Finite Group Databasebeta

← #10720171

Subgroups — #10720171

Order 768.

2634 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#935C211yesmaximal, characteristic
2C22×#877C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic
4C2×#5220C211yesmaximal, characteristic
5C22×C3⋊#95C211yesmaximal, characteristic, complemented
6#72127C211yesmaximal, characteristic, complemented
7#71547C212yesmaximal, complemented
8#71545C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69409C212yesmaximal, complemented
11#69406C212yesmaximal, complemented
12#14135—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2212yes—
20C22×#217C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C2×#935—24no—
25C2×#935—24no—
26C2×#935C418yescomplemented
27C22×Dic3⋊C4C2212yes—
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×C4×Dic3C2212yes—
31C2×#877—24no—
32C2×#877—24no—
33C2×#877—24no—
34C3×#386—24no—
35C2×C3×#95C2212yes—
36#5220—24no—
37C2×C3⋊#95—24no—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43C2×C3⋊#95C2212yes—
44C2×C3⋊#95C2212yes—
45C22×#123—31no—
46C22×#117—31no—
47C2×#386—31no—
48C2×#386D311yescharacteristic
49C22×#95—31no—
50#1441—32no—
51#1439—32no—
52#1437—32no—
53#1436—32no—
54C22⋊#95—31no—
55C22⋊#95—31no—
56C25×C3C2311yescharacteristic
57C25×C3C2311yescharacteristic
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4C2×C414yes—
65C23×C3×C4—22no—
66C23×C3×C4—24no—
67C23×C3×C4—22no—
68C23×C3×C4—22no—
69C23×C3×C4—42no—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2312yes—
72C23×C3×C4C2312yes—
73C23×Dic3—22no—
74C23×Dic3—22no—
75C23×Dic3—22no—
76C23×Dic3—22no—
77C23×Dic3—22no—
78C23×Dic3—24no—
79C23×Dic3—22no—
80C23×Dic3—22no—
81C23×Dic3—42no—
82C23×Dic3C2×C414yes—
83C23×Dic3D414yes—
84C23×Dic3D414yes—
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2312yes—
88C23×Dic3C2312yes—
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—42no—
96C2×C3×C22⋊C4D414yes—
97C2×#217—22no—
98C2×#217—22no—
99C2×#217—22no—
100C2×#217—22no—
101C2×#217—22no—
102C2×#217—22no—
103C2×#217—22no—
104C2×#217—22no—
105C2×#217—24no—
106C2×#217—24no—
107C2×#217—42no—
108C2×#217C2×C414yes—
109C2×#217C2×C414yescomplemented
110C2×#217C2×C414yescomplemented
111C2×#217D414yes—
112#935—232no—
113C2×Dic3⋊C4—24no—
114C2×Dic3⋊C4—24no—
115C2×Dic3⋊C4—24no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—22no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4C2×C414yescomplemented
121C2×Dic3⋊C4C2×C414yescomplemented
122C2×C4×Dic3—24no—
123C2×C4×Dic3—24no—
124C2×C4×Dic3—24no—
125#877—232no—
126C3×#95—24no—
127C3⋊#95—24no—
128C3⋊#95—24no—
129C3⋊#95—24no—
130C3⋊#95—24no—
131C3⋊#95—24no—
132C3⋊#95—42no—
133C3⋊#95—42no—
134C23×D4C2×D311yescharacteristic
135C24×C4—31no—
136C24×C4—31no—
137C24×C4C2×D311yescharacteristic
138C2×#123—38no—
139C2×#123—64no—
140C2×#123—64no—
141C2×#117—64no—
142C2×#117—64no—
143C2×#117—64no—
144C22×C4⋊C4—31no—
145C22×C4⋊C4—31no—
146C22×C4⋊C4—32no—
147C22×C22⋊C4—31no—
148C22×C22⋊C4—31no—
149C22×C22⋊C4—31no—
150C22×C22⋊C4—31no—
151C22×C22⋊C4—32no—
152C22×C22⋊C4C2×D312yes—
153C22×C22⋊C4C2×D311yescharacteristic
154C22×C42—32no—
155#386—24no—
156#386—64no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95—32no—
160C2×#95—32no—
161C2×#95—32no—
162C2×#95—32no—
163C2×#95—32no—
164C2×#95—64no—
165C2×#95C2×D312yes—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—21no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—21no—
177C24×C3—21no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3C22×C412yes—
181C24×C3C22×C412yes—
182C24×C3C2×D412yes—
183C24×C3C2×D412yes—
184C24×C3C2×D412yes—
185C24×C3C2×D412yes—
186C24×C3#4112yes—
187C24×C3#4112yes—
188C24×C3C2411yescharacteristic
189C2×C3×D4—28no—
190C2×C3×D4—28no—
191C2×C3×D4—28no—
192C2×C3×D4—44no—
193C2×C3×D4—44no—
194C2×C3×D4—44no—
195C2×C3×D4—44no—
196C22×C3×C4—28no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—48no—
216C22×C3×C4—48no—
217C22×C3×C4—44no—
218C22×C3×C4—44no—
219C22×C3×C4C22×C412yes—
220C22×C3×C4C2×D414yes—
221C22×C3×C4#4114yes—
222C22×Dic3—28no—
223C22×Dic3—28no—
224C22×Dic3—28no—
225C22×Dic3—28no—
226C22×Dic3—28no—
227C22×Dic3—28no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—28no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—21no—
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—48no—
258C22×Dic3—48no—
259C22×Dic3—44no—
260C22×Dic3—44no—
261C22×Dic3C22⋊C4116yescomplemented
262C22×Dic3C22×C412yes—
263C22×Dic3C22×C412yes—
264C22×Dic3C22×C412yes—
265C22×Dic3C22×C412yes—
266C22×Dic3C2×D414yes—
267C22×Dic3C2×D412yes—
268C22×Dic3C2×D412yes—
269C22×Dic3C2×D412yes—
270C22×Dic3C2×D412yes—
271C22×Dic3#4114yes—
272C3×C22⋊C4—28no—
273C3×C22⋊C4—48no—
274#217—28no—
275#217—28no—
276#217—28no—
277#217—28no—
278#217—48no—
279Dic3⋊C4—216no—
280Dic3⋊C4—28no—
281Dic3⋊C4—28no—
282C4×Dic3—216no—
283C25C22×D311yescharacteristic
284C25C22×D311yescharacteristic
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4C4×D314yes—
292C23×C4—22no—
293C23×C4—24no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—34no—
297C23×C4—34no—
298C23×C4—34no—
299C23×C4—31no—
300C23×C4—31no—
301C23×C4—31no—
302C23×C4—31no—
303C23×C4—32no—
304C23×C4—32no—
305C23×C4—42no—
306C23×C4—64no—
307C23×C4—62no—
308C23×C4—62no—
309C23×C4—62no—
310C23×C4—62no—
311C23×C4—62no—
312C23×C4—62no—
313C23×C4—62no—
314C23×C4—122no—
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D312yes—
317C23×C4C22×D312yes—
318#123—632no—
319#117—632no—
320C2×C4⋊C4—34no—
321C2×C4⋊C4—34no—
322C2×C4⋊C4—64no—
323C2×C4⋊C4—64no—
324C2×C4⋊C4—62no—
325C2×C4⋊C4—62no—
326C2×C4⋊C4—62no—
327C2×C4⋊C4—62no—
328C2×C4⋊C4—64no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—34no—
334C2×C22⋊C4—34no—
335C2×C22⋊C4—34no—
336C2×C22⋊C4—34no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—62no—
339C2×C22⋊C4—62no—
340C2×C22⋊C4—62no—
341C2×C22⋊C4—62no—
342C2×C22⋊C4—62no—
343C2×C22⋊C4—62no—
344C2×C22⋊C4—62no—
345C2×C22⋊C4—62no—
346C2×C22⋊C4—64no—
347C2×C22⋊C4—64no—
348C2×C22⋊C4—122no—
349C2×C22⋊C4#6714yes—
350C2×C42—64no—
351C2×C42—64no—
352C2×C42—64no—
353#95—24no—
354#95—64no—
355#95—64no—
356#95—64no—
357#95—64no—
358#95—64no—
359#95—122no—
360#95—122no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—24no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—42no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3C2×C22⋊C414yes—
401C23×C3C4×D414yes—
402C23×C3C4×D414yes—
403C23×C3#12014yes—
404C23×C3#12114yes—
405C23×C3#12114yes—
406C23×C3#12314yes—
407C23×C3C23×C411yescharacteristic
408C23×C3C22×D411yescharacteristic
409C23×C3C22×D411yescharacteristic
410C23×C3C22×D411yescharacteristic
411C23×C3C22×D411yescharacteristic
412C23×C3C2×#4111yescharacteristic
413C23×C3C2×#4111yescharacteristic
414C23×C3C2×#4112yes—
415C23×C3C2×#4112yes—
416C23×C3H(5,𝔽2)12yes—
417C23×C32−1+412yes—
418C3×D4—416no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—416no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—232no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—24no—
457C2×Dic3—24no—
458C2×Dic3—24no—
459C2×Dic3—24no—
460C2×Dic3—24no—
461C2×Dic3—24no—
462C2×Dic3—24no—
463C2×Dic3—24no—
464C2×Dic3—416no—
465C2×Dic3—42no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—41no—
471C2×Dic3—42no—
472C2×Dic3—41no—
473C2×Dic3—42no—
474C2×Dic3—42no—
475C2×Dic3—42no—
476C2×Dic3—42no—
477C2×Dic3—42no—
478C2×Dic3—42no—
479C2×Dic3C2×C22⋊C414yes—
480C2×Dic3C2×C22⋊C414yes—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—22no—
490C24—21no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—21no—
495C24C2×C4×D312yes—
496C24C2×C4×D312yes—
497C24#23512yes—
498C24D3×D412yes—
499C24D3×D412yes—
500C24D3×D412yes—
501C24#23712yes—
502C24C2×#6712yes—
503C24C23×D311yescharacteristic
504C2×D4—28no—
505C2×D4—28no—
506C2×D4—28no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—44no—
511C22×C4—28no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—316no—
531C22×C4—32no—
532C22×C4—32no—
533C22×C4—32no—
534C22×C4—32no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—34no—
540C22×C4—34no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—68no—
546C22×C4—68no—
547C22×C4—68no—
548C22×C4—68no—
549C22×C4—68no—
550C22×C4—68no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—68no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—128no—
581C22×C4—128no—
582C22×C4—124no—
583C22×C4—124no—
584C22×C4C2×C4×D312yes—
585C22×C4#23714yes—
586C22×C4C2×#6714yes—
587C4⋊C4—68no—
588C4⋊C4—68no—
589C4⋊C4—616no—
590C22⋊C4—28no—
591C22⋊C4—48no—
592C22⋊C4—68no—
593C22⋊C4—68no—
594C22⋊C4—68no—
595C22⋊C4—68no—
596C22⋊C4—128no—
597C42—616no—
598C22×C3—24no—
599C22×C3—28no—
600C22×C3—28no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—24no—
604C22×C3—24no—
605C22×C3—28no—
606C22×C3—28no—
607C22×C3—24no—
608C22×C3—42no—
609C22×C3—44no—
610C22×C3—44no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—82no—
618C22×C3—82no—
619C22×C3#38618yes—
620C22×C3C22×C22⋊C411yescharacteristic
621C22×C3C2×C4×D411yescharacteristic
622C22×C3C2×C4×D411yescharacteristic
623C22×C3C4×#4112yes—
624C22×C3#52012yes—
625C22×C3C2×#12011yescharacteristic
626C22×C3C2×#12111yescharacteristic
627C22×C3C2×#12111yescharacteristic
628C22×C3C2×#12311yescharacteristic
629C22×C3#52511yescharacteristic
630C22×C3#52511yescharacteristic
631C22×C3#53212yes—
632C22×C3#53511yescharacteristic
633C22×C3#53611yescharacteristic
634C22×C3#53712yes—
635C22×C3#54612yes—
636C22×C3#54612yes—
637C22×C3#54712yes—
638C22×C3#54712yes—
639C22×C3#55112yes—
640C22×C3#55112yes—
641C22×C3#55212yes—
642C22×C3#55212yes—
643C3×C4—44no—
644C3×C4—44no—
645C3×C4—42no—
646Dic3—24no—
647Dic3—24no—
648Dic3—42no—
649Dic3—44no—
650Dic3—44no—
651Dic3—42no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—22no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—41no—
674C23—42no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—42no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—41no—
685C23—42no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23D3×C22⋊C414yes—
692C23#67⋊C414yes—
693C23#88314yes—
694C23#88414yes—
695C23C4×#6714yes—
696C23#93714yes—
697C23#93814yes—
698C23C22×C4×D311yescharacteristic
699C23C2×#23511yescharacteristic
700C23C2×D3×D411yescharacteristic
701C23C2×D3×D411yescharacteristic
702C23C2×D3×D411yescharacteristic
703C23C2×#23711yescharacteristic
704C23C2×#23712yes—
705C23#100412yes—
706C23D3×#4112yes—
707C23#101012yes—
708C23C22×#6711yescharacteristic
709D4—416no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—34no—
720C2×C4—34no—
721C2×C4—416no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—632no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—64no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—64no—
751C2×C4—64no—
752C2×C4—64no—
753C2×C4—64no—
754C2×C4—64no—
755C2×C4—64no—
756C2×C4—64no—
757C2×C4—1216no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4—122no—
763C2×C4—122no—
764C2×C4—121no—
765C2×C4—122no—
766C2×C4—121no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C3—28no—
773C2×C3—82no—
774C2×C3C2×#38611yescharacteristic
775C2×C3#229711yescharacteristic
776C2×C3#231111yescharacteristic
777C2×C3#235912yes—
778C2×C3#235912yes—
779C2×C3#241111yescharacteristic
780C2×C3#241111yescharacteristic
781C2×C3#241311yescharacteristic
782C2×C3#241311yescharacteristic
783C2×C3#243012yes—
784C2×C3#249812yes—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—24no—
791C22—28no—
792C22—24no—
793C22—28no—
794C22—28no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—82no—
805C22—82no—
806C22#495618yes—
807C22C2×D3×C22⋊C411yescharacteristic
808C22C2×#67⋊C411yescharacteristic
809C22C2×#88311yescharacteristic
810C22C2×#88411yescharacteristic
811C22C4×#23712yes—
812C22#554112yes—
813C22#554612yes—
814C22#555612yes—
815C22#558611yescharacteristic
816C22#558712yes—
817C22#559211yescharacteristic
818C22#559612yes—
819C22#559712yes—
820C22#561012yes—
821C22#561112yes—
822C22#564811yescharacteristic
823C22#565012yes—
824C22#565611yescharacteristic
825C22C2×C4×#6711yescharacteristic
826C22C2×#93711yescharacteristic
827C22C2×#93811yescharacteristic
828C22#580612yes—
829C22#582412yes—
830C4—44no—
831C4—42no—
832C4—44no—
833C4—64no—
834C4—64no—
835C4—124no—
836C4—122no—
837C4—122no—
838C4—124no—
839C3#1413511yescharacteristic, complemented, Sylow
840C2—28no—
841C2—82no—
842C2#7465811yescharacteristic
843C2#7466211yescharacteristic
844C2#7467512yes—
845C2#7469111yescharacteristic
846C2#7474112yes—
847C2#7488911yescharacteristic
848C2C2×#495611yescharacteristic
849C2#8233912yes—
850C2#8258311yescharacteristic
851C2#8265112yes—
852C2#8284211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#386C2
socle, cosocleC24×C3C24
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#14135
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×#877C2semidirect
5. C22×C3⋊#95C2semidirect
6. #72127C2semidirect
7. #71547C2semidirect
8. #71545C2semidirect
9. #71544C2semidirect
10. #69409C2semidirect
11. #69406C2semidirect
26. C2×#935C4semidirect
109. C2×#217C2×C4semidirect
110. C2×#217C2×C4semidirect
120. C2×Dic3⋊C4C2×C4semidirect
121. C2×Dic3⋊C4C2×C4semidirect
261. C22×Dic3C22⋊C4semidirect
839. C3#14135semidirect

Maximal subgroups

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

subgroupindex
C22×#9352
C22×#8772
C2×C3×#3862
C2×#52202
C22×C3⋊#952
#721272
#715472
#715452
#715442
#694092
#694062
#141353