Finite Group Databasebeta

← #11824512

Subgroups — #11824512

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×#63918C211yesmaximal, characteristic, complemented
2C2×#63893C214yesmaximal, complemented
3C2×Dic3×D12C211yesmaximal, characteristic
4#10592634C211yesmaximal, characteristic, complemented
5C3×#4939C211yesmaximal, characteristic
6C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
7#10591349C211yesmaximal, characteristic, complemented
8#10591318C211yesmaximal, characteristic
9#10591317C214yesmaximal, complemented
10#76349—31nomaximal
11#73800—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C22×#627C2212yes—
14C22×D3×Dic3C2212yes—
15C2×C32×C42C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2214yes—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2214yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×Dic3⋊Dic3C2212yes—
25C2×Dic3⋊Dic3C2214yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2214yes—
28#63918—24no—
29#63893—216no—
30Dic3×D12—24no—
31C3×C3⋊#95C2212yes—
32C2×D4×Dic3—31no—
33C2×#897—34no—
34C2×#888—31no—
35C2×#878—34no—
36C2×C4×D12—31no—
37C2×#869—31no—
38C3×#390—31no—
39C3×C4×C4⋊C4—31no—
40#5221—31no—
41#4975—31no—
42#4949—34no—
43#4939—31no—
44#4939D311yescharacteristic
45#4935—31no—
46#4935—31no—
47#4935—31no—
48#4935—61no—
49C4×Dic3⋊C4D311yescharacteristic, complemented
50#4677—34no—
51C23×C3×D3C2312yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2311yescharacteristic
59C22×C3×Dic3C2311yescharacteristic
60C2×C3×D12—22no—
61C2×C3×D12—22no—
62C2×C3×D12Q814yescomplemented
63C2×#627—28no—
64C2×#627—24no—
65C2×D3×Dic3—24no—
66C2×D3×Dic3—28no—
67C32×C42—22no—
68C4⋊(C3⋊Dic3)—22no—
69C4⋊(C3⋊Dic3)—28no—
70C4⋊(C3⋊Dic3)—22no—
71C3×(C2×D3)⋊C4—28no—
72C3×C4⋊Dic3—22no—
73C3×Dic3⋊C4D418yescomplemented
74C3×C4×Dic3—22no—
75C3×C4×Dic3D414yes—
76Dic3⋊Dic3—28no—
77Dic3⋊Dic3—24no—
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—
87C2×C3×C4⋊C4—32no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C22⋊C4—34no—
90C2×C3×C42—21no—
91C2×C3×C42—31no—
92C2×C3×C42—31no—
93C2×C3×C42C2×D311yescharacteristic
94C2×C3×C42C2×D311yescharacteristic
95C2×#217—32no—
96C2×#217—34no—
97D4×Dic3—64no—
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4—34no—
100C2×(C2×D3)⋊C4C2×D314yes—
101C2×C4⋊Dic3—34no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—34no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—32no—
108C2×C4⋊Dic3—34no—
109C2×C4⋊Dic3—61no—
110C2×C4⋊Dic3—64no—
111C2×C4⋊Dic3—61no—
112C2×C4⋊Dic3C2×D311yescharacteristic
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—34no—
115C2×Dic3⋊C4C2×D312yes—
116C2×C4×Dic3C2×D311yescharacteristic
117C2×C4×Dic3C2×D311yescharacteristic
118#897—616no—
119#888—64no—
120#878—616no—
121C4×D12—64no—
122#869—64no—
123C3×#95—32no—
124C3⋊#95C2×D312yes—
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—22no—
133C2×C32×C4C2×D414yes—
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×Q812yes—
136C2×C32×C4#4112yes—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—24no—
139C2×C3⋊Dic3—24no—
140C2×C3⋊Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3C2×D412yes—
147C2×C3×Dic3C2×D414yes—
148C2×C3×Dic3C2×D412yes—
149C2×C3×Dic3C2×D414yes—
150C3×D12—28no—
151#627—48no—
152D3×Dic3—48no—
153C2×C4⋊Q8—91no—
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—31no—
162C24×C3—32no—
163C23×D3C22×D312yes—
164C2×C3×D4—34no—
165C2×C3×D4—62no—
166C2×C3×D4—62no—
167C22×C3×C4—22no—
168C22×C3×C4—21no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4C22×D312yes—
174C22×C3×C4C22×D312yes—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×Dic3—32no—
178C22×Dic3—32no—
179C22×Dic3—32no—
180C22×Dic3—32no—
181C22×Dic3—62no—
182C22×Dic3—62no—
183C22×Dic3—68no—
184C22×Dic3—64no—
185C22×Dic3C22×D312yes—
186C22×Dic3C22×D311yescharacteristic
187C22×Dic3C22×D312yes—
188C22×Dic3C22×D311yescharacteristic
189C2×D12—22no—
190C2×D12—22no—
191C2×D12Dic614yescomplemented
192C2×C4×D3—64no—
193C2×C4×D3—68no—
194C2×Dic6—64no—
195C2×Dic6—68no—
196C2×Dic6—68no—
197C2×Dic6—64no—
198C3×C4⋊C4—38no—
199C3×C4⋊C4—62no—
200C3×C22⋊C4—68no—
201C3×C42—24no—
202C3×C42—22no—
203C3×C42—22no—
204C3×C42—34no—
205C3×C42—62no—
206#217—68no—
207#217—64no—
208(C2×D3)⋊C4—28no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—68no—
211C4⋊Dic3—22no—
212C4⋊Dic3—64no—
213C4⋊Dic3—68no—
214C4⋊Dic3—68no—
215C4⋊Dic3—62no—
216C4⋊Dic3—62no—
217C4⋊Dic3—62no—
218C4⋊Dic3—62no—
219C4⋊Dic3—68no—
220C4⋊Dic3—122no—
221C4⋊Dic3—128no—
222C4⋊Dic3—122no—
223Dic3⋊C4—68no—
224Dic3⋊C4—64no—
225Dic3⋊C4D1218yescomplemented
226C4×Dic3—22no—
227C4×Dic3D1214yes—
228C22×C32C22×D411yescharacteristic
229C22×C32C22×D412yes—
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—24no—
239C32×C4C22⋊Q814yescomplemented
240C3⋊Dic3—42no—
241C3⋊Dic3—42no—
242C3×Dic3—22no—
243C3×Dic3—24no—
244C3×Dic3—42no—
245C3×Dic3#12714yes—
246C22×Q8—92no—
247C22×D4—31no—
248C23×C4—92no—
249C4⋊Q8—184no—
250C22⋊Q8—1816no—
251C4×D4—184no—
252C2×C4⋊C4—32no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—94no—
255C2×C4⋊C4—92no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—94no—
258C2×C4⋊C4—91no—
259C2×C22⋊C4—34no—
260C2×C22⋊C4—92no—
261C2×C22⋊C4—94no—
262C2×C42—31no—
263C2×C42—31no—
264C2×C42D3211yescharacteristic
265#95—32no—
266C23×C3—21no—
267C23×C3—34no—
268C23×C3—64no—
269C23×C3—62no—
270C23×C3—62no—
271C23×C3—64no—
272C23×C3C23×D311yescharacteristic
273C23×C3C23×D311yescharacteristic
274C22×D3—24no—
275C22×D3—22no—
276C22×D3—22no—
277C22×D3—24no—
278C22×D3C2×Dic614yes—
279C3×D4—68no—
280C2×C3×C4—24no—
281C2×C3×C4—24no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—24no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—32no—
291C2×C3×C4—34no—
292C2×C3×C4—32no—
293C2×C3×C4—34no—
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×C4C2×D1214yes—
301C2×C3×C4C2×D1212yes—
302C2×C3×C4D3×D414yes—
303C2×C3×C4D3×D412yes—
304C2×C3×C4#23712yes—
305C2×C3×C4#23712yes—
306C2×C3×C4D3×Q812yes—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—24no—
312C2×Dic3—62no—
313C2×Dic3—64no—
314C2×Dic3—64no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—64no—
318C2×Dic3—64no—
319C2×Dic3—62no—
320C2×Dic3—122no—
321C2×Dic3—124no—
322C2×Dic3—124no—
323C2×Dic3—122no—
324C2×Dic3—128no—
325C2×Dic3C2×D1212yes—
326C2×Dic3C2×D1214yes—
327C2×Dic3C2×D1212yes—
328C2×Dic3C2×D1214yes—
329D12—28no—
330C4×D3—128no—
331Dic6—128no—
332Dic6—128no—
333C2×C32C2×C22⋊Q811yescharacteristic
334C2×C32C2×#12711yescharacteristic
335C2×C32#53611yescharacteristic
336C2×C32#54712yes—
337C2×C32D4×Q812yes—
338C3×D3—44no—
339C24—32no—
340C2×Q8—188no—
341C2×Q8—184no—
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—38no—
356C4⋊C4—62no—
357C4⋊C4—188no—
358C4⋊C4—184no—
359C4⋊C4—182no—
360C4⋊C4—188no—
361C4⋊C4—182no—
362C22⋊C4—68no—
363C22⋊C4—184no—
364C22⋊C4—188no—
365C42—22no—
366C42—34no—
367C42—62no—
368C22×C3—21no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—64no—
374C22×C3—68no—
375C22×C3—122no—
376C22×C3—122no—
377C22×C3—124no—
378C22×C3C22×Dic611yescharacteristic
379C22×C3C22×D1211yescharacteristic
380C22×C3C22×D1212yes—
381C22×C3C2×D3×D411yescharacteristic
382C22×C3C2×D3×D412yes—
383C22×C3C2×#23711yescharacteristic
384C22×C3C2×#23711yescharacteristic
385C22×C3C2×D3×Q811yescharacteristic
386C22×C3#101012yes—
387C22×C3#101012yes—
388C2×D3—24no—
389C2×D3—28no—
390C2×D3—42no—
391C2×D3—42no—
392C2×D3—44no—
393C3×C4—28no—
394C3×C4—24no—
395C3×C4—24no—
396C3×C4—24no—
397C3×C4—34no—
398C3×C4—62no—
399C3×C4—64no—
400C3×C4—122no—
401C3×C4#87814yescomplemented
402C3×C4#89714yescomplemented
403Dic3—22no—
404Dic3—24no—
405Dic3—42no—
406Dic3—122no—
407Dic3—122no—
408Dic3—122no—
409Dic3—122no—
410Dic3—242no—
411Dic3—242no—
412Dic3#87414yes—
413C32#254211yescharacteristic, complemented, Sylow
414C23—34no—
415C23—64no—
416C23—64no—
417C23—62no—
418C23—62no—
419C23C22×D3211yescharacteristic
420Q8—368no—
421D4—68no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—32no—
425C2×C4—34no—
426C2×C4—32no—
427C2×C4—34no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—64no—
432C2×C4—62no—
433C2×C4—182no—
434C2×C4—184no—
435C2×C4—184no—
436C2×C4—182no—
437C2×C4—368no—
438C2×C4D3×Dic612yes—
439C2×C4D3×D1214yes—
440C2×C4D3×D1212yes—
441C2×C4#380512yes—
442C2×C3—22no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—22no—
446C2×C3—21no—
447C2×C3—124no—
448C2×C3C2×#87411yescharacteristic
449C2×C3C2×#87811yescharacteristic
450C2×C3C2×#89711yescharacteristic
451C2×C3#552611yescharacteristic
452C2×C3D4×Dic612yes—
453C2×C3#555512yes—
454C2×C3Q8×D1212yes—
455C2×C3#561112yes—
456C2×C3#567511yescharacteristic
457C2×C3D3×#12711yescharacteristic
458D3—44no—
459C22—64no—
460C22—68no—
461C22—124no—
462C22—122no—
463C22—122no—
464C22C2×D3×Dic611yescharacteristic
465C22#6429812yes—
466C22C2×D3×D1212yes—
467C22C2×D3×D1211yescharacteristic
468C22C2×#380511yescharacteristic
469C4—24no—
470C4—34no—
471C4—64no—
472C4—62no—
473C4—122no—
474C4—362no—
475C4—362no—
476C4#6389314yescomplemented
477C3—21no—
478C3#7380011yescharacteristic, complemented
479C3#7634911yescharacteristic, complemented
480C2—124no—
481C2#1059389411yescharacteristic
482C2Dic6×D1212yes—
483C2D3×#87411yescharacteristic
484C2#1059490712yes—
485C2C2×#6389311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#63918C2semidirect
2. C2×#63893C2semidirect
4. #10592634C2semidirect
6. C3×C4×Dic3⋊C4C2semidirect
7. #10591349C2semidirect
9. #10591317C2semidirect
49. C4×Dic3⋊C4D3semidirect
62. C2×C3×D12Q8semidirect
73. C3×Dic3⋊C4D4semidirect
191. C2×D12Dic6semidirect
225. Dic3⋊C4D12semidirect
239. C32×C4C22⋊Q8semidirect
401. C3×C4#878semidirect
402. C3×C4#897semidirect
413. C32#2542semidirect
476. C4#63893semidirect
478. C3#73800semidirect
479. C3#76349semidirect

Maximal subgroups

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

subgroupindex
C2×#639182
C2×#638932
C2×Dic3×D122
#105926342
C3×#49392
C3×C4×Dic3⋊C42
#105913492
#105913182
#105913172
#763493
#738003