Finite Group Databasebeta

← #16857519

Subgroups — #16857519

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
2#14521683C211yesmaximal, characteristic, complemented
3#14521394C211yesmaximal, characteristic, complemented
4#14521364C211yesmaximal, characteristic, complemented
5#14521360C211yesmaximal, characteristic, complemented
6#14521328C211yesmaximal, characteristic, complemented
7#14521284C211yesmaximal, characteristic, complemented
8#14521242C211yesmaximal, characteristic, complemented
9#14521182C211yesmaximal, characteristic, complemented
10#14521181C211yesmaximal, characteristic, complemented
11#14521129C211yesmaximal, characteristic, complemented
12C8×C22⋊D31C211yesmaximal, characteristic, complemented
13C2×#11758409C211yesmaximal, characteristic, complemented
14#102×D31C211yesmaximal, characteristic, complemented
15C31×#466C211yesmaximal, characteristic, complemented
16C2×#92497—21no—
17C2×D4×D31—21no—
18C2×D4×D31C2211yescharacteristic
19C22×D124C2211yescharacteristic
20C2×D8×C31C2211yescharacteristic, complemented
21C22×C8×C31C2211yescharacteristic, complemented
22C31×#121C2211yescharacteristic
23C31×#121C2211yescharacteristic, complemented
24#11758517C2211yescharacteristic
25#11758515C2211yescharacteristic, complemented
26#11758514—21no—
27#11758512—21no—
28D4×Dic31C2211yescharacteristic, complemented
29C2×#92479C2211yescharacteristic
30C2×#92479C2211yescharacteristic, complemented
31C4×C22⋊D31C2211yescharacteristic
32C2×C4⋊Dic31C2211yescharacteristic, complemented
33C2×C8×D31C2211yescharacteristic, complemented
34#11758472C2211yescharacteristic
35#11758470C2211yescharacteristic
36C4⋊C4×D31C2211yescharacteristic, complemented
37#11758465C2211yescharacteristic, complemented
38#11758461—21no—
39#11758460—21no—
40#11758459—21no—
41#11758455—21no—
42C31×#107C2211yescharacteristic, complemented
43C31×#102C2211yescharacteristic, complemented
44C31×#102C2211yescharacteristic, complemented
45#11758420C2211yescharacteristic, complemented
46#11758420C2211yescharacteristic, complemented
47C22⋊(C31⋊C8)C2211yescharacteristic, complemented
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758409C2211yescharacteristic, complemented
51#11758409C2211yescharacteristic, complemented
52(C2×D31)⋊C8C2211yescharacteristic, complemented
53Dic31⋊C8C2211yescharacteristic, complemented
54C8×Dic31C2211yescharacteristic, complemented
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic, complemented
57#11758395C2211yescharacteristic, complemented
58#11758395C2211yescharacteristic, complemented
59C23×D31—21no—
60C23×D31—21no—
61C2×D4×C31—21no—
62C2×D4×C31—21no—
63C2×D4×C31C2311yescharacteristic
64C2×D4×C31C2311yescharacteristic
65C22×C4×C31C2311yescharacteristic
66C2×C22⋊D31—21no—
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69C2×C22⋊D31—21no—
70C2×C22⋊D31D411yescharacteristic
71C22×Dic31—21no—
72C22×Dic31—21no—
73#92497—44no—
74D4×D31—22no—
75D4×D31—41no—
76D4×D31—44no—
77C2×D124—22no—
78C2×D124—21no—
79C2×D124—21no—
80C2×D124—41no—
81C2×D124C2311yescharacteristic
82C2×D124C2311yescharacteristic
83C2×C4×D31—21no—
84C2×C4×D31—21no—
85C2×C4×D31C2311yescharacteristic
86C2×Dic62—21no—
87D8×C31—41no—
88C2×C8×C31—41no—
89C2×C8×C31C2311yescharacteristic
90C2×C8×C31C2311yescharacteristic
91C4⋊C4×C31C2311yescharacteristic
92C4⋊C4×C31C2311yescharacteristic
93C22⋊C4×C31—21no—
94C22⋊C4×C31—21no—
95C22⋊Dic31—21no—
96C22⋊Dic31—21no—
97C22⋊Dic31D411yescharacteristic
98#92479—22no—
99#92479—41no—
100(C2×D31)⋊C4—21no—
101(C2×D31)⋊C4—21no—
102(C2×D31)⋊C4D411yescharacteristic
103C4⋊Dic31—21no—
104C4⋊Dic31C2311yescharacteristic
105C4⋊Dic31C2311yescharacteristic
106Dic31⋊C4—21no—
107Dic31⋊C4—21no—
108Dic31⋊C4D411yescharacteristic
109C4×Dic31C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C2×C31⋊C8C2311yescharacteristic
112C8×D31—41no—
113C23×C31—21no—
114C23×C31—21no—
115C23×C31C2×D411yescharacteristic
116C22×D31—21no—
117C22×D31—21no—
118C22×D31—42no—
119C22×D31—42no—
120C22×D31—42no—
121C22×D31—42no—
122C22×D31—81no—
123C22×D31—81no—
124C22×D31C2×D411yescharacteristic
125D4×C31—21no—
126D4×C31—21no—
127D4×C31—21no—
128D4×C31—21no—
129D4×C31—42no—
130D4×C31—42no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31C2×D411yescharacteristic
136C2×C4×C31C2411yescharacteristic
137C22⋊D31—42no—
138C22⋊D31—42no—
139C22⋊D31—42no—
140C22⋊D31—81no—
141C22⋊D31D814yescomplemented
142C2×Dic31—21no—
143C2×Dic31—21no—
144C2×Dic31—42no—
145C2×Dic31—42no—
146C2×Dic31C2×D411yescharacteristic
147C2×Dic31C2×D411yescharacteristic
148C2×Dic31C2×D411yescharacteristic
149D124—21no—
150D124—21no—
151D124—21no—
152D124—42no—
153D124—42no—
154D124#4112yescomplemented
155C4×D31—21no—
156C4×D31—21no—
157C4×D31—42no—
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—41no—
168C22×C31—41no—
169C22×C31—41no—
170C22×C31—41no—
171C22×C31—41no—
172C22×C31—41no—
173C22×C31C2×D812yes—
174C22×C31C22×D411yescharacteristic
175C2×D31—21no—
176C2×D31—21no—
177C2×D31—22no—
178C2×D31—41no—
179C2×D31—41no—
180C2×D31—41no—
181C2×D31—41no—
182C2×D31—41no—
183C2×D31—84no—
184C2×D31—84no—
185C2×D31C2×D812yes—
186C4×C31—21no—
187C4×C31—41no—
188C4×C31—41no—
189C4×C31C2×#4111yescharacteristic
190C4×C31H(5,𝔽2)11yescharacteristic
191Dic31—21no—
192Dic31—21no—
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#466D3111yescharacteristic, complemented
204#459—311no—
205#447—311no—
206#447—311no—
207C4×D8—311no—
208C8×D4—311no—
209C2×#102—311no—
210C2×#102—311no—
211C2×C31—22no—
212C2×C31—81no—
213C2×C31—81no—
214C2×C31#54611yescharacteristic
215C2×C31C22×D811yescharacteristic
216C2×C31#57711yescharacteristic
217D31—22no—
218D31—42no—
219D31—81no—
220C2×#41—621no—
221C22×D4—311no—
222C22×D4—311no—
223C22×D4—621no—
224C2×D8—311no—
225C2×D8—311no—
226C2×D8C2×D3111yescharacteristic, complemented
227C22×C8—311no—
228C22×C8C2×D3111yescharacteristic, complemented
229C4⋊Q8—311no—
230#127—311no—
231#123—621no—
232#123—621no—
233C22⋊Q8—621no—
234#121—311no—
235#121—311no—
236#121—621no—
237#121C2×D3111yescharacteristic
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#107C2×D3111yescharacteristic, complemented
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, complemented
259#102C2×D3111yescharacteristic, complemented
260C22⋊C8—311no—
261C22⋊C8—311no—
262C4×C8—311no—
263C31#329411yescharacteristic, complemented, Sylow
264C24—621no—
265C24—621no—
266#41—1244no—
267C2×Q8—621no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—311no—
271C2×D4—311no—
272C2×D4—311no—
273C2×D4—622no—
274C2×D4—621no—
275C2×D4—621no—
276C2×D4—621no—
277C2×D4—621no—
278C2×D4—622no—
279C2×D4—621no—
280C2×D4—621no—
281C2×D4—1241no—
282C2×D4—1241no—
283C2×D4—1244no—
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—41no—
293D8—622no—
294D8—1241no—
295C2×C8—41no—
296C2×C8—311no—
297C2×C8—311no—
298C2×C8—1241no—
299C2×C8C22×D3111yescharacteristic
300C2×C8C22×D3111yescharacteristic
301C4⋊C4—311no—
302C4⋊C4—311no—
303C4⋊C4—311no—
304C4⋊C4—621no—
305C4⋊C4—621no—
306C4⋊C4—621no—
307C4⋊C4C22×D3111yescharacteristic
308C4⋊C4C22×D3111yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—311no—
312C22⋊C4—311no—
313C22⋊C4—621no—
314C22⋊C4—621no—
315C22⋊C4—621no—
316C22⋊C4—621no—
317C42—311no—
318C23—21no—
319C23—21no—
320C23—311no—
321C23—621no—
322C23—621no—
323C23—1242no—
324C23—1242no—
325C23—1242no—
326C23—1242no—
327C23—2481no—
328C23—2481no—
329C23D4×D3111yescharacteristic
330Q8—1242no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—42no—
336D4—42no—
337D4—314no—
338D4—312no—
339D4—621no—
340D4—621no—
341D4—621no—
342D4—1242no—
343D4—1242no—
344D4—1242no—
345D4—1242no—
346D4—1242no—
347D4—2481no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—311no—
353C2×C4—311no—
354C2×C4—311no—
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—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—312no—
378C22—621no—
379C22—621no—
380C22—622no—
381C22—1241no—
382C22—1241no—
383C22—1241no—
384C22—1241no—
385C22—1241no—
386C22—2484no—
387C22—2484no—
388C22D8×D3112yes—
389C22C2×D4×D3111yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—312no—
394C4—621no—
395C4—621no—
396C4—1241no—
397C4—1241no—
398C4#1175856111yescharacteristic
399C4#41×D3111yescharacteristic
400C2—22no—
401C2—81no—
402C2—81no—
403C2—622no—
404C2—1242no—
405C2—2481no—
406C2#1452168811yescharacteristic
407C2C2×D8×D3111yescharacteristic
408C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#466C2
socleC22×C31C22×D4
hypercenter#466D31
hypocenterC31#3294
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #14521699C2semidirect
2. #14521683C2semidirect
3. #14521394C2semidirect
4. #14521364C2semidirect
5. #14521360C2semidirect
6. #14521328C2semidirect
7. #14521284C2semidirect
8. #14521242C2semidirect
9. #14521182C2semidirect
10. #14521181C2semidirect
11. #14521129C2semidirect
12. C8×C22⋊D31C2semidirect
13. C2×#11758409C2semidirect
14. #102×D31C2semidirect
15. C31×#466C2semidirect
20. C2×D8×C31C22semidirect
21. C22×C8×C31C22semidirect
23. C31×#121C22semidirect
25. #11758515C22semidirect
28. D4×Dic31C22semidirect
30. C2×#92479C22semidirect
32. C2×C4⋊Dic31C22semidirect
33. C2×C8×D31C22semidirect
36. C4⋊C4×D31C22semidirect
37. #11758465C22semidirect
42. C31×#107C22semidirect
43. C31×#102C22semidirect
44. C31×#102C22semidirect
45. #11758420C22semidirect
46. #11758420C22semidirect
47. C22⋊(C31⋊C8)C22semidirect
50. #11758409C22semidirect
51. #11758409C22semidirect
52. (C2×D31)⋊C8C22semidirect
53. Dic31⋊C8C22semidirect
54. C8×Dic31C22semidirect
56. #11758397C22semidirect
57. #11758395C22semidirect
58. #11758395C22semidirect
141. C22⋊D31D8semidirect
154. D124#41semidirect
203. #466D31semidirect
226. C2×D8C2×D31semidirect
228. C22×C8C2×D31semidirect
238. #121C2×D31semidirect
248. #107C2×D31semidirect
258. #102C2×D31semidirect
259. #102C2×D31semidirect
263. C31#3294semidirect

Maximal subgroups

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

subgroupindex
#145216992
#145216832
#145213942
#145213642
#145213602
#145213282
#145212842
#145212422
#145211822
#145211812
#145211292
C8×C22⋊D312
C2×#117584092
#102×D312
C31×#4662
#329431