Finite Group Databasebeta

← #10823168

Subgroups — #10823168

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×#911C211yesmaximal, characteristic
2C2×#4839C211yesmaximal, characteristic, complemented
3C2×#4772C211yesmaximal, characteristic, complemented
4C2×D3×#102C211yesmaximal, characteristic, complemented
5#76428C211yesmaximal, characteristic, complemented
6#76294C211yesmaximal, characteristic, complemented
7C3×#2054C211yesmaximal, characteristic, complemented
8#72040C211yesmaximal, characteristic, complemented
9#70482C211yesmaximal, characteristic, complemented
10#70217C211yesmaximal, characteristic, complemented
11#70212C211yesmaximal, characteristic, complemented
12#69651C211yesmaximal, characteristic, complemented
13#69650C211yesmaximal, characteristic, complemented
14#68867C211yesmaximal, characteristic, complemented
15#68863C211yesmaximal, characteristic, complemented
16#23544—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C22×#214C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#911—24no—
23C2×#911—24no—
24C2×#911—24no—
25C22×#204C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28C2×#892C2211yescharacteristic
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×#872C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic, complemented
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic, complemented
34C3×#390C2211yescharacteristic
35C3×#390C2211yescharacteristic, complemented
36#5221C2211yescharacteristic
37#5221C2211yescharacteristic, complemented
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic, complemented
40C2×#821C2211yescharacteristic
41C2×#816C2211yescharacteristic, complemented
42C2×Dic3⋊C8C2211yescharacteristic, complemented
43C2×Dic3⋊C8C2211yescharacteristic, complemented
44#4988C2211yescharacteristic
45#4973C2211yescharacteristic, complemented
46C2×#810C2211yescharacteristic, complemented
47C2×#809C2211yescharacteristic
48#4957—21no—
49#4957—21no—
50#4956—21no—
51#4956—21no—
52#4955—21no—
53#4955—21no—
54#4942—21no—
55#4942—21no—
56#4939C2211yescharacteristic
57#4929C2211yescharacteristic, complemented
58C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#4839—24no—
60#4772—24no—
61D3×#102—24no—
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#2055—31no—
76#2054—31no—
77#2054—31no—
78#2054—31no—
79#2054D311yescharacteristic, complemented
80#1736—31no—
81C24×D3—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C2×#237—22no—
88C2×#237—22no—
89C2×#237—22no—
90C2×#237—22no—
91C2×#237—22no—
92C2×#237D414yes—
93C2×D3×D4—22no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4—22no—
97C2×D3×D4—22no—
98C2×D3×D4D414yes—
99C22×D12C2311yescharacteristic
100C22×C4×D3—21no—
101C22×C4×D3C2311yescharacteristic
102C22×Dic6C2311yescharacteristic
103C2×C3×D8—22no—
104C2×C3×D8—22no—
105C2×C3×D8—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×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C42C2311yescharacteristic
115C2×#217—21no—
116C2×#217—21no—
117C2×#217—21no—
118C2×#217—21no—
119C2×#214—22no—
120C2×#214—22no—
121C2×#214—22no—
122C2×#213—22no—
123C2×#213—22no—
124C2×#213—22no—
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#911—232no—
142C2×#204—22no—
143C2×#204—22no—
144C2×#204—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×#102—22no—
159C3×#102—22no—
160#832—22no—
161#832—22no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166#821—22no—
167#816—22no—
168Dic3⋊C8—22no—
169Dic3⋊C8—22no—
170#810—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×SD16—31no—
180C22×D8—31no—
181C22×D8C2×D311yescharacteristic
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×#103—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—64no—
200C2×#102C2×D311yescharacteristic
201C2×#102C2×D311yescharacteristic, complemented
202#391—31no—
203#391—31no—
204#390—31no—
205#390—31no—
206#390—31no—
207#390—31no—
208#390—61no—
209#390—61no—
210#390C2×D311yescharacteristic
211#390C2×D311yescharacteristic, complemented
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—
223C24×C3—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×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
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×D4C2×D412yes—
244C2×C3×D4C2×D412yes—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2411yescharacteristic
250C2×#67—24no—
251C2×#67—24no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—42no—
256C22×Dic3—21no—
257C22×Dic3—24no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—42no—
261C22×Dic3—42no—
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265#237—28no—
266#237—28no—
267#237—44no—
268#237—44no—
269D3×D4—28no—
270D3×D4—28no—
271D3×D4—44no—
272D3×D4—44no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12C2×D412yes—
279C2×C4×D3—42no—
280C2×C4×D3—81no—
281C2×C4×D3—81no—
282C2×C4×D3C2×D412yes—
283C2×C4×D3C2×D412yes—
284C2×C4×D3C2×D412yes—
285C2×C4×D3#4112yes—
286C2×C4×D3#4112yes—
287C2×C4×D3#4112yes—
288C2×Dic6—21no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6C2×D412yes—
294C3×D8—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×C22⋊C4—81no—
308C3×C22⋊C4—81no—
309C3×C42—21no—
310C3×C42—21no—
311#217—81no—
312#217—81no—
313#217—81no—
314#217—81no—
315#214—28no—
316#213—28no—
317(C2×D3)⋊C4—22no—
318(C2×D3)⋊C4—22no—
319(C2×D3)⋊C4—42no—
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—
340#204—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×Q8—31no—
351C22×D4—34no—
352C22×D4—31no—
353C22×D4—62no—
354C22×D4—62no—
355C22×D4—62no—
356C22×D4—62no—
357C22×D4—62no—
358C22×D4—61no—
359C22×D4—61no—
360C22×D4C22×D311yescharacteristic
361C22×D4C22×D311yescharacteristic
362C23×C4—31no—
363C23×C4—61no—
364C23×C4—61no—
365AGL(1,ℤ/8)—632no—
366C2×SD16—62no—
367C2×SD16—62no—
368C2×SD16—62no—
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—
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—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—31no—
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—62no—
424#103—62no—
425#102—22no—
426#102—22no—
427#102—62no—
428#102—62no—
429#102—62no—
430#102—62no—
431#95—61no—
432#95—61no—
433#95—61no—
434#95—61no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3C22×D411yescharacteristic
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—22no—
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×D4—22no—
472C3×D4—22no—
473C3×D4—22no—
474C3×D4—22no—
475C3×D4—41no—
476C3×D4—41no—
477C3×D4—41no—
478C3×D4—41no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4C22×D411yescharacteristic
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C2×#4111yescharacteristic
495C2×C3×C4C2×#4111yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497#67—48no—
498#67—48no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—22no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—48no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3#12112yes—
516C2×Dic3#12112yes—
517C2×Dic3#12112yes—
518D12—22no—
519D12—22no—
520D12—41no—
521D12—41no—
522C4×D3—84no—
523C4×D3#12014yes—
524C4×D3#12314yes—
525C4×D3#12314yes—
526C4×D3#12414yes—
527Dic6—22no—
528Dic6—22no—
529Dic6—41no—
530Dic6—41no—
531C3×C8—22no—
532C3×C8—41no—
533C3⋊C8—22no—
534C3⋊C8—41no—
535C24—21no—
536C24—21no—
537C24—31no—
538C24—64no—
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—32no—
551C2×Q8—61no—
552C2×Q8—61no—
553C2×Q8—61no—
554C2×Q8—61no—
555C2×Q8—61no—
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—21no—
566C2×D4—32no—
567C2×D4—68no—
568C2×D4—68no—
569C2×D4—64no—
570C2×D4—64no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—124no—
577C2×D4—124no—
578C2×D4—122no—
579C2×D4—122no—
580C2×D4—122no—
581C2×D4—122no—
582C2×D4D3×D412yes—
583C2×D4D3×D412yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—31no—
587C22×C4—32no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—64no—
596C22×C4—61no—
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—68no—
608SD16—68no—
609D8—28no—
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—81no—
641C22⋊C4—81no—
642C22⋊C4—122no—
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—42no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3C2×#12111yescharacteristic
671C22×C3C2×#12111yescharacteristic
672C22×C3C2×#12111yescharacteristic
673C22×C3#57611yescharacteristic
674C22×C3#57611yescharacteristic
675C22×C3#57711yescharacteristic
676C22×C3#57711yescharacteristic
677C2×D3—22no—
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—42no—
684C2×D3—42no—
685C2×D3—42no—
686C2×D3—816no—
687C2×D3—81no—
688C2×D3—81no—
689C2×D3—81no—
690C2×D3—81no—
691C2×D3#39414yes—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—81no—
695C3×C4—81no—
696C3×C4C2×#12011yescharacteristic
697C3×C4C2×#12311yescharacteristic
698C3×C4C2×#12311yescharacteristic
699C3×C4C2×#12411yescharacteristic
700Dic3—42no—
701Dic3—41no—
702Dic3—41no—
703Dic3—81no—
704Dic3—81no—
705Dic3#39414yes—
706C23—22no—
707C23—22no—
708C23—32no—
709C23—32no—
710C23—32no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—61no—
724C23—61no—
725C23—61no—
726C23—61no—
727C23—62no—
728C23—128no—
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—62no—
743Q8—62no—
744Q8—121no—
745Q8—121no—
746D4—22no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—62no—
755D4—62no—
756D4—128no—
757D4—128no—
758D4—121no—
759D4—121no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—34no—
770C2×C4—34no—
771C2×C4—34no—
772C2×C4—34no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—62no—
786C2×C4—128no—
787C2×C4—121no—
788C2×C4—121no—
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×C3—82no—
808C2×C3C2×#39411yescharacteristic
809C2×C3#304111yescharacteristic
810C2×C3#304211yescharacteristic
811C2×C3#304511yescharacteristic
812C2×C3#304511yescharacteristic
813C2×C3#306211yescharacteristic
814C2×C3#306211yescharacteristic
815D3—24no—
816D3—82no—
817C22—34no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—62no—
825C22—62no—
826C22—62no—
827C22—62no—
828C22—62no—
829C22—62no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—122no—
839C22—122no—
840C22—122no—
841C22—2416no—
842C22—241no—
843C22—241no—
844C22—241no—
845C22—241no—
846C22D3×#12111yescharacteristic
847C22D3×#12111yescharacteristic
848C22D3×#12111yescharacteristic
849C22#575711yescharacteristic
850C22#577011yescharacteristic
851C22#577411yescharacteristic
852C22#577511yescharacteristic
853C4—34no—
854C4—41no—
855C4—41no—
856C4—81no—
857C4—81no—
858C4—122no—
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—82no—
871C2—242no—
872C2D3×#39411yescharacteristic
873C2#8033411yescharacteristic
874C2#8033511yescharacteristic
875C2#8053711yescharacteristic
876C2#8053811yescharacteristic
877C2#8071811yescharacteristic
878C2#8086711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2054C2
socleC23×C3C22×D4
prime radicalC22×#911C2
hypercenter#2054D3
hypocenterC3#23544
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2054

Complements

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

NH ≅ G/Ntype
2. C2×#4839C2semidirect
3. C2×#4772C2semidirect
4. C2×D3×#102C2semidirect
5. #76428C2semidirect
6. #76294C2semidirect
7. C3×#2054C2semidirect
8. #72040C2semidirect
9. #70482C2semidirect
10. #70217C2semidirect
11. #70212C2semidirect
12. #69651C2semidirect
13. #69650C2semidirect
14. #68867C2semidirect
15. #68863C2semidirect
31. C2×C3×C4⋊C8C22semidirect
33. C2×C3×#102C22semidirect
35. C3×#390C22semidirect
37. #5221C22semidirect
39. C2×#832C22semidirect
41. C2×#816C22semidirect
42. C2×Dic3⋊C8C22semidirect
43. C2×Dic3⋊C8C22semidirect
45. #4973C22semidirect
46. C2×#810C22semidirect
57. #4929C22semidirect
58. C2×C4⋊(C3⋊C8)C22semidirect
62. C3×#340C22semidirect
63. #4551C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
79. #2054D3semidirect
191. C2×C4⋊C8C2×D3semidirect
201. C2×#102C2×D3semidirect
211. #390C2×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×#9112
C2×#48392
C2×#47722
C2×D3×#1022
#764282
#762942
C3×#20542
#720402
#704822
#702172
#702122
#696512
#696502
#688672
#688632
#235443