Finite Group Databasebeta

← #16848730

Subgroups — #16848730

Order 3968.

788 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×#11758461C211yesmaximal, characteristic
2C2×#11758470C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D31C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D31C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×D31C211yesmaximal, characteristic, complemented
6#14520949C211yesmaximal, characteristic, complemented
7#14520944C211yesmaximal, characteristic, complemented
8#14520942C211yesmaximal, characteristic, complemented
9#14520939C211yesmaximal, characteristic, complemented
10#14520927C211yesmaximal, characteristic, complemented
11#14520925C211yesmaximal, characteristic, complemented
12#14520923C211yesmaximal, characteristic, complemented
13#14520900C211yesmaximal, characteristic, complemented
14#14520896C211yesmaximal, characteristic, complemented
15C31×#385C211yesmaximal, characteristic, complemented
16C23×C4×C31C2211yescharacteristic
17C22×C22⋊D31C2211yescharacteristic
18C22×C22⋊D31C2211yescharacteristic
19C22×D124C2211yescharacteristic
20C22×C4×D31C2211yescharacteristic
21C22×C4×D31C2211yescharacteristic
22C22×C4×D31C2211yescharacteristic
23C22×C4×D31C2211yescharacteristic
24C2×C4⋊C4×C31C2211yescharacteristic
25C2×C4⋊C4×C31C2211yescharacteristic
26C2×C22⋊C4×C31C2211yescharacteristic
27C2×C22⋊C4×C31C2211yescharacteristic
28C2×C22⋊Dic31C2211yescharacteristic
29C2×C22⋊Dic31C2211yescharacteristic
30C4×C22⋊D31—24no—
31C4×C22⋊D31—24no—
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×C4⋊Dic31C2211yescharacteristic
39C2×Dic31⋊C4C2211yescharacteristic
40C2×Dic31⋊C4C2211yescharacteristic
41C2×Dic31⋊C4C2211yescharacteristic
42C2×Dic31⋊C4C2211yescharacteristic
43C2×C4×Dic31C2211yescharacteristic
44C2×C4×Dic31C2211yescharacteristic
45C2×C4×Dic31C2211yescharacteristic
46C2×C4×Dic31C2211yescharacteristic
47#11758470—24no—
48C4⋊C4×D31—24no—
49#11758461C418yescomplemented
50C31×#95C2211yescharacteristic
51C31×#95C2211yescharacteristic
52C31⋊#95C2211yescharacteristic
53C31⋊#95C2211yescharacteristic
54C31⋊#95C2211yescharacteristic
55C31⋊#95C2211yescharacteristic
56C24×C31C2311yescharacteristic
57C23×D31C2311yescharacteristic
58C23×D31C2311yescharacteristic
59C22×C4×C31—22no—
60C22×C4×C31—22no—
61C22×C4×C31—41no—
62C22×C4×C31C2311yescharacteristic
63C22×C4×C31C2311yescharacteristic
64C22×C4×C31C2311yescharacteristic
65C22×C4×C31C2311yescharacteristic
66C22×C4×C31C2311yescharacteristic
67C22×C4×C31C2311yescharacteristic
68C2×C22⋊D31—22no—
69C2×C22⋊D31—22no—
70C2×C22⋊D31—22no—
71C2×C22⋊D31—22no—
72C2×C22⋊D31C2×C414yescomplemented
73C2×C22⋊D31C2×C414yescomplemented
74C22×Dic31C2311yescharacteristic
75C22×Dic31C2311yescharacteristic
76C22×Dic31C2311yescharacteristic
77C22×Dic31C2311yescharacteristic
78C22×Dic31C2311yescharacteristic
79C22×Dic31C2311yescharacteristic
80C2×D124—22no—
81C2×D124—22no—
82C2×D124C2×C414yescomplemented
83C2×C4×D31—22no—
84C2×C4×D31—22no—
85C2×C4×D31—22no—
86C2×C4×D31—22no—
87C2×C4×D31—22no—
88C2×C4×D31—22no—
89C2×C4×D31—22no—
90C2×C4×D31—22no—
91C2×C4×D31—41no—
92C2×C4×D31—41no—
93C2×C4×D31—41no—
94C2×C4×D31C2×C414yescomplemented
95C4⋊C4×C31—22no—
96C4⋊C4×C31—22no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31C2×C414yescomplemented
99C22⋊Dic31—22no—
100C22⋊Dic31—22no—
101(C2×D31)⋊C4—22no—
102(C2×D31)⋊C4—22no—
103(C2×D31)⋊C4—22no—
104(C2×D31)⋊C4—41no—
105(C2×D31)⋊C4C2×C414yescomplemented
106(C2×D31)⋊C4D414yescomplemented
107C4⋊Dic31—22no—
108Dic31⋊C4—22no—
109Dic31⋊C4—22no—
110Dic31⋊C4C2×C414yescomplemented
111Dic31⋊C4D414yescomplemented
112C4×Dic31—22no—
113C4×Dic31—22no—
114C4×Dic31—22no—
115C4×Dic31—22no—
116C23×C31—21no—
117C23×C31—21no—
118C23×C31—21no—
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—21no—
122C23×C31C22×C412yes—
123C23×C31C2411yescharacteristic
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×D31C22×C412yes—
135C22×D31C22×C412yes—
136C22×D31C2×D412yes—
137C22×D31#4112yes—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
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×C31—44no—
153C2×C4×C31C22×C412yes—
154C2×C4×C31C22×C412yes—
155C2×C4×C31C2×D412yes—
156C2×C4×C31C2×D412yes—
157C22⋊D31—28no—
158C22⋊D31—28no—
159C2×Dic31—21no—
160C2×Dic31—21no—
161C2×Dic31—21no—
162C2×Dic31—21no—
163C2×Dic31—21no—
164C2×Dic31—21no—
165C2×Dic31—21no—
166C2×Dic31—21no—
167C2×Dic31—21no—
168C2×Dic31—21no—
169C2×Dic31—21no—
170C2×Dic31—21no—
171C2×Dic31C22×C412yes—
172C2×Dic31C22×C412yes—
173C2×Dic31C2×D412yes—
174C2×Dic31C2×D412yes—
175C2×Dic31C2×D412yes—
176C2×Dic31#4112yes—
177D124—28no—
178C4×D31—28no—
179C4×D31—44no—
180C4×D31—44no—
181C4×D31—44no—
182#2361—311nomaximal, Sylow
183C22×C31—22no—
184C22×C31—22no—
185C22×C31—22no—
186C22×C31—41no—
187C22×C31—41no—
188C22×C31—41no—
189C22×C31—41no—
190C22×C31C23×C411yescharacteristic
191C22×C31C22×D411yescharacteristic
192C22×C31C22×D411yescharacteristic
193C22×C31C2×#4111yescharacteristic
194C22×C31C2×#4111yescharacteristic
195C22×C31H(5,𝔽2)11yescharacteristic
196C22×C312−1+411yescharacteristic
197C2×D31—22no—
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—41no—
207C2×D31—41no—
208C2×D31—41no—
209C2×D31—41no—
210C2×D31C4×D414yescomplemented
211C4×C31—22no—
212C4×C31—22no—
213C4×C31—22no—
214C4×C31—22no—
215C4×C31—41no—
216C4×C31—41no—
217Dic31—22no—
218Dic31—22no—
219Dic31—22no—
220Dic31—41no—
221Dic31—41no—
222Dic31C4×D414yescomplemented
223C2×#121—311no—
224C2×C4×D4—311no—
225C2×C4×D4—311no—
226C2×C4×D4—311no—
227C22×C4⋊C4—311no—
228#390—311no—
229#389—311no—
230#388—311no—
231#388—311no—
232#386—311no—
233#386—311no—
234#385—311no—
235#385D3111yescharacteristic, complemented
236C4×C4⋊C4—311no—
237C4×C22⋊C4—311no—
238C2×C31—42no—
239C2×C31C2×C4×D411yescharacteristic
240C2×C31C2×C4×D411yescharacteristic
241C2×C31#52011yescharacteristic
242C2×C31D4211yescharacteristic
243C2×C31#54711yescharacteristic
244C2×C31#54811yescharacteristic
245C2×C31#55311yescharacteristic
246D31—24no—
247D31—42no—
248C22×D4—311no—
249C22×D4—311no—
250C22×D4—311no—
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×C4⋊C4—624no—
266C2×C4⋊C4C2×D3111yescharacteristic
267C2×C4⋊C4C2×D3111yescharacteristic
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⋊C4C2×D3111yescharacteristic
277C2×C22⋊C4C2×D3111yescharacteristic
278C2×C42—311no—
279C2×C42—311no—
280C2×C42—311no—
281C2×C42—311no—
282#95—311no—
283#95—311no—
284#95—311no—
285#95—311no—
286#95C2×D3111yescharacteristic
287#95C2×D3111yescharacteristic
288C31#236111yescharacteristic, complemented, Sylow
289C24—311no—
290C24—311no—
291C24C22×D3111yescharacteristic
292C2×D4—314no—
293C2×D4—314no—
294C2×D4—314no—
295C2×D4—622no—
296C2×D4—622no—
297C2×D4—622no—
298C2×D4—622no—
299C2×D4—622no—
300C2×D4—622no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—311no—
305C22×C4—311no—
306C22×C4—311no—
307C22×C4—311no—
308C22×C4—314no—
309C22×C4—311no—
310C22×C4—311no—
311C22×C4—622no—
312C22×C4—622no—
313C22×C4—622no—
314C22×C4—622no—
315C22×C4—622no—
316C22×C4—622no—
317C22×C4—622no—
318C22×C4—622no—
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—22no—
329C4⋊C4—22no—
330C4⋊C4—314no—
331C4⋊C4—314no—
332C4⋊C4—622no—
333C4⋊C4—622no—
334C4⋊C4—622no—
335C22⋊C4—41no—
336C22⋊C4—314no—
337C22⋊C4—314no—
338C22⋊C4—622no—
339C22⋊C4—622no—
340C22⋊C4—622no—
341C22⋊C4—622no—
342C22⋊C4—622no—
343C22⋊C4—1241no—
344C22⋊C4C4×D3114yescomplemented
345C42—622no—
346C42—622no—
347C42—622no—
348C42—622no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—312no—
356C23—312no—
357C23—312no—
358C23—312no—
359C23—621no—
360C23—621no—
361C23—621no—
362C23—621no—
363C23—621no—
364C23—621no—
365C23—621no—
366C23—621no—
367C23—621no—
368C23—621no—
369C23C2×C4×D3112yes—
370C23C23×D3111yescharacteristic
371D4—628no—
372D4—628no—
373D4—628no—
374C2×C4—21no—
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—21no—
388C2×C4—44no—
389C2×C4—312no—
390C2×C4—312no—
391C2×C4—312no—
392C2×C4—312no—
393C2×C4—312no—
394C2×C4—312no—
395C2×C4—628no—
396C2×C4—621no—
397C2×C4—621no—
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—1244no—
409C2×C4—1244no—
410C2×C4—1244no—
411C2×C4C2×C4×D3112yes—
412C2×C4C2×C4×D3112yes—
413C2×C4D4×D3112yes—
414C2×C4D4×D3112yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—314no—
423C22—622no—
424C22—622no—
425C22—622no—
426C22—622no—
427C22—622no—
428C22—622no—
429C22—622no—
430C22—622no—
431C22—622no—
432C22—1241no—
433C22—1241no—
434C22—1241no—
435C22—1241no—
436C22C22×C4×D3111yescharacteristic
437C22C2×D4×D3111yescharacteristic
438C22C2×D4×D3111yescharacteristic
439C22#1175856111yescharacteristic
440C22#1175856411yescharacteristic
441C22#41×D3111yescharacteristic
442C22#41×D3111yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—41no—
448C4—41no—
449C4—314no—
450C4—622no—
451C4—622no—
452C4—622no—
453C4—1241no—
454C4—1241no—
455C2—42no—
456C2—624no—
457C2—1242no—
458C2C4×D4×D3111yescharacteristic
459C2C4×D4×D3111yescharacteristic
460C2#1452153011yescharacteristic
461C2#1452168111yescharacteristic
462C2#1452170111yescharacteristic
463C2#1452170911yescharacteristic
464C2#1452174411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#385C2
socle, cosocleC23×C31C24
prime radicalC2×#11758461C2
hypercenter#385D31
hypocenterC31#2361
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#11758470C2semidirect
3. C2×C4×C22⋊D31C2semidirect
4. C2×C4×C22⋊D31C2semidirect
5. C2×C4⋊C4×D31C2semidirect
6. #14520949C2semidirect
7. #14520944C2semidirect
8. #14520942C2semidirect
9. #14520939C2semidirect
10. #14520927C2semidirect
11. #14520925C2semidirect
12. #14520923C2semidirect
13. #14520900C2semidirect
14. #14520896C2semidirect
15. C31×#385C2semidirect
49. #11758461C4semidirect
72. C2×C22⋊D31C2×C4semidirect
73. C2×C22⋊D31C2×C4semidirect
82. C2×D124C2×C4semidirect
94. C2×C4×D31C2×C4semidirect
98. C22⋊C4×C31C2×C4semidirect
105. (C2×D31)⋊C4C2×C4semidirect
106. (C2×D31)⋊C4D4semidirect
110. Dic31⋊C4C2×C4semidirect
111. Dic31⋊C4D4semidirect
210. C2×D31C4×D4semidirect
222. Dic31C4×D4semidirect
235. #385D31semidirect
288. C31#2361semidirect
344. C22⋊C4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584612
C2×#117584702
C2×C4×C22⋊D312
C2×C4⋊C4×D312
#145209492
#145209442
#145209422
#145209392
#145209272
#145209252
#145209232
#145209002
#145208962
C31×#3852
#236131