Finite Group Databasebeta

← #10827370

Subgroups — #10827370

Order 768.

1500 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5614C211yesmaximal, characteristic, complemented
2C2×#5156C211yesmaximal, characteristic, complemented
3#82640C211yesmaximal, characteristic, complemented
4C2×D3×#102C211yesmaximal, characteristic, complemented
5C3×#1999C211yesmaximal, characteristic, complemented
6#72037C211yesmaximal, characteristic, complemented
7#71684C211yesmaximal, characteristic, complemented
8#71678C211yesmaximal, characteristic, complemented
9#70202C211yesmaximal, characteristic, complemented
10#70172C211yesmaximal, characteristic, complemented
11#70164C211yesmaximal, characteristic, complemented
12#69957C211yesmaximal, characteristic, complemented
13#69933C211yesmaximal, characteristic, complemented
14#68899C211yesmaximal, characteristic, complemented
15#68872C211yesmaximal, characteristic, complemented
16#23963—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic, complemented
21C2×#938—21no—
22C2×#938C2211yescharacteristic
23C2×#937—21no—
24C2×#935—21no—
25C2×D4×Dic3C2211yescharacteristic, complemented
26C22×#213C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C2×C4×#67C2211yescharacteristic
29C2×#926C2211yescharacteristic, complemented
30C22×D3×C8C2211yescharacteristic
31#5614—24no—
32#5614—24no—
33C2×D3×C4⋊C4C2211yescharacteristic
34C2×#890C2211yescharacteristic, complemented
35C2×#67⋊C4—21no—
36C2×#879—21no—
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic, complemented
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40#5223—21no—
41#5221C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic, complemented
45C2×#830C2211yescharacteristic, complemented
46#5156—24no—
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50#4988C2211yescharacteristic
51#4987C2211yescharacteristic
52C2×#809C2211yescharacteristic
53#4959—21no—
54#4955—21no—
55D3×#102—24no—
56C3×#340C2211yescharacteristic, complemented
57#4551C2211yescharacteristic, complemented
58#4551C2211yescharacteristic, complemented
59#4550C2211yescharacteristic, complemented
60#4550C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64C2×#553—31no—
65C2×#447—31no—
66C22×#102—31no—
67#2408—31no—
68#2025—31no—
69#2025—31no—
70#1999—31no—
71#1999D311yescharacteristic, complemented
72#1893—31no—
73#1879—31no—
74#1879—31no—
75#1875—31no—
76#1875—31no—
77#1869—31no—
78#1824—31no—
79C24×D3—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C22×#67—21no—
88C22×#67D411yescharacteristic
89C23×Dic3—21no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4—22no—
94C2×D3×D4—41no—
95C2×D3×D4—41no—
96C22×D12C2311yescharacteristic
97C22×C4×D3—21no—
98C22×C4×D3C2311yescharacteristic
99C2×C3×D8—22no—
100C2×C3×D8—22no—
101C2×C3×D8—41no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×#121—22no—
105C3×#121—22no—
106C3×#121—22no—
107C3×#121—41no—
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#217—21no—
117C2×#217D411yescharacteristic
118#938—28no—
119#938—22no—
120#938D414yescomplemented
121#937—44no—
122#935—28no—
123D4×Dic3—22no—
124D4×Dic3—22no—
125C2×#213—22no—
126C2×#213—22no—
127C2×#213—41no—
128#930—22no—
129#930—41no—
130C4×#67—22no—
131C4×#67—22no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4D411yescharacteristic
137#926—22no—
138#926—22no—
139C2×C4⋊Dic3—21no—
140C2×C4⋊Dic3C2311yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×C4⋊Dic3C2311yescharacteristic
143C2×Dic3⋊C4—21no—
144C2×Dic3⋊C4—21no—
145C2×Dic3⋊C4D411yescharacteristic
146C2×C4×Dic3—21no—
147C2×C4×Dic3C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150C2×D3×C8—22no—
151C2×D3×C8—41no—
152C2×D3×C8—41no—
153D3×C4⋊C4—22no—
154D3×C4⋊C4D414yescomplemented
155#890—22no—
156#890—22no—
157#67⋊C4—28no—
158#879—28no—
159C3×#102—22no—
160C3×#102—41no—
161C3×C22⋊C8—41no—
162#832—22no—
163#832—22no—
164#832—41no—
165C3⋊#95—21no—
166#830—41no—
167#821—22no—
168#821—22no—
169(C2×D3)⋊C8—22no—
170#809—22no—
171C23×D4—31no—
172C22×D8—31no—
173C22×D8C2×D311yescharacteristic
174C23×C8—31no—
175#553—64no—
176#553—64no—
177C2×#126—61no—
178C2×#125—31no—
179C2×#123—61no—
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—61no—
183C2×#121C2×D311yescharacteristic
184C2×#121C2×D311yescharacteristic, complemented
185C2×#120—61no—
186C2×C4×D4—31no—
187C2×C4×D4—31no—
188C2×C4×D4—61no—
189C2×#117—31no—
190C22×C4⋊C4—31no—
191#447—64no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—64no—
199C2×#102C2×D311yescharacteristic
200C2×#102C2×D311yescharacteristic, complemented
201C2×C22⋊C8—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8C2×D311yescharacteristic, complemented
204#394—61no—
205#392—61no—
206#390—31no—
207#390—31no—
208#380—31no—
209#379—61no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#340C2×D311yescharacteristic, complemented
216#336—31no—
217#336—31no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3C2×D411yescharacteristic
221C23×D3—21no—
222C23×D3—42no—
223C23×D3—42no—
224C23×D3—42no—
225C23×D3—42no—
226C23×D3—42no—
227C23×D3—81no—
228C23×D3—81no—
229C23×D3C2×D411yescharacteristic
230C2×C3×D4—24no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C2×C3×D4—81no—
244C2×C3×D4—81no—
245C2×C3×D4—81no—
246C2×C3×D4C2×D412yes—
247C2×C3×D4#4112yes—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2411yescharacteristic
258C2×#67—24no—
259C2×#67—22no—
260C2×#67—22no—
261C2×#67—22no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—42no—
265C2×#67—42no—
266C2×#67—42no—
267C2×#67—42no—
268C2×#67—42no—
269C2×#67—81no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—24no—
273C22×Dic3—21no—
274C22×Dic3—81no—
275C22×Dic3—81no—
276C22×Dic3C2×D411yescharacteristic
277C22×Dic3C2×D411yescharacteristic
278C22×Dic3C2×D411yescharacteristic
279D3×D4—28no—
280D3×D4—44no—
281D3×D4—44no—
282D3×D4—44no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12#4112yes—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—24no—
294C2×C4×D3—81no—
295C2×C4×D3—81no—
296C2×C4×D3C2×D412yes—
297C2×C4×D3C2×D412yes—
298C3×D8—44no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4C2×D412yes—
309C3×C22⋊C4—24no—
310C3×C22⋊C4—42no—
311#217—24no—
312#217—24no—
313#217—24no—
314#217—22no—
315#217—42no—
316#217—81no—
317#213—44no—
318(C2×D3)⋊C4—22no—
319(C2×D3)⋊C4—42no—
320(C2×D3)⋊C4—42no—
321(C2×D3)⋊C4—42no—
322(C2×D3)⋊C4—81no—
323C4⋊Dic3—24no—
324C4⋊Dic3—21no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3C2×D412yes—
329C4⋊Dic3C2×D412yes—
330Dic3⋊C4—24no—
331Dic3⋊C4—22no—
332Dic3⋊C4—24no—
333C4×Dic3—24no—
334C4×Dic3—21no—
335C4×Dic3—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342D3×C8—44no—
343C25—61no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—31no—
347C22×D4—31no—
348C22×D4—62no—
349C22×D4—62no—
350C22×D4—61no—
351C22×D4—62no—
352C22×D4—62no—
353C22×D4—61no—
354C22×D4—61no—
355C22×D4—121no—
356C22×D4—121no—
357C22×D4C22×D311yescharacteristic
358C22×D4C22×D311yescharacteristic
359C23×C4—31no—
360C23×C4—61no—
361C23×C4—61no—
362C23×C4C22×D311yescharacteristic
363C2×D8—22no—
364C2×D8—22no—
365C2×D8—41no—
366C2×D8—62no—
367C2×D8—62no—
368C2×D8—121no—
369C22×C8—31no—
370C22×C8—31no—
371C22×C8—62no—
372C22×C8—121no—
373C22×C8—121no—
374C22×C8C22×D311yescharacteristic
375C22×C8C22×D311yescharacteristic
376#126—68no—
377#125—62no—
378#125—62no—
379#123—68no—
380#121—22no—
381#121—22no—
382#121—22no—
383#121—34no—
384#121—41no—
385#121—62no—
386#121—68no—
387#121—62no—
388#121—121no—
389#120—124no—
390C4×D4—68no—
391C4×D4—62no—
392C4×D4—62no—
393C4×D4—62no—
394C4×D4—62no—
395#117—62no—
396#117—62no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—61no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4—61no—
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—31no—
411C2×C22⋊C4—31no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C42—31no—
422C2×C42—61no—
423#102—22no—
424#102—41no—
425#102—62no—
426#102—62no—
427#102—62no—
428#102—62no—
429#102—62no—
430#102—121no—
431C22⋊C8—41no—
432C22⋊C8—62no—
433C22⋊C8—121no—
434#95—61no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3C22×D411yescharacteristic
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—22no—
462C22×D3—48no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—84no—
470C22×D3—84no—
471C22×D3—84no—
472C22×D3—84no—
473C22×D3—84no—
474C22×D3—84no—
475C22×D3#12012yes—
476C22×D3#13512yes—
477C22×D3AGL(1,ℤ/8)12yes—
478C3×D4—22no—
479C3×D4—22no—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—41no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—84no—
487C3×D4—84no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4C22×D411yescharacteristic
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4C2×#4111yescharacteristic
504C2×C3×C4C2×#4111yescharacteristic
505C2×C3×C4H(5,𝔽2)11yescharacteristic
506C2×C3×C4H(5,𝔽2)11yescharacteristic
507#67—48no—
508#67—44no—
509#67—48no—
510#67—84no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—84no—
529C2×Dic3#12012yes—
530D12—22no—
531D12—22no—
532D12—41no—
533D12—41no—
534C4×D3—22no—
535C4×D3—22no—
536C4×D3—22no—
537C4×D3—22no—
538C4×D3—84no—
539C3×C8—41no—
540C3×C8—41no—
541C3⋊C8—41no—
542C3⋊C8—41no—
543C24—21no—
544C24—21no—
545C24—31no—
546C24—61no—
547C24—122no—
548C24—122no—
549C24—122no—
550C24—122no—
551C24—122no—
552C24—241no—
553C24—241no—
554C24D3×D411yescharacteristic
555C2×D4—24no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—32no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—68no—
570C2×D4—64no—
571C2×D4—62no—
572C2×D4—62no—
573C2×D4—62no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4—122no—
583C2×D4—124no—
584C2×D4—124no—
585C2×D4—124no—
586C2×D4—122no—
587C2×D4—122no—
588C2×D4—122no—
589C2×D4—122no—
590C2×D4—122no—
591C2×D4—122no—
592C2×D4—241no—
593C2×D4D3×D412yes—
594C2×D4#23712yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—31no—
604C22×C4—32no—
605C22×C4—32no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—64no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—64no—
616C22×C4—61no—
617C22×C4—241no—
618C22×C4—241no—
619C22×C4—241no—
620C22×C4—241no—
621C22×C4D3×D411yescharacteristic
622C22×C4C23×D311yescharacteristic
623D8—44no—
624D8—124no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—61no—
632C2×C8—61no—
633C2×C8—61no—
634C2×C8—61no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—124no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—32no—
642C4⋊C4—32no—
643C4⋊C4—64no—
644C4⋊C4—62no—
645C4⋊C4—64no—
646C4⋊C4—64no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4D3×D412yes—
652C22⋊C4—24no—
653C22⋊C4—42no—
654C22⋊C4—62no—
655C22⋊C4—62no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—122no—
660C22⋊C4—122no—
661C22⋊C4—122no—
662C22⋊C4—122no—
663C22⋊C4—241no—
664C22⋊C4—241no—
665C42—64no—
666C42—61no—
667C42—61no—
668C22×C3—42no—
669C22×C3—41no—
670C22×C3—42no—
671C22×C3—41no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—41no—
675C22×C3—42no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—42no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3C2×#12011yescharacteristic
690C22×C3#54611yescharacteristic
691C22×C3#54611yescharacteristic
692C22×C3C2×#13511yescharacteristic
693C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
694C22×C3#57611yescharacteristic
695C22×C3#57611yescharacteristic
696C2×D3—22no—
697C2×D3—22no—
698C2×D3—22no—
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—22no—
702C2×D3—42no—
703C2×D3—42no—
704C2×D3—42no—
705C2×D3—816no—
706C2×D3—81no—
707C2×D3—81no—
708C2×D3—81no—
709C2×D3—81no—
710C2×D3#44914yes—
711C3×C4—41no—
712C3×C4—42no—
713C3×C4—81no—
714C3×C4#52511yescharacteristic
715C3×C4#53511yescharacteristic
716C3×C4#54611yescharacteristic
717C3×C4#54611yescharacteristic
718Dic3—22no—
719Dic3—41no—
720Dic3—42no—
721Dic3—42no—
722Dic3—41no—
723Dic3—81no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—21no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—32no—
734C23—32no—
735C23—32no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—61no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—62no—
753C23—128no—
754C23—121no—
755C23—121no—
756C23—121no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—244no—
761C23—244no—
762C23—244no—
763C23—244no—
764C23—244no—
765C23—244no—
766C23C2×D3×D411yescharacteristic
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—62no—
776D4—62no—
777D4—84no—
778D4—84no—
779D4—128no—
780D4—124no—
781D4—128no—
782D4—121no—
783D4—121no—
784D4—244no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—32no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—121no—
814C2×C4—121no—
815C2×C4—121no—
816C2×C4—121no—
817C2×C4—121no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—244no—
821C2×C4—244no—
822C2×C4C2×D3×D411yescharacteristic
823C2×C4C2×D3×D411yescharacteristic
824C2×C4C2×#23711yescharacteristic
825C2×C4#100411yescharacteristic
826C2×C4#100411yescharacteristic
827C2×C4D3×#4111yescharacteristic
828C8—41no—
829C8—41no—
830C8—121no—
831C8—121no—
832C2×C3—82no—
833C2×C3—81no—
834C2×C3—82no—
835C2×C3#240411yescharacteristic
836C2×C3C2×#44911yescharacteristic
837C2×C3#300811yescharacteristic
838C2×C3#329711yescharacteristic
839C2×C3#329711yescharacteristic
840C2×C3#331811yescharacteristic
841C2×C3#331811yescharacteristic
842D3—24no—
843D3—82no—
844C22—34no—
845C22—41no—
846C22—42no—
847C22—41no—
848C22—41no—
849C22—42no—
850C22—41no—
851C22—42no—
852C22—41no—
853C22—42no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—62no—
859C22—62no—
860C22—62no—
861C22—62no—
862C22—62no—
863C22—62no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—122no—
873C22—122no—
874C22—122no—
875C22—2416no—
876C22—241no—
877C22—241no—
878C22—241no—
879C22—241no—
880C22D3×#12011yescharacteristic
881C22#559111yescharacteristic
882C22#561011yescharacteristic
883C22#575711yescharacteristic
884C22D3×#13511yescharacteristic
885C22D3×AGL(1,ℤ/8)11yescharacteristic
886C22#577411yescharacteristic
887C4—42no—
888C4—41no—
889C4—62no—
890C4—81no—
891C4—121no—
892C4—122no—
893C4—121no—
894C4—122no—
895C4—241no—
896C4#559111yescharacteristic
897C4#560611yescharacteristic
898C4#561011yescharacteristic
899C4#571511yescharacteristic
900C3#2396311yescharacteristic, complemented, Sylow
901C2—64no—
902C2—81no—
903C2—82no—
904C2—82no—
905C2—242no—
906C2#7675411yescharacteristic
907C2#8000411yescharacteristic
908C2#8001811yescharacteristic
909C2D3×#44911yescharacteristic
910C2#8010211yescharacteristic
911C2#8072511yescharacteristic
912C2#8087611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1999C2
socleC23×C3C22×D4
hypercenter#1999D3
hypocenterC3#23963
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1999

Complements

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

NH ≅ G/Ntype
1. C2×#5614C2semidirect
2. C2×#5156C2semidirect
3. #82640C2semidirect
4. C2×D3×#102C2semidirect
5. C3×#1999C2semidirect
6. #72037C2semidirect
7. #71684C2semidirect
8. #71678C2semidirect
9. #70202C2semidirect
10. #70172C2semidirect
11. #70164C2semidirect
12. #69957C2semidirect
13. #69933C2semidirect
14. #68899C2semidirect
15. #68872C2semidirect
20. C2×C3×#121C22semidirect
25. C2×D4×Dic3C22semidirect
29. C2×#926C22semidirect
34. C2×#890C22semidirect
38. C2×C3×#102C22semidirect
39. C2×C3×C22⋊C8C22semidirect
44. C2×#832C22semidirect
45. C2×#830C22semidirect
56. C3×#340C22semidirect
57. #4551C22semidirect
58. #4551C22semidirect
59. #4550C22semidirect
60. #4550C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4529C22semidirect
71. #1999D3semidirect
120. #938D4semidirect
154. D3×C4⋊C4D4semidirect
184. C2×#121C2×D3semidirect
200. C2×#102C2×D3semidirect
203. C2×C22⋊C8C2×D3semidirect
215. #340C2×D3semidirect
900. C3#23963semidirect

Maximal subgroups

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

subgroupindex
C2×#56142
C2×#51562
#826402
C2×D3×#1022
C3×#19992
#720372
#716842
#716782
#702022
#701722
#701642
#699572
#699332
#688992
#688722
#239633