Finite Group Databasebeta

← #11824515

Subgroups — #11824515

Order 1152.

1445 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#888C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic
3C2×#63887C214yesmaximal, complemented
4#10592674C211yesmaximal, characteristic, complemented
5C3×#4988C211yesmaximal, characteristic
6#10591349C211yesmaximal, characteristic, complemented
7C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8#10591323C211yesmaximal, characteristic
9#10591303C214yesmaximal, complemented
10#83259—31nomaximal
11#76349—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2212yes—
14C22×D3×Dic3C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750C2214yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2214yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#888—24no—
25C2×Dic3⋊Dic3C2214yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2214yes—
29Dic3×D12—24no—
30#63887—216no—
31#63579C2212yes—
32C2×C3×C4⋊Q8—31no—
33C2×#946—34no—
34C2×D4×Dic3—31no—
35C2×#888D311yescharacteristic, complemented
36C2×#878—34no—
37C2×C4×D12—31no—
38C3×#390—31no—
39#5221—31no—
40#4993—34no—
41#4988—31no—
42#4988D311yescharacteristic
43#4975—31no—
44#4975—31no—
45#4975—31no—
46#4975—61no—
47#4949—34no—
48#4935—31no—
49C4×C4⋊Dic3—31no—
50C4×Dic3⋊C4—31no—
51C23×C3×D3C2312yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2311yescharacteristic
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2311yescharacteristic
60C2×C3×D12—22no—
61C2×C3×D12—22no—
62C2×C3×D12Q814yescomplemented
63C2×C3×Dic6—24no—
64C2×C3×Dic6—28no—
65C2×D3×Dic3—28no—
66C2×D3×Dic3—24no—
67C32×C4⋊C4—22no—
68C4⋊(C3⋊Dic3)—22no—
69#3750—28no—
70C4×C3⋊Dic3—22no—
71C3×(C2×D3)⋊C4—28no—
72C3×C4⋊Dic3—22no—
73C3×Dic3⋊C4—24no—
74C3×C4×Dic3—22no—
75C3×C4×Dic3D414yes—
76Dic3⋊Dic3—28no—
77Dic3⋊Dic3D418yescomplemented
78(C2×D3)⋊Dic3—28no—
79(C2×D3)⋊Dic3—24no—
80#2542—91noSylow
81C22×C3×Q8—32no—
82C22×C3×D4—31no—
83C23×Dic3—32no—
84C22×D12C2×D311yescharacteristic
85C22×C4×D3—32no—
86C22×Dic6C2×D312yes—
87C3×C4⋊Q8—64no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—32no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C22⋊C4—34no—
94C2×C3×C42—31no—
95C2×C3×C42—31no—
96C2×#217—32no—
97C2×#217—34no—
98#946—616no—
99D4×Dic3—64no—
100C2×(C2×D3)⋊C4—32no—
101C2×(C2×D3)⋊C4—34no—
102C2×(C2×D3)⋊C4C2×D314yes—
103C2×C4⋊Dic3—32no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—34no—
107C2×C4⋊Dic3—61no—
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×Dic3⋊C4—32no—
110C2×Dic3⋊C4—34no—
111C2×Dic3⋊C4—34no—
112C2×Dic3⋊C4—34no—
113C2×Dic3⋊C4—64no—
114C2×Dic3⋊C4C2×D312yes—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—61no—
118C2×C4×Dic3C2×D311yescharacteristic
119C2×C4×Dic3C2×D311yescharacteristic
120#888—24no—
121#878—616no—
122C4×D12—64no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C23×C32C2411yescharacteristic
126C22×C3×D3—24no—
127C22×C3×D3—22no—
128C22×C3×D3—22no—
129C22×C3×D3—24no—
130C22×C3×D3C2×Q814yes—
131C2×C32×C4—22no—
132C2×C32×C4—24no—
133C2×C32×C4C2×D412yes—
134C2×C32×C4C2×Q812yes—
135C2×C32×C4#4112yes—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—24no—
140C2×C3⋊Dic3C2×D414yes—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3C2×D414yes—
147C2×C3×Dic3C2×D414yes—
148C2×C3×Dic3C2×D412yes—
149C2×C3×Dic3C2×D412yes—
150C3×D12—28no—
151C3×Dic6—48no—
152D3×Dic3—48no—
153C2×C4⋊Q8—31no—
154C2×C22⋊Q8—94no—
155C2×C4×D4—91no—
156#399—94no—
157#390—31no—
158#390—91no—
159#384—91no—
160#384—91no—
161C4×C4⋊C4—91no—
162C24×C3—32no—
163C23×D3C22×D312yes—
164C2×C3×Q8—68no—
165C2×C3×Q8—64no—
166C2×C3×D4—34no—
167C2×C3×D4—62no—
168C2×C3×D4—62no—
169C22×C3×C4—21no—
170C22×C3×C4—22no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4C22×D312yes—
176C22×C3×C4C22×D312yes—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×Dic3—32no—
180C22×Dic3—32no—
181C22×Dic3—32no—
182C22×Dic3—32no—
183C22×Dic3—62no—
184C22×Dic3—62no—
185C22×Dic3—68no—
186C22×Dic3—64no—
187C22×Dic3C22×D312yes—
188C22×Dic3C22×D312yes—
189C22×Dic3C22×D311yescharacteristic
190C22×Dic3C22×D311yescharacteristic
191C2×D12—22no—
192C2×D12—22no—
193C2×D12Dic614yescomplemented
194C2×C4×D3—64no—
195C2×C4×D3—68no—
196C2×Dic6—28no—
197C2×Dic6—24no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—42no—
201C3×C4⋊C4—64no—
202C3×C4⋊C4—62no—
203C3×C22⋊C4—68no—
204C3×C42—34no—
205C3×C42—62no—
206#217—68no—
207#217—64no—
208(C2×D3)⋊C4—28no—
209(C2×D3)⋊C4—68no—
210(C2×D3)⋊C4—64no—
211C4⋊Dic3—22no—
212C4⋊Dic3—38no—
213C4⋊Dic3—68no—
214C4⋊Dic3—62no—
215C4⋊Dic3—62no—
216C4⋊Dic3—122no—
217Dic3⋊C4—24no—
218Dic3⋊C4—38no—
219Dic3⋊C4—68no—
220Dic3⋊C4—68no—
221Dic3⋊C4—68no—
222Dic3⋊C4—128no—
223C4×Dic3—22no—
224C4×Dic3—64no—
225C4×Dic3—62no—
226C4×Dic3—62no—
227C4×Dic3#6714yes—
228C22×C32C22×D412yes—
229C22×C32C22×D411yescharacteristic
230C22×C32C22×Q811yescharacteristic
231C22×C32C2×#4111yescharacteristic
232C22×C322−1+412yes—
233C2×C3×D3—24no—
234C2×C3×D3—28no—
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—44no—
238C32×C4—42no—
239C32×C4C22⋊Q814yescomplemented
240C3⋊Dic3—24no—
241C3⋊Dic3—42no—
242C3×Dic3—22no—
243C3×Dic3—24no—
244C3×Dic3—42no—
245C3×Dic3#12714yes—
246C22×Q8—32no—
247C22×D4—31no—
248C23×C4—92no—
249C4⋊Q8—64no—
250C22⋊Q8—1816no—
251C4×D4—184no—
252C2×C4⋊C4—31no—
253C2×C4⋊C4—32no—
254C2×C4⋊C4—92no—
255C2×C4⋊C4—94no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—94no—
258C2×C4⋊C4D3211yescharacteristic
259C2×C22⋊C4—34no—
260C2×C22⋊C4—92no—
261C2×C22⋊C4—94no—
262C2×C42—31no—
263C2×C42—31no—
264C2×C42—91no—
265#95—92no—
266C23×C3—21no—
267C23×C3—34no—
268C23×C3—64no—
269C23×C3—62no—
270C23×C3—64no—
271C23×C3—62no—
272C23×C3C23×D311yescharacteristic
273C23×C3C23×D311yescharacteristic
274C22×D3—24no—
275C22×D3—22no—
276C22×D3—22no—
277C22×D3—24no—
278C22×D3C2×Dic614yes—
279C3×Q8—128no—
280C3×D4—68no—
281C2×C3×C4—24no—
282C2×C3×C4—24no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—34no—
289C2×C3×C4—32no—
290C2×C3×C4—34no—
291C2×C3×C4—32no—
292C2×C3×C4—44no—
293C2×C3×C4—42no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—64no—
298C2×C3×C4—62no—
299C2×C3×C4C2×Dic612yes—
300C2×C3×C4D3×D412yes—
301C2×C3×C4#23712yes—
302C2×C3×C4D3×Q812yes—
303C2×C3×C4#23912yes—
304C2×C3×C4C2×#6712yes—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—24no—
309C2×Dic3—22no—
310C2×Dic3—34no—
311C2×Dic3—34no—
312C2×Dic3—64no—
313C2×Dic3—64no—
314C2×Dic3—64no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—64no—
320C2×Dic3—64no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—124no—
324C2×Dic3—122no—
325C2×Dic3—128no—
326C2×Dic3D3×D414yes—
327C2×Dic3D3×D414yes—
328C2×Dic3C2×#6712yes—
329C2×Dic3C2×#6712yes—
330D12—28no—
331C4×D3—128no—
332Dic6—48no—
333C2×C32C2×C22⋊Q811yescharacteristic
334C2×C32C2×#12711yescharacteristic
335C2×C32#53611yescharacteristic
336C2×C32#54712yes—
337C2×C32D4×Q812yes—
338C3×D3—44no—
339C24—32no—
340C2×Q8—68no—
341C2×Q8—64no—
342C2×D4—34no—
343C2×D4—62no—
344C2×D4—62no—
345C22×C4—31no—
346C22×C4—31no—
347C22×C4—32no—
348C22×C4—32no—
349C22×C4—92no—
350C22×C4—92no—
351C22×C4—184no—
352C22×C4—188no—
353C22×C4C2×D3212yes—
354C22×C4C2×D3211yescharacteristic
355C4⋊C4—22no—
356C4⋊C4—64no—
357C4⋊C4—62no—
358C4⋊C4—98no—
359C4⋊C4—188no—
360C4⋊C4—188no—
361C4⋊C4—182no—
362C22⋊C4—68no—
363C22⋊C4—184no—
364C22⋊C4—188no—
365C42—34no—
366C42—62no—
367C42—182no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—21no—
373C22×C3—68no—
374C22×C3—64no—
375C22×C3—124no—
376C22×C3—122no—
377C22×C3—122no—
378C22×C3C22×Dic611yescharacteristic
379C22×C3C2×D3×D412yes—
380C22×C3C2×D3×D412yes—
381C22×C3C2×D3×D411yescharacteristic
382C22×C3C2×#23711yescharacteristic
383C22×C3C2×D3×Q811yescharacteristic
384C22×C3C2×#23911yescharacteristic
385C22×C3#100712yes—
386C22×C3#101012yes—
387C22×C3C22×#6711yescharacteristic
388C2×D3—24no—
389C2×D3—28no—
390C2×D3—42no—
391C2×D3—42no—
392C2×D3—44no—
393C3×C4—24no—
394C3×C4—34no—
395C3×C4—42no—
396C3×C4—42no—
397C3×C4—62no—
398C3×C4—64no—
399C3×C4—82no—
400C3×C4—122no—
401C3×C4#87814yescomplemented
402C3×C4#94614yescomplemented
403Dic3—22no—
404Dic3—24no—
405Dic3—42no—
406Dic3—68no—
407Dic3—64no—
408Dic3—64no—
409Dic3—122no—
410Dic3—122no—
411Dic3—242no—
412Dic3#94014yes—
413C32#254211yescharacteristic, complemented, Sylow
414C23—34no—
415C23—62no—
416C23—64no—
417C23—64no—
418C23—62no—
419C23C22×D3211yescharacteristic
420Q8—128no—
421D4—68no—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—34no—
425C2×C4—32no—
426C2×C4—34no—
427C2×C4—32no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—64no—
432C2×C4—62no—
433C2×C4—94no—
434C2×C4—182no—
435C2×C4—182no—
436C2×C4—184no—
437C2×C4—182no—
438C2×C4—368no—
439C2×C4D3×Dic612yes—
440C2×C4#379612yes—
441C2×C4D3×#6712yes—
442C2×C3—22no—
443C2×C3—21no—
444C2×C3—22no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—124no—
448C2×C3C2×#87811yescharacteristic
449C2×C3D4×Dic612yes—
450C2×C3#561112yes—
451C2×C3#567511yescharacteristic
452C2×C3D3×#12711yescharacteristic
453C2×C3#572612yes—
454C2×C3#572712yes—
455C2×C3C2×#94011yescharacteristic
456C2×C3C2×#94611yescharacteristic
457C2×C3#581611yescharacteristic
458D3—44no—
459C22—68no—
460C22—64no—
461C22—124no—
462C22—122no—
463C22—122no—
464C22C2×D3×Dic611yescharacteristic
465C22C2×#379611yescharacteristic
466C22D32×D412yes—
467C22#6431512yes—
468C22C2×D3×#6711yescharacteristic
469C4—34no—
470C4—42no—
471C4—64no—
472C4—62no—
473C4—122no—
474C4—184no—
475C4—362no—
476C4#6388714yescomplemented
477C3—21no—
478C3#7634911yescharacteristic, complemented
479C3#8325911yescharacteristic, complemented
480C2—124no—
481C2#1059437312yes—
482C2#1059437612yes—
483C2C2×#6388711yescharacteristic
484C2D3×#94011yescharacteristic
485C2#1059539911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#888C2semidirect
3. C2×#63887C2semidirect
4. #10592674C2semidirect
6. #10591349C2semidirect
7. C4×Dic3⋊Dic3C2semidirect
9. #10591303C2semidirect
35. C2×#888D3semidirect
62. C2×C3×D12Q8semidirect
77. Dic3⋊Dic3D4semidirect
193. C2×D12Dic6semidirect
239. C32×C4C22⋊Q8semidirect
401. C3×C4#878semidirect
402. C3×C4#946semidirect
413. C32#2542semidirect
476. C4#63887semidirect
478. C3#76349semidirect
479. C3#83259semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8882
C2×Dic3×D122
C2×#638872
#105926742
C3×#49882
#105913492
C4×Dic3⋊Dic32
#105913232
#105913032
#832593
#763493