Finite Group Databasebeta

← #10810698

Subgroups — #10810698

Order 768.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5831C211yesmaximal, characteristic
2C2×C3×#417C211yesmaximal, characteristic, complemented
3C2×#5127C211yesmaximal, characteristic, complemented
4C4⋊C4×#67C211yesmaximal, characteristic, complemented
5C2×D3×#103C211yesmaximal, characteristic, complemented
6#72135C211yesmaximal, characteristic, complemented
7#71989C211yesmaximal, characteristic, complemented
8#71559C211yesmaximal, characteristic, complemented
9#70266C211yesmaximal, characteristic, complemented
10#70221C211yesmaximal, characteristic, complemented
11#70220C211yesmaximal, characteristic, complemented
12#70202C211yesmaximal, characteristic, complemented
13#70200C211yesmaximal, characteristic, complemented
14#70162C211yesmaximal, characteristic, complemented
15#70159C211yesmaximal, characteristic, complemented
16#22421—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21#5831—24no—
22#5831C418yescomplemented
23C2×Q8×Dic3C2211yescharacteristic
24C2×#938—21no—
25C2×#938C2211yescharacteristic
26C2×#936—21no—
27C2×#936C2211yescharacteristic
28C2×C4×#67—21no—
29C2×C4×#67—21no—
30C2×C4×#67C2211yescharacteristic
31C2×#924—21no—
32C2×#924C2211yescharacteristic
33C22×D3×C8C2211yescharacteristic
34C2×D3×C4⋊C4C2211yescharacteristic
35C3×#417—24no—
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44#5212C2211yescharacteristic
45#5210—21no—
46C2×#830C2211yescharacteristic
47#5127—24no—
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×#816C2211yescharacteristic
50C2×#816C2211yescharacteristic
51C2×#815C2211yescharacteristic
52C2×Dic3⋊C8C2211yescharacteristic
53#4989—21no—
54#4987C2211yescharacteristic
55#4976—21no—
56#4975C2211yescharacteristic
57Dic3×C4⋊C4C2211yescharacteristic
58C2×#810C2211yescharacteristic
59C2×#810C2211yescharacteristic
60D3×#103—24no—
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#548—31no—
66C2×#435—31no—
67C2×#417D311yescharacteristic, complemented
68C22×#103—31no—
69D4×C4⋊C4—31no—
70#1983—31no—
71#1959—31no—
72#1894—31no—
73#1893—31no—
74#1874—31no—
75#1872—31no—
76#1803—31no—
77#1788—31no—
78#1787—31no—
79#1763—31no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C2×C3×#41C2×C414yescomplemented
86C22×C3×Q8C2311yescharacteristic
87C22×C3×D4—21no—
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C22×#67—21no—
93C22×#67D411yescharacteristic
94C2×D3×Q8—22no—
95C2×D3×Q8—22no—
96C2×D3×Q8—22no—
97C2×D3×Q8—41no—
98C2×D3×Q8—41no—
99C2×D3×Q8C2×C414yescomplemented
100C22×C4×D3—21no—
101C22×C4×D3—21no—
102C22×C4×D3C2311yescharacteristic
103C22×Dic6—21no—
104C22×Dic6C2311yescharacteristic
105C2×C3×M16—22no—
106C2×C3×M16—22no—
107C2×C3×M16—41no—
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—41no—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×#217—21no—
116C2×#217—21no—
117C2×#217—21no—
118C2×#217—21no—
119C2×#217—21no—
120C2×#217D411yescharacteristic
121Q8×Dic3—22no—
122Q8×Dic3C2×C414yescomplemented
123#938—28no—
124#938—22no—
125#938C2×C414yescomplemented
126#936—28no—
127#936—22no—
128#936C2×C414yescomplemented
129C4×#67—28no—
130C4×#67—44no—
131C4×#67C2×C414yes—
132C4×#67D414yes—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4D411yescharacteristic
135C2×C4⋊Dic3—21no—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139#924—22no—
140#924—28no—
141#924C2×C414yescomplemented
142C2×Dic3⋊C4—21no—
143C2×Dic3⋊C4—21no—
144C2×Dic3⋊C4—21no—
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4D411yescharacteristic
147C2×C4×Dic3—21no—
148C2×C4×Dic3—21no—
149C2×C4×Dic3C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C2×D3×C8—22no—
153C2×D3×C8—22no—
154C2×D3×C8—41no—
155D3×C4⋊C4—22no—
156D3×C4⋊C4—41no—
157C3×#103—22no—
158C3×#103D414yescomplemented
159C3×#102—22no—
160C3×#102—22no—
161#835—22no—
162#835—22no—
163#832—41no—
164#832—41no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168#830—22no—
169(C2×D3)⋊C8—22no—
170#816—22no—
171#816—41no—
172#815—22no—
173Dic3⋊C8—22no—
174#810—22no—
175#810—41no—
176C22×#41C2×D311yescharacteristic
177C23×Q8—31no—
178C22×M16C2×D311yescharacteristic
179C23×C8—31no—
180#548—38no—
181#548—64no—
182C2×#124—31no—
183C2×#124—61no—
184C2×C22⋊Q8—31no—
185C2×C22⋊Q8—61no—
186C2×#121—31no—
187C2×#121—61no—
188C2×C4×Q8—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4C2×D311yescharacteristic
194#435—64no—
195C2×C4⋊C8—31no—
196#417—24no—
197C2×#103—31no—
198C2×#103—31no—
199C2×#103—31no—
200C2×#103—31no—
201C2×#103—31no—
202C2×#103—31no—
203C2×#103—64no—
204C2×#103C2×D311yescharacteristic
205C2×#103C2×D311yescharacteristic
206C2×#102—31no—
207C2×#102—31no—
208C2×#102C2×D311yescharacteristic
209C2×#102C2×D311yescharacteristic
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212C2×#97—31no—
213#389—61no—
214#385—61no—
215#385—61no—
216#384—31no—
217#380—31no—
218#380—31no—
219C4×C4⋊C4—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223#340—31no—
224C24×C3—21no—
225C24×C3C2×D411yescharacteristic
226C23×D3C2×D411yescharacteristic
227C3×#41—28no—
228C3×#41—44no—
229C3×#41—44no—
230C3×#41—44no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8C22×C412yes—
235C2×C3×Q8C2×D412yes—
236C2×C3×Q8#4112yes—
237C2×C3×D4—24no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4C22×C412yes—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—24no—
253C22×C3×C4—21no—
254C22×C3×C4—42no—
255C22×C3×C4—42no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4—81no—
259C22×C3×C4C22×C412yes—
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D412yes—
262C22×C3×C4C2411yescharacteristic
263C2×#67—22no—
264C2×#67—22no—
265C2×#67—24no—
266C2×#67—42no—
267C2×#67—42no—
268C2×#67C22⋊C414yes—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3C2×D411yescharacteristic
274C22×Dic3C2×D411yescharacteristic
275C22×Dic3C2×D411yescharacteristic
276D3×Q8—28no—
277D3×Q8—44no—
278D3×Q8—44no—
279D3×Q8—44no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—24no—
285C2×C4×D3—42no—
286C2×C4×D3—42no—
287C2×C4×D3—42no—
288C2×C4×D3—42no—
289C2×C4×D3—81no—
290C2×C4×D3C22×C412yes—
291C2×C4×D3C2×D412yes—
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C2×Dic6—21no—
297C2×Dic6—24no—
298C2×Dic6—42no—
299C2×Dic6—42no—
300C2×Dic6C22×C412yes—
301C3×M16—44no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C2×C3×C8C2×D412yes—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—42no—
312C3×C4⋊C4C2×D412yes—
313#217—24no—
314#217—24no—
315#217—24no—
316#217—24no—
317#217—42no—
318#217C22⋊C414yes—
319(C2×D3)⋊C4—42no—
320(C2×D3)⋊C4C22⋊C414yes—
321C4⋊Dic3—21no—
322C4⋊Dic3—24no—
323C4⋊Dic3—21no—
324C4⋊Dic3—21no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3C22×C412yes—
328Dic3⋊C4—24no—
329Dic3⋊C4—42no—
330Dic3⋊C4—42no—
331Dic3⋊C4—81no—
332Dic3⋊C4C22⋊C414yes—
333C4×Dic3—24no—
334C4×Dic3—42no—
335C4×Dic3C22×C412yes—
336C4×Dic3C2×D412yes—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343D3×C8—44no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—41no—
348C2×#41—41no—
349C2×#41C4×D314yescomplemented
350C22×Q8—34no—
351C22×Q8—31no—
352C22×Q8—61no—
353C22×Q8—62no—
354C22×Q8—62no—
355C22×Q8—62no—
356C22×Q8—121no—
357C22×Q8—121no—
358C22×Q8C22×D311yescharacteristic
359C22×D4—21no—
360C22×D4—31no—
361C22×D4—61no—
362C22×D4C22×D311yescharacteristic
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—31no—
366C23×C4—61no—
367C23×C4—61no—
368C23×C4C22×D311yescharacteristic
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—41no—
372C22×C8—31no—
373C22×C8—31no—
374C22×C8—62no—
375C22×C8—62no—
376C22×C8—121no—
377C22×C8C22×D311yescharacteristic
378C22×C8C22×D311yescharacteristic
379#124—34no—
380#124—62no—
381#124—68no—
382C22⋊Q8—34no—
383C22⋊Q8—68no—
384C22⋊Q8—62no—
385#121—34no—
386#121—62no—
387#121—68no—
388C4×Q8—34no—
389C4×Q8—62no—
390C4×D4—34no—
391C4×D4—34no—
392C4×D4—68no—
393C4×D4—124no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—61no—
402C2×C4⋊C4—61no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4—61no—
406C2×C4⋊C4—61no—
407C2×C4⋊C4—121no—
408C2×C4⋊C4C22×D311yescharacteristic
409C2×C4⋊C4C22×D311yescharacteristic
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×C42—31no—
419C2×C42—61no—
420C2×C42—61no—
421C4⋊C8—62no—
422#103—22no—
423#103—62no—
424#103—62no—
425#103—62no—
426#103—62no—
427#103—121no—
428#103—121no—
429#103#6714yescomplemented
430#102—22no—
431#102—22no—
432#102—121no—
433#102—121no—
434C22⋊C8—62no—
435C22⋊C8—62no—
436#97—62no—
437#95—61no—
438#95—61no—
439#95—61no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—22no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3C2×C22⋊C412yes—
454C23×C3C22×D411yescharacteristic
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3C2×C22⋊C412yes—
460C22×D3AGL(1,ℤ/8)12yes—
461C22×D3#13712yes—
462C3×Q8—22no—
463C3×Q8—22no—
464C3×Q8—22no—
465C3×Q8C4×D414yescomplemented
466C3×D4—22no—
467C3×D4—22no—
468C3×D4—48no—
469C3×D4—41no—
470C3×D4—41no—
471C2×C3×C4—22no—
472C2×C3×C4—21no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—48no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—84no—
488C2×C3×C4C2×C22⋊C412yes—
489C2×C3×C4C23×C411yescharacteristic
490C2×C3×C4C22×D411yescharacteristic
491C2×C3×C4C22×D411yescharacteristic
492C2×C3×C4C2×#4111yescharacteristic
493C2×C3×C4H(5,𝔽2)11yescharacteristic
494C2×C3×C4H(5,𝔽2)11yescharacteristic
495#67—28no—
496#67—48no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3C2×C22⋊C412yes—
516C2×Dic3C2×C22⋊C412yes—
517C2×Dic3C2×C22⋊C412yes—
518C4×D3—22no—
519C4×D3—22no—
520C4×D3—22no—
521C4×D3—22no—
522C4×D3—48no—
523C4×D3—84no—
524Dic6—22no—
525Dic6—22no—
526Dic6—48no—
527Dic6—41no—
528Dic6—41no—
529C3×C8—22no—
530C3×C8—41no—
531C3⋊C8—41no—
532C3⋊C8—41no—
533C24—21no—
534C24—31no—
535C24D3×D411yescharacteristic
536#41—28no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—32no—
544C2×Q8—64no—
545C2×Q8—61no—
546C2×Q8—68no—
547C2×Q8—61no—
548C2×Q8—61no—
549C2×Q8—61no—
550C2×Q8—61no—
551C2×Q8—122no—
552C2×Q8—122no—
553C2×Q8—124no—
554C2×Q8—124no—
555C2×Q8—124no—
556C2×Q8C2×C4×D312yes—
557C2×Q8#23512yes—
558C2×Q8C2×#6712yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—34no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—62no—
569C2×D4—62no—
570C2×D4—64no—
571C2×D4—122no—
572C2×D4—122no—
573C2×D4C2×C4×D312yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—24no—
581C22×C4—21no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—32no—
586C22×C4—32no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—64no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—81no—
601C22×C4—122no—
602C22×C4—122no—
603C22×C4—122no—
604C22×C4—122no—
605C22×C4—241no—
606C22×C4C2×C4×D312yes—
607C22×C4D3×D411yescharacteristic
608C22×C4D3×D412yes—
609C22×C4C23×D311yescharacteristic
610M16—44no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—61no—
617C2×C8—61no—
618C2×C8—61no—
619C2×C8—61no—
620C2×C8—61no—
621C2×C8—61no—
622C2×C8—124no—
623C2×C8C2×#6712yes—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—34no—
628C4⋊C4—32no—
629C4⋊C4—42no—
630C4⋊C4—64no—
631C4⋊C4—64no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4—61no—
636C4⋊C4—61no—
637C4⋊C4—122no—
638C4⋊C4—122no—
639C4⋊C4—241no—
640C4⋊C4C2×#6712yes—
641C22⋊C4—34no—
642C22⋊C4—34no—
643C22⋊C4—64no—
644C22⋊C4—64no—
645C22⋊C4—64no—
646C22⋊C4—64no—
647C22⋊C4—122no—
648C22⋊C4—122no—
649C42—32no—
650C42—32no—
651C42—64no—
652C42—122no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3C22×C22⋊C411yescharacteristic
668C22×C3D4211yescharacteristic
669C22×C3#54611yescharacteristic
670C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
671C22×C3C2×#13711yescharacteristic
672C22×C3#57711yescharacteristic
673C22×C3#57811yescharacteristic
674C2×D3—22no—
675C2×D3—22no—
676C2×D3—22no—
677C2×D3—22no—
678C2×D3—22no—
679C2×D3—22no—
680C2×D3#41714yescomplemented
681C3×C4—24no—
682C3×C4—22no—
683C3×C4—42no—
684C3×C4—81no—
685C3×C4C2×C4×D411yescharacteristic
686C3×C4#51811yescharacteristic
687C3×C4D4211yescharacteristic
688C3×C4#54611yescharacteristic
689Dic3—22no—
690Dic3—22no—
691Dic3—22no—
692Dic3—42no—
693Dic3—42no—
694Dic3—81no—
695Dic3—81no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—32no—
704C23—32no—
705C23—32no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23—61no—
716C23D3×C22⋊C412yes—
717C23C2×D3×D411yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—62no—
722Q8—62no—
723Q8—128no—
724Q8—121no—
725Q8—121no—
726Q8C4×#6714yescomplemented
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—68no—
733D4—128no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—32no—
745C2×C4—32no—
746C2×C4—32no—
747C2×C4—48no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—84no—
766C2×C4—128no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—121no—
774C2×C4—121no—
775C2×C4—121no—
776C2×C4—121no—
777C2×C4—244no—
778C2×C4D3×C22⋊C412yes—
779C2×C4C22×C4×D311yescharacteristic
780C2×C4C2×#23511yescharacteristic
781C2×C4C2×D3×D411yescharacteristic
782C2×C4#100411yescharacteristic
783C2×C4#100411yescharacteristic
784C2×C4C22×#6711yescharacteristic
785C8—22no—
786C8—41no—
787C8—121no—
788C8—121no—
789C2×C3—42no—
790C2×C3—82no—
791C2×C3D4×C22⋊C411yescharacteristic
792C2×C3C2×#41711yescharacteristic
793C2×C3#289811yescharacteristic
794C2×C3#326511yescharacteristic
795C2×C3#327011yescharacteristic
796C2×C3#330811yescharacteristic
797C2×C3#331611yescharacteristic
798D3—24no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—34no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—62no—
811C22—62no—
812C22—62no—
813C22—62no—
814C22—62no—
815C22—62no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22C2×D3×C22⋊C411yescharacteristic
821C22#549011yescharacteristic
822C22D3×AGL(1,ℤ/8)11yescharacteristic
823C22#577511yescharacteristic
824C22D3×#13711yescharacteristic
825C22#577911yescharacteristic
826C22D4×#6711yescharacteristic
827C4—22no—
828C4—24no—
829C4—42no—
830C4—62no—
831C4—62no—
832C4—62no—
833C4—81no—
834C4—122no—
835C4—122no—
836C4—241no—
837C4—241no—
838C4#548611yescharacteristic
839C4#549011yescharacteristic
840C4C2×C4×#6711yescharacteristic
841C4D4×#6711yescharacteristic
842C3#2242111yescharacteristic, complemented, Sylow
843C2—42no—
844C2—64no—
845C2—82no—
846C2D3×#41711yescharacteristic
847C2#7888311yescharacteristic
848C2#7889611yescharacteristic
849C2#7890011yescharacteristic
850C2C22⋊C4×#6711yescharacteristic
851C2#8395311yescharacteristic
852C2#8398911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#417C2
socleC23×C3C22×D4
prime radicalC2×#5831C2
cosocleC22×C3×C4C24
hypercenterC2×#417D3
hypocenterC3#22421
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×C3×#417C2semidirect
3. C2×#5127C2semidirect
4. C4⋊C4×#67C2semidirect
5. C2×D3×#103C2semidirect
6. #72135C2semidirect
7. #71989C2semidirect
8. #71559C2semidirect
9. #70266C2semidirect
10. #70221C2semidirect
11. #70220C2semidirect
12. #70202C2semidirect
13. #70200C2semidirect
14. #70162C2semidirect
15. #70159C2semidirect
22. #5831C4semidirect
67. C2×#417D3semidirect
85. C2×C3×#41C2×C4semidirect
99. C2×D3×Q8C2×C4semidirect
122. Q8×Dic3C2×C4semidirect
125. #938C2×C4semidirect
128. #936C2×C4semidirect
141. #924C2×C4semidirect
158. C3×#103D4semidirect
349. C2×#41C4×D3semidirect
429. #103#67semidirect
465. C3×Q8C4×D4semidirect
680. C2×D3#417semidirect
726. Q8C4×#67semidirect
842. C3#22421semidirect

Maximal subgroups

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

subgroupindex
C2×#58312
C2×C3×#4172
C2×#51272
C4⋊C4×#672
C2×D3×#1032
#721352
#719892
#715592
#702662
#702212
#702202
#702022
#702002
#701622
#701592
#224213