Finite Group Databasebeta

← #10944088

Subgroups — #10944088

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×#5504C211yesmaximal, characteristic, complemented
2#82676C211yesmaximal, characteristic, complemented
3C2×#5037C211yesmaximal, characteristic, complemented
4C2×#4762C211yesmaximal, characteristic, complemented
5C2×#4786C211yesmaximal, characteristic, complemented
6C2×#4734C211yesmaximal, characteristic, complemented
7C3×#1874C211yesmaximal, characteristic, complemented
8#71560C211yesmaximal, characteristic, complemented
9#70213C211yesmaximal, characteristic, complemented
10#70208C211yesmaximal, characteristic, complemented
11#69909C211yesmaximal, characteristic, complemented
12#68909C211yesmaximal, characteristic, complemented
13#68905C211yesmaximal, characteristic, complemented
14#68897C211yesmaximal, characteristic, complemented
15#68893C211yesmaximal, characteristic, complemented
16#32913—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C2×#940C2211yescharacteristic
21C22×#214C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×C4×#67—21no—
25C2×C4×#67—21no—
26C2×#926C2211yescharacteristic
27C22×D24C2211yescharacteristic
28C22×#204C2211yescharacteristic
29#5504—24no—
30#5504—24no—
31C2×#893C2211yescharacteristic
32C2×#893C2211yescharacteristic
33C2×#892—21no—
34C2×D3×C4⋊C4—21no—
35C2×#887C2211yescharacteristic
36C2×#887C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40#5223—21no—
41#5223—21no—
42#5221C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#816C2211yescharacteristic
46C2×Dic3⋊C8C2211yescharacteristic
47C2×Dic3⋊C8C2211yescharacteristic
48#5037—24no—
49#4988C2211yescharacteristic
50#4977C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55#4961—21no—
56#4961—21no—
57#4786—24no—
58#4762—24no—
59#4734—24no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#520—31no—
67C2×#460—31no—
68C2×#459—31no—
69C2×#449—31no—
70C2×#449—31no—
71#2619—31no—
72#1880—31no—
73#1880—31no—
74#1879—31no—
75#1879—31no—
76#1874—31no—
77#1874D311yescharacteristic, complemented
78#1805—31no—
79#1804—31no—
80#1798—31no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C22×#67—21no—
88C22×#67—21no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235—22no—
94C2×#235D414yescomplemented
95C22×D12C2311yescharacteristic
96C22×D12C2311yescharacteristic
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C4×D3—21no—
100C22×Dic6C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×#121—22no—
104C3×#121—22no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217D411yescharacteristic
115C2×#217D411yescharacteristic
116#940—22no—
117#940—22no—
118C2×#214—22no—
119C2×#214—22no—
120C2×#214—22no—
121C2×#213—22no—
122C2×#213—22no—
123C2×#213—22no—
124#930—22no—
125#930—22no—
126C4×#67—28no—
127C4×#67—28no—
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—
133#926—22no—
134#926—22no—
135C2×C4⋊Dic3D411yescharacteristic
136C2×C4⋊Dic3D411yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C2×C4×Dic3C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C2×D24—22no—
147C2×D24—22no—
148C2×D24—22no—
149C2×#204—22no—
150C2×#204—22no—
151C2×#204—22no—
152#893—22no—
153#893—22no—
154#893—22no—
155#893D414yescomplemented
156#892—28no—
157D3×C4⋊C4—28no—
158#887—22no—
159#887—22no—
160#887—22no—
161#887D414yescomplemented
162C3×#102—22no—
163C3×#102—22no—
164C3×C22⋊C8—22no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167#830—22no—
168#821—22no—
169#816—22no—
170Dic3⋊C8—22no—
171Dic3⋊C8—22no—
172#810—22no—
173#809—22no—
174#809—22no—
175#809—22no—
176C22×#41—31no—
177C22×SD16—31no—
178C22×SD16—31no—
179C22×D8—31no—
180C22×D8—31no—
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—61no—
195C22×C4⋊C4C2×D311yescharacteristic
196#460—64no—
197#459—64no—
198#449—64no—
199#449—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#102—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102C2×D311yescharacteristic
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#340C2×D311yescharacteristic
222#340C2×D311yescharacteristic
223#336—31no—
224#336—31no—
225C24×C3—21no—
226C24×C3C2×D411yescharacteristic
227C23×D3—21no—
228C23×D3—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—42no—
236C2×C3×D4—81no—
237C2×C3×D4—81no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—24no—
245C22×C3×C4—21no—
246C22×C3×C4—81no—
247C22×C3×C4—81no—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D412yes—
250C22×C3×C4#4112yes—
251C22×C3×C4C2411yescharacteristic
252C2×#67—24no—
253C2×#67—24no—
254C2×#67—24no—
255C2×#67—42no—
256C2×#67—42no—
257C2×#67—42no—
258C2×#67—81no—
259C2×#67—81no—
260C2×#67—81no—
261C2×#67—81no—
262C2×#67—81no—
263C2×#67—81no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3C2×D411yescharacteristic
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
269C22×Dic3C2×D411yescharacteristic
270#235—28no—
271#235—28no—
272#235—28no—
273#235—28no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12C2×D412yes—
284C2×D12C2×D412yes—
285C2×D12#4112yes—
286C2×C4×D3—24no—
287C2×C4×D3—24no—
288C2×C4×D3—24no—
289C2×C4×D3—24no—
290C2×C4×D3—24no—
291C2×C4×D3—81no—
292C2×C4×D3—81no—
293C2×C4×D3—81no—
294C2×C4×D3—81no—
295C2×Dic6—21no—
296C2×Dic6—21no—
297C2×Dic6—21no—
298C2×Dic6C2×D412yes—
299C2×Dic6C2×D412yes—
300C2×Dic6#4112yes—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C3×C4⋊C4—24no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4C2×D412yes—
313C3×C4⋊C4C2×D412yes—
314C3×C22⋊C4—42no—
315#217—22no—
316#217—22no—
317#217—81no—
318#217—81no—
319#214—44no—
320#213—44no—
321(C2×D3)⋊C4—24no—
322(C2×D3)⋊C4—24no—
323(C2×D3)⋊C4—42no—
324(C2×D3)⋊C4—81no—
325(C2×D3)⋊C4—81no—
326C4⋊Dic3—22no—
327C4⋊Dic3—22no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330Dic3⋊C4—24no—
331Dic3⋊C4—24no—
332C4×Dic3—24no—
333C4×Dic3—21no—
334C4×Dic3—21no—
335C4×Dic3—24no—
336C4×Dic3C2×D412yes—
337C4×Dic3C2×D412yes—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344D24—44no—
345#204—44no—
346C2×#41—34no—
347C2×#41—62no—
348C2×#41—62no—
349C2×#41—62no—
350C2×#41—62no—
351C2×#41—62no—
352C22×Q8—31no—
353C22×D4—21no—
354C22×D4—31no—
355C22×D4—31no—
356C22×D4—61no—
357C22×D4—61no—
358C22×D4—61no—
359C22×D4—61no—
360C22×D4C22×D311yescharacteristic
361C23×C4—21no—
362C23×C4—61no—
363C23×C4—61no—
364C23×C4—61no—
365C23×C4C22×D311yescharacteristic
366C2×SD16—62no—
367C2×SD16—62no—
368C2×SD16—62no—
369C2×SD16—62no—
370C2×SD16—62no—
371C2×SD16—62no—
372C2×D8—62no—
373C2×D8—62no—
374C2×D8—62no—
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—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—68no—
408C2×C4⋊C4—61no—
409C2×C4⋊C4—61no—
410C2×C4⋊C4C22×D311yescharacteristic
411C2×C4⋊C4C22×D311yescharacteristic
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—62no—
430#103—62no—
431#102—22no—
432#102—22no—
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—21no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3#12112yes—
455C23×C3C22×D411yescharacteristic
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C3×D4—41no—
471C3×D4—41no—
472C3×D4—41no—
473C3×D4—41no—
474C3×D4—84no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—84no—
491C2×C3×C4#12112yes—
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C2×#4111yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498#67—216no—
499#67—84no—
500#67—84no—
501#67—84no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3#12012yes—
519C2×Dic3#12012yes—
520D12—22no—
521D12—22no—
522D12—22no—
523D12—41no—
524D12—41no—
525D12—41no—
526D12—41no—
527D12#12114yes—
528C4×D3—216no—
529C4×D3—84no—
530C4×D3—84no—
531Dic6—22no—
532Dic6—22no—
533Dic6—22no—
534Dic6#12114yes—
535C3×C8—41no—
536C3×C8—41no—
537C3⋊C8—41no—
538C3⋊C8—41no—
539C24—21no—
540C24—61no—
541C24—61no—
542C24D3×D411yescharacteristic
543#41—68no—
544#41—68no—
545#41—68no—
546#41—68no—
547C2×Q8—32no—
548C2×Q8—32no—
549C2×Q8—32no—
550C2×Q8—61no—
551C2×Q8—61no—
552C2×Q8—61no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—32no—
560C2×D4—32no—
561C2×D4—32no—
562C2×D4—42no—
563C2×D4—64no—
564C2×D4—64no—
565C2×D4—64no—
566C2×D4—61no—
567C2×D4—61no—
568C2×D4—61no—
569C2×D4—61no—
570C2×D4—61no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4—122no—
578C2×D4—122no—
579C2×D4—122no—
580C2×D4—241no—
581C2×D4—241no—
582C2×D4—241no—
583C2×D4—241no—
584C2×D4—241no—
585C2×D4—241no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—21no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—64no—
599C22×C4—64no—
600C22×C4—64no—
601C22×C4—64no—
602C22×C4—61no—
603C22×C4—64no—
604C22×C4—61no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—241no—
608C22×C4—241no—
609C22×C4—241no—
610C22×C4—241no—
611C22×C4#23512yes—
612C22×C4D3×D411yescharacteristic
613C22×C4D3×D412yes—
614C22×C4C23×D311yescharacteristic
615SD16—124no—
616SD16—124no—
617D8—124no—
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—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—62no—
637C4⋊C4—62no—
638C4⋊C4—64no—
639C4⋊C4—64no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4D3×D412yes—
643C4⋊C4D3×D412yes—
644C22⋊C4—42no—
645C22⋊C4—64no—
646C22⋊C4—64no—
647C22⋊C4—62no—
648C22⋊C4—62no—
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—22no—
662C22×C3—22no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3C2×#12011yescharacteristic
675C22×C3C2×#12111yescharacteristic
676C22×C3#52511yescharacteristic
677C22×C3#57611yescharacteristic
678C22×C3#57611yescharacteristic
679C22×C3#57711yescharacteristic
680C22×C3#57711yescharacteristic
681C2×D3—24no—
682C2×D3—42no—
683C2×D3—42no—
684C2×D3—42no—
685C2×D3—42no—
686C2×D3—42no—
687C2×D3—42no—
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—42no—
697C3×C4—42no—
698C3×C4—81no—
699C3×C4C2×#12111yescharacteristic
700C3×C4C2×#12111yescharacteristic
701C3×C4#52511yescharacteristic
702C3×C4#52511yescharacteristic
703Dic3—24no—
704Dic3—22no—
705Dic3—22no—
706Dic3—41no—
707Dic3—41no—
708Dic3—81no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—62no—
723C23—62no—
724C23—62no—
725C23—121no—
726C23—121no—
727C23—121no—
728C23—121no—
729C23—121no—
730C23—121no—
731C23—121no—
732C23—121no—
733C23—121no—
734C23—121no—
735C23—121no—
736C23#88412yes—
737C23C2×D3×D411yescharacteristic
738Q8—34no—
739Q8—62no—
740Q8—62no—
741Q8—62no—
742D4—34no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—616no—
748D4—62no—
749D4—62no—
750D4—62no—
751D4—84no—
752D4—121no—
753D4—121no—
754D4—121no—
755D4—121no—
756D4—244no—
757D4—244no—
758D4—244no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—616no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—62no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—84no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—244no—
795C2×C4—244no—
796C2×C4#88412yes—
797C2×C4C2×#23511yescharacteristic
798C2×C4C2×D3×D411yescharacteristic
799C2×C4C2×D3×D411yescharacteristic
800C2×C4C2×D3×D411yescharacteristic
801C2×C4D3×#4111yescharacteristic
802C2×C4D3×#4111yescharacteristic
803C8—41no—
804C8—41no—
805C8—121no—
806C8—121no—
807C2×C3—42no—
808C2×C3—161no—
809C2×C3#284711yescharacteristic
810C2×C3#300811yescharacteristic
811C2×C3#301011yescharacteristic
812C2×C3#304511yescharacteristic
813C2×C3#304511yescharacteristic
814C2×C3#311911yescharacteristic
815C2×C3#311911yescharacteristic
816D3—44no—
817D3—161no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—64no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—122no—
834C22—122no—
835C22—122no—
836C22—122no—
837C22—122no—
838C22—122no—
839C22—241no—
840C22—241no—
841C22—241no—
842C22—241no—
843C22—241no—
844C22—241no—
845C22—241no—
846C22C2×#88411yescharacteristic
847C22D3×#12011yescharacteristic
848C22#565611yescharacteristic
849C22#575711yescharacteristic
850C22#576211yescharacteristic
851C22#577411yescharacteristic
852C22#577811yescharacteristic
853C4—22no—
854C4—42no—
855C4—42no—
856C4—62no—
857C4—62no—
858C4—64no—
859C4—81no—
860C4—121no—
861C4—121no—
862C4—241no—
863C4#554711yescharacteristic
864C4#554711yescharacteristic
865C4D3×#12111yescharacteristic
866C4D3×#12111yescharacteristic
867C3#3291311yescharacteristic, complemented, Sylow
868C2—42no—
869C2—124no—
870C2—161no—
871C2—481no—
872C2#7493511yescharacteristic
873C2#7876711yescharacteristic
874C2#7891111yescharacteristic
875C2#8000411yescharacteristic
876C2#8004111yescharacteristic
877C2#8127211yescharacteristic
878C2#8131211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1874C2
socleC23×C3C22×D4
hypercenter#1874D3
hypocenterC3#32913
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×#5504C2semidirect
2. #82676C2semidirect
3. C2×#5037C2semidirect
4. C2×#4762C2semidirect
5. C2×#4786C2semidirect
6. C2×#4734C2semidirect
7. C3×#1874C2semidirect
8. #71560C2semidirect
9. #70213C2semidirect
10. #70208C2semidirect
11. #69909C2semidirect
12. #68909C2semidirect
13. #68905C2semidirect
14. #68897C2semidirect
15. #68893C2semidirect
77. #1874D3semidirect
94. C2×#235D4semidirect
155. #893D4semidirect
161. #887D4semidirect
867. C3#32913semidirect

Maximal subgroups

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

subgroupindex
C2×#55042
#826762
C2×#50372
C2×#47622
C2×#47862
C2×#47342
C3×#18742
#715602
#702132
#702082
#699092
#689092
#689052
#688972
#688932
#329133