Finite Group Databasebeta

← #10728744

Subgroups — #10728744

Order 768.

2470 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#117C211yesmaximal, characteristic, complemented
2C2×#5213C212yesmaximal, complemented
3C2×#4991C211yesmaximal, characteristic, complemented
4C2×#4960C211yesmaximal, characteristic
5C2×#4939C211yesmaximal, characteristic, complemented
6#71570C212yesmaximal, complemented
7#71565C211yesmaximal, characteristic, complemented
8#71550C212yesmaximal, complemented
9#71546C211yesmaximal, characteristic, complemented
10#71537C212yesmaximal, complemented
11#71534C211yesmaximal, characteristic, complemented
12#14886—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×#67C2212yes—
15C23×D12C2211yescharacteristic
16C2×C3×#117—24no—
17C2×C3×#117—24no—
18C2×C3×#117—24no—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×#217C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2212yes—
30C22×(C2×D3)⋊C4C2212yes—
31C22×C4⋊Dic3C2211yescharacteristic
32#5213—28no—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40#4991—24no—
41#4960—24no—
42#4939—24no—
43C22×#117D311yescharacteristic, complemented
44C2×#394—31no—
45C2×#392—31no—
46C2×#390—31no—
47C2×#386—32no—
48#1441—31no—
49#1439—32no—
50#1439—31no—
51#1438—32no—
52#1437—32no—
53#1434—31no—
54C25×C3C2311yescharacteristic
55C24×D3C2312yes—
56C23×C3×C4—22no—
57C23×C3×C4—22no—
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4—22no—
61C23×C3×C4—22no—
62C23×C3×C4D414yescomplemented
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—24no—
72C22×#67—24no—
73C22×#67—24no—
74C22×#67—42no—
75C22×#67—42no—
76C23×Dic3C2312yes—
77C23×Dic3C2312yes—
78C23×Dic3C2312yes—
79C22×D12—24no—
80C22×D12—22no—
81C22×D12—22no—
82C22×D12—22no—
83C22×D12—42no—
84C3×#117—232no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4D414yescomplemented
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4D414yes—
97C2×C3×C42—22no—
98C2×C3×C42—22no—
99C2×C3×C42—22no—
100C2×C3×C42—22no—
101C2×C3×C42—22no—
102C2×C3×C42D414yescomplemented
103C2×#217—24no—
104C2×#217—42no—
105C2×#217—42no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—24no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—42no—
118C2×(C2×D3)⋊C4—42no—
119C2×(C2×D3)⋊C4—42no—
120C2×(C2×D3)⋊C4—42no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3—42no—
123C3⋊#95—24no—
124C3⋊#95—24no—
125C3⋊#95—22no—
126C3⋊#95—22no—
127C3⋊#95—24no—
128C3⋊#95—42no—
129C3⋊#95—42no—
130C23×D4—32no—
131C23×D4—31no—
132C24×C4C2×D311yescharacteristic
133C2×#117—24no—
134C2×#117—24no—
135C2×#117—24no—
136C22×C4⋊C4—31no—
137C22×C4⋊C4C2×D311yescharacteristic
138C22×C4⋊C4C2×D311yescharacteristic
139C22×C22⋊C4—32no—
140C22×C22⋊C4—32no—
141C22×C22⋊C4—32no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4C2×D311yescharacteristic
146C22×C22⋊C4C2×D311yescharacteristic
147C22×C42C2×D311yescharacteristic
148C22×C42C2×D311yescharacteristic
149#394—64no—
150#392—64no—
151#390—64no—
152#386—68no—
153C2×#95—31no—
154C2×#95—31no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95—32no—
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—21no—
165C24×C3—21no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3C2×D412yes—
169C24×C3C2×D412yes—
170C24×C3#4112yes—
171C24×C3C2411yescharacteristic
172C23×D3—22no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—22no—
179C23×D3—22no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3#4114yes—
187C22×C3×C4—28no—
188C22×C3×C4—28no—
189C22×C3×C4—28no—
190C22×C3×C4—28no—
191C22×C3×C4—28no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—22no—
202C22×C3×C4—28no—
203C22×C3×C4—28no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×D412yes—
218C22×C3×C4C2×D412yes—
219C22×C3×C4C2×D412yes—
220C22×C3×C4C2×D412yes—
221C22×C3×C4C2×D412yes—
222C22×C3×C4C2×D412yes—
223C22×C3×C4C2×D412yes—
224C22×C3×C4C2×D412yes—
225C22×C3×C4C2×D412yes—
226C22×C3×C4#4112yes—
227C22×C3×C4#4112yes—
228C2×#67—216no—
229C2×#67—48no—
230C2×#67—48no—
231C2×#67—48no—
232C2×#67—48no—
233C2×#67—48no—
234C2×#67—48no—
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#4114yes—
256C2×D12—28no—
257C2×D12—48no—
258C2×D12—48no—
259C2×D12—44no—
260C2×D12—44no—
261C3×C4⋊C4—28no—
262C3×C4⋊C4—28no—
263C3×C22⋊C4—28no—
264C3×C22⋊C4—28no—
265C3×C42—28no—
266C3×C42—28no—
267#217—48no—
268(C2×D3)⋊C4—48no—
269(C2×D3)⋊C4—48no—
270(C2×D3)⋊C4—48no—
271(C2×D3)⋊C4—48no—
272(C2×D3)⋊C4—48no—
273C4⋊Dic3—44no—
274C25—32no—
275C25C22×D311yescharacteristic
276C22×D4—64no—
277C22×D4—64no—
278C22×D4—64no—
279C22×D4—64no—
280C22×D4—64no—
281C22×D4—64no—
282C22×D4—62no—
283C22×D4—62no—
284C22×D4—62no—
285C22×D4—122no—
286C22×D4—122no—
287C22×D4—122no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—32no—
295C23×C4—32no—
296C23×C4—32no—
297C23×C4D1214yescomplemented
298C23×C4C22×D311yescharacteristic
299C23×C4C22×D311yescharacteristic
300C23×C4C22×D311yescharacteristic
301C23×C4C22×D311yescharacteristic
302C23×C4C22×D311yescharacteristic
303C23×C4C22×D311yescharacteristic
304#117—232no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—62no—
311C2×C4⋊C4—122no—
312C2×C4⋊C4#6714yescomplemented
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—64no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—64no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—122no—
331C2×C22⋊C4—122no—
332C2×C22⋊C4—122no—
333C2×C22⋊C4—122no—
334C2×C22⋊C4—122no—
335C2×C22⋊C4—122no—
336C2×C22⋊C4#6714yes—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42#6714yescomplemented
343#95—64no—
344#95—64no—
345#95—64no—
346#95—62no—
347#95—62no—
348#95—122no—
349#95—122no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—24no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—41no—
363C23×C3—42no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3#12114yes—
373C23×C3C22×D411yescharacteristic
374C23×C3C22×D411yescharacteristic
375C23×C3C22×D411yescharacteristic
376C23×C3C22×D411yescharacteristic
377C23×C3C2×#4111yescharacteristic
378C23×C3C2×#4111yescharacteristic
379C23×C3C2×#4111yescharacteristic
380C23×C3C2×#4112yes—
381C23×C3C2×#4112yes—
382C23×C3H(5,𝔽2)12yes—
383C23×C3H(5,𝔽2)12yes—
384C22×D3—24no—
385C22×D3—24no—
386C22×D3—24no—
387C22×D3—24no—
388C22×D3—24no—
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3—42no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—42no—
417C22×D3—42no—
418C22×D3—42no—
419C2×C3×C4—232no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—24no—
435C2×C3×C4—24no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4#12014yes—
452C2×C3×C4#12114yes—
453C2×C3×C4#12114yes—
454#67—432no—
455C2×Dic3—24no—
456C2×Dic3—24no—
457C2×Dic3—24no—
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—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3—42no—
475C2×Dic3—42no—
476D12—416no—
477C24—21no—
478C24—21no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—21no—
484C24—21no—
485C24—34no—
486C24—62no—
487C24—62no—
488C24—62no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—62no—
493C24—62no—
494C24—62no—
495C24—62no—
496C24—62no—
497C24—62no—
498C24—62no—
499C24—62no—
500C24C2×D1212yes—
501C24#23512yes—
502C24C2×#6712yes—
503C24C23×D311yescharacteristic
504C2×D4—68no—
505C2×D4—616no—
506C2×D4—128no—
507C2×D4—128no—
508C2×D4—124no—
509C2×D4—128no—
510C2×D4—128no—
511C2×D4—128no—
512C2×D4—128no—
513C2×D4—128no—
514C2×D4—128no—
515C2×D4—124no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—34no—
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—62no—
566C22×C4C2×D1212yes—
567C22×C4C2×D1212yes—
568C22×C4#23512yes—
569C22×C4#23512yes—
570C22×C4C2×#6712yes—
571C22×C4C2×#6712yes—
572C22×C4C2×#6712yes—
573C22×C4C2×#6712yes—
574C22×C4C2×#6712yes—
575C22×C4C2×#6712yes—
576C22×C4C2×#6712yes—
577C22×C4C2×#6712yes—
578C4⋊C4—28no—
579C4⋊C4—28no—
580C4⋊C4—124no—
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—128no—
584C22⋊C4—128no—
585C22⋊C4—128no—
586C22⋊C4—128no—
587C22⋊C4—128no—
588C22⋊C4—128no—
589C42—28no—
590C42—28no—
591C22×C3—24no—
592C22×C3—28no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—44no—
599C22×C3—42no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3C2×#12011yescharacteristic
603C22×C3C2×#12111yescharacteristic
604C22×C3C2×#12111yescharacteristic
605C22×C3C2×#12111yescharacteristic
606C22×C3#52512yes—
607C22×C3#52511yescharacteristic
608C22×C3#52511yescharacteristic
609C22×C3#52511yescharacteristic
610C22×C3#52511yescharacteristic
611C22×C3#52912yes—
612C22×C3#53211yescharacteristic
613C22×C3#53512yes—
614C22×C3#53511yescharacteristic
615C22×C3#53511yescharacteristic
616C22×C3#54012yes—
617C22×C3#54612yes—
618C22×C3#54612yes—
619C22×C3#54612yes—
620C22×C3#55012yes—
621C22×C3#55112yes—
622C22×C3#55112yes—
623C22×C3#55312yes—
624C22×C3#55512yes—
625C2×D3—44no—
626C2×D3—44no—
627C2×D3—44no—
628C2×D3—44no—
629C2×D3—44no—
630C2×D3—44no—
631C2×D3—44no—
632C2×D3—82no—
633C2×D3—82no—
634C2×D3—82no—
635C2×D3—82no—
636C2×D3—82no—
637C2×D3—82no—
638C2×D3—82no—
639C2×D3—82no—
640C3×C4—24no—
641C3×C4—24no—
642C3×C4—24no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—42no—
646Dic3—44no—
647Dic3—82no—
648Dic3—82no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—64no—
672C23—64no—
673C23—64no—
674C23—64no—
675C23—64no—
676C23—64no—
677C23—64no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—122no—
683C23—122no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—122no—
688C23—122no—
689C23—122no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23—122no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23—122no—
698C23—122no—
699C23—122no—
700C23—122no—
701C23—122no—
702C23—122no—
703C23—122no—
704C23—122no—
705C23—122no—
706C23#93014yes—
707C23C22×D1211yescharacteristic
708C23C2×#23511yescharacteristic
709C23C2×#23511yescharacteristic
710C23C2×#23511yescharacteristic
711C23D3×#4112yes—
712C23D3×#4112yes—
713C23#100912yes—
714C23#100912yes—
715C23C22×#6711yescharacteristic
716C23C22×#6711yescharacteristic
717C23C22×#6711yescharacteristic
718D4—1216no—
719D4—1232no—
720C2×C4—232no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—64no—
753C2×C4—64no—
754C2×C4—64no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4—122no—
763C2×C4—122no—
764C2×C4—122no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4—122no—
773C2×C4#93014yes—
774C2×C4#93014yes—
775C2×C4#95314yes—
776C2×C3—44no—
777C2×C3#239211yescharacteristic
778C2×C3#240411yescharacteristic
779C2×C3#241112yes—
780C2×C3#241412yes—
781C2×C3#243111yescharacteristic
782C2×C3#247112yes—
783C2×C3#247612yes—
784C2×C3#259811yescharacteristic
785C2×C3#261011yescharacteristic
786C2×C3#261911yescharacteristic
787C2×C3#284711yescharacteristic
788D3—84no—
789C22—24no—
790C22—28no—
791C22—42no—
792C22—42no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—124no—
801C22—124no—
802C22—124no—
803C22—124no—
804C22—124no—
805C22—124no—
806C22—124no—
807C22—242no—
808C22—242no—
809C22—242no—
810C22—242no—
811C22—242no—
812C22—242no—
813C22—242no—
814C22—242no—
815C22#552412yes—
816C22#552512yes—
817C22#552712yes—
818C22#552712yes—
819C22#552812yes—
820C22#553012yes—
821C22#553212yes—
822C22#553512yes—
823C22C2×#93011yescharacteristic
824C22C2×#93011yescharacteristic
825C22C2×#93011yescharacteristic
826C22#579111yescharacteristic
827C22#579111yescharacteristic
828C22#579111yescharacteristic
829C22#582811yescharacteristic
830C22#582912yes—
831C22#582912yes—
832C22#582912yes—
833C22#583011yescharacteristic
834C22#583011yescharacteristic
835C22#583211yescharacteristic
836C22#583412yes—
837C22C2×#95311yescharacteristic
838C4—24no—
839C4—24no—
840C4—24no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—124no—
845C4—242no—
846C4—242no—
847C3#1488611yescharacteristic, complemented, Sylow
848C2—44no—
849C2—244no—
850C2#8226011yescharacteristic
851C2#8227311yescharacteristic
852C2#8227512yes—
853C2#8227612yes—
854C2#8227912yes—
855C2#8228012yes—
856C2#8228411yescharacteristic
857C2#8228611yescharacteristic
858C2#8403211yescharacteristic
859C2#8409211yescharacteristic
860C2#8409611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#117C2
prime radicalC2×#4960C2
hypercenterC22×#117D3
hypocenterC3#14886
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×C3×#117C2semidirect
2. C2×#5213C2semidirect
3. C2×#4991C2semidirect
5. C2×#4939C2semidirect
6. #71570C2semidirect
7. #71565C2semidirect
8. #71550C2semidirect
9. #71546C2semidirect
10. #71537C2semidirect
11. #71534C2semidirect
43. C22×#117D3semidirect
62. C23×C3×C4D4semidirect
90. C2×C3×C4⋊C4D4semidirect
102. C2×C3×C42D4semidirect
297. C23×C4D12semidirect
312. C2×C4⋊C4#67semidirect
342. C2×C42#67semidirect
847. C3#14886semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1172
C2×#52132
C2×#49912
C2×#49602
C2×#49392
#715702
#715652
#715502
#715462
#715372
#715342
#148863