Finite Group Databasebeta

← #10944086

Subgroups — #10944086

Order 768.

1506 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5827C211yesmaximal, characteristic, complemented
2C2×C3×#449C211yesmaximal, characteristic, complemented
3C2×#5238C211yesmaximal, characteristic, complemented
4C2×#5163C211yesmaximal, characteristic, complemented
5C2×#5150C211yesmaximal, characteristic, complemented
6#82676C211yesmaximal, characteristic, complemented
7#72048C211yesmaximal, characteristic, complemented
8#72037C211yesmaximal, characteristic, complemented
9#71677C211yesmaximal, characteristic, complemented
10#70240C211yesmaximal, characteristic, complemented
11#70222C211yesmaximal, characteristic, complemented
12#70172C211yesmaximal, characteristic, complemented
13#70154C211yesmaximal, characteristic, complemented
14#69932C211yesmaximal, characteristic, complemented
15#69909C211yesmaximal, characteristic, complemented
16#32913—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21#5827—24no—
22#5827—24no—
23C2×Q8×Dic3C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C22×#215C2211yescharacteristic
26C2×#940C2211yescharacteristic
27C2×D4×Dic3—21no—
28C2×D4×Dic3—21no—
29C2×D4×Dic3C2211yescharacteristic
30C2×D4×Dic3C2211yescharacteristic
31C22×#213C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×#926—21no—
34C2×#926C2211yescharacteristic
35C22×C4⋊Dic3—21no—
36C22×C4⋊Dic3C2211yescharacteristic
37C3×#449—24no—
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41#5238—24no—
42C2×#835C2211yescharacteristic
43#5223—21no—
44#5223—21no—
45#5221C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#832C2211yescharacteristic
48C2×#832C2211yescharacteristic
49C2×#830C2211yescharacteristic
50#5163—24no—
51#5150—24no—
52C2×#821C2211yescharacteristic
53C2×#821C2211yescharacteristic
54C2×Dic3⋊C8C2211yescharacteristic
55C2×Dic3⋊C8C2211yescharacteristic
56#4988C2211yescharacteristic
57#4977C2211yescharacteristic
58#4961—21no—
59#4961—21no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#520—31no—
67C2×#460—31no—
68C2×#459—31no—
69C2×#449—31no—
70C2×#449D311yescharacteristic, complemented
71#2619—31no—
72#1880—31no—
73#1880—31no—
74#1879—31no—
75#1879—31no—
76#1874—31no—
77#1874—31no—
78#1805—31no—
79#1804—31no—
80#1798—31no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41D414yescomplemented
87C22×C3×Q8C2311yescharacteristic
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4C2311yescharacteristic
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C22×#67—21no—
95C22×#67—21no—
96C22×#67—21no—
97C23×Dic3—21no—
98C23×Dic3—21no—
99C23×Dic3—21no—
100C22×D12C2311yescharacteristic
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×D8—22no—
105C2×C3×D8—22no—
106C2×C3×D8—22no—
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C3×#121—22no—
110C3×#121—22no—
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#217—21no—
117C2×#217D411yescharacteristic
118C2×#217D411yescharacteristic
119Q8×Dic3—22no—
120Q8×Dic3—22no—
121Q8×Dic3—22no—
122Q8×Dic3D414yescomplemented
123C2×#215—22no—
124C2×#215—22no—
125C2×#215—22no—
126#940—22no—
127#940—22no—
128D4×Dic3—28no—
129D4×Dic3—28no—
130D4×Dic3—22no—
131D4×Dic3—22no—
132D4×Dic3—22no—
133D4×Dic3D414yescomplemented
134C2×#213—22no—
135C2×#213—22no—
136C2×#213—22no—
137#930—22no—
138#930—22no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142#926—28no—
143#926—22no—
144#926—22no—
145C2×C4⋊Dic3—28no—
146C2×C4⋊Dic3—21no—
147C2×C4⋊Dic3—21no—
148C2×C4⋊Dic3—21no—
149C2×C4⋊Dic3—22no—
150C2×C4⋊Dic3—22no—
151C2×C4⋊Dic3D411yescharacteristic
152C2×C4⋊Dic3D411yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4×Dic3—21no—
157C2×C4×Dic3—21no—
158C2×C4×Dic3C2311yescharacteristic
159C2×C4×Dic3C2311yescharacteristic
160C22×C3⋊C8C2311yescharacteristic
161C22×C3⋊C8C2311yescharacteristic
162C3×#103—22no—
163C3×#102—22no—
164C3×C22⋊C8—22no—
165#835—22no—
166#832—22no—
167#832—22no—
168#832—22no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#830—22no—
172#821—22no—
173#821—22no—
174Dic3⋊C8—22no—
175Dic3⋊C8—22no—
176C22×#41C2×D311yescharacteristic
177C22×SD16—31no—
178C22×SD16C2×D311yescharacteristic
179C22×D8—31no—
180C22×D8C2×D311yescharacteristic
181C2×#127—31no—
182C2×#121—31no—
183C2×#121C2×D311yescharacteristic
184#520—64no—
185#520—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×#117—31no—
193C2×#117—61no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—61no—
196#460—64no—
197#459—64no—
198#449—24no—
199#449—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103C2×D311yescharacteristic
204C2×#102—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102C2×D311yescharacteristic
210C2×C22⋊C8—31no—
211C2×C22⋊C8C2×D311yescharacteristic
212#394—61no—
213#394—61no—
214#392—61no—
215#392—61no—
216#390—31no—
217#390—31no—
218#382—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223#336—31no—
224#336—31no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3C2×D411yescharacteristic
228C23×D3—21no—
229C3×#41—28no—
230C3×#41—28no—
231C3×#41—28no—
232C3×#41—28no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8C2×D412yes—
237C2×C3×Q8C2×D412yes—
238C2×C3×Q8#4112yes—
239C2×C3×D4—24no—
240C2×C3×D4—24no—
241C2×C3×D4—24no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—42no—
252C2×C3×D4—81no—
253C2×C3×D4—81no—
254C2×C3×D4C2×D412yes—
255C2×C3×D4C2×D412yes—
256C2×C3×D4#4112yes—
257C22×C3×C4—24no—
258C22×C3×C4—24no—
259C22×C3×C4—21no—
260C22×C3×C4—24no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D412yes—
268C22×C3×C4#4112yes—
269C22×C3×C4C2411yescharacteristic
270C2×#67—42no—
271C2×#67—42no—
272C2×#67—42no—
273C2×#67—81no—
274C2×#67—81no—
275C2×#67—81no—
276C2×#67—81no—
277C2×#67—81no—
278C2×#67—81no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—24no—
282C22×Dic3—24no—
283C22×Dic3—24no—
284C22×Dic3—21no—
285C22×Dic3—81no—
286C22×Dic3—81no—
287C22×Dic3—81no—
288C22×Dic3—81no—
289C22×Dic3—81no—
290C22×Dic3—81no—
291C22×Dic3C2×D411yescharacteristic
292C22×Dic3C2×D411yescharacteristic
293C22×Dic3C2×D411yescharacteristic
294C22×Dic3C2×D411yescharacteristic
295C2×D12—21no—
296C2×D12—21no—
297C2×D12—21no—
298C2×D12—21no—
299C2×D12—21no—
300C2×D12—21no—
301C3×SD16—44no—
302C3×D8—44no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C22⋊C4—42no—
312#217—24no—
313#217—22no—
314#217—22no—
315#217—24no—
316#217—81no—
317#217—81no—
318#215—44no—
319#213—44no—
320(C2×D3)⋊C4—42no—
321(C2×D3)⋊C4—81no—
322(C2×D3)⋊C4—81no—
323C4⋊Dic3—24no—
324C4⋊Dic3—24no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—22no—
328C4⋊Dic3—24no—
329C4⋊Dic3—22no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3C2×D412yes—
333C4⋊Dic3C2×D412yes—
334C4×Dic3—24no—
335C4×Dic3—21no—
336C4×Dic3—21no—
337C4×Dic3—24no—
338C4×Dic3C2×D412yes—
339C4×Dic3C2×D412yes—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41#6714yescomplemented
352C22×Q8C22×D311yescharacteristic
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—31no—
356C22×D4—61no—
357C22×D4—61no—
358C22×D4—61no—
359C22×D4C22×D311yescharacteristic
360C22×D4C22×D311yescharacteristic
361C23×C4—21no—
362C23×C4—61no—
363C23×C4—61no—
364C23×C4—61no—
365C23×C4C22×D311yescharacteristic
366C2×SD16—22no—
367C2×SD16—22no—
368C2×SD16—22no—
369C2×SD16—62no—
370C2×SD16—62no—
371C2×SD16—62no—
372C2×D8—22no—
373C2×D8—22no—
374C2×D8—22no—
375C2×D8—62no—
376C2×D8—62no—
377C2×D8—62no—
378C22×C8—31no—
379C22×C8—31no—
380C22×C8C22×D311yescharacteristic
381C22×C8C22×D311yescharacteristic
382#127—62no—
383#127—62no—
384#121—22no—
385#121—22no—
386#121—62no—
387#121—62no—
388C4×Q8—34no—
389C4×Q8—62no—
390C4×Q8—62no—
391C4×Q8—62no—
392C4×D4—34no—
393C4×D4—62no—
394C4×D4—62no—
395C4×D4—68no—
396C4×D4—68no—
397C4×D4—62no—
398#117—62no—
399#117—62no—
400#117—68no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—62no—
407C2×C4⋊C4—62no—
408C2×C4⋊C4—61no—
409C2×C4⋊C4—61no—
410C2×C4⋊C4—68no—
411C2×C4⋊C4—61no—
412C2×C4⋊C4C22×D311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—31no—
415C2×C22⋊C4—31no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C42—31no—
424C2×C42—31no—
425C2×C42—61no—
426C2×C42—61no—
427C4⋊C8—62no—
428C4⋊C8—62no—
429#103—22no—
430#103—62no—
431#102—22no—
432#102—62no—
433#102—62no—
434#102—62no—
435#102—62no—
436#102—62no—
437C22⋊C8—22no—
438C22⋊C8—62no—
439#95—61no—
440#95—61no—
441C23×C3—21no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—21no—
445C23×C3—22no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3#12112yes—
462C23×C3C22×D411yescharacteristic
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C3×Q8—22no—
471C3×Q8—22no—
472C3×Q8—22no—
473C3×Q8#12114yes—
474C3×D4—216no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—22no—
478C3×D4—41no—
479C3×D4—41no—
480C3×D4—41no—
481C3×D4—41no—
482C3×D4—84no—
483C3×D4#12114yes—
484C2×C3×C4—216no—
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—22no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4#12112yes—
498C2×C3×C4C22×D411yescharacteristic
499C2×C3×C4C22×D411yescharacteristic
500C2×C3×C4C22×D411yescharacteristic
501C2×C3×C4C2×#4111yescharacteristic
502C2×C3×C4C2×#4111yescharacteristic
503C2×C3×C4C2×#4111yescharacteristic
504#67—84no—
505#67—84no—
506#67—84no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—84no—
527C2×Dic3—84no—
528C2×Dic3—84no—
529C2×Dic3#12012yes—
530C2×Dic3#12012yes—
531D12—41no—
532D12—41no—
533D12—41no—
534D12—41no—
535C3×C8—41no—
536C3×C8—41no—
537C3⋊C8—41no—
538C3⋊C8—41no—
539C24—21no—
540C24—21no—
541C24—61no—
542C24D3×D411yescharacteristic
543#41—28no—
544#41—28no—
545#41—28no—
546#41—28no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8D3×D412yes—
551C2×Q8#23712yes—
552C2×Q8C2×#6712yes—
553C2×D4—24no—
554C2×D4—24no—
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—42no—
566C2×D4—61no—
567C2×D4—61no—
568C2×D4—61no—
569C2×D4—61no—
570C2×D4—61no—
571C2×D4—61no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—122no—
575C2×D4—122no—
576C2×D4—122no—
577C2×D4—241no—
578C2×D4—241no—
579C2×D4—241no—
580C2×D4—241no—
581C2×D4—241no—
582C2×D4—241no—
583C2×D4D3×D412yes—
584C2×D4#23712yes—
585C2×D4C2×#6712yes—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—64no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—64no—
603C22×C4—64no—
604C22×C4—61no—
605C22×C4—241no—
606C22×C4—241no—
607C22×C4—241no—
608C22×C4—241no—
609C22×C4—241no—
610C22×C4—241no—
611C22×C4D3×D411yescharacteristic
612C22×C4#23712yes—
613C22×C4C2×#6712yes—
614C22×C4C23×D311yescharacteristic
615SD16—44no—
616SD16—124no—
617D8—44no—
618D8—124no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—61no—
626C2×C8—61no—
627C2×C8—61no—
628C2×C8—61no—
629C2×C8—61no—
630C2×C8—61no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—32no—
634C4⋊C4—32no—
635C4⋊C4—62no—
636C4⋊C4—62no—
637C4⋊C4—64no—
638C4⋊C4—64no—
639C4⋊C4—64no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C22⋊C4—42no—
645C22⋊C4—62no—
646C22⋊C4—62no—
647C22⋊C4—64no—
648C22⋊C4—64no—
649C22⋊C4—122no—
650C22⋊C4—241no—
651C22⋊C4—241no—
652C22⋊C4—241no—
653C22⋊C4—241no—
654C42—32no—
655C42—32no—
656C42—64no—
657C42—64no—
658C42—61no—
659C42—61no—
660C22×C3—22no—
661C22×C3—24no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—41no—
669C22×C3—42no—
670C22×C3—41no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3C2×#12011yescharacteristic
682C22×C3C2×#12111yescharacteristic
683C22×C3#52511yescharacteristic
684C22×C3#57611yescharacteristic
685C22×C3#57611yescharacteristic
686C22×C3#57711yescharacteristic
687C22×C3#57711yescharacteristic
688C2×D3—81no—
689C2×D3—81no—
690C2×D3—81no—
691C2×D3—81no—
692C2×D3—81no—
693C2×D3—81no—
694C2×D3—81no—
695C3×C4—22no—
696C3×C4—24no—
697C3×C4—81no—
698C3×C4C2×#12111yescharacteristic
699C3×C4C2×#12111yescharacteristic
700C3×C4#52511yescharacteristic
701C3×C4#52511yescharacteristic
702Dic3—22no—
703Dic3—22no—
704Dic3—41no—
705Dic3—42no—
706Dic3—42no—
707Dic3—41no—
708Dic3—81no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—21no—
715C23—22no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—121no—
730C23—121no—
731C23—121no—
732C23—121no—
733C23—121no—
734C23—121no—
735C23—121no—
736C23#93912yes—
737C23C2×D3×D411yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8#93914yes—
742D4—216no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—121no—
752D4—121no—
753D4—121no—
754D4—121no—
755D4—244no—
756D4—244no—
757D4—244no—
758D4#93914yes—
759C2×C4—216no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—61no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—244no—
794C2×C4—244no—
795C2×C4—244no—
796C2×C4#93912yes—
797C2×C4C2×D3×D411yescharacteristic
798C2×C4C2×D3×D411yescharacteristic
799C2×C4C2×#23711yescharacteristic
800C2×C4C2×#23711yescharacteristic
801C2×C4C2×#23711yescharacteristic
802C2×C4C22×#6711yescharacteristic
803C8—41no—
804C8—41no—
805C8—121no—
806C8—121no—
807C2×C3—42no—
808C2×C3—44no—
809C2×C3—161no—
810C2×C3#284711yescharacteristic
811C2×C3#300811yescharacteristic
812C2×C3#301011yescharacteristic
813C2×C3#304511yescharacteristic
814C2×C3#304511yescharacteristic
815C2×C3#311911yescharacteristic
816C2×C3#311911yescharacteristic
817D3—161no—
818C22—22no—
819C22—24no—
820C22—22no—
821C22—22no—
822C22—42no—
823C22—41no—
824C22—42no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—42no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—241no—
840C22—241no—
841C22—241no—
842C22—241no—
843C22—241no—
844C22—241no—
845C22—241no—
846C22#558611yescharacteristic
847C22D3×#12011yescharacteristic
848C22#576911yescharacteristic
849C22#577011yescharacteristic
850C22#577411yescharacteristic
851C22#577511yescharacteristic
852C22C2×#93911yescharacteristic
853C4—22no—
854C4—24no—
855C4—62no—
856C4—62no—
857C4—81no—
858C4—121no—
859C4—122no—
860C4—122no—
861C4—121no—
862C4—241no—
863C4#558611yescharacteristic
864C4#558611yescharacteristic
865C4C2×#93911yescharacteristic
866C4C2×#93911yescharacteristic
867C3#3291311yescharacteristic, complemented, Sylow
868C2—42no—
869C2—44no—
870C2—161no—
871C2—481no—
872C2#8007211yescharacteristic
873C2#8007311yescharacteristic
874C2#8008511yescharacteristic
875C2#8008611yescharacteristic
876C2#8260111yescharacteristic
877C2#8390111yescharacteristic
878C2#8393611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3#32913
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#5827C2semidirect
2. C2×C3×#449C2semidirect
3. C2×#5238C2semidirect
4. C2×#5163C2semidirect
5. C2×#5150C2semidirect
6. #82676C2semidirect
7. #72048C2semidirect
8. #72037C2semidirect
9. #71677C2semidirect
10. #70240C2semidirect
11. #70222C2semidirect
12. #70172C2semidirect
13. #70154C2semidirect
14. #69932C2semidirect
15. #69909C2semidirect
70. C2×#449D3semidirect
86. C2×C3×#41D4semidirect
122. Q8×Dic3D4semidirect
133. D4×Dic3D4semidirect
351. C2×#41#67semidirect
867. C3#32913semidirect

Maximal subgroups

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

subgroupindex
C2×#58272
C2×C3×#4492
C2×#52382
C2×#51632
C2×#51502
#826762
#720482
#720372
#716772
#702402
#702222
#701722
#701542
#699322
#699092
#329133