Finite Group Databasebeta

← #10701983

Subgroups — #10701983

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
2C22×C3×#102C211yesmaximal, characteristic, complemented
3C2×#5221C211yesmaximal, characteristic, complemented
4C22×#821C211yesmaximal, characteristic, complemented
5C2×#4988C211yesmaximal, characteristic, complemented
6C2×#4550C211yesmaximal, characteristic, complemented
7C2×#4529C211yesmaximal, characteristic, complemented
8#11022—31nomaximal, Sylow
9C23×C3×D4C2211yescharacteristic
10C23×D12C2211yescharacteristic
11C23×C3×C8C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C22×#217—22no—
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
23C22×C4×Dic3C2211yescharacteristic
24C23×C3⋊C8C2211yescharacteristic
25C2×C3×#102—22no—
26C2×C3×#102—22no—
27C2×C3×#102—22no—
28#5221—22no—
29#5221—22no—
30C2×#821—22no—
31C2×#821—22no—
32C2×#821—22no—
33#4988—22no—
34#4988—22no—
35#4550—22no—
36#4529—22no—
37C23×D8—31no—
38C22×#102—31no—
39C22×#102D311yescharacteristic, complemented
40C2×#390—31no—
41C2×#390—31no—
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×C4C2311yescharacteristic
62C23×Dic3—21no—
63C23×Dic3D412yes—
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—
78C22×C3×C8—21no—
79C22×C3×C8—21no—
80C22×C3×C8—21no—
81C22×C3×C8—21no—
82C22×C3×C8—21no—
83C22×C3×C8—21no—
84C22×C3×C8D412yes—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4D412yes—
91C2×#217—28no—
92C2×#217—44no—
93C2×#217—44no—
94C2×#213—28no—
95C2×#213—28no—
96C2×#213—28no—
97C2×#213—28no—
98C2×#213—28no—
99C2×#213—28no—
100C2×#213—28no—
101C2×(C2×D3)⋊C4—28no—
102C2×(C2×D3)⋊C4—44no—
103C2×(C2×D3)⋊C4—44no—
104C2×C4⋊Dic3—21no—
105C2×C4⋊Dic3—21no—
106C2×C4⋊Dic3—21no—
107C2×C4⋊Dic3—21no—
108C2×C4⋊Dic3—21no—
109C2×C4⋊Dic3D412yes—
110C2×C4×Dic3—21no—
111C2×C4×Dic3—21no—
112C2×C4×Dic3—21no—
113C2×C4×Dic3—21no—
114C2×C4×Dic3—21no—
115C2×C4×Dic3—21no—
116C22×C3⋊C8—21no—
117C22×C3⋊C8—21no—
118C22×C3⋊C8—21no—
119C22×C3⋊C8—21no—
120C22×C3⋊C8C2×C412yes—
121C22×C3⋊C8D412yes—
122C22×C3⋊C8D412yes—
123C3×#102—28no—
124#821—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×C8C2×D311yescharacteristic
136C22×C4⋊C4—31no—
137C22×C4⋊C4C2×D311yescharacteristic
138C22×C22⋊C4—62no—
139C22×C22⋊C4—62no—
140C22×C42—31no—
141C2×#102—22no—
142C2×#102—22no—
143C2×#102—22no—
144C2×#102—62no—
145C2×#102—62no—
146C2×#102—62no—
147#390—62no—
148#390—62no—
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—41no—
206C22×C3×C4—41no—
207C22×C3×C4—42no—
208C22×C3×C4—42no—
209C22×C3×C4C22×C411yescharacteristic
210C22×C3×C4C2×D411yescharacteristic
211C22×C3×C4C2×D411yescharacteristic
212C22×C3×C4C2×D411yescharacteristic
213C22×C3×C4C2×D411yescharacteristic
214C22×C3×C4C2×D411yescharacteristic
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4#4111yescharacteristic
220C22×C3×C4#4111yescharacteristic
221C22×C3×C4#4111yescharacteristic
222C22×C3×C4#4111yescharacteristic
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—41no—
231C22×Dic3—41no—
232C22×Dic3—42no—
233C22×Dic3—42no—
234C22×Dic3D814yescomplemented
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
263C2×C3×C8—22no—
264C2×C3×C8—22no—
265C2×C3×C8—22no—
266C2×C3×C8—41no—
267C2×C3×C8—41no—
268C2×C3×C8—41no—
269C2×C3×C8—41no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—41no—
273C3×C4⋊C4—41no—
274#217—416no—
275#213—232no—
276(C2×D3)⋊C4—416no—
277C4⋊Dic3—22no—
278C4⋊Dic3—22no—
279C4⋊Dic3—41no—
280C4⋊Dic3—41no—
281C4×Dic3—41no—
282C4×Dic3—41no—
283C4×Dic3—41no—
284C4×Dic3—41no—
285C2×C3⋊C8—22no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8—22no—
288C2×C3⋊C8—22no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—22no—
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—32no—
324C23×C4—61no—
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—21no—
334C22×C8—21no—
335C22×C8—21no—
336C22×C8—21no—
337C22×C8—21no—
338C22×C8—21no—
339C22×C8—32no—
340C22×C8—32no—
341C22×C8—32no—
342C22×C8—61no—
343C22×C8—61no—
344C22×C8—61no—
345C22×C8—61no—
346C22×C8#6712yes—
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—68no—
360C2×C22⋊C4—68no—
361C2×C22⋊C4—124no—
362C2×C22⋊C4—124no—
363C2×C22⋊C4—124no—
364C2×C22⋊C4—124no—
365C2×C42—61no—
366C2×C42—61no—
367C2×C42—61no—
368C2×C42—61no—
369C2×C42—61no—
370C2×C42—61no—
371#102—28no—
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—42no—
439C2×C3×C4—44no—
440C2×C3×C4—82no—
441C2×C3×C4—81no—
442C2×C3×C4—81no—
443C2×C3×C4C2×C22⋊C411yescharacteristic
444C2×C3×C4C2×C22⋊C411yescharacteristic
445C2×C3×C4C2×C22⋊C411yescharacteristic
446C2×C3×C4C4×D411yescharacteristic
447C2×C3×C4C4×D411yescharacteristic
448C2×C3×C4C4×D411yescharacteristic
449C2×C3×C4#12011yescharacteristic
450C2×C3×C4#12011yescharacteristic
451C2×C3×C4#12011yescharacteristic
452C2×C3×C4#12011yescharacteristic
453C2×C3×C4#12011yescharacteristic
454C2×C3×C4#12011yescharacteristic
455C2×C3×C4#12111yescharacteristic
456C2×C3×C4#12111yescharacteristic
457C2×C3×C4#12111yescharacteristic
458C2×C3×C4#12111yescharacteristic
459C2×C3×C4#12111yescharacteristic
460C2×C3×C4#12111yescharacteristic
461C2×C3×C4#12111yescharacteristic
462C2×C3×C4#12111yescharacteristic
463C2×C3×C4#12111yescharacteristic
464C2×C3×C4#12311yescharacteristic
465C2×C3×C4#12311yescharacteristic
466C2×C3×C4#12311yescharacteristic
467C2×C3×C4#12311yescharacteristic
468C2×C3×C4#12411yescharacteristic
469C2×C3×C4#12411yescharacteristic
470C2×C3×C4#12711yescharacteristic
471C2×Dic3—24no—
472C2×Dic3—24no—
473C2×Dic3—24no—
474C2×Dic3—42no—
475C2×Dic3—42no—
476C2×Dic3—42no—
477C2×Dic3—42no—
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—42no—
492C3⋊C8—24no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—41no—
497C24—41no—
498C24—42no—
499C24—42no—
500C24—42no—
501C24—42no—
502C24—41no—
503C24—41no—
504C24—62no—
505C24—62no—
506C24—62no—
507C24—121no—
508C24—121no—
509C24—122no—
510C24—122no—
511C24—122no—
512C24—122no—
513C24—121no—
514C24—121no—
515C24D3×D411yescharacteristic
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—34no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4—62no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—121no—
586C22×C4—122no—
587C22×C4—122no—
588C22×C4—121no—
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×C4#23711yescharacteristic
599C22×C4#23711yescharacteristic
600C22×C4C2×#6711yescharacteristic
601C22×C4C2×#6711yescharacteristic
602C22×C4C2×#6711yescharacteristic
603D8—632no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—34no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—62no—
613C2×C8—62no—
614C2×C8—62no—
615C2×C8—62no—
616C2×C8—62no—
617C2×C8—62no—
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—1216no—
627C22⋊C4—1216no—
628C42—121no—
629C42—121no—
630C42—121no—
631C42—121no—
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—82no—
678C3×C4#37911yescharacteristic
679C3×C4#38611yescharacteristic
680C3×C4#38611yescharacteristic
681C3×C4#39011yescharacteristic
682C3×C4#39211yescharacteristic
683C3×C4#39411yescharacteristic
684C3×C4#39411yescharacteristic
685C3×C4#39411yescharacteristic
686Dic3—44no—
687Dic3—82no—
688C23—24no—
689C23—44no—
690C23—44no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—64no—
702C23—81no—
703C23—81no—
704C23—82no—
705C23—81no—
706C23—82no—
707C23—81no—
708C23—82no—
709C23—82no—
710C23—82no—
711C23—82no—
712C23—124no—
713C23—124no—
714C23—122no—
715C23—122no—
716C23—122no—
717C23—122no—
718C23—122no—
719C23—122no—
720C23—124no—
721C23—124no—
722C23—124no—
723C23—124no—
724C23—242no—
725C23—241no—
726C23—241no—
727C23—242no—
728C23—241no—
729C23—241no—
730C23—242no—
731C23—242no—
732C23—242no—
733C23—242no—
734C23#67⋊C411yescharacteristic
735C23#88211yescharacteristic
736C23#88411yescharacteristic
737C23#88411yescharacteristic
738C23D3×D812yes—
739C23#91112yes—
740C23#91412yes—
741C23#91612yes—
742C23#93711yescharacteristic
743C23#93911yescharacteristic
744C23#94011yescharacteristic
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—44no—
762C2×C4—42no—
763C2×C4—64no—
764C2×C4—64no—
765C2×C4—64no—
766C2×C4—82no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4—122no—
773C2×C4—122no—
774C2×C4—124no—
775C2×C4—241no—
776C2×C4—241no—
777C2×C4—242no—
778C2×C4D3×C22⋊C411yescharacteristic
779C2×C4D3×C22⋊C411yescharacteristic
780C2×C4#67⋊C411yescharacteristic
781C2×C4#88211yescharacteristic
782C2×C4#88211yescharacteristic
783C2×C4#88311yescharacteristic
784C2×C4#88311yescharacteristic
785C2×C4#88411yescharacteristic
786C2×C4#88411yescharacteristic
787C2×C4#88511yescharacteristic
788C2×C4#88511yescharacteristic
789C2×C4#88611yescharacteristic
790C2×C4C2×(C2×D3)⋊C411yescharacteristic
791C2×C4C4×#6711yescharacteristic
792C2×C4C4×#6711yescharacteristic
793C2×C4#92911yescharacteristic
794C2×C4#93011yescharacteristic
795C2×C4#93011yescharacteristic
796C2×C4#93711yescharacteristic
797C2×C4#93711yescharacteristic
798C2×C4#93711yescharacteristic
799C2×C4#93811yescharacteristic
800C2×C4#93811yescharacteristic
801C2×C4#93911yescharacteristic
802C2×C4#93911yescharacteristic
803C2×C4#93911yescharacteristic
804C2×C4#94011yescharacteristic
805C2×C4#95311yescharacteristic
806C8—42no—
807C8—64no—
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—48no—
822C22—44no—
823C22—82no—
824C22—82no—
825C22—84no—
826C22—84no—
827C22—82no—
828C22—84no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—128no—
833C22—124no—
834C22—244no—
835C22—242no—
836C22—242no—
837C22—244no—
838C22—242no—
839C22—244no—
840C22—242no—
841C22—242no—
842C22—242no—
843C22#475612yes—
844C22#477312yes—
845C22#477512yes—
846C22#478112yes—
847C22#478212yes—
848C22#478512yes—
849C22#478612yes—
850C22#478712yes—
851C22#495611yescharacteristic
852C22#495711yescharacteristic
853C22#495811yescharacteristic
854C22#495911yescharacteristic
855C22#496011yescharacteristic
856C22#496011yescharacteristic
857C22#515012yes—
858C22#515111yescharacteristic
859C22#515411yescharacteristic
860C22#515612yes—
861C22#516512yes—
862C22#516811yescharacteristic
863C22#517212yes—
864C22#517611yescharacteristic
865C22#522311yescharacteristic
866C4—82no—
867C4—124no—
868C4—242no—
869C4#495511yescharacteristic
870C4#495611yescharacteristic
871C4#495711yescharacteristic
872C4#495911yescharacteristic
873C4#496111yescharacteristic
874C4#496111yescharacteristic
875C4#521311yescharacteristic
876C4#522311yescharacteristic
877C3#1102211yescharacteristic, complemented, Sylow
878C2—84no—
879C2—244no—
880C2#7017212yes—
881C2#7019011yescharacteristic
882C2#7019111yescharacteristic
883C2#7020412yes—
884C2#7020812yes—
885C2#7020911yescharacteristic
886C2#7021212yes—
887C2#7021411yescharacteristic
888C2#7155011yescharacteristic
889C2#7204411yescharacteristic
890C2#7205511yescharacteristic
subgroupG/H
centerC24D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC22×C3×#102C2
socleC24×C3C2×D4
prime radicalC23×#213C2
cosocleC23×C3×C4C23
hypercenterC22×#102D3
hypocenterC3#11022
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×C3×#102C2semidirect
3. C2×#5221C2semidirect
4. C22×#821C2semidirect
5. C2×#4988C2semidirect
6. C2×#4550C2semidirect
7. C2×#4529C2semidirect
20. C22×#213C4semidirect
39. C22×#102D3semidirect
203. C2×C3×D4C22⋊C4semidirect
234. C22×Dic3D8semidirect
262. C2×D12C22⋊C4semidirect
291. C2×C3⋊C8C22⋊C4semidirect
571. C2×D4(C2×D3)⋊C4semidirect
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
C22×C3×#1022
C2×#52212
C22×#8212
C2×#49882
C2×#45502
C2×#45292
#110223