Finite Group Databasebeta

← #10726598

Subgroups — #10726598

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×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic, complemented
4C2×#5220C211yesmaximal, characteristic, complemented
5C2×#5213C211yesmaximal, characteristic, complemented
6C2×#4961C212yesmaximal, complemented
7C2×#4958C211yesmaximal, characteristic, complemented
8#71546C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69427C212yesmaximal, complemented
11#69411C212yesmaximal, 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×#217C2211yescharacteristic
23C22×#217C2212yes—
24C2×#939—24no—
25C2×#939—24no—
26C2×#939—24no—
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2212yes—
30C22×C4⋊Dic3—24no—
31C22×C4⋊Dic3—28no—
32C22×C4⋊Dic3C2212yes—
33C22×C4⋊Dic3C2212yes—
34C22×Dic3⋊C4C2211yescharacteristic
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#4961—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—22no—
69C23×C3×C4—24no—
70C23×C3×C4—24no—
71C23×C3×C4D414yescomplemented
72C23×C3×C4C2312yes—
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2312yes—
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—22no—
90C23×Dic3—24no—
91C23×Dic3—24no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—42no—
95C23×Dic3—42no—
96C23×Dic3D414yes—
97C23×Dic3C2312yes—
98C23×Dic3C2312yes—
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—24no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—24no—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—24no—
116C2×#217—42no—
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×C4⋊Dic3—232no—
128C2×C4⋊Dic3—24no—
129C2×C4⋊Dic3—24no—
130C2×C4⋊Dic3—24no—
131C2×C4⋊Dic3—24no—
132C2×C4⋊Dic3—24no—
133C2×C4⋊Dic3D418yescomplemented
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4—22no—
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—31no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4—32no—
160C22×C22⋊C4—31no—
161C22×C22⋊C4—32no—
162C22×C22⋊C4—32no—
163C22×C22⋊C4C2×D312yes—
164C22×C22⋊C4C2×D311yescharacteristic
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—22no—
181C24×C3—21no—
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—22no—
200C23×D3—21no—
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—216no—
219C22×C3×C4—28no—
220C22×C3×C4—28no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—216no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2×D414yes—
241C22×C3×C4C2×D414yes—
242C22×C3×C4#4114yes—
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—21no—
256C22×Dic3—21no—
257C22×Dic3—22no—
258C22×Dic3—28no—
259C22×Dic3—28no—
260C22×Dic3—21no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—28no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—44no—
285C22×Dic3—48no—
286C22×Dic3—48no—
287C22×Dic3—48no—
288C22×Dic3—48no—
289C22×Dic3—44no—
290C22×Dic3—44no—
291C22×Dic3C2×D412yes—
292C22×Dic3C2×D412yes—
293C22×Dic3C2×D414yes—
294C22×Dic3C2×D414yes—
295C22×Dic3C2×D412yes—
296C3×C22⋊C4—44no—
297C3×C22⋊C4—48no—
298#217—28no—
299#217—48no—
300#217—44no—
301(C2×D3)⋊C4—28no—
302(C2×D3)⋊C4—48no—
303(C2×D3)⋊C4—48no—
304C4⋊Dic3—216no—
305C4⋊Dic3—216no—
306Dic3⋊C4—28no—
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×D4D1214yes—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—24no—
332C23×C4—24no—
333C23×C4—31no—
334C23×C4—32no—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—34no—
338C23×C4—32no—
339C23×C4—64no—
340C23×C4—64no—
341C23×C4—62no—
342C23×C4—62no—
343C23×C4—62no—
344C23×C4—62no—
345C23×C4—62no—
346C23×C4—122no—
347C23×C4—122no—
348C23×C4#6714yescomplemented
349C23×C4C22×D312yes—
350C23×C4C22×D311yescharacteristic
351C23×C4C22×D312yes—
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—62no—
362C2×C4⋊C4—64no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
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—62no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—64no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—122no—
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×D411yescharacteristic
442C23×C3C22×D412yes—
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—232no—
475C2×C3×C4—24no—
476C2×C3×C4—24no—
477C2×C3×C4—24no—
478C2×C3×C4—24no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
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#12118yescomplemented
496#67—416no—
497#67—416no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—24no—
501C2×Dic3—24no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—24no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—24no—
510C2×Dic3—24no—
511C2×Dic3—416no—
512C2×Dic3—416no—
513C2×Dic3—42no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—42no—
519C2×Dic3—42no—
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—42no—
530C2×Dic3#12014yes—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—21no—
536C24—22no—
537C24—21no—
538C24—21no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24—21no—
545C24—32no—
546C24—61no—
547C24—61no—
548C24—62no—
549C24—61no—
550C24—62no—
551C24—61no—
552C24—61no—
553C24—62no—
554C24—62no—
555C24—61no—
556C24C2×D1212yes—
557C24C2×D1212yes—
558C24#23512yes—
559C24D3×D412yes—
560C24D3×D412yes—
561C24#23712yes—
562C24#23712yes—
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—216no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—216no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—34no—
607C22×C4—32no—
608C22×C4—32no—
609C22×C4—34no—
610C22×C4—32no—
611C22×C4—68no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—62no—
615C22×C4—68no—
616C22×C4—68no—
617C22×C4—62no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—62no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—62no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—61no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—124no—
641C22×C4—128no—
642C22×C4—128no—
643C22×C4—128no—
644C22×C4—128no—
645C22×C4—124no—
646C22×C4—124no—
647C22×C4C2×D1212yes—
648C22×C4D3×D414yes—
649C22×C4#23714yes—
650C22×C4C2×#6714yes—
651C4⋊C4—616no—
652C4⋊C4—616no—
653C4⋊C4—68no—
654C22⋊C4—44no—
655C22⋊C4—48no—
656C22⋊C4—68no—
657C22⋊C4—68no—
658C22⋊C4—128no—
659C22⋊C4—128no—
660C22⋊C4—124no—
661C22⋊C4—128no—
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—28no—
719C3×C4—42no—
720C3×C4—82no—
721Dic3—24no—
722Dic3—42no—
723Dic3—42no—
724Dic3—44no—
725Dic3—82no—
726C23—22no—
727C23—22no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—22no—
736C23—24no—
737C23—22no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—24no—
746C23—24no—
747C23—41no—
748C23—41no—
749C23—42no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—42no—
754C23—41no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—41no—
759C23—42no—
760C23—41no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—62no—
766C23—62no—
767C23—62no—
768C23—64no—
769C23—64no—
770C23—121no—
771C23—121no—
772C23—122no—
773C23—121no—
774C23—121no—
775C23—121no—
776C23—122no—
777C23—121no—
778C23—122no—
779C23—122no—
780C23—122no—
781C23—122no—
782C23—122no—
783C23—121no—
784C23—122no—
785C23—121no—
786C23—122no—
787C23—122no—
788C23#88214yes—
789C23#88314yes—
790C23#88514yes—
791C23#88614yes—
792C23#93014yes—
793C23#93814yes—
794C23#93914yes—
795C23C22×D1211yescharacteristic
796C23C2×#23511yescharacteristic
797C23C2×D3×D411yescharacteristic
798C23C2×D3×D411yescharacteristic
799C23C2×D3×D412yes—
800C23C2×#23711yescharacteristic
801C23C2×#23711yescharacteristic
802C23C2×#23712yes—
803C23#100912yes—
804C23#101012yes—
805C23C22×#6711yescharacteristic
806D4—416no—
807D4—1216no—
808D4—1216no—
809C2×C4—232no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—34no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—64no—
834C2×C4—64no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—64no—
841C2×C4—64no—
842C2×C4—62no—
843C2×C4—64no—
844C2×C4—1216no—
845C2×C4—1216no—
846C2×C4—122no—
847C2×C4—122no—
848C2×C4—121no—
849C2×C4—121no—
850C2×C4—121no—
851C2×C4—121no—
852C2×C4—122no—
853C2×C4—122no—
854C2×C4—122no—
855C2×C4—122no—
856C2×C4—122no—
857C2×C4—122no—
858C2×C4—122no—
859C2×C4—122no—
860C2×C4—122no—
861C2×C4—122no—
862C2×C4—122no—
863C2×C4#93918yescomplemented
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—28no—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—28no—
883C22—24no—
884C22—24no—
885C22—24no—
886C22—28no—
887C22—28no—
888C22—42no—
889C22—44no—
890C22—42no—
891C22—42no—
892C22—44no—
893C22—82no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—82no—
899C22—124no—
900C22—122no—
901C22—122no—
902C22—122no—
903C22—124no—
904C22—241no—
905C22—241no—
906C22—242no—
907C22—241no—
908C22—241no—
909C22—242no—
910C22#496118yescomplemented
911C22C2×#88211yescharacteristic
912C22C2×#88311yescharacteristic
913C22C2×#88511yescharacteristic
914C22C2×#88611yescharacteristic
915C22D4×D1212yes—
916C22#555212yes—
917C22#555512yes—
918C22#556512yes—
919C22#558611yescharacteristic
920C22#558612yes—
921C22D3×#12011yescharacteristic
922C22#559812yes—
923C22#560912yes—
924C22#561112yes—
925C22#561812yes—
926C22#564811yescharacteristic
927C22#565311yescharacteristic
928C22#566512yes—
929C22C2×#93011yescharacteristic
930C22C2×#93811yescharacteristic
931C22C2×#93912yes—
932C22C2×#93911yescharacteristic
933C22#583312yes—
934C4—28no—
935C4—42no—
936C4—64no—
937C4—82no—
938C4—122no—
939C4—124no—
940C4—122no—
941C4—242no—
942C3#1471911yescharacteristic, complemented, Sylow
943C2—28no—
944C2—82no—
945C2—242no—
946C2#7468711yescharacteristic
947C2#7470111yescharacteristic
948C2#7470312yes—
949C2#7470412yes—
950C2#7477111yescharacteristic
951C2#7488411yescharacteristic
952C2C2×#496111yescharacteristic
953C2#8235212yes—
954C2#8260111yescharacteristic
955C2#8270512yes—
956C2#8286511yescharacteristic
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×C4⋊Dic3C2semidirect
3. C2×C3×#386C2semidirect
4. C2×#5220C2semidirect
5. C2×#5213C2semidirect
6. C2×#4961C2semidirect
7. C2×#4958C2semidirect
8. #71546C2semidirect
9. #71544C2semidirect
10. #69427C2semidirect
11. #69411C2semidirect
52. C2×#386D3semidirect
71. C23×C3×C4D4semidirect
133. C2×C4⋊Dic3D4semidirect
348. C23×C4#67semidirect
495. C2×C3×C4#121semidirect
683. C22×C3#394semidirect
863. C2×C4#939semidirect
910. C22#4961semidirect
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×C4⋊Dic32
C2×C3×#3862
C2×#52202
C2×#52132
C2×#49612
C2×#49582
#715462
#715442
#694272
#694112
#147193