Finite Group Databasebeta

← #10944124

Subgroups — #10944124

Order 768.

1588 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5545C211yesmaximal, characteristic, complemented
2C2×#5156C211yesmaximal, characteristic
3C2×#5153C211yesmaximal, characteristic, complemented
4C2×#4787C211yesmaximal, characteristic, complemented
5C2×#4776C211yesmaximal, characteristic, complemented
6#76457C211yesmaximal, characteristic, complemented
7C3×#1879C211yesmaximal, characteristic, complemented
8#71612C211yesmaximal, characteristic, complemented
9#70201C211yesmaximal, characteristic, complemented
10#70153C211yesmaximal, characteristic, complemented
11#69657C211yesmaximal, characteristic, complemented
12#68892C211yesmaximal, characteristic, complemented
13#68879C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68663C211yesmaximal, characteristic, complemented
16#32917—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C2×#936C2211yescharacteristic, complemented
22C2×D4×Dic3C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C2×C4×#67—21no—
26C22×(C2×D3)⋊C4—21no—
27C22×#204C2211yescharacteristic
28#5545—24no—
29#5545—24no—
30C2×#897C2211yescharacteristic
31C2×#893C2211yescharacteristic
32C2×#892C2211yescharacteristic
33C2×#67⋊C4—21no—
34C2×D3×C22⋊C4—21no—
35C2×C4×D12C2211yescharacteristic
36C2×#872C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic, complemented
39C3×#390C2211yescharacteristic, complemented
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic, complemented
42#5156—24no—
43#5153—24no—
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#816C2211yescharacteristic, complemented
48C2×Dic3⋊C8C2211yescharacteristic, complemented
49C2×Dic3⋊C8C2211yescharacteristic, complemented
50#4975C2211yescharacteristic, complemented
51C2×#810C2211yescharacteristic, complemented
52C2×#809C2211yescharacteristic
53#4959—21no—
54#4959—21no—
55#4948—21no—
56#4948—21no—
57#4929C2211yescharacteristic, complemented
58#4787—24no—
59#4776—24no—
60C3×#340C2211yescharacteristic, complemented
61C3×#336C2211yescharacteristic, complemented
62#4551C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4524C2211yescharacteristic, complemented
66C2×#518—31no—
67C2×#463—31no—
68C2×#463—31no—
69C2×#450—31no—
70C2×#447—31no—
71#2620—31no—
72#1879—31no—
73#1879D311yescharacteristic, complemented
74#1877—31no—
75#1877—31no—
76#1875—31no—
77#1873—31no—
78#1802—31no—
79#1802—31no—
80#1798—31no—
81C24×D3—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C22×#67—21no—
86C22×#67—21no—
87C23×Dic3—21no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4D414yes—
94C22×D12C2311yescharacteristic
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×C4×D3C2311yescharacteristic
98C22×Dic6C2311yescharacteristic
99C2×C3×D8—22no—
100C2×C3×D8—22no—
101C2×C3×D8—22no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×C4×D4—22no—
105C3×C4×D4—22no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C42C2311yescharacteristic
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116#938—22no—
117#938—22no—
118#936—22no—
119#936—22no—
120D4×Dic3—22no—
121D4×Dic3D414yescomplemented
122C2×#214—22no—
123C2×#214—22no—
124C2×#214—22no—
125C2×#213—22no—
126C2×#213—22no—
127C2×#213—22no—
128C4×#67—28no—
129C2×(C2×D3)⋊C4—28no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4D411yescharacteristic
135C2×(C2×D3)⋊C4D411yescharacteristic
136C2×C4⋊Dic3—21no—
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4D411yescharacteristic
142C2×Dic3⋊C4D411yescharacteristic
143C2×C4×Dic3—21no—
144C2×C4×Dic3C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C2×#204—22no—
148C2×#204—22no—
149C2×#204—22no—
150#897—22no—
151#897—22no—
152#893—22no—
153#893D414yescomplemented
154#892—22no—
155#892—22no—
156#67⋊C4—28no—
157D3×C22⋊C4—28no—
158C4×D12—22no—
159C4×D12—22no—
160#872—22no—
161#872—22no—
162C3×#102—22no—
163C3×#102—22no—
164#832—22no—
165#832—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168#821—22no—
169(C2×D3)⋊C8—22no—
170(C2×D3)⋊C8—22no—
171#816—22no—
172Dic3⋊C8—22no—
173Dic3⋊C8—22no—
174#810—22no—
175#809—22no—
176C23×D4—31no—
177C22×SD16—31no—
178C22×SD16—31no—
179C22×D8—31no—
180C22×D8C2×D311yescharacteristic
181C2×#124—31no—
182C2×C22⋊Q8—31no—
183C2×#121—31no—
184#518—64no—
185#518—64no—
186C2×C4×D4—31no—
187C2×C4×D4—31no—
188C2×C4×D4—31no—
189C2×C4×D4—61no—
190C2×C4×D4—61no—
191C2×C4×D4C2×D311yescharacteristic
192C2×#117—31no—
193C2×#117—31no—
194C22×C22⋊C4—61no—
195C22×C22⋊C4—61no—
196#463—64no—
197#463—64no—
198#450—64no—
199#447—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, complemented
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212#396—61no—
213#396—61no—
214#394—61no—
215#394—61no—
216#391—31no—
217#390C2×D311yescharacteristic, complemented
218#384—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340C2×D311yescharacteristic, complemented
223#336—31no—
224#336C2×D311yescharacteristic, complemented
225C24×C3—21no—
226C24×C3—21no—
227C23×D3—21no—
228C23×D3—24no—
229C23×D3—24no—
230C23×D3—24no—
231C23×D3—81no—
232C23×D3—81no—
233C23×D3—81no—
234C23×D3—81no—
235C23×D3C2×D411yescharacteristic
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4C2×D412yes—
246C2×C3×D4C2×D412yes—
247C2×C3×D4#4112yes—
248C22×C3×C4—21no—
249C22×C3×C4—24no—
250C22×C3×C4—21no—
251C22×C3×C4—81no—
252C22×C3×C4—81no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2411yescharacteristic
256C2×#67—24no—
257C2×#67—24no—
258C2×#67—24no—
259C2×#67—42no—
260C2×#67—81no—
261C2×#67—81no—
262C22×Dic3—21no—
263C22×Dic3—24no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—81no—
267C22×Dic3—81no—
268C22×Dic3C2×D411yescharacteristic
269C22×Dic3C2×D411yescharacteristic
270C22×Dic3C2×D411yescharacteristic
271D3×D4—28no—
272D3×D4—28no—
273D3×D4—28no—
274D3×D4—28no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12C2×D412yes—
279C2×D12C2×D412yes—
280C2×D12#4112yes—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—24no—
286C2×C4×D3—24no—
287C2×C4×D3—81no—
288C2×C4×D3—81no—
289C2×C4×D3—81no—
290C2×C4×D3—81no—
291C2×C4×D3C2×D412yes—
292C2×C4×D3#4112yes—
293C2×Dic6—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C2×Dic6—21no—
297C2×Dic6—21no—
298C2×Dic6—21no—
299C3×D8—44no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4C2×D412yes—
310C3×C22⋊C4—24no—
311C3×C22⋊C4—81no—
312C3×C22⋊C4—81no—
313C3×C42—21no—
314C3×C42—21no—
315#217—24no—
316#217—42no—
317#217—42no—
318#217—42no—
319#214—44no—
320#213—44no—
321(C2×D3)⋊C4—24no—
322(C2×D3)⋊C4—24no—
323(C2×D3)⋊C4—22no—
324(C2×D3)⋊C4—22no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—42no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3—42no—
331C4⋊Dic3C2×D412yes—
332Dic3⋊C4—22no—
333Dic3⋊C4—22no—
334Dic3⋊C4—81no—
335Dic3⋊C4—81no—
336C4×Dic3—24no—
337C4×Dic3C2×D412yes—
338C4×Dic3C2×D412yes—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345#204—44no—
346C25—61no—
347C22×Q8—31no—
348C22×D4—34no—
349C22×D4—31no—
350C22×D4—62no—
351C22×D4—61no—
352C22×D4—62no—
353C22×D4—62no—
354C22×D4—62no—
355C22×D4—62no—
356C22×D4—61no—
357C22×D4C22×D311yescharacteristic
358C22×D4C22×D311yescharacteristic
359C23×C4—21no—
360C23×C4—31no—
361C23×C4—61no—
362C23×C4—61no—
363C23×C4—61no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×SD16—62no—
367C2×SD16—62no—
368C2×SD16—62no—
369C2×SD16—62no—
370C2×D8—22no—
371C2×D8—22no—
372C2×D8—22no—
373C2×D8—62no—
374C2×D8—62no—
375C2×D8—62no—
376C22×C8—31no—
377C22×C8—31no—
378C22×C8C22×D311yescharacteristic
379C22×C8C22×D311yescharacteristic
380#124—62no—
381#124—62no—
382C22⋊Q8—62no—
383C22⋊Q8—62no—
384#121—62no—
385#121—62no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—34no—
389C4×D4—34no—
390C4×D4—62no—
391C4×D4—62no—
392C4×D4—62no—
393C4×D4—62no—
394C4×D4—68no—
395C4×D4—68no—
396#117—62no—
397#117—62no—
398#117—62no—
399#117—62no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4—61no—
406C2×C4⋊C4—61no—
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—31no—
413C2×C22⋊C4—31no—
414C2×C22⋊C4—68no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—68no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C42—31no—
425C2×C42—61no—
426C2×C42C22×D311yescharacteristic
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—62no—
438C22⋊C8—62no—
439#95—61no—
440#95—61no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
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×C3C22×D411yescharacteristic
456C22×D3—21no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—21no—
460C22×D3—22no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—216no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—84no—
471C22×D3—84no—
472C22×D3—84no—
473C22×D3—84no—
474C22×D3—84no—
475C22×D3—84no—
476C22×D3#12112yes—
477C3×D4—22no—
478C3×D4—22no—
479C3×D4—22no—
480C3×D4—41no—
481C3×D4—41no—
482C3×D4—41no—
483C3×D4—41no—
484C3×D4#12114yes—
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
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—84no—
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—216no—
505#67—84no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—22no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—84no—
522C2×Dic3#12012yes—
523C2×Dic3#12012yes—
524C2×Dic3#12112yes—
525D12—22no—
526D12—22no—
527D12—22no—
528D12#12114yes—
529C4×D3—22no—
530C4×D3—22no—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—84no—
534C4×D3—84no—
535Dic6—41no—
536Dic6—41no—
537Dic6—41no—
538Dic6—41no—
539C3×C8—41no—
540C3×C8—41no—
541C3⋊C8—41no—
542C3⋊C8—41no—
543C24—21no—
544C24—21no—
545C24—31no—
546C24—64no—
547C24—64no—
548C24—64no—
549C24—61no—
550C24—241no—
551C24—241no—
552C24—241no—
553C24—241no—
554C2×Q8—61no—
555C2×Q8—61no—
556C2×Q8—61no—
557C2×Q8—61no—
558C2×Q8—61no—
559C2×Q8—61no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—32no—
570C2×D4—32no—
571C2×D4—32no—
572C2×D4—64no—
573C2×D4—68no—
574C2×D4—68no—
575C2×D4—68no—
576C2×D4—64no—
577C2×D4—64no—
578C2×D4—68no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—122no—
583C2×D4—241no—
584C2×D4—241no—
585C2×D4#23512yes—
586C2×D4D3×D412yes—
587C2×D4D3×D412yes—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—32no—
595C22×C4—32no—
596C22×C4—64no—
597C22×C4—64no—
598C22×C4—64no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—241no—
609C22×C4—241no—
610C22×C4—241no—
611C22×C4—241no—
612C22×C4—241no—
613C22×C4—241no—
614C22×C4D3×D411yescharacteristic
615C22×C4D3×D411yescharacteristic
616C22×C4C23×D311yescharacteristic
617SD16—124no—
618SD16—124no—
619D8—44no—
620D8—124no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—61no—
628C2×C8—61no—
629C2×C8—61no—
630C2×C8—61no—
631C2×C8—61no—
632C2×C8—61no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—32no—
637C4⋊C4—62no—
638C4⋊C4—62no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—122no—
643C4⋊C4—241no—
644C4⋊C4—241no—
645C4⋊C4D3×D412yes—
646C22⋊C4—24no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—64no—
650C22⋊C4—64no—
651C22⋊C4—64no—
652C22⋊C4—64no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C22⋊C4—122no—
656C22⋊C4—122no—
657C22⋊C4—122no—
658C22⋊C4—122no—
659C42—21no—
660C42—21no—
661C42—32no—
662C42—32no—
663C42—64no—
664C22×C3—24no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3C2×#12011yescharacteristic
679C22×C3C2×#12111yescharacteristic
680C22×C3#52511yescharacteristic
681C22×C3#57611yescharacteristic
682C22×C3#57611yescharacteristic
683C22×C3#57711yescharacteristic
684C22×C3#57711yescharacteristic
685C2×D3—22no—
686C2×D3—24no—
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—42no—
692C2×D3—42no—
693C2×D3—42no—
694C2×D3—42no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—42no—
698C2×D3—42no—
699C2×D3—816no—
700C3×C4—41no—
701C3×C4—42no—
702C3×C4—41no—
703C3×C4—81no—
704C3×C4C2×#12111yescharacteristic
705C3×C4C2×#12111yescharacteristic
706C3×C4#52511yescharacteristic
707C3×C4#52511yescharacteristic
708Dic3—22no—
709Dic3—22no—
710Dic3—22no—
711Dic3—42no—
712Dic3—81no—
713Dic3—81no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—32no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—616no—
730C23—61no—
731C23—61no—
732C23—61no—
733C23—61no—
734C23—61no—
735C23—62no—
736C23—61no—
737C23—62no—
738C23—62no—
739C23—121no—
740C23—121no—
741C23—121no—
742C23—121no—
743C23—244no—
744C23—244no—
745C23—244no—
746C23—244no—
747C23—244no—
748C23—244no—
749C23C2×D3×D411yescharacteristic
750Q8—121no—
751Q8—121no—
752Q8—121no—
753Q8—121no—
754D4—22no—
755D4—22no—
756D4—22no—
757D4—34no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—616no—
763D4—62no—
764D4—62no—
765D4—62no—
766D4—244no—
767D4#88414yes—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—84no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—121no—
802C2×C4—121no—
803C2×C4—244no—
804C2×C4—244no—
805C2×C4—244no—
806C2×C4C2×#23511yescharacteristic
807C2×C4C2×D3×D411yescharacteristic
808C2×C4C2×D3×D411yescharacteristic
809C2×C4C2×D3×D411yescharacteristic
810C2×C4D3×#4111yescharacteristic
811C2×C4D3×#4111yescharacteristic
812C8—41no—
813C8—41no—
814C8—121no—
815C8—121no—
816C2×C3—44no—
817C2×C3—161no—
818C2×C3#284711yescharacteristic
819C2×C3#301211yescharacteristic
820C2×C3#301211yescharacteristic
821C2×C3#304111yescharacteristic
822C2×C3#304211yescharacteristic
823C2×C3#311811yescharacteristic
824C2×C3#311811yescharacteristic
825D3—42no—
826D3—44no—
827C22—24no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—62no—
835C22—62no—
836C22—64no—
837C22—62no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—121no—
846C22—122no—
847C22—122no—
848C22—121no—
849C22—122no—
850C22—122no—
851C22—122no—
852C22—121no—
853C22—121no—
854C22—122no—
855C22—2416no—
856C22#554711yescharacteristic
857C22D3×#12011yescharacteristic
858C22D3×#12111yescharacteristic
859C22#575711yescharacteristic
860C22#577011yescharacteristic
861C22#577411yescharacteristic
862C22#577511yescharacteristic
863C4—41no—
864C4—42no—
865C4—41no—
866C4—62no—
867C4—62no—
868C4—62no—
869C4—81no—
870C4—122no—
871C4—241no—
872C4—241no—
873C4C2×#88411yescharacteristic
874C4#554711yescharacteristic
875C4D3×#12111yescharacteristic
876C4#565611yescharacteristic
877C3#3291711yescharacteristic, complemented, Sylow
878C2—44no—
879C2—122no—
880C2—124no—
881C2—161no—
882C2#7493511yescharacteristic
883C2#7959411yescharacteristic
884C2#7988611yescharacteristic
885C2#8000511yescharacteristic
886C2#8008711yescharacteristic
887C2#8033411yescharacteristic
888C2#8053711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1879C2
socleC23×C3C22×D4
prime radicalC2×#5156C2
hypercenter#1879D3
hypocenterC3#32917
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×#5545C2semidirect
3. C2×#5153C2semidirect
4. C2×#4787C2semidirect
5. C2×#4776C2semidirect
6. #76457C2semidirect
7. C3×#1879C2semidirect
8. #71612C2semidirect
9. #70201C2semidirect
10. #70153C2semidirect
11. #69657C2semidirect
12. #68892C2semidirect
13. #68879C2semidirect
14. #68672C2semidirect
15. #68663C2semidirect
21. C2×#936C22semidirect
38. C2×C3×#102C22semidirect
39. C3×#390C22semidirect
41. C2×#832C22semidirect
47. C2×#816C22semidirect
48. C2×Dic3⋊C8C22semidirect
49. C2×Dic3⋊C8C22semidirect
50. #4975C22semidirect
51. C2×#810C22semidirect
57. #4929C22semidirect
60. C3×#340C22semidirect
61. C3×#336C22semidirect
62. #4551C22semidirect
63. #4529C22semidirect
64. #4529C22semidirect
65. #4524C22semidirect
73. #1879D3semidirect
121. D4×Dic3D4semidirect
153. #893D4semidirect
209. C2×#102C2×D3semidirect
217. #390C2×D3semidirect
222. #340C2×D3semidirect
224. #336C2×D3semidirect
877. C3#32917semidirect

Maximal subgroups

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

subgroupindex
C2×#55452
C2×#51562
C2×#51532
C2×#47872
C2×#47762
#764572
C3×#18792
#716122
#702012
#701532
#696572
#688922
#688792
#686722
#686632
#329173