Finite Group Databasebeta

← #10823173

Subgroups — #10823173

Order 768.

1570 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
1C22×#914C211yesmaximal, characteristic
2C2×#4839C211yesmaximal, characteristic, complemented
3C2×#4804C211yesmaximal, characteristic, complemented
4C2×D3×#102C211yesmaximal, characteristic, complemented
5#76482C211yesmaximal, characteristic, complemented
6#76428C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8#72051C211yesmaximal, characteristic, complemented
9#70481C211yesmaximal, characteristic, complemented
10#70280C211yesmaximal, characteristic, complemented
11#70212C211yesmaximal, characteristic, complemented
12#69680C211yesmaximal, characteristic, complemented
13#69650C211yesmaximal, characteristic, complemented
14#68867C211yesmaximal, characteristic, complemented
15#68862C211yesmaximal, characteristic, complemented
16#23544—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#914—24no—
23C2×#914—24no—
24C2×#914—24no—
25C22×D24C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28C2×#892C2211yescharacteristic
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×#872C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic, complemented
32C2×C3×#103C2211yescharacteristic, complemented
33C2×C3×#102C2211yescharacteristic
34C3×#391C2211yescharacteristic, complemented
35C3×#390C2211yescharacteristic
36#5229C2211yescharacteristic, complemented
37C2×#835C2211yescharacteristic, complemented
38#5221C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#821C2211yescharacteristic, complemented
42C2×Dic3⋊C8C2211yescharacteristic, complemented
43C2×Dic3⋊C8C2211yescharacteristic, complemented
44#4988C2211yescharacteristic
45#4988C2211yescharacteristic, complemented
46C2×#809C2211yescharacteristic
47C2×#809C2211yescharacteristic, complemented
48#4957—21no—
49#4957—21no—
50#4955—21no—
51#4955—21no—
52#4939C2211yescharacteristic
53#4939C2211yescharacteristic, complemented
54C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55#4839—24no—
56#4804—24no—
57D3×#102—24no—
58#4667—21no—
59#4667—21no—
60#4665—21no—
61#4665—21no—
62C3×#340C2211yescharacteristic, complemented
63#4551C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)—31no—
67C2×#424—31no—
68C2×#416—31no—
69C22×#102—31no—
70#2311—31no—
71#2309—31no—
72#2055—31no—
73#2055—31no—
74#2055—31no—
75#2055D311yescharacteristic, complemented
76#2054—31no—
77#2054—31no—
78#2054—31no—
79#2054—31no—
80#1736—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×#67—21no—
85C2×#239—22no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239D414yes—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4—22no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4D414yes—
97C22×D12—21no—
98C22×D12C2311yescharacteristic
99C22×D12C2311yescharacteristic
100C22×C4×D3—21no—
101C22×C4×D3—21no—
102C22×C4×D3C2311yescharacteristic
103C2×C3×SD16—22no—
104C2×C3×SD16—22no—
105C2×C3×SD16—22no—
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C42C2311yescharacteristic
113C2×#217—21no—
114C2×#217—21no—
115C2×#215—22no—
116C2×#215—22no—
117C2×#215—22no—
118C2×#213—22no—
119C2×#213—22no—
120C2×#213—22no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×(C2×D3)⋊C4D411yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4D411yescharacteristic
136C2×Dic3⋊C4D411yescharacteristic
137C2×C4×Dic3—21no—
138C2×C4×Dic3C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141#914—232no—
142C2×D24—22no—
143C2×D24—22no—
144C2×D24—22no—
145C2×ΓL(1,𝔽25)—22no—
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)D414yes—
148C2×D3×C8—22no—
149C2×D3×C8—22no—
150C2×D3×C8—22no—
151#892—22no—
152#892—22no—
153D3×C4⋊C4—22no—
154D3×C4⋊C4—22no—
155#872—22no—
156#872—22no—
157C3×C4⋊C8—22no—
158C3×#103—22no—
159C3×#102—22no—
160C3×#95—21no—
161C3×#95—21no—
162#835—22no—
163#832—22no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166#821—22no—
167#821—22no—
168Dic3⋊C8—22no—
169Dic3⋊C8—22no—
170#809—22no—
171#809—22no—
172C4⋊(C3⋊C8)—22no—
173C22×#41—31no—
174C23×D4—31no—
175C2×AGL(1,ℤ/8)—64no—
176C2×AGL(1,ℤ/8)—64no—
177C2×AGL(1,ℤ/8)—64no—
178C22×SD16—31no—
179C22×SD16C2×D311yescharacteristic
180C22×D8—31no—
181C22×D8—31no—
182C22×M16—31no—
183C23×C8—31no—
184C2×#117—31no—
185C2×#117—31no—
186C22×C4⋊C4—31no—
187#424—64no—
188C2×C4⋊C8—31no—
189C2×C4⋊C8—31no—
190C2×C4⋊C8—31no—
191C2×C4⋊C8C2×D311yescharacteristic, complemented
192#416—64no—
193C2×#103—31no—
194C2×#103C2×D311yescharacteristic, complemented
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×#102—64no—
201C2×#102C2×D311yescharacteristic
202#391—31no—
203#391C2×D311yescharacteristic, complemented
204#390—31no—
205#390—31no—
206#390—31no—
207#390—31no—
208#390—31no—
209#390—61no—
210#390—61no—
211#390C2×D311yescharacteristic
212#386—61no—
213#386—61no—
214#380—61no—
215#380—61no—
216#379—61no—
217#379—61no—
218#340—31no—
219#340—31no—
220#340—31no—
221#340C2×D311yescharacteristic, complemented
222C24×C3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—24no—
226C23×D3—42no—
227C23×D3—42no—
228C23×D3—81no—
229C23×D3—81no—
230C23×D3—81no—
231C23×D3—81no—
232C23×D3C2×D411yescharacteristic
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8C2×D412yes—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4C2×D412yes—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2411yescharacteristic
251C2×#67—24no—
252C2×#67—42no—
253C2×#67—42no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258C22×Dic3C2×D411yescharacteristic
259#239—28no—
260#239—28no—
261#239—44no—
262#239—44no—
263D3×D4—28no—
264D3×D4—28no—
265D3×D4—44no—
266D3×D4—44no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—24no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—42no—
279C2×D12—42no—
280C2×D12C2×D412yes—
281C2×D12C2×D412yes—
282C2×C4×D3—24no—
283C2×C4×D3—42no—
284C2×C4×D3—42no—
285C2×C4×D3—42no—
286C2×C4×D3—81no—
287C2×C4×D3—81no—
288C2×C4×D3C2×D412yes—
289C2×C4×D3C2×D412yes—
290C2×C4×D3C2×D412yes—
291C2×C4×D3#4112yes—
292C2×C4×D3#4112yes—
293C2×C4×D3#4112yes—
294C3×SD16—28no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8C2×D412yes—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C22⋊C4—81no—
306C3×C22⋊C4—81no—
307C3×C42—21no—
308C3×C42—21no—
309#217—81no—
310#217—81no—
311#215—28no—
312#213—28no—
313(C2×D3)⋊C4—22no—
314(C2×D3)⋊C4—22no—
315(C2×D3)⋊C4—42no—
316(C2×D3)⋊C4—81no—
317(C2×D3)⋊C4—81no—
318(C2×D3)⋊C4—81no—
319(C2×D3)⋊C4—81no—
320(C2×D3)⋊C4—81no—
321(C2×D3)⋊C4—81no—
322(C2×D3)⋊C4—81no—
323(C2×D3)⋊C4—81no—
324C4⋊Dic3—21no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328Dic3⋊C4—22no—
329Dic3⋊C4—22no—
330Dic3⋊C4—42no—
331C4×Dic3—21no—
332C4×Dic3—21no—
333C4×Dic3—42no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8C2×D412yes—
340D24—28no—
341ΓL(1,𝔽25)—28no—
342D3×C8—44no—
343C25—61no—
344C2×#41—34no—
345C2×#41—62no—
346C2×#41—62no—
347C2×#41—62no—
348C2×#41—62no—
349C2×#41—62no—
350C22×Q8C22×D311yescharacteristic
351C22×D4—34no—
352C22×D4—31no—
353C22×D4—31no—
354C22×D4—61no—
355C22×D4—62no—
356C22×D4—62no—
357C22×D4—62no—
358C22×D4—62no—
359C22×D4—62no—
360C22×D4—61no—
361C22×D4C22×D311yescharacteristic
362C23×C4—31no—
363C23×C4—61no—
364C23×C4—61no—
365AGL(1,ℤ/8)—632no—
366C2×SD16—22no—
367C2×SD16—22no—
368C2×SD16—22no—
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—
378C2×M16—34no—
379C2×M16—62no—
380C2×M16—62no—
381C22×C8—31no—
382C22×C8—31no—
383C22×C8—62no—
384C22×C8—62no—
385C22×C8—62no—
386C22×C8C22×D311yescharacteristic
387C22×C8C22×D311yescharacteristic
388#117—62no—
389#117—62no—
390#117—62no—
391#117—62no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C22⋊C4—61no—
410C2×C22⋊C4—61no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—61no—
416C2×C42—31no—
417C2×C42—61no—
418C2×C42C22×D311yescharacteristic
419C4⋊C8—22no—
420C4⋊C8—62no—
421C4⋊C8—62no—
422C4⋊C8—62no—
423#103—22no—
424#103—62no—
425#102—22no—
426#102—62no—
427#102—62no—
428#102—62no—
429#102—62no—
430#102—62no—
431#95—21no—
432#95—21no—
433#95—61no—
434#95—61no—
435C23×C3—22no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3C22×D411yescharacteristic
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C22×D3—41no—
458C22×D3—41no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—48no—
462C22×D3—84no—
463C22×D3—84no—
464C22×D3—84no—
465C22×D3—84no—
466C22×D3—84no—
467C22×D3—84no—
468C22×D3#12112yes—
469C22×D3#12112yes—
470C22×D3#12112yes—
471C3×Q8—22no—
472C3×Q8—22no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—41no—
478C3×D4—41no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499C2×C3×C4C2×#4111yescharacteristic
500#67—48no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3#12112yes—
514C2×Dic3#12112yes—
515C2×Dic3#12112yes—
516D12—22no—
517D12—22no—
518D12—22no—
519D12—22no—
520D12—48no—
521D12—41no—
522D12—41no—
523D12—41no—
524D12—41no—
525C4×D3—48no—
526C4×D3—84no—
527C4×D3#12014yes—
528C4×D3#12314yes—
529C4×D3#12314yes—
530C4×D3#12414yes—
531C3×C8—22no—
532C3×C8—41no—
533C3⋊C8—22no—
534C3⋊C8—41no—
535C24—21no—
536C24—31no—
537C24—64no—
538C24—61no—
539C24—61no—
540C24—122no—
541C24—122no—
542C24—241no—
543C24—241no—
544C24—241no—
545C24—241no—
546#41—68no—
547#41—68no—
548#41—124no—
549#41—124no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8D3×D412yes—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—32no—
562C2×D4—32no—
563C2×D4—64no—
564C2×D4—68no—
565C2×D4—68no—
566C2×D4—64no—
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—61no—
576C2×D4—61no—
577C2×D4—124no—
578C2×D4—124no—
579C2×D4—122no—
580C2×D4—122no—
581C2×D4—122no—
582C2×D4—122no—
583C2×D4D3×D412yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—31no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—64no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—122no—
600C22×C4—122no—
601C22×C4—122no—
602C22×C4—241no—
603C22×C4—241no—
604C22×C4D3×D411yescharacteristic
605C22×C4D3×D411yescharacteristic
606C22×C4C23×D311yescharacteristic
607SD16—28no—
608SD16—68no—
609D8—68no—
610D8—68no—
611M16—68no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—32no—
618C2×C8—61no—
619C2×C8—61no—
620C2×C8—61no—
621C2×C8—61no—
622C2×C8—61no—
623C2×C8—124no—
624C2×C8D3×D412yes—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—62no—
630C4⋊C4—62no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4—122no—
636C22⋊C4—62no—
637C22⋊C4—62no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—122no—
641C22⋊C4—241no—
642C22⋊C4—241no—
643C22⋊C4—241no—
644C22⋊C4—241no—
645C22⋊C4—241no—
646C22⋊C4—241no—
647C22⋊C4—241no—
648C22⋊C4—241no—
649C22⋊C4—241no—
650C22⋊C4—241no—
651C42—21no—
652C42—21no—
653C42—61no—
654C42—61no—
655C42—122no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3C2×#12111yescharacteristic
664C22×C3C2×#12111yescharacteristic
665C22×C3C2×#12111yescharacteristic
666C22×C3#57611yescharacteristic
667C22×C3#57611yescharacteristic
668C22×C3#57711yescharacteristic
669C22×C3#57711yescharacteristic
670C2×D3—22no—
671C2×D3—22no—
672C2×D3—22no—
673C2×D3—22no—
674C2×D3—22no—
675C2×D3—22no—
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—42no—
679C2×D3—42no—
680C2×D3—42no—
681C2×D3—42no—
682C2×D3—816no—
683C2×D3—81no—
684C2×D3—81no—
685C2×D3—81no—
686C2×D3—81no—
687C2×D3—81no—
688C2×D3—81no—
689C2×D3—81no—
690C2×D3—81no—
691C2×D3#39414yes—
692C3×C4—42no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4C2×#12011yescharacteristic
698C3×C4C2×#12311yescharacteristic
699C3×C4C2×#12311yescharacteristic
700C3×C4C2×#12411yescharacteristic
701Dic3—41no—
702Dic3—41no—
703Dic3—81no—
704Dic3—81no—
705Dic3#39414yes—
706C23—22no—
707C23—32no—
708C23—32no—
709C23—32no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—61no—
717C23—61no—
718C23—61no—
719C23—61no—
720C23—62no—
721C23—62no—
722C23—128no—
723C23—121no—
724C23—121no—
725C23—121no—
726C23—121no—
727C23—121no—
728C23—121no—
729C23—121no—
730C23—121no—
731C23—121no—
732C23—121no—
733C23—121no—
734C23—121no—
735C23—244no—
736C23—244no—
737C23—244no—
738C23—244no—
739C23—244no—
740C23—244no—
741C23C2×D3×D411yescharacteristic
742Q8—22no—
743Q8—22no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—41no—
750D4—62no—
751D4—62no—
752D4—62no—
753D4—62no—
754D4—128no—
755D4—128no—
756D4—121no—
757D4—121no—
758D4—121no—
759D4—121no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—34no—
771C2×C4—34no—
772C2×C4—34no—
773C2×C4—34no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—128no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—244no—
796C2×C4C2×D3×D411yescharacteristic
797C2×C4C2×D3×D411yescharacteristic
798C2×C4C2×D3×D411yescharacteristic
799C2×C4D3×#4111yescharacteristic
800C2×C4D3×#4111yescharacteristic
801C2×C4D3×#4111yescharacteristic
802C8—22no—
803C8—41no—
804C8—62no—
805C8—121no—
806C2×C3—82no—
807C2×C3C2×#39411yescharacteristic
808C2×C3#304111yescharacteristic
809C2×C3#304211yescharacteristic
810C2×C3#304511yescharacteristic
811C2×C3#304511yescharacteristic
812C2×C3#306211yescharacteristic
813C2×C3#306211yescharacteristic
814D3—24no—
815D3—82no—
816D3—82no—
817C22—34no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—62no—
822C22—62no—
823C22—62no—
824C22—62no—
825C22—62no—
826C22—62no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—122no—
832C22—122no—
833C22—122no—
834C22—122no—
835C22—122no—
836C22—122no—
837C22—2416no—
838C22—241no—
839C22—241no—
840C22—241no—
841C22—241no—
842C22—241no—
843C22—241no—
844C22—241no—
845C22—241no—
846C22D3×#12111yescharacteristic
847C22D3×#12111yescharacteristic
848C22D3×#12111yescharacteristic
849C22#576211yescharacteristic
850C22#576911yescharacteristic
851C22#577411yescharacteristic
852C22#577811yescharacteristic
853C4—34no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—81no—
858C4—81no—
859C4—121no—
860C4—121no—
861C4—241no—
862C4—241no—
863C4D3×#12011yescharacteristic
864C4D3×#12311yescharacteristic
865C4D3×#12311yescharacteristic
866C4D3×#12411yescharacteristic
867C3#2354411yescharacteristic, complemented, Sylow
868C2—64no—
869C2—82no—
870C2—242no—
871C2—242no—
872C2D3×#39411yescharacteristic
873C2#8038611yescharacteristic
874C2#8043011yescharacteristic
875C2#8053611yescharacteristic
876C2#8060211yescharacteristic
877C2#8066111yescharacteristic
878C2#8080911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2055C2
socleC23×C3C22×D4
prime radicalC22×#914C2
hypercenter#2055D3
hypocenterC3#23544
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
2. C2×#4839C2semidirect
3. C2×#4804C2semidirect
4. C2×D3×#102C2semidirect
5. #76482C2semidirect
6. #76428C2semidirect
7. C3×#2055C2semidirect
8. #72051C2semidirect
9. #70481C2semidirect
10. #70280C2semidirect
11. #70212C2semidirect
12. #69680C2semidirect
13. #69650C2semidirect
14. #68867C2semidirect
15. #68862C2semidirect
31. C2×C3×C4⋊C8C22semidirect
32. C2×C3×#103C22semidirect
34. C3×#391C22semidirect
36. #5229C22semidirect
37. C2×#835C22semidirect
41. C2×#821C22semidirect
42. C2×Dic3⋊C8C22semidirect
43. C2×Dic3⋊C8C22semidirect
45. #4988C22semidirect
47. C2×#809C22semidirect
53. #4939C22semidirect
54. C2×C4⋊(C3⋊C8)C22semidirect
62. C3×#340C22semidirect
63. #4551C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
75. #2055D3semidirect
191. C2×C4⋊C8C2×D3semidirect
194. C2×#103C2×D3semidirect
203. #391C2×D3semidirect
221. #340C2×D3semidirect
867. C3#23544semidirect

Maximal subgroups

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

subgroupindex
C22×#9142
C2×#48392
C2×#48042
C2×D3×#1022
#764822
#764282
C3×#20552
#720512
#704812
#702802
#702122
#696802
#696502
#688672
#688622
#235443