Finite Group Databasebeta

← #10727932

Subgroups — #10727932

Order 768.

3350 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C22⋊C4C211yesmaximal, characteristic
2C2×C3×#397C211yesmaximal, characteristic, complemented
3C2×#4992C211yesmaximal, characteristic, complemented
4C2×#4987C211yesmaximal, characteristic, complemented
5C2×#4955C212yesmaximal
6#71548C212yesmaximal, complemented
7#71546C211yesmaximal, characteristic, complemented
8#69429C212yesmaximal, complemented
9#69427C211yesmaximal, characteristic, complemented
10(C2×D3)⋊#95C212yesmaximal, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12#14820—31nomaximal, Sylow
13C25×D3C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic, complemented
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2211yescharacteristic
20C22×#217C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2212yes—
27C22×C4⋊Dic3C2211yescharacteristic, complemented
28C2×D3×C22⋊C4—24no—
29C2×D3×C22⋊C4—24no—
30C2×D3×C22⋊C4—24no—
31C3×#397—24no—
32C2×C3×#95C2211yescharacteristic, complemented
33C2×C3×#95C2212yescomplemented
34C2×C3⋊#95C2212yescomplemented
35C2×C3⋊#95C2211yescharacteristic, complemented
36C2×C3⋊#95C2212yescomplemented
37C2×C3⋊#95C2212yescomplemented
38C2×C3⋊#95C2212yescomplemented
39C2×C3⋊#95C2212yescomplemented
40#4992—24no—
41#4987—24no—
42#4955—28no—
43C23×C22⋊C4—31no—
44C2×#397—31no—
45C2×#397D311yescharacteristic, complemented
46C2×#380—31no—
47C2×#379—32no—
48#1440—32no—
49#1440—32no—
50#1439—31no—
51#1439—31no—
52C22⋊#95—31no—
53C22⋊#95—32no—
54C25×C3C2311yescharacteristic
55C24×D3—22no—
56C24×D3—22no—
57C24×D3—22no—
58C24×D3—22no—
59C24×D3—22no—
60C24×D3—22no—
61C24×D3—24no—
62C24×D3—24no—
63C24×D3—42no—
64C24×D3—42no—
65C24×D3D414yes—
66C24×D3C2311yescharacteristic
67C24×D3C2311yescharacteristic
68C23×C3×C4C2312yes—
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×Dic3C2312yes—
73C23×Dic3C2312yes—
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2311yescharacteristic
76C22×C4×D3—22no—
77C22×C4×D3—24no—
78C22×C4×D3—22no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—24no—
83C22×C4×D3—42no—
84C22×C4×D3—42no—
85C22×C4×D3D414yes—
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4D414yes—
95C2×#217—22no—
96C2×#217—22no—
97C2×#217—22no—
98C2×#217—24no—
99C2×#217—42no—
100C2×#217—42no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
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—42no—
117C2×(C2×D3)⋊C4—42no—
118C2×(C2×D3)⋊C4D414yes—
119C2×C4⋊Dic3—22no—
120C2×C4⋊Dic3—42no—
121D3×C22⋊C4—232no—
122C3×#95—22no—
123C3×#95—24no—
124C3⋊#95—22no—
125C3⋊#95—24no—
126C3⋊#95—24no—
127C3⋊#95—42no—
128C3⋊#95—42no—
129C3⋊#95—42no—
130C26—31no—
131C24×C4—31no—
132C24×C4—31no—
133C22×C4⋊C4—31no—
134C22×C4⋊C4C2×D311yescharacteristic, complemented
135C22×C22⋊C4—31no—
136C22×C22⋊C4—31no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4—31no—
139C22×C22⋊C4—32no—
140C22×C22⋊C4—32no—
141C22×C22⋊C4—32no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—64no—
144C22×C22⋊C4—64no—
145C22×C22⋊C4—64no—
146C22×C22⋊C4C2×D312yes—
147C22×C22⋊C4C2×D311yescharacteristic
148#397—24no—
149#397—64no—
150#380—64no—
151#379—68no—
152C2×#95—31no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95C2×D311yescharacteristic, complemented
159C2×#95C2×D312yescomplemented
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3C2×D412yes—
169C24×C3C2×D412yes—
170C24×C3#4112yes—
171C24×C3C2411yescharacteristic
172C23×D3—21no—
173C23×D3—21no—
174C23×D3—21no—
175C23×D3—21no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—28no—
179C23×D3—28no—
180C23×D3—28no—
181C23×D3—28no—
182C23×D3—28no—
183C23×D3—21no—
184C23×D3—21no—
185C23×D3—21no—
186C23×D3—21no—
187C23×D3—22no—
188C23×D3—22no—
189C23×D3—22no—
190C23×D3—22no—
191C23×D3—28no—
192C23×D3—28no—
193C23×D3—216no—
194C23×D3—48no—
195C23×D3—48no—
196C23×D3—48no—
197C23×D3—48no—
198C23×D3—48no—
199C23×D3—48no—
200C23×D3—48no—
201C23×D3—48no—
202C23×D3—48no—
203C23×D3—44no—
204C23×D3—44no—
205C23×D3—48no—
206C23×D3—44no—
207C23×D3—44no—
208C23×D3—48no—
209C23×D3C2×D412yes—
210C23×D3C2×D412yes—
211C23×D3C2×D412yes—
212C23×D3C2×D412yes—
213C23×D3#4112yes—
214C23×D3#4112yes—
215C23×D3#4114yes—
216C23×D3#4114yes—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2×D412yes—
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—22no—
258C22×Dic3—22no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3C2×D412yes—
264C22×Dic3C2×D412yes—
265C2×C4×D3—28no—
266C2×C4×D3—28no—
267C2×C4×D3—28no—
268C2×C4×D3—44no—
269C2×C4×D3—48no—
270C2×C4×D3—48no—
271C2×C4×D3—48no—
272C2×C4×D3—48no—
273C2×C4×D3—44no—
274C2×C4×D3—44no—
275C3×C4⋊C4—44no—
276C3×C22⋊C4—28no—
277C3×C22⋊C4—48no—
278#217—28no—
279#217—48no—
280(C2×D3)⋊C4—28no—
281(C2×D3)⋊C4—28no—
282(C2×D3)⋊C4—48no—
283(C2×D3)⋊C4—48no—
284(C2×D3)⋊C4—48no—
285(C2×D3)⋊C4—48no—
286C4⋊Dic3—44no—
287C25—31no—
288C25—31no—
289C25—34no—
290C25—62no—
291C25—62no—
292C25—62no—
293C25—62no—
294C25—64no—
295C25—64no—
296C25—62no—
297C25—62no—
298C25—122no—
299C25—122no—
300C25C22×D311yescharacteristic
301C23×C4—31no—
302C23×C4—31no—
303C23×C4—34no—
304C23×C4—32no—
305C23×C4—32no—
306C23×C4—62no—
307C23×C4—62no—
308C23×C4—64no—
309C23×C4—64no—
310C23×C4—62no—
311C23×C4—62no—
312C23×C4—62no—
313C23×C4—122no—
314C23×C4—122no—
315C23×C4C22×D312yes—
316C23×C4C22×D312yes—
317C23×C4C22×D311yescharacteristic
318C23×C4C22×D311yescharacteristic
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—62no—
323C2×C4⋊C4—122no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—34no—
330C2×C22⋊C4—632no—
331C2×C22⋊C4—62no—
332C2×C22⋊C4—62no—
333C2×C22⋊C4—62no—
334C2×C22⋊C4—62no—
335C2×C22⋊C4—62no—
336C2×C22⋊C4—62no—
337C2×C22⋊C4—62no—
338C2×C22⋊C4—62no—
339C2×C22⋊C4—64no—
340C2×C22⋊C4—64no—
341C2×C22⋊C4—64no—
342C2×C22⋊C4—64no—
343C2×C22⋊C4—64no—
344C2×C22⋊C4—64no—
345C2×C22⋊C4—64no—
346C2×C22⋊C4—64no—
347C2×C22⋊C4—64no—
348C2×C22⋊C4—64no—
349C2×C22⋊C4—64no—
350C2×C22⋊C4—122no—
351C2×C22⋊C4—122no—
352C2×C22⋊C4—122no—
353C2×C22⋊C4—122no—
354C2×C22⋊C4#6714yes—
355#95—22no—
356#95—24no—
357#95—64no—
358#95—64no—
359#95—62no—
360#95—122no—
361#95—122no—
362#95—122no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—24no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—42no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3#12114yes—
386C23×C3C22×D411yescharacteristic
387C23×C3C22×D411yescharacteristic
388C23×C3C22×D411yescharacteristic
389C23×C3C22×D411yescharacteristic
390C23×C3C2×#4111yescharacteristic
391C23×C3C2×#4111yescharacteristic
392C23×C3C2×#4111yescharacteristic
393C23×C3C2×#4112yes—
394C23×C3C2×#4112yes—
395C23×C3H(5,𝔽2)12yes—
396C23×C3H(5,𝔽2)12yes—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—22no—
403C22×D3—22no—
404C22×D3—24no—
405C22×D3—22no—
406C22×D3—24no—
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—24no—
410C22×D3—24no—
411C22×D3—24no—
412C22×D3—24no—
413C22×D3—24no—
414C22×D3—24no—
415C22×D3—232no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—24no—
420C22×D3—22no—
421C22×D3—22no—
422C22×D3—22no—
423C22×D3—24no—
424C22×D3—24no—
425C22×D3—24no—
426C22×D3—24no—
427C22×D3—24no—
428C22×D3—432no—
429C22×D3—432no—
430C22×D3—416no—
431C22×D3—416no—
432C22×D3—416no—
433C22×D3—416no—
434C22×D3—432no—
435C22×D3—432no—
436C22×D3—416no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—42no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—42no—
443C22×D3—42no—
444C22×D3—42no—
445C22×D3—42no—
446C22×D3—42no—
447C22×D3—416no—
448C22×D3#12114yes—
449C22×D3#12114yes—
450C22×D3#12318yes—
451C22×D3#12314yes—
452C22×D3#12414yes—
453C22×D3#12618yes—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—24no—
457C2×C3×C4—24no—
458C2×C3×C4—22no—
459C2×C3×C4—24no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4—42no—
476C2×C3×C4—42no—
477C2×C3×C4#12014yes—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—24no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—42no—
486C2×Dic3—42no—
487C2×Dic3—42no—
488C2×Dic3—42no—
489C2×Dic3—42no—
490C2×Dic3—42no—
491C2×Dic3—42no—
492C2×Dic3—42no—
493C2×Dic3—42no—
494C2×Dic3—42no—
495C2×Dic3—42no—
496C2×Dic3—42no—
497C2×Dic3—42no—
498C2×Dic3—42no—
499C2×Dic3—42no—
500C2×Dic3—42no—
501C2×Dic3—42no—
502C4×D3—416no—
503C4×D3—416no—
504C24—21no—
505C24—21no—
506C24—22no—
507C24—22no—
508C24—21no—
509C24—21no—
510C24—22no—
511C24—22no—
512C24—32no—
513C24—32no—
514C24—32no—
515C24—34no—
516C24—34no—
517C24—32no—
518C24—32no—
519C24—32no—
520C24—68no—
521C24—68no—
522C24—616no—
523C24—68no—
524C24—68no—
525C24—68no—
526C24—68no—
527C24—61no—
528C24—61no—
529C24—61no—
530C24—62no—
531C24—62no—
532C24—61no—
533C24—68no—
534C24—61no—
535C24—61no—
536C24—62no—
537C24—62no—
538C24—61no—
539C24—62no—
540C24—62no—
541C24—61no—
542C24—128no—
543C24—128no—
544C24—128no—
545C24—128no—
546C24—128no—
547C24—124no—
548C24—124no—
549C24—128no—
550C24—128no—
551C24—128no—
552C24—128no—
553C24—128no—
554C24—124no—
555C24—124no—
556C24—128no—
557C24D3×D412yes—
558C24#23712yes—
559C24C2×#6712yes—
560C24C23×D311yescharacteristic
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—68no—
584C22×C4—68no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—62no—
590C22×C4—62no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—68no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—124no—
609C22×C4—128no—
610C22×C4—128no—
611C22×C4—128no—
612C22×C4—128no—
613C22×C4—124no—
614C22×C4—124no—
615C22×C4D3×D412yes—
616C22×C4D3×D412yes—
617C22×C4C2×#6712yes—
618C22×C4C2×#6712yes—
619C4⋊C4—44no—
620C4⋊C4—124no—
621C22⋊C4—28no—
622C22⋊C4—48no—
623C22⋊C4—68no—
624C22⋊C4—68no—
625C22⋊C4—68no—
626C22⋊C4—128no—
627C22⋊C4—128no—
628C22⋊C4—128no—
629C22⋊C4—128no—
630C22⋊C4—128no—
631C22×C3—24no—
632C22×C3—28no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—44no—
638C22×C3—42no—
639C22×C3—44no—
640C22×C3—44no—
641C22×C3—42no—
642C22×C3C2×#12011yescharacteristic
643C22×C3C2×#12111yescharacteristic
644C22×C3C2×#12111yescharacteristic
645C22×C3C2×#12111yescharacteristic
646C22×C3C2×#12311yescharacteristic
647C22×C3C2×#12312yes—
648C22×C3#52511yescharacteristic
649C22×C3#52511yescharacteristic
650C22×C3#52511yescharacteristic
651C22×C3C2×#12411yescharacteristic
652C22×C3C2×#12612yes—
653C22×C3#53411yescharacteristic
654C22×C3#53412yes—
655C22×C3#53511yescharacteristic
656C22×C3#53812yes—
657C22×C3#54612yes—
658C22×C3#54612yes—
659C22×C3#54612yes—
660C22×C3#54612yes—
661C22×C3#55112yes—
662C22×C3#55112yes—
663C22×C3#55112yes—
664C22×C3#55112yes—
665C2×D3—24no—
666C2×D3—24no—
667C2×D3—24no—
668C2×D3—24no—
669C2×D3—28no—
670C2×D3—28no—
671C2×D3—24no—
672C2×D3—28no—
673C2×D3—28no—
674C2×D3—24no—
675C2×D3—24no—
676C2×D3—28no—
677C2×D3—464no—
678C2×D3—42no—
679C2×D3—42no—
680C2×D3—42no—
681C2×D3—42no—
682C2×D3—44no—
683C2×D3—42no—
684C2×D3—44no—
685C2×D3—44no—
686C2×D3—42no—
687C2×D3#39718yescomplemented
688C3×C4—24no—
689C3×C4—42no—
690C3×C4—82no—
691C3×C4—82no—
692Dic3—42no—
693Dic3—42no—
694Dic3—82no—
695Dic3—82no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—38no—
709C23—34no—
710C23—34no—
711C23—38no—
712C23—34no—
713C23—34no—
714C23—41no—
715C23—41no—
716C23—42no—
717C23—41no—
718C23—41no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—632no—
725C23—62no—
726C23—64no—
727C23—64no—
728C23—64no—
729C23—64no—
730C23—62no—
731C23—64no—
732C23—64no—
733C23—64no—
734C23—64no—
735C23—62no—
736C23—62no—
737C23—62no—
738C23—64no—
739C23—64no—
740C23—62no—
741C23—62no—
742C23—62no—
743C23—64no—
744C23—64no—
745C23—64no—
746C23—64no—
747C23—64no—
748C23—64no—
749C23—62no—
750C23—62no—
751C23—62no—
752C23—62no—
753C23—62no—
754C23—62no—
755C23—1232no—
756C23—1216no—
757C23—1232no—
758C23—1216no—
759C23—1216no—
760C23—1216no—
761C23—1216no—
762C23—1232no—
763C23—1232no—
764C23—1216no—
765C23—121no—
766C23—121no—
767C23—122no—
768C23—122no—
769C23—121no—
770C23—121no—
771C23—122no—
772C23—122no—
773C23—122no—
774C23—122no—
775C23#93814yes—
776C23C2×D3×D411yescharacteristic
777C23C2×D3×D411yescharacteristic
778C23C2×D3×D411yescharacteristic
779C23C2×#23711yescharacteristic
780C23D3×#4112yes—
781C23D3×#4112yes—
782C23D3×#4111yescharacteristic
783C23D3×#4111yescharacteristic
784C23#100912yes—
785C23#100912yes—
786C23C22×#6711yescharacteristic
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—64no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—1216no—
816C2×C4—1216no—
817C2×C4—122no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4—122no—
823C2×C4—122no—
824C2×C4—122no—
825C2×C4—122no—
826C2×C4—122no—
827C2×C4—122no—
828C2×C4—122no—
829C2×C4—122no—
830C2×C4—122no—
831C2×C4—122no—
832C2×C4—122no—
833C2×C4—122no—
834C2×C4—122no—
835C2×C4—122no—
836C2×C4#93714yes—
837C2×C3—44no—
838C2×C3C2×#39711yescharacteristic
839C2×C3#240511yescharacteristic
840C2×C3#241212yes—
841C2×C3#241212yes—
842C2×C3#243511yescharacteristic
843C2×C3#248012yes—
844C2×C3#248012yes—
845C2×C3#248211yescharacteristic
846C2×C3#256111yescharacteristic
847C2×C3#261711yescharacteristic
848C2×C3#284711yescharacteristic
849D3—28no—
850D3—44no—
851C22—24no—
852C22—28no—
853C22—38no—
854C22—42no—
855C22—42no—
856C22—44no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—44no—
861C22—44no—
862C22—42no—
863C22—64no—
864C22—64no—
865C22—68no—
866C22—64no—
867C22—64no—
868C22—64no—
869C22—68no—
870C22—68no—
871C22—64no—
872C22—68no—
873C22—64no—
874C22—68no—
875C22—1264no—
876C22—122no—
877C22—122no—
878C22—122no—
879C22—122no—
880C22—122no—
881C22—124no—
882C22—124no—
883C22—122no—
884C22—124no—
885C22D3×#12111yescharacteristic
886C22D3×#12111yescharacteristic
887C22#560611yescharacteristic
888C22#560611yescharacteristic
889C22D3×#12312yes—
890C22D3×#12311yescharacteristic
891C22#565312yes—
892C22#565311yescharacteristic
893C22#565412yes—
894C22#565812yes—
895C22#565812yes—
896C22D3×#12411yescharacteristic
897C22#567411yescharacteristic
898C22#567612yes—
899C22D3×#12612yes—
900C22#570412yes—
901C22#570512yes—
902C22#570512yes—
903C22C2×#93711yescharacteristic
904C22C2×#93811yescharacteristic
905C22#582811yescharacteristic
906C22#582912yes—
907C22#582912yes—
908C4—24no—
909C4—42no—
910C4—82no—
911C4—82no—
912C4—122no—
913C4—122no—
914C4—242no—
915C4—242no—
916C3#1482011yescharacteristic, complemented, Sylow
917C2—44no—
918C2—68no—
919C2—124no—
920C2#7748112yes—
921C2D3×#39711yescharacteristic
922C2#7766812yes—
923C2#7767611yescharacteristic
924C2#7768311yescharacteristic
925C2#7768411yescharacteristic
926C2#8272311yescharacteristic
927C2#8289311yescharacteristic
928C2#8289512yes—
929C2#8296011yescharacteristic
930C2#8308112yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#397C2
prime radicalC25×D3C22
hypercenterC2×#397D3
hypocenterC3#14820
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C2×C3×#397C2semidirect
3. C2×#4992C2semidirect
4. C2×#4987C2semidirect
6. #71548C2semidirect
7. #71546C2semidirect
8. #69429C2semidirect
9. #69427C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. (C2×D3)⋊#95C2semidirect
16. C22×C3×C4⋊C4C22semidirect
27. C22×C4⋊Dic3C22semidirect
32. C2×C3×#95C22semidirect
33. C2×C3×#95C22semidirect
34. C2×C3⋊#95C22semidirect
35. C2×C3⋊#95C22semidirect
36. C2×C3⋊#95C22semidirect
37. C2×C3⋊#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
45. C2×#397D3semidirect
134. C22×C4⋊C4C2×D3semidirect
158. C2×#95C2×D3semidirect
159. C2×#95C2×D3semidirect
687. C2×D3#397semidirect
916. C3#14820semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊C42
C2×C3×#3972
C2×#49922
C2×#49872
C2×#49552
#715482
#715462
#694292
#694272
(C2×D3)⋊#952
#148203