Finite Group Databasebeta

← #10847372

Subgroups — #10847372

Order 768.

1412 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5548C211yesmaximal, characteristic
2C2×#4864C211yesmaximal, characteristic, complemented
3C2×#4778C211yesmaximal, characteristic, complemented
4#76287C211yesmaximal, characteristic, complemented
5C3×#1864C211yesmaximal, characteristic, complemented
6#71612C211yesmaximal, characteristic, complemented
7#70565C211yesmaximal, characteristic, complemented
8#70211C211yesmaximal, characteristic, complemented
9#70210C211yesmaximal, characteristic, complemented
10#70202C211yesmaximal, characteristic, complemented
11#69626C211yesmaximal, characteristic, complemented
12#68910C211yesmaximal, characteristic, complemented
13#68883C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15D3×#336C211yesmaximal, characteristic, complemented
16#25495—31nomaximal, Sylow
17C22×#235—21no—
18C2×C3×C4×D4C2211yescharacteristic
19C2×#940C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C22×#214C2211yescharacteristic
22C2×C4×#67—21no—
23C22×#204C2211yescharacteristic
24C22×D3×C8C2211yescharacteristic
25C22×D3×C8C2211yescharacteristic
26#5548—24no—
27#5548—24no—
28C2×#897C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#888C2211yescharacteristic
31C2×#885—21no—
32C2×#884—21no—
33C2×C4×D12C2211yescharacteristic
34C2×C42×D3C2211yescharacteristic
35C2×C3×#106C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C3×#389C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#816C2211yescharacteristic
42#4989—21no—
43#4987C2211yescharacteristic
44#4980—21no—
45#4973C2211yescharacteristic
46#4972C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#808C2211yescharacteristic
51#4929C2211yescharacteristic
52#4864—24no—
53#4778—24no—
54#4664—21no—
55#4655—21no—
56C3×#340C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#532—31no—
65C2×#465—31no—
66C2×#465—31no—
67#2855—31no—
68#2058—31no—
69#2041—31no—
70#2024—31no—
71#2014—31no—
72#1893—31no—
73#1893—31no—
74#1877—31no—
75#1877—31no—
76#1864—31no—
77#1864D311yescharacteristic, complemented
78C2×#336—31no—
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×#67—21no—
82C22×#67—21no—
83C22×#67—21no—
84C2×#235—28no—
85C2×#235—44no—
86C2×#235—44no—
87C22×D12—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3—21no—
90C22×C4×D3D411yescharacteristic
91C22×C4×D3D411yescharacteristic
92C22×C4×D3C2311yescharacteristic
93C22×Dic6—21no—
94C22×Dic6C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×C3×C42C2311yescharacteristic
105C2×#217—21no—
106#940—22no—
107#940—22no—
108#938—22no—
109#938D414yes—
110C2×#214—22no—
111C2×#214—22no—
112C2×#214—41no—
113C4×#67—28no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3C2311yescharacteristic
120C2×C4⋊Dic3C2311yescharacteristic
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—21no—
123C2×C4×Dic3D411yescharacteristic
124C2×C4×Dic3D411yescharacteristic
125C2×C4×Dic3C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128C2×#204—22no—
129C2×#204—22no—
130C2×#204—41no—
131C2×D3×C8—22no—
132C2×D3×C8—22no—
133C2×D3×C8—22no—
134C2×D3×C8—22no—
135C2×D3×C8—41no—
136C2×D3×C8—41no—
137#897—22no—
138#897—22no—
139#895—22no—
140#895D414yes—
141#888—22no—
142#888—22no—
143#885—28no—
144#884—28no—
145C4×D12—22no—
146C4×D12—22no—
147C42×D3—22no—
148C42×D3—22no—
149C3×#106—22no—
150C3×#102—22no—
151C3×#102—22no—
152C3×#95—21no—
153#832—41no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160#821—41no—
161#816—22no—
162#810—22no—
163#809—22no—
164#809—22no—
165#808—22no—
166C22×#41—61no—
167C22×SD16—31no—
168C22×SD16—31no—
169C23×C8—31no—
170C23×C8—31no—
171#532—64no—
172#532—64no—
173C2×C4⋊Q8—31no—
174C2×#127—31no—
175C2×#124—61no—
176C2×C22⋊Q8—31no—
177C2×#121—31no—
178C2×#121—31no—
179C2×#121—61no—
180C2×C4×D4—31no—
181C2×C4×D4—61no—
182C2×C4×D4C2×D311yescharacteristic
183C22×C42—31no—
184#465—64no—
185#465—64no—
186C2×#106—31no—
187C2×#106C2×D311yescharacteristic
188C2×#103—31no—
189C2×#103—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×#102C2×D311yescharacteristic
196#391—31no—
197#391—31no—
198#389—31no—
199#389C2×D311yescharacteristic
200#387—61no—
201#387—61no—
202#385—61no—
203#381—61no—
204#380—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340C2×D311yescharacteristic
209#336—31no—
210#336—31no—
211#336—31no—
212#336C2×D311yescharacteristic
213C24×C3—21no—
214C23×D3—21no—
215C23×D3C2×D411yescharacteristic
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4C2×D412yes—
222C22×C3×C4—24no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—42no—
227C22×C3×C4—42no—
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2411yescharacteristic
231C2×#67—24no—
232C2×#67—24no—
233C2×#67—24no—
234C2×#67—42no—
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3C2×D411yescharacteristic
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246#235—432no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—24no—
252C2×D12—21no—
253C2×D12—42no—
254C2×D12—42no—
255C2×D12C2×D412yes—
256C2×C4×D3—22no—
257C2×C4×D3—22no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—24no—
263C2×C4×D3—22no—
264C2×C4×D3—22no—
265C2×C4×D3—41no—
266C2×C4×D3—42no—
267C2×C4×D3—42no—
268C2×C4×D3SD1614yescomplemented
269C2×C4×D3C2×D412yes—
270C2×C4×D3C2×D412yes—
271C2×Dic6—24no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—42no—
279C2×Dic6—42no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8#4112yescomplemented
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—42no—
292C3×C4⋊C4C2×D412yes—
293C3×C22⋊C4—24no—
294C3×C42—21no—
295C3×C42—21no—
296#217—24no—
297#214—44no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—42no—
306C4⋊Dic3C2×D412yes—
307Dic3⋊C4—24no—
308Dic3⋊C4—42no—
309C4×Dic3—21no—
310C4×Dic3—21no—
311C4×Dic3—22no—
312C4×Dic3—22no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8#4112yescomplemented
319#204—44no—
320D3×C8—44no—
321D3×C8—44no—
322C2×#41—68no—
323C2×#41—124no—
324C2×#41—124no—
325C22×Q8—31no—
326C22×Q8—61no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4—61no—
332C22×D4C22×D311yescharacteristic
333C23×C4—21no—
334C23×C4—31no—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—61no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—62no—
341C2×SD16—62no—
342C2×SD16—121no—
343C2×SD16—121no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8—62no—
347C22×C8—62no—
348C22×C8—62no—
349C22×C8—62no—
350C22×C8—121no—
351C22×C8—121no—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354C4⋊Q8—62no—
355C4⋊Q8—62no—
356#127—62no—
357#127—62no—
358#124—68no—
359C22⋊Q8—62no—
360C22⋊Q8—62no—
361#121—34no—
362#121—34no—
363#121—68no—
364#121—62no—
365#121—62no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—62no—
369C4×D4—62no—
370C4×D4—68no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C42—31no—
387C2×C42—31no—
388C2×C42—31no—
389C2×C42—62no—
390C2×C42—62no—
391C2×C42C22×D311yescharacteristic
392#106—22no—
393#106—62no—
394#103—62no—
395#103—62no—
396#102—22no—
397#102—22no—
398#102—62no—
399#102—62no—
400#102—121no—
401#102—121no—
402#95—21no—
403#95—61no—
404#95—61no—
405#95—61no—
406#95—61no—
407#95—61no—
408#95—61no—
409C23×C3—22no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3C22×D411yescharacteristic
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—22no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3#12012yes—
429C22×D3C2×SD1612yes—
430C22×D3AGL(1,ℤ/8)12yes—
431C3×D4—22no—
432C3×D4—22no—
433C3×D4—41no—
434C3×D4—41no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—48no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4C2×SD1612yes—
451C2×C3×C4C22×D411yescharacteristic
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4H(5,𝔽2)11yescharacteristic
456C2×C3×C42−1+411yescharacteristic
457#67—48no—
458#67—48no—
459#67—48no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—22no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3#12012yes—
476C2×Dic3C2×SD1612yes—
477C2×Dic3#13512yes—
478D12—22no—
479D12—22no—
480D12—48no—
481D12—41no—
482D12—41no—
483C4×D3—28no—
484C4×D3—22no—
485C4×D3—22no—
486C4×D3—22no—
487C4×D3—22no—
488C4×D3—44no—
489C4×D3—48no—
490Dic6—48no—
491Dic6—41no—
492Dic6—41no—
493Dic6—41no—
494Dic6—41no—
495C3×C8—22no—
496C3×C8—41no—
497C3⋊C8—22no—
498C3⋊C8—41no—
499C24—21no—
500C24—31no—
501C24—61no—
502#41—1232no—
503C2×Q8—64no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—122no—
511C2×Q8—122no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—32no—
518C2×D4—64no—
519C2×D4—64no—
520C2×D4—64no—
521C2×D4—64no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—122no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4D3×D412yes—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—34no—
544C22×C4—32no—
545C22×C4—32no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—64no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—121no—
561C22×C4—122no—
562C22×C4—122no—
563C22×C4D3×D411yescharacteristic
564C22×C4D3×D411yescharacteristic
565C22×C4C23×D311yescharacteristic
566SD16—124no—
567SD16—124no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—32no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—124no—
580C2×C8—124no—
581C2×C8#23512yescomplemented
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—32no—
588C4⋊C4—42no—
589C4⋊C4—64no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—122no—
594C4⋊C4—122no—
595C4⋊C4D3×D412yes—
596C22⋊C4—24no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C42—21no—
603C42—21no—
604C42—62no—
605C42—62no—
606C42—61no—
607C42—61no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3C2×#12011yescharacteristic
616C22×C3#53211yescharacteristic
617C22×C3#53711yescharacteristic
618C22×C3C22×SD1611yescharacteristic
619C22×C3C2×#13511yescharacteristic
620C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
621C22×C3#57511yescharacteristic
622C2×D3—22no—
623C2×D3—22no—
624C2×D3—22no—
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—81no—
632C2×D3—81no—
633C2×D3—81no—
634C2×D3—81no—
635C2×D3#45014yes—
636C3×C4—22no—
637C3×C4—42no—
638C3×C4—41no—
639C3×C4—81no—
640C3×C4—81no—
641C3×C4#54611yescharacteristic
642C3×C4#54611yescharacteristic
643C3×C4#54711yescharacteristic
644C3×C4#54711yescharacteristic
645Dic3—22no—
646Dic3—22no—
647Dic3—22no—
648Dic3—42no—
649Dic3—81no—
650Dic3—81no—
651C23—22no—
652C23—32no—
653C23—32no—
654C23—32no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—61no—
662C23—61no—
663C23—61no—
664C23—61no—
665C23—62no—
666C23—121no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23C2×D3×D411yescharacteristic
673Q8—128no—
674Q8—121no—
675Q8—121no—
676Q8—121no—
677Q8—121no—
678D4—22no—
679D4—22no—
680D4—41no—
681D4—41no—
682D4—62no—
683D4—62no—
684D4—128no—
685D4—128no—
686D4—128no—
687D4—128no—
688D4—121no—
689D4—121no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—48no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—68no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—128no—
721C2×C4—124no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4D3×SD1612yes—
731C2×C4C2×#23511yescharacteristic
732C2×C4C2×D3×D411yescharacteristic
733C2×C4C2×D3×D411yescharacteristic
734C2×C4#100711yescharacteristic
735C2×C4D3×#4111yescharacteristic
736C2×C4#100911yescharacteristic
737C8—22no—
738C8—41no—
739C8—62no—
740C8—121no—
741C2×C3—82no—
742C2×C3#243011yescharacteristic
743C2×C3C2×#45011yescharacteristic
744C2×C3#300211yescharacteristic
745C2×C3#316711yescharacteristic
746C2×C3#318011yescharacteristic
747C2×C3#324611yescharacteristic
748C2×C3#324711yescharacteristic
749D3—24no—
750D3—82no—
751C22—34no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—62no—
756C22—62no—
757C22—62no—
758C22—62no—
759C22—62no—
760C22—62no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—122no—
766C22—122no—
767C22—122no—
768C22—241no—
769C22—241no—
770C22—241no—
771C22—241no—
772C22#554811yescharacteristic
773C22D3×#12011yescharacteristic
774C22#562911yescharacteristic
775C22C2×D3×SD1611yescharacteristic
776C22D3×#13511yescharacteristic
777C22D3×AGL(1,ℤ/8)11yescharacteristic
778C22#577311yescharacteristic
779C4—22no—
780C4—42no—
781C4—41no—
782C4—62no—
783C4—62no—
784C4—62no—
785C4—81no—
786C4—81no—
787C4—122no—
788C4—241no—
789C4—241no—
790C4#550711yescharacteristic
791C4#555011yescharacteristic
792C4#563111yescharacteristic
793C4#565411yescharacteristic
794C3#2549511yescharacteristic, complemented, Sylow
795C2—64no—
796C2—82no—
797C2—242no—
798C2#7460611yescharacteristic
799C2#7966211yescharacteristic
800C2#7987611yescharacteristic
801C2#8008211yescharacteristic
802C2D3×#45011yescharacteristic
803C2#8107011yescharacteristic
804C2#8114811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1864C2
socleC23×C3C22×D4
prime radicalC2×#5548C2
hypercenter#1864D3
hypocenterC3#25495
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#4864C2semidirect
3. C2×#4778C2semidirect
4. #76287C2semidirect
5. C3×#1864C2semidirect
6. #71612C2semidirect
7. #70565C2semidirect
8. #70211C2semidirect
9. #70210C2semidirect
10. #70202C2semidirect
11. #69626C2semidirect
12. #68910C2semidirect
13. #68883C2semidirect
14. #68672C2semidirect
15. D3×#336C2semidirect
77. #1864D3semidirect
268. C2×C4×D3SD16semidirect
285. C2×C3×C8#41semidirect
318. C2×C3⋊C8#41semidirect
581. C2×C8#235semidirect
794. C3#25495semidirect

Maximal subgroups

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

subgroupindex
C2×#55482
C2×#48642
C2×#47782
#762872
C3×#18642
#716122
#705652
#702112
#702102
#702022
#696262
#689102
#688832
#686722
D3×#3362
#254953