Finite Group Databasebeta

← #16857517

Subgroups — #16857517

Order 3968.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521699C211yesmaximal, characteristic, complemented
2D4×C22⋊D31C211yesmaximal, characteristic, complemented
3#14521394C211yesmaximal, characteristic, complemented
4#14521363C211yesmaximal, characteristic, complemented
5#14521361C211yesmaximal, characteristic, complemented
6#14521327C211yesmaximal, characteristic, complemented
7#14521283C211yesmaximal, characteristic, complemented
8#14521282C211yesmaximal, characteristic, complemented
9#14521242C211yesmaximal, characteristic, complemented
10#14521181C211yesmaximal, characteristic, complemented
11D8×Dic31C211yesmaximal, characteristic, complemented
12(C22⋊D31)⋊C8C211yesmaximal, characteristic, complemented
13C2×#11758420C211yesmaximal, characteristic, complemented
14#102×D31C211yesmaximal, characteristic, complemented
15C31×#447C211yesmaximal, characteristic, complemented
16C22×D4×C31C2211yescharacteristic
17C22×C22⋊D31—21no—
18C2×#92497—21no—
19C2×D4×D31C2211yescharacteristic
20C2×D8×C31C2211yescharacteristic
21C2×D8×C31C2211yescharacteristic, complemented
22C31×#121C2211yescharacteristic, complemented
23#11758530—21no—
24#11758517C2211yescharacteristic
25#11758516—21no—
26#11758515C2211yescharacteristic
27#11758515C2211yescharacteristic, complemented
28#11758514—21no—
29#11758512—21no—
30D4×Dic31C2211yescharacteristic
31D4×Dic31C2211yescharacteristic, complemented
32C2×#92479C2211yescharacteristic, complemented
33#11758507C2211yescharacteristic
34C4×C22⋊D31C2211yescharacteristic
35C2×C4⋊Dic31C2211yescharacteristic, complemented
36C22×C31⋊C8C2211yescharacteristic, complemented
37C2×C8×D31C2211yescharacteristic, complemented
38C4⋊C4×D31C2211yescharacteristic, complemented
39#11758465C2211yescharacteristic, complemented
40#11758460—21no—
41#11758455—21no—
42C31×#102C2211yescharacteristic
43C31×#102C2211yescharacteristic, complemented
44C31×C22⋊C8C2211yescharacteristic, complemented
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic, complemented
48#11758420C2211yescharacteristic, complemented
49#11758420C2211yescharacteristic, complemented
50#11758409C2211yescharacteristic, complemented
51#11758409C2211yescharacteristic, complemented
52(C2×D31)⋊C8C2211yescharacteristic, complemented
53#11758406C2211yescharacteristic, complemented
54#11758406C2211yescharacteristic, complemented
55Dic31⋊C8C2211yescharacteristic, complemented
56C8×Dic31C2211yescharacteristic, complemented
57#11758397C2211yescharacteristic, complemented
58#11758395C2211yescharacteristic, complemented
59C24×C31—21no—
60C23×D31—21no—
61C2×D4×C31—22no—
62C2×D4×C31—21no—
63C2×D4×C31—21no—
64C2×D4×C31—41no—
65C2×D4×C31C2311yescharacteristic
66C2×D4×C31C2311yescharacteristic
67C2×D4×C31C2311yescharacteristic
68C22×C4×C31C2311yescharacteristic
69C2×C22⋊D31—21no—
70C2×C22⋊D31—21no—
71C2×C22⋊D31—21no—
72C2×C22⋊D31—21no—
73C2×C22⋊D31—21no—
74C2×C22⋊D31—21no—
75C2×C22⋊D31—44no—
76C2×C22⋊D31D411yescharacteristic
77C22×Dic31—21no—
78C22×Dic31—21no—
79C22×Dic31—21no—
80#92497—44no—
81D4×D31—22no—
82D4×D31—41no—
83C2×D124C2311yescharacteristic
84C2×C4×D31—21no—
85C2×C4×D31C2311yescharacteristic
86C2×Dic62—21no—
87D8×C31—22no—
88D8×C31—41no—
89C2×C8×C31C2311yescharacteristic
90C2×C8×C31C2311yescharacteristic
91C4⋊C4×C31C2311yescharacteristic
92C22⋊C4×C31—21no—
93C22⋊Dic31—21no—
94C22⋊Dic31—21no—
95C22⋊Dic31—21no—
96C22⋊Dic31—21no—
97C22⋊Dic31D411yescharacteristic
98#92479—41no—
99(C2×D31)⋊C4—21no—
100(C2×D31)⋊C4D411yescharacteristic
101C4⋊Dic31—21no—
102C4⋊Dic31C2311yescharacteristic
103C4⋊Dic31C2311yescharacteristic
104C4⋊Dic31C2311yescharacteristic
105Dic31⋊C4—21no—
106Dic31⋊C4—21no—
107Dic31⋊C4D411yescharacteristic
108C4×Dic31C2311yescharacteristic
109C2×C31⋊C8—41no—
110C2×C31⋊C8C2311yescharacteristic
111C2×C31⋊C8C2311yescharacteristic
112C8×D31—41no—
113C23×C31—21no—
114C23×C31—21no—
115C23×C31—21no—
116C23×C31—42no—
117C23×C31—42no—
118C23×C31—81no—
119C23×C31C2×D411yescharacteristic
120C22×D31—21no—
121C22×D31—42no—
122C22×D31—42no—
123C22×D31—81no—
124C22×D31C2×D411yescharacteristic
125D4×C31—21no—
126D4×C31—21no—
127D4×C31—21no—
128D4×C31—21no—
129D4×C31—21no—
130D4×C31—42no—
131D4×C31—42no—
132D4×C31#4112yescomplemented
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31C2×D411yescharacteristic
137C2×C4×C31C2411yescharacteristic
138C22⋊D31—42no—
139C22⋊D31—42no—
140C22⋊D31—42no—
141C22⋊D31—42no—
142C22⋊D31—42no—
143C22⋊D31—81no—
144C22⋊D31D814yescomplemented
145C2×Dic31—21no—
146C2×Dic31—21no—
147C2×Dic31—21no—
148C2×Dic31—42no—
149C2×Dic31—42no—
150C2×Dic31—42no—
151C2×Dic31C2×D411yescharacteristic
152C2×Dic31C2×D411yescharacteristic
153C2×Dic31C2×D411yescharacteristic
154D124—21no—
155D124—21no—
156C4×D31—21no—
157C4×D31—21no—
158C4×D31—42no—
159Dic62—42no—
160C8×C31—21no—
161C8×C31—21no—
162C31⋊C8—21no—
163C31⋊C8—21no—
164#3294—311nomaximal, Sylow
165C22×C31—21no—
166C22×C31—21no—
167C22×C31—22no—
168C22×C31—41no—
169C22×C31—41no—
170C22×C31—41no—
171C22×C31—41no—
172C22×C31—41no—
173C22×C31—41no—
174C22×C31—41no—
175C22×C31—41no—
176C22×C31—84no—
177C22×C31C2×D812yes—
178C22×C31C22×D411yescharacteristic
179C2×D31—21no—
180C2×D31—21no—
181C2×D31—41no—
182C2×D31—41no—
183C2×D31—41no—
184C2×D31—84no—
185C2×D31C2×D812yes—
186C4×C31—21no—
187C4×C31—41no—
188C4×C31C2×#4111yescharacteristic
189C4×C31H(5,𝔽2)11yescharacteristic
190Dic31—21no—
191Dic31—21no—
192Dic31—41no—
193Dic31—41no—
194Dic31—41no—
195Dic31C2×D812yes—
196#547—311no—
197D42—311no—
198#486—311no—
199#480—311no—
200#480—311no—
201#474—311no—
202#466—311no—
203#466—311no—
204#459—311no—
205#447—311no—
206#447D3111yescharacteristic, complemented
207C4×D8—311no—
208C8×D4—311no—
209C2×#102—311no—
210C2×#102—311no—
211C2×C31—22no—
212C2×C31—42no—
213C2×C31—81no—
214C2×C31—81no—
215C2×C31#54611yescharacteristic
216C2×C31C22×D811yescharacteristic
217C2×C31#57711yescharacteristic
218D31—22no—
219D31—81no—
220C2×#41—621no—
221C22×D4—311no—
222C22×D4—621no—
223C22×D4C2×D3111yescharacteristic
224C2×D8—311no—
225C2×D8C2×D3111yescharacteristic
226C2×D8C2×D3111yescharacteristic, complemented
227C22×C8—311no—
228C22×C8—311no—
229C4⋊Q8—311no—
230#127—311no—
231#123—621no—
232#123—621no—
233C22⋊Q8—621no—
234#121—311no—
235#121—311no—
236#121—311no—
237#121—621no—
238#121C2×D3111yescharacteristic, complemented
239#120—621no—
240#120—621no—
241C4×D4—311no—
242C4×D4—311no—
243C4×D4—311no—
244C2×C4⋊C4—311no—
245C2×C4⋊C4—311no—
246#107—311no—
247#107—311no—
248#107—311no—
249C4⋊C8—311no—
250#102—311no—
251#102—311no—
252#102—311no—
253#102—311no—
254#102—311no—
255#102—311no—
256#102—311no—
257#102—311no—
258#102C2×D3111yescharacteristic
259#102C2×D3111yescharacteristic, complemented
260C22⋊C8—311no—
261C22⋊C8C2×D3111yescharacteristic, complemented
262C4×C8—311no—
263C31#329411yescharacteristic, complemented, Sylow
264C24—21no—
265C24—621no—
266#41—1244no—
267C2×Q8—621no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—311no—
273C2×D4—311no—
274C2×D4—621no—
275C2×D4—621no—
276C2×D4—621no—
277C2×D4—622no—
278C2×D4—621no—
279C2×D4—621no—
280C2×D4—621no—
281C2×D4—1241no—
282C2×D4—1244no—
283C2×D4C22×D3111yescharacteristic
284C2×D4C22×D3111yescharacteristic
285C2×D4C22×D3111yescharacteristic
286C22×C4—311no—
287C22×C4—621no—
288C22×C4—621no—
289C22×C4—621no—
290C22×C4—621no—
291C22×C4C22×D3111yescharacteristic
292D8—22no—
293D8—41no—
294D8—1241no—
295C2×C8—311no—
296C2×C8—311no—
297C2×C8—1241no—
298C2×C8—1241no—
299C2×C8C22×D3111yescharacteristic
300C2×C8C22×D3111yescharacteristic
301C4⋊C4—311no—
302C4⋊C4—311no—
303C4⋊C4—311no—
304C4⋊C4—311no—
305C4⋊C4—621no—
306C4⋊C4—621no—
307C4⋊C4—621no—
308C4⋊C4C22×D3111yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—311no—
311C22⋊C4—311no—
312C22⋊C4—621no—
313C22⋊C4—621no—
314C22⋊C4—621no—
315C22⋊C4—621no—
316C22⋊C4—621no—
317C42—311no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—311no—
325C23—621no—
326C23—1242no—
327C23—1242no—
328C23—2481no—
329C23D4×D3111yescharacteristic
330Q8—1242no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—42no—
338D4—314no—
339D4—621no—
340D4—621no—
341D4—1242no—
342D4—1242no—
343D4—1242no—
344D4—1242no—
345D4—1242no—
346D4—2481no—
347D4#9249712yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—311no—
352C2×C4—311no—
353C2×C4—311no—
354C2×C4—621no—
355C2×C4—621no—
356C2×C4—621no—
357C2×C4—621no—
358C2×C4—621no—
359C2×C4—1242no—
360C2×C4—1242no—
361C2×C4—1242no—
362C2×C4—1242no—
363C2×C4D4×D3111yescharacteristic
364C2×C4C23×D3111yescharacteristic
365C8—21no—
366C8—21no—
367C8—621no—
368C8—621no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—312no—
382C22—621no—
383C22—621no—
384C22—1241no—
385C22—1241no—
386C22—1241no—
387C22—2484no—
388C22D8×D3112yes—
389C22C2×D4×D3111yescharacteristic
390C4—21no—
391C4—41no—
392C4—312no—
393C4—621no—
394C4—621no—
395C4—1241no—
396C4—1241no—
397C4—1241no—
398C4C2×#9249711yescharacteristic
399C4#1175856111yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—81no—
404C2—622no—
405C2—2481no—
406C2#1452168611yescharacteristic
407C2C2×D8×D3111yescharacteristic
408C2#1452185911yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#447C2
socleC22×C31C22×D4
hypercenter#447D31
hypocenterC31#3294
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. #14521699C2semidirect
2. D4×C22⋊D31C2semidirect
3. #14521394C2semidirect
4. #14521363C2semidirect
5. #14521361C2semidirect
6. #14521327C2semidirect
7. #14521283C2semidirect
8. #14521282C2semidirect
9. #14521242C2semidirect
10. #14521181C2semidirect
11. D8×Dic31C2semidirect
12. (C22⋊D31)⋊C8C2semidirect
13. C2×#11758420C2semidirect
14. #102×D31C2semidirect
15. C31×#447C2semidirect
21. C2×D8×C31C22semidirect
22. C31×#121C22semidirect
27. #11758515C22semidirect
31. D4×Dic31C22semidirect
32. C2×#92479C22semidirect
35. C2×C4⋊Dic31C22semidirect
36. C22×C31⋊C8C22semidirect
37. C2×C8×D31C22semidirect
38. C4⋊C4×D31C22semidirect
39. #11758465C22semidirect
43. C31×#102C22semidirect
44. C31×C22⋊C8C22semidirect
47. #11758420C22semidirect
48. #11758420C22semidirect
49. #11758420C22semidirect
50. #11758409C22semidirect
51. #11758409C22semidirect
52. (C2×D31)⋊C8C22semidirect
53. #11758406C22semidirect
54. #11758406C22semidirect
55. Dic31⋊C8C22semidirect
56. C8×Dic31C22semidirect
57. #11758397C22semidirect
58. #11758395C22semidirect
132. D4×C31#41semidirect
144. C22⋊D31D8semidirect
206. #447D31semidirect
226. C2×D8C2×D31semidirect
238. #121C2×D31semidirect
259. #102C2×D31semidirect
261. C22⋊C8C2×D31semidirect
263. C31#3294semidirect
347. D4#92497semidirect

Maximal subgroups

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

subgroupindex
#145216992
D4×C22⋊D312
#145213942
#145213632
#145213612
#145213272
#145212832
#145212822
#145212422
#145211812
D8×Dic312
(C22⋊D31)⋊C82
C2×#117584202
#102×D312
C31×#4472
#329431