Finite Group Databasebeta

← #11860755

Subgroups — #11860755

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63796C211yesmaximal, characteristic
2#10593996C211yesmaximal, characteristic
3#10593848C211yesmaximal, characteristic, complemented
4#10592388C211yesmaximal, characteristic, complemented
5C3×C4×#204C212yesmaximal, complemented
6#10590941C211yesmaximal, characteristic
7#10590775C212yesmaximal, complemented
8#10590743C212yesmaximal, complemented
9#10590712C211yesmaximal, characteristic, complemented
10#10590691C211yesmaximal, characteristic, complemented
11#10590358C212yesmaximal, complemented
12#79649—32nomaximal
13C2×#3802C2211yescharacteristic
14C2×#3797C2211yescharacteristic
15C2×#3743C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17#64081C2211yescharacteristic
18C2×C3×#204C2212yes—
19C3×C4×D12C2212yes—
20C3×C4×Dic6C2212yescomplemented
21D3×(C2×D3)⋊C4—22no—
22#63898C2212yes—
23#63879—22no—
24#63849C2211yescharacteristic
25#63849C2211yescharacteristic
26#63843C2212yescomplemented
27#63837—22no—
28#63836—22no—
29C2×#3715C2212yes—
30#63796C418yescomplemented
31C32×C4×C8C2211yescharacteristic, complemented
32#63642C2211yescharacteristic, complemented
33C8×C3⋊Dic3C2211yescharacteristic, complemented
34#63630C2211yescharacteristic, complemented
35C3×#821C2212yes—
36C3×#817C2212yescomplemented
37C3×#816C2212yescomplemented
38#63576C2212yescomplemented
39#63565C2212yescomplemented
40#63562C2212yes—
41C2×D3×SD16—32no—
42#5572—32no—
43#5545—32no—
44C3×C4×SD16—32no—
45Dic3×SD16—32no—
46#5026—32no—
47#5018—32no—
48#4860—32no—
49#4852—32no—
50#4817—32no—
51#4802—32no—
52#4770—32no—
53#4757—32no—
54C4×#204D312yescomplemented
55#4689—32no—
56#4689—61no—
57C22×D32—21no—
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C3×D12C2312yes—
60C2×C3×C4×D3—22no—
61C2×C3×Dic6C2312yes—
62C2×#627—21no—
63C2×#625—21no—
64C2×#624—21no—
65C2×D3×Dic3—22no—
66#3802—22no—
67#3802C2×C414yes—
68#3797—22no—
69#3797C2×C414yescomplemented
70C2×C32×C8C2311yescharacteristic
71C2×C32×C8C2311yescharacteristic
72C32×C42C2311yescharacteristic
73#3752D412yes—
74#3750D412yes—
75C4×C3⋊Dic3C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78#3743—22no—
79C8×C3⋊D3C2×C414yescomplemented
80C3×(C2×D3)⋊C4—22no—
81C3×C4⋊Dic3C2312yes—
82C3×C4⋊Dic3C2312yes—
83C3×Dic3⋊C4—22no—
84C3×C4×Dic3—22no—
85C3×#204C2×C418yescomplemented
86Dic3⋊Dic3—22no—
87#3722—21no—
88#3722—21no—
89(C2×D3)⋊Dic3—22no—
90Dic32—22no—
91Dic32—21no—
92Dic32—21no—
93#3715C2×C418yescomplemented
94#2949—91noSylow
95C2×D3×Q8—32no—
96C2×D3×D4—32no—
97C2×C3×SD16—32no—
98C3×C4×Q8—32no—
99C3×C4×D4—32no—
100Q8×Dic3—32no—
101C2×#215—32no—
102D4×Dic3—32no—
103C2×#214—32no—
104C4×#67—62no—
105C2×(C2×D3)⋊C4—62no—
106D3×SD16—316no—
107C2×#204C2×D312yes—
108C2×ΓL(1,𝔽25)—32no—
109C2×ΓL(1,𝔽25)—61no—
110C2×D3×C8—32no—
111C2×D3×C8—61no—
112#893—32no—
113#892—32no—
114#892—32no—
115#892—62no—
116#887—32no—
117#887—62no—
118#67⋊C4—62no—
119D3×C22⋊C4—62no—
120C4×D12C2×D312yes—
121#872—32no—
122#872—61no—
123#872—62no—
124C4×Dic6—62no—
125C4×Dic6C2×D312yescomplemented
126C3×#106—32no—
127C3×#103—32no—
128C3×#102—32no—
129C3×C4×C8—21no—
130C3×C4×C8C2×D312yescomplemented
131#835—32no—
132#832—32no—
133#821C2×D312yes—
134#817C2×D312yescomplemented
135#816C2×D312yescomplemented
136#815—32no—
137#815—61no—
138C8×Dic3—32no—
139C8×Dic3—61no—
140#810—32no—
141#809—32no—
142#807—32no—
143#807—32no—
144#803—32no—
145#803—61no—
146C22×C3⋊D3C2×D411yescharacteristic
147C22×C3×D3—22no—
148C2×D32—24no—
149C2×D32—82no—
150C2×C32×C4C2×D412yes—
151C2×C32×C4C2411yescharacteristic
152C2×C3⋊Dic3C2×D412yes—
153C2×C3⋊Dic3C2×D411yescharacteristic
154C4×C3⋊D3C22×C412yes—
155C4×C3⋊D3#4112yes—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C3×D12—22no—
160C3×D12C22×C414yes—
161C3×C4×D3—82no—
162C3×Dic6—22no—
163C3×Dic6C22×C414yes—
164#627—24no—
165#625—24no—
166#624—24no—
167D3×Dic3—82no—
168C32×C8—21no—
169C32×C8C22×C412yes—
170C3⋊(C3⋊C8)—21no—
171C3⋊(C3⋊C8)C22×C412yes—
172C22×SD16—91no—
173#519—91no—
174#518—91no—
175#440—92no—
176#440—92no—
177C4×SD16—32no—
178C4×SD16—92no—
179#427—91no—
180#419—91no—
181#418—91no—
182#405—91no—
183C23×D3—62no—
184C2×C3×Q8—32no—
185C2×C3×D4—32no—
186C22×C3×C4—62no—
187C2×#67—62no—
188C22×Dic3—62no—
189D3×Q8—38no—
190D3×Q8—64no—
191D3×D4—38no—
192D3×D4—64no—
193C2×D12C22×D312yes—
194C2×C4×D3—22no—
195C2×C4×D3—32no—
196C2×C4×D3—61no—
197C2×C4×D3—62no—
198C2×C4×D3—62no—
199C2×Dic6—62no—
200C2×Dic6C22×D312yes—
201C3×SD16—38no—
202C2×C3×C8—21no—
203C2×C3×C8—21no—
204C2×C3×C8C22×D312yes—
205C2×C3×C8C22×D312yes—
206C3×C4⋊C4—32no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—62no—
209C3×C22⋊C4—62no—
210C3×C42—21no—
211C3×C42—62no—
212C3×C42C22×D312yes—
213#217—62no—
214#215—38no—
215#214—38no—
216(C2×D3)⋊C4—22no—
217(C2×D3)⋊C4—32no—
218(C2×D3)⋊C4—32no—
219(C2×D3)⋊C4—62no—
220(C2×D3)⋊C4—62no—
221(C2×D3)⋊C4—62no—
222(C2×D3)⋊C4—62no—
223C4⋊Dic3—62no—
224C4⋊Dic3C22×D312yes—
225C4⋊Dic3C22×D312yes—
226Dic3⋊C4—22no—
227Dic3⋊C4—32no—
228Dic3⋊C4—32no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231C4×Dic3—22no—
232C4×Dic3—32no—
233C4×Dic3—61no—
234C4×Dic3—62no—
235C4×Dic3—62no—
236C4×Dic3—62no—
237C4×Dic3—62no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—61no—
242#204C4×D318yescomplemented
243ΓL(1,𝔽25)—64no—
244ΓL(1,𝔽25)—64no—
245D3×C8—38no—
246D3×C8—64no—
247C22×C32C22×D411yescharacteristic
248C2×C3⋊D3—22no—
249C2×C3⋊D3C4×D412yes—
250C2×C3×D3—24no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253D32—84no—
254C32×C4—22no—
255C32×C4C23×C411yescharacteristic
256C32×C4C2×#4111yescharacteristic
257C3⋊Dic3—22no—
258C3⋊Dic3C4×D412yes—
259C3×Dic3—24no—
260C3×Dic3—42no—
261C3×Dic3—42no—
262C22×Q8—91no—
263C22×D4—91no—
264C2×SD16—32no—
265C2×SD16—98no—
266C2×SD16—92no—
267C2×M16—91no—
268C22×C8—91no—
269C4×Q8—32no—
270C4×Q8—92no—
271C4×Q8—182no—
272C4×D4—32no—
273C4×D4—92no—
274C4×D4—182no—
275#117—91no—
276#117—91no—
277#117—91no—
278#117—182no—
279C2×C22⋊C4—182no—
280#107—92no—
281#106—32no—
282#103—32no—
283#103—92no—
284#102—32no—
285#102—92no—
286#97—91no—
287#97—91no—
288C4×C8—91no—
289C4×C8D3211yescharacteristic, complemented
290C23×C3—62no—
291C22×D3—22no—
292C22×D3—32no—
293C22×D3—61no—
294C22×D3—68no—
295C22×D3—242no—
296C22×D3—242no—
297C3×Q8—34no—
298C3×Q8—62no—
299C3×D4—34no—
300C3×D4—62no—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—242no—
307C2×C3×C4D3×D412yes—
308C2×C3×C4D3×D412yes—
309C2×C3×C4C23×D312yes—
310#67—68no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—32no—
315C2×Dic3—32no—
316C2×Dic3—32no—
317C2×Dic3—61no—
318C2×Dic3—62no—
319C2×Dic3—242no—
320D12—22no—
321D12C2×C4×D314yes—
322C4×D3—34no—
323C4×D3—34no—
324C4×D3—62no—
325C4×D3—62no—
326C4×D3—68no—
327C4×D3—82no—
328C4×D3—242no—
329Dic6—22no—
330Dic6—68no—
331Dic6C2×C4×D314yes—
332C3×C8—22no—
333C3×C8—22no—
334C3×C8—22no—
335C3×C8C2×C4×D314yes—
336C3⋊C8—34no—
337C3⋊C8—62no—
338C3⋊C8—62no—
339C3⋊C8—62no—
340C2×C32C2×C4×D411yescharacteristic
341C2×C32#57712yes—
342C3⋊D3—22no—
343C3×D3—44no—
344C24—181no—
345C2×Q8—32no—
346C2×Q8—94no—
347C2×Q8—181no—
348C2×Q8—182no—
349C2×D4—32no—
350C2×D4—94no—
351C2×D4—182no—
352C2×D4—181no—
353C22×C4—62no—
354C22×C4—91no—
355C22×C4—181no—
356C22×C4—182no—
357SD16—38no—
358SD16—98no—
359M16—182no—
360C2×C8—91no—
361C2×C8—94no—
362C2×C8—91no—
363C2×C8C2×D3211yescharacteristic
364C2×C8C2×D3211yescharacteristic
365C4⋊C4—32no—
366C4⋊C4—32no—
367C4⋊C4—62no—
368C4⋊C4—92no—
369C4⋊C4—182no—
370C22⋊C4—62no—
371C22⋊C4—92no—
372C22⋊C4—181no—
373C22⋊C4—181no—
374C22⋊C4—182no—
375C42—62no—
376C42—91no—
377C42—181no—
378C42—181no—
379C42—182no—
380C42C2×D3211yescharacteristic
381C22×C3—21no—
382C22×C3—64no—
383C22×C3—122no—
384C22×C3—122no—
385C22×C3C2×D3×D412yes—
386C2×D3—24no—
387C2×D3—34no—
388C2×D3—42no—
389C2×D3—42no—
390C2×D3—62no—
391C2×D3—62no—
392C2×D3—62no—
393C2×D3—122no—
394C2×D3—248no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—42no—
400C3×C4—64no—
401C3×C4—122no—
402C3×C4—122no—
403C3×C4C22×C4×D312yes—
404C3×C4D3×#4112yes—
405Dic3—24no—
406Dic3—34no—
407Dic3—42no—
408Dic3—42no—
409Dic3—62no—
410Dic3—62no—
411Dic3—62no—
412Dic3—122no—
413C32#294911yescharacteristic, complemented, Sylow
414C23—62no—
415C23—91no—
416C23—184no—
417C23—722no—
418Q8—34no—
419Q8—62no—
420Q8—184no—
421D4—34no—
422D4—62no—
423D4—184no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—91no—
428C2×C4—92no—
429C2×C4—92no—
430C2×C4—92no—
431C2×C4—184no—
432C2×C4—242no—
433C2×C4—722no—
434C2×C4#380212yes—
435C2×C4C22×D3211yescharacteristic
436C8—21no—
437C8—92no—
438C8—181no—
439C8C4×D3212yes—
440C2×C3—22no—
441C2×C3—21no—
442C2×C3—124no—
443C2×C3C4×D3×D412yes—
444C2×C3#576212yes—
445C2×C3#577012yes—
446D3—44no—
447D3—64no—
448D3—122no—
449C22—64no—
450C22—92no—
451C22—122no—
452C22—122no—
453C22—182no—
454C22—724no—
455C22C2×#380211yescharacteristic
456C4—22no—
457C4—64no—
458C4—92no—
459C4—122no—
460C4—122no—
461C4—182no—
462C4C2×C4×D3211yescharacteristic
463C4#6430611yescharacteristic
464C3—21no—
465C3#7964912yescomplemented
466C2—124no—
467C2—182no—
468C2C4×#380211yescharacteristic
469C2#1059468612yes—
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. #10593848C2semidirect
4. #10592388C2semidirect
5. C3×C4×#204C2semidirect
7. #10590775C2semidirect
8. #10590743C2semidirect
9. #10590712C2semidirect
10. #10590691C2semidirect
11. #10590358C2semidirect
20. C3×C4×Dic6C22semidirect
26. #63843C22semidirect
30. #63796C4semidirect
31. C32×C4×C8C22semidirect
32. #63642C22semidirect
33. C8×C3⋊Dic3C22semidirect
34. #63630C22semidirect
36. C3×#817C22semidirect
37. C3×#816C22semidirect
38. #63576C22semidirect
39. #63565C22semidirect
54. C4×#204D3semidirect
69. #3797C2×C4semidirect
79. C8×C3⋊D3C2×C4semidirect
85. C3×#204C2×C4semidirect
93. #3715C2×C4semidirect
125. C4×Dic6C2×D3semidirect
130. C3×C4×C8C2×D3semidirect
134. #817C2×D3semidirect
135. #816C2×D3semidirect
242. #204C4×D3semidirect
289. C4×C8D32semidirect
413. C32#2949semidirect
465. C3#79649semidirect

Maximal subgroups

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

subgroupindex
C2×#637962
#105939962
#105938482
#105923882
C3×C4×#2042
#105909412
#105907752
#105907432
#105907122
#105906912
#105903582
#796493