Finite Group Databasebeta

← #10826969

Subgroups — #10826969

Order 768.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5606C211yesmaximal, characteristic, complemented
2C2×#5524C211yesmaximal, characteristic, complemented
3C2×#5037C211yesmaximal, characteristic, complemented
4C2×#4783C211yesmaximal, characteristic, complemented
5C2×#4781C211yesmaximal, characteristic, complemented
6C2×#4733C211yesmaximal, characteristic, complemented
7C3×#1875C211yesmaximal, characteristic, complemented
8#71585C211yesmaximal, characteristic, complemented
9#70205C211yesmaximal, characteristic, complemented
10#70204C211yesmaximal, characteristic, complemented
11#69955C211yesmaximal, characteristic, complemented
12#68888C211yesmaximal, characteristic, complemented
13#68887C211yesmaximal, characteristic, complemented
14#68881C211yesmaximal, characteristic, complemented
15#68879C211yesmaximal, characteristic, complemented
16#23923—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×#117C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C2×#937—21no—
24C2×D4×Dic3—21no—
25C22×#214C2211yescharacteristic, complemented
26C22×#213C2211yescharacteristic, complemented
27C2×#924C2211yescharacteristic
28C22×Dic12C2211yescharacteristic, complemented
29C22×#204C2211yescharacteristic, complemented
30#5606—24no—
31#5606—24no—
32#5524—24no—
33#5524—24no—
34C2×#897C2211yescharacteristic
35C2×#897C2211yescharacteristic
36C2×#897C2211yescharacteristic
37C2×#895C2211yescharacteristic
38C2×#895C2211yescharacteristic
39C2×#892C2211yescharacteristic
40C2×#886—21no—
41C2×#883—21no—
42C2×#882—21no—
43C2×#67⋊C4—21no—
44C2×C4×D12—21no—
45C2×C4×D12—21no—
46C2×C3×#102C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic, complemented
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×#830C2211yescharacteristic
50C2×#821C2211yescharacteristic, complemented
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×#816C2211yescharacteristic, complemented
56#5037—24no—
57C2×#810C2211yescharacteristic, complemented
58C2×#810C2211yescharacteristic, complemented
59C2×#810C2211yescharacteristic, complemented
60C2×#809C2211yescharacteristic, complemented
61#4783—24no—
62#4781—24no—
63#4733—24no—
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C2×#525—31no—
69C2×#525—31no—
70C2×#452—31no—
71C2×#452—31no—
72C2×#449—31no—
73C2×#449—31no—
74#2001—31no—
75#2000—31no—
76#2000—31no—
77#1999—31no—
78#1875—31no—
79#1875D311yescharacteristic, complemented
80#1873—31no—
81#1873—31no—
82#1779—31no—
83C24×D3D411yescharacteristic
84C22×C3×D4—21no—
85C22×C3×D4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—21no—
88C22×#67—21no—
89C22×#67—21no—
90C23×Dic3—21no—
91C23×Dic3D411yescharacteristic
92C2×#237—22no—
93C2×#237—22no—
94C2×#237—22no—
95C2×#237—22no—
96C2×#237—41no—
97C2×#237—41no—
98C2×#235—22no—
99C2×#235—22no—
100C2×#235—22no—
101C2×#235—22no—
102C2×#235—41no—
103C2×#235—41no—
104C22×D12—21no—
105C22×D12—21no—
106C22×D12C2311yescharacteristic
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—21no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3—41no—
113C22×C4×D3—41no—
114C22×C4×D3D411yescharacteristic
115C22×C4×D3D411yescharacteristic
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×Dic6C2311yescharacteristic
119C22×Dic6C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2311yescharacteristic
122C3×#121—22no—
123C3×#121D414yescomplemented
124C3×#117—22no—
125C3×#117—22no—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C42—21no—
132C2×#217—21no—
133C2×#217—21no—
134#938—22no—
135#938—22no—
136#937—28no—
137D4×Dic3—28no—
138C2×#214—22no—
139C2×#214—22no—
140C2×#214—41no—
141C2×#213—22no—
142C2×#213—22no—
143C2×#213—41no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4—21no—
147C2×(C2×D3)⋊C4—21no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4—21no—
150C2×C4⋊Dic3—21no—
151C2×C4⋊Dic3—21no—
152C2×C4⋊Dic3—21no—
153C2×C4⋊Dic3C2311yescharacteristic
154#924—22no—
155#924D414yescomplemented
156C2×Dic3⋊C4—21no—
157C2×C4×Dic3—21no—
158C22×C3⋊C8C2311yescharacteristic
159C22×C3⋊C8C2311yescharacteristic
160C2×Dic12—22no—
161C2×Dic12—22no—
162C2×Dic12—41no—
163C2×#204—22no—
164C2×#204—22no—
165C2×#204—41no—
166#897—22no—
167#897—22no—
168#897—22no—
169#897—22no—
170#897—22no—
171#897D414yescomplemented
172#895—22no—
173#895—22no—
174#895—22no—
175#895D414yescomplemented
176#892—22no—
177#892—22no—
178#886—28no—
179#883—28no—
180#882—28no—
181#67⋊C4—28no—
182C4×D12—28no—
183C4×D12—28no—
184C3×#102—22no—
185C3×#102—22no—
186C3×C22⋊C8—22no—
187#830—22no—
188#821—22no—
189(C2×D3)⋊C8—22no—
190(C2×D3)⋊C8—22no—
191(C2×D3)⋊C8—41no—
192(C2×D3)⋊C8—41no—
193#816—22no—
194#810—22no—
195#810—22no—
196#810—22no—
197#809—22no—
198C22×#41—31no—
199C22×#41—31no—
200C24×C4—31no—
201C22×Q16—31no—
202C22×SD16—31no—
203C22×SD16—31no—
204C22×D8—31no—
205#525—64no—
206#525—64no—
207#525—64no—
208#525—64no—
209C2×#123—61no—
210C2×#123—61no—
211C2×C22⋊Q8—31no—
212C2×C22⋊Q8—31no—
213C2×C22⋊Q8—31no—
214C2×C22⋊Q8—31no—
215C2×#121—31no—
216C2×#121—31no—
217C2×#121—31no—
218C2×#121C2×D311yescharacteristic
219C2×#120—61no—
220C2×#120—61no—
221C2×C4×D4—61no—
222C2×C4×D4—61no—
223C2×C4×D4—61no—
224C2×C4×D4—61no—
225C2×#117—31no—
226C2×#117C2×D311yescharacteristic
227#452—64no—
228#452—64no—
229#449—64no—
230#449—64no—
231C2×#103—31no—
232C2×#103—31no—
233C2×#103—31no—
234C2×#103—31no—
235C2×#102—31no—
236C2×#102—31no—
237C2×#102C2×D311yescharacteristic, complemented
238C2×#102C2×D311yescharacteristic, complemented
239C2×C22⋊C8—31no—
240C2×C22⋊C8—31no—
241C2×C22⋊C8—31no—
242C2×C22⋊C8—31no—
243C2×C22⋊C8—31no—
244C2×C22⋊C8C2×D311yescharacteristic
245#340—31no—
246#340—31no—
247#340C2×D311yescharacteristic, complemented
248#340C2×D311yescharacteristic, complemented
249C24×C3—21no—
250C24×C3C2×D411yescharacteristic
251C23×D3—22no—
252C23×D3—21no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—41no—
256C23×D3—41no—
257C23×D3—41no—
258C23×D3—41no—
259C23×D3C2×D411yescharacteristic
260C23×D3C2×D411yescharacteristic
261C2×C3×D4—24no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—42no—
268C2×C3×D4—42no—
269C2×C3×D4C2×D412yes—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4C2×D412yes—
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2411yescharacteristic
281C2×#67—24no—
282C2×#67—24no—
283C2×#67—24no—
284C2×#67—42no—
285C2×#67—42no—
286C2×#67—42no—
287C2×#67—42no—
288C2×#67—42no—
289C2×#67—42no—
290C22×Dic3—24no—
291C22×Dic3—22no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—22no—
296C22×Dic3—41no—
297C22×Dic3—42no—
298C22×Dic3—42no—
299C22×Dic3C2×D411yescharacteristic
300C22×Dic3C2×D411yescharacteristic
301#237—44no—
302#237—44no—
303#237—44no—
304#237—44no—
305#235—44no—
306#235—44no—
307#235—44no—
308#235—44no—
309C2×D12—21no—
310C2×D12—21no—
311C2×D12—21no—
312C2×D12—21no—
313C2×D12—24no—
314C2×D12—24no—
315C2×D12—21no—
316C2×D12—42no—
317C2×D12—42no—
318C2×D12—42no—
319C2×D12—42no—
320C2×D12C2×D412yes—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—24no—
326C2×C4×D3—22no—
327C2×C4×D3—22no—
328C2×C4×D3—22no—
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—22no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C2×C4×D3—44no—
339C2×C4×D3—44no—
340C2×C4×D3—41no—
341C2×C4×D3—41no—
342C2×C4×D3—42no—
343C2×C4×D3—42no—
344C2×C4×D3C2×D412yes—
345C2×C4×D3C2×D412yes—
346C2×Dic6—21no—
347C2×Dic6—21no—
348C2×Dic6—21no—
349C2×Dic6—21no—
350C2×Dic6—21no—
351C2×Dic6—21no—
352C2×Dic6—21no—
353C2×Dic6—21no—
354C2×Dic6—21no—
355C2×Dic6—21no—
356C2×Dic6C2×D412yes—
357C2×Dic6C2×D412yes—
358C2×C3×C8—21no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—21no—
362C2×C3×C8—21no—
363C2×C3×C8—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4C2×D412yes—
368C3×C4⋊C4C2×D412yes—
369C3×C4⋊C4C2×D412yes—
370C3×C22⋊C4—24no—
371C3×C22⋊C4—24no—
372C3×C42—24no—
373#217—24no—
374#217—24no—
375#214—44no—
376#213—44no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4—24no—
382(C2×D3)⋊C4—24no—
383C4⋊Dic3—24no—
384C4⋊Dic3—24no—
385C4⋊Dic3—21no—
386C4⋊Dic3—24no—
387C4⋊Dic3C2×D412yes—
388Dic3⋊C4—24no—
389C4×Dic3—24no—
390C2×C3⋊C8—21no—
391C2×C3⋊C8—21no—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—21no—
394C2×C3⋊C8—21no—
395C2×C3⋊C8—21no—
396Dic12—44no—
397#204—44no—
398C25—31no—
399C2×#41—62no—
400C2×#41—62no—
401C2×#41—62no—
402C2×#41—62no—
403C2×#41—62no—
404C2×#41—62no—
405C2×#41—62no—
406C2×#41—62no—
407C2×#41—121no—
408C2×#41—121no—
409C2×#41—121no—
410C2×#41—121no—
411C22×Q8—31no—
412C22×Q8—31no—
413C22×D4—21no—
414C22×D4—31no—
415C22×D4—61no—
416C22×D4—61no—
417C22×D4—61no—
418C22×D4—61no—
419C22×D4—61no—
420C22×D4C22×D311yescharacteristic
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—62no—
427C23×C4—62no—
428C23×C4—61no—
429C23×C4—62no—
430C23×C4—61no—
431C23×C4—62no—
432C23×C4—121no—
433C23×C4—121no—
434C23×C4C22×D311yescharacteristic
435C2×Q16—62no—
436C2×Q16—62no—
437C2×Q16—121no—
438C2×SD16—62no—
439C2×SD16—62no—
440C2×SD16—62no—
441C2×SD16—62no—
442C2×SD16—121no—
443C2×SD16—121no—
444C2×D8—62no—
445C2×D8—62no—
446C2×D8—121no—
447C22×C8—31no—
448C22×C8—31no—
449C22×C8C22×D311yescharacteristic
450C22×C8C22×D311yescharacteristic
451#123—68no—
452#123—68no—
453C22⋊Q8—34no—
454C22⋊Q8—34no—
455C22⋊Q8—62no—
456C22⋊Q8—62no—
457C22⋊Q8—62no—
458C22⋊Q8—62no—
459C22⋊Q8—62no—
460C22⋊Q8—62no—
461#121—22no—
462#121—34no—
463#121—62no—
464#121—62no—
465#121—62no—
466#121—62no—
467#121—62no—
468#121D1214yescomplemented
469#120—68no—
470#120—68no—
471C4×D4—68no—
472C4×D4—68no—
473C4×D4—68no—
474C4×D4—68no—
475#117—22no—
476#117—22no—
477#117—62no—
478#117—62no—
479C2×C4⋊C4—31no—
480C2×C4⋊C4—61no—
481C2×C4⋊C4—61no—
482C2×C4⋊C4—61no—
483C2×C4⋊C4—61no—
484C2×C4⋊C4C22×D311yescharacteristic
485C2×C4⋊C4C22×D311yescharacteristic
486C2×C4⋊C4C22×D311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—61no—
490C2×C22⋊C4—61no—
491C2×C22⋊C4—61no—
492C2×C22⋊C4—61no—
493C2×C22⋊C4—61no—
494C2×C22⋊C4—61no—
495C2×C22⋊C4—61no—
496C2×C22⋊C4—61no—
497C2×C42—21no—
498C2×C42—61no—
499#103—62no—
500#103—62no—
501#103—62no—
502#103—62no—
503#102—22no—
504#102—22no—
505#102—62no—
506#102—62no—
507C22⋊C8—22no—
508C22⋊C8—62no—
509C22⋊C8—62no—
510C22⋊C8—62no—
511C22⋊C8—121no—
512C22⋊C8—121no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—22no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3#12012yes—
527C23×C3C22×D411yescharacteristic
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—22no—
541C22×D3—44no—
542C22×D3—44no—
543C22×D3—44no—
544C22×D3—44no—
545C22×D3—44no—
546C22×D3—44no—
547C22×D3—44no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3#12012yes—
555C22×D3#13512yes—
556C3×D4—22no—
557C3×D4—22no—
558C3×D4—48no—
559C3×D4—41no—
560C3×D4—41no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4#12012yes—
577C2×C3×C4C22×D411yescharacteristic
578C2×C3×C4C22×D411yescharacteristic
579C2×C3×C4C22×D411yescharacteristic
580C2×C3×C4C22×D411yescharacteristic
581C2×C3×C4H(5,𝔽2)11yescharacteristic
582C2×C3×C4H(5,𝔽2)11yescharacteristic
583#67—48no—
584#67—48no—
585#67—48no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—44no—
595C2×Dic3—48no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3#12012yes—
603D12—22no—
604D12—22no—
605D12—48no—
606D12—48no—
607D12—41no—
608D12—41no—
609C4×D3—22no—
610C4×D3—22no—
611C4×D3—22no—
612C4×D3—22no—
613C4×D3—44no—
614C4×D3—44no—
615C4×D3—48no—
616C4×D3—41no—
617C4×D3—41no—
618C4×D3—41no—
619C4×D3—41no—
620Dic6—22no—
621Dic6—22no—
622Dic6—22no—
623Dic6—22no—
624Dic6—41no—
625Dic6—41no—
626Dic6—41no—
627Dic6—41no—
628C3×C8—41no—
629C3×C8—41no—
630C3⋊C8—41no—
631C3⋊C8—41no—
632C24—21no—
633C24—31no—
634C24—31no—
635C24—62no—
636C24—62no—
637C24—62no—
638C24—61no—
639C24—121no—
640C24—121no—
641C24—121no—
642C24—121no—
643C24D3×D411yescharacteristic
644#41—124no—
645#41—124no—
646#41—124no—
647#41—124no—
648#41—124no—
649#41—124no—
650#41—124no—
651#41—124no—
652C2×Q8—32no—
653C2×Q8—32no—
654C2×Q8—61no—
655C2×Q8—61no—
656C2×Q8—61no—
657C2×Q8—61no—
658C2×Q8—61no—
659C2×Q8—61no—
660C2×Q8—61no—
661C2×Q8—61no—
662C2×Q8—61no—
663C2×Q8—61no—
664C2×D4—24no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—32no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—64no—
674C2×D4—64no—
675C2×D4—64no—
676C2×D4—64no—
677C2×D4—64no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—122no—
684C2×D4—122no—
685C2×D4—122no—
686C2×D4—122no—
687C2×D4—122no—
688C2×D4—122no—
689C2×D4—122no—
690C2×D4—122no—
691C2×D4—122no—
692C2×D4—122no—
693C2×D4C2×D1212yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—31no—
702C22×C4—32no—
703C22×C4—32no—
704C22×C4—31no—
705C22×C4—62no—
706C22×C4—62no—
707C22×C4—64no—
708C22×C4—62no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—64no—
714C22×C4—62no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—62no—
719C22×C4—62no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—121no—
727C22×C4—121no—
728C22×C4—124no—
729C22×C4—124no—
730C22×C4—124no—
731C22×C4—124no—
732C22×C4—122no—
733C22×C4—122no—
734C22×C4—121no—
735C22×C4—122no—
736C22×C4—122no—
737C22×C4C2×D1212yes—
738C22×C4D3×D411yescharacteristic
739C22×C4D3×D412yes—
740C22×C4C23×D311yescharacteristic
741Q16—124no—
742SD16—124no—
743SD16—124no—
744D8—124no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—61no—
752C2×C8—61no—
753C2×C8—61no—
754C2×C8—61no—
755C2×C8—61no—
756C2×C8—61no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—32no—
761C4⋊C4—64no—
762C4⋊C4—64no—
763C4⋊C4—64no—
764C4⋊C4—64no—
765C4⋊C4—61no—
766C4⋊C4C2×D1212yes—
767C4⋊C4D3×D412yes—
768C4⋊C4D3×D412yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—64no—
772C22⋊C4—64no—
773C22⋊C4—64no—
774C22⋊C4—64no—
775C22⋊C4—64no—
776C22⋊C4—64no—
777C22⋊C4—64no—
778C22⋊C4—64no—
779C42—24no—
780C42—64no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—42no—
789C22×C3—42no—
790C22×C3—42no—
791C22×C3—81no—
792C22×C3—81no—
793C22×C3—81no—
794C22×C3—81no—
795C22×C3C2×#12011yescharacteristic
796C22×C3C2×#12011yescharacteristic
797C22×C3#53411yescharacteristic
798C22×C3C2×#13511yescharacteristic
799C22×C3#57511yescharacteristic
800C22×C3#57511yescharacteristic
801C22×C3#57511yescharacteristic
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—22no—
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—416no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—42no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—81no—
821C2×D3—81no—
822C2×D3—81no—
823C2×D3—81no—
824C3×C4—22no—
825C3×C4—42no—
826C3×C4—42no—
827C3×C4—42no—
828C3×C4D4211yescharacteristic
829C3×C4D4211yescharacteristic
830C3×C4D4211yescharacteristic
831C3×C4D4211yescharacteristic
832Dic3—22no—
833Dic3—42no—
834Dic3—42no—
835Dic3—41no—
836Dic3—42no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—22no—
844C23—32no—
845C23—32no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—61no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—62no—
865C23—124no—
866C23—124no—
867C23—124no—
868C23—124no—
869C23—124no—
870C23—124no—
871C23—124no—
872C23—121no—
873C23—121no—
874C23—121no—
875C23—121no—
876C23—121no—
877C23—121no—
878C23#88212yes—
879C23C2×D3×D411yescharacteristic
880Q8—62no—
881Q8—62no—
882Q8—62no—
883Q8—62no—
884Q8—121no—
885Q8—121no—
886Q8—121no—
887Q8—121no—
888D4—22no—
889D4—22no—
890D4—48no—
891D4—41no—
892D4—41no—
893D4—62no—
894D4—62no—
895D4—128no—
896D4—128no—
897D4—128no—
898D4—128no—
899D4—128no—
900D4—121no—
901D4—121no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—32no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—61no—
925C2×C4—62no—
926C2×C4—61no—
927C2×C4—62no—
928C2×C4—61no—
929C2×C4—62no—
930C2×C4—124no—
931C2×C4—124no—
932C2×C4—128no—
933C2×C4—124no—
934C2×C4—128no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—121no—
943C2×C4—121no—
944C2×C4—121no—
945C2×C4#88212yes—
946C2×C4C22×D1211yescharacteristic
947C2×C4C2×D3×D411yescharacteristic
948C2×C4C2×D3×D411yescharacteristic
949C2×C4C2×D3×D411yescharacteristic
950C2×C4#100911yescharacteristic
951C2×C4#100911yescharacteristic
952C8—41no—
953C8—41no—
954C8—121no—
955C8—121no—
956C2×C3—42no—
957C2×C3—82no—
958C2×C3#240311yescharacteristic
959C2×C3#300211yescharacteristic
960C2×C3#300211yescharacteristic
961C2×C3#300511yescharacteristic
962C2×C3#300511yescharacteristic
963C2×C3#319111yescharacteristic
964C2×C3#319711yescharacteristic
965D3—42no—
966D3—42no—
967D3—82no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—62no—
979C22—62no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—1216no—
989C22—121no—
990C22—121no—
991C22—121no—
992C22—121no—
993C22—121no—
994C22—121no—
995C22—121no—
996C22—121no—
997C22—122no—
998C22—122no—
999C22—122no—
1000C22—241no—
1001C22—241no—
1002C22—241no—
1003C22—241no—
1004C22C2×#88211yescharacteristic
1005C22D3×#12011yescharacteristic
1006C22#565311yescharacteristic
1007C22D3×#13511yescharacteristic
1008C22#576811yescharacteristic
1009C22#577311yescharacteristic
1010C22#577311yescharacteristic
1011C4—22no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—62no—
1016C4—121no—
1017C4—122no—
1018C4—122no—
1019C4—122no—
1020C4D4×D1211yescharacteristic
1021C4D4×D1211yescharacteristic
1022C4#560911yescharacteristic
1023C4#560911yescharacteristic
1024C3#2392311yescharacteristic, complemented, Sylow
1025C2—42no—
1026C2—82no—
1027C2—122no—
1028C2—122no—
1029C2—242no—
1030C2#7488411yescharacteristic
1031C2#7883311yescharacteristic
1032C2#7892711yescharacteristic
1033C2#8008211yescharacteristic
1034C2#8008311yescharacteristic
1035C2#8139711yescharacteristic
1036C2#8139811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1875C2
socleC23×C3C22×D4
hypercenter#1875D3
hypocenterC3#23923
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. C2×#5606C2semidirect
2. C2×#5524C2semidirect
3. C2×#5037C2semidirect
4. C2×#4783C2semidirect
5. C2×#4781C2semidirect
6. C2×#4733C2semidirect
7. C3×#1875C2semidirect
8. #71585C2semidirect
9. #70205C2semidirect
10. #70204C2semidirect
11. #69955C2semidirect
12. #68888C2semidirect
13. #68887C2semidirect
14. #68881C2semidirect
15. #68879C2semidirect
25. C22×#214C22semidirect
26. C22×#213C22semidirect
28. C22×Dic12C22semidirect
29. C22×#204C22semidirect
46. C2×C3×#102C22semidirect
47. C2×C3×#102C22semidirect
50. C2×#821C22semidirect
55. C2×#816C22semidirect
57. C2×#810C22semidirect
58. C2×#810C22semidirect
59. C2×#810C22semidirect
60. C2×#809C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
79. #1875D3semidirect
123. C3×#121D4semidirect
155. #924D4semidirect
171. #897D4semidirect
175. #895D4semidirect
237. C2×#102C2×D3semidirect
238. C2×#102C2×D3semidirect
247. #340C2×D3semidirect
248. #340C2×D3semidirect
468. #121D12semidirect
1024. C3#23923semidirect

Maximal subgroups

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

subgroupindex
C2×#56062
C2×#55242
C2×#50372
C2×#47832
C2×#47812
C2×#47332
C3×#18752
#715852
#702052
#702042
#699552
#688882
#688872
#688812
#688792
#239233