Finite Group Databasebeta

← #16855888

Subgroups — #16855888

Order 3968.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521666C211yesmaximal, characteristic, complemented
2#14521524C211yesmaximal, characteristic, complemented
3#14521391C211yesmaximal, characteristic, complemented
4#14521370C211yesmaximal, characteristic, complemented
5#14521337C211yesmaximal, characteristic, complemented
6#14521327C211yesmaximal, characteristic, complemented
7#14521262C211yesmaximal, characteristic, complemented
8#14521262C211yesmaximal, characteristic, complemented
9#14521200C211yesmaximal, characteristic, complemented
10#14521161C211yesmaximal, characteristic, complemented
11#14521146C211yesmaximal, characteristic, complemented
12#14521140C211yesmaximal, characteristic, complemented
13D8×Dic31C211yesmaximal, characteristic, complemented
14#14521107C211yesmaximal, characteristic, complemented
15C31×#447C211yesmaximal, characteristic
16C22×D4×C31C2211yescharacteristic
17C2×D8×C31C2211yescharacteristic
18C2×D8×C31C2211yescharacteristic
19C31×#121C2211yescharacteristic
20C2×C22⋊Dic31—21no—
21C2×C22⋊Dic31—21no—
22#11758513—21no—
23#11758513C2211yescharacteristic, complemented
24#11758512—21no—
25D4×Dic31—21no—
26D4×Dic31—21no—
27D4×Dic31C2211yescharacteristic
28D4×Dic31C2211yescharacteristic
29D4×Dic31C2211yescharacteristic
30D4×Dic31C2211yescharacteristic
31D4×Dic31C2211yescharacteristic, complemented
32C2×#92480C2211yescharacteristic
33C2×#92480C2211yescharacteristic
34#11758503C2211yescharacteristic
35#11758503C2211yescharacteristic
36#11758501C2211yescharacteristic
37#11758465C2211yescharacteristic, complemented
38#11758464C2211yescharacteristic, complemented
39#11758456—21no—
40#11758455—21no—
41C31×#102C2211yescharacteristic
42C31×#102C2211yescharacteristic
43C31×C22⋊C8C2211yescharacteristic
44#11758420C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic, complemented
47#11758420C2211yescharacteristic, complemented
48C22⋊(C31⋊C8)C2211yescharacteristic
49#11758406C2211yescharacteristic, complemented
50#11758405C2211yescharacteristic, complemented
51#11758404C2211yescharacteristic, complemented
52#11758404C2211yescharacteristic, complemented
53#11758403C2211yescharacteristic, complemented
54Dic31⋊C8C2211yescharacteristic, complemented
55Dic31⋊C8C2211yescharacteristic, complemented
56C8×Dic31C2211yescharacteristic, complemented
57#11758396C2211yescharacteristic, complemented
58#11758395C2211yescharacteristic, complemented
59C24×C31—21no—
60C2×D4×C31—22no—
61C2×D4×C31—22no—
62C2×D4×C31—21no—
63C2×D4×C31—21no—
64C2×D4×C31C2311yescharacteristic
65C2×D4×C31C2311yescharacteristic
66C2×D4×C31C2311yescharacteristic
67C22×C4×C31C2311yescharacteristic
68C22×Dic31—21no—
69C22×Dic31—21no—
70C22×Dic31—21no—
71C22×Dic31—21no—
72C22×Dic31—21no—
73C2×Dic62—21no—
74C2×Dic62C2311yescharacteristic
75D8×C31—22no—
76D8×C31—22no—
77C2×C8×C31C2311yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C22⋊C4×C31—21no—
81C22⋊Dic31—21no—
82C22⋊Dic31—21no—
83C22⋊Dic31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89C22⋊Dic31—21no—
90C22⋊Dic31D411yescharacteristic
91C22⋊Dic31D411yescharacteristic
92#92480—22no—
93#92480—22no—
94C4⋊Dic31D411yescharacteristic
95C4⋊Dic31D411yescharacteristic
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31C2311yescharacteristic
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—24no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—81no—
113C23×C31—81no—
114C23×C31C2×D411yescharacteristic
115D4×C31—24no—
116D4×C31—21no—
117D4×C31—21no—
118D4×C31—21no—
119D4×C31—21no—
120D4×C31—81no—
121D4×C31#4112yes—
122D4×C31#4112yes—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2411yescharacteristic
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—81no—
133C2×Dic31—81no—
134C2×Dic31—81no—
135C2×Dic31—81no—
136C2×Dic31—81no—
137C2×Dic31C2×D411yescharacteristic
138C2×Dic31C2×D411yescharacteristic
139C2×Dic31C2×D411yescharacteristic
140C2×Dic31C2×D411yescharacteristic
141Dic62—21no—
142Dic62—21no—
143Dic62—81no—
144C8×C31—21no—
145C8×C31—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3118—311nomaximal, Sylow
149C22×C31—21no—
150C22×C31—22no—
151C22×C31—22no—
152C22×C31—21no—
153C22×C31—21no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31—41no—
159C22×C31—41no—
160C22×C31—41no—
161C22×C31—84no—
162C22×C31C22×D411yescharacteristic
163C4×C31—21no—
164C4×C31—41no—
165C4×C31C2×#4111yescharacteristic
166C4×C31C2×#4111yescharacteristic
167Dic31—21no—
168Dic31—21no—
169Dic31—21no—
170Dic31—21no—
171Dic31—41no—
172Dic31—41no—
173Dic31—41no—
174Dic31—41no—
175#542—311no—
176#518—311no—
177#485—311no—
178#482—311no—
179#476—311no—
180#474—311no—
181#463—311no—
182#463—311no—
183#450—311no—
184#447D3111yescharacteristic
185#442—311no—
186#440—311no—
187C4×SD16—311no—
188C4×D8—311no—
189#433—311no—
190C2×C31—41no—
191C2×C31—42no—
192C2×C31—42no—
193C2×C31—81no—
194C2×C31#52511yescharacteristic
195C2×C31#57611yescharacteristic
196C2×C31#57711yescharacteristic
197C22×D4C2×D3111yescharacteristic
198C2×SD16—311no—
199C2×SD16—311no—
200C2×D8C2×D3111yescharacteristic
201C2×D8C2×D3111yescharacteristic
202C4⋊Q8—311no—
203#126—621no—
204#124—311no—
205#124—621no—
206#123—621no—
207C22⋊Q8—311no—
208C22⋊Q8—621no—
209#121C2×D3111yescharacteristic
210C4×Q8—311no—
211C4×D4—311no—
212C4×D4—311no—
213C4×D4—311no—
214C4×D4—311no—
215C4×D4—311no—
216C4×D4—621no—
217C4×D4—621no—
218#117—311no—
219#117—311no—
220C2×C22⋊C4—621no—
221C2×C22⋊C4—621no—
222#107—311no—
223#107—311no—
224#106—311no—
225#106—311no—
226C4⋊C8—311no—
227C4⋊C8—311no—
228#103—311no—
229#103—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234#102C2×D3111yescharacteristic
235#102C2×D3111yescharacteristic
236C22⋊C8—311no—
237C22⋊C8C2×D3111yescharacteristic
238#97—311no—
239C4×C8—311no—
240C31#311811yescharacteristic, complemented, Sylow
241C24—21no—
242C2×Q8—311no—
243C2×Q8—621no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22×D3111yescharacteristic
249C2×D4C22×D3111yescharacteristic
250C2×D4C22×D3111yescharacteristic
251C22×C4—621no—
252C22×C4—621no—
253C22×C4—621no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4C22×D3111yescharacteristic
257SD16—622no—
258SD16—622no—
259D8—22no—
260D8—22no—
261C2×C8—311no—
262C2×C8—311no—
263C2×C8C22×D3111yescharacteristic
264C2×C8C22×D3111yescharacteristic
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—311no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4C22×D3111yescharacteristic
274C22⋊C4—21no—
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—
285C22⋊C4—621no—
286C42—311no—
287C42—311no—
288C42—621no—
289C42—621no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23D4×D3111yescharacteristic
297Q8—621no—
298Q8—621no—
299Q8—2481no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4#9249712yes—
307D4#9249712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—311no—
312C2×C4—311no—
313C2×C4—311no—
314C2×C4—311no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—2481no—
320C2×C4—2481no—
321C2×C4—2481no—
322C2×C4—2481no—
323C2×C4—2481no—
324C2×C4D4×D3111yescharacteristic
325C2×C4C23×D3111yescharacteristic
326C8—21no—
327C8—21no—
328C8—621no—
329C8—621no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—22no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C2×D4×D3111yescharacteristic
344C4—21no—
345C4—41no—
346C4—621no—
347C4—621no—
348C4—621no—
349C4—621no—
350C4—1241no—
351C4—1241no—
352C4—1241no—
353C4—1241no—
354C4C2×#9249711yescharacteristic
355C4C2×#9249711yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2#1452155511yescharacteristic
361C2#1452185011yescharacteristic
362C2#1452185911yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalC31×#447C2
socleC22×C31C22×D4
hypercenter#447D31
hypocenterC31#3118
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14521666C2semidirect
2. #14521524C2semidirect
3. #14521391C2semidirect
4. #14521370C2semidirect
5. #14521337C2semidirect
6. #14521327C2semidirect
7. #14521262C2semidirect
8. #14521262C2semidirect
9. #14521200C2semidirect
10. #14521161C2semidirect
11. #14521146C2semidirect
12. #14521140C2semidirect
13. D8×Dic31C2semidirect
14. #14521107C2semidirect
23. #11758513C22semidirect
31. D4×Dic31C22semidirect
37. #11758465C22semidirect
38. #11758464C22semidirect
46. #11758420C22semidirect
47. #11758420C22semidirect
49. #11758406C22semidirect
50. #11758405C22semidirect
51. #11758404C22semidirect
52. #11758404C22semidirect
53. #11758403C22semidirect
54. Dic31⋊C8C22semidirect
55. Dic31⋊C8C22semidirect
56. C8×Dic31C22semidirect
57. #11758396C22semidirect
58. #11758395C22semidirect
240. C31#3118semidirect

Maximal subgroups

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

subgroupindex
#145216662
#145215242
#145213912
#145213702
#145213372
#145213272
#145212622
#145212002
#145211612
#145211462
#145211402
D8×Dic312
#145211072
C31×#4472
#311831