Finite Group Databasebeta

← #10729026

Subgroups — #10729026

Order 768.

2314 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic
2C2×#5220C211yesmaximal, characteristic
3C2×#5220C211yesmaximal, characteristic
4C2×#5211C211yesmaximal, characteristic, complemented
5C22×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×#4946C211yesmaximal, characteristic, complemented
7#71567C212yesmaximal, complemented
8#71566C212yesmaximal, complemented
9#71549C212yesmaximal, complemented
10#71547C212yesmaximal, complemented
11#71544C211yesmaximal, characteristic, complemented
12#14912—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C2×C3×#123—24no—
18C2×C3×#123—24no—
19C2×C3×#123—24no—
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2212yes—
27C22×#217C2212yes—
28C22×#217C2211yescharacteristic
29C22×Dic3⋊C4C2212yes—
30#5220—24no—
31#5220—24no—
32#5211—24no—
33C2×C3⋊#95—24no—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43#4946—24no—
44C22×#123D311yescharacteristic
45C2×#386—31no—
46C2×#386—31no—
47C2×#385—31no—
48C2×#381—31no—
49C22×#95—31no—
50#1442—32no—
51#1441—32no—
52#1440—32no—
53#1439—32no—
54C22⋊#95—31no—
55C25×C3C2311yescharacteristic
56C25×C3C2311yescharacteristic
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4D414yes—
64C23×C3×C4—22no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—22no—
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4D414yes—
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×Dic3—22no—
77C23×Dic3—22no—
78C23×Dic3—24no—
79C23×Dic3—24no—
80C23×Dic3—22no—
81C23×Dic3—22no—
82C23×Dic3—22no—
83C23×Dic3—22no—
84C23×Dic3—42no—
85C23×Dic3—42no—
86C23×Dic3C2312yes—
87C23×Dic3C2312yes—
88C23×Dic3C2312yes—
89C23×Dic3C2312yes—
90C3×#123—232no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4D414yes—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—24no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—24no—
113C2×#217—24no—
114C2×#217—24no—
115C2×#217—42no—
116C2×#217—42no—
117C2×#217D414yes—
118C2×Dic3⋊C4—24no—
119C2×Dic3⋊C4—24no—
120C2×Dic3⋊C4—42no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95—24no—
125C3⋊#95—24no—
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95—24no—
129C3⋊#95—42no—
130C23×D4C2×D311yescharacteristic
131C24×C4—31no—
132C24×C4—31no—
133C24×C4C2×D311yescharacteristic
134C2×#123—24no—
135C2×#123—24no—
136C2×#123—24no—
137C22×C4⋊C4—32no—
138C22×C4⋊C4C2×D311yescharacteristic
139C22×C4⋊C4C2×D311yescharacteristic
140C22×C22⋊C4—31no—
141C22×C22⋊C4—31no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4C2×D311yescharacteristic
145C22×C22⋊C4C2×D311yescharacteristic
146C22×C22⋊C4C2×D311yescharacteristic
147#386—64no—
148#386—64no—
149#385—64no—
150#381—64no—
151C2×#95—32no—
152C2×#95—32no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95—32no—
160C2×#95—64no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3C2×D412yes—
176C24×C3C2×D412yes—
177C24×C3C2×D412yes—
178C24×C3C2×D412yes—
179C24×C3C2×D412yes—
180C24×C3#4112yes—
181C24×C3#4112yes—
182C24×C3#4112yes—
183C24×C3C2411yescharacteristic
184C2×C3×D4—28no—
185C2×C3×D4—28no—
186C2×C3×D4—28no—
187C2×C3×D4—44no—
188C2×C3×D4—44no—
189C2×C3×D4—44no—
190C2×C3×D4—44no—
191C22×C3×C4—28no—
192C22×C3×C4—28no—
193C22×C3×C4—28no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—44no—
221C22×C3×C4—44no—
222C22×C3×C4—44no—
223C22×C3×C4—44no—
224C22×C3×C4C2×D412yes—
225C22×C3×C4C2×D412yes—
226C22×C3×C4C2×D412yes—
227C22×C3×C4C2×D412yes—
228C22×C3×C4C2×D412yes—
229C22×Dic3—28no—
230C22×Dic3—28no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
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—48no—
257C22×Dic3—48no—
258C22×Dic3—48no—
259C22×Dic3—48no—
260C22×Dic3—44no—
261C22×Dic3—44no—
262C22×Dic3—44no—
263C22×Dic3—44no—
264C22×Dic3C2×D414yes—
265C22×Dic3#4114yes—
266C22×Dic3#4114yes—
267C3×C4⋊C4—28no—
268C3×C4⋊C4—28no—
269C3×C22⋊C4—28no—
270C3×C22⋊C4—28no—
271C3×C22⋊C4—28no—
272#217—28no—
273#217—48no—
274#217—48no—
275#217—44no—
276Dic3⋊C4—48no—
277C25C22×D311yescharacteristic
278C25C22×D311yescharacteristic
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4#6714yes—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—32no—
293C23×C4—32no—
294C23×C4—32no—
295C23×C4—32no—
296C23×C4—64no—
297C23×C4—64no—
298C23×C4—62no—
299C23×C4—62no—
300C23×C4—62no—
301C23×C4—62no—
302C23×C4—62no—
303C23×C4—62no—
304C23×C4—122no—
305C23×C4—122no—
306C23×C4#6714yes—
307C23×C4C22×D311yescharacteristic
308C23×C4C22×D311yescharacteristic
309C23×C4C22×D311yescharacteristic
310C23×C4C22×D311yescharacteristic
311C23×C4C22×D311yescharacteristic
312#123—232no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—64no—
320C2×C4⋊C4—64no—
321C2×C4⋊C4—122no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—34no—
331C2×C22⋊C4—62no—
332C2×C22⋊C4—62no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—64no—
335C2×C22⋊C4—64no—
336C2×C22⋊C4—62no—
337C2×C22⋊C4—62no—
338C2×C22⋊C4—64no—
339C2×C22⋊C4—62no—
340C2×C22⋊C4—122no—
341C2×C22⋊C4—122no—
342C2×C22⋊C4#6714yes—
343#95—64no—
344#95—64no—
345#95—64no—
346#95—64no—
347#95—64no—
348#95—64no—
349#95—64no—
350#95—64no—
351#95—122no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—22no—
357C23×C3—22no—
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—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3#12014yes—
392C23×C3#12114yes—
393C23×C3#12114yes—
394C23×C3#12114yes—
395C23×C3#12314yes—
396C23×C3#12314yes—
397C23×C3#12414yes—
398C23×C3C22×D411yescharacteristic
399C23×C3C22×D411yescharacteristic
400C23×C3C22×D411yescharacteristic
401C23×C3C22×D411yescharacteristic
402C23×C3C2×#4111yescharacteristic
403C23×C3C2×#4111yescharacteristic
404C23×C3C2×#4111yescharacteristic
405C23×C3C2×#4112yes—
406C23×C3C2×#4112yes—
407C23×C3H(5,𝔽2)12yes—
408C23×C32−1+412yes—
409C3×D4—416no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—416no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—24no—
445C2×Dic3—24no—
446C2×Dic3—24no—
447C2×Dic3—24no—
448C2×Dic3—24no—
449C2×Dic3—24no—
450C2×Dic3—24no—
451C2×Dic3—416no—
452C2×Dic3—416no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—21no—
486C24D3×D412yes—
487C24#23712yes—
488C24#23712yes—
489C24#23712yes—
490C24C2×#6712yes—
491C24C2×#6712yes—
492C24C2×#6712yes—
493C24C2×#6712yes—
494C24C23×D311yescharacteristic
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—34no—
532C22×C4—34no—
533C22×C4—34no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—68no—
539C22×C4—68no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—128no—
566C22×C4—128no—
567C22×C4—128no—
568C22×C4—128no—
569C22×C4—124no—
570C22×C4—124no—
571C22×C4—124no—
572C22×C4—124no—
573C22×C4C2×#6712yes—
574C22×C4C2×#6712yes—
575C22×C4C2×#6712yes—
576C22×C4C2×#6712yes—
577C22×C4C2×#6712yes—
578C4⋊C4—28no—
579C4⋊C4—28no—
580C4⋊C4—128no—
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—28no—
584C22⋊C4—68no—
585C22⋊C4—128no—
586C22⋊C4—128no—
587C22⋊C4—124no—
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—28no—
595C22×C3—28no—
596C22×C3—28no—
597C22×C3—28no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—82no—
608C22×C3—82no—
609C22×C3#39418yes—
610C22×C3C2×#12011yescharacteristic
611C22×C3C2×#12111yescharacteristic
612C22×C3C2×#12111yescharacteristic
613C22×C3C2×#12111yescharacteristic
614C22×C3C2×#12311yescharacteristic
615C22×C3C2×#12311yescharacteristic
616C22×C3#52511yescharacteristic
617C22×C3#52511yescharacteristic
618C22×C3C2×#12411yescharacteristic
619C22×C3#52912yes—
620C22×C3#52912yes—
621C22×C3#53511yescharacteristic
622C22×C3#53611yescharacteristic
623C22×C3#53912yes—
624C22×C3#53912yes—
625C22×C3#54612yes—
626C22×C3#54612yes—
627C22×C3#54612yes—
628C22×C3#54712yes—
629C22×C3#54712yes—
630C22×C3#54712yes—
631C22×C3#55112yes—
632C22×C3#55212yes—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—42no—
637C3×C4—42no—
638Dic3—44no—
639Dic3—44no—
640Dic3—44no—
641Dic3—82no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23#93514yes—
682C23#93514yes—
683C23#93614yes—
684C23#93814yes—
685C23#93914yes—
686C23#93914yes—
687C23#95314yes—
688C23C2×D3×D411yescharacteristic
689C23C2×#23711yescharacteristic
690C23C2×#23711yescharacteristic
691C23C2×#23711yescharacteristic
692C23D3×#4112yes—
693C23D3×#4112yes—
694C23#100912yes—
695C23#101012yes—
696C23C22×#6711yescharacteristic
697C23C22×#6711yescharacteristic
698C23C22×#6711yescharacteristic
699D4—416no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—416no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—64no—
733C2×C4—64no—
734C2×C4—64no—
735C2×C4—64no—
736C2×C4—64no—
737C2×C4—64no—
738C2×C4—64no—
739C2×C4—64no—
740C2×C4—64no—
741C2×C4—1216no—
742C2×C4—1216no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C3—28no—
763C2×C3—82no—
764C2×C3C2×#39411yescharacteristic
765C2×C3#240411yescharacteristic
766C2×C3#240611yescharacteristic
767C2×C3#241111yescharacteristic
768C2×C3#241311yescharacteristic
769C2×C3#241912yes—
770C2×C3#242512yes—
771C2×C3#242512yes—
772C2×C3#248812yes—
773C2×C3#262311yescharacteristic
774C2×C3#285311yescharacteristic
775C22—24no—
776C22—24no—
777C22—24no—
778C22—28no—
779C22—28no—
780C22—28no—
781C22—28no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—44no—
789C22—44no—
790C22—81no—
791C22—82no—
792C22—82no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22#522218yes—
797C22#564912yes—
798C22#564912yes—
799C22#565012yes—
800C22#565412yes—
801C22#565512yes—
802C22#565812yes—
803C22#566512yes—
804C22#566512yes—
805C22C2×#93511yescharacteristic
806C22C2×#93511yescharacteristic
807C22C2×#93611yescharacteristic
808C22C2×#93811yescharacteristic
809C22C2×#93911yescharacteristic
810C22C2×#93911yescharacteristic
811C22#582412yes—
812C22#582412yes—
813C22#582511yescharacteristic
814C22#582811yescharacteristic
815C22#582811yescharacteristic
816C22#582912yes—
817C22#582912yes—
818C22#583011yescharacteristic
819C22C2×#95311yescharacteristic
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—124no—
826C4—124no—
827C4—124no—
828C4—242no—
829C3#1491211yescharacteristic, complemented, Sylow
830C2—28no—
831C2—82no—
832C2#8284311yescharacteristic
833C2#8284412yes—
834C2#8284612yes—
835C2#8284712yes—
836C2#8285712yes—
837C2#8286611yescharacteristic
838C2#8289011yescharacteristic
839C2#8289411yescharacteristic
840C2C2×#522211yescharacteristic
841C2#8409011yescharacteristic
842C2#8409611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#123C2
prime radicalC23×C3×D4C22
hypercenterC22×#123D3
hypocenterC3#14912
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
4. C2×#5211C2semidirect
5. C22×C3⋊#95C2semidirect
6. C2×#4946C2semidirect
7. #71567C2semidirect
8. #71566C2semidirect
9. #71549C2semidirect
10. #71547C2semidirect
11. #71544C2semidirect
829. C3#14912semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C2×#52202
C2×#52112
C22×C3⋊#952
C2×#49462
#715672
#715662
#715492
#715472
#715442
#149123