Finite Group Databasebeta

← #11857979

Subgroups — #11857979

Order 1152.

1625 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C2×C3×#892C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4#10592665C211yesmaximal, characteristic, complemented
5C3×#4966C211yesmaximal, characteristic, complemented
6#10591106C211yesmaximal, characteristic, complemented
7#10591087C211yesmaximal, characteristic, complemented
8#10590610C212yesmaximal, complemented
9#10590608C212yesmaximal, complemented
10#10590600C212yesmaximal, complemented
11#10590592C212yesmaximal, complemented
12#82213—31nomaximal
13#78881—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C2×D3×#67—21no—
18C2×#3804—21no—
19D3×#235—24no—
20D3×#235C418yescomplemented
21C2×D3×D12C2211yescharacteristic
22C2×C4×D32—21no—
23C2×#3799C2211yescharacteristic
24C2×#3798—21no—
25C2×#3795C2211yescharacteristic
26C2×D3×Dic6C2211yescharacteristic
27C2×C32×C4⋊C4C2211yescharacteristic, complemented
28C2×#3748C2211yescharacteristic, complemented
29C2×C3×(C2×D3)⋊C4—21no—
30C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
31C2×C3×C4×Dic3—21no—
32C2×C3×#208C2211yescharacteristic, complemented
33C3×#892—21no—
34C3×#892—21no—
35C3×#892C2212yes—
36C3×#892C2212yescomplemented
37C2×#3711C2212yes—
38D3×#208—24no—
39C2×D3×C3⋊C8C2212yescomplemented
40#63637C2212yescomplemented
41#63636C2212yescomplemented
42C3×#810C2212yescomplemented
43C3×#809C2212yescomplemented
44#63567C2212yescomplemented
45#63565C2212yescomplemented
46#63564C2212yescomplemented
47#63562C2212yescomplemented
48C2×D3×#41—31no—
49C22×#235—31no—
50C2×C3×#117—31no—
51C22×#208—31no—
52C2×D3×M16—31no—
53C2×#892D311yescharacteristic, complemented
54C3×#417—31no—
55#5232—31no—
56#5133—31no—
57#5004—32no—
58#5002—32no—
59#5002—32no—
60#5001—32no—
61#4966—31no—
62#4966—31no—
63#4966—31no—
64#4966—31no—
65#4966—61no—
66#4966D311yescharacteristic, complemented
67#4804—32no—
68#4802—32no—
69#4772—32no—
70#4770—32no—
71C23×C3×D3D411yescharacteristic
72C22×D32—21no—
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×#638—21no—
76#3828—22no—
77#3828C2×C414yes—
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4×C3⋊D3—21no—
80C2×#634C2311yescharacteristic
81C2×C3×#67—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3D411yescharacteristic
84C3×#235—22no—
85C3×#235C2×C414yes—
86C2×C3×D12C2311yescharacteristic
87C2×C3×C4×D3—21no—
88C2×C3×C4×D3C2×C414yes—
89C2×C3×C4×D3D411yescharacteristic
90C2×C3×C4×D3D411yescharacteristic
91C2×C3×C4×D3D414yes—
92C2×C3×C4×D3C2311yescharacteristic
93C2×C3×C4×D3C2311yescharacteristic
94C2×C3×Dic6C2311yescharacteristic
95D3×#67—28no—
96C2×#627—21no—
97C2×#626—21no—
98C2×#626—21no—
99C2×#625—21no—
100C2×#624—21no—
101#3804—28no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104D3×D12—22no—
105D3×D12C2×C414yescomplemented
106C4×D32—28no—
107#3799—22no—
108#3799C2×C414yescomplemented
109#3798—28no—
110#3795—22no—
111#3795C2×C414yescomplemented
112D3×Dic6—22no—
113D3×Dic6C2×C414yescomplemented
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2312yes—
116#3748—22no—
117C2×C3⋊(C3⋊C8)C2312yes—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4—22no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2312yes—
122C3×C4×Dic3—22no—
123C3×C4×Dic3—22no—
124C3×#208—22no—
125C2×C3×C3⋊C8C2312yes—
126#3711—24no—
127D3×C3⋊C8—24no—
128#2896—91noSylow
129C2×C3×#41—31no—
130C23×C3×C4—31no—
131C22×#67—61no—
132D3×#41—38no—
133D3×#41—64no—
134C2×#239—31no—
135C2×D3×Q8—31no—
136C2×#237—31no—
137C2×#237—61no—
138C2×D3×D4—31no—
139C2×D3×D4—61no—
140C2×#235—31no—
141C2×#235—31no—
142C2×#235—38no—
143C2×#235—31no—
144C2×#235—31no—
145C2×#235—61no—
146C2×#235—61no—
147C2×#235—64no—
148C2×#235—61no—
149C2×#235—61no—
150C2×#235C2×D311yescharacteristic
151C22×D12—31no—
152C22×C4×D3—61no—
153C22×C4×D3—61no—
154C22×C4×D3C2×D311yescharacteristic
155C22×Dic6—31no—
156C2×C3×M16—31no—
157C3×#117—32no—
158C3×#117—32no—
159C3×#117—61no—
160C3×#117—61no—
161C2×C3×C4⋊C4—21no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
164C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
165C2×C3×C22⋊C4—61no—
166C2×C3×C42—61no—
167C2×(C2×D3)⋊C4—21no—
168C2×C4⋊Dic3C2×D311yescharacteristic, complemented
169C2×C4×Dic3—21no—
170C2×#208—31no—
171C2×#208—31no—
172C2×#208—32no—
173C2×#208—61no—
174C2×#208—64no—
175C2×#208C2×D311yescharacteristic, complemented
176C22×C3⋊C8—32no—
177D3×M16—64no—
178C2×ΓL(1,𝔽25)—32no—
179C2×D3×C8—32no—
180#892—21no—
181#892—21no—
182#892C2×D312yes—
183#892C2×D312yescomplemented
184C3×#103—32no—
185C3×#102—32no—
186#835—32no—
187#832—32no—
188#821—32no—
189#816—32no—
190#810—32no—
191#810—32no—
192#810—32no—
193#810—32no—
194#810—62no—
195#810C2×D312yescomplemented
196#809—32no—
197#809—32no—
198#809—32no—
199#809—32no—
200#809—62no—
201#809C2×D312yescomplemented
202C23×C32C2×D411yescharacteristic
203C22×C3⋊D3—21no—
204C22×C3×D3—21no—
205C22×C3×D3—41no—
206C22×C3×D3—41no—
207C22×C3×D3C22⋊C414yes—
208C22×C3×D3C2×D411yescharacteristic
209C22×C3×D3C2×D411yescharacteristic
210C2×D32—24no—
211C2×D32—42no—
212C2×D32—42no—
213C2×C32×C4—22no—
214C2×C32×C4—42no—
215C2×C32×C4C22×C412yes—
216C2×C32×C4C2×D412yes—
217C2×C32×C4C2×D411yescharacteristic
218C2×C32×C4C2411yescharacteristic
219#638—24no—
220C2×C3⋊Dic3—21no—
221C4⋊(C3⋊D3)—21no—
222C4⋊(C3⋊D3)C22×C412yes—
223C4×C3⋊D3—24no—
224#634—21no—
225#634C22×C412yes—
226C3×#67—24no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—42no—
230C2×C3×Dic3C22⋊C414yes—
231C2×C3×Dic3C2×D411yescharacteristic
232C2×C3×Dic3C2×D411yescharacteristic
233C3×D12—21no—
234C3×D12C22×C412yes—
235C3×C4×D3—24no—
236C3×C4×D3C22⋊C414yes—
237C3×C4×D3C22⋊C414yes—
238C3×C4×D3C22×C412yes—
239C3×C4×D3C22×C412yes—
240C3×C4×D3C2×D412yes—
241C3×C4×D3C2×D412yes—
242C3×Dic6—21no—
243C3×Dic6C22×C412yes—
244#627—24no—
245#626—24no—
246#626—24no—
247#625—24no—
248#624—24no—
249D3×Dic3—24no—
250D3×Dic3—24no—
251C3⋊(C3⋊C8)—22no—
252C3×C3⋊C8—22no—
253C22×#41—91no—
254C22×M16—91no—
255C2×#117—31no—
256#419—92no—
257#418—92no—
258#417—31no—
259#417—91no—
260#417—91no—
261#417—91no—
262#416—92no—
263#416—92no—
264C24×C3—31no—
265C23×D3—61no—
266C23×D3—61no—
267C23×D3#6711yescharacteristic
268C3×#41—34no—
269C3×#41—62no—
270C2×C3×Q8—31no—
271C2×C3×D4—31no—
272C2×C3×D4—61no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—31no—
277C22×C3×C4—34no—
278C22×C3×C4—34no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—41no—
284C22×C3×C4—61no—
285C22×C3×C4—61no—
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C2×#67—21no—
289C2×#67—61no—
290C2×#67—68no—
291C2×#67—61no—
292C2×#67—61no—
293C2×#67—61no—
294C2×#67—61no—
295C2×#67—61no—
296C2×#67—121no—
297C22×Dic3—21no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3#6711yescharacteristic
301#239—34no—
302#239—62no—
303D3×Q8—34no—
304D3×Q8—62no—
305#237—34no—
306#237—68no—
307#237—62no—
308D3×D4—34no—
309D3×D4—68no—
310D3×D4—62no—
311#235—22no—
312#235—34no—
313#235—34no—
314#235—34no—
315#235—34no—
316#235—64no—
317#235—62no—
318#235—68no—
319#235—62no—
320#235—68no—
321#235—62no—
322#235—62no—
323#235—68no—
324#235—122no—
325#235C4×D314yes—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—34no—
329C2×D12—61no—
330C2×D12—62no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12C22×D311yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3—68no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—68no—
343C2×C4×D3—121no—
344C2×C4×D3C4×D314yes—
345C2×C4×D3D1214yes—
346C2×C4×D3#6711yescharacteristic
347C2×C4×D3#6711yescharacteristic
348C2×C4×D3C22×D311yescharacteristic
349C2×C4×D3C22×D311yescharacteristic
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—34no—
353C2×Dic6—61no—
354C2×Dic6—62no—
355C2×Dic6—61no—
356C2×Dic6—61no—
357C2×Dic6C22×D311yescharacteristic
358C3×M16—62no—
359C2×C3×C8—32no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—22no—
363C3×C4⋊C4—32no—
364C3×C4⋊C4—41no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4C22×D312yes—
367C3×C4⋊C4C22×D312yes—
368C3×C22⋊C4—62no—
369C3×C22⋊C4—62no—
370C3×C42—62no—
371C3×C42—62no—
372(C2×D3)⋊C4—22no—
373(C2×D3)⋊C4—22no—
374C4⋊Dic3—21no—
375C4⋊Dic3C22×D312yes—
376C4×Dic3—22no—
377C4×Dic3—22no—
378#208—22no—
379#208—64no—
380#208—62no—
381#208—62no—
382#208—122no—
383C2×C3⋊C8—32no—
384C2×C3⋊C8—32no—
385C2×C3⋊C8—62no—
386C2×C3⋊C8—64no—
387C2×C3⋊C8C22×D312yes—
388ΓL(1,𝔽25)—64no—
389D3×C8—64no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32C2×C22⋊C412yes—
393C22×C32C22×D411yescharacteristic
394C2×C3⋊D3—22no—
395C2×C3⋊D3—41no—
396C2×C3⋊D3—41no—
397C2×C3×D3—21no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—22no—
402C2×C3×D3—44no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3C2×C22⋊C412yes—
406C2×C3×D3C2×C22⋊C412yes—
407D32—48no—
408C32×C4—42no—
409C32×C4C2×C22⋊C412yes—
410C32×C4C23×C411yescharacteristic
411C32×C4C22×D411yescharacteristic
412C3⋊Dic3—22no—
413C3×Dic3—22no—
414C3×Dic3—42no—
415C3×Dic3C2×C22⋊C412yes—
416C3×Dic3C2×C22⋊C412yes—
417C2×#41—31no—
418C2×#41—91no—
419C2×#41—91no—
420C2×#41—98no—
421C2×#41—91no—
422C2×#41—181no—
423C2×#41—181no—
424C2×#41—184no—
425C22×Q8—91no—
426C22×D4—91no—
427C22×D4—181no—
428C23×C4—31no—
429C23×C4—181no—
430C2×M16—31no—
431C2×M16—92no—
432C2×M16—91no—
433C2×M16—184no—
434C22×C8—92no—
435#117—32no—
436#117—32no—
437#117—61no—
438#117—61no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4D3211yescharacteristic, complemented
441C2×C22⋊C4—61no—
442C2×C42—61no—
443#103—32no—
444#103—92no—
445#103—92no—
446#103—92no—
447#102—32no—
448#102—92no—
449#102—92no—
450#102—92no—
451C23×C3—21no—
452C23×C3—31no—
453C23×C3—31no—
454C23×C3—34no—
455C23×C3—61no—
456C23×C3—121no—
457C23×C3—121no—
458C23×C3D3×D411yescharacteristic
459C23×C3C2×#6711yescharacteristic
460C22×D3—21no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—64no—
464C22×D3—61no—
465C22×D3—61no—
466C22×D3—64no—
467C22×D3—121no—
468C22×D3—122no—
469C22×D3—122no—
470C22×D3—122no—
471C22×D3—122no—
472C22×D3(C2×D3)⋊C414yes—
473C22×D3C2×#6711yescharacteristic
474C22×D3C2×#6711yescharacteristic
475C3×Q8—32no—
476C3×Q8—61no—
477C3×D4—32no—
478C3×D4—64no—
479C3×D4—61no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—21no—
486C2×C3×C4—34no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—34no—
490C2×C3×C4—34no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—42no—
496C2×C3×C4—42no—
497C2×C3×C4—42no—
498C2×C3×C4—61no—
499C2×C3×C4—64no—
500C2×C3×C4—62no—
501C2×C3×C4—82no—
502C2×C3×C4—122no—
503C2×C3×C4C2×C4×D312yes—
504C2×C3×C4C2×C4×D312yes—
505C2×C3×C4C2×D1212yes—
506C2×C3×C4D3×D412yes—
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4C2×#6711yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—24no—
512#67—64no—
513#67—64no—
514#67—64no—
515#67—64no—
516#67—64no—
517#67—64no—
518#67—124no—
519C2×Dic3—21no—
520C2×Dic3—22no—
521C2×Dic3—42no—
522C2×Dic3—64no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—64no—
526C2×Dic3—121no—
527C2×Dic3(C2×D3)⋊C414yes—
528C2×Dic3C2×#6711yescharacteristic
529C2×Dic3C2×#6711yescharacteristic
530D12—21no—
531D12—32no—
532D12—32no—
533D12—62no—
534D12—64no—
535D12—64no—
536D12—61no—
537D12—61no—
538D12—121no—
539D12C2×C4×D312yes—
540C4×D3—24no—
541C4×D3—64no—
542C4×D3—64no—
543C4×D3—64no—
544C4×D3—64no—
545C4×D3—64no—
546C4×D3—64no—
547C4×D3—124no—
548C4×D3(C2×D3)⋊C414yes—
549C4×D3(C2×D3)⋊C414yes—
550C4×D3C2×C4×D312yes—
551C4×D3C2×C4×D312yes—
552C4×D3C2×D1212yes—
553C4×D3C2×D1212yes—
554Dic6—21no—
555Dic6—32no—
556Dic6—32no—
557Dic6—62no—
558Dic6—64no—
559Dic6—61no—
560Dic6—61no—
561Dic6—64no—
562Dic6—121no—
563Dic6C2×C4×D312yes—
564C3×C8—62no—
565C3⋊C8—22no—
566C3⋊C8—62no—
567C3⋊C8—62no—
568C3⋊C8—122no—
569C2×C32—22no—
570C2×C32C22×C22⋊C411yescharacteristic
571C2×C32#57511yescharacteristic
572C2×C32#57511yescharacteristic
573C3⋊D3—42no—
574C3×D3—22no—
575C3×D3—22no—
576C3×D3—42no—
577C24—31no—
578C24—181no—
579#41—34no—
580#41—62no—
581#41—94no—
582#41—94no—
583#41—94no—
584#41—188no—
585#41—188no—
586#41—182no—
587#41—182no—
588#41—182no—
589C2×Q8—31no—
590C2×Q8—94no—
591C2×Q8—91no—
592C2×Q8—181no—
593C2×Q8—182no—
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—94no—
597C2×D4—91no—
598C2×D4—182no—
599C2×D4—181no—
600C2×D4—181no—
601C2×D4—188no—
602C2×D4—181no—
603C2×D4—181no—
604C22×C4—21no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—34no—
609C22×C4—34no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—181no—
615C22×C4—188no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4C2×D3211yescharacteristic
620M16—62no—
621M16—184no—
622M16—182no—
623C2×C8—32no—
624C2×C8—92no—
625C2×C8—184no—
626C4⋊C4—21no—
627C4⋊C4—32no—
628C4⋊C4—61no—
629C4⋊C4C2×D3212yes—
630C22⋊C4—62no—
631C22⋊C4—62no—
632C42—62no—
633C42—62no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—22no—
640C22×C3—32no—
641C22×C3—32no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—62no—
649C22×C3—124no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3D3×C22⋊C412yes—
653C22×C3C2×(C2×D3)⋊C412yes—
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C22×#6711yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—22no—
661C2×D3—44no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—62no—
665C2×D3—62no—
666C2×D3—122no—
667C2×D3—128no—
668C2×D3—128no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—241no—
674C2×D3—241no—
675C2×D3C2×(C2×D3)⋊C412yes—
676C2×D3C2×(C2×D3)⋊C412yes—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—22no—
680C3×C4—32no—
681C3×C4—32no—
682C3×C4—42no—
683C3×C4—42no—
684C3×C4—62no—
685C3×C4—82no—
686C3×C4—122no—
687C3×C4D3×C22⋊C412yes—
688C3×C4C2×(C2×D3)⋊C412yes—
689C3×C4C22×C4×D311yescharacteristic
690C3×C4C22×C4×D311yescharacteristic
691C3×C4C22×D1211yescharacteristic
692C3×C4C2×D3×D411yescharacteristic
693Dic3—22no—
694Dic3—42no—
695Dic3—62no—
696Dic3—62no—
697Dic3—122no—
698Dic3C2×(C2×D3)⋊C412yes—
699Dic3C2×(C2×D3)⋊C412yes—
700C32#289611yescharacteristic, complemented, Sylow
701C23—31no—
702C23—31no—
703C23—34no—
704C23—61no—
705C23—121no—
706C23—121no—
707C23—184no—
708C23—181no—
709C23—362no—
710C23—362no—
711C23D3×#6711yescharacteristic
712Q8—32no—
713Q8—61no—
714Q8—92no—
715Q8—184no—
716Q8—181no—
717D4—32no—
718D4—64no—
719D4—61no—
720D4—92no—
721D4—184no—
722D4—184no—
723D4—184no—
724D4—184no—
725D4—181no—
726C2×C4—22no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—34no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—34no—
735C2×C4—34no—
736C2×C4—42no—
737C2×C4—61no—
738C2×C4—64no—
739C2×C4—62no—
740C2×C4—122no—
741C2×C4—184no—
742C2×C4—184no—
743C2×C4—184no—
744C2×C4—181no—
745C2×C4—184no—
746C2×C4C4×D3212yes—
747C2×C4D3×D1212yes—
748C2×C4D3×#6711yescharacteristic
749C2×C4C22×D3211yescharacteristic
750C8—62no—
751C8—182no—
752C2×C3—22no—
753C2×C3—22no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—42no—
758C2×C3—62no—
759C2×C3—62no—
760C2×C3—122no—
761C2×C3C2×D3×C22⋊C411yescharacteristic
762C2×C3#577311yescharacteristic
763C2×C3#577711yescharacteristic
764C2×C3C22×(C2×D3)⋊C411yescharacteristic
765C2×C3#582211yescharacteristic
766C2×C3#582211yescharacteristic
767D3—22no—
768D3—22no—
769D3—42no—
770D3—122no—
771D3—122no—
772D3—242no—
773C22—21no—
774C22—21no—
775C22—32no—
776C22—32no—
777C22—61no—
778C22—61no—
779C22—61no—
780C22—61no—
781C22—62no—
782C22—124no—
783C22—121no—
784C22—121no—
785C22—182no—
786C22—368no—
787C22—361no—
788C22—361no—
789C22D3×(C2×D3)⋊C412yes—
790C22C2×D3×#6711yescharacteristic
791C4—32no—
792C4—32no—
793C4—42no—
794C4—62no—
795C4—122no—
796C4—182no—
797C4D3×(C2×D3)⋊C412yes—
798C4C2×C4×D3211yescharacteristic
799C4C2×D3×D1211yescharacteristic
800C3—21no—
801C3#7888111yescharacteristic, complemented
802C3#8221311yescharacteristic, complemented
803C2—22no—
804C2—62no—
805C2—62no—
806C2—122no—
807C2—362no—
808C2C2×D3×(C2×D3)⋊C411yescharacteristic
809C2#1059509511yescharacteristic
810C2#1059531711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×D3×#235C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#892C2semidirect
3. C2×D3×#208C2semidirect
4. #10592665C2semidirect
5. C3×#4966C2semidirect
6. #10591106C2semidirect
7. #10591087C2semidirect
8. #10590610C2semidirect
9. #10590608C2semidirect
10. #10590600C2semidirect
11. #10590592C2semidirect
20. D3×#235C4semidirect
27. C2×C32×C4⋊C4C22semidirect
28. C2×#3748C22semidirect
30. C2×C3×C4⋊Dic3C22semidirect
32. C2×C3×#208C22semidirect
36. C3×#892C22semidirect
39. C2×D3×C3⋊C8C22semidirect
40. #63637C22semidirect
41. #63636C22semidirect
42. C3×#810C22semidirect
43. C3×#809C22semidirect
44. #63567C22semidirect
45. #63565C22semidirect
46. #63564C22semidirect
47. #63562C22semidirect
53. C2×#892D3semidirect
66. #4966D3semidirect
105. D3×D12C2×C4semidirect
108. #3799C2×C4semidirect
111. #3795C2×C4semidirect
113. D3×Dic6C2×C4semidirect
163. C2×C3×C4⋊C4C2×D3semidirect
164. C2×C3×C4⋊C4C2×D3semidirect
168. C2×C4⋊Dic3C2×D3semidirect
175. C2×#208C2×D3semidirect
183. #892C2×D3semidirect
195. #810C2×D3semidirect
201. #809C2×D3semidirect
440. C2×C4⋊C4D32semidirect
700. C32#2896semidirect
801. C3#78881semidirect
802. C3#82213semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×C3×#8922
C2×D3×#2082
#105926652
C3×#49662
#105911062
#105910872
#105906102
#105906082
#105906002
#105905922
#822133
#788813