Finite Group Databasebeta

← #11786464

Subgroups — #11786464

Order 1152.

785 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2C2×#63635C211yesmaximal, characteristic, complemented
3#10591313C211yesmaximal, characteristic
4C2×#63573C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#71556—31nomaximal
9#68875—31nomaximal
10C22×C3×C4×D3—21no—
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×D3×C4⋊C4—22no—
20C3×D3×C4⋊C4—22no—
21C2×(C2×D3)⋊Dic3—21no—
22#63635—22no—
23#63579—21no—
24#63573—22no—
25(C2×D3)⋊(C3⋊C8)C414yescomplemented
26C22×C3×C4⋊C4—31no—
27C2×D3×C4⋊C4D311yescharacteristic
28#5212—31no—
29C2×#830—31no—
30C2×(C2×D3)⋊C8—31no—
31C2×#817—31no—
32#4987—31no—
33C2×#808—31no—
34C2×#808—31no—
35C2×#808—31no—
36C2×#808—61no—
37C3×#340—31no—
38#4529—31no—
39#4529—31no—
40#4529D311yescharacteristic, complemented
41C23×C3×D3D411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—24no—
53C2×C3×C4×D3—42no—
54C2×C3×C4×D3—42no—
55C2×C3×C4×D3C2×C412yes—
56C2×C3×C4×D3Q812yes—
57C32×C4⋊C4—21no—
58C32×C4⋊C4D412yes—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)C2×C412yescomplemented
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3D412yes—
68C3×Dic3⋊C4—24no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8C2×C412yescomplemented
72(C2×D3)⋊Dic3—42no—
73#1853—91noSylow
74C23×C3×C4—31no—
75C23×C3×C4—61no—
76C22×C4×D3—21no—
77C22×C4×D3C2×D311yescharacteristic
78C22×C3×C8—31no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—62no—
83C2×C3×C4⋊C4—61no—
84C2×C3×C4⋊C4—62no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×#217—61no—
88C2×(C2×D3)⋊C4—61no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×Dic3⋊C4—21no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—31no—
97C22×C3⋊C8—61no—
98C22×C3⋊C8C2×D311yescharacteristic
99D3×C4⋊C4—22no—
100D3×C4⋊C4—22no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103#830—34no—
104(C2×D3)⋊C8—34no—
105#817—62no—
106#808—62no—
107#808—64no—
108#808—62no—
109#808—62no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—21no—
112C22×C3×D3—21no—
113C22×C3×D3—21no—
114C22×C3×D3—21no—
115C22×C3×D3C4⋊C412yes—
116C22×C3×D3SD1612yes—
117C22×C3×D3SD1612yes—
118C2×C32×C4—22no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×Q811yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3C4⋊C412yes—
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141C3×C4×D3—22no—
142C3×C4×D3—22no—
143C3×C4×D3—48no—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—22no—
146C22×C4⋊C4—31no—
147C2×#106—91no—
148C2×#106—91no—
149C2×C22⋊C8—91no—
150#380—91no—
151#340—31no—
152#340—91no—
153C24×C3—31no—
154C23×D3#6711yescharacteristic
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—32no—
160C22×C3×C4—32no—
161C22×C3×C4—41no—
162C22×C3×C4—64no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4—122no—
170C22×C3×C4—122no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—121no—
178C22×Dic3#6711yescharacteristic
179C2×C4×D3—21no—
180C2×C4×D3—21no—
181C2×C4×D3—21no—
182C2×C4×D3—21no—
183C2×C4×D3—24no—
184C2×C4×D3—42no—
185C2×C4×D3—42no—
186C2×C4×D3Dic612yes—
187C2×C4×D3C4×D312yes—
188C2×C3×C8—32no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—22no—
194C3×C4⋊C4—32no—
195C3×C4⋊C4—41no—
196C3×C4⋊C4—64no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4D1212yes—
201C3×C4⋊C4#6712yes—
202#217—122no—
203(C2×D3)⋊C4—122no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—62no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—121no—
213C4⋊Dic3#6712yes—
214Dic3⋊C4—24no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—32no—
218C2×C3⋊C8—32no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8C4×D312yescomplemented
227C22×C32C2×C4⋊C411yescharacteristic
228C22×C32#12011yescharacteristic
229C22×C32#12311yescharacteristic
230C22×C32C2×SD1611yescharacteristic
231C22×C32C2×SD1611yescharacteristic
232C22×C32AGL(1,ℤ/8)11yescharacteristic
233C22×C32#13711yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—22no—
236C2×C3×D3—22no—
237C2×C3×D3—22no—
238C2×C3×D3—22no—
239C2×C3×D3—22no—
240C2×C3×D3#10614yescomplemented
241C32×C4—42no—
242C32×C4C4×D411yescharacteristic
243C32×C4C4×D411yescharacteristic
244C32×C4C22⋊Q811yescharacteristic
245C32×C4C22⋊Q811yescharacteristic
246C3⋊Dic3—81no—
247C3×Dic3—22no—
248C3×Dic3—42no—
249C3×Dic3—81no—
250C23×C4—31no—
251C23×C4—61no—
252C22×C8—31no—
253C22×C8—91no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—62no—
257C2×C4⋊C4—61no—
258C2×C4⋊C4—62no—
259C2×C4⋊C4—91no—
260C2×C4⋊C4D3211yescharacteristic
261C2×C22⋊C4—181no—
262#106—182no—
263#106—182no—
264C22⋊C8—94no—
265#95—181no—
266C23×C3—21no—
267C23×C3—32no—
268C23×C3—32no—
269C23×C3—32no—
270C23×C3—61no—
271C23×C3—61no—
272C23×C3—61no—
273C23×C3—61no—
274C23×C3D3×D411yescharacteristic
275C23×C3C2×#6711yescharacteristic
276C22×D3—21no—
277C22×D3—21no—
278C22×D3—21no—
279C22×D3—21no—
280C22×D3Dic3⋊C412yes—
281C22×D3#21412yes—
282C22×D3#21512yes—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—32no—
292C2×C3×C4—42no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—81no—
305C2×C3×C4—81no—
306C2×C3×C4—128no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4C2×Dic611yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4#23511yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4#23711yescharacteristic
321C2×C3×C4D3×Q811yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—22no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—122no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3—241no—
340C2×Dic3—241no—
341C2×Dic3Dic3⋊C412yes—
342C4×D3—22no—
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—22no—
346C4×D3—48no—
347C3×C8—62no—
348C3⋊C8—22no—
349C3⋊C8—64no—
350C3⋊C8—62no—
351C3⋊C8—62no—
352C2×C32#38511yescharacteristic
353C2×C32C2×#10611yescharacteristic
354C2×C32#42811yescharacteristic
355C2×C32#44811yescharacteristic
356C2×C32#45011yescharacteristic
357C2×C32#48111yescharacteristic
358C2×C32#48311yescharacteristic
359C3×D3—24no—
360C24—31no—
361C22×C4—21no—
362C22×C4—31no—
363C22×C4—32no—
364C22×C4—32no—
365C22×C4—64no—
366C22×C4—61no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—122no—
373C22×C4—122no—
374C22×C4—181no—
375C22×C4C2×D3211yescharacteristic
376C2×C8—32no—
377C2×C8—61no—
378C2×C8—61no—
379C2×C8—92no—
380C2×C8—181no—
381C2×C8—181no—
382C4⋊C4—21no—
383C4⋊C4—32no—
384C4⋊C4—64no—
385C4⋊C4—61no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4#62612yes—
391C22⋊C4—362no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—34no—
400C22×C3—62no—
401C22×C3—62no—
402C22×C3—62no—
403C22×C3—62no—
404C22×C3—62no—
405C22×C3—62no—
406C22×C3#88211yescharacteristic
407C22×C3#88311yescharacteristic
408C22×C3D3×C4⋊C411yescharacteristic
409C22×C3#91111yescharacteristic
410C22×C3D3×SD1611yescharacteristic
411C22×C3D3×SD1611yescharacteristic
412C22×C3#91811yescharacteristic
413C22×C3C2×Dic3⋊C411yescharacteristic
414C22×C3#92911yescharacteristic
415C22×C3#93211yescharacteristic
416C22×C3C2×#21411yescharacteristic
417C22×C3C2×#21511yescharacteristic
418C22×C3#94211yescharacteristic
419C22×C3#95311yescharacteristic
420C2×D3—22no—
421C2×D3—22no—
422C2×D3—22no—
423C2×D3—22no—
424C2×D3—22no—
425C2×D3—22no—
426C2×D3#80814yescomplemented
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—62no—
434C3×C4—82no—
435C3×C4—122no—
436C3×C4—241no—
437C3×C4C4×D1211yescharacteristic
438C3×C4#67⋊C411yescharacteristic
439C3×C4#89611yescharacteristic
440C3×C4#89711yescharacteristic
441C3×C4#92411yescharacteristic
442C3×C4#92411yescharacteristic
443C3×C4C4×#6711yescharacteristic
444C3×C4C4×#6711yescharacteristic
445Dic3—22no—
446Dic3—42no—
447Dic3—81no—
448Dic3—242no—
449Dic3—241no—
450Dic3—241no—
451C32#185311yescharacteristic, complemented, Sylow
452C23—32no—
453C23—32no—
454C23—32no—
455C23—61no—
456C23—61no—
457C23—61no—
458C23—61no—
459C23D3×#6711yescharacteristic
460C2×C4—22no—
461C2×C4—32no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—128no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—361no—
478C2×C4—361no—
479C2×C4—361no—
480C2×C4D3×Dic611yescharacteristic
481C2×C4#379511yescharacteristic
482C2×C4#379811yescharacteristic
483C2×C4C4×D3211yescharacteristic
484C2×C4C2×#62611yescharacteristic
485C2×C4D3×#6711yescharacteristic
486C8—62no—
487C8—182no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—64no—
496C2×C3#466811yescharacteristic
497C2×C3#477611yescharacteristic
498C2×C3#477711yescharacteristic
499C2×C3#480511yescharacteristic
500C2×C3#480611yescharacteristic
501C2×C3D3×#10611yescharacteristic
502C2×C3#488111yescharacteristic
503C2×C3C2×#80811yescharacteristic
504C2×C3#496411yescharacteristic
505C2×C3#496811yescharacteristic
506C2×C3#497111yescharacteristic
507C2×C3#521011yescharacteristic
508C2×C3#521811yescharacteristic
509C2×C3#522711yescharacteristic
510D3—24no—
511C22—34no—
512C22—62no—
513C22—62no—
514C22—62no—
515C22—62no—
516C22—62no—
517C22—62no—
518C22D3×Dic3⋊C411yescharacteristic
519C22#6390511yescharacteristic
520C22D3×#21411yescharacteristic
521C22#6393211yescharacteristic
522C22D3×#21511yescharacteristic
523C22#6394811yescharacteristic
524C22#6397711yescharacteristic
525C4—42no—
526C4—62no—
527C4—122no—
528C4—241no—
529C4—721no—
530C4#6385111yescharacteristic
531C4#6385711yescharacteristic
532C4#6387911yescharacteristic
533C4C4×#62611yescharacteristic
534C3—21no—
535C3#6887511yescharacteristic, complemented
536C3#7155611yescharacteristic, complemented
537C2—64no—
538C2#1059050011yescharacteristic
539C2#1059051611yescharacteristic
540C2D3×#80811yescharacteristic
541C2#1059058011yescharacteristic
542C2#1059127811yescharacteristic
543C2#1059145911yescharacteristic
544C2#1059158411yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1853
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63635C2semidirect
4. C2×#63573C2semidirect
6. C3×#4529C2semidirect
7. #10589163C2semidirect
25. (C2×D3)⋊(C3⋊C8)C4semidirect
40. #4529D3semidirect
63. C2×C3⋊(C3⋊C8)C2×C4semidirect
71. C2×C3×C3⋊C8C2×C4semidirect
226. C2×C3⋊C8C4×D3semidirect
240. C2×C3×D3#106semidirect
426. C2×D3#808semidirect
451. C32#1853semidirect
535. C3#68875semidirect
536. C3#71556semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×#636352
#105913132
C2×#635732
C2×(C2×D3)⋊(C3⋊C8)2
C3×#45292
#105891632
#715563
#688753