Finite Group Databasebeta

← #11860771

Subgroups — #11860771

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596269C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3#10594818C211yesmaximal, characteristic, complemented
4C3×#5215C211yesmaximal, characteristic
5#10591446C214yesmaximal, complemented
6#10591445C214yesmaximal, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10591100C211yesmaximal, characteristic, complemented
9#10591059C211yesmaximal, characteristic, complemented
10#83843—31nomaximal
11#78916—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×#3757—22no—
15D4×C3⋊Dic3—22no—
16D4×C3⋊Dic3C2214yes—
17#64135C2211yescharacteristic
18#64135C2211yescharacteristic
19C2×C3×#214C418yescomplemented
20C2×C3×#214C2212yes—
21C2×C3×#214C2212yes—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25#63955—22no—
26#63843C2214yescomplemented
27Dic3×Dic6—22no—
28C3×#832C2214yes—
29#63575C2212yescomplemented
30#63573C2212yescomplemented
31#63566C2214yescomplemented
32#63555C2212yescomplemented
33#63553C2212yescomplemented
34C22×C3×SD16—31no—
35#5812—31no—
36#5798—31no—
37#5798—31no—
38#5798—61no—
39C22×#214D311yescharacteristic
40#5516—31no—
41C3×#418—31no—
42#5225—31no—
43#5215D311yescharacteristic
44#5164—34no—
45Dic3×SD16—34no—
46#5122—31no—
47#5120—31no—
48#5106—31no—
49#5101—31no—
50#4998—31no—
51#4758—34no—
52#4757—34no—
53C24×C32—21no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4C2×C414yes—
57C2×C32×D4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—24no—
60C22×C3×Dic3—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6C2×C414yescomplemented
64C2×C3×Dic6C2312yes—
65#3757—21no—
66#3757—24no—
67#3757D412yes—
68C4⋊(C3⋊Dic3)D412yes—
69C4⋊(C3⋊Dic3)C2312yes—
70C4×C3⋊Dic3—21no—
71C4×C3⋊Dic3C2312yes—
72C3×#217—21no—
73C3×#214C2×C418yescomplemented
74C3×#214C2×C418yescomplemented
75C3×C4⋊Dic3C2312yes—
76C3×C4×Dic3—21no—
77C3×#208—22no—
78C2×C3×C3⋊C8C2×C414yescomplemented
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2311yescharacteristic
81C2×C3×C3⋊C8C2311yescharacteristic
82Dic3⋊Dic3—24no—
83Dic32—24no—
84#2949—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—21no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C22×Dic6C2×D311yescharacteristic
90C2×C3×SD16—38no—
91C2×C3×SD16—32no—
92C2×C3×SD16—32no—
93C2×C3×M16—31no—
94C22×C3×C8—31no—
95C3×#117—31no—
96C2×#217—62no—
97C2×#217—62no—
98C2×#217—64no—
99Q8×Dic3—34no—
100Q8×Dic3—62no—
101D4×Dic3—34no—
102D4×Dic3—34no—
103D4×Dic3—64no—
104D4×Dic3—62no—
105D4×Dic3—62no—
106D4×Dic3—64no—
107C2×#214Dic318yescomplemented
108C2×#214C2×D312yes—
109C2×#214C2×D312yes—
110#926—31no—
111#926—31no—
112#926—31no—
113#926—31no—
114#926—61no—
115#926—61no—
116#926—62no—
117#926C2×D311yescharacteristic
118C2×#208C2×D311yescharacteristic
119C22×C3⋊C8C2×D311yescharacteristic
120#887—34no—
121#877—62no—
122C4×Dic6—62no—
123C3×#102—34no—
124#835—34no—
125#832C2×D314yes—
126#818—32no—
127#817—32no—
128#816—34no—
129#815—32no—
130#815—32no—
131C8×Dic3—32no—
132C8×Dic3—32no—
133#808—32no—
134#807—32no—
135C23×C32—22no—
136C23×C32—24no—
137C23×C32—82no—
138C23×C32C2×D411yescharacteristic
139C32×D4—24no—
140C32×D4—22no—
141C32×D4C22×C414yes—
142C2×C32×C4C22×C412yes—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—84no—
148C2×C3⋊Dic3C2×D414yes—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C3×Dic6—24no—
153C3×Dic6—22no—
154C3×Dic6C22×C414yes—
155C3×C3⋊C8—22no—
156C3×C3⋊C8C22×C412yes—
157C3×C3⋊C8C22×C412yes—
158C22×SD16—31no—
159#519—91no—
160#518—91no—
161#440—94no—
162C4×SD16—94no—
163#427—91no—
164#419—91no—
165#418—31no—
166#405—91no—
167C24×C3—22no—
168C24×C3—21no—
169C24×C3—21no—
170C2×C3×Q8—34no—
171C2×C3×Q8—32no—
172C2×C3×Q8—61no—
173C2×C3×Q8—62no—
174C2×C3×D4—22no—
175C2×C3×D4—24no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4—24no—
181C2×C3×D4—22no—
182C2×C3×D4C4×D314yes—
183C2×C3×D4C2×Dic314yes—
184C2×C3×D4C22×D312yes—
185C2×C3×D4C22×D312yes—
186C22×C3×C4—21no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×Dic3—21no—
191C22×Dic3—64no—
192C22×Dic3—64no—
193C22×Dic3—68no—
194C2×Dic6—21no—
195C2×Dic6—22no—
196C2×Dic6C2×Dic314yescomplemented
197C2×Dic6C22×D312yes—
198C3×SD16—38no—
199C3×SD16—38no—
200C3×M16—62no—
201C2×C3×C8—34no—
202C2×C3×C8—31no—
203C2×C3×C8—31no—
204C2×C3×C8—32no—
205C3×C4⋊C4—32no—
206C3×C22⋊C4—61no—
207C3×C42—61no—
208#217—21no—
209#217—32no—
210#217—32no—
211#217—62no—
212#217—64no—
213#217—64no—
214#217—62no—
215#217—68no—
216#217—61no—
217#217—61no—
218#214C2×Dic318yescomplemented
219#214C2×Dic318yescomplemented
220C4⋊Dic3—32no—
221C4⋊Dic3—32no—
222C4⋊Dic3—32no—
223C4⋊Dic3—32no—
224C4⋊Dic3—62no—
225C4⋊Dic3—62no—
226C4⋊Dic3—64no—
227C4⋊Dic3C22×D312yes—
228Dic3⋊C4—64no—
229C4×Dic3—21no—
230C4×Dic3—32no—
231C4×Dic3—32no—
232C4×Dic3—62no—
233C4×Dic3—64no—
234C4×Dic3—64no—
235C4×Dic3—62no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238#208—22no—
239C2×C3⋊C8C2×Dic314yescomplemented
240C2×C3⋊C8C22×D312yes—
241C2×C3⋊C8C22×D311yescharacteristic
242C2×C3⋊C8C22×D311yescharacteristic
243C22×C32—24no—
244C22×C32—22no—
245C22×C32—44no—
246C22×C32—84no—
247C22×C32C4×D412yes—
248C22×C32C22×D411yescharacteristic
249C32×C4C4×D412yes—
250C32×C4C23×C411yescharacteristic
251C32×C4C2×#4111yescharacteristic
252C3⋊Dic3—24no—
253C3⋊Dic3—42no—
254C3×Dic3—24no—
255C3×Dic3—42no—
256C22×Q8—31no—
257C22×D4D3211yescharacteristic
258C2×SD16—38no—
259C2×SD16—32no—
260C2×SD16—32no—
261C2×M16—31no—
262C22×C8—31no—
263C4×Q8—94no—
264C4×Q8—182no—
265C4×D4—94no—
266C4×D4—182no—
267#117—31no—
268#117—91no—
269#117—91no—
270#117—182no—
271C2×C22⋊C4—182no—
272#107—92no—
273#106—92no—
274#103—94no—
275#102—34no—
276#97—92no—
277C4×C8—92no—
278C23×C3—24no—
279C23×C3—28no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—24no—
283C23×C3—24no—
284C23×C3—21no—
285C23×C3—82no—
286C23×C3—82no—
287C23×C3—84no—
288C23×C3D3×D411yescharacteristic
289C23×C3D3×D411yescharacteristic
290C3×Q8—34no—
291C3×Q8—64no—
292C3×Q8—62no—
293C3×D4—24no—
294C3×D4—28no—
295C3×D4—24no—
296C3×D4—24no—
297C3×D4—22no—
298C3×D4—22no—
299C3×D4—24no—
300C3×D4C2×C4×D314yes—
301C3×D4C22×Dic314yes—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—64no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4C2×C4×D312yes—
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4#23712yes—
313C2×C3×C4#23712yes—
314C2×C3×C4C22×Dic312yes—
315C2×C3×C4C23×D311yescharacteristic
316C2×C3×C4C23×D311yescharacteristic
317C2×Dic3—24no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—34no—
321C2×Dic3—34no—
322C2×Dic3—64no—
323C2×Dic3—64no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—244no—
327C2×Dic3—244no—
328C2×Dic3—248no—
329Dic6—24no—
330Dic6—22no—
331Dic6C22×Dic314yes—
332C3×C8—32no—
333C3×C8—32no—
334C3×C8—62no—
335C3⋊C8—22no—
336C3⋊C8C22×Dic312yes—
337C3⋊C8C22×Dic312yes—
338C2×C32—22no—
339C2×C32—44no—
340C2×C32C2×C4×D411yescharacteristic
341C2×C32#57712yes—
342C24—21no—
343C2×Q8—32no—
344C2×Q8—34no—
345C2×Q8—62no—
346C2×Q8—61no—
347C2×D4—22no—
348C2×D4—21no—
349C2×D4D3×Dic314yes—
350C2×D4C2×D3212yes—
351C22×C4—61no—
352C22×C4—184no—
353C22×C4C2×D3211yescharacteristic
354SD16—38no—
355SD16—38no—
356M16—62no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—34no—
360C2×C8—32no—
361C4⋊C4—32no—
362C4⋊C4—92no—
363C4⋊C4—92no—
364C4⋊C4—184no—
365C22⋊C4—61no—
366C22⋊C4—92no—
367C22⋊C4—184no—
368C22⋊C4—181no—
369C42—61no—
370C42—92no—
371C42—184no—
372C42—181no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—28no—
376C22×C3—24no—
377C22×C3—24no—
378C22×C3—21no—
379C22×C3—22no—
380C22×C3—42no—
381C22×C3—48no—
382C22×C3—44no—
383C22×C3—44no—
384C22×C3—84no—
385C22×C3—84no—
386C22×C3—88no—
387C22×C3#67⋊C412yes—
388C22×C3D4×Dic312yes—
389C22×C3C2×D3×D411yescharacteristic
390C22×C3C2×D3×D411yescharacteristic
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—22no—
394C3×C4—64no—
395C3×C4—122no—
396C3×C4#67⋊C412yes—
397C3×C4D4×Dic312yes—
398C3×C4C22×C4×D311yescharacteristic
399C3×C4C2×#23711yescharacteristic
400C3×C4C2×#23711yescharacteristic
401C3×C4C23×Dic311yescharacteristic
402Dic3—24no—
403Dic3—42no—
404Dic3—64no—
405Dic3—64no—
406Dic3—124no—
407Dic3—124no—
408Dic3—122no—
409Dic3—122no—
410C32#294911yescharacteristic, complemented, Sylow
411C23—22no—
412C23—24no—
413C23—82no—
414C23#381111yescharacteristic
415Q8—34no—
416Q8—62no—
417Q8—64no—
418D4—22no—
419D4—24no—
420D4C2×D3×Dic314yes—
421C2×C4—62no—
422C2×C4—64no—
423C2×C4—62no—
424C2×C4—94no—
425C2×C4—182no—
426C2×C4—724no—
427C2×C4C2×D3×Dic312yes—
428C2×C4#380512yes—
429C2×C4#381111yescharacteristic
430C2×C4C22×D3211yescharacteristic
431C8—32no—
432C8—32no—
433C8—62no—
434C2×C3—22no—
435C2×C3—22no—
436C2×C3—22no—
437C2×C3—21no—
438C2×C3—42no—
439C2×C3—48no—
440C2×C3—44no—
441C2×C3—44no—
442C2×C3C2×#67⋊C411yescharacteristic
443C2×C3#576212yes—
444C2×C3#577512yes—
445C2×C3C2×D4×Dic311yescharacteristic
446C22—22no—
447C22—24no—
448C22—44no—
449C22—84no—
450C22#67⋊Dic312yes—
451C22C2×#381111yescharacteristic
452C4—64no—
453C4—122no—
454C4—184no—
455C4—362no—
456C4#67⋊Dic312yes—
457C4C22×D3×Dic311yescharacteristic
458C4C2×#380511yescharacteristic
459C3—21no—
460C3#7891611yescharacteristic, complemented
461C3#8384311yescharacteristic, complemented
462C2—22no—
463C2—44no—
464C2#1059511512yes—
465C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C22×D4
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10594818C2semidirect
5. #10591446C2semidirect
6. #10591445C2semidirect
7. #10591122C2semidirect
8. #10591100C2semidirect
9. #10591059C2semidirect
19. C2×C3×#214C4semidirect
26. #63843C22semidirect
29. #63575C22semidirect
30. #63573C22semidirect
31. #63566C22semidirect
32. #63555C22semidirect
33. #63553C22semidirect
63. C2×C3×Dic6C2×C4semidirect
73. C3×#214C2×C4semidirect
74. C3×#214C2×C4semidirect
78. C2×C3×C3⋊C8C2×C4semidirect
107. C2×#214Dic3semidirect
196. C2×Dic6C2×Dic3semidirect
218. #214C2×Dic3semidirect
219. #214C2×Dic3semidirect
239. C2×C3⋊C8C2×Dic3semidirect
410. C32#2949semidirect
460. C3#78916semidirect
461. C3#83843semidirect

Maximal subgroups

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

subgroupindex
#105962692
C22×C3×#2142
#105948182
C3×#52152
#105914462
#105914452
#105911222
#105911002
#105910592
#838433
#789163