Finite Group Databasebeta

← #16848403

Subgroups — #16848403

Order 3968.

668 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758461C211yesmaximal, characteristic
2C2×C4×C22⋊D31C211yesmaximal, characteristic, complemented
3C2×#11758469C211yesmaximal, characteristic, complemented
4#14520950C211yesmaximal, characteristic, complemented
5#14520949C211yesmaximal, characteristic, complemented
6#14520949C211yesmaximal, characteristic, complemented
7#14520944C211yesmaximal, characteristic, complemented
8#14520942C211yesmaximal, characteristic, complemented
9#14520941C211yesmaximal, characteristic, complemented
10#14520928C211yesmaximal, characteristic, complemented
11#14520927C211yesmaximal, characteristic, complemented
12#14520920C211yesmaximal, characteristic, complemented
13#14520908C211yesmaximal, characteristic, complemented
14#14520900C211yesmaximal, characteristic, complemented
15C31×#385C211yesmaximal, characteristic, complemented
16C23×C4×C31C2211yescharacteristic
17C22×C22⋊D31C2211yescharacteristic
18C22×C22⋊D31C2211yescharacteristic
19C22×D124C2211yescharacteristic
20C22×C4×D31C2211yescharacteristic
21C22×C4×D31C2211yescharacteristic
22C2×C4⋊C4×C31C2211yescharacteristic
23C2×C4⋊C4×C31C2211yescharacteristic
24C2×C22⋊C4×C31C2211yescharacteristic
25C2×C22⋊C4×C31C2211yescharacteristic
26C2×C22⋊Dic31C2211yescharacteristic
27C2×C22⋊Dic31C2211yescharacteristic
28C4×C22⋊D31—24no—
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×C4⋊Dic31C2211yescharacteristic
38C2×Dic31⋊C4C2211yescharacteristic
39C2×Dic31⋊C4C2211yescharacteristic
40C2×Dic31⋊C4C2211yescharacteristic
41C2×Dic31⋊C4C2211yescharacteristic
42C2×C4×Dic31C2211yescharacteristic
43C2×C4×Dic31C2211yescharacteristic
44C2×C4×Dic31C2211yescharacteristic
45C2×C4×Dic31C2211yescharacteristic
46#11758469—24no—
47#11758461C418yescomplemented
48C31×#95C2211yescharacteristic
49C31×#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C31⋊#95C2211yescharacteristic
52C31⋊#95C2211yescharacteristic
53C31⋊#95C2211yescharacteristic
54C24×C31C2311yescharacteristic
55C23×D31C2311yescharacteristic
56C23×D31C2311yescharacteristic
57C22×C4×C31—22no—
58C22×C4×C31—41no—
59C22×C4×C31—41no—
60C22×C4×C31C2311yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C22×C4×C31C2311yescharacteristic
64C22×C4×C31C2311yescharacteristic
65C22×C4×C31C2311yescharacteristic
66C2×C22⋊D31—22no—
67C2×C22⋊D31—22no—
68C2×C22⋊D31—41no—
69C2×C22⋊D31—41no—
70C2×C22⋊D31C2×C414yes—
71C2×C22⋊D31C2×C414yescomplemented
72C22×Dic31C2311yescharacteristic
73C22×Dic31C2311yescharacteristic
74C22×Dic31C2311yescharacteristic
75C22×Dic31C2311yescharacteristic
76C22×Dic31C2311yescharacteristic
77C22×Dic31C2311yescharacteristic
78C2×D124—41no—
79C2×D124—41no—
80C2×D124C2×C414yescomplemented
81C2×C4×D31—22no—
82C2×C4×D31—22no—
83C2×C4×D31—22no—
84C2×C4×D31—41no—
85C2×C4×D31—41no—
86C2×C4×D31C2×C414yescomplemented
87C4⋊C4×C31—22no—
88C4⋊C4×C31—41no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31C2×C414yescomplemented
91C22⋊Dic31—22no—
92C22⋊Dic31—41no—
93(C2×D31)⋊C4—22no—
94(C2×D31)⋊C4—22no—
95(C2×D31)⋊C4—22no—
96(C2×D31)⋊C4—41no—
97(C2×D31)⋊C4—41no—
98(C2×D31)⋊C4—41no—
99(C2×D31)⋊C4—41no—
100(C2×D31)⋊C4C2×C414yescomplemented
101C4⋊Dic31—22no—
102Dic31⋊C4—22no—
103Dic31⋊C4—22no—
104Dic31⋊C4—41no—
105Dic31⋊C4C2×C414yescomplemented
106C4×Dic31—22no—
107C4×Dic31—41no—
108C4×Dic31—41no—
109C4×Dic31D414yescomplemented
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×D31C22×C412yes—
131C22×D31C22×C412yes—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
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—44no—
148C2×C4×C31C22×C412yes—
149C2×C4×C31C22×C412yes—
150C2×C4×C31C2×D412yes—
151C22⋊D31—28no—
152C22⋊D31—44no—
153C2×Dic31—21no—
154C2×Dic31—21no—
155C2×Dic31—21no—
156C2×Dic31—21no—
157C2×Dic31—21no—
158C2×Dic31—21no—
159C2×Dic31—21no—
160C2×Dic31—21no—
161C2×Dic31—21no—
162C2×Dic31—21no—
163C2×Dic31—21no—
164C2×Dic31—21no—
165C2×Dic31—21no—
166C2×Dic31C22×C412yes—
167C2×Dic31C22×C412yes—
168C2×Dic31C2×D412yes—
169C2×Dic31C2×D412yes—
170C2×Dic31#4112yes—
171D124—44no—
172C4×D31—28no—
173C4×D31—44no—
174#2324—311nomaximal, Sylow
175C22×C31—22no—
176C22×C31—22no—
177C22×C31—22no—
178C22×C31—41no—
179C22×C31—41no—
180C22×C31—41no—
181C22×C31—41no—
182C22×C31C23×C411yescharacteristic
183C22×C31C22×D411yescharacteristic
184C22×C31C2×#4111yescharacteristic
185C22×C31H(5,𝔽2)11yescharacteristic
186C22×C31H(5,𝔽2)11yescharacteristic
187C22×C31H(5,𝔽2)11yescharacteristic
188C22×C312−1+411yescharacteristic
189C2×D31—22no—
190C2×D31—22no—
191C2×D31—22no—
192C2×D31—22no—
193C2×D31—22no—
194C2×D31—22no—
195C2×D31—41no—
196C2×D31—41no—
197C2×D31—41no—
198C2×D31—41no—
199C2×D31—41no—
200C2×D31—41no—
201C2×D31—41no—
202C2×D31—41no—
203C4×C31—22no—
204C4×C31—22no—
205C4×C31—22no—
206C4×C31—41no—
207C4×C31—41no—
208C4×C31—41no—
209Dic31—22no—
210Dic31—22no—
211Dic31—41no—
212Dic31—41no—
213Dic31—41no—
214Dic31C4×D414yes—
215C2×#121—311no—
216C2×C4×D4—311no—
217C2×#117—311no—
218#390—311no—
219#390—311no—
220#390—311no—
221#389—311no—
222#388—311no—
223#388—311no—
224#386—311no—
225#386—311no—
226#385—311no—
227#385D3111yescharacteristic, complemented
228#380—311no—
229C4×C4⋊C4—311no—
230C2×C31—42no—
231C2×C31C2×C4×D411yescharacteristic
232C2×C31#51811yescharacteristic
233C2×C31#52011yescharacteristic
234C2×C31#53511yescharacteristic
235C2×C31#53711yescharacteristic
236C2×C31#54011yescharacteristic
237C2×C31#54211yescharacteristic
238D31—42no—
239D31—42no—
240C22×D4—311no—
241C22×D4—311no—
242C22×D4—311no—
243C23×C4—311no—
244C23×C4—311no—
245C23×C4C2×D3111yescharacteristic
246#121—318no—
247C4×D4—624no—
248#117—624no—
249C2×C4⋊C4—311no—
250C2×C4⋊C4—311no—
251C2×C4⋊C4—311no—
252C2×C4⋊C4—311no—
253C2×C4⋊C4—311no—
254C2×C4⋊C4C2×D3111yescharacteristic
255C2×C4⋊C4C2×D3111yescharacteristic
256C2×C22⋊C4—311no—
257C2×C22⋊C4—311no—
258C2×C22⋊C4—311no—
259C2×C22⋊C4—311no—
260C2×C22⋊C4—311no—
261C2×C22⋊C4—311no—
262C2×C22⋊C4—311no—
263C2×C22⋊C4—311no—
264C2×C22⋊C4—311no—
265C2×C22⋊C4—311no—
266C2×C22⋊C4C2×D3111yescharacteristic
267C2×C22⋊C4C2×D3111yescharacteristic
268C2×C42—311no—
269C2×C42—311no—
270C2×C42—311no—
271C2×C42—311no—
272#95—311no—
273#95—311no—
274#95—311no—
275#95—311no—
276#95C2×D3111yescharacteristic
277#95C2×D3111yescharacteristic
278C31#232411yescharacteristic, complemented, Sylow
279C24—311no—
280C24—311no—
281C24C22×D3111yescharacteristic
282C2×D4—314no—
283C2×D4—314no—
284C2×D4—314no—
285C2×D4—622no—
286C2×D4—622no—
287C2×D4—1241no—
288C2×D4—1241no—
289C2×D4—1241no—
290C2×D4—1241no—
291C22×C4—22no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—311no—
295C22×C4—311no—
296C22×C4—311no—
297C22×C4—314no—
298C22×C4—311no—
299C22×C4—311no—
300C22×C4—311no—
301C22×C4—622no—
302C22×C4—622no—
303C22×C4—622no—
304C22×C4—1241no—
305C22×C4—1241no—
306C22×C4C22×D3111yescharacteristic
307C22×C4C22×D3111yescharacteristic
308C22×C4C22×D3111yescharacteristic
309C22×C4C22×D3111yescharacteristic
310C22×C4C22×D3111yescharacteristic
311C22×C4C22×D3111yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—314no—
315C4⋊C4—622no—
316C4⋊C4—622no—
317C4⋊C4—622no—
318C4⋊C4—1241no—
319C22⋊C4—41no—
320C22⋊C4—314no—
321C22⋊C4—622no—
322C22⋊C4—622no—
323C22⋊C4—622no—
324C22⋊C4—622no—
325C22⋊C4—1241no—
326C22⋊C4—1241no—
327C22⋊C4—1241no—
328C22⋊C4—1241no—
329C22⋊C4—1241no—
330C22⋊C4C4×D3114yescomplemented
331C42—314no—
332C42—622no—
333C42—1241no—
334C42—1241no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—312no—
342C23—312no—
343C23—621no—
344C23—621no—
345C23—621no—
346C23—621no—
347C23—621no—
348C23—621no—
349C23—621no—
350C23—621no—
351C23—621no—
352C23—621no—
353C23—621no—
354C23—621no—
355C23C2×C4×D3112yes—
356C23C23×D3111yescharacteristic
357D4—628no—
358D4—1244no—
359D4—1244no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—44no—
376C2×C4—312no—
377C2×C4—312no—
378C2×C4—312no—
379C2×C4—312no—
380C2×C4—312no—
381C2×C4—628no—
382C2×C4—621no—
383C2×C4—621no—
384C2×C4—621no—
385C2×C4—621no—
386C2×C4—621no—
387C2×C4—621no—
388C2×C4—621no—
389C2×C4—621no—
390C2×C4—621no—
391C2×C4—621no—
392C2×C4—621no—
393C2×C4—621no—
394C2×C4—621no—
395C2×C4—1244no—
396C2×C4C2×C4×D3112yes—
397C2×C4C2×C4×D3112yes—
398C2×C4D4×D3112yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—622no—
407C22—622no—
408C22—622no—
409C22—622no—
410C22—622no—
411C22—622no—
412C22—1241no—
413C22—1241no—
414C22—1241no—
415C22—1241no—
416C22—1241no—
417C22—1241no—
418C22—1241no—
419C22—1241no—
420C22C22×C4×D3111yescharacteristic
421C22C2×D4×D3111yescharacteristic
422C22#1175856111yescharacteristic
423C22#1175856111yescharacteristic
424C22#1175856411yescharacteristic
425C22#41×D3111yescharacteristic
426C22#1175856611yescharacteristic
427C4—22no—
428C4—22no—
429C4—22no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—314no—
434C4—622no—
435C4—622no—
436C4—1241no—
437C4—1241no—
438C4—1241no—
439C2—42no—
440C2—1242no—
441C2—1242no—
442C2C4×D4×D3111yescharacteristic
443C2#1452152111yescharacteristic
444C2#1452153011yescharacteristic
445C2#1452161411yescharacteristic
446C2#1452162911yescharacteristic
447C2#1452165111yescharacteristic
448C2#1452166911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#385C2
socle, cosocleC23×C31C24
prime radicalC2×#11758461C2
hypercenter#385D31
hypocenterC31#2324
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D31C2semidirect
3. C2×#11758469C2semidirect
4. #14520950C2semidirect
5. #14520949C2semidirect
6. #14520949C2semidirect
7. #14520944C2semidirect
8. #14520942C2semidirect
9. #14520941C2semidirect
10. #14520928C2semidirect
11. #14520927C2semidirect
12. #14520920C2semidirect
13. #14520908C2semidirect
14. #14520900C2semidirect
15. C31×#385C2semidirect
47. #11758461C4semidirect
71. C2×C22⋊D31C2×C4semidirect
80. C2×D124C2×C4semidirect
86. C2×C4×D31C2×C4semidirect
90. C22⋊C4×C31C2×C4semidirect
100. (C2×D31)⋊C4C2×C4semidirect
105. Dic31⋊C4C2×C4semidirect
109. C4×Dic31D4semidirect
227. #385D31semidirect
278. C31#2324semidirect
330. 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×C4×C22⋊D312
C2×#117584692
#145209502
#145209492
#145209442
#145209422
#145209412
#145209282
#145209272
#145209202
#145209082
#145209002
C31×#3852
#232431