Finite Group Databasebeta

← #10823444

Subgroups — #10823444

Order 768.

1424 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×#5596C211yesmaximal, characteristic
2C2×#4889C211yesmaximal, characteristic, complemented
3C2×#4757C211yesmaximal, characteristic, complemented
4#73866C211yesmaximal, characteristic, complemented
5C3×#2033C211yesmaximal, characteristic, complemented
6#71685C211yesmaximal, characteristic, complemented
7#70617C211yesmaximal, characteristic, complemented
8#70211C211yesmaximal, characteristic, complemented
9#70210C211yesmaximal, characteristic, complemented
10#70152C211yesmaximal, characteristic, complemented
11#69962C211yesmaximal, characteristic, complemented
12#69906C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#68910C211yesmaximal, characteristic, complemented
15#68782C211yesmaximal, characteristic, complemented
16#23576—31nomaximal, Sylow
17C22×#237—21no—
18C2×C3×#121C2211yescharacteristic
19C2×#940C2211yescharacteristic
20C2×#939—21no—
21C2×D4×Dic3C2211yescharacteristic
22C22×#214C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×#924C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C22×#204C2211yescharacteristic
27#5596—24no—
28#5596—24no—
29C2×#893C2211yescharacteristic
30C2×#888C2211yescharacteristic
31C2×#887C2211yescharacteristic
32C2×#885—21no—
33C2×#67⋊C4—21no—
34C2×C3×#107C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#816C2211yescharacteristic
43C2×#815C2211yescharacteristic
44C2×#815C2211yescharacteristic
45Dic3×C4⋊C4C2211yescharacteristic
46#4973C2211yescharacteristic
47#4972C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4946—21no—
53Dic3×C22⋊C4—21no—
54#4889—24no—
55#4757—24no—
56#4652—21no—
57#4649—21no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#532—31no—
65C2×#440—31no—
66C2×#440—31no—
67C4×C22⋊Q8—31no—
68#2057—31no—
69#2041—31no—
70#2033—31no—
71#2033D311yescharacteristic, complemented
72#2024—31no—
73#2014—31no—
74#2000—31no—
75#2000—31no—
76#1762—31no—
77#1762—31no—
78#1749—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C23×Dic3—21no—
86C23×Dic3D411yescharacteristic
87C23×Dic3D411yescharacteristic
88C2×#237—28no—
89C2×#237—44no—
90C2×#237—44no—
91C22×D12C2311yescharacteristic
92C22×C4×D3—21no—
93C22×Dic6—21no—
94C22×Dic6C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×#121—22no—
98C3×#121—22no—
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×#217—21no—
105C2×#217—21no—
106#940—22no—
107#940—22no—
108#939—28no—
109D4×Dic3—22no—
110D4×Dic3D414yes—
111C2×#214—22no—
112C2×#214—22no—
113C2×#214—22no—
114#930—22no—
115#930—22no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×C4⋊Dic3C2311yescharacteristic
119C2×C4⋊Dic3C2311yescharacteristic
120#924—22no—
121#924—22no—
122C2×Dic3⋊C4—21no—
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×C4×Dic3—22no—
127C2×C4×Dic3—22no—
128C2×C4×Dic3—21no—
129C2×C4×Dic3—21no—
130C2×C4×Dic3D411yescharacteristic
131C2×C4×Dic3D411yescharacteristic
132C2×C4×Dic3C2311yescharacteristic
133C2×C4×Dic3C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C2×#204—22no—
137C2×#204—22no—
138C2×#204—22no—
139#893—22no—
140#893D414yes—
141#888—22no—
142#888—22no—
143#887—22no—
144#887—22no—
145#885—28no—
146#67⋊C4—28no—
147C3×#107—22no—
148C3×#102—22no—
149C3×#102—22no—
150C3×C22⋊C8—22no—
151C3×#95—21no—
152#832—22no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#830—22no—
158#821—22no—
159#816—22no—
160#815—22no—
161#815—22no—
162#810—22no—
163#809—22no—
164#809—22no—
165#807—22no—
166C22×#41—61no—
167C22×SD16—31no—
168C22×SD16—31no—
169#532—64no—
170#532—64no—
171C2×C4⋊Q8—31no—
172C2×#127—31no—
173C2×#124—61no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—61no—
177C2×#121C2×D311yescharacteristic
178C2×C4×Q8—31no—
179C2×C4×D4—31no—
180C2×C4×D4—31no—
181C2×C4×D4—61no—
182C22×C42—31no—
183#440—64no—
184#440—64no—
185C2×#107—31no—
186C2×#107C2×D311yescharacteristic
187C2×#103—31no—
188C2×#103—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102C2×D311yescharacteristic
194C2×#102C2×D311yescharacteristic
195C2×C22⋊C8—31no—
196C2×C22⋊C8C2×D311yescharacteristic
197C2×#97—31no—
198C2×#97—31no—
199#391—31no—
200#389—31no—
201#387—61no—
202#385—61no—
203#380C2×D311yescharacteristic
204C4×C4⋊C4—31no—
205C4×C4⋊C4—61no—
206C4×C22⋊C4—61no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340C2×D311yescharacteristic
211#336—31no—
212#336—31no—
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C23×D3—21no—
216C2×C3×D4—24no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—42no—
223C2×C3×D4—42no—
224C2×C3×D4C2×D412yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C2×#67—24no—
237C2×#67—24no—
238C2×#67—24no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—24no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—41no—
255C22×Dic3—42no—
256C22×Dic3—42no—
257C22×Dic3C2×D411yescharacteristic
258C22×Dic3C2×D411yescharacteristic
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261#237—432no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12C2×D412yes—
268C2×C4×D3—24no—
269C2×C4×D3—42no—
270C2×C4×D3—42no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—24no—
276C2×Dic6—21no—
277C2×Dic6—42no—
278C2×Dic6—42no—
279C2×Dic6#4112yescomplemented
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⋊C4C2×D412yes—
292C3×C22⋊C4—24no—
293C3×C22⋊C4—42no—
294#217—24no—
295#217—24no—
296#214—28no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—24no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3C2×D412yes—
302C4⋊Dic3#4112yescomplemented
303Dic3⋊C4—24no—
304Dic3⋊C4—24no—
305Dic3⋊C4—42no—
306Dic3⋊C4—42no—
307C4×Dic3—21no—
308C4×Dic3—21no—
309C4×Dic3—22no—
310C4×Dic3—22no—
311C4×Dic3—42no—
312C4×Dic3—42no—
313C4×Dic3C2×D412yes—
314C4×Dic3C2×D412yes—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8#4112yescomplemented
321#204—28no—
322C2×#41—68no—
323C2×#41—124no—
324C2×#41—124no—
325C22×Q8—31no—
326C22×Q8—61no—
327C22×D4—21no—
328C22×D4—31no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4—61no—
332C22×D4C22×D311yescharacteristic
333C23×C4—31no—
334C23×C4—31no—
335C23×C4—61no—
336C23×C4—61no—
337C23×C4C22×D311yescharacteristic
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—62no—
341C2×SD16—62no—
342C2×SD16—62no—
343C2×SD16—62no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8C22×D311yescharacteristic
347C22×C8C22×D311yescharacteristic
348C4⋊Q8—62no—
349C4⋊Q8—62no—
350#127—62no—
351#127—62no—
352#124—68no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355#121—22no—
356#121—22no—
357#121—62no—
358#121—62no—
359#121—68no—
360C4×Q8—62no—
361C4×Q8—62no—
362C4×D4—34no—
363C4×D4—34no—
364C4×D4—62no—
365C4×D4—62no—
366C4×D4—68no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C4⋊C4C22×D311yescharacteristic
375C2×C4⋊C4C22×D311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C42—31no—
383C2×C42—31no—
384C2×C42—31no—
385C2×C42—31no—
386C2×C42—62no—
387C2×C42—62no—
388C2×C42—61no—
389C2×C42—61no—
390#107—22no—
391#107—62no—
392#103—62no—
393#103—62no—
394#102—22no—
395#102—22no—
396#102—62no—
397#102—62no—
398#102—62no—
399#102—62no—
400C22⋊C8—22no—
401C22⋊C8—62no—
402#97—62no—
403#97—62no—
404#95—21no—
405#95—61no—
406#95—61no—
407#95—61no—
408#95—61no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—22no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3AGL(1,ℤ/8)12yes—
423C23×C3C22×D411yescharacteristic
424C22×D3—22no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C3×D4—22no—
432C3×D4—22no—
433C3×D4—48no—
434C3×D4—41no—
435C3×D4—41no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
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×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458#67—48no—
459#67—48no—
460#67—48no—
461C2×Dic3—28no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—44no—
474C2×Dic3—48no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3#12012yes—
482C2×Dic3#12012yes—
483C2×Dic3AGL(1,ℤ/8)12yes—
484C2×Dic3#13712yes—
485D12—22no—
486D12—22no—
487D12—41no—
488D12—41no—
489C4×D3—48no—
490Dic6—22no—
491Dic6—22no—
492Dic6—48no—
493Dic6—41no—
494Dic6—41no—
495C3×C8—22no—
496C3×C8—41no—
497C3⋊C8—22no—
498C3⋊C8—41no—
499C24—21no—
500C24—61no—
501C24D3×D411yescharacteristic
502#41—1232no—
503C2×Q8—32no—
504C2×Q8—64no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—122no—
511C2×Q8—122no—
512C2×D4—24no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—32no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—64no—
522C2×D4—64no—
523C2×D4—64no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4D3×D412yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—64no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—64no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—122no—
560C22×C4—122no—
561C22×C4—121no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4D3×D411yescharacteristic
565C22×C4C23×D311yescharacteristic
566SD16—68no—
567SD16—68no—
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#23712yescomplemented
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—32no—
586C4⋊C4—32no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—122no—
592C4⋊C4—122no—
593C4⋊C4D3×D412yes—
594C22⋊C4—24no—
595C22⋊C4—42no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C42—32no—
601C42—32no—
602C42—62no—
603C42—62no—
604C42—61no—
605C42—61no—
606C42—122no—
607C42—122no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3C2×#12011yescharacteristic
623C22×C3#52511yescharacteristic
624C22×C3#53211yescharacteristic
625C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
626C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
627C22×C3C2×#13711yescharacteristic
628C22×C3#57511yescharacteristic
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—81no—
633C2×D3—81no—
634C2×D3—81no—
635C2×D3—81no—
636C3×C4—41no—
637C3×C4—42no—
638C3×C4—81no—
639C3×C4—81no—
640C3×C4#52511yescharacteristic
641C3×C4#52511yescharacteristic
642C3×C4#53211yescharacteristic
643C3×C4#53211yescharacteristic
644Dic3—22no—
645Dic3—22no—
646Dic3—22no—
647Dic3—22no—
648Dic3—42no—
649Dic3—42no—
650Dic3—42no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—62no—
665C23—121no—
666C23—121no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23#91112yes—
672C23C2×D3×D411yescharacteristic
673Q8—62no—
674Q8—62no—
675Q8—128no—
676Q8—121no—
677Q8—121no—
678D4—22no—
679D4—22no—
680D4—48no—
681D4—41no—
682D4—41no—
683D4—62no—
684D4—62no—
685D4—128no—
686D4—128no—
687D4—128no—
688D4—121no—
689D4—121no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—32no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—41no—
699C2×C4—41no—
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—41no—
709C2×C4—41no—
710C2×C4—68no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—128no—
723C2×C4—124no—
724C2×C4—128no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4C2×D3×D411yescharacteristic
732C2×C4C2×D3×D411yescharacteristic
733C2×C4C2×#23711yescharacteristic
734C2×C4D3×#4111yescharacteristic
735C2×C4D3×#4111yescharacteristic
736C2×C4D3×#4111yescharacteristic
737C8—22no—
738C8—41no—
739C8—62no—
740C8—121no—
741C2×C3—42no—
742C2×C3—82no—
743C2×C3#238811yescharacteristic
744C2×C3#300311yescharacteristic
745C2×C3#300711yescharacteristic
746C2×C3#311211yescharacteristic
747C2×C3#311511yescharacteristic
748C2×C3#318011yescharacteristic
749C2×C3#318211yescharacteristic
750D3—82no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—122no—
766C22—122no—
767C22—122no—
768C22—241no—
769C22—241no—
770C22—241no—
771C22—241no—
772C22D3×#12011yescharacteristic
773C22#559611yescharacteristic
774C22#565611yescharacteristic
775C22C2×#91111yescharacteristic
776C22#576811yescharacteristic
777C22D3×AGL(1,ℤ/8)11yescharacteristic
778C22D3×#13711yescharacteristic
779C4—41no—
780C4—42no—
781C4—62no—
782C4—62no—
783C4—62no—
784C4—62no—
785C4—81no—
786C4—81no—
787C4—122no—
788C4—122no—
789C4—122no—
790C4#559611yescharacteristic
791C4#560611yescharacteristic
792C4#565611yescharacteristic
793C4#566811yescharacteristic
794C3#2357611yescharacteristic, complemented, Sylow
795C2—42no—
796C2—82no—
797C2—242no—
798C2#7688911yescharacteristic
799C2#8000211yescharacteristic
800C2#8022811yescharacteristic
801C2#8070111yescharacteristic
802C2#8079011yescharacteristic
803C2#8127011yescharacteristic
804C2#8135111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2033C2
socleC23×C3C22×D4
prime radicalC2×#5596C2
hypercenter#2033D3
hypocenterC3#23576
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. C2×#4889C2semidirect
3. C2×#4757C2semidirect
4. #73866C2semidirect
5. C3×#2033C2semidirect
6. #71685C2semidirect
7. #70617C2semidirect
8. #70211C2semidirect
9. #70210C2semidirect
10. #70152C2semidirect
11. #69962C2semidirect
12. #69906C2semidirect
13. #69523C2semidirect
14. #68910C2semidirect
15. #68782C2semidirect
71. #2033D3semidirect
279. C2×Dic6#41semidirect
285. C2×C3×C8#41semidirect
302. C4⋊Dic3#41semidirect
320. C2×C3⋊C8#41semidirect
579. C2×C8#237semidirect
794. C3#23576semidirect

Maximal subgroups

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

subgroupindex
C2×#55962
C2×#48892
C2×#47572
#738662
C3×#20332
#716852
#706172
#702112
#702102
#701522
#699622
#699062
#695232
#689102
#687822
#235763