Finite Group Databasebeta

← #16848432

Subgroups — #16848432

Order 3968.

740 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758517C211yesmaximal, characteristic
2C2×C4×C22⋊D31C211yesmaximal, characteristic, complemented
3C2×(C22⋊D31)⋊C4C211yesmaximal, characteristic, complemented
4#14520949C211yesmaximal, characteristic, complemented
5#14520949C211yesmaximal, characteristic, complemented
6#14520929C211yesmaximal, characteristic, complemented
7#14520928C211yesmaximal, characteristic, complemented
8#14520927C211yesmaximal, characteristic, complemented
9#14520927C211yesmaximal, characteristic, complemented
10#14520926C211yesmaximal, characteristic, complemented
11#14520925C211yesmaximal, characteristic, complemented
12#14520925C211yesmaximal, characteristic, complemented
13#14520913C211yesmaximal, characteristic, complemented
14#14520894C211yesmaximal, characteristic, complemented
15C31×#386C211yesmaximal, characteristic, complemented
16C22×D4×C31C2211yescharacteristic
17C23×C4×C31C2211yescharacteristic
18C22×C22⋊D31C2211yescharacteristic
19C22×C22⋊D31C2211yescharacteristic
20C22×C22⋊D31C2211yescharacteristic
21C22×C22⋊D31C2211yescharacteristic
22C23×Dic31C2211yescharacteristic
23C22×D124C2211yescharacteristic
24C22×C4×D31C2211yescharacteristic
25C22×C4×D31C2211yescharacteristic
26C2×C22⋊C4×C31C2211yescharacteristic
27C2×C22⋊C4×C31C2211yescharacteristic
28C2×C22⋊C4×C31C2211yescharacteristic
29C2×C22⋊Dic31C2211yescharacteristic
30C2×C22⋊Dic31C2211yescharacteristic
31C2×C22⋊Dic31C2211yescharacteristic
32#11758517C418yescomplemented
33C4×C22⋊D31—24no—
34C2×(C2×D31)⋊C4C2211yescharacteristic
35C2×(C2×D31)⋊C4C2211yescharacteristic
36C2×(C2×D31)⋊C4C2211yescharacteristic
37C2×(C2×D31)⋊C4C2211yescharacteristic
38C2×(C2×D31)⋊C4C2211yescharacteristic
39C2×(C2×D31)⋊C4C2211yescharacteristic
40C2×Dic31⋊C4C2211yescharacteristic
41C2×Dic31⋊C4C2211yescharacteristic
42C2×C4×Dic31C2211yescharacteristic
43C2×C4×Dic31C2211yescharacteristic
44C2×C4×Dic31C2211yescharacteristic
45(C22⋊D31)⋊C4—24no—
46C31×#95C2211yescharacteristic
47C31×#95C2211yescharacteristic
48C31⋊#95C2211yescharacteristic
49C31⋊#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C31⋊#95C2211yescharacteristic
52C31⋊#95C2211yescharacteristic
53C31⋊#95C2211yescharacteristic
54C24×C31C2311yescharacteristic
55C24×C31C2311yescharacteristic
56C23×D31C2311yescharacteristic
57C23×D31C2311yescharacteristic
58C2×D4×C31—41no—
59C2×D4×C31—41no—
60C2×D4×C31C2×C414yescomplemented
61C22×C4×C31—22no—
62C22×C4×C31—41no—
63C22×C4×C31—41no—
64C22×C4×C31C2311yescharacteristic
65C22×C4×C31C2311yescharacteristic
66C22×C4×C31C2311yescharacteristic
67C22×C4×C31C2311yescharacteristic
68C22×C4×C31C2311yescharacteristic
69C2×C22⋊D31—22no—
70C2×C22⋊D31—22no—
71C2×C22⋊D31—22no—
72C2×C22⋊D31—22no—
73C2×C22⋊D31—41no—
74C2×C22⋊D31—41no—
75C2×C22⋊D31—41no—
76C2×C22⋊D31—41no—
77C2×C22⋊D31C2×C414yescomplemented
78C2×C22⋊D31C2×C414yescomplemented
79C2×C22⋊D31C2×C414yescomplemented
80C2×C22⋊D31C2×C414yescomplemented
81C22×Dic31—22no—
82C22×Dic31—41no—
83C22×Dic31—41no—
84C22×Dic31C2311yescharacteristic
85C22×Dic31C2311yescharacteristic
86C22×Dic31C2311yescharacteristic
87C22×Dic31C2311yescharacteristic
88C22×Dic31C2311yescharacteristic
89C22×Dic31C2311yescharacteristic
90C2×D124—41no—
91C2×D124—41no—
92C2×D124C2×C414yescomplemented
93C2×C4×D31—22no—
94C2×C4×D31—22no—
95C2×C4×D31—41no—
96C2×C4×D31—41no—
97C2×C4×D31—41no—
98C2×C4×D31—41no—
99C22⋊C4×C31—22no—
100C22⋊C4×C31—41no—
101C22⋊C4×C31—41no—
102C22⋊Dic31—22no—
103C22⋊Dic31—41no—
104C22⋊Dic31—41no—
105(C2×D31)⋊C4—22no—
106(C2×D31)⋊C4—22no—
107(C2×D31)⋊C4—41no—
108(C2×D31)⋊C4—41no—
109(C2×D31)⋊C4—41no—
110(C2×D31)⋊C4—41no—
111Dic31⋊C4—22no—
112Dic31⋊C4—22no—
113C4×Dic31—22no—
114C4×Dic31C2×C414yescomplemented
115C4×Dic31D414yescomplemented
116C23×C31—21no—
117C23×C31—21no—
118C23×C31—21no—
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—21no—
123C23×C31—21no—
124C23×C31—21no—
125C23×C31—21no—
126C23×C31—21no—
127C23×C31—21no—
128C23×C31C22×C412yes—
129C23×C31C22×C412yes—
130C23×C31C2411yescharacteristic
131C22×D31—21no—
132C22×D31—21no—
133C22×D31—21no—
134C22×D31—21no—
135C22×D31—21no—
136C22×D31—21no—
137C22×D31—21no—
138C22×D31—21no—
139C22×D31—21no—
140C22×D31—21no—
141C22×D31—21no—
142C22×D31—21no—
143C22×D31C22×C412yes—
144C22×D31C22×C412yes—
145D4×C31—44no—
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—44no—
160C2×C4×C31C22×C412yes—
161C2×C4×C31C2×D412yes—
162C22⋊D31—28no—
163C22⋊D31—28no—
164C22⋊D31—44no—
165C22⋊D31—44no—
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×Dic31—44no—
180C2×Dic31C22×C412yes—
181C2×Dic31C22×C412yes—
182C2×Dic31C2×D412yes—
183C2×Dic31C2×D412yes—
184C2×Dic31#4112yes—
185D124—44no—
186C4×D31—44no—
187C4×D31—44no—
188#2328—311nomaximal, Sylow
189C22×C31—22no—
190C22×C31—22no—
191C22×C31—22no—
192C22×C31—22no—
193C22×C31—22no—
194C22×C31—22no—
195C22×C31—41no—
196C22×C31—41no—
197C22×C31—41no—
198C22×C31—41no—
199C22×C31—41no—
200C22×C31—41no—
201C22×C31—41no—
202C22×C31—41no—
203C22×C31C23×C411yescharacteristic
204C22×C31C22×D411yescharacteristic
205C22×C31C2×#4111yescharacteristic
206C22×C31H(5,𝔽2)11yescharacteristic
207C22×C31H(5,𝔽2)11yescharacteristic
208C22×C31H(5,𝔽2)11yescharacteristic
209C22×C31H(5,𝔽2)11yescharacteristic
210C2×D31—22no—
211C2×D31—22no—
212C2×D31—22no—
213C2×D31—22no—
214C2×D31—22no—
215C2×D31—22no—
216C2×D31—41no—
217C2×D31—41no—
218C2×D31—41no—
219C2×D31—41no—
220C2×D31—41no—
221C2×D31—41no—
222C2×D31—41no—
223C2×D31—41no—
224C4×C31—22no—
225C4×C31—22no—
226C4×C31—41no—
227C4×C31—41no—
228C4×C31—41no—
229Dic31—22no—
230Dic31—22no—
231Dic31—41no—
232Dic31—41no—
233Dic31—41no—
234Dic31C4×D414yes—
235C2×#127—311no—
236C2×C4×D4—311no—
237C2×C4×D4—311no—
238#390—311no—
239#390—311no—
240#386—311no—
241#386—311no—
242#386—311no—
243#386—311no—
244#386—311no—
245#386—311no—
246#386—311no—
247#386D3111yescharacteristic, complemented
248#382—311no—
249#376—311no—
250C2×C31—42no—
251C2×C31—42no—
252C2×C31C2×C4×D411yescharacteristic
253C2×C31#51811yescharacteristic
254C2×C31#51811yescharacteristic
255C2×C31#53511yescharacteristic
256C2×C31#53511yescharacteristic
257C2×C31#54011yescharacteristic
258C2×C31#54011yescharacteristic
259D31—42no—
260D31—42no—
261C22×D4—311no—
262C22×D4—311no—
263C22×D4—311no—
264C22×D4—311no—
265C22×D4—311no—
266C22×D4C2×D3111yescharacteristic
267C23×C4—311no—
268C23×C4—311no—
269C23×C4—311no—
270C23×C4C2×D3111yescharacteristic
271#127—318no—
272C4×D4—624no—
273C4×D4—624no—
274C2×C4⋊C4—311no—
275C2×C4⋊C4—311no—
276C2×C22⋊C4—311no—
277C2×C22⋊C4—311no—
278C2×C22⋊C4—311no—
279C2×C22⋊C4—311no—
280C2×C22⋊C4—311no—
281C2×C22⋊C4—311no—
282C2×C22⋊C4—311no—
283C2×C22⋊C4—311no—
284C2×C22⋊C4—311no—
285C2×C22⋊C4C2×D3111yescharacteristic
286C2×C22⋊C4C2×D3111yescharacteristic
287C2×C22⋊C4C2×D3111yescharacteristic
288C2×C42—311no—
289C2×C42—311no—
290C2×C42—311no—
291#95—311no—
292#95—311no—
293#95—311no—
294#95—311no—
295#95—311no—
296#95—311no—
297#95C2×D3111yescharacteristic
298#95C2×D3111yescharacteristic
299C31#232811yescharacteristic, complemented, Sylow
300C24—311no—
301C24—311no—
302C24C22×D3111yescharacteristic
303C24C22×D3111yescharacteristic
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—314no—
307C2×D4—314no—
308C2×D4—314no—
309C2×D4—314no—
310C2×D4—314no—
311C2×D4—622no—
312C2×D4—622no—
313C2×D4—622no—
314C2×D4—622no—
315C2×D4—1241no—
316C2×D4—1241no—
317C2×D4—1241no—
318C2×D4—1241no—
319C2×D4—1241no—
320C2×D4—1241no—
321C2×D4C4×D3114yescomplemented
322C22×C4—22no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—311no—
326C22×C4—311no—
327C22×C4—311no—
328C22×C4—311no—
329C22×C4—311no—
330C22×C4—311no—
331C22×C4—622no—
332C22×C4—622no—
333C22×C4—622no—
334C22×C4—1241no—
335C22×C4—1241no—
336C22×C4—1241no—
337C22×C4—1241no—
338C22×C4—1241no—
339C22×C4—1241no—
340C22×C4C22×D3111yescharacteristic
341C22×C4C22×D3111yescharacteristic
342C22×C4C22×D3111yescharacteristic
343C22×C4C22×D3111yescharacteristic
344C22×C4C22×D3111yescharacteristic
345C4⋊C4—622no—
346C4⋊C4—622no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—622no—
351C22⋊C4—622no—
352C22⋊C4—622no—
353C22⋊C4—1241no—
354C22⋊C4—1241no—
355C22⋊C4—1241no—
356C22⋊C4—1241no—
357C22⋊C4—1241no—
358C22⋊C4—1241no—
359C42—314no—
360C42—314no—
361C42—622no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—312no—
375C23—312no—
376C23—621no—
377C23—621no—
378C23—621no—
379C23—621no—
380C23—621no—
381C23—621no—
382C23—621no—
383C23—621no—
384C23—621no—
385C23—621no—
386C23—621no—
387C23—621no—
388C23C2×C4×D3112yes—
389C23C2×C4×D3112yes—
390C23C23×D3111yescharacteristic
391D4—44no—
392D4—628no—
393D4—628no—
394D4—1244no—
395D4—1244no—
396D4—1244no—
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—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—44no—
411C2×C4—312no—
412C2×C4—312no—
413C2×C4—312no—
414C2×C4—312no—
415C2×C4—312no—
416C2×C4—621no—
417C2×C4—621no—
418C2×C4—621no—
419C2×C4—621no—
420C2×C4—621no—
421C2×C4—621no—
422C2×C4—621no—
423C2×C4—621no—
424C2×C4—621no—
425C2×C4—621no—
426C2×C4—621no—
427C2×C4—621no—
428C2×C4—621no—
429C2×C4—1244no—
430C2×C4—1244no—
431C2×C4—1244no—
432C2×C4C2×C4×D3112yes—
433C2×C4D4×D3112yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—622no—
449C22—622no—
450C22—622no—
451C22—622no—
452C22—622no—
453C22—622no—
454C22—1241no—
455C22—1241no—
456C22—1241no—
457C22—1241no—
458C22—1241no—
459C22—1241no—
460C22—1241no—
461C22—1241no—
462C22C22×C4×D3111yescharacteristic
463C22C2×D4×D3111yescharacteristic
464C22#1175856111yescharacteristic
465C22#1175856111yescharacteristic
466C22#1175856111yescharacteristic
467C22#41×D3111yescharacteristic
468C22#1175856611yescharacteristic
469C4—22no—
470C4—22no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—314no—
475C4—622no—
476C4—622no—
477C4—1241no—
478C4—1241no—
479C4—1241no—
480C2—42no—
481C2—42no—
482C2—1242no—
483C2—1242no—
484C2C4×D4×D3111yescharacteristic
485C2#1452152111yescharacteristic
486C2#1452152211yescharacteristic
487C2#1452161411yescharacteristic
488C2#1452161511yescharacteristic
489C2#1452164911yescharacteristic
490C2#1452165111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#386C2
socle, cosocleC23×C31C24
prime radicalC2×#11758517C2
hypercenter#386D31
hypocenterC31#2328
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D31C2semidirect
3. C2×(C22⋊D31)⋊C4C2semidirect
4. #14520949C2semidirect
5. #14520949C2semidirect
6. #14520929C2semidirect
7. #14520928C2semidirect
8. #14520927C2semidirect
9. #14520927C2semidirect
10. #14520926C2semidirect
11. #14520925C2semidirect
12. #14520925C2semidirect
13. #14520913C2semidirect
14. #14520894C2semidirect
15. C31×#386C2semidirect
32. #11758517C4semidirect
60. C2×D4×C31C2×C4semidirect
77. C2×C22⋊D31C2×C4semidirect
78. C2×C22⋊D31C2×C4semidirect
79. C2×C22⋊D31C2×C4semidirect
80. C2×C22⋊D31C2×C4semidirect
92. C2×D124C2×C4semidirect
114. C4×Dic31C2×C4semidirect
115. C4×Dic31D4semidirect
247. #386D31semidirect
299. C31#2328semidirect
321. C2×D4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585172
C2×C4×C22⋊D312
C2×(C22⋊D31)⋊C42
#145209492
#145209292
#145209282
#145209272
#145209262
#145209252
#145209132
#145208942
C31×#3862
#232831