Finite Group Databasebeta

← #16857750

Subgroups — #16857750

Order 3968.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521767C211yesmaximal, characteristic, complemented
2#14521690C211yesmaximal, characteristic
3#14521410C211yesmaximal, characteristic, complemented
4#14521376C211yesmaximal, characteristic, complemented
5#14521338C211yesmaximal, characteristic, complemented
6#14521305C211yesmaximal, characteristic, complemented
7#14521279C211yesmaximal, characteristic, complemented
8#14521274C211yesmaximal, characteristic, complemented
9#14521214C211yesmaximal, characteristic, complemented
10#14521202C211yesmaximal, characteristic, complemented
11#14521148C211yesmaximal, characteristic, complemented
12#14521123C211yesmaximal, characteristic, complemented
13#14521053C211yesmaximal, characteristic, complemented
14#14521044C211yesmaximal, characteristic, complemented
15C31×#485C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C22×D124C2211yescharacteristic
18C31×C22⋊Q8C2211yescharacteristic
19C31×#117C2211yescharacteristic
20#11758524C2211yescharacteristic
21C2×#92482C2211yescharacteristic, complemented
22C4×C22⋊D31C2211yescharacteristic
23#11758501C2211yescharacteristic
24C2×#92474C2211yescharacteristic
25C2×#92470C2211yescharacteristic
26C2×#92470C2211yescharacteristic
27C2×C8×D31C2211yescharacteristic, complemented
28#11758474C2211yescharacteristic, complemented
29#11758472—21no—
30#11758472C2211yescharacteristic
31#11758471—21no—
32#11758470C2211yescharacteristic
33#11758469C2211yescharacteristic, complemented
34#11758465C2211yescharacteristic, complemented
35#11758464C2211yescharacteristic, complemented
36#11758462—21no—
37#11758459—21no—
38C22⋊C4×D31—21no—
39#11758456—21no—
40#11758453—21no—
41C4×Dic62—21no—
42C31×#107C2211yescharacteristic, complemented
43C31×#106C2211yescharacteristic, complemented
44C31×#103C2211yescharacteristic, complemented
45C31×#103C2211yescharacteristic, complemented
46C31×C22⋊C8C2211yescharacteristic
47#11758423C2211yescharacteristic, complemented
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic, complemented
51#11758403C2211yescharacteristic, complemented
52Dic31⋊C8C2211yescharacteristic, complemented
53#11758398C2211yescharacteristic, complemented
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758397C2211yescharacteristic
58#11758396C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×Q8×C31C2311yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C2×C22⋊D31D411yescharacteristic
63#92499—22no—
64#92499—41no—
65C2×D124—22no—
66C2×D124—21no—
67C2×D124—21no—
68C2×D124—21no—
69C2×D124—41no—
70C2×D124C2311yescharacteristic
71C2×D124C2311yescharacteristic
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×C4×D31C2311yescharacteristic
75C2×Dic62—21no—
76C2×Dic62C2311yescharacteristic
77C2×C8×C31C2311yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C4⋊C4×C31—21no—
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
88#92482—41no—
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)⋊C4D411yescharacteristic
96C4⋊Dic31—21no—
97C4⋊Dic31C2311yescharacteristic
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4D411yescharacteristic
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31C2311yescharacteristic
105#92474—41no—
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108#92470—22no—
109#92470—41no—
110C8×D31—41no—
111C23×C31C2×D411yescharacteristic
112C22×D31—21no—
113C22×D31—21no—
114C22×D31—42no—
115C22×D31—42no—
116C22×D31—81no—
117C22×D31C2×D411yescharacteristic
118Q8×C31—21no—
119Q8×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2411yescharacteristic
128C22⋊D31—41no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31C2×D411yescharacteristic
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134D124—21no—
135D124—21no—
136D124—21no—
137D124—42no—
138D124—42no—
139D124—81no—
140D124#4112yes—
141C4×D31—21no—
142C4×D31—21no—
143C4×D31—42no—
144C4×D31—81no—
145Dic62—21no—
146Dic62—21no—
147Dic62—42no—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3311—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—21no—
156C22×C31C22×D411yescharacteristic
157C2×D31—21no—
158C2×D31—22no—
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C2×D31—84no—
167C4×C31—21no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31—41no—
171C4×C31—41no—
172C4×C31C2×#4111yescharacteristic
173C4×C31H(5,𝔽2)11yescharacteristic
174Dic31—21no—
175Dic31—21no—
176Dic31—21no—
177Dic31—41no—
178Dic31—41no—
179#556—311no—
180#546—311no—
181#489—311no—
182#485D3111yescharacteristic, complemented
183#482—311no—
184#476—311no—
185#470—311no—
186#465—311no—
187#464—311no—
188#452—311no—
189#450—311no—
190#440—311no—
191#435—311no—
192#418—311no—
193#416—311no—
194C2×C31—41no—
195C2×C31#54611yescharacteristic
196C2×C31#57511yescharacteristic
197C2×C31#57711yescharacteristic
198D31—41no—
199D31—42no—
200D31—81no—
201C2×#41—311no—
202C22×D4—311no—
203C2×Q16—311no—
204C2×SD16—311no—
205C2×SD16—311no—
206C2×M16—311no—
207C22×C8—311no—
208C4⋊Q8—311no—
209#126—621no—
210#126—621no—
211#124—311no—
212#124—621no—
213#123—621no—
214C22⋊Q8—311no—
215C22⋊Q8—311no—
216C22⋊Q8C2×D3111yescharacteristic
217#121—311no—
218#121—621no—
219#120—621no—
220C4×Q8—311no—
221C4×Q8—621no—
222C4×D4—311no—
223C4×D4—311no—
224#117—311no—
225#117C2×D3111yescharacteristic
226C2×C22⋊C4—621no—
227#107C2×D3111yescharacteristic, complemented
228#106—311no—
229#106C2×D3111yescharacteristic, complemented
230C4⋊C8—311no—
231#103—311no—
232#103—311no—
233#103C2×D3111yescharacteristic, complemented
234#103C2×D3111yescharacteristic, complemented
235#102—311no—
236#102—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240#102—311no—
241C22⋊C8—311no—
242C22⋊C8C2×D3111yescharacteristic
243#97—311no—
244C31#331111yescharacteristic, complemented, Sylow
245C24—621no—
246#41—622no—
247#41—1241no—
248C2×Q8—311no—
249C2×Q8—621no—
250C2×Q8C22×D3111yescharacteristic
251C2×D4—311no—
252C2×D4—311no—
253C2×D4—311no—
254C2×D4—622no—
255C2×D4—621no—
256C2×D4—621no—
257C2×D4—621no—
258C2×D4—1241no—
259C22×C4—311no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4C22×D3111yescharacteristic
263Q16—1241no—
264SD16—622no—
265SD16—1241no—
266M16—1241no—
267C2×C8—311no—
268C2×C8—311no—
269C2×C8—1241no—
270C2×C8C22×D3111yescharacteristic
271C2×C8C22×D3111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—311no—
274C4⋊C4—311no—
275C4⋊C4—621no—
276C4⋊C4—621no—
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—621no—
296C42—621no—
297C23—311no—
298C23—621no—
299C23—621no—
300C23—1242no—
301C23—1242no—
302C23—2481no—
303C23D4×D3111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—621no—
307Q8—621no—
308Q8—1242no—
309D4—312no—
310D4—621no—
311D4—621no—
312D4—621no—
313D4—1242no—
314D4—1242no—
315D4—1241no—
316D4—2481no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—311no—
324C2×C4—311no—
325C2×C4—311no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—621no—
329C2×C4—621no—
330C2×C4—1242no—
331C2×C4—2481no—
332C2×C4D4×D3111yescharacteristic
333C2×C4C23×D3111yescharacteristic
334C8—21no—
335C8—21no—
336C8—621no—
337C8—621no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—621no—
342C22—621no—
343C22—622no—
344C22—621no—
345C22—1241no—
346C22—1241no—
347C22—1241no—
348C22—1241no—
349C22—1241no—
350C22—2484no—
351C22C2×D4×D3111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—621no—
358C4—621no—
359C4—621no—
360C4—1241no—
361C4—1241no—
362C4#41×D3111yescharacteristic
363C4#1175856611yescharacteristic
364C2—41no—
365C2—1241no—
366C2—1242no—
367C2—2481no—
368C2#1452169111yescharacteristic
369C2#1452184811yescharacteristic
370C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#485C2
socleC22×C31C22×D4
prime radical#14521690C2
hypercenter#485D31
hypocenterC31#3311
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #14521767C2semidirect
3. #14521410C2semidirect
4. #14521376C2semidirect
5. #14521338C2semidirect
6. #14521305C2semidirect
7. #14521279C2semidirect
8. #14521274C2semidirect
9. #14521214C2semidirect
10. #14521202C2semidirect
11. #14521148C2semidirect
12. #14521123C2semidirect
13. #14521053C2semidirect
14. #14521044C2semidirect
15. C31×#485C2semidirect
21. C2×#92482C22semidirect
27. C2×C8×D31C22semidirect
28. #11758474C22semidirect
33. #11758469C22semidirect
34. #11758465C22semidirect
35. #11758464C22semidirect
42. C31×#107C22semidirect
43. C31×#106C22semidirect
44. C31×#103C22semidirect
45. C31×#103C22semidirect
47. #11758423C22semidirect
50. (C2×D31)⋊C8C22semidirect
51. #11758403C22semidirect
52. Dic31⋊C8C22semidirect
53. #11758398C22semidirect
58. #11758396C22semidirect
182. #485D31semidirect
227. #107C2×D31semidirect
229. #106C2×D31semidirect
233. #103C2×D31semidirect
234. #103C2×D31semidirect
244. C31#3311semidirect

Maximal subgroups

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

subgroupindex
#145217672
#145216902
#145214102
#145213762
#145213382
#145213052
#145212792
#145212742
#145212142
#145212022
#145211482
#145211232
#145210532
#145210442
C31×#4852
#331131