Finite Group Databasebeta

← C2×#10682487 #72271601

Subgroups — C2×#10682487 #72271601

Order 1536.

3992 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#72130C212yesmaximal
2#10682487C214yesmaximal, direct product factor
3C2×C3×#1783C211yesmaximal, characteristic
4C2×#7316—31nomaximal, Sylow
5C24×C3×D4C2211yescharacteristic
6C22×C3×#100—22no—
7C2×C3×#407C412yescomplemented
8C2×#5247C414yescomplemented
9C22×#834—22no—
10C22×#834—22no—
11C3×#1783—22no—
12C3×#1783C412yescomplemented
13C3×#1783C2212yes—
14#72130—22no—
15#72130—22no—
16#72130C414yescomplemented
17#72130C2214yes—
18C2×#1783D311yescharacteristic
19C2×#1781—32no—
20#7316—34no—
21C26×C3C2×C412yes—
22C23×C3×D4—44no—
23C23×C3×D4—44no—
24C23×C3×D4—42no—
25C23×C3×D4—42no—
26C23×C3×D4C2×C411yescharacteristic
27C23×C3×D4C2×C412yes—
28C23×C3×D4D411yescharacteristic
29C23×C3×D4D411yescharacteristic
30C23×C3×D4D412yes—
31C23×C3×D4D412yes—
32C23×C3×D4Q811yescharacteristic
33C23×C3×D4Q811yescharacteristic
34C23×C3×D4C2311yescharacteristic
35C24×C3×C4C2×C411yescharacteristic
36C22×C3×M16—22no—
37C22×#217—24no—
38C22×#217—44no—
39C2×C3×#100—24no—
40C2×C3×#100—24no—
41C2×C3×#100—44no—
42C2×C3×#100—44no—
43C3×#407—22no—
44C3×#407—42no—
45C3×#407C2×C414yescomplemented
46C2×C3×C22⋊C8—42no—
47#5247—24no—
48#5247—44no—
49#5247C2×C418yescomplemented
50C2×#834—24no—
51C2×#834—24no—
52C2×#834—24no—
53C2×#834—24no—
54C2×#834—44no—
55C2×#834—44no—
56C2×#834—44no—
57C2×#834—44no—
58C24×D4C2×D311yescharacteristic
59C22×#100—22no—
60C22×#99—62no—
61C22×#99—62no—
62C2×#407Dic312yescomplemented
63C2×#379—34no—
64#1783—22no—
65#1783Dic312yescomplemented
66#1783C2×D312yes—
67#1781—34no—
68#1781—34no—
69#1781—62no—
70#1781—62no—
71C25×C3—24no—
72C25×C3—24no—
73C25×C3—42no—
74C25×C3—42no—
75C25×C3—42no—
76C25×C3—42no—
77C25×C3—88no—
78C25×C3C4211yescharacteristic
79C25×C3C4212yes—
80C25×C3C22⋊C412yes—
81C25×C3C22⋊C412yes—
82C25×C3C4⋊C412yes—
83C25×C3C4⋊C412yes—
84C25×C3C22×C412yes—
85C22×C3×D4—24no—
86C22×C3×D4—24no—
87C22×C3×D4—24no—
88C22×C3×D4—24no—
89C22×C3×D4—24no—
90C22×C3×D4—24no—
91C22×C3×D4—44no—
92C22×C3×D4—42no—
93C22×C3×D4—42no—
94C22×C3×D4—44no—
95C22×C3×D4—42no—
96C22×C3×D4—42no—
97C22×C3×D4—41no—
98C22×C3×D4—41no—
99C22×C3×D4—42no—
100C22×C3×D4—42no—
101C22×C3×D4—41no—
102C22×C3×D4—41no—
103C22×C3×D4—42no—
104C22×C3×D4—42no—
105C22×C3×D4—44no—
106C22×C3×D4—44no—
107C22×C3×D4—44no—
108C22×C3×D4—44no—
109C22×C3×D4—44no—
110C22×C3×D4—44no—
111C22×C3×D4—44no—
112C22×C3×D4—44no—
113C22×C3×D4—416no—
114C22×C3×D4—416no—
115C22×C3×D4—432no—
116C22×C3×D4C22⋊C412yes—
117C22×C3×D4C22⋊C412yes—
118C22×C3×D4C22⋊C412yes—
119C22×C3×D4C4⋊C412yes—
120C22×C3×D4C4⋊C412yes—
121C22×C3×D4C4⋊C411yescharacteristic
122C22×C3×D4C4⋊C411yescharacteristic
123C22×C3×D4C2×D411yescharacteristic
124C22×C3×D4C2×D412yes—
125C22×C3×D4C2×Q811yescharacteristic
126C23×C3×C4—22no—
127C23×C3×C4—22no—
128C23×C3×C4—42no—
129C23×C3×C4—42no—
130C23×C3×C4C4211yescharacteristic
131C23×C3×C4C22⋊C411yescharacteristic
132C23×C3×C4C22⋊C411yescharacteristic
133C23×C3×C4C4⋊C411yescharacteristic
134C23×C3×C4C4⋊C411yescharacteristic
135C23×C3×C4C22×C411yescharacteristic
136C23×Dic3—44no—
137C2×C3×M16—24no—
138C2×C3×M16—42no—
139C2×C3×M16—44no—
140C2×C3×M16—44no—
141C22×C3×C8—42no—
142C2×#217—28no—
143C2×#217—44no—
144C2×#217—44no—
145C2×#217—44no—
146C2×#217—44no—
147C2×#217—48no—
148C2×#217—44no—
149C2×#217—48no—
150C2×#217—816no—
151C3×#100—48no—
152C3×#100—48no—
153C3×C22⋊C8—44no—
154C3×C22⋊C8—44no—
155#834—48no—
156#834—48no—
157#834—48no—
158#834—48no—
159C26C4×D312yes—
160C23×D4—42no—
161C23×D4—42no—
162C23×D4—44no—
163C23×D4—44no—
164C23×D4Dic611yescharacteristic
165C23×D4Dic611yescharacteristic
166C23×D4C4×D312yes—
167C23×D4D1211yescharacteristic
168C23×D4D1211yescharacteristic
169C23×D4C2×Dic311yescharacteristic
170C23×D4#6712yes—
171C23×D4#6712yes—
172C23×D4C22×D311yescharacteristic
173C24×C4C2×Dic311yescharacteristic
174C22×M16—22no—
175C22×C22⋊C4—64no—
176C22×C22⋊C4—124no—
177C2×#100—24no—
178C2×#100—24no—
179C2×#100—44no—
180C2×#100—44no—
181C2×#99—64no—
182C2×#99—64no—
183C2×#99—64no—
184C2×#99—64no—
185C2×#99—124no—
186C2×#99—124no—
187C2×#99—124no—
188C2×#99—124no—
189#407—22no—
190#407—42no—
191#407C2×Dic314yescomplemented
192C2×C22⋊C8—42no—
193#379—38no—
194#379—64no—
195#379—124no—
196C24×C3—22no—
197C24×C3—21no—
198C24×C3—22no—
199C24×C3—22no—
200C24×C3—22no—
201C24×C3—22no—
202C24×C3—22no—
203C24×C3—22no—
204C24×C3—21no—
205C24×C3—24no—
206C24×C3—24no—
207C24×C3—24no—
208C24×C3—24no—
209C24×C3—22no—
210C24×C3—22no—
211C24×C3—22no—
212C24×C3—22no—
213C24×C3—22no—
214C24×C3—44no—
215C24×C3—42no—
216C24×C3—42no—
217C24×C3—42no—
218C24×C3—42no—
219C24×C3—42no—
220C24×C3—42no—
221C24×C3—42no—
222C24×C3—42no—
223C24×C3—48no—
224C24×C3—48no—
225C24×C3—48no—
226C24×C3—48no—
227C24×C3—416no—
228C24×C3—88no—
229C24×C3—88no—
230C24×C3—84no—
231C24×C3—84no—
232C24×C3—84no—
233C24×C3—84no—
234C24×C3—84no—
235C24×C3—84no—
236C24×C3—88no—
237C24×C3—88no—
238C24×C3—88no—
239C24×C3—88no—
240C24×C3—88no—
241C24×C3—88no—
242C24×C3—88no—
243C24×C3—88no—
244C24×C3—88no—
245C24×C3#9511yescharacteristic
246C24×C3#9512yes—
247C24×C3#9512yes—
248C24×C3#9511yescharacteristic
249C24×C3#9914yes—
250C24×C3#9914yes—
251C24×C3C2×C4211yescharacteristic
252C24×C3C2×C22⋊C412yes—
253C24×C3C2×C4⋊C412yes—
254C2×C3×D4—24no—
255C2×C3×D4—24no—
256C2×C3×D4—24no—
257C2×C3×D4—24no—
258C2×C3×D4—24no—
259C2×C3×D4—24no—
260C2×C3×D4—24no—
261C2×C3×D4—24no—
262C2×C3×D4—24no—
263C2×C3×D4—24no—
264C2×C3×D4—24no—
265C2×C3×D4—24no—
266C2×C3×D4—42no—
267C2×C3×D4—42no—
268C2×C3×D4—42no—
269C2×C3×D4—42no—
270C2×C3×D4—42no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4—41no—
274C2×C3×D4—41no—
275C2×C3×D4—42no—
276C2×C3×D4—41no—
277C2×C3×D4—42no—
278C2×C3×D4—41no—
279C2×C3×D4—42no—
280C2×C3×D4—48no—
281C2×C3×D4—48no—
282C2×C3×D4—48no—
283C2×C3×D4—48no—
284C2×C3×D4—44no—
285C2×C3×D4—48no—
286C2×C3×D4—44no—
287C2×C3×D4—432no—
288C2×C3×D4—416no—
289C2×C3×D4—416no—
290C2×C3×D4—432no—
291C2×C3×D4—416no—
292C2×C3×D4—416no—
293C2×C3×D4—48no—
294C2×C3×D4—44no—
295C2×C3×D4—44no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—42no—
307C22×C3×C4—42no—
308C22×C3×C4—42no—
309C22×C3×C4—42no—
310C22×C3×C4—44no—
311C22×C3×C4—44no—
312C22×C3×C4—48no—
313C22×C3×C4#9511yescharacteristic
314C22×C3×C4#9511yescharacteristic
315C22×C3×C4#9912yes—
316C22×C3×C4#9912yes—
317C22×C3×C4C2×C22⋊C411yescharacteristic
318C22×C3×C4C2×C4⋊C411yescharacteristic
319C22×Dic3—48no—
320C22×Dic3—84no—
321C22×Dic3—84no—
322C22×Dic3—816no—
323C3×M16—48no—
324C3×M16—84no—
325C2×C3×C8—44no—
326C2×C3×C8—82no—
327C2×C3×C8—82no—
328#217—48no—
329#217—48no—
330#217—84no—
331#217—84no—
332#217—816no—
333#217—816no—
334C25—24no—
335C25—24no—
336C25—42no—
337C25—42no—
338C25—42no—
339C25—42no—
340C25—88no—
341C25C4×Dic311yescharacteristic
342C25C4×Dic312yes—
343C25Dic3⋊C412yes—
344C25Dic3⋊C412yes—
345C25(C2×D3)⋊C412yes—
346C25(C2×D3)⋊C412yes—
347C25C2×C4×D312yes—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—42no—
355C22×D4—44no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—44no—
359C22×D4—42no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—41no—
365C22×D4—41no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—44no—
369C22×D4—44no—
370C22×D4—44no—
371C22×D4—44no—
372C22×D4—44no—
373C22×D4—44no—
374C22×D4—44no—
375C22×D4—44no—
376C22×D4—416no—
377C22×D4—432no—
378C22×D4—416no—
379C22×D4Dic3⋊C412yes—
380C22×D4Dic3⋊C412yes—
381C22×D4C4⋊Dic311yescharacteristic
382C22×D4C4⋊Dic311yescharacteristic
383C22×D4(C2×D3)⋊C412yes—
384C22×D4(C2×D3)⋊C412yes—
385C22×D4#21712yes—
386C22×D4C2×Dic611yescharacteristic
387C22×D4C2×D1211yescharacteristic
388C22×D4C2×#6712yes—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—124no—
394C23×C4C4×Dic311yescharacteristic
395C23×C4C4⋊Dic311yescharacteristic
396C23×C4C4⋊Dic311yescharacteristic
397C23×C4#21711yescharacteristic
398C23×C4#21711yescharacteristic
399C23×C4C22×Dic311yescharacteristic
400C2×M16—24no—
401C2×M16—42no—
402C2×M16—44no—
403C2×M16—44no—
404C22×C8—42no—
405C2×C22⋊C4—68no—
406C2×C22⋊C4—124no—
407C2×C22⋊C4—124no—
408C2×C22⋊C4—124no—
409C2×C22⋊C4—124no—
410C2×C22⋊C4—128no—
411C2×C22⋊C4—124no—
412C2×C22⋊C4—128no—
413C2×C22⋊C4—2416no—
414#100—48no—
415#100—48no—
416#99—128no—
417#99—128no—
418#99—128no—
419#99—128no—
420C22⋊C8—44no—
421C22⋊C8—44no—
422C23×C3—28no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—24no—
431C23×C3—24no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—42no—
443C23×C3—42no—
444C23×C3—42no—
445C23×C3—48no—
446C23×C3—44no—
447C23×C3—42no—
448C23×C3—44no—
449C23×C3—44no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—48no—
453C23×C3—48no—
454C23×C3—48no—
455C23×C3—48no—
456C23×C3—48no—
457C23×C3—48no—
458C23×C3—48no—
459C23×C3—48no—
460C23×C3—48no—
461C23×C3—42no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—42no—
465C23×C3—42no—
466C23×C3—42no—
467C23×C3—42no—
468C23×C3—84no—
469C23×C3—84no—
470C23×C3—84no—
471C23×C3—84no—
472C23×C3—84no—
473C23×C3—84no—
474C23×C3—84no—
475C23×C3—84no—
476C23×C3—84no—
477C23×C3—84no—
478C23×C3—84no—
479C23×C3—84no—
480C23×C3—82no—
481C23×C3—82no—
482C23×C3—84no—
483C23×C3—82no—
484C23×C3—82no—
485C23×C3—84no—
486C23×C3—84no—
487C23×C3—84no—
488C23×C3—84no—
489C23×C3—84no—
490C23×C3—84no—
491C23×C3—84no—
492C23×C3—832no—
493C23×C3—832no—
494C23×C3—84no—
495C23×C3—84no—
496C23×C3—84no—
497C23×C3—84no—
498C23×C3—84no—
499C23×C3—84no—
500C23×C3—84no—
501C23×C3—84no—
502C23×C3—84no—
503C23×C3—84no—
504C23×C3—832no—
505C23×C3—832no—
506C23×C3#34211yescharacteristic
507C23×C3#34211yescharacteristic
508C23×C3#34212yes—
509C23×C3#34214yes—
510C23×C3#34212yes—
511C23×C3C2×#9511yescharacteristic
512C23×C3C2×#9914yes—
513C3×D4—48no—
514C3×D4—48no—
515C3×D4—48no—
516C3×D4—48no—
517C3×D4—44no—
518C3×D4—48no—
519C3×D4—44no—
520C3×D4—48no—
521C3×D4—44no—
522C3×D4—44no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—24no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—44no—
533C2×C3×C4—44no—
534C2×C3×C4—44no—
535C2×C3×C4—44no—
536C2×C3×C4—42no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4#34212yes—
540C2×C3×C4C2×#9912yes—
541C2×Dic3—88no—
542C2×Dic3—816no—
543C2×Dic3—168no—
544C2×Dic3—168no—
545C3×C8—84no—
546C24—21no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—21no—
553C24—22no—
554C24—22no—
555C24—24no—
556C24—24no—
557C24—24no—
558C24—24no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—44no—
565C24—42no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—42no—
572C24—42no—
573C24—416no—
574C24—48no—
575C24—48no—
576C24—48no—
577C24—48no—
578C24—88no—
579C24—88no—
580C24—84no—
581C24—84no—
582C24—84no—
583C24—84no—
584C24—84no—
585C24—84no—
586C24—88no—
587C24—88no—
588C24—88no—
589C24—88no—
590C24—88no—
591C24—88no—
592C24—88no—
593C24—88no—
594C24—88no—
595C24#80614yes—
596C24#80614yes—
597C24C3⋊#9511yescharacteristic
598C24C3⋊#9512yes—
599C24C3⋊#9512yes—
600C24C3⋊#9511yescharacteristic
601C24C2×C4×Dic311yescharacteristic
602C24C2×Dic3⋊C412yes—
603C24C2×(C2×D3)⋊C412yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—24no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—41no—
629C2×D4—42no—
630C2×D4—48no—
631C2×D4—48no—
632C2×D4—48no—
633C2×D4—48no—
634C2×D4—48no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—416no—
638C2×D4—432no—
639C2×D4—416no—
640C2×D4—416no—
641C2×D4—432no—
642C2×D4—416no—
643C2×D4—48no—
644C2×D4—44no—
645C2×D4—44no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—44no—
661C22×C4—48no—
662C22×C4—44no—
663C22×C4—128no—
664C22×C4—244no—
665C22×C4—244no—
666C22×C4—2416no—
667C22×C4C3⋊#9511yescharacteristic
668C22×C4C3⋊#9511yescharacteristic
669C22×C4#83412yes—
670C22×C4#83412yes—
671C22×C4C2×C4⋊Dic311yescharacteristic
672C22×C4C2×#21711yescharacteristic
673M16—48no—
674M16—84no—
675C2×C8—44no—
676C2×C8—82no—
677C2×C8—82no—
678C22⋊C4—128no—
679C22⋊C4—128no—
680C22⋊C4—244no—
681C22⋊C4—244no—
682C22⋊C4—2416no—
683C22⋊C4—2416no—
684C22×C3—24no—
685C22×C3—22no—
686C22×C3—24no—
687C22×C3—24no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—24no—
691C22×C3—24no—
692C22×C3—41no—
693C22×C3—42no—
694C22×C3—41no—
695C22×C3—44no—
696C22×C3—44no—
697C22×C3—48no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—48no—
703C22×C3—44no—
704C22×C3—44no—
705C22×C3—44no—
706C22×C3—48no—
707C22×C3—44no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—82no—
713C22×C3—82no—
714C22×C3—82no—
715C22×C3—82no—
716C22×C3—84no—
717C22×C3—84no—
718C22×C3—82no—
719C22×C3—82no—
720C22×C3—82no—
721C22×C3—82no—
722C22×C3—84no—
723C22×C3—84no—
724C22×C3—84no—
725C22×C3—816no—
726C22×C3—816no—
727C22×C3—816no—
728C22×C3—816no—
729C22×C3—84no—
730C22×C3#130412yes—
731C22×C3#130411yescharacteristic
732C22×C3#130411yescharacteristic
733C22×C3C2×#34211yescharacteristic
734C22×C3C2×#34212yes—
735C3×C4—22no—
736C3×C4—22no—
737C3×C4—41no—
738C3×C4—41no—
739Dic3—168no—
740C23—28no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—22no—
748C23—24no—
749C23—24no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—48no—
764C23—44no—
765C23—42no—
766C23—44no—
767C23—44no—
768C23—42no—
769C23—42no—
770C23—48no—
771C23—48no—
772C23—48no—
773C23—48no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—48no—
779C23—41no—
780C23—42no—
781C23—41no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23—84no—
792C23—84no—
793C23—84no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—82no—
800C23—82no—
801C23—82no—
802C23—82no—
803C23—84no—
804C23—84no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23—832no—
811C23—832no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23—832no—
823C23—832no—
824C23#452611yescharacteristic
825C23#452611yescharacteristic
826C23#452712yes—
827C23#452714yes—
828C23#452712yes—
829C23C2×#80614yes—
830C23C2×C3⋊#9511yescharacteristic
831D4—48no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—48no—
839D4—44no—
840D4—44no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—42no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—248no—
858C2×C4—2416no—
859C2×C4—488no—
860C2×C4—488no—
861C2×C4#452612yes—
862C2×C4C2×#83412yes—
863C8—84no—
864C2×C3—22no—
865C2×C3—21no—
866C2×C3—22no—
867C2×C3—21no—
868C2×C3—44no—
869C2×C3—42no—
870C2×C3—42no—
871C2×C3—44no—
872C2×C3—82no—
873C2×C3—82no—
874C2×C3#731612yescomplemented
875C2×C3C2×#130411yescharacteristic
876C22—24no—
877C22—22no—
878C22—24no—
879C22—24no—
880C22—22no—
881C22—22no—
882C22—24no—
883C22—24no—
884C22—41no—
885C22—41no—
886C22—42no—
887C22—44no—
888C22—44no—
889C22—48no—
890C22—42no—
891C22—42no—
892C22—41no—
893C22—41no—
894C22—48no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—41no—
899C22—41no—
900C22—48no—
901C22—44no—
902C22—42no—
903C22—42no—
904C22—82no—
905C22—82no—
906C22—82no—
907C22—82no—
908C22—84no—
909C22—84no—
910C22—82no—
911C22—82no—
912C22—82no—
913C22—82no—
914C22—84no—
915C22—84no—
916C22—84no—
917C22—816no—
918C22—816no—
919C22—816no—
920C22—816no—
921C22—84no—
922C22C3⋊#130412yes—
923C22C3⋊#130411yescharacteristic
924C22C3⋊#130411yescharacteristic
925C22C2×#452611yescharacteristic
926C22C2×#452712yes—
927C4—22no—
928C4—22no—
929C4—41no—
930C4—41no—
931C4—488no—
932C3C2×#731611yescharacteristic, complemented, Sylow
933C2—22no—
934C2—21no—
935C2—22no—
936C2—21no—
937C2—44no—
938C2—42no—
939C2—42no—
940C2—44no—
941C2—82no—
942C2—82no—
943C2#1068248712yesdirect product factor
944C2C2×C3⋊#130411yescharacteristic
subgroupG/H
centerC22C3⋊#1304
commutatorC24×C3C2×C42
FrattiniC23×D4C22×D3
FittingC2×C3×#1783C2
socleC22×C3#1304
prime radicalC24×C3×D4C22
cosocleC23×C3×D4C23
hypercenterC2×#1783D3
hypocenterC3C2×#7316
LCSG ▷ C24×C3 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24 ◁ C24×D4 ◁ C2×#1783

Complements

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

NH ≅ G/Ntype
2. #10682487C2direct (N × H)
7. C2×C3×#407C4semidirect
8. C2×#5247C4semidirect
12. C3×#1783C4semidirect
16. #72130C4semidirect
45. C3×#407C2×C4semidirect
49. #5247C2×C4semidirect
62. C2×#407Dic3semidirect
65. #1783Dic3semidirect
191. #407C2×Dic3semidirect
874. C2×C3#7316semidirect
932. C3C2×#7316semidirect
943. C2#10682487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#721302
#106824872
C2×C3×#17832
C2×#73163