Finite Group Databasebeta

← #16855950

Subgroups — #16855950

Order 3968.

418 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#14521652C211yesmaximal, characteristic, complemented
2#14521523C211yesmaximal, characteristic, complemented
3#14521373C211yesmaximal, characteristic, complemented
4#14521352C211yesmaximal, characteristic, complemented
5#14521348C211yesmaximal, characteristic, complemented
6#14521243C211yesmaximal, characteristic, complemented
7#14521243C211yesmaximal, characteristic, complemented
8#14521185C211yesmaximal, characteristic, complemented
9#14521182C211yesmaximal, characteristic, complemented
10#14521160C211yesmaximal, characteristic, complemented
11#14521158C211yesmaximal, characteristic, complemented
12#14521131C211yesmaximal, characteristic, complemented
13#14521129C211yesmaximal, characteristic, complemented
14#14521107C211yesmaximal, characteristic, complemented
15C31×#482C211yesmaximal, characteristic, complemented
16C22×D124C2211yescharacteristic
17C31×#121C2211yescharacteristic
18C31×#117C2211yescharacteristic
19#11758517C2211yescharacteristic, complemented
20#11758516—21no—
21#11758515—21no—
22D4×Dic31C2211yescharacteristic, complemented
23C2×#92479C2211yescharacteristic
24C2×#92479C2211yescharacteristic
25#11758507C2211yescharacteristic
26#11758503C2211yescharacteristic
27C2×D248C2211yescharacteristic
28C2×D248C2211yescharacteristic
29#11758470C2211yescharacteristic
30#11758470C2211yescharacteristic
31#11758470C2211yescharacteristic
32#11758470C2211yescharacteristic
33#11758470C2211yescharacteristic, complemented
34#11758467C2211yescharacteristic, complemented
35#11758463—21no—
36#11758460—21no—
37C22⋊C4×D31—21no—
38C22⋊C4×D31—21no—
39C4×D124—21no—
40C4×D124—21no—
41C31×#107C2211yescharacteristic, complemented
42C31×#106C2211yescharacteristic, complemented
43C31×#102C2211yescharacteristic, complemented
44C31×#102C2211yescharacteristic, complemented
45C31×C22⋊C8C2211yescharacteristic
46C22⋊(C31⋊C8)C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758403C2211yescharacteristic, complemented
50Dic31⋊C8C2211yescharacteristic, complemented
51Dic31⋊C8C2211yescharacteristic, complemented
52C8×Dic31C2211yescharacteristic, complemented
53#11758397C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic, complemented
56#11758397C2211yescharacteristic, complemented
57#11758396C2211yescharacteristic, complemented
58#11758395C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×D4×C31—21no—
61C2×D4×C31C2311yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C22×Dic31—21no—
67C2×D124—21no—
68C2×D124—22no—
69C2×D124—22no—
70C2×D124C2311yescharacteristic
71C2×D124C2311yescharacteristic
72C2×D124C2311yescharacteristic
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31—21no—
77C2×C4×D31—21no—
78C2×C8×C31C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C4⋊C4×C31C2311yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C22⋊C4×C31—21no—
85C42×C31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31D411yescharacteristic
88C22⋊Dic31D411yescharacteristic
89#92479—22no—
90#92479—22no—
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)⋊C4—21no—
97C4⋊Dic31—21no—
98C4⋊Dic31D411yescharacteristic
99C4⋊Dic31D411yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4—21no—
102C4×Dic31C2311yescharacteristic
103C4×Dic31C2311yescharacteristic
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106D248—22no—
107D248—22no—
108C23×C31—21no—
109C23×C31C2×D411yescharacteristic
110C22×D31—21no—
111C22×D31—21no—
112C22×D31—24no—
113C22×D31—21no—
114C22×D31—81no—
115C22×D31—81no—
116D4×C31—21no—
117D4×C31—21no—
118D4×C31—81no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2411yescharacteristic
126C22⋊D31—81no—
127C22⋊D31—81no—
128C22⋊D31—81no—
129C2×Dic31—21no—
130C2×Dic31—81no—
131C2×Dic31C2×D411yescharacteristic
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135D124—24no—
136D124—21no—
137D124—21no—
138D124—21no—
139D124—21no—
140D124#4112yes—
141D124#4112yes—
142C4×D31—81no—
143C4×D31—81no—
144C4×D31—81no—
145C4×D31—81no—
146C4×D31—81no—
147C8×C31—21no—
148C8×C31—21no—
149C31⋊C8—21no—
150C31⋊C8—21no—
151#3122—311nomaximal, Sylow
152C22×C31—21no—
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31C22×D411yescharacteristic
159C2×D31—22no—
160C2×D31—22no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C2×D31—41no—
167C2×D31—41no—
168C2×D31—84no—
169C4×C31—21no—
170C4×C31—41no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31C2×#4111yescharacteristic
174C4×C31C2×#4111yescharacteristic
175Dic31—21no—
176Dic31—21no—
177Dic31—21no—
178Dic31—21no—
179Dic31—41no—
180#540—311no—
181#518—311no—
182#482—311no—
183#482D3111yescharacteristic, complemented
184#478—311no—
185#478—311no—
186#459—311no—
187#459—311no—
188#447—311no—
189#447—311no—
190#442—311no—
191#442—311no—
192C4×D8—311no—
193C4×D8—311no—
194#433—311no—
195C2×C31—41no—
196C2×C31—81no—
197C2×C31#52511yescharacteristic
198C2×C31#57611yescharacteristic
199C2×C31#57611yescharacteristic
200D31—42no—
201D31—42no—
202D31—81no—
203C22×D4—311no—
204C2×D8—311no—
205C2×D8—311no—
206C2×D8—311no—
207C2×D8—311no—
208#127—311no—
209#125—311no—
210#123—621no—
211#123—621no—
212#121—311no—
213#121—621no—
214#121—621no—
215#121C2×D3111yescharacteristic
216C4×D4—311no—
217C4×D4—311no—
218C4×D4—311no—
219C4×D4—311no—
220C4×D4—311no—
221C4×D4—311no—
222C4×D4—621no—
223C4×D4—621no—
224#117—311no—
225#117C2×D3111yescharacteristic
226C2×C22⋊C4—621no—
227C2×C22⋊C4—621no—
228#107—311no—
229#107C2×D3111yescharacteristic, complemented
230#106—311no—
231#106C2×D3111yescharacteristic, complemented
232C4⋊C8—311no—
233C4⋊C8—311no—
234#102—311no—
235#102—311no—
236#102—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240#102C2×D3111yescharacteristic, complemented
241#102C2×D3111yescharacteristic, complemented
242C22⋊C8—311no—
243C22⋊C8C2×D3111yescharacteristic
244#97—311no—
245C4×C8—311no—
246C31#312211yescharacteristic, complemented, Sylow
247C24—621no—
248C2×D4—21no—
249C2×D4—311no—
250C2×D4—311no—
251C2×D4—311no—
252C2×D4—622no—
253C2×D4—622no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4—621no—
257C2×D4—621no—
258C2×D4C22×D3111yescharacteristic
259C22×C4—621no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4—621no—
263C22×C4—621no—
264C22×C4—621no—
265C22×C4C22×D3111yescharacteristic
266D8—622no—
267D8—622no—
268D8—622no—
269D8—622no—
270C2×C8—311no—
271C2×C8—311no—
272C2×C8C22×D3111yescharacteristic
273C2×C8C22×D3111yescharacteristic
274C4⋊C4—311no—
275C4⋊C4—311no—
276C4⋊C4—311no—
277C4⋊C4—621no—
278C4⋊C4—621no—
279C4⋊C4C22×D3111yescharacteristic
280C4⋊C4C22×D3111yescharacteristic
281C4⋊C4C22×D3111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—311no—
285C22⋊C4—311no—
286C22⋊C4—621no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C42—21no—
294C42—311no—
295C42—311no—
296C23—21no—
297C23—624no—
298C23—621no—
299C23—621no—
300C23—621no—
301C23—2481no—
302C23—2481no—
303C23D4×D3111yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—312no—
308D4—312no—
309D4—624no—
310D4—621no—
311D4—621no—
312D4—621no—
313D4—621no—
314D4—2481no—
315D4—2481no—
316D4—2481no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—311no—
323C2×C4—311no—
324C2×C4—311no—
325C2×C4—311no—
326C2×C4—621no—
327C2×C4—2481no—
328C2×C4—2481no—
329C2×C4—2481no—
330C2×C4—2481no—
331C2×C4—2481no—
332C2×C4—2481no—
333C2×C4D4×D3111yescharacteristic
334C2×C4C23×D3111yescharacteristic
335C8—21no—
336C8—21no—
337C8—621no—
338C8—621no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—622no—
346C22—622no—
347C22—1241no—
348C22—1241no—
349C22—1241no—
350C22—1241no—
351C22—1241no—
352C22—1241no—
353C22—1241no—
354C22—2484no—
355C22C2×D4×D3111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—621no—
361C4—621no—
362C4—621no—
363C4—621no—
364C4—1241no—
365C4#41×D3111yescharacteristic
366C4#41×D3111yescharacteristic
367C2—41no—
368C2—81no—
369C2—1242no—
370C2—1242no—
371C2—2481no—
372C2#1452155711yescharacteristic
373C2#1452185111yescharacteristic
374C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#482C2
socleC22×C31C22×D4
hypercenter#482D31
hypocenterC31#3122
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #14521652C2semidirect
2. #14521523C2semidirect
3. #14521373C2semidirect
4. #14521352C2semidirect
5. #14521348C2semidirect
6. #14521243C2semidirect
7. #14521243C2semidirect
8. #14521185C2semidirect
9. #14521182C2semidirect
10. #14521160C2semidirect
11. #14521158C2semidirect
12. #14521131C2semidirect
13. #14521129C2semidirect
14. #14521107C2semidirect
15. C31×#482C2semidirect
19. #11758517C22semidirect
22. D4×Dic31C22semidirect
33. #11758470C22semidirect
34. #11758467C22semidirect
41. C31×#107C22semidirect
42. C31×#106C22semidirect
43. C31×#102C22semidirect
44. C31×#102C22semidirect
49. #11758403C22semidirect
50. Dic31⋊C8C22semidirect
51. Dic31⋊C8C22semidirect
52. C8×Dic31C22semidirect
55. #11758397C22semidirect
56. #11758397C22semidirect
57. #11758396C22semidirect
58. #11758395C22semidirect
183. #482D31semidirect
229. #107C2×D31semidirect
231. #106C2×D31semidirect
240. #102C2×D31semidirect
241. #102C2×D31semidirect
246. C31#3122semidirect

Maximal subgroups

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

subgroupindex
#145216522
#145215232
#145213732
#145213522
#145213482
#145212432
#145211852
#145211822
#145211602
#145211582
#145211312
#145211292
#145211072
C31×#4822
#312231