Finite Group Databasebeta

← #16848851

Subgroups — #16848851

Order 3968.

688 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758459C211yesmaximal, characteristic
2#14520951C211yesmaximal, characteristic, complemented
3#14520950C211yesmaximal, characteristic, complemented
4#14520949C211yesmaximal, characteristic, complemented
5#14520942C211yesmaximal, characteristic, complemented
6#14520941C211yesmaximal, characteristic, complemented
7#14520940C211yesmaximal, characteristic, complemented
8#14520939C211yesmaximal, characteristic, complemented
9#14520938C211yesmaximal, characteristic, complemented
10#14520927C211yesmaximal, characteristic, complemented
11#14520927C211yesmaximal, characteristic, complemented
12#14520925C211yesmaximal, characteristic, complemented
13#14520904C211yesmaximal, characteristic, complemented
14#14520904C211yesmaximal, characteristic, complemented
15C31×#388C211yesmaximal, characteristic, complemented
16C24×D31C2211yescharacteristic
17C22×C22⋊D31C2211yescharacteristic
18C22×D124C2211yescharacteristic
19C22×D124C2211yescharacteristic
20C22×C4×D31C2211yescharacteristic, complemented
21C2×C4⋊C4×C31C2211yescharacteristic, complemented
22C2×C22⋊C4×C31C2211yescharacteristic
23C2×C22⋊C4×C31C2211yescharacteristic
24C2×C22⋊C4×C31C2211yescharacteristic
25C2×C42×C31C2211yescharacteristic, complemented
26C2×C22⋊Dic31C2211yescharacteristic
27C2×C22⋊Dic31C2211yescharacteristic
28C2×(C2×D31)⋊C4C2211yescharacteristic
29C2×(C2×D31)⋊C4C2211yescharacteristic
30C2×(C2×D31)⋊C4C2211yescharacteristic
31C2×(C2×D31)⋊C4C2211yescharacteristic
32C2×(C2×D31)⋊C4C2211yescharacteristic
33C2×(C2×D31)⋊C4C2211yescharacteristic
34C2×(C2×D31)⋊C4C2211yescharacteristic
35C2×(C2×D31)⋊C4C2211yescharacteristic
36C2×(C2×D31)⋊C4C2211yescharacteristic
37C2×(C2×D31)⋊C4C2211yescharacteristic
38C2×(C2×D31)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D31)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D31)⋊C4C2211yescharacteristic, complemented
41C2×C4⋊Dic31C2211yescharacteristic, complemented
42C2×Dic31⋊C4C2211yescharacteristic, complemented
43C2×C4×Dic31C2211yescharacteristic, complemented
44C2×C4×Dic31C2211yescharacteristic, complemented
45#11758459C418yescomplemented
46C31×#95C2211yescharacteristic, complemented
47C31×#95C2211yescharacteristic, complemented
48C31⋊#95C2211yescharacteristic, complemented
49C31⋊#95C2211yescharacteristic, complemented
50C31⋊#95C2211yescharacteristic, complemented
51C31⋊#95C2211yescharacteristic, complemented
52C24×C31C2311yescharacteristic
53C23×D31—41no—
54C23×D31—41no—
55C23×D31—41no—
56C23×D31—41no—
57C23×D31—41no—
58C23×D31—41no—
59C23×D31C2×C414yescomplemented
60C23×D31C2311yescharacteristic
61C23×D31C2311yescharacteristic
62C23×D31C2311yescharacteristic
63C22×C4×C31C2311yescharacteristic
64C22×C4×C31C2311yescharacteristic
65C22×C4×C31C2311yescharacteristic
66C22×C4×C31C2311yescharacteristic
67C22×C4×C31C2311yescharacteristic
68C22×C4×C31C2311yescharacteristic
69C2×C22⋊D31—41no—
70C2×C22⋊D31—41no—
71C2×C22⋊D31C2×C414yes—
72C22×Dic31C2311yescharacteristic
73C22×Dic31C2311yescharacteristic
74C22×Dic31C2311yescharacteristic
75C22×Dic31C2311yescharacteristic
76C22×Dic31C2311yescharacteristic
77C2×D124—41no—
78C2×D124—41no—
79C2×D124—41no—
80C2×D124—41no—
81C2×D124C2×C414yes—
82C2×D124C2×C414yes—
83C2×C4×D31—41no—
84C2×C4×D31—41no—
85C2×C4×D31—41no—
86C4⋊C4×C31—41no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—41no—
89C22⋊C4×C31C2×C414yescomplemented
90C42×C31—41no—
91C22⋊Dic31—41no—
92C22⋊Dic31—41no—
93(C2×D31)⋊C4—41no—
94(C2×D31)⋊C4—41no—
95(C2×D31)⋊C4—41no—
96(C2×D31)⋊C4—41no—
97(C2×D31)⋊C4—41no—
98(C2×D31)⋊C4—41no—
99(C2×D31)⋊C4—41no—
100(C2×D31)⋊C4—41no—
101(C2×D31)⋊C4—41no—
102(C2×D31)⋊C4—41no—
103(C2×D31)⋊C4—41no—
104(C2×D31)⋊C4C2×C414yescomplemented
105(C2×D31)⋊C4C2×C414yescomplemented
106C4⋊Dic31—41no—
107Dic31⋊C4—41no—
108C4×Dic31—41no—
109C4×Dic31—41no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—21no—
115C23×C31—21no—
116C23×C31C22×C412yes—
117C23×C31C2411yescharacteristic
118C22×D31—21no—
119C22×D31—21no—
120C22×D31—21no—
121C22×D31—21no—
122C22×D31—21no—
123C22×D31—21no—
124C22×D31—21no—
125C22×D31—21no—
126C22×D31—21no—
127C22×D31—21no—
128C22×D31—21no—
129C22×D31—21no—
130C22×D31—21no—
131C22×D31—21no—
132C22×D31—21no—
133C22×D31—21no—
134C22×D31—21no—
135C22×D31—21no—
136C22×D31—44no—
137C22×D31—44no—
138C22×D31—44no—
139C22×D31—44no—
140C22×D31—44no—
141C22×D31—44no—
142C22×D31—44no—
143C22×D31C22×C412yes—
144C22×D31C22×C412yes—
145C22×D31C22×C412yes—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
153C2×C4×C31—21no—
154C2×C4×C31—21no—
155C2×C4×C31—21no—
156C2×C4×C31—21no—
157C2×C4×C31—21no—
158C2×C4×C31—21no—
159C2×C4×C31—21no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31C22×C412yes—
163C2×C4×C31C22×C412yes—
164C22⋊D31—44no—
165C2×Dic31—21no—
166C2×Dic31—21no—
167C2×Dic31—21no—
168C2×Dic31—21no—
169C2×Dic31—21no—
170C2×Dic31—21no—
171C2×Dic31—21no—
172C2×Dic31—21no—
173C2×Dic31—21no—
174C2×Dic31—21no—
175C2×Dic31—21no—
176C2×Dic31—21no—
177C2×Dic31—21no—
178C2×Dic31—21no—
179C2×Dic31C22×C412yes—
180D124—44no—
181D124—44no—
182C4×D31—44no—
183#2375—311nomaximal, Sylow
184C22×C31—22no—
185C22×C31—22no—
186C22×C31—22no—
187C22×C31—41no—
188C22×C31—41no—
189C22×C31—41no—
190C22×C31—41no—
191C22×C31C23×C411yescharacteristic
192C22×C31H(5,𝔽2)11yescharacteristic
193C22×C31H(5,𝔽2)11yescharacteristic
194C22×C31H(5,𝔽2)11yescharacteristic
195C22×C31H(5,𝔽2)11yescharacteristic
196C22×C31H(5,𝔽2)11yescharacteristic
197C22×C31H(5,𝔽2)11yescharacteristic
198C2×D31—22no—
199C2×D31—22no—
200C2×D31—22no—
201C2×D31—22no—
202C2×D31—22no—
203C2×D31—22no—
204C2×D31—22no—
205C2×D31—22no—
206C2×D31—22no—
207C2×D31—416no—
208C2×D31—41no—
209C2×D31—41no—
210C2×D31—41no—
211C2×D31—41no—
212C2×D31—41no—
213C2×D31—41no—
214C2×D31—41no—
215C2×D31—41no—
216C2×D31—41no—
217C2×D31—41no—
218C2×D31—41no—
219C2×D31—41no—
220C4×C31—22no—
221C4×C31—22no—
222C4×C31—41no—
223C4×C31—41no—
224C4×C31—41no—
225C4×C31—41no—
226Dic31—22no—
227Dic31—41no—
228Dic31—41no—
229Dic31—41no—
230Dic31—41no—
231C2×#120—311no—
232#390—311no—
233#390—311no—
234#390—311no—
235#388—311no—
236#388—311no—
237#388—311no—
238#388—311no—
239#388—311no—
240#388D3111yescharacteristic, complemented
241#386—311no—
242#386—311no—
243#386—311no—
244#379—311no—
245#379—311no—
246C2×C31—42no—
247C2×C31#51811yescharacteristic
248C2×C31#51811yescharacteristic
249C2×C31#51811yescharacteristic
250C2×C31#56011yescharacteristic
251C2×C31#56011yescharacteristic
252C2×C31#56011yescharacteristic
253C2×C31H(3,𝔽4)11yescharacteristic
254D31—42no—
255D31—42no—
256D31—42no—
257C25—311no—
258C22×D4—311no—
259C22×D4—311no—
260C22×D4—311no—
261C23×C4—311no—
262#120—318no—
263C2×C4⋊C4—311no—
264C2×C4⋊C4—311no—
265C2×C4⋊C4C2×D3111yescharacteristic, complemented
266C2×C22⋊C4—311no—
267C2×C22⋊C4—311no—
268C2×C22⋊C4—311no—
269C2×C22⋊C4—311no—
270C2×C22⋊C4—311no—
271C2×C22⋊C4—311no—
272C2×C22⋊C4—311no—
273C2×C22⋊C4—311no—
274C2×C22⋊C4—311no—
275C2×C22⋊C4—311no—
276C2×C22⋊C4—311no—
277C2×C22⋊C4—311no—
278C2×C22⋊C4—311no—
279C2×C22⋊C4—311no—
280C2×C22⋊C4—311no—
281C2×C22⋊C4C2×D3111yescharacteristic
282C2×C22⋊C4C2×D3111yescharacteristic
283C2×C22⋊C4C2×D3111yescharacteristic
284C2×C42—311no—
285C2×C42—311no—
286C2×C42C2×D3111yescharacteristic, complemented
287#95—311no—
288#95—311no—
289#95—311no—
290#95—311no—
291#95C2×D3111yescharacteristic, complemented
292#95C2×D3111yescharacteristic, complemented
293C31#237511yescharacteristic, complemented, Sylow
294C24—311no—
295C24—311no—
296C24—311no—
297C24—314no—
298C24—1241no—
299C24—1241no—
300C24—1241no—
301C24—1241no—
302C24—1241no—
303C24—1241no—
304C24C22×D3111yescharacteristic
305C2×D4—314no—
306C2×D4—314no—
307C2×D4—314no—
308C2×D4—1241no—
309C2×D4—1241no—
310C2×D4—1241no—
311C2×D4—1241no—
312C2×D4—1241no—
313C2×D4—1241no—
314C22×C4—311no—
315C22×C4—311no—
316C22×C4—311no—
317C22×C4—311no—
318C22×C4—311no—
319C22×C4—1241no—
320C22×C4—1241no—
321C22×C4—1241no—
322C22×C4C22×D3111yescharacteristic
323C22×C4C22×D3111yescharacteristic
324C22×C4C22×D3111yescharacteristic
325C22×C4C22×D3111yescharacteristic
326C22×C4C22×D3111yescharacteristic
327C22×C4C22×D3111yescharacteristic
328C4⋊C4—41no—
329C4⋊C4—1241no—
330C4⋊C4—1241no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—314no—
334C22⋊C4—314no—
335C22⋊C4—1241no—
336C22⋊C4—1241no—
337C22⋊C4—1241no—
338C22⋊C4—1241no—
339C22⋊C4—1241no—
340C22⋊C4—1241no—
341C22⋊C4—1241no—
342C22⋊C4—1241no—
343C22⋊C4—1241no—
344C22⋊C4—1241no—
345C22⋊C4—1241no—
346C22⋊C4—1241no—
347C22⋊C4—1241no—
348C22⋊C4C4×D3114yescomplemented
349C42—41no—
350C42—1241no—
351C42—1241no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—312no—
359C23—312no—
360C23—312no—
361C23—621no—
362C23—621no—
363C23—621no—
364C23—621no—
365C23—621no—
366C23—621no—
367C23—621no—
368C23—621no—
369C23—621no—
370C23—621no—
371C23—621no—
372C23—621no—
373C23—621no—
374C23—621no—
375C23—621no—
376C23—621no—
377C23—621no—
378C23—621no—
379C23—1244no—
380C23—1244no—
381C23—1244no—
382C23—1244no—
383C23—1244no—
384C23—1244no—
385C23—1244no—
386C23C2×C4×D3112yes—
387C23C23×D3111yescharacteristic
388D4—1244no—
389D4—1244no—
390D4—1244no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—312no—
408C2×C4—621no—
409C2×C4—621no—
410C2×C4—621no—
411C2×C4—621no—
412C2×C4—621no—
413C2×C4—621no—
414C2×C4—621no—
415C2×C4—621no—
416C2×C4—621no—
417C2×C4—621no—
418C2×C4—621no—
419C2×C4—621no—
420C2×C4—621no—
421C2×C4—621no—
422C2×C4—1244no—
423C2×C4C2×C4×D3112yes—
424C2×C4C2×C4×D3112yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—622no—
433C22—622no—
434C22—622no—
435C22—622no—
436C22—622no—
437C22—622no—
438C22—622no—
439C22—622no—
440C22—622no—
441C22—12416no—
442C22—1241no—
443C22—1241no—
444C22—1241no—
445C22—1241no—
446C22—1241no—
447C22—1241no—
448C22—1241no—
449C22—1241no—
450C22—1241no—
451C22—1241no—
452C22—1241no—
453C22—1241no—
454C22C22×C4×D3111yescharacteristic
455C22#1175856111yescharacteristic
456C22#1175856111yescharacteristic
457C22#1175856611yescharacteristic
458C22#1175856611yescharacteristic
459C22#1175856611yescharacteristic
460C22#1175856611yescharacteristic
461C4—22no—
462C4—22no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—622no—
468C4—1241no—
469C4—1241no—
470C4—1241no—
471C4—1241no—
472C2—42no—
473C2—1242no—
474C2—1242no—
475C2—1242no—
476C2#1452152111yescharacteristic
477C2#1452152111yescharacteristic
478C2#1452152311yescharacteristic
479C2#1452178711yescharacteristic
480C2#1452178911yescharacteristic
481C2#1452179011yescharacteristic
482C2#1452179111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#388C2
socle, cosocleC23×C31C24
prime radicalC2×#11758459C2
hypercenter#388D31
hypocenterC31#2375
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #14520951C2semidirect
3. #14520950C2semidirect
4. #14520949C2semidirect
5. #14520942C2semidirect
6. #14520941C2semidirect
7. #14520940C2semidirect
8. #14520939C2semidirect
9. #14520938C2semidirect
10. #14520927C2semidirect
11. #14520927C2semidirect
12. #14520925C2semidirect
13. #14520904C2semidirect
14. #14520904C2semidirect
15. C31×#388C2semidirect
20. C22×C4×D31C22semidirect
21. C2×C4⋊C4×C31C22semidirect
25. C2×C42×C31C22semidirect
38. C2×(C2×D31)⋊C4C22semidirect
39. C2×(C2×D31)⋊C4C22semidirect
40. C2×(C2×D31)⋊C4C22semidirect
41. C2×C4⋊Dic31C22semidirect
42. C2×Dic31⋊C4C22semidirect
43. C2×C4×Dic31C22semidirect
44. C2×C4×Dic31C22semidirect
45. #11758459C4semidirect
46. C31×#95C22semidirect
47. C31×#95C22semidirect
48. C31⋊#95C22semidirect
49. C31⋊#95C22semidirect
50. C31⋊#95C22semidirect
51. C31⋊#95C22semidirect
59. C23×D31C2×C4semidirect
89. C22⋊C4×C31C2×C4semidirect
104. (C2×D31)⋊C4C2×C4semidirect
105. (C2×D31)⋊C4C2×C4semidirect
240. #388D31semidirect
265. C2×C4⋊C4C2×D31semidirect
286. C2×C42C2×D31semidirect
291. #95C2×D31semidirect
292. #95C2×D31semidirect
293. C31#2375semidirect
348. C22⋊C4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584592
#145209512
#145209502
#145209492
#145209422
#145209412
#145209402
#145209392
#145209382
#145209272
#145209252
#145209042
C31×#3882
#237531