Finite Group Databasebeta

← #10723340

Subgroups — #10723340

Order 768.

2982 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#940C211yesmaximal, characteristic
2C2×C3×#386C211yesmaximal, characteristic, complemented
3C2×#5220C211yesmaximal, characteristic, complemented
4C2×#5213C212yesmaximal, complemented
5C2×#4958C212yesmaximal, complemented
6#71550C212yesmaximal, complemented
7#71550C212yesmaximal, complemented
8#69426C212yesmaximal, complemented
9#69402C212yesmaximal, complemented
10#14419—31nomaximal, Sylow
11C23×C3×D4C2211yescharacteristic
12C24×C3×C4C2211yescharacteristic
13C23×#67C2212yes—
14C23×#67C2212yes—
15C24×Dic3C2211yescharacteristic
16C23×D12C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2212yes—
20C22×#217C2211yescharacteristic
21C2×#940—24no—
22C2×#940—24no—
23C2×#940C418yescomplemented
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×C4×Dic3C2211yescharacteristic
29C3×#386—24no—
30C2×C3×#95C2212yes—
31#5220—24no—
32#5213—28no—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38#4958—28no—
39C22×#127—31no—
40C2×#386—31no—
41C2×#386—32no—
42C2×#386—32no—
43C2×#386D311yescharacteristic, complemented
44#1438—32no—
45#1438—32no—
46#1438—32no—
47#1434—32no—
48C25×C3C2311yescharacteristic
49C25×C3C2311yescharacteristic
50C24×D3C2312yes—
51C22×C3×D4—41no—
52C22×C3×D4—41no—
53C22×C3×D4—41no—
54C22×C3×D4—41no—
55C22×C3×D4C2×C414yes—
56C22×C3×D4D414yes—
57C22×C3×D4D414yes—
58C23×C3×C4—22no—
59C23×C3×C4—24no—
60C23×C3×C4—41no—
61C23×C3×C4—41no—
62C23×C3×C4—42no—
63C23×C3×C4C2312yes—
64C23×C3×C4C2312yes—
65C23×C3×C4C2311yescharacteristic
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—24no—
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—24no—
72C22×#67—24no—
73C22×#67—24no—
74C22×#67—42no—
75C22×#67—42no—
76C22×#67—42no—
77C22×#67—42no—
78C22×#67C2×C418yescomplemented
79C22×#67C2×C418yescomplemented
80C23×Dic3—22no—
81C23×Dic3—24no—
82C23×Dic3—41no—
83C23×Dic3—41no—
84C23×Dic3—42no—
85C23×Dic3C2312yes—
86C23×Dic3C2312yes—
87C23×Dic3C2312yes—
88C22×D12—22no—
89C22×D12—22no—
90C22×D12—41no—
91C22×D12—41no—
92C22×D12—41no—
93C22×D12—41no—
94C22×D12C2×C414yescomplemented
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—42no—
99C2×C3×C22⋊C4—41no—
100C2×C3×C22⋊C4—41no—
101C2×#217—24no—
102C2×#217—22no—
103C2×#217—24no—
104C2×#217—42no—
105C2×#217—41no—
106C2×#217—41no—
107#940—232no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—42no—
113C2×(C2×D3)⋊C4—42no—
114C2×(C2×D3)⋊C4—42no—
115C2×(C2×D3)⋊C4—42no—
116C2×(C2×D3)⋊C4—42no—
117C2×(C2×D3)⋊C4—42no—
118C2×(C2×D3)⋊C4—42no—
119C2×(C2×D3)⋊C4—42no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3—22no—
122C2×C4×Dic3C2×C414yescomplemented
123C3×#95—24no—
124C3⋊#95—24no—
125C3⋊#95—24no—
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95D418yescomplemented
129C23×D4—32no—
130C23×D4—32no—
131C23×D4—31no—
132C23×D4C2×D311yescharacteristic
133C24×C4—31no—
134C24×C4C2×D311yescharacteristic
135C2×#127—38no—
136C2×#127—64no—
137C2×#127—64no—
138C22×C22⋊C4—32no—
139C22×C22⋊C4—32no—
140C22×C22⋊C4—31no—
141C22×C22⋊C4—32no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4C2×D312yes—
145C22×C22⋊C4C2×D311yescharacteristic
146C22×C42—31no—
147#386—24no—
148#386—68no—
149#386—68no—
150#386—64no—
151C2×#95—32no—
152C2×#95—32no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95C2×D312yes—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—22no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—22no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3—22no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3C22×C412yes—
174C24×C3C22×C412yes—
175C24×C3C2×D412yes—
176C24×C3C2×D412yes—
177C24×C3C2×D412yes—
178C24×C3C2×D412yes—
179C24×C3C2411yescharacteristic
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—22no—
189C23×D3—22no—
190C23×D3—22no—
191C23×D3—22no—
192C23×D3—22no—
193C23×D3—22no—
194C23×D3C22×C414yes—
195C2×C3×D4—44no—
196C2×C3×D4—44no—
197C2×C3×D4—44no—
198C2×C3×D4—44no—
199C2×C3×D4—44no—
200C2×C3×D4—44no—
201C2×C3×D4C22⋊C4116yescomplemented
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—44no—
220C22×C3×C4—48no—
221C22×C3×C4—48no—
222C22×C3×C4—44no—
223C22×C3×C4—44no—
224C22×C3×C4C22×C412yes—
225C22×C3×C4C2×D412yes—
226C22×C3×C4C2×D414yes—
227C22×C3×C4C2×D412yes—
228C2×#67—216no—
229C2×#67—216no—
230C2×#67—216no—
231C2×#67—216no—
232C2×#67—48no—
233C2×#67—48no—
234C2×#67—48no—
235C2×#67—48no—
236C2×#67—48no—
237C2×#67—48no—
238C2×#67—48no—
239C2×#67—48no—
240C2×#67—48no—
241C2×#67—48no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—44no—
260C22×Dic3—48no—
261C22×Dic3—48no—
262C22×Dic3—44no—
263C22×Dic3—44no—
264C22×Dic3C22×C414yes—
265C22×Dic3C2×D414yes—
266C22×Dic3C2×D414yes—
267C22×Dic3#4114yes—
268C2×D12—28no—
269C2×D12—44no—
270C2×D12—44no—
271C2×D12—44no—
272C2×D12—44no—
273C2×D12—44no—
274C2×D12—44no—
275C3×C22⋊C4—48no—
276C3×C22⋊C4—44no—
277#217—48no—
278#217—44no—
279(C2×D3)⋊C4—48no—
280(C2×D3)⋊C4—48no—
281(C2×D3)⋊C4—48no—
282(C2×D3)⋊C4—48no—
283C4×Dic3—28no—
284C25—32no—
285C25C22×D311yescharacteristic
286C25C22×D311yescharacteristic
287C22×D4—38no—
288C22×D4—38no—
289C22×D4—34no—
290C22×D4—41no—
291C22×D4—41no—
292C22×D4—41no—
293C22×D4—41no—
294C22×D4—64no—
295C22×D4—64no—
296C22×D4—64no—
297C22×D4—64no—
298C22×D4—64no—
299C22×D4—64no—
300C22×D4—64no—
301C22×D4—64no—
302C22×D4—62no—
303C22×D4—62no—
304C22×D4—121no—
305C22×D4—121no—
306C22×D4—121no—
307C22×D4—121no—
308C22×D4—122no—
309C22×D4—122no—
310C22×D4—122no—
311C22×D4—122no—
312C22×D4C4×D314yes—
313C22×D4D1214yes—
314C22×D4#6714yes—
315C23×C4—22no—
316C23×C4—24no—
317C23×C4—32no—
318C23×C4—32no—
319C23×C4—32no—
320C23×C4—42no—
321C23×C4—41no—
322C23×C4—41no—
323C23×C4—64no—
324C23×C4—62no—
325C23×C4—121no—
326C23×C4—121no—
327C23×C4—122no—
328C23×C4C22×D312yes—
329C23×C4C22×D312yes—
330C23×C4C22×D311yescharacteristic
331#127—632no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—64no—
339C2×C22⋊C4—64no—
340C2×C22⋊C4—64no—
341C2×C22⋊C4—64no—
342C2×C22⋊C4—62no—
343C2×C22⋊C4—64no—
344C2×C22⋊C4—64no—
345C2×C22⋊C4—122no—
346C2×C22⋊C4—122no—
347C2×C22⋊C4—122no—
348C2×C22⋊C4—122no—
349C2×C22⋊C4—122no—
350C2×C22⋊C4—122no—
351C2×C22⋊C4—122no—
352C2×C22⋊C4—122no—
353C2×C22⋊C4—122no—
354C2×C22⋊C4—121no—
355C2×C22⋊C4—121no—
356C2×C42—34no—
357C2×C42—62no—
358C2×C42—62no—
359#95—24no—
360#95—38no—
361#95—64no—
362#95—64no—
363#95—64no—
364#95—64no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—24no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—42no—
408C23×C3—42no—
409C23×C3C2×C22⋊C414yes—
410C23×C3C2×C22⋊C414yes—
411C23×C3C23×C411yescharacteristic
412C23×C3C22×D411yescharacteristic
413C23×C3C22×D412yes—
414C23×C3C22×D411yescharacteristic
415C23×C3C2×#4112yes—
416C23×C3H(5,𝔽2)11yescharacteristic
417C23×C3H(5,𝔽2)11yescharacteristic
418C23×C3H(5,𝔽2)11yescharacteristic
419C23×C3H(5,𝔽2)11yescharacteristic
420C23×C3H(5,𝔽2)12yes—
421C23×C3H(5,𝔽2)12yes—
422C22×D3—24no—
423C22×D3—24no—
424C22×D3—24no—
425C22×D3—24no—
426C22×D3—24no—
427C22×D3—24no—
428C22×D3—24no—
429C22×D3—42no—
430C22×D3—42no—
431C22×D3—42no—
432C22×D3—42no—
433C22×D3—42no—
434C22×D3—42no—
435C22×D3—42no—
436C22×D3—42no—
437C22×D3—42no—
438C22×D3—42no—
439C22×D3—42no—
440C22×D3—42no—
441C22×D3—42no—
442C22×D3—42no—
443C22×D3—42no—
444C22×D3—42no—
445C22×D3—42no—
446C22×D3—42no—
447C22×D3—42no—
448C22×D3—42no—
449C22×D3—42no—
450C22×D3—42no—
451C22×D3—42no—
452C22×D3—42no—
453C22×D3—42no—
454C22×D3—42no—
455C22×D3—42no—
456C22×D3—42no—
457C3×D4—416no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—24no—
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—416no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4—42no—
476C2×C3×C4—42no—
477C2×C3×C4—42no—
478C2×C3×C4—42no—
479C2×C3×C4C2×C22⋊C414yes—
480#67—432no—
481#67—432no—
482C2×Dic3—24no—
483C2×Dic3—24no—
484C2×Dic3—24no—
485C2×Dic3—24no—
486C2×Dic3—24no—
487C2×Dic3—24no—
488C2×Dic3—24no—
489C2×Dic3—24no—
490C2×Dic3—24no—
491C2×Dic3—416no—
492C2×Dic3—42no—
493C2×Dic3—42no—
494C2×Dic3—42no—
495C2×Dic3—42no—
496C2×Dic3—42no—
497C2×Dic3—42no—
498C2×Dic3—42no—
499C2×Dic3—42no—
500C2×Dic3—42no—
501C2×Dic3—42no—
502C2×Dic3—42no—
503C2×Dic3C4×D418yes—
504D12—416no—
505C24—22no—
506C24—22no—
507C24—21no—
508C24—21no—
509C24—22no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—21no—
516C24—21no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—34no—
522C24—62no—
523C24—62no—
524C24—62no—
525C24—62no—
526C24—62no—
527C24—62no—
528C24—62no—
529C24—62no—
530C24—62no—
531C24—62no—
532C24—62no—
533C24—62no—
534C24—62no—
535C24—62no—
536C24C2×C4×D312yes—
537C24C2×C4×D312yes—
538C24C2×D1212yes—
539C24C2×D1212yes—
540C24C2×#6712yes—
541C24C2×#6712yes—
542C24C23×D311yescharacteristic
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—616no—
550C2×D4—616no—
551C2×D4—616no—
552C2×D4—616no—
553C2×D4—68no—
554C2×D4—124no—
555C2×D4—124no—
556C2×D4—124no—
557C2×D4—124no—
558C2×D4—124no—
559C2×D4—124no—
560C2×D4—128no—
561C2×D4—128no—
562C2×D4—128no—
563C2×D4—128no—
564C2×D4—128no—
565C2×D4—128no—
566C2×D4—128no—
567C2×D4—128no—
568C2×D4—128no—
569C2×D4—128no—
570C2×D4(C2×D3)⋊C4116yescomplemented
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—34no—
589C22×C4—34no—
590C22×C4—34no—
591C22×C4—34no—
592C22×C4—44no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—124no—
615C22×C4—128no—
616C22×C4—128no—
617C22×C4—124no—
618C22×C4—124no—
619C22×C4C2×C4×D312yes—
620C22×C4C2×D1212yes—
621C22×C4D3×D414yes—
622C22×C4C2×#6712yes—
623C22⋊C4—48no—
624C22⋊C4—44no—
625C22⋊C4—128no—
626C22⋊C4—128no—
627C22⋊C4—128no—
628C22⋊C4—128no—
629C22⋊C4—128no—
630C22⋊C4—124no—
631C42—68no—
632C22×C3—24no—
633C22×C3—24no—
634C22×C3—28no—
635C22×C3—28no—
636C22×C3—44no—
637C22×C3—44no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—44no—
647C22×C3—44no—
648C22×C3—44no—
649C22×C3—44no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3C22×C22⋊C411yescharacteristic
655C22×C3C2×C4×D412yes—
656C22×C3#51811yescharacteristic
657C22×C3#51811yescharacteristic
658C22×C3#51812yes—
659C22×C3#53411yescharacteristic
660C22×C3#53411yescharacteristic
661C22×C3#53411yescharacteristic
662C22×C3#53411yescharacteristic
663C22×C3#53512yes—
664C22×C3#53512yes—
665C22×C3#54012yes—
666C22×C3#54012yes—
667C22×C3D4212yes—
668C22×C3D4212yes—
669C22×C3D4211yescharacteristic
670C22×C3#54612yes—
671C22×C3#54612yes—
672C22×C3#55012yes—
673C22×C3#55911yescharacteristic
674C22×C3#56011yescharacteristic
675C22×C3#56011yescharacteristic
676C22×C3#56012yes—
677C2×D3—44no—
678C2×D3—44no—
679C2×D3—44no—
680C2×D3—44no—
681C2×D3—44no—
682C2×D3—44no—
683C2×D3—44no—
684C2×D3—82no—
685C2×D3—82no—
686C2×D3—82no—
687C2×D3—82no—
688C2×D3—82no—
689C2×D3—82no—
690C2×D3—82no—
691C2×D3—82no—
692C3×C4—24no—
693C3×C4—44no—
694C3×C4—82no—
695Dic3—28no—
696Dic3—44no—
697Dic3—82no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—64no—
743C23—64no—
744C23—64no—
745C23—64no—
746C23—64no—
747C23—64no—
748C23—64no—
749C23—122no—
750C23—122no—
751C23—122no—
752C23—122no—
753C23—122no—
754C23—122no—
755C23—122no—
756C23—122no—
757C23—122no—
758C23—122no—
759C23—122no—
760C23—122no—
761C23—122no—
762C23—122no—
763C23—122no—
764C23—122no—
765C23—122no—
766C23—122no—
767C23—122no—
768C23—122no—
769C23—122no—
770C23—122no—
771C23—122no—
772C23—122no—
773C23—122no—
774C23—122no—
775C23—122no—
776C23—122no—
777C23C2×(C2×D3)⋊C414yes—
778C23C2×(C2×D3)⋊C414yes—
779C23C22×C4×D311yescharacteristic
780C23C22×D1211yescharacteristic
781C23C2×D3×D412yes—
782C23#100411yescharacteristic
783C23#100411yescharacteristic
784C23#100411yescharacteristic
785C23#100411yescharacteristic
786C23#100412yes—
787C23D3×#4112yes—
788C23#100912yes—
789C23C22×#6711yescharacteristic
790D4—416no—
791D4—1216no—
792D4—1232no—
793D4—1232no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—38no—
804C2×C4—416no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—64no—
817C2×C4—64no—
818C2×C4—64no—
819C2×C4—64no—
820C2×C4—64no—
821C2×C4—64no—
822C2×C4—64no—
823C2×C4—64no—
824C2×C4—64no—
825C2×C4—1216no—
826C2×C4—122no—
827C2×C4—122no—
828C2×C4—122no—
829C2×C4—122no—
830C2×C4—122no—
831C2×C4—122no—
832C2×C4—122no—
833C2×C4—122no—
834C2×C4—122no—
835C2×C4—122no—
836C2×C4—122no—
837C2×C4C2×(C2×D3)⋊C414yes—
838C2×C3—44no—
839C2×C3—44no—
840C2×C3#230811yescharacteristic
841C2×C3#232812yes—
842C2×C3D4×C22⋊C412yes—
843C2×C3#236611yescharacteristic
844C2×C3#238011yescharacteristic
845C2×C3#266911yescharacteristic
846C2×C3#266911yescharacteristic
847C2×C3#267312yes—
848C2×C3#267312yes—
849C2×C3#270911yescharacteristic
850C2×C3#270911yescharacteristic
851D3—84no—
852C22—24no—
853C22—24no—
854C22—28no—
855C22—28no—
856C22—44no—
857C22—44no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—44no—
865C22—44no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—44no—
873C22—44no—
874C22—124no—
875C22—124no—
876C22—124no—
877C22—124no—
878C22—124no—
879C22—124no—
880C22—124no—
881C22—242no—
882C22—242no—
883C22—242no—
884C22—242no—
885C22—242no—
886C22—242no—
887C22—242no—
888C22—242no—
889C22#548611yescharacteristic
890C22#548611yescharacteristic
891C22#549311yescharacteristic
892C22#549311yescharacteristic
893C22C4×D3×D412yes—
894C22#554512yes—
895C22D4×D1212yes—
896C22#555412yes—
897C22#559011yescharacteristic
898C22#559212yes—
899C22#559511yescharacteristic
900C22#559912yes—
901C22#560712yes—
902C22#561512yes—
903C22#562012yes—
904C22#566312yes—
905C22#566411yescharacteristic
906C22#566611yescharacteristic
907C22C22×(C2×D3)⋊C411yescharacteristic
908C22D4×#6712yes—
909C22#580411yescharacteristic
910C22#580411yescharacteristic
911C22#582912yes—
912C4—24no—
913C4—44no—
914C4—68no—
915C4—82no—
916C4—124no—
917C4—242no—
918C3#1441911yescharacteristic, complemented, Sylow
919C2—44no—
920C2—44no—
921C2—244no—
922C2#7466712yes—
923C2#7467911yescharacteristic
924C2#7468511yescharacteristic
925C2#7479212yes—
926C2#7482011yescharacteristic
927C2#7491211yescharacteristic
928C2#8212111yescharacteristic
929C2D4×(C2×D3)⋊C412yes—
930C2#8259411yescharacteristic
931C2#8268312yes—
932C2#8288411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#386C2
socle, cosocleC24×C3C24
prime radicalC22×#940C2
hypercenterC2×#386D3
hypocenterC3#14419
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×C3×#386C2semidirect
3. C2×#5220C2semidirect
4. C2×#5213C2semidirect
5. C2×#4958C2semidirect
6. #71550C2semidirect
7. #71550C2semidirect
8. #69426C2semidirect
9. #69402C2semidirect
23. C2×#940C4semidirect
43. C2×#386D3semidirect
78. C22×#67C2×C4semidirect
79. C22×#67C2×C4semidirect
94. C22×D12C2×C4semidirect
122. C2×C4×Dic3C2×C4semidirect
128. C3⋊#95D4semidirect
201. C2×C3×D4C22⋊C4semidirect
570. C2×D4(C2×D3)⋊C4semidirect
918. C3#14419semidirect

Maximal subgroups

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

subgroupindex
C22×#9402
C2×C3×#3862
C2×#52202
C2×#52132
C2×#49582
#715502
#694262
#694022
#144193