Finite Group Databasebeta

← #10726596

Subgroups — #10726596

Order 768.

2982 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic
2C23×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic, complemented
4C2×#5220C211yesmaximal, characteristic, complemented
5C2×#5213C211yesmaximal, characteristic, complemented
6C2×#4959C212yesmaximal, complemented
7C2×#4958C211yesmaximal, characteristic, complemented
8#71547C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69428C212yesmaximal, complemented
11#69409C212yesmaximal, complemented
12#14719—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C23×#67C2211yescharacteristic
17C24×Dic3C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2212yes—
21C22×#217C2211yescharacteristic
22C22×#217C2212yes—
23C22×#217C2211yescharacteristic
24C2×#939—24no—
25C2×#939—24no—
26C2×#939—24no—
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2212yes—
30C22×Dic3⋊C4—24no—
31C22×Dic3⋊C4—28no—
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2212yes—
34C22×Dic3⋊C4C2212yes—
35C3×#386—24no—
36C2×C3×#95C2212yes—
37#5220—24no—
38#5213—24no—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43C2×C3⋊#95C2212yes—
44#4959—28no—
45#4958—24no—
46C22×#121—31no—
47C23×C4⋊C4—31no—
48C2×#394—32no—
49C2×#386—31no—
50C2×#386—31no—
51C2×#386—31no—
52C2×#386D311yescharacteristic, complemented
53#1441—32no—
54#1439—32no—
55#1439—32no—
56C22⋊#95—31no—
57C25×C3C2311yescharacteristic
58C25×C3C2311yescharacteristic
59C24×D3C2311yescharacteristic
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4D414yes—
67C23×C3×C4—22no—
68C23×C3×C4—24no—
69C23×C3×C4—22no—
70C23×C3×C4—22no—
71C23×C3×C4—42no—
72C23×C3×C4C2312yes—
73C23×C3×C4C2312yes—
74C23×C3×C4C2311yescharacteristic
75C22×#67—22no—
76C22×#67—22no—
77C22×#67—22no—
78C22×#67—22no—
79C22×#67—22no—
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—24no—
85C22×#67—42no—
86C22×#67D414yes—
87C23×Dic3—22no—
88C23×Dic3—22no—
89C23×Dic3—24no—
90C23×Dic3—24no—
91C23×Dic3—22no—
92C23×Dic3—22no—
93C23×Dic3—24no—
94C23×Dic3—42no—
95C23×Dic3D414yes—
96C23×Dic3D414yescomplemented
97C23×Dic3C2312yes—
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2312yes—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—42no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—24no—
115C2×#217—24no—
116C2×#217—24no—
117#939—232no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—24no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—24no—
125C2×(C2×D3)⋊C4—24no—
126C2×(C2×D3)⋊C4—42no—
127C2×Dic3⋊C4—232no—
128C2×Dic3⋊C4—24no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—24no—
131C2×Dic3⋊C4—24no—
132C2×Dic3⋊C4—24no—
133C2×Dic3⋊C4—24no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4D418yescomplemented
137C3×#95—24no—
138C3⋊#95—24no—
139C3⋊#95—24no—
140C3⋊#95—24no—
141C3⋊#95—24no—
142C3⋊#95—42no—
143C23×D4—31no—
144C23×D4—31no—
145C23×D4C2×D311yescharacteristic
146C24×C4—31no—
147C24×C4—31no—
148C24×C4C2×D311yescharacteristic
149C2×#121—64no—
150C2×#121—64no—
151C2×#121—64no—
152C22×C4⋊C4—32no—
153C22×C4⋊C4—32no—
154C22×C4⋊C4—31no—
155C22×C4⋊C4—68no—
156C22×C4⋊C4—64no—
157C22×C22⋊C4—32no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—32no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—32no—
163C22×C22⋊C4C2×D311yescharacteristic
164C22×C22⋊C4C2×D312yes—
165#394—68no—
166#386—24no—
167#386—64no—
168#386—64no—
169#386—64no—
170C2×#95—32no—
171C2×#95—32no—
172C2×#95—32no—
173C2×#95—32no—
174C2×#95—32no—
175C2×#95C2×D312yes—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—21no—
181C24×C3—22no—
182C24×C3—21no—
183C24×C3—21no—
184C24×C3—22no—
185C24×C3—21no—
186C24×C3—21no—
187C24×C3—21no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3C2×D412yes—
191C24×C3C2×D412yes—
192C24×C3C2×D412yes—
193C24×C3C2×D412yes—
194C24×C3C2×D412yes—
195C24×C3#4112yes—
196C24×C3#4112yes—
197C24×C3#4112yes—
198C24×C3C2411yescharacteristic
199C23×D3—21no—
200C23×D3—22no—
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—22no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—22no—
208C23×D3—22no—
209C23×D3C2×D412yes—
210C2×C3×D4—28no—
211C2×C3×D4—28no—
212C2×C3×D4—28no—
213C2×C3×D4—44no—
214C2×C3×D4—44no—
215C2×C3×D4—44no—
216C2×C3×D4—44no—
217C22×C3×C4—28no—
218C22×C3×C4—21no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—48no—
238C22×C3×C4—48no—
239C22×C3×C4—44no—
240C22×C3×C4—44no—
241C22×C3×C4C2×D414yes—
242C22×C3×C4C2×D412yes—
243C2×#67—28no—
244C2×#67—28no—
245C2×#67—28no—
246C2×#67—28no—
247C2×#67—48no—
248C2×#67—48no—
249C2×#67—44no—
250C2×#67—44no—
251C2×#67—44no—
252C2×#67—44no—
253C2×#67—44no—
254C2×#67—44no—
255C22×Dic3—28no—
256C22×Dic3—216no—
257C22×Dic3—28no—
258C22×Dic3—28no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—216no—
267C22×Dic3—28no—
268C22×Dic3—21no—
269C22×Dic3—22no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—22no—
278C22×Dic3—28no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—44no—
287C22×Dic3—48no—
288C22×Dic3—48no—
289C22×Dic3C2×D412yes—
290C22×Dic3C2×D412yes—
291C22×Dic3C2×D414yes—
292C22×Dic3C2×D412yes—
293C22×Dic3C2×D414yes—
294C22×Dic3C2×D414yes—
295C22×Dic3#4114yes—
296C3×C22⋊C4—48no—
297C3×C22⋊C4—44no—
298#217—28no—
299#217—44no—
300#217—48no—
301(C2×D3)⋊C4—28no—
302(C2×D3)⋊C4—48no—
303(C2×D3)⋊C4—48no—
304Dic3⋊C4—216no—
305Dic3⋊C4—28no—
306Dic3⋊C4—216no—
307C25—31no—
308C25C22×D311yescharacteristic
309C25C22×D311yescharacteristic
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—34no—
317C22×D4—62no—
318C22×D4—64no—
319C22×D4—62no—
320C22×D4—62no—
321C22×D4—62no—
322C22×D4—62no—
323C22×D4—62no—
324C22×D4—62no—
325C22×D4—62no—
326C22×D4—62no—
327C22×D4—122no—
328C22×D4#6714yes—
329C23×C4—22no—
330C23×C4—24no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—32no—
334C23×C4—31no—
335C23×C4—34no—
336C23×C4—31no—
337C23×C4—31no—
338C23×C4—34no—
339C23×C4—32no—
340C23×C4—42no—
341C23×C4—64no—
342C23×C4—64no—
343C23×C4—64no—
344C23×C4—62no—
345C23×C4—62no—
346C23×C4—62no—
347C23×C4—62no—
348C23×C4—122no—
349C23×C4C22×D312yes—
350C23×C4C22×D312yes—
351C23×C4C22×D311yescharacteristic
352#121—632no—
353C2×C4⋊C4—38no—
354C2×C4⋊C4—64no—
355C2×C4⋊C4—64no—
356C2×C4⋊C4—64no—
357C2×C4⋊C4—64no—
358C2×C4⋊C4—62no—
359C2×C4⋊C4—62no—
360C2×C4⋊C4—632no—
361C2×C4⋊C4—64no—
362C2×C4⋊C4—62no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—62no—
371C2×C22⋊C4—62no—
372C2×C22⋊C4—62no—
373C2×C22⋊C4—62no—
374C2×C22⋊C4—62no—
375C2×C22⋊C4—64no—
376C2×C22⋊C4—64no—
377C2×C22⋊C4—64no—
378C2×C22⋊C4—64no—
379C2×C22⋊C4—64no—
380C2×C22⋊C4—64no—
381C2×C22⋊C4—64no—
382C2×C22⋊C4—62no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—62no—
385C2×C22⋊C4—64no—
386C2×C22⋊C4—122no—
387#95—24no—
388#95—64no—
389#95—64no—
390#95—64no—
391#95—64no—
392#95—122no—
393C23×C3—22no—
394C23×C3—24no—
395C23×C3—22no—
396C23×C3—24no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—24no—
400C23×C3—24no—
401C23×C3—24no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—24no—
405C23×C3—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—41no—
415C23×C3—42no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—42no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—42no—
425C23×C3—42no—
426C23×C3—42no—
427C23×C3—42no—
428C23×C3—42no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3#12014yes—
433C23×C3#12114yes—
434C23×C3#12114yes—
435C23×C3#12114yes—
436C23×C3#12314yes—
437C23×C3#12314yes—
438C23×C3#12414yes—
439C23×C3C22×D411yescharacteristic
440C23×C3C22×D411yescharacteristic
441C23×C3C22×D412yes—
442C23×C3C22×D411yescharacteristic
443C23×C3C22×D411yescharacteristic
444C23×C3C2×#4111yescharacteristic
445C23×C3C2×#4111yescharacteristic
446C23×C3C2×#4111yescharacteristic
447C23×C3C2×#4112yes—
448C23×C3H(5,𝔽2)12yes—
449C23×C32−1+412yes—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—24no—
454C22×D3—24no—
455C22×D3—41no—
456C22×D3—42no—
457C22×D3—41no—
458C22×D3—41no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—42no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—42no—
466C22×D3—42no—
467C22×D3—42no—
468C22×D3—42no—
469C22×D3—42no—
470C22×D3—42no—
471C22×D3—42no—
472C22×D3—42no—
473C3×D4—416no—
474C2×C3×C4—24no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—24no—
479C2×C3×C4—24no—
480C2×C3×C4—416no—
481C2×C3×C4—42no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—42no—
487C2×C3×C4—42no—
488C2×C3×C4—42no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—42no—
494C2×C3×C4—42no—
495C2×C3×C4—42no—
496#67—416no—
497#67—416no—
498C2×Dic3—232no—
499C2×Dic3—24no—
500C2×Dic3—22no—
501C2×Dic3—24no—
502C2×Dic3—24no—
503C2×Dic3—24no—
504C2×Dic3—24no—
505C2×Dic3—24no—
506C2×Dic3—22no—
507C2×Dic3—24no—
508C2×Dic3—24no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—416no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—42no—
521C2×Dic3—42no—
522C2×Dic3—42no—
523C2×Dic3—42no—
524C2×Dic3—42no—
525C2×Dic3—42no—
526C2×Dic3—42no—
527C2×Dic3—42no—
528C2×Dic3—42no—
529C2×Dic3#12014yes—
530C2×Dic3#12118yescomplemented
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—21no—
536C24—21no—
537C24—22no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—32no—
546C24—61no—
547C24—61no—
548C24—61no—
549C24—62no—
550C24—61no—
551C24—61no—
552C24—62no—
553C24—62no—
554C24—62no—
555C24—61no—
556C24#23512yes—
557C24#23512yes—
558C24D3×D412yes—
559C24D3×D412yes—
560C24D3×D412yes—
561C24#23712yes—
562C24C2×#6712yes—
563C24C2×#6712yes—
564C24C23×D311yescharacteristic
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—28no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—68no—
573C2×D4—68no—
574C2×D4—68no—
575C2×D4—68no—
576C2×D4—124no—
577C2×D4—128no—
578C2×D4—128no—
579C2×D4—124no—
580C2×D4—124no—
581C2×D4—124no—
582C2×D4—124no—
583C2×D4—124no—
584C22×C4—28no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—34no—
605C22×C4—34no—
606C22×C4—34no—
607C22×C4—32no—
608C22×C4—34no—
609C22×C4—32no—
610C22×C4—32no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—616no—
616C22×C4—68no—
617C22×C4—68no—
618C22×C4—68no—
619C22×C4—616no—
620C22×C4—68no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—61no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—61no—
628C22×C4—68no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—62no—
635C22×C4—61no—
636C22×C4—62no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—62no—
646C22×C4—124no—
647C22×C4—128no—
648C22×C4—128no—
649C22×C4D3×D414yes—
650C22×C4C2×#6712yes—
651C4⋊C4—616no—
652C4⋊C4—616no—
653C4⋊C4—68no—
654C22⋊C4—48no—
655C22⋊C4—44no—
656C22⋊C4—68no—
657C22⋊C4—68no—
658C22⋊C4—128no—
659C22⋊C4—128no—
660C22⋊C4—128no—
661C22⋊C4—124no—
662C22×C3—24no—
663C22×C3—24no—
664C22×C3—24no—
665C22×C3—24no—
666C22×C3—24no—
667C22×C3—28no—
668C22×C3—28no—
669C22×C3—24no—
670C22×C3—28no—
671C22×C3—28no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—44no—
676C22×C3—44no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—82no—
681C22×C3—81no—
682C22×C3—82no—
683C22×C3#39418yescomplemented
684C22×C3C2×#12011yescharacteristic
685C22×C3C2×#12011yescharacteristic
686C22×C3C2×#12111yescharacteristic
687C22×C3C2×#12111yescharacteristic
688C22×C3C2×#12111yescharacteristic
689C22×C3C2×#12112yes—
690C22×C3C2×#12311yescharacteristic
691C22×C3C2×#12311yescharacteristic
692C22×C3#52511yescharacteristic
693C22×C3#52512yes—
694C22×C3C2×#12411yescharacteristic
695C22×C3#53411yescharacteristic
696C22×C3#53611yescharacteristic
697C22×C3#53712yes—
698C22×C3#53912yes—
699C22×C3D4212yes—
700C22×C3D4212yes—
701C22×C3#54712yes—
702C22×C3#54712yes—
703C22×C3#54812yes—
704C22×C3#54812yes—
705C22×C3#55312yes—
706C22×C3#55312yes—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—42no—
710C2×D3—44no—
711C2×D3—44no—
712C2×D3—81no—
713C2×D3—81no—
714C2×D3—81no—
715C2×D3—82no—
716C2×D3—81no—
717C2×D3—82no—
718C3×C4—42no—
719C3×C4—44no—
720C3×C4—82no—
721Dic3—28no—
722Dic3—24no—
723Dic3—42no—
724Dic3—42no—
725Dic3—82no—
726C23—22no—
727C23—24no—
728C23—22no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—22no—
736C23—22no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—22no—
743C23—22no—
744C23—24no—
745C23—22no—
746C23—24no—
747C23—41no—
748C23—42no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—41no—
759C23—41no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—64no—
766C23—62no—
767C23—62no—
768C23—62no—
769C23—64no—
770C23—121no—
771C23—121no—
772C23—121no—
773C23—121no—
774C23—121no—
775C23—122no—
776C23—122no—
777C23—121no—
778C23—122no—
779C23—122no—
780C23—122no—
781C23—122no—
782C23—121no—
783C23—121no—
784C23—122no—
785C23—122no—
786C23—122no—
787C23—122no—
788C23#88314yes—
789C23#88414yes—
790C23#88414yes—
791C23#88514yes—
792C23#92914yes—
793C23#93714yes—
794C23#93914yes—
795C23C2×#23511yescharacteristic
796C23C2×#23511yescharacteristic
797C23C2×D3×D411yescharacteristic
798C23C2×D3×D411yescharacteristic
799C23C2×D3×D411yescharacteristic
800C23C2×D3×D412yes—
801C23C2×#23711yescharacteristic
802C23#100412yes—
803C23D3×#4112yes—
804C23#101012yes—
805C23C22×#6711yescharacteristic
806D4—416no—
807D4—1216no—
808D4—1216no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—34no—
816C2×C4—38no—
817C2×C4—416no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—632no—
834C2×C4—64no—
835C2×C4—64no—
836C2×C4—62no—
837C2×C4—64no—
838C2×C4—64no—
839C2×C4—64no—
840C2×C4—64no—
841C2×C4—62no—
842C2×C4—64no—
843C2×C4—64no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—1216no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—122no—
855C2×C4—121no—
856C2×C4—122no—
857C2×C4—122no—
858C2×C4—122no—
859C2×C4—122no—
860C2×C4—122no—
861C2×C4—122no—
862C2×C4—122no—
863C2×C4—122no—
864C2×C3—28no—
865C2×C3—82no—
866C2×C3C2×#39411yescharacteristic
867C2×C3#240311yescharacteristic
868C2×C3#240611yescharacteristic
869C2×C3#241612yes—
870C2×C3#241612yes—
871C2×C3#243611yescharacteristic
872C2×C3#244312yes—
873C2×C3#244312yes—
874C2×C3#259111yescharacteristic
875C2×C3#261811yescharacteristic
876C2×C3#284711yescharacteristic
877D3—82no—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—28no—
883C22—24no—
884C22—28no—
885C22—24no—
886C22—28no—
887C22—28no—
888C22—42no—
889C22—42no—
890C22—44no—
891C22—42no—
892C22—44no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—81no—
898C22—82no—
899C22—122no—
900C22—122no—
901C22—124no—
902C22—122no—
903C22—124no—
904C22—241no—
905C22—241no—
906C22—242no—
907C22—241no—
908C22—241no—
909C22—242no—
910C22#495918yescomplemented
911C22C2×#88311yescharacteristic
912C22C2×#88411yescharacteristic
913C22C2×#88411yescharacteristic
914C22C2×#88511yescharacteristic
915C22#554012yes—
916C22#554712yes—
917C22#555212yes—
918C22#556412yes—
919C22D3×#12011yescharacteristic
920C22#558911yescharacteristic
921C22#559012yes—
922C22#559712yes—
923C22#559812yes—
924C22#560112yes—
925C22D3×#12112yes—
926C22#564811yescharacteristic
927C22#565512yes—
928C22#565611yescharacteristic
929C22C2×#92911yescharacteristic
930C22C2×#93711yescharacteristic
931C22D4×#6712yes—
932C22C2×#93911yescharacteristic
933C22#582412yes—
934C4—44no—
935C4—42no—
936C4—64no—
937C4—68no—
938C4—82no—
939C4—122no—
940C4—122no—
941C4—242no—
942C3#1471911yescharacteristic, complemented, Sylow
943C2—28no—
944C2—82no—
945C2—242no—
946C2#7469212yes—
947C2#7470111yescharacteristic
948C2#7470212yes—
949C2#7477211yescharacteristic
950C2#7478111yescharacteristic
951C2#7493511yescharacteristic
952C2C2×#495911yescharacteristic
953C2#8235612yes—
954C2#8260411yescharacteristic
955C2#8264212yes—
956C2#8284111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC22×#939C2
hypercenterC2×#386D3
hypocenterC3#14719
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×Dic3⋊C4C2semidirect
3. C2×C3×#386C2semidirect
4. C2×#5220C2semidirect
5. C2×#5213C2semidirect
6. C2×#4959C2semidirect
7. C2×#4958C2semidirect
8. #71547C2semidirect
9. #71544C2semidirect
10. #69428C2semidirect
11. #69409C2semidirect
52. C2×#386D3semidirect
96. C23×Dic3D4semidirect
136. C2×Dic3⋊C4D4semidirect
530. C2×Dic3#121semidirect
683. C22×C3#394semidirect
910. C22#4959semidirect
942. C3#14719semidirect

Maximal subgroups

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

subgroupindex
C22×#9392
C23×Dic3⋊C42
C2×C3×#3862
C2×#52202
C2×#52132
C2×#49592
C2×#49582
#715472
#715442
#694282
#694092
#147193