Finite Group Databasebeta

← #11785794

Subgroups — #11785794

Order 1152.

745 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2#10591313C211yesmaximal, characteristic
3C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
4#10589395C211yesmaximal, characteristic, complemented
5C3×#4529C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#71554—31nomaximal
9#68872—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⋊C4C414yescomplemented
21C2×(C2×D3)⋊Dic3—21no—
22#63579—21no—
23(C2×D3)⋊(C3⋊C8)—22no—
24C22×C3×C4⋊C4—31no—
25C2×D3×C4⋊C4D311yescharacteristic
26#5212—31no—
27C2×#830—31no—
28C2×(C2×D3)⋊C8—31no—
29#4987—31no—
30C3×#340—31no—
31#4551—31no—
32#4529—31no—
33#4529—31no—
34#4529—31no—
35#4529—31no—
36#4529—31no—
37#4529—61no—
38#4529D311yescharacteristic, complemented
39C23×C3×D3D411yescharacteristic
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—21no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—24no—
51C2×C3×C4×D3—42no—
52C2×C3×C4×D3—42no—
53C2×C3×C4×D3C2×C412yes—
54C2×C3×C4×D3D412yes—
55C32×C4⋊C4—21no—
56C32×C4⋊C4C2×C412yes—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3C2×C412yes—
66C3×Dic3⋊C4—24no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70(C2×D3)⋊Dic3—42no—
71#1824—91noSylow
72C23×C3×C4—31no—
73C23×C3×C4—61no—
74C22×C4×D3—21no—
75C22×C4×D3C2×D311yescharacteristic
76C22×C3×C8—31no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—34no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C4⋊C4—62no—
82C2×C3×C4⋊C4—61no—
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×#217—61no—
86C2×(C2×D3)⋊C4—61no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—61no—
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×Dic3⋊C4—21no—
93C22×C3⋊C8—31no—
94C22×C3⋊C8—31no—
95C22×C3⋊C8—61no—
96C22×C3⋊C8C2×D311yescharacteristic
97D3×C4⋊C4—22no—
98D3×C4⋊C4Dic314yescomplemented
99C3⋊#95—61no—
100C3⋊#95—61no—
101#830—62no—
102(C2×D3)⋊C8—62no—
103C23×C32C2×D411yescharacteristic
104C22×C3×D3—21no—
105C22×C3×D3—21no—
106C22×C3×D3—21no—
107C22×C3×D3—21no—
108C22×C3×D3C22⋊C412yes—
109C22×C3×D3SD1612yes—
110C22×C3×D3Q1612yes—
111C2×C32×C4—22no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3C22⋊C412yes—
132C3×C4×D3—22no—
133C3×C4×D3—22no—
134C3×C4×D3—22no—
135C3×C4×D3—22no—
136C3×C4×D3—48no—
137C3⋊(C3⋊C8)—41no—
138C3×C3⋊C8—41no—
139C22×C4⋊C4—31no—
140C2×C22⋊C8—91no—
141#380—91no—
142#340—31no—
143#340—91no—
144#340—91no—
145#340—91no—
146C24×C3—31no—
147C23×D3#6711yescharacteristic
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—32no—
153C22×C3×C4—32no—
154C22×C3×C4—41no—
155C22×C3×C4—64no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4—122no—
163C22×C3×C4—122no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—121no—
171C22×Dic3#6711yescharacteristic
172C2×C4×D3—21no—
173C2×C4×D3—21no—
174C2×C4×D3—21no—
175C2×C4×D3—21no—
176C2×C4×D3—24no—
177C2×C4×D3—42no—
178C2×C4×D3—42no—
179C2×C4×D3C2×Dic312yes—
180C2×C4×D3#6712yes—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—22no—
187C3×C4⋊C4—32no—
188C3×C4⋊C4—41no—
189C3×C4⋊C4—64no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4C4×D312yes—
194C3×C4⋊C4C2×Dic312yes—
195#217—122no—
196(C2×D3)⋊C4—122no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—62no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3—121no—
206C4⋊Dic3C2×Dic312yes—
207Dic3⋊C4—24no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—121no—
219C2×C3⋊C8—121no—
220C22×C32C2×C22⋊C411yescharacteristic
221C22×C32#12311yescharacteristic
222C22×C32#12311yescharacteristic
223C22×C32C2×SD1611yescharacteristic
224C22×C32C2×Q1611yescharacteristic
225C22×C32AGL(1,ℤ/8)11yescharacteristic
226C22×C32AGL(1,ℤ/8)11yescharacteristic
227C2×C3×D3—22no—
228C2×C3×D3—22no—
229C2×C3×D3—22no—
230C2×C3×D3—22no—
231C2×C3×D3—22no—
232C2×C3×D3—22no—
233C2×C3×D3#10314yes—
234C32×C4—42no—
235C32×C4#11711yescharacteristic
236C32×C4#11711yescharacteristic
237C32×C4#12311yescharacteristic
238C32×C4#12311yescharacteristic
239C3⋊Dic3—81no—
240C3×Dic3—22no—
241C3×Dic3—42no—
242C3×Dic3—81no—
243C23×C4—31no—
244C23×C4—61no—
245C22×C8—31no—
246C22×C8—91no—
247C2×C4⋊C4—31no—
248C2×C4⋊C4—34no—
249C2×C4⋊C4—31no—
250C2×C4⋊C4—62no—
251C2×C4⋊C4—61no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4D3211yescharacteristic
254C2×C22⋊C4—181no—
255C22⋊C8—182no—
256#95—181no—
257C23×C3—21no—
258C23×C3—32no—
259C23×C3—32no—
260C23×C3—32no—
261C23×C3—61no—
262C23×C3—61no—
263C23×C3—61no—
264C23×C3—61no—
265C23×C3D3×D411yescharacteristic
266C23×C3C2×#6711yescharacteristic
267C22×D3—21no—
268C22×D3—21no—
269C22×D3—21no—
270C22×D3—21no—
271C22×D3#21512yes—
272C22×D3#21612yes—
273C22×D3#21712yes—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—32no—
283C2×C3×C4—42no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—81no—
296C2×C3×C4—81no—
297C2×C3×C4—128no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4C2×C4×D311yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4#23511yescharacteristic
307C2×C3×C4#23511yescharacteristic
308C2×C3×C4#23511yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4#23911yescharacteristic
313C2×C3×C4C22×Dic311yescharacteristic
314C2×C3×C4C2×#6711yescharacteristic
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—22no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—122no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—241no—
331C2×Dic3—241no—
332C2×Dic3#21712yes—
333C4×D3—22no—
334C4×D3—22no—
335C4×D3—22no—
336C4×D3—22no—
337C4×D3—48no—
338C3×C8—121no—
339C3⋊C8—41no—
340C3⋊C8—122no—
341C3⋊C8—121no—
342C3⋊C8—121no—
343C2×C32#38111yescharacteristic
344C2×C32C2×#10311yescharacteristic
345C2×C32#41811yescharacteristic
346C2×C32#48111yescharacteristic
347C2×C32#48111yescharacteristic
348C2×C32#48411yescharacteristic
349C2×C32#48411yescharacteristic
350C3×D3—24no—
351C24—31no—
352C22×C4—21no—
353C22×C4—31no—
354C22×C4—32no—
355C22×C4—32no—
356C22×C4—64no—
357C22×C4—61no—
358C22×C4—61no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4—61no—
363C22×C4—122no—
364C22×C4—122no—
365C22×C4—181no—
366C22×C4C2×D3211yescharacteristic
367C2×C8—61no—
368C2×C8—61no—
369C2×C8—61no—
370C2×C8—181no—
371C2×C8—181no—
372C2×C8—181no—
373C4⋊C4—21no—
374C4⋊C4—32no—
375C4⋊C4—64no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—181no—
380C4⋊C4—181no—
381C4⋊C4D3×Dic312yes—
382C22⋊C4—362no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—34no—
391C22×C3—62no—
392C22×C3—62no—
393C22×C3—62no—
394C22×C3—62no—
395C22×C3—62no—
396C22×C3—62no—
397C22×C3D3×C22⋊C411yescharacteristic
398C22×C3#88311yescharacteristic
399C22×C3#89411yescharacteristic
400C22×C3#91111yescharacteristic
401C22×C3D3×SD1611yescharacteristic
402C22×C3#91411yescharacteristic
403C22×C3D3×Q1611yescharacteristic
404C22×C3#92911yescharacteristic
405C22×C3#92911yescharacteristic
406C22×C3#93211yescharacteristic
407C22×C3#93211yescharacteristic
408C22×C3C2×#21511yescharacteristic
409C22×C3C2×#21611yescharacteristic
410C22×C3C2×#21711yescharacteristic
411C2×D3—22no—
412C2×D3—22no—
413C2×D3—22no—
414C2×D3—22no—
415C2×D3—22no—
416C2×D3—22no—
417C2×D3#83514yes—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—42no—
423C3×C4—42no—
424C3×C4—62no—
425C3×C4—82no—
426C3×C4—122no—
427C3×C4—241no—
428C3×C4#87211yescharacteristic
429C3×C4#88311yescharacteristic
430C3×C4#89211yescharacteristic
431C3×C4#89411yescharacteristic
432C3×C4#92611yescharacteristic
433C3×C4#92611yescharacteristic
434C3×C4#92911yescharacteristic
435C3×C4#92911yescharacteristic
436Dic3—22no—
437Dic3—42no—
438Dic3—81no—
439Dic3—242no—
440Dic3—241no—
441Dic3—241no—
442C32#182411yescharacteristic, complemented, Sylow
443C23—32no—
444C23—32no—
445C23—32no—
446C23—61no—
447C23—61no—
448C23—61no—
449C23—61no—
450C23D3×#6711yescharacteristic
451C2×C4—22no—
452C2×C4—32no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—128no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—121no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—361no—
469C2×C4—361no—
470C2×C4—361no—
471C2×C4#379511yescharacteristic
472C2×C4#379811yescharacteristic
473C2×C4#379811yescharacteristic
474C2×C4#379911yescharacteristic
475C2×C4C2×D3×Dic311yescharacteristic
476C2×C4D3×#6711yescharacteristic
477C8—121no—
478C8—361no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—64no—
487C2×C3#466411yescharacteristic
488C2×C3#477011yescharacteristic
489C2×C3#477711yescharacteristic
490C2×C3D3×#10311yescharacteristic
491C2×C3#481111yescharacteristic
492C2×C3#486311yescharacteristic
493C2×C3#488411yescharacteristic
494C2×C3#496811yescharacteristic
495C2×C3#496811yescharacteristic
496C2×C3#497011yescharacteristic
497C2×C3#497011yescharacteristic
498C2×C3#521111yescharacteristic
499C2×C3#521511yescharacteristic
500C2×C3C2×#83511yescharacteristic
501D3—24no—
502C22—34no—
503C22—62no—
504C22—62no—
505C22—62no—
506C22—62no—
507C22—62no—
508C22—62no—
509C22#6385011yescharacteristic
510C22#6390511yescharacteristic
511C22#6393211yescharacteristic
512C22#6393411yescharacteristic
513C22D3×#21511yescharacteristic
514C22D3×#21611yescharacteristic
515C22D3×#21711yescharacteristic
516C4—42no—
517C4—62no—
518C4—122no—
519C4—241no—
520C4—721no—
521C4#6384111yescharacteristic
522C4#6385011yescharacteristic
523C4#6385511yescharacteristic
524C4#6390511yescharacteristic
525C3—21no—
526C3#6887211yescharacteristic, complemented
527C3#7155411yescharacteristic, complemented
528C2—64no—
529C2#1059042311yescharacteristic
530C2#1059042711yescharacteristic
531C2#1059050011yescharacteristic
532C2#1059051711yescharacteristic
533C2#1059129411yescharacteristic
534C2#1059142111yescharacteristic
535C2D3×#83511yescharacteristic
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#1824
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
4. #10589395C2semidirect
5. C3×#4529C2semidirect
6. #10589164C2semidirect
7. #10589163C2semidirect
20. C3×D3×C4⋊C4C4semidirect
38. #4529D3semidirect
98. D3×C4⋊C4Dic3semidirect
442. C32#1824semidirect
526. C3#68872semidirect
527. C3#71554semidirect

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
#105913132
C2×(C2×D3)⋊(C3⋊C8)2
#105893952
C3×#45292
#105891642
#105891632
#715543
#688723