Finite Group Databasebeta

← #16848221

Subgroups — #16848221

Order 3968.

824 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758516C211yesmaximal, characteristic
2C2×D4×Dic31C211yesmaximal, characteristic, complemented
3C2×(C22⋊D31)⋊C4C211yesmaximal, characteristic, complemented
4C2×(C22⋊D31)⋊C4C211yesmaximal, characteristic, complemented
5C22×C4×Dic31C211yesmaximal, characteristic, complemented
6#14520949C211yesmaximal, characteristic, complemented
7#14520946C211yesmaximal, characteristic, complemented
8#14520941C211yesmaximal, characteristic, complemented
9#14520937C211yesmaximal, characteristic, complemented
10#14520928C211yesmaximal, characteristic, complemented
11#14520907C211yesmaximal, characteristic, complemented
12#14520900C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic31C211yesmaximal, characteristic, complemented
14#14520896C211yesmaximal, characteristic, complemented
15C31×#386C211yesmaximal, characteristic, complemented
16C22×D4×C31C2211yescharacteristic
17C23×C4×C31C2211yescharacteristic
18C22×C22⋊D31C2211yescharacteristic
19C22×C22⋊D31C2211yescharacteristic
20C23×Dic31C2211yescharacteristic
21C23×Dic31C2211yescharacteristic
22C23×Dic31C2211yescharacteristic
23C22×C4×D31C2211yescharacteristic
24C2×C22⋊C4×C31C2211yescharacteristic
25C2×C22⋊C4×C31C2211yescharacteristic
26C2×C22⋊C4×C31C2211yescharacteristic
27C2×C22⋊Dic31C2211yescharacteristic
28C2×C22⋊Dic31C2211yescharacteristic
29C2×C22⋊Dic31C2211yescharacteristic
30#11758516C418yescomplemented
31D4×Dic31—24no—
32C2×(C2×D31)⋊C4C2211yescharacteristic
33C2×(C2×D31)⋊C4C2211yescharacteristic
34C2×(C2×D31)⋊C4C2211yescharacteristic
35C2×(C2×D31)⋊C4C2211yescharacteristic
36C2×C4⋊Dic31C2211yescharacteristic
37C2×Dic31⋊C4C2211yescharacteristic
38C2×Dic31⋊C4C2211yescharacteristic
39C2×Dic31⋊C4C2211yescharacteristic
40C2×Dic31⋊C4C2211yescharacteristic
41C2×C4×Dic31—24no—
42C2×C4×Dic31C2211yescharacteristic
43C2×C4×Dic31C2211yescharacteristic
44C2×C4×Dic31C2211yescharacteristic
45C2×C4×Dic31C2211yescharacteristic
46C2×C4×Dic31C2211yescharacteristic
47C2×C4×Dic31C2211yescharacteristic
48(C22⋊D31)⋊C4—24no—
49(C22⋊D31)⋊C4—24no—
50C31×#95C2211yescharacteristic
51C31×#95C2211yescharacteristic
52C31⋊#95C2211yescharacteristic
53C31⋊#95C2211yescharacteristic
54C31⋊#95C2211yescharacteristic
55C31⋊#95C2211yescharacteristic
56C24×C31C2311yescharacteristic
57C24×C31C2311yescharacteristic
58C23×D31C2311yescharacteristic
59C2×D4×C31—22no—
60C2×D4×C31—22no—
61C2×D4×C31C2×C414yescomplemented
62C22×C4×C31—22no—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31C2311yescharacteristic
66C22×C4×C31C2311yescharacteristic
67C22×C4×C31C2311yescharacteristic
68C22×C4×C31C2311yescharacteristic
69C22×C4×C31C2311yescharacteristic
70C2×C22⋊D31—22no—
71C2×C22⋊D31—22no—
72C2×C22⋊D31—22no—
73C2×C22⋊D31—22no—
74C2×C22⋊D31C2×C414yescomplemented
75C2×C22⋊D31C2×C414yescomplemented
76C22×Dic31—22no—
77C22×Dic31—22no—
78C22×Dic31—22no—
79C22×Dic31—22no—
80C22×Dic31—22no—
81C22×Dic31—22no—
82C22×Dic31—22no—
83C22×Dic31C2×C414yescomplemented
84C22×Dic31D414yescomplemented
85C22×Dic31C2311yescharacteristic
86C22×Dic31C2311yescharacteristic
87C22×Dic31C2311yescharacteristic
88C22×Dic31C2311yescharacteristic
89C22×Dic31C2311yescharacteristic
90C22×Dic31C2311yescharacteristic
91C22×Dic31C2311yescharacteristic
92C2×C4×D31—22no—
93C2×C4×D31—22no—
94C2×C4×D31—22no—
95C22⋊C4×C31—22no—
96C22⋊C4×C31—22no—
97C22⋊C4×C31—22no—
98C22⋊Dic31—22no—
99C22⋊Dic31—22no—
100C22⋊Dic31C2×C414yescomplemented
101(C2×D31)⋊C4—22no—
102(C2×D31)⋊C4—22no—
103(C2×D31)⋊C4—22no—
104(C2×D31)⋊C4C2×C414yescomplemented
105C4⋊Dic31—22no—
106Dic31⋊C4—22no—
107Dic31⋊C4—22no—
108Dic31⋊C4—22no—
109Dic31⋊C4C2×C414yescomplemented
110C4×Dic31—22no—
111C4×Dic31—22no—
112C4×Dic31—22no—
113C4×Dic31—22no—
114C4×Dic31—22no—
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×C31C22×C412yes—
127C23×C31C22×C412yes—
128C23×C31C2×D412yes—
129C23×C31#4112yes—
130C23×C31C2411yescharacteristic
131C22×D31—21no—
132C22×D31—21no—
133C22×D31—21no—
134C22×D31—21no—
135C22×D31—21no—
136C22×D31—21no—
137C22×D31C22×C412yes—
138D4×C31—28no—
139C2×C4×C31—28no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
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×C31C22×C412yes—
153C2×C4×C31C2×D412yes—
154C2×C4×C31#4112yes—
155C22⋊D31—28no—
156C22⋊D31—28no—
157C2×Dic31—21no—
158C2×Dic31—21no—
159C2×Dic31—21no—
160C2×Dic31—21no—
161C2×Dic31—21no—
162C2×Dic31—21no—
163C2×Dic31—28no—
164C2×Dic31—28no—
165C2×Dic31—21no—
166C2×Dic31—21no—
167C2×Dic31—21no—
168C2×Dic31—21no—
169C2×Dic31—21no—
170C2×Dic31—21no—
171C2×Dic31—44no—
172C2×Dic31C22×C412yes—
173C2×Dic31C22×C412yes—
174C2×Dic31C22×C412yes—
175C2×Dic31C2×D412yes—
176C2×Dic31C2×D412yes—
177C2×Dic31C2×D412yes—
178C2×Dic31C2×D412yes—
179C2×Dic31#4112yes—
180C2×Dic31#4112yes—
181C4×D31—44no—
182C4×#121—311nomaximal, Sylow
183C22×C31—22no—
184C22×C31—22no—
185C22×C31—22no—
186C22×C31—22no—
187C22×C31—22no—
188C22×C31—22no—
189C22×C31—22no—
190C22×C31—22no—
191C22×C31—22no—
192C22×C31—41no—
193C22×C31—41no—
194C22×C31—41no—
195C22×C31—41no—
196C22×C31C4×D414yescomplemented
197C22×C31C23×C411yescharacteristic
198C22×C31C22×D411yescharacteristic
199C22×C31C22×D411yescharacteristic
200C22×C31C2×#4111yescharacteristic
201C22×C31C2×#4111yescharacteristic
202C22×C31C2×#4111yescharacteristic
203C22×C31C2×#4111yescharacteristic
204C2×D31—22no—
205C2×D31—22no—
206C2×D31—22no—
207C2×D31—41no—
208C2×D31—41no—
209C2×D31—41no—
210C2×D31—41no—
211C4×C31—22no—
212C4×C31—22no—
213C4×C31—22no—
214C4×C31—41no—
215C4×C31—41no—
216Dic31—22no—
217Dic31—22no—
218Dic31—22no—
219Dic31—41no—
220Dic31—41no—
221Dic31C4×D414yescomplemented
222Dic31#12114yescomplemented
223C2×#121—311no—
224C2×C4×D4—311no—
225C2×C4×D4—311no—
226C2×C4×D4—311no—
227C22×C42—311no—
228#390—311no—
229#389—311no—
230#388—311no—
231#388—311no—
232#386—311no—
233#386D3111yescharacteristic, complemented
234#380—311no—
235C4×C4⋊C4—311no—
236C4×C22⋊C4—311no—
237C4×C22⋊C4—311no—
238C2×C31—24no—
239C2×C31—42no—
240C2×C31C2×C4×D411yescharacteristic
241C2×C31C2×C4×D411yescharacteristic
242C2×C31C4×#4111yescharacteristic
243C2×C31C2×#12111yescharacteristic
244C2×C31#52511yescharacteristic
245C2×C31#52911yescharacteristic
246C2×C31#53211yescharacteristic
247D31—42no—
248C22×D4—311no—
249C22×D4—311no—
250C22×D4C2×D3111yescharacteristic
251C23×C4—311no—
252C23×C4—311no—
253C23×C4—311no—
254C23×C4—311no—
255C23×C4C2×D3111yescharacteristic
256#121—318no—
257C4×D4—624no—
258C4×D4—624no—
259C4×D4—624no—
260C2×C4⋊C4—311no—
261C2×C4⋊C4—311no—
262C2×C4⋊C4—311no—
263C2×C4⋊C4—311no—
264C2×C4⋊C4—311no—
265C2×C22⋊C4—311no—
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⋊C4C2×D3111yescharacteristic
273C2×C22⋊C4C2×D3111yescharacteristic
274C2×C22⋊C4C2×D3111yescharacteristic
275C2×C42—311no—
276C2×C42—311no—
277C2×C42—311no—
278C2×C42—311no—
279C2×C42—311no—
280C2×C42—311no—
281C2×C42—624no—
282#95—311no—
283#95—311no—
284#95—311no—
285#95—311no—
286#95C2×D3111yescharacteristic
287#95C2×D3111yescharacteristic
288C31C4×#12111yescharacteristic, complemented, Sylow
289C24—311no—
290C24C22×D3111yescharacteristic
291C24C22×D3111yescharacteristic
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—314no—
295C2×D4—314no—
296C2×D4—622no—
297C2×D4—622no—
298C2×D4—622no—
299C2×D4—622no—
300C2×D4C4×D3114yescomplemented
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—311no—
305C22×C4—311no—
306C22×C4—314no—
307C22×C4—314no—
308C22×C4—311no—
309C22×C4—311no—
310C22×C4—311no—
311C22×C4—311no—
312C22×C4—311no—
313C22×C4—622no—
314C22×C4—622no—
315C22×C4—622no—
316C22×C4—622no—
317C22×C4—622no—
318C22×C4—622no—
319C22×C4—622no—
320C22×C4—622no—
321C22×C4—622no—
322C22×C4—622no—
323C22×C4C22×D3111yescharacteristic
324C22×C4C22×D3111yescharacteristic
325C22×C4C22×D3111yescharacteristic
326C22×C4C22×D3111yescharacteristic
327C22×C4C22×D3111yescharacteristic
328C4⋊C4—314no—
329C4⋊C4—622no—
330C4⋊C4—622no—
331C4⋊C4—622no—
332C4⋊C4—622no—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—314no—
337C22⋊C4—314no—
338C22⋊C4—622no—
339C22⋊C4—622no—
340C22⋊C4—622no—
341C22⋊C4—622no—
342C22⋊C4—622no—
343C42—314no—
344C42—622no—
345C42—622no—
346C42—622no—
347C42—622no—
348C42—622no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—312no—
360C23—621no—
361C23—621no—
362C23—621no—
363C23—621no—
364C23—621no—
365C23—621no—
366C23C2×C4×D3112yes—
367C23C2×C4×D3112yes—
368C23D4×D3112yes—
369C23#9249712yes—
370C23C23×D3111yescharacteristic
371D4—28no—
372D4—628no—
373D4—628no—
374C2×C4—28no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—312no—
388C2×C4—312no—
389C2×C4—312no—
390C2×C4—312no—
391C2×C4—312no—
392C2×C4—312no—
393C2×C4—312no—
394C2×C4—312no—
395C2×C4—312no—
396C2×C4—628no—
397C2×C4—628no—
398C2×C4—621no—
399C2×C4—621no—
400C2×C4—621no—
401C2×C4—621no—
402C2×C4—621no—
403C2×C4—621no—
404C2×C4—621no—
405C2×C4—621no—
406C2×C4—621no—
407C2×C4—621no—
408C2×C4—621no—
409C2×C4—621no—
410C2×C4—1244no—
411C2×C4—1244no—
412C2×C4C2×C4×D3112yes—
413C2×C4D4×D3112yes—
414C2×C4#9249712yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—622no—
429C22—622no—
430C22—622no—
431C22—1241no—
432C22—1241no—
433C22—1241no—
434C22—1241no—
435C22(C22⋊D31)⋊C414yescomplemented
436C22C22×C4×D3111yescharacteristic
437C22C2×D4×D3111yescharacteristic
438C22C2×D4×D3111yescharacteristic
439C22C2×#9249711yescharacteristic
440C22C2×#9249711yescharacteristic
441C22#41×D3111yescharacteristic
442C22#41×D3111yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—41no—
447C4—41no—
448C4—314no—
449C4—314no—
450C4—622no—
451C4—622no—
452C4—622no—
453C4—1241no—
454C4—1241no—
455C2—24no—
456C2—42no—
457C2—1242no—
458C2C4×D4×D3111yescharacteristic
459C2C2×(C22⋊D31)⋊C411yescharacteristic
460C2C4×#9249711yescharacteristic
461C2#121×D3111yescharacteristic
462C2#1452155511yescharacteristic
463C2#1452157611yescharacteristic
464C2#1452159411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#386C2
socle, cosocleC23×C31C24
prime radicalC2×#11758516C2
hypercenter#386D31
hypocenterC31C4×#121
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic31C2semidirect
3. C2×(C22⋊D31)⋊C4C2semidirect
4. C2×(C22⋊D31)⋊C4C2semidirect
5. C22×C4×Dic31C2semidirect
6. #14520949C2semidirect
7. #14520946C2semidirect
8. #14520941C2semidirect
9. #14520937C2semidirect
10. #14520928C2semidirect
11. #14520907C2semidirect
12. #14520900C2semidirect
13. C22⋊C4×Dic31C2semidirect
14. #14520896C2semidirect
15. C31×#386C2semidirect
30. #11758516C4semidirect
61. C2×D4×C31C2×C4semidirect
74. C2×C22⋊D31C2×C4semidirect
75. C2×C22⋊D31C2×C4semidirect
83. C22×Dic31C2×C4semidirect
84. C22×Dic31D4semidirect
100. C22⋊Dic31C2×C4semidirect
104. (C2×D31)⋊C4C2×C4semidirect
109. Dic31⋊C4C2×C4semidirect
115. C4×Dic31D4semidirect
196. C22×C31C4×D4semidirect
221. Dic31C4×D4semidirect
222. Dic31#121semidirect
233. #386D31semidirect
288. C31C4×#121semidirect
300. C2×D4C4×D31semidirect
435. C22(C22⋊D31)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#117585162
C2×D4×Dic312
C2×(C22⋊D31)⋊C42
C22×C4×Dic312
#145209492
#145209462
#145209412
#145209372
#145209282
#145209072
#145209002
C22⋊C4×Dic312
#145208962
C31×#3862
C4×#12131