Finite Group Databasebeta

← #10846076

Subgroups — #10846076

Order 768.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#468C211yesmaximal, characteristic, complemented
2C2×#5165C211yesmaximal, characteristic, complemented
3C2×#5127C211yesmaximal, characteristic, complemented
4#82779C211yesmaximal, characteristic, complemented
5#82667C211yesmaximal, characteristic, complemented
6C2×#4775C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#71990C211yesmaximal, characteristic, complemented
9#71695C211yesmaximal, characteristic, complemented
10#71684C211yesmaximal, characteristic, complemented
11#70634C211yesmaximal, characteristic, complemented
12#70615C211yesmaximal, characteristic, complemented
13#70270C211yesmaximal, characteristic, complemented
14#70227C211yesmaximal, characteristic, complemented
15#70152C211yesmaximal, characteristic, complemented
16#25397—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#947C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#939—21no—
24C2×#938C2211yescharacteristic
25C2×D4×Dic3C2211yescharacteristic
26C22×#213C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C2×C4×#67C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30C2×#895C2211yescharacteristic
31C3×#468—24no—
32C2×C3×#107C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37#5222—21no—
38C2×#832C2211yescharacteristic
39#5212C2211yescharacteristic
40C2×#830C2211yescharacteristic
41#5165—24no—
42#5127—24no—
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#815C2211yescharacteristic
47C2×Dic3⋊C8C2211yescharacteristic
48#4993—21no—
49#4988—21no—
50#4987C2211yescharacteristic
51#4975C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4960—21no—
56#4959—21no—
57#4957—21no—
58#4942—21no—
59#4775—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468D311yescharacteristic, complemented
65C2×#466—31no—
66C2×#463—31no—
67C2×#435—31no—
68#2540—31no—
69#2537—31no—
70#2036—31no—
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1959—31no—
75#1947—31no—
76#1895—31no—
77#1892—31no—
78#1762—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67D411yescharacteristic
86C23×Dic3—21no—
87C22×D12—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—41no—
93C2×C3×M16—22no—
94C2×C3×M16—22no—
95C2×C3×M16—41no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×C22⋊Q8—22no—
99C3×C22⋊Q8—41no—
100C3×#121—22no—
101C3×#121—41no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217D411yescharacteristic
111#947—22no—
112#947—22no—
113#946—22no—
114#946—41no—
115#939—44no—
116#938—22no—
117#938—41no—
118D4×Dic3—22no—
119D4×Dic3—22no—
120C2×#213—22no—
121C2×#213—22no—
122C2×#213—41no—
123#930—22no—
124#930—41no—
125C4×#67—22no—
126C4×#67—22no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4D411yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4D411yescharacteristic
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×D3×C8—22no—
146C2×D3×C8—22no—
147C2×D3×C8—41no—
148#895—22no—
149#895—41no—
150C3×#107—22no—
151C3×#103—22no—
152C3×#102D414yescomplemented
153#835—22no—
154#835—41no—
155#832—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#830—22no—
160#821—22no—
161#821—22no—
162(C2×D3)⋊C8—22no—
163#815—22no—
164Dic3⋊C8D414yescomplemented
165#809—41no—
166#807—22no—
167C22×SD16C2×D311yescharacteristic
168C22×D8—31no—
169C22×M16C2×D311yescharacteristic
170C23×C8—31no—
171C2×#124—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—61no—
178C2×#121C2×D311yescharacteristic
179C2×C4×D4—31no—
180C2×C4×D4—31no—
181#468—24no—
182#466—64no—
183#463—64no—
184#435—64no—
185C2×#107—31no—
186C2×#107C2×D311yescharacteristic
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102C2×D311yescharacteristic
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×#97—31no—
199#399—61no—
200#394—61no—
201#394—61no—
202#392—61no—
203#390—61no—
204#390—61no—
205#384—31no—
206#380—31no—
207#380—31no—
208#380—61no—
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
216C23×D3—21no—
217C23×D3C2×D411yescharacteristic
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—81no—
232C2×C3×D4C2×D412yes—
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×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C2×#67—22no—
245C2×#67—22no—
246C2×#67—41no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—81no—
252C2×#67—81no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—42no—
257C22×Dic3—42no—
258C22×Dic3—42no—
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—42no—
269C2×D12—42no—
270C2×D12—81no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C3×SD16—44no—
278C3×M16—44no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8C2×D412yes—
284C2×C3×C8C2×D412yes—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—42no—
289C3×C4⋊C4C2×D412yes—
290C3×C22⋊C4—42no—
291C3×C22⋊C4—42no—
292#217—22no—
293#217—42no—
294#217—42no—
295#217—42no—
296#213—44no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3#4112yes—
310Dic3⋊C4—22no—
311Dic3⋊C4—42no—
312Dic3⋊C4—42no—
313Dic3⋊C4—81no—
314C4×Dic3—81no—
315C4×Dic3C2×D412yes—
316C4×Dic3#4112yes—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8C2×D412yes—
323D3×C8—44no—
324C22×Q8C22×D311yescharacteristic
325C22×D4—21no—
326C22×D4—31no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4C22×D311yescharacteristic
332C23×C4—31no—
333C23×C4—61no—
334C23×C4C22×D311yescharacteristic
335C2×SD16—22no—
336C2×SD16—22no—
337C2×SD16—41no—
338C2×D8—62no—
339C2×D8—62no—
340C2×D8—121no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—41no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8—62no—
347C22×C8—62no—
348C22×C8—121no—
349C22×C8C22×D311yescharacteristic
350C22×C8C22×D311yescharacteristic
351#124—62no—
352#124—62no—
353C22⋊Q8—22no—
354C22⋊Q8—41no—
355C22⋊Q8—62no—
356C22⋊Q8—121no—
357#121—22no—
358#121—41no—
359#121—62no—
360#121—62no—
361#121—62no—
362#121—121no—
363#121—121no—
364#121—121no—
365#121—124no—
366C4×D4—62no—
367C4×D4—62no—
368C4×D4—62no—
369C4×D4—62no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C42—31no—
394C2×C42—61no—
395#107—22no—
396#107—62no—
397C4⋊C8—34no—
398#103—22no—
399#103—62no—
400#103—121no—
401#102—62no—
402#102—62no—
403#102—62no—
404#102—121no—
405#102#6714yescomplemented
406C22⋊C8—62no—
407C22⋊C8—62no—
408#97—62no—
409#95—61no—
410#95—61no—
411#95—61no—
412C23×C3—21no—
413C23×C3—22no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3C22×D411yescharacteristic
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3AGL(1,ℤ/8)12yes—
441C3×Q8—41no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—22no—
446C3×D4—22no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—84no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471C2×C3×C4H(5,𝔽2)11yescharacteristic
472#67—44no—
473#67—84no—
474#67—84no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—22no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—84no—
492C2×Dic3#12112yes—
493C2×Dic3#12112yes—
494D12—41no—
495D12—41no—
496D12—41no—
497D12—41no—
498D12—84no—
499C4×D3—41no—
500C4×D3—41no—
501C4×D3—41no—
502C4×D3—41no—
503C3×C8—22no—
504C3×C8—22no—
505C3⋊C8—22no—
506C3⋊C8—41no—
507C24—21no—
508C24—31no—
509C24—61no—
510C24D3×D411yescharacteristic
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—62no—
525C2×D4—62no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—81no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—121no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—241no—
541C2×D4—241no—
542C2×D4—241no—
543C2×D4C2×#6712yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—122no—
566C22×C4—122no—
567C22×C4—122no—
568C22×C4D3×D411yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—44no—
571D8—124no—
572M16—44no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—32no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—124no—
584C2×C8D3×D412yes—
585C2×C8C2×#6712yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—32no—
590C4⋊C4—42no—
591C4⋊C4—62no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—122no—
598C4⋊C4—122no—
599C4⋊C4—241no—
600C4⋊C4C2×#6712yes—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—62no—
604C22⋊C4—62no—
605C22⋊C4—122no—
606C22⋊C4—122no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—32no—
615C42—32no—
616C42—241no—
617C22×C3—41no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—42no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3C2×#12111yescharacteristic
632C22×C3D4211yescharacteristic
633C22×C3#54611yescharacteristic
634C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
635C22×C3#57511yescharacteristic
636C22×C3#57611yescharacteristic
637C22×C3#57811yescharacteristic
638C2×D3—22no—
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—81no—
646C2×D3—81no—
647C2×D3—81no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C3×C4—41no—
653C3×C4—42no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4#53211yescharacteristic
657C3×C4#54011yescharacteristic
658C3×C4D4211yescharacteristic
659C3×C4#55011yescharacteristic
660Dic3—22no—
661Dic3—22no—
662Dic3—41no—
663Dic3—42no—
664Dic3—81no—
665Dic3—81no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—22no—
672C23—21no—
673C23—21no—
674C23—32no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23C2×D3×D411yescharacteristic
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—41no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—84no—
704D4—124no—
705D4—121no—
706D4—121no—
707D4—121no—
708D4—121no—
709D4—244no—
710D4—244no—
711D4—244no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—32no—
717C2×C4—32no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—62no—
737C2×C4—61no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—244no—
751C2×C4C2×D3×D411yescharacteristic
752C2×C4#100411yescharacteristic
753C2×C4#100411yescharacteristic
754C2×C4D3×#4111yescharacteristic
755C2×C4D3×#4111yescharacteristic
756C2×C4C22×#6711yescharacteristic
757C8—22no—
758C8—22no—
759C8—62no—
760C8—121no—
761C2×C3—81no—
762C2×C3—82no—
763C2×C3#242811yescharacteristic
764C2×C3#305511yescharacteristic
765C2×C3#306111yescharacteristic
766C2×C3#326411yescharacteristic
767C2×C3#326911yescharacteristic
768C2×C3#330811yescharacteristic
769C2×C3#331911yescharacteristic
770D3—42no—
771D3—161no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—41no—
781C22—42no—
782C22—62no—
783C22—62no—
784C22—62no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22D3×#12111yescharacteristic
801C22#561011yescharacteristic
802C22D3×AGL(1,ℤ/8)11yescharacteristic
803C22#577411yescharacteristic
804C22#577711yescharacteristic
805C22#577911yescharacteristic
806C22D4×#6711yescharacteristic
807C4—41no—
808C4—42no—
809C4—62no—
810C4—62no—
811C4—81no—
812C4—81no—
813C4—122no—
814C4—121no—
815C4—241no—
816C4—241no—
817C4#559911yescharacteristic
818C4#561511yescharacteristic
819C4D4×#6711yescharacteristic
820C4#583211yescharacteristic
821C3#2539711yescharacteristic, complemented, Sylow
822C2—81no—
823C2—82no—
824C2—122no—
825C2—481no—
826C2#8080511yescharacteristic
827C2#8080811yescharacteristic
828C2#8082011yescharacteristic
829C2#8082511yescharacteristic
830C2#8265011yescharacteristic
831C2#8395211yescharacteristic
832C2#8398811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#468C2
socleC23×C3C22×D4
hypercenterC2×#468D3
hypocenterC3#25397
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×C3×#468C2semidirect
2. C2×#5165C2semidirect
3. C2×#5127C2semidirect
4. #82779C2semidirect
5. #82667C2semidirect
6. C2×#4775C2semidirect
7. #72054C2semidirect
8. #71990C2semidirect
9. #71695C2semidirect
10. #71684C2semidirect
11. #70634C2semidirect
12. #70615C2semidirect
13. #70270C2semidirect
14. #70227C2semidirect
15. #70152C2semidirect
64. C2×#468D3semidirect
152. C3×#102D4semidirect
164. Dic3⋊C8D4semidirect
405. #102#67semidirect
821. C3#25397semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4682
C2×#51652
C2×#51272
#827792
#826672
C2×#47752
#720542
#719902
#716952
#716842
#706342
#706152
#702702
#702272
#701522
#253973