Finite Group Databasebeta

← #11824514

Subgroups — #11824514

Order 1152.

1497 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic
3C2×#63896C214yesmaximal, complemented
4C3×#4988C211yesmaximal, characteristic
5C3×#4975C211yesmaximal, characteristic, complemented
6#10591349C211yesmaximal, characteristic, complemented
7C4×#3724C211yesmaximal, characteristic, complemented
8#10591318C211yesmaximal, characteristic
9#10591303C214yesmaximal, complemented
10#76349—31nomaximal
11#74334—31nomaximal
12C22×#634C2212yes—
13C22×C3×D12C2211yescharacteristic
14C22×D3×Dic3C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19#64097—24no—
20C2×C3×(C2×D3)⋊C4C2214yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4C2214yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×#3724C2212yes—
26C2×Dic3⋊Dic3C2214yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2214yes—
29#63898—24no—
30#63896—216no—
31#63579C2212yes—
32C2×D4×Dic3—31no—
33C2×#896—34no—
34C2×#893—31no—
35C2×#888—31no—
36C2×#888—31no—
37C2×#888—61no—
38C2×#878—34no—
39C3×#390—31no—
40C3×#384—31no—
41#5221—31no—
42#4993—34no—
43#4988D311yescharacteristic
44#4975—31no—
45#4975D311yescharacteristic, complemented
46#4949—34no—
47#4939—31no—
48#4935—31no—
49C4×Dic3⋊C4—31no—
50C4×Dic3⋊C4—31no—
51C23×C3×D3C2312yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C2×#634—24no—
58C2×#634—28no—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C2×C3×D12—22no—
63C2×C3×D12—22no—
64C2×C3×D12Q814yescomplemented
65C2×D3×Dic3—28no—
66C2×D3×Dic3—24no—
67C32×C4⋊C4—22no—
68C4⋊(C3⋊Dic3)—22no—
69#3750—24no—
70C4×C3⋊Dic3D414yes—
71C3×(C2×D3)⋊C4—28no—
72C3×C4⋊Dic3—22no—
73C3×Dic3⋊C4—28no—
74C3×C4×Dic3—22no—
75C3×C4×Dic3—22no—
76#3724D418yescomplemented
77Dic3⋊Dic3—28no—
78(C2×D3)⋊Dic3—24no—
79(C2×D3)⋊Dic3—28no—
80#2542—91noSylow
81C22×C3×D4—31no—
82C23×Dic3—32no—
83C22×D12C2×D311yescharacteristic
84C22×C4×D3—32no—
85C22×Dic6—32no—
86C22×Dic6—32no—
87C22×Dic6—62no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—34no—
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—
98D4×Dic3—64no—
99C2×(C2×D3)⋊C4—34no—
100C2×(C2×D3)⋊C4—32no—
101C2×(C2×D3)⋊C4C2×D314yes—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—34no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×Dic3⋊C4—32no—
108C2×Dic3⋊C4—32no—
109C2×Dic3⋊C4—32no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—34no—
112C2×Dic3⋊C4—62no—
113C2×Dic3⋊C4C2×D314yes—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3C2×D311yescharacteristic
118C2×C4×Dic3C2×D311yescharacteristic
119#896—616no—
120#893—64no—
121#888—64no—
122#888—64no—
123#888—68no—
124#878—616no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C23×C32C2411yescharacteristic
128C22×C3×D3—24no—
129C22×C3×D3—22no—
130C22×C3×D3—22no—
131C22×C3×D3—24no—
132C22×C3×D3C2×Q814yes—
133C2×C32×C4—22no—
134C2×C32×C4—24no—
135C2×C32×C4C2×D412yes—
136C2×C32×C4C2×Q812yes—
137C2×C32×C4#4112yes—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—24no—
141C2×C3⋊Dic3C2×D412yes—
142C2×C3⋊Dic3C2×D414yes—
143C2×C3⋊Dic3C2×D412yes—
144#634—48no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3C2×D414yes—
152C2×C3×Dic3C2×D414yes—
153C3×D12—28no—
154D3×Dic3—48no—
155C2×C4⋊Q8—91no—
156C2×C22⋊Q8—94no—
157C2×C4×D4—91no—
158#399—94no—
159#390—31no—
160#390—91no—
161#384—31no—
162#384—91no—
163C4×C4⋊C4—91no—
164C24×C3—32no—
165C23×D3C22×D312yes—
166C2×C3×D4—34no—
167C2×C3×D4—62no—
168C2×C3×D4—62no—
169C22×C3×C4—21no—
170C22×C3×C4—22no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4C22×D312yes—
175C22×C3×C4C22×D312yes—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—32no—
183C22×Dic3—32no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—62no—
187C22×Dic3—68no—
188C22×Dic3—64no—
189C22×Dic3C22×D312yes—
190C22×Dic3C22×D312yes—
191C22×Dic3C22×D312yes—
192C2×D12—22no—
193C2×D12—22no—
194C2×D12Dic614yescomplemented
195C2×C4×D3—64no—
196C2×C4×D3—68no—
197C2×Dic6—68no—
198C2×Dic6—64no—
199C2×Dic6—64no—
200C2×Dic6—68no—
201C2×Dic6—68no—
202C2×Dic6—128no—
203C3×C4⋊C4—24no—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—68no—
207C3×C4⋊C4—62no—
208C3×C22⋊C4—68no—
209C3×C42—62no—
210C3×C42—62no—
211#217—64no—
212#217—68no—
213(C2×D3)⋊C4—28no—
214(C2×D3)⋊C4—64no—
215(C2×D3)⋊C4—68no—
216C4⋊Dic3—22no—
217C4⋊Dic3—68no—
218C4⋊Dic3—64no—
219C4⋊Dic3—62no—
220C4⋊Dic3—62no—
221Dic3⋊C4—28no—
222Dic3⋊C4—38no—
223Dic3⋊C4—38no—
224Dic3⋊C4—64no—
225Dic3⋊C4—64no—
226Dic3⋊C4—68no—
227Dic3⋊C4—68no—
228C4×Dic3—22no—
229C4×Dic3—22no—
230C4×Dic3—34no—
231C4×Dic3—34no—
232C4×Dic3—64no—
233C22×C32C22×D411yescharacteristic
234C22×C32C22×D412yes—
235C22×C32C22×Q811yescharacteristic
236C22×C32C2×#4111yescharacteristic
237C22×C322−1+412yes—
238C2×C3×D3—24no—
239C2×C3×D3—28no—
240C2×C3×D3—42no—
241C2×C3×D3—42no—
242C2×C3×D3—44no—
243C32×C4—42no—
244C32×C4C22⋊Q814yescomplemented
245C3⋊Dic3—22no—
246C3⋊Dic3—42no—
247C3⋊Dic3#12714yes—
248C3×Dic3—24no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C22×Q8—92no—
252C22×D4—31no—
253C23×C4—92no—
254C4⋊Q8—184no—
255C22⋊Q8—1816no—
256C4×D4—184no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—34no—
259C2×C4⋊C4—92no—
260C2×C4⋊C4—94no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—92no—
263C2×C4⋊C4D3211yescharacteristic
264C2×C22⋊C4—34no—
265C2×C22⋊C4—92no—
266C2×C22⋊C4—94no—
267C2×C42—31no—
268C2×C42—31no—
269C2×C42—91no—
270#95—92no—
271C23×C3—21no—
272C23×C3—34no—
273C23×C3—62no—
274C23×C3—64no—
275C23×C3—62no—
276C23×C3—64no—
277C23×C3C23×D311yescharacteristic
278C23×C3C23×D311yescharacteristic
279C22×D3—24no—
280C22×D3—22no—
281C22×D3—22no—
282C22×D3—24no—
283C22×D3C2×Dic614yes—
284C3×D4—68no—
285C2×C3×C4—24no—
286C2×C3×C4—24no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—24no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—34no—
294C2×C3×C4—34no—
295C2×C3×C4—44no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—64no—
301C2×C3×C4—62no—
302C2×C3×C4C2×Dic612yes—
303C2×C3×C4#23512yes—
304C2×C3×C4D3×D412yes—
305C2×C3×C4D3×D412yes—
306C2×C3×C4#23712yes—
307C2×C3×C4D3×Q812yes—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—24no—
313C2×Dic3—22no—
314C2×Dic3—32no—
315C2×Dic3—32no—
316C2×Dic3—34no—
317C2×Dic3—34no—
318C2×Dic3—32no—
319C2×Dic3—32no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—64no—
323C2×Dic3—64no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—64no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—64no—
330C2×Dic3—64no—
331C2×Dic3—124no—
332C2×Dic3—128no—
333C2×Dic3D3×D414yes—
334C2×Dic3D3×D414yes—
335D12—28no—
336C4×D3—128no—
337Dic6—128no—
338Dic6—128no—
339Dic6—1216no—
340C2×C32C2×C22⋊Q811yescharacteristic
341C2×C32C2×#12711yescharacteristic
342C2×C32#53611yescharacteristic
343C2×C32#54712yes—
344C2×C32D4×Q812yes—
345C3×D3—44no—
346C24—32no—
347C2×Q8—188no—
348C2×Q8—184no—
349C2×D4—34no—
350C2×D4—62no—
351C2×D4—62no—
352C22×C4—32no—
353C22×C4—32no—
354C22×C4—32no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4—92no—
358C22×C4—184no—
359C22×C4—188no—
360C22×C4C2×D3212yes—
361C22×C4C2×D3211yescharacteristic
362C4⋊C4—22no—
363C4⋊C4—68no—
364C4⋊C4—62no—
365C4⋊C4—98no—
366C4⋊C4—184no—
367C4⋊C4—188no—
368C4⋊C4—182no—
369C22⋊C4—68no—
370C22⋊C4—188no—
371C22⋊C4—184no—
372C42—62no—
373C42—62no—
374C42—94no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—68no—
381C22×C3—64no—
382C22×C3—122no—
383C22×C3—122no—
384C22×C3—124no—
385C22×C3C22×Dic611yescharacteristic
386C22×C3C2×#23511yescharacteristic
387C22×C3C2×D3×D412yes—
388C22×C3C2×D3×D412yes—
389C22×C3C2×D3×D411yescharacteristic
390C22×C3C2×D3×D411yescharacteristic
391C22×C3C2×#23711yescharacteristic
392C22×C3C2×D3×Q811yescharacteristic
393C22×C3#100712yes—
394C22×C3#101012yes—
395C2×D3—24no—
396C2×D3—28no—
397C2×D3—42no—
398C2×D3—42no—
399C2×D3—44no—
400C3×C4—24no—
401C3×C4—44no—
402C3×C4—42no—
403C3×C4—42no—
404C3×C4—64no—
405C3×C4—64no—
406C3×C4—122no—
407C3×C4#87814yescomplemented
408C3×C4#89614yescomplemented
409Dic3—24no—
410Dic3—24no—
411Dic3—34no—
412Dic3—34no—
413Dic3—42no—
414Dic3—64no—
415Dic3—64no—
416Dic3—62no—
417Dic3—62no—
418Dic3—124no—
419Dic3—122no—
420Dic3—122no—
421C32#254211yescharacteristic, complemented, Sylow
422C23—34no—
423C23—62no—
424C23—64no—
425C23—64no—
426C23—62no—
427C23C22×D3211yescharacteristic
428Q8—368no—
429D4—68no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—34no—
433C2×C4—34no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—64no—
439C2×C4—62no—
440C2×C4—94no—
441C2×C4—92no—
442C2×C4—92no—
443C2×C4—182no—
444C2×C4—184no—
445C2×C4—182no—
446C2×C4—368no—
447C2×C4D3×Dic612yes—
448C2×C4#379512yes—
449C2×C4#381112yes—
450C2×C3—21no—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—124no—
456C2×C3C2×#87811yescharacteristic
457C2×C3#550712yes—
458C2×C3C2×#89611yescharacteristic
459C2×C3D4×Dic612yes—
460C2×C3#561112yes—
461C2×C3#567511yescharacteristic
462C2×C3D3×#12711yescharacteristic
463C2×C3D3×#12711yescharacteristic
464C2×C3#572411yescharacteristic
465C2×C3#572712yes—
466D3—44no—
467C22—68no—
468C22—64no—
469C22—122no—
470C22—124no—
471C22—122no—
472C22C2×D3×Dic611yescharacteristic
473C22C2×#379511yescharacteristic
474C22D32×D412yes—
475C22#6431512yes—
476C22C2×#381111yescharacteristic
477C4—42no—
478C4—64no—
479C4—64no—
480C4—94no—
481C4—122no—
482C4—182no—
483C4—362no—
484C4#6389614yescomplemented
485C3—21no—
486C3#7433411yescharacteristic, complemented
487C3#7634911yescharacteristic, complemented
488C2—124no—
489C2#1059437012yes—
490C2#1059437612yes—
491C2C2×#6389611yescharacteristic
492C2#1059530011yescharacteristic
493C2#1059536411yescharacteristic
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×#64097C2semidirect
3. C2×#63896C2semidirect
5. C3×#4975C2semidirect
6. #10591349C2semidirect
7. C4×#3724C2semidirect
9. #10591303C2semidirect
45. #4975D3semidirect
64. C2×C3×D12Q8semidirect
76. #3724D4semidirect
194. C2×D12Dic6semidirect
244. C32×C4C22⋊Q8semidirect
407. C3×C4#878semidirect
408. C3×C4#896semidirect
421. C32#2542semidirect
484. C4#63896semidirect
486. C3#74334semidirect
487. C3#76349semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
C2×#638982
C2×#638962
C3×#49882
C3×#49752
#105913492
C4×#37242
#105913182
#105913032
#763493
#743343