
246. C31#3314semidirect

Maximal subgroups

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

subgroupindex
#145216952
#145214112
#145213842
#145213622
#145213262
#145212972
#145212882
#145212712
#145212092
#145211992
#145211472
#145211212
#145210482
C2×#117583972
C31×#5542
#331431