Finite Group Databasebeta

← #10823442

Subgroups — #10823442

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×#5164C211yesmaximal, characteristic, complemented
3Dic3×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×#4817C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic, complemented
6#72056C211yesmaximal, characteristic, complemented
7#71699C211yesmaximal, characteristic, complemented
8#71679C211yesmaximal, characteristic, complemented
9#70231C211yesmaximal, characteristic, complemented
10#70177C211yesmaximal, characteristic, complemented
11#70152C211yesmaximal, characteristic, complemented
12#69934C211yesmaximal, characteristic, complemented
13#69906C211yesmaximal, characteristic, complemented
14#68826C211yesmaximal, characteristic, complemented
15#68782C211yesmaximal, characteristic, complemented
16#23576—31nomaximal, Sylow
17C22×#237—21no—
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×#940C2211yescharacteristic
24C2×#939—21no—
25C2×D4×Dic3C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28#5596—24no—
29#5596—24no—
30C2×#893C2211yescharacteristic
31C2×#888C2211yescharacteristic
32C2×#885—21no—
33C2×#67⋊C4—21no—
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37#5229C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41#5212C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5164—24no—
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#818C2211yescharacteristic
47C2×#815C2211yescharacteristic
48C2×#815C2211yescharacteristic
49#4984C2211yescharacteristic
50#4980—21no—
51Dic3×C4⋊C4—21no—
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4950—21no—
56Dic3×C22⋊C4—21no—
57#4817—24no—
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#2033—31no—
72#2024—31no—
73#2014—31no—
74#2000—31no—
75#2000D311yescharacteristic, complemented
76#1762—31no—
77#1762—31no—
78#1749—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C23×Dic3D411yescharacteristic
88C23×Dic3D411yescharacteristic
89C2×#237—28no—
90C2×#237—44no—
91C2×#237—44no—
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×Dic6—21no—
95C2×C3×SD16—22no—
96C2×C3×SD16—22no—
97C2×C3×SD16—22no—
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8—22no—
102C3×#121—22no—
103C3×#121—22no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×#217—21no—
110C2×#217—21no—
111Q8×Dic3—22no—
112Q8×Dic3—22no—
113C2×#215—22no—
114C2×#215—22no—
115C2×#215—22no—
116#940—22no—
117#940—22no—
118#939—28no—
119D4×Dic3—22no—
120D4×Dic3D414yes—
121#930—22no—
122#930—22no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×C4×Dic3—22no—
132C2×C4×Dic3—22no—
133C2×C4×Dic3—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3D411yescharacteristic
136C2×C4×Dic3D411yescharacteristic
137C2×C4×Dic3C2311yescharacteristic
138C2×C4×Dic3C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141#893—22no—
142#893D414yes—
143#888—22no—
144#888—22no—
145#885—28no—
146#67⋊C4—28no—
147C3×#103—22no—
148C3×#102—22no—
149C3×C22⋊C8—22no—
150#835—22no—
151#832—22no—
152#832—22no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#830—22no—
159#821—22no—
160#821—22no—
161#818—22no—
162#815—22no—
163#815—22no—
164#809—22no—
165#807—22no—
166C22×#41—61no—
167C22×SD16—31no—
168C22×SD16C2×D311yescharacteristic
169#532—64no—
170#532—64no—
171C2×C4⋊Q8—31no—
172C2×#127—31no—
173C2×#124—61no—
174C2×C22⋊Q8C2×D311yescharacteristic
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×#107—31no—
187C2×#103—31no—
188C2×#103C2×D311yescharacteristic
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
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#380—31no—
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×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8#4112yescomplemented
222C2×C3×D4—24no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4C2×D412yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C2×#67—24no—
243C2×#67—24no—
244C2×#67—24no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—21no—
255C22×Dic3—24no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—41no—
261C22×Dic3—42no—
262C22×Dic3—42no—
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C22×Dic3C2×D411yescharacteristic
266C22×Dic3C2×D411yescharacteristic
267#237—432no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12C2×D412yes—
274C2×C4×D3—24no—
275C2×C4×D3—42no—
276C2×C4×D3—42no—
277C2×Dic6—24no—
278C2×Dic6—42no—
279C2×Dic6—42no—
280C3×SD16—28no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8#4112yescomplemented
287C3×C4⋊C4—24no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4C2×D412yes—
291C3×C4⋊C4#4112yescomplemented
292C3×C22⋊C4—24no—
293C3×C22⋊C4—24no—
294#217—24no—
295#217—42no—
296#215—28no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—24no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—42no—
305C4⋊Dic3—42no—
306C4⋊Dic3C2×D412yes—
307Dic3⋊C4—24no—
308C4×Dic3—21no—
309C4×Dic3—21no—
310C4×Dic3—22no—
311C4×Dic3—22no—
312C4×Dic3—42no—
313C4×Dic3—42no—
314C4×Dic3C2×D412yes—
315C4×Dic3C2×D412yes—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8#4112yescomplemented
322C2×#41—68no—
323C2×#41—124no—
324C2×#41—124no—
325C22×Q8—61no—
326C22×Q8C22×D311yescharacteristic
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—22no—
339C2×SD16—22no—
340C2×SD16—22no—
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—22no—
354C22⋊Q8—22no—
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—21no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
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—62no—
391#107—62no—
392#103—22no—
393#103—62no—
394#102—22no—
395#102—62no—
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—61no—
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×Q8—22no—
432C3×Q8—22no—
433C3×Q8—41no—
434C3×Q8—41no—
435C3×D4—22no—
436C3×D4—22no—
437C3×D4—48no—
438C3×D4—41no—
439C3×D4—41no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
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×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462#67—48no—
463#67—48no—
464#67—48no—
465C2×Dic3—28no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3—44no—
476C2×Dic3—48no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3#12012yes—
486C2×Dic3#12012yes—
487C2×Dic3AGL(1,ℤ/8)12yes—
488C2×Dic3#13712yes—
489D12—22no—
490D12—22no—
491D12—41no—
492D12—41no—
493C4×D3—48no—
494Dic6—48no—
495C3×C8—22no—
496C3×C8—41no—
497C3⋊C8—22no—
498C3⋊C8—41no—
499C24—21no—
500C24—61no—
501C24D3×D411yescharacteristic
502#41—1232no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—64no—
509C2×Q8—122no—
510C2×Q8—122no—
511C2×Q8#23712yescomplemented
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—28no—
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—24no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—32no—
584C4⋊C4—64no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—122no—
591C4⋊C4—122no—
592C4⋊C4D3×D412yes—
593C4⋊C4#23712yescomplemented
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—122no—
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—42no—
637C3×C4—41no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4#52511yescharacteristic
641C3×C4#52511yescharacteristic
642C3×C4#53211yescharacteristic
643C3×C4#53211yescharacteristic
644Dic3—22no—
645Dic3—22no—
646Dic3—22no—
647Dic3—22no—
648Dic3—42no—
649Dic3—81no—
650Dic3—81no—
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#91412yes—
672C23C2×D3×D411yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—41no—
676Q8—41no—
677Q8—128no—
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—22no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—32no—
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—128no—
721C2×C4—124no—
722C2×C4—128no—
723C2×C4—121no—
724C2×C4—121no—
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×C4C2×#23711yescharacteristic
735C2×C4C2×#23711yescharacteristic
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—
772C22#558611yescharacteristic
773C22D3×#12011yescharacteristic
774C22#559611yescharacteristic
775C22C2×#91411yescharacteristic
776C22#576811yescharacteristic
777C22D3×AGL(1,ℤ/8)11yescharacteristic
778C22D3×#13711yescharacteristic
779C4—42no—
780C4—41no—
781C4—42no—
782C4—42no—
783C4—62no—
784C4—62no—
785C4—62no—
786C4—62no—
787C4—122no—
788C4—241no—
789C4—241no—
790C4#558611yescharacteristic
791C4#559611yescharacteristic
792C4#560611yescharacteristic
793C4#571611yescharacteristic
794C3#2357611yescharacteristic, complemented, Sylow
795C2—42no—
796C2—82no—
797C2—242no—
798C2#7666511yescharacteristic
799C2#8003011yescharacteristic
800C2#8007111yescharacteristic
801C2#8014611yescharacteristic
802C2#8022811yescharacteristic
803C2#8063811yescharacteristic
804C2#8079011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radicalC2×#5596C2
hypercenter#2000D3
hypocenterC3#23576
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
2. C2×#5164C2semidirect
3. Dic3×C22⋊Q8C2semidirect
4. C2×#4817C2semidirect
5. C3×#2000C2semidirect
6. #72056C2semidirect
7. #71699C2semidirect
8. #71679C2semidirect
9. #70231C2semidirect
10. #70177C2semidirect
11. #70152C2semidirect
12. #69934C2semidirect
13. #69906C2semidirect
14. #68826C2semidirect
15. #68782C2semidirect
75. #2000D3semidirect
221. C2×C3×Q8#41semidirect
286. C2×C3×C8#41semidirect
291. C3×C4⋊C4#41semidirect
321. C2×C3⋊C8#41semidirect
511. C2×Q8#237semidirect
579. C2×C8#237semidirect
593. C4⋊C4#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×#51642
Dic3×C22⋊Q82
C2×#48172
C3×#20002
#720562
#716992
#716792
#702312
#701772
#701522
#699342
#699062
#688262
#687822
#235763