Finite Group Databasebeta

← #10701984

Subgroups — #10701984

Order 768.

1822 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#213C211yesmaximal, characteristic
2C2×C3×#390C211yesmaximal, characteristic, complemented
3C22×#832C211yesmaximal, characteristic, complemented
4C22×#809C211yesmaximal, characteristic, complemented
5C2×#4939C211yesmaximal, characteristic, complemented
6C2×#4529C211yesmaximal, characteristic, complemented
7C2×#4524C211yesmaximal, characteristic, complemented
8#11022—31nomaximal, Sylow
9C23×C3×D4C2211yescharacteristic
10C23×D12C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C3×C22⋊C4—22no—
13C22×C3×C42C2211yescharacteristic
14C22×#213—22no—
15C22×#213—22no—
16C22×#213—22no—
17C22×#213—22no—
18C22×#213—22no—
19C22×#213—22no—
20C22×#213C414yescomplemented
21C22×(C2×D3)⋊C4—22no—
22C22×C4⋊Dic3C2211yescharacteristic
23C23×C3⋊C8C2211yescharacteristic
24C23×C3⋊C8C2211yescharacteristic
25C3×#390—22no—
26C3×#390—22no—
27C2×#832—22no—
28C2×#832—22no—
29C2×#832—22no—
30C2×#809—22no—
31C2×#809—22no—
32C2×#809—22no—
33#4939—22no—
34#4939—22no—
35#4529—22no—
36#4524—22no—
37C23×D8—31no—
38C22×#102—31no—
39C22×#102—31no—
40C2×#390—31no—
41C2×#390D311yescharacteristic, complemented
42C2×#340—31no—
43C2×#336—31no—
44C25×C3—21no—
45C24×D3—21no—
46C22×C3×D4—21no—
47C22×C3×D4—21no—
48C22×C3×D4—21no—
49C22×C3×D4—21no—
50C22×C3×D4—21no—
51C22×C3×D4—21no—
52C22×C3×D4—21no—
53C22×C3×D4—21no—
54C22×C3×D4—21no—
55C22×C3×D4—21no—
56C22×C3×D4—21no—
57C22×C3×D4C2×C412yes—
58C22×C3×D4D412yes—
59C22×C3×D4D412yes—
60C23×C3×C4—21no—
61C23×C3×C4D412yes—
62C23×C3×C4C2311yescharacteristic
63C23×Dic3—21no—
64C22×D12—21no—
65C22×D12—21no—
66C22×D12—21no—
67C22×D12—21no—
68C22×D12—21no—
69C22×D12—21no—
70C22×D12—21no—
71C22×D12—21no—
72C22×D12—21no—
73C22×D12—21no—
74C22×D12—21no—
75C22×D12C2×C412yes—
76C22×D12D412yes—
77C22×D12D412yes—
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4D412yes—
84C2×C3×C22⋊C4—28no—
85C2×C3×C22⋊C4—44no—
86C2×C3×C22⋊C4—44no—
87C2×C3×C42—21no—
88C2×C3×C42—21no—
89C2×C3×C42—21no—
90C2×C3×C42—21no—
91C2×C3×C42—21no—
92C2×C3×C42—21no—
93C2×#213—28no—
94C2×#213—28no—
95C2×#213—28no—
96C2×#213—28no—
97C2×#213—28no—
98C2×#213—28no—
99C2×#213—28no—
100C2×(C2×D3)⋊C4—28no—
101C2×(C2×D3)⋊C4—44no—
102C2×(C2×D3)⋊C4—44no—
103C2×C4⋊Dic3—21no—
104C2×C4⋊Dic3—21no—
105C2×C4⋊Dic3—21no—
106C2×C4⋊Dic3—21no—
107C2×C4⋊Dic3—21no—
108C2×C4⋊Dic3D412yes—
109C22×C3⋊C8—21no—
110C22×C3⋊C8—21no—
111C22×C3⋊C8—21no—
112C22×C3⋊C8—21no—
113C22×C3⋊C8—21no—
114C22×C3⋊C8—21no—
115C22×C3⋊C8—21no—
116C22×C3⋊C8—21no—
117C22×C3⋊C8—21no—
118C22×C3⋊C8—21no—
119C22×C3⋊C8C2×C412yes—
120C22×C3⋊C8D412yes—
121C22×C3⋊C8D412yes—
122C22×C3⋊C8D412yes—
123#832—28no—
124#809—28no—
125C23×D4—31no—
126C23×D4C2×D311yescharacteristic
127C22×D8—34no—
128C22×D8—62no—
129C22×D8—62no—
130C22×D8—62no—
131C22×D8—62no—
132C22×D8—62no—
133C22×D8—62no—
134C23×C8—31no—
135C23×C8—31no—
136C22×C4⋊C4—31no—
137C22×C4⋊C4C2×D311yescharacteristic
138C22×C22⋊C4—22no—
139C22×C22⋊C4—62no—
140C22×C42C2×D311yescharacteristic
141C2×#102—62no—
142C2×#102—62no—
143C2×#102—62no—
144C2×#102—62no—
145C2×#102—62no—
146C2×#102—62no—
147#390—22no—
148#390—22no—
149#390—62no—
150#390—62no—
151#340—62no—
152#336—62no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—41no—
157C24×C3—41no—
158C24×C3—41no—
159C24×C3—41no—
160C24×C3—42no—
161C24×C3—42no—
162C24×C3—42no—
163C24×C3—42no—
164C24×C3C2×D411yescharacteristic
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—41no—
169C23×D3—41no—
170C23×D3—41no—
171C23×D3—41no—
172C23×D3—42no—
173C23×D3—42no—
174C23×D3—42no—
175C23×D3—42no—
176C2×C3×D4—22no—
177C2×C3×D4—22no—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—22no—
183C2×C3×D4—22no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—41no—
192C2×C3×D4—41no—
193C2×C3×D4—41no—
194C2×C3×D4—41no—
195C2×C3×D4—41no—
196C2×C3×D4—41no—
197C2×C3×D4—41no—
198C2×C3×D4—41no—
199C2×C3×D4—41no—
200C2×C3×D4—41no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4C22⋊C414yescomplemented
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—41no—
212C22×C3×C4—41no—
213C22×C3×C4—42no—
214C22×C3×C4—42no—
215C22×C3×C4D814yescomplemented
216C22×C3×C4C22×C411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4#4111yescharacteristic
227C22×C3×C4#4111yescharacteristic
228C22×C3×C4#4111yescharacteristic
229C22×C3×C4#4111yescharacteristic
230C22×Dic3—22no—
231C22×Dic3—41no—
232C22×Dic3—41no—
233C22×Dic3—42no—
234C22×Dic3—42no—
235C2×D12—22no—
236C2×D12—22no—
237C2×D12—22no—
238C2×D12—22no—
239C2×D12—22no—
240C2×D12—22no—
241C2×D12—22no—
242C2×D12—22no—
243C2×D12—22no—
244C2×D12—22no—
245C2×D12—22no—
246C2×D12—22no—
247C2×D12—22no—
248C2×D12—22no—
249C2×D12—22no—
250C2×D12—41no—
251C2×D12—41no—
252C2×D12—41no—
253C2×D12—41no—
254C2×D12—41no—
255C2×D12—41no—
256C2×D12—41no—
257C2×D12—41no—
258C2×D12—41no—
259C2×D12—41no—
260C2×D12—41no—
261C2×D12—41no—
262C2×D12C22⋊C414yescomplemented
263C3×C4⋊C4—22no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—41no—
266C3×C4⋊C4—41no—
267C3×C22⋊C4—416no—
268C3×C42—41no—
269C3×C42—41no—
270C3×C42—41no—
271C3×C42—41no—
272#213—232no—
273(C2×D3)⋊C4—416no—
274C4⋊Dic3—22no—
275C4⋊Dic3—22no—
276C4⋊Dic3—41no—
277C4⋊Dic3—41no—
278C2×C3⋊C8—22no—
279C2×C3⋊C8—22no—
280C2×C3⋊C8—22no—
281C2×C3⋊C8—22no—
282C2×C3⋊C8—22no—
283C2×C3⋊C8—22no—
284C2×C3⋊C8—22no—
285C2×C3⋊C8—22no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8—41no—
288C2×C3⋊C8—41no—
289C2×C3⋊C8—41no—
290C2×C3⋊C8—41no—
291C2×C3⋊C8C22⋊C414yescomplemented
292C25—21no—
293C25—61no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—32no—
306C22×D4—32no—
307C22×D4—32no—
308C22×D4—61no—
309C22×D4—61no—
310C22×D4—61no—
311C22×D4—61no—
312C22×D4—61no—
313C22×D4—61no—
314C22×D4—61no—
315C22×D4—61no—
316C22×D4—61no—
317C22×D4—61no—
318C22×D4—61no—
319C22×D4C4×D312yes—
320C22×D4D1212yes—
321C22×D4#6712yes—
322C23×C4—21no—
323C23×C4—61no—
324C23×C4#6712yes—
325C23×C4C22×D311yescharacteristic
326C2×D8—68no—
327C2×D8—68no—
328C2×D8—68no—
329C2×D8—68no—
330C2×D8—68no—
331C2×D8—68no—
332C2×D8—68no—
333C22×C8—32no—
334C22×C8—32no—
335C22×C8—32no—
336C22×C8—32no—
337C22×C8—61no—
338C22×C8—61no—
339C22×C8—61no—
340C22×C8—61no—
341C22×C8—61no—
342C22×C8—61no—
343C22×C8—61no—
344C22×C8—61no—
345C22×C8—61no—
346C22×C8—61no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—32no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4#6712yes—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—68no—
363C2×C22⋊C4—124no—
364C2×C22⋊C4—124no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371#102—68no—
372#102—68no—
373C23×C3—24no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—44no—
381C23×C3—44no—
382C23×C3—44no—
383C23×C3—44no—
384C23×C3—44no—
385C23×C3—44no—
386C23×C3—82no—
387C23×C3—82no—
388C23×C3—82no—
389C23×C3—82no—
390C23×C3—82no—
391C23×C3—82no—
392C23×C3—81no—
393C23×C3—81no—
394C23×C3—81no—
395C23×C3—81no—
396C23×C3C4×D411yescharacteristic
397C23×C3#12011yescharacteristic
398C23×C3#12011yescharacteristic
399C23×C3#12111yescharacteristic
400C23×C3#12111yescharacteristic
401C23×C3#12111yescharacteristic
402C23×C3#12711yescharacteristic
403C23×C3C2×D812yes—
404C23×C3#13512yes—
405C23×C3AGL(1,ℤ/8)12yes—
406C23×C3AGL(1,ℤ/8)12yes—
407C22×D3—24no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3—44no—
415C22×D3—44no—
416C22×D3—44no—
417C22×D3—44no—
418C22×D3—44no—
419C22×D3—44no—
420C22×D3—82no—
421C22×D3—82no—
422C22×D3—82no—
423C22×D3—82no—
424C22×D3—82no—
425C22×D3—82no—
426C22×D3—81no—
427C22×D3—81no—
428C22×D3—81no—
429C22×D3—81no—
430C3×D4—24no—
431C3×D4—24no—
432C3×D4—42no—
433C3×D4—42no—
434C3×D4—42no—
435C3×D4—42no—
436C3×D4—42no—
437C3×D4—42no—
438C2×C3×C4—24no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—44no—
447C2×C3×C4—82no—
448C2×C3×C4—81no—
449C2×C3×C4—81no—
450C2×C3×C4C2×C22⋊C411yescharacteristic
451C2×C3×C4C2×C22⋊C411yescharacteristic
452C2×C3×C4C2×C22⋊C411yescharacteristic
453C2×C3×C4C4×D411yescharacteristic
454C2×C3×C4C4×D411yescharacteristic
455C2×C3×C4C4×D411yescharacteristic
456C2×C3×C4#12011yescharacteristic
457C2×C3×C4#12011yescharacteristic
458C2×C3×C4#12011yescharacteristic
459C2×C3×C4#12011yescharacteristic
460C2×C3×C4#12011yescharacteristic
461C2×C3×C4#12011yescharacteristic
462C2×C3×C4#12111yescharacteristic
463C2×C3×C4#12111yescharacteristic
464C2×C3×C4#12111yescharacteristic
465C2×C3×C4#12111yescharacteristic
466C2×C3×C4#12111yescharacteristic
467C2×C3×C4#12111yescharacteristic
468C2×C3×C4#12111yescharacteristic
469C2×C3×C4#12111yescharacteristic
470C2×C3×C4#12111yescharacteristic
471C2×C3×C4#12311yescharacteristic
472C2×C3×C4#12311yescharacteristic
473C2×C3×C4#12311yescharacteristic
474C2×C3×C4#12311yescharacteristic
475C2×C3×C4#12411yescharacteristic
476C2×C3×C4#12411yescharacteristic
477C2×C3×C4#12711yescharacteristic
478C2×Dic3—42no—
479C2×Dic3—44no—
480C2×Dic3—82no—
481C2×Dic3—81no—
482C2×Dic3—81no—
483D12—24no—
484D12—24no—
485D12—42no—
486D12—42no—
487D12—42no—
488D12—42no—
489D12—42no—
490D12—42no—
491C3⋊C8—24no—
492C3⋊C8—42no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—42no—
497C24—42no—
498C24—41no—
499C24—41no—
500C24—41no—
501C24—41no—
502C24—42no—
503C24—42no—
504C24—62no—
505C24—62no—
506C24—62no—
507C24—121no—
508C24—122no—
509C24—122no—
510C24—121no—
511C24—121no—
512C24—122no—
513C24—122no—
514C24—121no—
515C24C2×#6711yescharacteristic
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—34no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—62no—
547C2×D4—62no—
548C2×D4—62no—
549C2×D4—62no—
550C2×D4—62no—
551C2×D4—62no—
552C2×D4—62no—
553C2×D4—62no—
554C2×D4—62no—
555C2×D4—62no—
556C2×D4—62no—
557C2×D4—62no—
558C2×D4—62no—
559C2×D4—121no—
560C2×D4—121no—
561C2×D4—121no—
562C2×D4—121no—
563C2×D4—121no—
564C2×D4—121no—
565C2×D4—121no—
566C2×D4—121no—
567C2×D4—121no—
568C2×D4—121no—
569C2×D4—121no—
570C2×D4—121no—
571C2×D4(C2×D3)⋊C414yescomplemented
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—62no—
584C22×C4—121no—
585C22×C4—122no—
586C22×C4—121no—
587C22×C4—122no—
588C22×C4#21314yescomplemented
589C22×C4C2×C4×D311yescharacteristic
590C22×C4C2×D1211yescharacteristic
591C22×C4#23511yescharacteristic
592C22×C4#23511yescharacteristic
593C22×C4D3×D411yescharacteristic
594C22×C4D3×D411yescharacteristic
595C22×C4D3×D411yescharacteristic
596C22×C4D3×D411yescharacteristic
597C22×C4D3×D411yescharacteristic
598C22×C4D3×D411yescharacteristic
599C22×C4#23711yescharacteristic
600C22×C4#23711yescharacteristic
601C22×C4C2×#6711yescharacteristic
602C22×C4C2×#6711yescharacteristic
603D8—632no—
604C2×C8—34no—
605C2×C8—62no—
606C2×C8—62no—
607C2×C8—62no—
608C2×C8—62no—
609C2×C8—62no—
610C2×C8—62no—
611C2×C8—62no—
612C2×C8—62no—
613C2×C8—62no—
614C2×C8—121no—
615C2×C8—121no—
616C2×C8—121no—
617C2×C8—121no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—62no—
623C4⋊C4—62no—
624C4⋊C4—121no—
625C4⋊C4—121no—
626C22⋊C4—416no—
627C22⋊C4—1216no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C22×C3—48no—
633C22×C3—44no—
634C22×C3—84no—
635C22×C3—84no—
636C22×C3—82no—
637C22×C3—82no—
638C22×C3—84no—
639C22×C3—82no—
640C22×C3—82no—
641C22×C3—82no—
642C22×C3—82no—
643C22×C3#38611yescharacteristic
644C22×C3#38611yescharacteristic
645C22×C3#39011yescharacteristic
646C22×C3#39211yescharacteristic
647C22×C3#39211yescharacteristic
648C22×C3#39211yescharacteristic
649C22×C3#39411yescharacteristic
650C22×C3C4×D812yes—
651C22×C3#44212yes—
652C22×C3#44712yes—
653C22×C3#44712yes—
654C22×C3#44912yes—
655C22×C3#44912yes—
656C22×C3#45912yes—
657C22×C3#45912yes—
658C22×C3#46312yes—
659C22×C3#46312yes—
660C22×C3#46612yes—
661C22×C3#46912yes—
662C22×C3#49311yescharacteristic
663C22×C3#49511yescharacteristic
664C22×C3#49611yescharacteristic
665C22×C3#49611yescharacteristic
666C2×D3—48no—
667C2×D3—44no—
668C2×D3—84no—
669C2×D3—84no—
670C2×D3—82no—
671C2×D3—82no—
672C2×D3—84no—
673C2×D3—82no—
674C2×D3—82no—
675C2×D3—82no—
676C2×D3—82no—
677C3×C4—44no—
678C3×C4—82no—
679C3×C4#37911yescharacteristic
680C3×C4#38611yescharacteristic
681C3×C4#38611yescharacteristic
682C3×C4#39011yescharacteristic
683C3×C4#39211yescharacteristic
684C3×C4#39411yescharacteristic
685C3×C4#39411yescharacteristic
686C3×C4#39411yescharacteristic
687Dic3—82no—
688C23—24no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—42no—
695C23—42no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—64no—
702C23—82no—
703C23—82no—
704C23—82no—
705C23—82no—
706C23—82no—
707C23—81no—
708C23—81no—
709C23—82no—
710C23—81no—
711C23—81no—
712C23—122no—
713C23—122no—
714C23—122no—
715C23—122no—
716C23—122no—
717C23—122no—
718C23—124no—
719C23—124no—
720C23—124no—
721C23—124no—
722C23—124no—
723C23—124no—
724C23—242no—
725C23—242no—
726C23—242no—
727C23—242no—
728C23—242no—
729C23—242no—
730C23—241no—
731C23—241no—
732C23—241no—
733C23—241no—
734C23C4×#6711yescharacteristic
735C23#93011yescharacteristic
736C23C2×#21312yes—
737C23#93212yes—
738C23#93711yescharacteristic
739C23#93811yescharacteristic
740C23#93911yescharacteristic
741C23#94011yescharacteristic
742C23#94912yes—
743C23#95012yes—
744C23#95311yescharacteristic
745D4—24no—
746D4—24no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—42no—
752D4—42no—
753D4—64no—
754D4—64no—
755D4—122no—
756D4—122no—
757D4—122no—
758D4—122no—
759D4—122no—
760D4—122no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—82no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—122no—
774C2×C4—124no—
775C2×C4—242no—
776C2×C4—241no—
777C2×C4—241no—
778C2×C4D3×C22⋊C411yescharacteristic
779C2×C4D3×C22⋊C411yescharacteristic
780C2×C4#67⋊C411yescharacteristic
781C2×C4#67⋊C411yescharacteristic
782C2×C4#88211yescharacteristic
783C2×C4#88211yescharacteristic
784C2×C4#88211yescharacteristic
785C2×C4#88311yescharacteristic
786C2×C4#88311yescharacteristic
787C2×C4#88411yescharacteristic
788C2×C4#88411yescharacteristic
789C2×C4#88411yescharacteristic
790C2×C4#88411yescharacteristic
791C2×C4#88511yescharacteristic
792C2×C4#88511yescharacteristic
793C2×C4#88611yescharacteristic
794C2×C4C2×(C2×D3)⋊C411yescharacteristic
795C2×C4C4×#6711yescharacteristic
796C2×C4#92911yescharacteristic
797C2×C4#93011yescharacteristic
798C2×C4#93711yescharacteristic
799C2×C4#93711yescharacteristic
800C2×C4#93711yescharacteristic
801C2×C4#93811yescharacteristic
802C2×C4#93911yescharacteristic
803C2×C4#93911yescharacteristic
804C2×C4#93911yescharacteristic
805C2×C4#94011yescharacteristic
806C8—64no—
807C8—122no—
808C2×C3—84no—
809C2×C3#143811yescharacteristic
810C2×C3#187912yes—
811C2×C3#187912yes—
812C2×C3#197011yescharacteristic
813C2×C3#197211yescharacteristic
814C2×C3#199912yes—
815C2×C3#201111yescharacteristic
816C2×C3#201111yescharacteristic
817C2×C3#201211yescharacteristic
818C2×C3#201211yescharacteristic
819C2×C3#205412yes—
820D3—84no—
821C22—44no—
822C22—48no—
823C22—84no—
824C22—82no—
825C22—82no—
826C22—84no—
827C22—84no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—128no—
833C22—124no—
834C22—244no—
835C22—242no—
836C22—242no—
837C22—244no—
838C22—242no—
839C22—242no—
840C22—242no—
841C22—242no—
842C22—244no—
843C22#495611yescharacteristic
844C22#495711yescharacteristic
845C22#496011yescharacteristic
846C22#496111yescharacteristic
847C22C4×#21312yes—
848C22#501412yes—
849C22#501512yes—
850C22#501612yes—
851C22#503612yes—
852C22#503712yes—
853C22#503812yes—
854C22#503912yes—
855C22#505712yes—
856C22#505811yescharacteristic
857C22#505911yescharacteristic
858C22#507212yes—
859C22#507311yescharacteristic
860C22#507411yescharacteristic
861C22#521311yescharacteristic
862C22#521712yes—
863C22#522311yescharacteristic
864C22#522311yescharacteristic
865C22#523812yes—
866C4—44no—
867C4—82no—
868C4—242no—
869C4#495511yescharacteristic
870C4#495611yescharacteristic
871C4#495711yescharacteristic
872C4#495811yescharacteristic
873C4#495911yescharacteristic
874C4#495911yescharacteristic
875C4#496011yescharacteristic
876C4#496111yescharacteristic
877C3#1102211yescharacteristic, complemented, Sylow
878C2—84no—
879C2—244no—
880C2#6964711yescharacteristic
881C2#6964811yescharacteristic
882C2#6965012yes—
883C2#6965712yes—
884C2#6965811yescharacteristic
885C2#6965911yescharacteristic
886C2#7155011yescharacteristic
887C2#7161312yes—
888C2#7168412yes—
889C2#7172811yescharacteristic
890C2#7176711yescharacteristic
subgroupG/H
centerC24C2×#67
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#390C2
socleC24×C3C2×D4
prime radicalC23×#213C2
cosocleC23×C3×C4C23
hypercenterC2×#390D3
hypocenterC3#11022
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×C3×#390C2semidirect
3. C22×#832C2semidirect
4. C22×#809C2semidirect
5. C2×#4939C2semidirect
6. C2×#4529C2semidirect
7. C2×#4524C2semidirect
20. C22×#213C4semidirect
41. C2×#390D3semidirect
203. C2×C3×D4C22⋊C4semidirect
215. C22×C3×C4D8semidirect
262. C2×D12C22⋊C4semidirect
291. C2×C3⋊C8C22⋊C4semidirect
571. C2×D4(C2×D3)⋊C4semidirect
588. C22×C4#213semidirect
877. C3#11022semidirect

Maximal subgroups

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

subgroupindex
C23×#2132
C2×C3×#3902
C22×#8322
C22×#8092
C2×#49392
C2×#45292
C2×#45242
#110223