Finite Group Databasebeta

← #10827342

Subgroups — #10827342

Order 768.

1690 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5507C211yesmaximal, characteristic, complemented
2#82640C211yesmaximal, characteristic, complemented
3C2×#4773C211yesmaximal, characteristic, complemented
4C2×D3×#102C211yesmaximal, characteristic, complemented
5C3×#1874C211yesmaximal, characteristic, complemented
6#71684C211yesmaximal, characteristic, complemented
7#71560C211yesmaximal, characteristic, complemented
8#70208C211yesmaximal, characteristic, complemented
9#70163C211yesmaximal, characteristic, complemented
10#69961C211yesmaximal, characteristic, complemented
11#69957C211yesmaximal, characteristic, complemented
12#68898C211yesmaximal, characteristic, complemented
13#68897C211yesmaximal, characteristic, complemented
14#68883C211yesmaximal, characteristic, complemented
15#68871C211yesmaximal, characteristic, complemented
16#23960—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×#235—21no—
19C2×C3×#121C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic, complemented
21C2×#937—21no—
22C22×#213C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×#930C2211yescharacteristic, complemented
25C2×#929—21no—
26C2×C4×#67C2211yescharacteristic
27C22×D24C2211yescharacteristic
28C22×D3×C8C2211yescharacteristic
29C2×#896—21no—
30#5507—24no—
31#5507—24no—
32C2×#895C2211yescharacteristic
33C2×#894—21no—
34C2×#893C2211yescharacteristic, complemented
35C2×D3×C4⋊C4C2211yescharacteristic
36C2×#888C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40#5223—21no—
41#5221C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#830C2211yescharacteristic, complemented
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic, complemented
46C2×(C2×D3)⋊C8C2211yescharacteristic
47#4988C2211yescharacteristic
48#4987C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic, complemented
52#4959—21no—
53#4955—21no—
54#4773—24no—
55D3×#102—24no—
56C3×#340C2211yescharacteristic, complemented
57C3×#340C2211yescharacteristic, complemented
58#4551C2211yescharacteristic, complemented
59#4550C2211yescharacteristic, complemented
60#4550C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64C2×#547—31no—
65C2×#447—31no—
66C22×#102—31no—
67#2408—31no—
68#2023—31no—
69#2023—31no—
70#1999—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1879—31no—
75#1874—31no—
76#1874D311yescharacteristic, complemented
77#1869—31no—
78#1823—31no—
79C24×D3—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C22×#67D411yescharacteristic
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—41no—
93C2×D3×D4—41no—
94C2×#235—28no—
95C2×#235—44no—
96C2×#235—44no—
97C22×D12—21no—
98C22×D12C2311yescharacteristic
99C22×D12C2311yescharacteristic
100C22×C4×D3—21no—
101C22×C4×D3—21no—
102C22×C4×D3C2311yescharacteristic
103C22×Dic6—21no—
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×#121—22no—
107C3×#121—41no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×#217—21no—
116C2×#217—21no—
117C2×#217D411yescharacteristic
118#937—44no—
119C2×#213—22no—
120C2×#213—22no—
121C2×#213—41no—
122#930—22no—
123#930—22no—
124#930—22no—
125#930—41no—
126#929—28no—
127C4×#67—22no—
128C4×#67—22no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4D411yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4D411yescharacteristic
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×D24—22no—
146C2×D24—22no—
147C2×D24—41no—
148C2×D3×C8—22no—
149C2×D3×C8—41no—
150C2×D3×C8—41no—
151#896—28no—
152#895—22no—
153#895D414yescomplemented
154#894—28no—
155#893—22no—
156#893—22no—
157D3×C4⋊C4—22no—
158D3×C4⋊C4D414yescomplemented
159#888—22no—
160#888—22no—
161C3×#102—22no—
162C3×#102—22no—
163C3×C22⋊C8—41no—
164#832—22no—
165C3⋊#95—21no—
166#830—41no—
167#821—22no—
168#821—41no—
169(C2×D3)⋊C8—22no—
170#809—22no—
171#809—22no—
172#809—41no—
173C22×#41—61no—
174C23×D4—31no—
175C22×D8—31no—
176C22×D8—31no—
177C23×C8—31no—
178#547—64no—
179#547—64no—
180C2×C4⋊Q8—31no—
181C2×#123—61no—
182C2×#123—61no—
183C2×C22⋊Q8—61no—
184C2×#121—31no—
185C2×#121—31no—
186C2×#121—31no—
187C2×#121C2×D311yescharacteristic
188C2×#120—61no—
189C2×C4×D4—31no—
190C2×C4×D4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4C2×D311yescharacteristic, complemented
193#447—64no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×#102—64no—
201C2×#102C2×D311yescharacteristic
202C2×#102C2×D311yescharacteristic
203C2×C22⋊C8—31no—
204C2×C22⋊C8—31no—
205C2×C22⋊C8C2×D311yescharacteristic, complemented
206#394—61no—
207#392—61no—
208#390—31no—
209#390—31no—
210#380—31no—
211#379—61no—
212#340—31no—
213#340—31no—
214#340—31no—
215#340—31no—
216#340C2×D311yescharacteristic, complemented
217#340C2×D311yescharacteristic, complemented
218#336—31no—
219#336—31no—
220C24×C3—21no—
221C24×C3C2×D411yescharacteristic
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—42no—
225C23×D3—42no—
226C23×D3—42no—
227C23×D3—42no—
228C23×D3—42no—
229C23×D3—81no—
230C23×D3—81no—
231C23×D3C2×D411yescharacteristic
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—81no—
240C2×C3×D4#4112yescomplemented
241C22×C3×C4—24no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—42no—
252C22×C3×C4—42no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2411yescharacteristic
255C2×#67—22no—
256C2×#67—22no—
257C2×#67—24no—
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—42no—
265C2×#67—81no—
266C2×#67D814yescomplemented
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3C2×D411yescharacteristic
270C22×Dic3C2×D411yescharacteristic
271C22×Dic3C2×D411yescharacteristic
272D3×D4—28no—
273D3×D4—44no—
274D3×D4—44no—
275D3×D4—44no—
276#235—432no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—24no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—42no—
289C2×D12—42no—
290C2×D12C2×D412yes—
291C2×D12#4112yescomplemented
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—24no—
297C2×C4×D3—24no—
298C2×C4×D3—42no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×C4×D3C2×D412yes—
303C2×C4×D3C2×D412yes—
304C2×Dic6—24no—
305C2×Dic6—42no—
306C2×Dic6—42no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C3×C4⋊C4—24no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4C2×D412yes—
319C3×C4⋊C4C2×D412yes—
320C3×C22⋊C4—42no—
321#217—22no—
322#217—42no—
323#217—81no—
324#213—44no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—22no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—42no—
330(C2×D3)⋊C4—42no—
331(C2×D3)⋊C4—42no—
332(C2×D3)⋊C4—81no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3C2×D412yes—
337Dic3⋊C4—24no—
338Dic3⋊C4—24no—
339Dic3⋊C4—22no—
340C4×Dic3—21no—
341C4×Dic3—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348D24—44no—
349D3×C8—44no—
350C25—61no—
351C2×#41—68no—
352C2×#41—124no—
353C2×#41—124no—
354C22×Q8—61no—
355C22×D4—21no—
356C22×D4—31no—
357C22×D4—31no—
358C22×D4—31no—
359C22×D4—61no—
360C22×D4—62no—
361C22×D4—62no—
362C22×D4—61no—
363C22×D4—62no—
364C22×D4—62no—
365C22×D4—61no—
366C22×D4—61no—
367C22×D4—121no—
368C22×D4—121no—
369C22×D4C22×D311yescharacteristic
370C23×C4—21no—
371C23×C4—31no—
372C23×C4—61no—
373C23×C4—61no—
374C23×C4C22×D311yescharacteristic
375C2×D8—62no—
376C2×D8—62no—
377C2×D8—62no—
378C2×D8—62no—
379C2×D8—121no—
380C2×D8—121no—
381C22×C8—31no—
382C22×C8—31no—
383C22×C8—62no—
384C22×C8—121no—
385C22×C8—121no—
386C22×C8C22×D311yescharacteristic
387C22×C8C22×D311yescharacteristic
388C4⋊Q8—62no—
389C4⋊Q8—62no—
390#123—68no—
391#123—68no—
392C22⋊Q8—68no—
393#121—22no—
394#121—34no—
395#121—41no—
396#121—62no—
397#121—62no—
398#121—62no—
399#121—62no—
400#121—121no—
401#120—124no—
402C4×D4—62no—
403C4×D4—62no—
404C4×D4—62no—
405C4×D4—62no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C4⋊C4C22×D311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—31no—
421C2×C22⋊C4—31no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C42—31no—
432#102—22no—
433#102—22no—
434#102—62no—
435#102—62no—
436#102—62no—
437#102—62no—
438#102—121no—
439#102—121no—
440C22⋊C8—41no—
441C22⋊C8—62no—
442C22⋊C8—121no—
443#95—61no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—22no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3C2×D812yes—
458C23×C3C22×D411yescharacteristic
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—48no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—41no—
478C22×D3—84no—
479C22×D3—84no—
480C22×D3—84no—
481C22×D3—84no—
482C22×D3—84no—
483C22×D3—84no—
484C22×D3#12012yes—
485C22×D3C2×D812yes—
486C22×D3AGL(1,ℤ/8)12yes—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—84no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—48no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4C22×D411yescharacteristic
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C2×#4111yescharacteristic
512C2×C3×C4C2×#4111yescharacteristic
513C2×C3×C4H(5,𝔽2)11yescharacteristic
514C2×C3×C4H(5,𝔽2)11yescharacteristic
515#67—28no—
516#67—48no—
517#67—48no—
518#67—84no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—22no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3#12012yes—
533C2×Dic3C2×D812yes—
534D12—22no—
535D12—22no—
536D12—22no—
537D12—22no—
538D12—48no—
539D12—41no—
540D12—41no—
541D12—41no—
542D12—41no—
543C4×D3—22no—
544C4×D3—22no—
545C4×D3—22no—
546C4×D3—22no—
547C4×D3—48no—
548C4×D3—48no—
549Dic6—48no—
550C3×C8—41no—
551C3×C8—41no—
552C3⋊C8—41no—
553C3⋊C8—41no—
554C24—21no—
555C24—31no—
556C24—61no—
557C24—61no—
558C24—122no—
559C24—122no—
560C24—122no—
561C24—122no—
562C24—122no—
563C24—241no—
564C24—241no—
565C24D3×D411yescharacteristic
566#41—1232no—
567C2×Q8—64no—
568C2×Q8—122no—
569C2×Q8—122no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—34no—
576C2×D4—32no—
577C2×D4—32no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—64no—
581C2×D4—68no—
582C2×D4—62no—
583C2×D4—62no—
584C2×D4—64no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—81no—
596C2×D4—122no—
597C2×D4—122no—
598C2×D4—122no—
599C2×D4—124no—
600C2×D4—124no—
601C2×D4—124no—
602C2×D4—122no—
603C2×D4—122no—
604C2×D4—122no—
605C2×D4—122no—
606C2×D4—122no—
607C2×D4—122no—
608C2×D4—241no—
609C2×D4#23512yescomplemented
610C22×C4—24no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—32no—
623C22×C4—32no—
624C22×C4—31no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—64no—
628C22×C4—64no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—122no—
636C22×C4—122no—
637C22×C4—122no—
638C22×C4—122no—
639C22×C4D3×D411yescharacteristic
640C22×C4C23×D311yescharacteristic
641D8—124no—
642D8—124no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—61no—
650C2×C8—61no—
651C2×C8—61no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—124no—
656C4⋊C4—24no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—32no—
662C4⋊C4—64no—
663C4⋊C4—62no—
664C4⋊C4—64no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4D3×D412yes—
669C4⋊C4D3×D412yes—
670C22⋊C4—42no—
671C22⋊C4—64no—
672C22⋊C4—62no—
673C22⋊C4—64no—
674C22⋊C4—64no—
675C22⋊C4—62no—
676C22⋊C4—122no—
677C22⋊C4—122no—
678C22⋊C4—122no—
679C22⋊C4—122no—
680C22⋊C4—241no—
681C22⋊C4—241no—
682C42—61no—
683C42—61no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3C2×#12011yescharacteristic
699C22×C3#54611yescharacteristic
700C22×C3#54611yescharacteristic
701C22×C3C22×D811yescharacteristic
702C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
703C22×C3#57711yescharacteristic
704C22×C3#57711yescharacteristic
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—42no—
712C2×D3—42no—
713C2×D3—42no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3—42no—
717C2×D3—816no—
718C2×D3—81no—
719C2×D3—81no—
720C2×D3—81no—
721C2×D3—81no—
722C2×D3—81no—
723C2×D3—81no—
724C2×D3—81no—
725C2×D3—81no—
726C2×D3#44714yes—
727C3×C4—41no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—81no—
731C3×C4#52511yescharacteristic
732C3×C4#53511yescharacteristic
733C3×C4#54611yescharacteristic
734C3×C4#54611yescharacteristic
735Dic3—22no—
736Dic3—22no—
737Dic3—42no—
738Dic3—41no—
739Dic3—81no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—32no—
748C23—32no—
749C23—32no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—62no—
761C23—62no—
762C23—128no—
763C23—121no—
764C23—121no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—121no—
771C23—121no—
772C23—121no—
773C23—121no—
774C23—121no—
775C23—244no—
776C23—244no—
777C23—244no—
778C23—244no—
779C23—244no—
780C23—244no—
781C23D3×D812yes—
782C23C2×D3×D411yescharacteristic
783Q8—128no—
784D4—22no—
785D4—22no—
786D4—41no—
787D4—41no—
788D4—68no—
789D4—62no—
790D4—62no—
791D4—62no—
792D4—62no—
793D4—84no—
794D4—128no—
795D4—128no—
796D4—128no—
797D4—121no—
798D4—121no—
799D4—121no—
800D4—121no—
801D4—244no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—48no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—62no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—62no—
833C2×C4—128no—
834C2×C4—128no—
835C2×C4—121no—
836C2×C4—121no—
837C2×C4—121no—
838C2×C4—121no—
839C2×C4—121no—
840C2×C4C2×#23511yescharacteristic
841C2×C4C2×D3×D411yescharacteristic
842C2×C4C2×D3×D411yescharacteristic
843C2×C4#100411yescharacteristic
844C2×C4D3×#4111yescharacteristic
845C2×C4#100911yescharacteristic
846C8—41no—
847C8—41no—
848C8—121no—
849C8—121no—
850C2×C3—42no—
851C2×C3—82no—
852C2×C3#240411yescharacteristic
853C2×C3C2×#44711yescharacteristic
854C2×C3#301011yescharacteristic
855C2×C3#329411yescharacteristic
856C2×C3#329411yescharacteristic
857C2×C3#330611yescharacteristic
858C2×C3#330611yescharacteristic
859D3—24no—
860D3—82no—
861D3—82no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—34no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—62no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—62no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—122no—
884C22—122no—
885C22—122no—
886C22—122no—
887C22—122no—
888C22—122no—
889C22—2416no—
890C22—241no—
891C22—241no—
892C22—241no—
893C22—241no—
894C22—241no—
895C22—241no—
896C22—241no—
897C22—241no—
898C22#549011yescharacteristic
899C22D3×#12011yescharacteristic
900C22#565411yescharacteristic
901C22C2×D3×D811yescharacteristic
902C22#576211yescharacteristic
903C22D3×AGL(1,ℤ/8)11yescharacteristic
904C22#577811yescharacteristic
905C4—42no—
906C4—42no—
907C4—41no—
908C4—62no—
909C4—62no—
910C4—81no—
911C4—122no—
912C4—121no—
913C4—241no—
914C4#554711yescharacteristic
915C4#555011yescharacteristic
916C4#560711yescharacteristic
917C4#561211yescharacteristic
918C3#2396011yescharacteristic, complemented, Sylow
919C2—42no—
920C2—64no—
921C2—82no—
922C2—242no—
923C2—242no—
924C2#7488611yescharacteristic
925C2#7875711yescharacteristic
926C2#7889411yescharacteristic
927C2D3×#44711yescharacteristic
928C2#8004111yescharacteristic
929C2#8130211yescharacteristic
930C2#8133111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1874C2
socleC23×C3C22×D4
hypercenter#1874D3
hypocenterC3#23960
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#5507C2semidirect
2. #82640C2semidirect
3. C2×#4773C2semidirect
4. C2×D3×#102C2semidirect
5. C3×#1874C2semidirect
6. #71684C2semidirect
7. #71560C2semidirect
8. #70208C2semidirect
9. #70163C2semidirect
10. #69961C2semidirect
11. #69957C2semidirect
12. #68898C2semidirect
13. #68897C2semidirect
14. #68883C2semidirect
15. #68871C2semidirect
20. C22×C3×C4⋊C4C22semidirect
24. C2×#930C22semidirect
34. C2×#893C22semidirect
36. C2×#888C22semidirect
39. C2×C3×C22⋊C8C22semidirect
43. C2×#830C22semidirect
45. C2×#821C22semidirect
51. C2×#809C22semidirect
56. C3×#340C22semidirect
57. C3×#340C22semidirect
58. #4551C22semidirect
59. #4550C22semidirect
60. #4550C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4529C22semidirect
76. #1874D3semidirect
153. #895D4semidirect
158. D3×C4⋊C4D4semidirect
192. C22×C4⋊C4C2×D3semidirect
205. C2×C22⋊C8C2×D3semidirect
216. #340C2×D3semidirect
217. #340C2×D3semidirect
240. C2×C3×D4#41semidirect
266. C2×#67D8semidirect
291. C2×D12#41semidirect
609. C2×D4#235semidirect
918. C3#23960semidirect

Maximal subgroups

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

subgroupindex
C2×#55072
#826402
C2×#47732
C2×D3×#1022
C3×#18742
#716842
#715602
#702082
#701632
#699612
#699572
#688982
#688972
#688832
#688712
#239603