Finite Group Databasebeta

← #16855956

Subgroups — #16855956

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#14521655C211yesmaximal, characteristic, complemented
2#14521521C211yesmaximal, characteristic, complemented
3#14521376C211yesmaximal, characteristic, complemented
4#14521375C211yesmaximal, characteristic, complemented
5#14521346C211yesmaximal, characteristic, complemented
6#14521245C211yesmaximal, characteristic, complemented
7#14521244C211yesmaximal, characteristic, complemented
8#14521184C211yesmaximal, characteristic, complemented
9#14521184C211yesmaximal, characteristic, complemented
10#14521160C211yesmaximal, characteristic, complemented
11#14521158C211yesmaximal, characteristic, complemented
12#14521131C211yesmaximal, characteristic, complemented
13#14521129C211yesmaximal, characteristic, complemented
14#14521109C211yesmaximal, characteristic, complemented
15C31×#478C211yesmaximal, characteristic, complemented
16C2×D4×D31C2211yescharacteristic
17C31×#125C2211yescharacteristic, complemented
18C4×D4×C31C2211yescharacteristic
19D4×Dic31C2211yescharacteristic
20C2×#92479C2211yescharacteristic
21C2×#92479C2211yescharacteristic
22C4×C22⋊D31—21no—
23C2×(C2×D31)⋊C4—21no—
24C2×D248C2211yescharacteristic
25C2×D248C2211yescharacteristic
26#11758472—21no—
27#11758472—21no—
28#11758472C2211yescharacteristic
29#11758472C2211yescharacteristic
30#11758471—21no—
31#11758471—21no—
32#11758470C2211yescharacteristic
33#11758470C2211yescharacteristic, complemented
34#11758470C2211yescharacteristic, complemented
35#11758469C2211yescharacteristic
36(C22⋊D31)⋊C4—21no—
37C22⋊C4×D31—21no—
38#11758451C2211yescharacteristic, complemented
39C4×D124C2211yescharacteristic
40#11758449C2211yescharacteristic
41C31×#107C2211yescharacteristic, complemented
42C31×#106C2211yescharacteristic, complemented
43C31×C4⋊C8C2211yescharacteristic, complemented
44C31×#102C2211yescharacteristic
45C31×#102C2211yescharacteristic
46#11758409C2211yescharacteristic, complemented
47#11758409C2211yescharacteristic, complemented
48(C2×D31)⋊C8C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758403C2211yescharacteristic, complemented
51C8×Dic31C2211yescharacteristic, complemented
52#11758397C2211yescharacteristic
53#11758397C2211yescharacteristic
54#11758397C2211yescharacteristic, complemented
55#11758397C2211yescharacteristic, complemented
56#11758396C2211yescharacteristic, complemented
57#11758395C2211yescharacteristic, complemented
58C4⋊(C31⋊C8)C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C2×C22⋊D31—21no—
63C22×Dic31—21no—
64D4×D31—22no—
65D4×D31—22no—
66C2×D124—21no—
67C2×D124—21no—
68C2×D124—21no—
69C2×D124—21no—
70C2×D124C2311yescharacteristic
71C2×D124C2311yescharacteristic
72C2×D124C2311yescharacteristic
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31—21no—
77C2×C4×D31C2311yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C4⋊C4×C31—21no—
81C4⋊C4×C31—21no—
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C22⋊C4×C31—21no—
86C42×C31C2311yescharacteristic
87C22⋊Dic31—21no—
88#92479—22no—
89#92479—22no—
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)⋊C4—21no—
97(C2×D31)⋊C4D411yescharacteristic
98(C2×D31)⋊C4D411yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100Dic31⋊C4D411yescharacteristic
101Dic31⋊C4D411yescharacteristic
102C4×Dic31—21no—
103C4×Dic31C2311yescharacteristic
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106D248—22no—
107D248—22no—
108C23×C31—21no—
109C22×D31—21no—
110C22×D31—24no—
111C22×D31—21no—
112C22×D31—21no—
113C22×D31—81no—
114C22×D31—81no—
115C22×D31C2×D411yescharacteristic
116D4×C31—21no—
117D4×C31#4112yes—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—81no—
122C2×C4×C31C2×D411yescharacteristic
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2411yescharacteristic
125C22⋊D31—24no—
126C2×Dic31—21no—
127C2×Dic31—81no—
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130C2×Dic31C2×D411yescharacteristic
131D124—21no—
132D124—21no—
133D124—21no—
134D124—21no—
135D124—21no—
136D124—81no—
137D124—81no—
138D124—81no—
139D124—81no—
140D124#4112yes—
141C4×D31—21no—
142C4×D31—21no—
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—22no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31C22×D411yescharacteristic
156C2×D31—21no—
157C2×D31—22no—
158C2×D31—21no—
159C2×D31—21no—
160C2×D31—41no—
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—21no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31—41no—
174C4×C31C2×#4111yescharacteristic
175C4×C31C2×#4111yescharacteristic
176Dic31—21no—
177Dic31—21no—
178Dic31—21no—
179Dic31—41no—
180#540—311no—
181#518—311no—
182#482—311no—
183#482—311no—
184#478—311no—
185#478D3111yescharacteristic, complemented
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—42no—
196C2×C31#52511yescharacteristic
197C2×C31#57611yescharacteristic
198C2×C31#57611yescharacteristic
199D31—41no—
200D31—42no—
201D31—81no—
202D31—81no—
203C22×D4—311no—
204C2×D8—311no—
205C2×D8—311no—
206C2×D8—311no—
207C2×D8—311no—
208#127—311no—
209#125C2×D3111yescharacteristic, complemented
210#123—621no—
211#123—621no—
212#121—311no—
213#121—311no—
214#121—621no—
215#121—621no—
216C4×D4—311no—
217C4×D4—311no—
218C4×D4—311no—
219C4×D4—311no—
220C4×D4—311no—
221C4×D4—621no—
222C4×D4—621no—
223C4×D4C2×D3111yescharacteristic
224#117—311no—
225#117—311no—
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⋊C8C2×D3111yescharacteristic, complemented
234#102—311no—
235#102—311no—
236#102—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240#102C2×D3111yescharacteristic
241#102C2×D3111yescharacteristic
242C22⋊C8—311no—
243C22⋊C8—311no—
244#97—311no—
245C4×C8—311no—
246C31#312211yescharacteristic, complemented, Sylow
247C24—621no—
248C2×D4—311no—
249C2×D4—311no—
250C2×D4—311no—
251C2×D4—621no—
252C2×D4—621no—
253C2×D4—621no—
254C2×D4—622no—
255C2×D4—622no—
256C2×D4—621no—
257C2×D4—621no—
258C2×D4C22×D3111yescharacteristic
259C22×C4—21no—
260C22×C4—311no—
261C22×C4—621no—
262C22×C4—621no—
263C22×C4—621no—
264C22×C4—621no—
265C22×C4—621no—
266D8—622no—
267D8—622no—
268D8—622no—
269D8—622no—
270C2×C8—311no—
271C2×C8—311no—
272C2×C8C22×D3111yescharacteristic
273C2×C8C22×D3111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—311no—
277C4⋊C4—311no—
278C4⋊C4—311no—
279C4⋊C4C22×D3111yescharacteristic
280C4⋊C4C22×D3111yescharacteristic
281C4⋊C4C22×D3111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—311no—
284C22⋊C4—311no—
285C22⋊C4—621no—
286C22⋊C4—621no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C42—311no—
294C42—621no—
295C42C22×D3111yescharacteristic
296C23—21no—
297C23—311no—
298C23—624no—
299C23—621no—
300C23—621no—
301C23—621no—
302C23—2481no—
303C23—2481no—
304D4—21no—
305D4—312no—
306D4—624no—
307D4—621no—
308D4—621no—
309D4—621no—
310D4—621no—
311D4—621no—
312D4—2481no—
313D4—2481no—
314D4—2481no—
315D4—2481no—
316D4#9249912yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—311no—
322C2×C4—311no—
323C2×C4—311no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—2481no—
328C2×C4—2481no—
329C2×C4—2481no—
330C2×C4—2481no—
331C2×C4—2481no—
332C2×C4D4×D3111yescharacteristic
333C2×C4D4×D3111yescharacteristic
334C2×C4C23×D3111yescharacteristic
335C8—21no—
336C8—21no—
337C8—621no—
338C8—621no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—621no—
343C22—622no—
344C22—621no—
345C22—621no—
346C22—1241no—
347C22—1241no—
348C22—1241no—
349C22—1241no—
350C22—1241no—
351C22—1241no—
352C22—1241no—
353C22—1241no—
354C22—2484no—
355C22C2×D4×D3111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—621no—
362C4—621no—
363C4—621no—
364C4—1241no—
365C4C2×#9249911yescharacteristic
366C4#41×D3111yescharacteristic
367C2—42no—
368C2—1241no—
369C2—1242no—
370C2—2481no—
371C2—2481no—
372C2#1452156211yescharacteristic
373C2#1452185111yescharacteristic
374C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#478C2
socleC22×C31C22×D4
hypercenter#478D31
hypocenterC31#3122
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14521655C2semidirect
2. #14521521C2semidirect
3. #14521376C2semidirect
4. #14521375C2semidirect
5. #14521346C2semidirect
6. #14521245C2semidirect
7. #14521244C2semidirect
8. #14521184C2semidirect
9. #14521184C2semidirect
10. #14521160C2semidirect
11. #14521158C2semidirect
12. #14521131C2semidirect
13. #14521129C2semidirect
14. #14521109C2semidirect
15. C31×#478C2semidirect
17. C31×#125C22semidirect
33. #11758470C22semidirect
34. #11758470C22semidirect
38. #11758451C22semidirect
41. C31×#107C22semidirect
42. C31×#106C22semidirect
43. C31×C4⋊C8C22semidirect
46. #11758409C22semidirect
47. #11758409C22semidirect
50. #11758403C22semidirect
51. C8×Dic31C22semidirect
54. #11758397C22semidirect
55. #11758397C22semidirect
56. #11758396C22semidirect
57. #11758395C22semidirect
58. C4⋊(C31⋊C8)C22semidirect
185. #478D31semidirect
209. #125C2×D31semidirect
229. #107C2×D31semidirect
231. #106C2×D31semidirect
233. C4⋊C8C2×D31semidirect
246. C31#3122semidirect

Maximal subgroups

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

subgroupindex
#145216552
#145215212
#145213762
#145213752
#145213462
#145212452
#145212442
#145211842
#145211602
#145211582
#145211312
#145211292
#145211092
C31×#4782
#312231