Finite Group Databasebeta

← #10716970

Subgroups — #10716970

Order 768.

3502 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic3C211yesmaximal, characteristic, complemented
2C22×#67⋊C4C212yesmaximal, complemented
3C2×#5223C211yesmaximal, characteristic
4C2×Dic3×C22⋊C4C212yesmaximal, complemented
5C2×#4666C211yesmaximal, characteristic, complemented
6C3×#1438C211yesmaximal, characteristic, complemented
7#71550C212yesmaximal, complemented
8#71547C212yesmaximal, complemented
9#69427C211yesmaximal, characteristic, complemented
10#69420C211yesmaximal, characteristic, complemented
11Dic3×#95C211yesmaximal, characteristic, complemented
12C4×#392—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2212yes—
15C24×Dic3C2212yes—
16C23×C4×D3C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2212yes—
19C22×#217C2212yes—
20C22×#217C2212yes—
21C2×D4×Dic3—28no—
22C2×D4×Dic3—24no—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×Dic3⋊C4C2212yes—
28C22×C4×Dic3C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C22×C4×Dic3C2212yes—
31C2×#67⋊C4—28no—
32C2×#67⋊C4—28no—
33C2×#67⋊C4—28no—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36#5223C418yescomplemented
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42Dic3×C22⋊C4—28no—
43#4666—24no—
44C22×C4×D4—31no—
45C22×C4×D4—32no—
46C2×#392—31no—
47C2×C4×C22⋊C4—31no—
48C2×C4×C22⋊C4—32no—
49#1444—31no—
50#1439—31no—
51#1439—32no—
52#1438—32no—
53#1438D311yescharacteristic, complemented
54C4×#95—31no—
55C25×C3C2312yes—
56C24×D3C2311yescharacteristic
57C22×C3×D4—24no—
58C22×C3×D4—24no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4C2×C414yescomplemented
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2312yes—
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—24no—
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—24no—
72C22×#67C2×C418yescomplemented
73C23×Dic3—24no—
74C23×Dic3—24no—
75C23×Dic3—24no—
76C23×Dic3—24no—
77C23×Dic3—24no—
78C23×Dic3—24no—
79C23×Dic3D418yescomplemented
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2312yes—
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2312yes—
84C23×Dic3C2311yescharacteristic
85C22×C4×D3—22no—
86C22×C4×D3—24no—
87C22×C4×D3—24no—
88C22×C4×D3—22no—
89C22×C4×D3D414yescomplemented
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—24no—
99C2×#217—24no—
100C2×#217—24no—
101C2×#217C2×C418yescomplemented
102D4×Dic3—232no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4C2×C414yescomplemented
112C2×C4⋊Dic3—22no—
113C2×C4⋊Dic3—24no—
114C2×Dic3⋊C4—24no—
115C2×Dic3⋊C4—24no—
116C2×Dic3⋊C4—24no—
117C2×C4×Dic3—24no—
118C2×C4×Dic3—24no—
119C2×C4×Dic3—24no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3—24no—
122C2×C4×Dic3D414yescomplemented
123C2×C4×Dic3D418yescomplemented
124#67⋊C4—264no—
125C3×#95—22no—
126C3×#95—22no—
127C3⋊#95—24no—
128C3⋊#95—22no—
129C3⋊#95—24no—
130C3⋊#95—24no—
131C3⋊#95C2×C414yescomplemented
132C23×D4—32no—
133C23×D4C2×D311yescharacteristic
134C24×C4—32no—
135C24×C4—31no—
136C2×C4×D4—68no—
137C2×C4×D4—64no—
138C2×C4×D4—68no—
139C2×C4×D4—68no—
140C2×C4×D4—68no—
141C22×C4⋊C4—32no—
142C22×C4⋊C4—31no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—31no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—31no—
148C22×C22⋊C4C2×D312yes—
149C22×C22⋊C4C2×D312yes—
150C22×C42—32no—
151C22×C42—31no—
152C22×C42—31no—
153#392—38no—
154C4×C22⋊C4—64no—
155C4×C22⋊C4—68no—
156C2×#95—31no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95—31no—
160C2×#95—32no—
161C2×#95C2×D311yescharacteristic
162C2×#95C2×D311yescharacteristic
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3C22×C414yes—
176C24×C3C2×D414yes—
177C24×C3#4114yes—
178C24×C3C2411yescharacteristic
179C23×D3—21no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—21no—
183C23×D3—21no—
184C23×D3—21no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3C22×C412yes—
188C23×D3C2×D412yes—
189C23×D3#4112yes—
190C2×C3×D4—28no—
191C2×C3×D4—28no—
192C2×C3×D4—216no—
193C2×C3×D4—216no—
194C2×C3×D4—28no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—21no—
211C22×C3×C4C22×C412yes—
212C22×C3×C4C2×D414yes—
213C22×C3×C4C2×D412yes—
214C22×C3×C4C2×D412yes—
215C22×C3×C4#4112yes—
216C22×C3×C4#4112yes—
217C2×#67—216no—
218C2×#67—216no—
219C2×#67—216no—
220C2×#67—216no—
221C2×#67—216no—
222C2×#67—216no—
223C2×#67—216no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—21no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—216no—
243C22×Dic3—216no—
244C22×Dic3—216no—
245C22×Dic3—48no—
246C22×Dic3—48no—
247C22×Dic3—48no—
248C22×Dic3—48no—
249C22×Dic3C22×C412yes—
250C22×Dic3C22×C414yes—
251C22×Dic3C2×D412yes—
252C22×Dic3C2×D414yes—
253C22×Dic3C2×D414yes—
254C22×Dic3C2×D414yes—
255C22×Dic3C2×D412yes—
256C22×Dic3C2×D414yes—
257C22×Dic3C2×D412yes—
258C22×Dic3#4114yes—
259C22×Dic3#4112yes—
260C2×C4×D3—216no—
261C2×C4×D3—28no—
262C2×C4×D3—44no—
263C2×C4×D3—48no—
264C2×C4×D3—44no—
265C3×C22⋊C4—216no—
266C3×C22⋊C4—216no—
267#217—216no—
268#217—216no—
269(C2×D3)⋊C4—216no—
270(C2×D3)⋊C4—28no—
271(C2×D3)⋊C4—28no—
272C4⋊Dic3—28no—
273Dic3⋊C4—216no—
274C4×Dic3—216no—
275C4×Dic3—28no—
276C4×Dic3—44no—
277C25—31no—
278C25C22×D312yes—
279C22×D4—24no—
280C22×D4—24no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—38no—
284C22×D4—64no—
285C22×D4—64no—
286C22×D4—64no—
287C22×D4—64no—
288C22×D4—64no—
289C22×D4—64no—
290C22×D4C4×D314yescomplemented
291C23×C4—31no—
292C23×C4—32no—
293C23×C4—38no—
294C23×C4—31no—
295C23×C4—31no—
296C23×C4—32no—
297C23×C4—34no—
298C23×C4—64no—
299C23×C4—64no—
300C23×C4—62no—
301C23×C4—62no—
302C23×C4—64no—
303C23×C4—64no—
304C23×C4—64no—
305C23×C4—64no—
306C23×C4—64no—
307C23×C4—64no—
308C23×C4C22×D312yes—
309C23×C4C22×D311yescharacteristic
310C23×C4C22×D311yescharacteristic
311C23×C4C22×D311yescharacteristic
312C4×D4—664no—
313C4×D4—632no—
314C2×C4⋊C4—64no—
315C2×C4⋊C4—64no—
316C2×C4⋊C4—64no—
317C2×C4⋊C4—64no—
318C2×C4⋊C4—62no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—38no—
326C2×C22⋊C4—34no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—62no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—62no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—64no—
335C2×C22⋊C4—64no—
336C2×C22⋊C4—64no—
337C2×C22⋊C4—62no—
338C2×C22⋊C4—62no—
339C2×C22⋊C4—62no—
340C2×C42—38no—
341C2×C42—34no—
342C2×C42—64no—
343C2×C42—64no—
344C2×C42—64no—
345C2×C42—62no—
346C2×C42—64no—
347#95—22no—
348#95—22no—
349#95—34no—
350#95—64no—
351#95—62no—
352#95—64no—
353#95—64no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3C4×D418yescomplemented
389C23×C3C23×C411yescharacteristic
390C23×C3C22×D411yescharacteristic
391C23×C3C22×D412yes—
392C23×C3C22×D411yescharacteristic
393C23×C3C22×D412yes—
394C23×C3C2×#4112yes—
395C23×C3C2×#4111yescharacteristic
396C23×C3C2×#4111yescharacteristic
397C23×C3C2×#4111yescharacteristic
398C23×C3C2×#4112yes—
399C23×C3C2×#4111yescharacteristic
400C22×D3—22no—
401C22×D3—24no—
402C22×D3—24no—
403C22×D3—22no—
404C22×D3—24no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—24no—
410C22×D3—22no—
411C22×D3—22no—
412C22×D3—41no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—41no—
417C22×D3—42no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—42no—
421C22×D3—42no—
422C22×D3C4×D414yescomplemented
423C3×D4—232no—
424C2×C3×C4—24no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—24no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—41no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—41no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4C4×D414yescomplemented
446#67—264no—
447C2×Dic3—24no—
448C2×Dic3—24no—
449C2×Dic3—24no—
450C2×Dic3—24no—
451C2×Dic3—24no—
452C2×Dic3—24no—
453C2×Dic3—22no—
454C2×Dic3—24no—
455C2×Dic3—22no—
456C2×Dic3—24no—
457C2×Dic3—24no—
458C2×Dic3—24no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464C2×Dic3—42no—
465C2×Dic3—41no—
466C2×Dic3—42no—
467C2×Dic3—41no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—432no—
471C2×Dic3C4×D418yescomplemented
472C2×Dic3#12018yes—
473C2×Dic3#12014yes—
474C2×Dic3#12114yes—
475C2×Dic3#12118yes—
476C2×Dic3#12714yes—
477C4×D3—416no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—32no—
491C24—32no—
492C24—32no—
493C24—61no—
494C24—62no—
495C24—62no—
496C24—61no—
497C24—61no—
498C24—62no—
499C24—61no—
500C24—62no—
501C24C2×C4×D314yes—
502C24D3×D414yes—
503C24#23714yes—
504C24C23×D311yescharacteristic
505C2×D4—28no—
506C2×D4—28no—
507C2×D4—216no—
508C2×D4—216no—
509C2×D4—28no—
510C2×D4—616no—
511C2×D4—616no—
512C2×D4—616no—
513C2×D4—616no—
514C2×D4—616no—
515C2×D4—616no—
516C2×D4—616no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—32no—
534C22×C4—34no—
535C22×C4—34no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—34no—
539C22×C4—34no—
540C22×C4—34no—
541C22×C4—32no—
542C22×C4—32no—
543C22×C4—34no—
544C22×C4—616no—
545C22×C4—68no—
546C22×C4—616no—
547C22×C4—616no—
548C22×C4—616no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—61no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—61no—
566C22×C4—62no—
567C22×C4—124no—
568C22×C4—124no—
569C22×C4—128no—
570C22×C4—128no—
571C22×C4—128no—
572C22×C4—128no—
573C22×C4—128no—
574C22×C4C2×C4×D312yes—
575C22×C4D3×D414yes—
576C22×C4D3×D412yes—
577C22×C4D3×D412yes—
578C22×C4#23712yes—
579C22×C4#23712yes—
580C4⋊C4—616no—
581C4⋊C4—68no—
582C22⋊C4—216no—
583C22⋊C4—216no—
584C22⋊C4—616no—
585C22⋊C4—68no—
586C22⋊C4—616no—
587C22⋊C4—616no—
588C22⋊C4—68no—
589C42—68no—
590C42—616no—
591C42—124no—
592C22×C3—28no—
593C22×C3—28no—
594C22×C3—28no—
595C22×C3—44no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—44no—
599C22×C3—44no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—44no—
606C22×C3—44no—
607C22×C3C2×C4×D411yescharacteristic
608C22×C3C2×C4×D412yes—
609C22×C3C2×C4×D412yes—
610C22×C3C2×C4×D411yescharacteristic
611C22×C3C4×#4111yescharacteristic
612C22×C3C2×#12011yescharacteristic
613C22×C3C2×#12012yes—
614C22×C3C2×#12112yes—
615C22×C3C2×#12111yescharacteristic
616C22×C3#52512yes—
617C22×C3#52512yes—
618C22×C3#52512yes—
619C22×C3#52511yescharacteristic
620C22×C3#52512yes—
621C22×C3#52511yescharacteristic
622C22×C3#52512yes—
623C22×C3#52912yes—
624C22×C3#52911yescharacteristic
625C22×C3C2×#12711yescharacteristic
626C22×C3#53211yescharacteristic
627C22×C3#53211yescharacteristic
628C22×C3#53212yes—
629C22×C3#53212yes—
630C2×D3—28no—
631C2×D3—24no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—44no—
636C2×D3—44no—
637C2×D3—42no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—44no—
641C3×C4—24no—
642C3×C4—42no—
643C3×C4—44no—
644C3×C4—42no—
645Dic3—28no—
646Dic3—42no—
647Dic3—44no—
648Dic3—42no—
649Dic3#39218yescomplemented
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—34no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—64no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23—64no—
690C23—62no—
691C23—64no—
692C23—64no—
693C23—62no—
694C23—62no—
695C23—64no—
696C23—64no—
697C23—122no—
698C23—121no—
699C23—121no—
700C23—122no—
701C23—121no—
702C23—122no—
703C23—121no—
704C23—122no—
705C23—122no—
706C23—122no—
707C23#67⋊C418yescomplemented
708C23C22×C4×D311yescharacteristic
709C23C2×D3×D412yes—
710C23C2×D3×D411yescharacteristic
711C23C2×D3×D412yes—
712C23C2×D3×D411yescharacteristic
713C23C2×#23712yes—
714C23C2×#23711yescharacteristic
715C23C2×#23711yescharacteristic
716C23D3×#4111yescharacteristic
717C23D3×#4112yes—
718C23D3×#4111yescharacteristic
719D4—232no—
720D4—664no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—34no—
733C2×C4—34no—
734C2×C4—38no—
735C2×C4—34no—
736C2×C4—38no—
737C2×C4—38no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—64no—
749C2×C4—64no—
750C2×C4—64no—
751C2×C4—64no—
752C2×C4—64no—
753C2×C4—64no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—64no—
757C2×C4—62no—
758C2×C4—64no—
759C2×C4—64no—
760C2×C4—64no—
761C2×C4—62no—
762C2×C4—1216no—
763C2×C4—1232no—
764C2×C4—122no—
765C2×C4—121no—
766C2×C4—121no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4—122no—
773C2×C4#67⋊C414yescomplemented
774C2×C3—48no—
775C2×C3C4×#12011yescharacteristic
776C2×C3C4×#12012yes—
777C2×C3C4×#12111yescharacteristic
778C2×C3C4×#12112yes—
779C2×C3C4×#12711yescharacteristic
780C2×C3C2×#39211yescharacteristic
781C2×C3#238811yescharacteristic
782C2×C3#238812yes—
783C2×C3#239212yes—
784C2×C3#239211yescharacteristic
785C2×C3#239711yescharacteristic
786D3—44no—
787C22—28no—
788C22—28no—
789C22—28no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—64no—
803C22—68no—
804C22—122no—
805C22—122no—
806C22—122no—
807C22—124no—
808C22—122no—
809C22—124no—
810C22—122no—
811C22—124no—
812C22—122no—
813C22C2×#67⋊C411yescharacteristic
814C22C2×#67⋊C412yes—
815C22C4×#23711yescharacteristic
816C22C4×D3×D411yescharacteristic
817C22C4×D3×D412yes—
818C22#558612yes—
819C22#558611yescharacteristic
820C22#558612yes—
821C22D3×#12011yescharacteristic
822C22D3×#12012yes—
823C22#559612yes—
824C22#559612yes—
825C22D3×#12111yescharacteristic
826C22D3×#12112yes—
827C22#560611yescharacteristic
828C22#560612yes—
829C22#560612yes—
830C22#564912yes—
831C22#565612yes—
832C22#566811yescharacteristic
833C22#568011yescharacteristic
834C22D3×#12711yescharacteristic
835C22#571611yescharacteristic
836C4—24no—
837C4—38no—
838C4—44no—
839C4—42no—
840C4—42no—
841C4—68no—
842C4—122no—
843C4—122no—
844C4—124no—
845C3C4×#39211yescharacteristic, complemented, Sylow
846C2—48no—
847C2—124no—
848C2#7381811yescharacteristic
849C2#7465912yes—
850C2#7466012yes—
851C2#7629111yescharacteristic
852C2#7629311yescharacteristic
853C2#7666512yes—
854C2#7666711yescharacteristic
855C2D3×#39211yescharacteristic
856C2#7688911yescharacteristic
857C2#7689012yes—
858C2#7689111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1438C2
socle, cosocleC24×C3C24
prime radicalC2×#5223C2
hypercenter#1438D3
hypocenterC3C4×#392
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic3C2semidirect
2. C22×#67⋊C4C2semidirect
4. C2×Dic3×C22⋊C4C2semidirect
5. C2×#4666C2semidirect
6. C3×#1438C2semidirect
7. #71550C2semidirect
8. #71547C2semidirect
9. #69427C2semidirect
10. #69420C2semidirect
11. Dic3×#95C2semidirect
36. #5223C4semidirect
53. #1438D3semidirect
61. C22×C3×D4C2×C4semidirect
72. C22×#67C2×C4semidirect
79. C23×Dic3D4semidirect
89. C22×C4×D3D4semidirect
101. C2×#217C2×C4semidirect
111. C2×(C2×D3)⋊C4C2×C4semidirect
122. C2×C4×Dic3D4semidirect
123. C2×C4×Dic3D4semidirect
131. C3⋊#95C2×C4semidirect
290. C22×D4C4×D3semidirect
388. C23×C3C4×D4semidirect
422. C22×D3C4×D4semidirect
445. C2×C3×C4C4×D4semidirect
471. C2×Dic3C4×D4semidirect
649. Dic3#392semidirect
707. C23#67⋊C4semidirect
773. C2×C4#67⋊C4semidirect
845. C3C4×#392semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic32
C22×#67⋊C42
C2×#52232
C2×Dic3×C22⋊C42
C2×#46662
C3×#14382
#715502
#715472
#694272
#694202
Dic3×#952
C4×#3923