Finite Group Databasebeta

← #10823191

Subgroups — #10823191

Order 768.

1674 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#914C211yesmaximal, characteristic
2C2×#4837C211yesmaximal, characteristic, complemented
3C2×#4803C211yesmaximal, characteristic, complemented
4C2×#4770C211yesmaximal, characteristic, complemented
5#76478C211yesmaximal, characteristic, complemented
6D3×#390C211yesmaximal, 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#23546—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×ΓL(1,𝔽25)C2211yescharacteristic
28C2×#892C2211yescharacteristic
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×D3×C22⋊C4—21no—
31C2×D3×C22⋊C4—21no—
32C2×C42×D3C2211yescharacteristic
33C2×C3×C4⋊C8C2211yescharacteristic, complemented
34C2×C3×#103C2211yescharacteristic, complemented
35C2×C3×#102C2211yescharacteristic
36C3×#391C2211yescharacteristic, complemented
37C3×#390C2211yescharacteristic
38#5229C2211yescharacteristic, complemented
39C2×#835C2211yescharacteristic, complemented
40#5221C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic, complemented
44C2×Dic3⋊C8C2211yescharacteristic, complemented
45C2×Dic3⋊C8C2211yescharacteristic, complemented
46#4988C2211yescharacteristic
47#4988C2211yescharacteristic, complemented
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic, complemented
50#4957—21no—
51#4957—21no—
52#4939C2211yescharacteristic
53#4939C2211yescharacteristic, complemented
54C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55#4837—24no—
56#4803—24no—
57#4770—24no—
58#4666—21no—
59#4666—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×#423—31no—
68C2×#417—31no—
69C2×#418—31no—
70#2297—31no—
71C2×#390—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×D3D411yescharacteristic
103C22×C4×D3D411yescharacteristic
104C22×C4×D3C2311yescharacteristic
105C2×C3×SD16—22no—
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C42C2311yescharacteristic
115C2×#217—21no—
116C2×#217—21no—
117C2×#215—22no—
118C2×#215—22no—
119C2×#215—22no—
120C2×#213—22no—
121C2×#213—22no—
122C2×#213—22no—
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)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×C4×Dic3—21no—
136C2×C4×Dic3D411yescharacteristic
137C2×C4×Dic3D411yescharacteristic
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)—22no—
148C2×ΓL(1,𝔽25)—22no—
149C2×ΓL(1,𝔽25)—22no—
150C2×ΓL(1,𝔽25)D414yes—
151#892—22no—
152#892—22no—
153D3×C4⋊C4—22no—
154D3×C4⋊C4—22no—
155D3×C22⋊C4—44no—
156D3×C22⋊C4—44no—
157C42×D3—22no—
158C42×D3—22no—
159C3×C4⋊C8—22no—
160C3×#103—22no—
161C3×#102—22no—
162C3×#95—21no—
163C3×#95—21no—
164#835—22no—
165#832—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168#821—22no—
169#821—22no—
170Dic3⋊C8—22no—
171Dic3⋊C8—22no—
172#809—22no—
173#809—22no—
174C4⋊(C3⋊C8)—22no—
175C22×#41—31no—
176C23×D4—31no—
177C2×AGL(1,ℤ/8)—64no—
178C2×AGL(1,ℤ/8)—64no—
179C2×AGL(1,ℤ/8)—64no—
180C22×SD16—31no—
181C22×SD16C2×D311yescharacteristic
182C22×D8—31no—
183C22×D8—31no—
184C22×M16—31no—
185C22×M16—31no—
186C2×#117—31no—
187C22×C4⋊C4—31no—
188C22×C22⋊C4—61no—
189C22×C22⋊C4—61no—
190C22×C42—31no—
191#423—64no—
192C2×C4⋊C8—31no—
193C2×C4⋊C8—31no—
194C2×C4⋊C8—31no—
195C2×C4⋊C8C2×D311yescharacteristic, complemented
196#418—64no—
197#417—64no—
198C2×#103—31no—
199C2×#103C2×D311yescharacteristic, complemented
200C2×#102—31no—
201C2×#102—31no—
202C2×#102—31no—
203C2×#102—31no—
204C2×#102—31no—
205C2×#102C2×D311yescharacteristic
206#391—31no—
207#391C2×D311yescharacteristic, complemented
208#390—31no—
209#390—31no—
210#390—31no—
211#390—31no—
212#390—31no—
213#390—61no—
214#390—61no—
215#390C2×D311yescharacteristic
216#386—61no—
217#386—61no—
218C4×C22⋊C4—61no—
219C4×C22⋊C4—61no—
220#340—31no—
221#340—31no—
222#340—31no—
223#340C2×D311yescharacteristic, complemented
224C24×C3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—24no—
228C23×D3—42no—
229C23×D3—42no—
230C23×D3—42no—
231C23×D3—42no—
232C23×D3—42no—
233C23×D3—42no—
234C23×D3C2×D411yescharacteristic
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8C2×D412yes—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4C2×D412yes—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2411yescharacteristic
253C2×#67—24no—
254C2×#67—42no—
255C2×#67—42no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3C2×D411yescharacteristic
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261#239—28no—
262#239—28no—
263#239—44no—
264#239—44no—
265D3×D4—28no—
266D3×D4—28no—
267D3×D4—44no—
268D3×D4—44no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—24no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—42no—
281C2×D12—42no—
282C2×D12C2×D412yes—
283C2×D12C2×D412yes—
284C2×C4×D3—22no—
285C2×C4×D3—22no—
286C2×C4×D3—22no—
287C2×C4×D3—24no—
288C2×C4×D3—22no—
289C2×C4×D3—41no—
290C2×C4×D3—41no—
291C2×C4×D3—42no—
292C2×C4×D3—42no—
293C2×C4×D3—42no—
294C2×C4×D3—42no—
295C2×C4×D3—42no—
296C2×C4×D3C2×D412yes—
297C2×C4×D3C2×D412yes—
298C2×C4×D3C2×D412yes—
299C2×C4×D3#4112yes—
300C2×C4×D3#4112yes—
301C2×C4×D3#4112yes—
302C3×SD16—28no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C2×C3×C8C2×D412yes—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C42—21no—
316C3×C42—21no—
317#217—42no—
318#217—42no—
319#215—28no—
320#213—28no—
321(C2×D3)⋊C4—42no—
322(C2×D3)⋊C4—42no—
323(C2×D3)⋊C4—42no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4—42no—
326(C2×D3)⋊C4—42no—
327(C2×D3)⋊C4—42no—
328(C2×D3)⋊C4—42no—
329(C2×D3)⋊C4—42no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334Dic3⋊C4—42no—
335C4×Dic3—21no—
336C4×Dic3—21no—
337C4×Dic3—22no—
338C4×Dic3—22no—
339C4×Dic3—42no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8C2×D412yes—
346D24—28no—
347ΓL(1,𝔽25)—28no—
348ΓL(1,𝔽25)—44no—
349C25—61no—
350C2×#41—34no—
351C2×#41—62no—
352C2×#41—62no—
353C2×#41—62no—
354C2×#41—62no—
355C2×#41—62no—
356C22×Q8C22×D311yescharacteristic
357C22×D4—34no—
358C22×D4—31no—
359C22×D4—31no—
360C22×D4—61no—
361C22×D4—62no—
362C22×D4—62no—
363C22×D4—62no—
364C22×D4—62no—
365C22×D4—62no—
366C22×D4—61no—
367C22×D4C22×D311yescharacteristic
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—61no—
372C23×C4—61no—
373AGL(1,ℤ/8)—632no—
374C2×SD16—22no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16—62no—
378C2×SD16—62no—
379C2×SD16—62no—
380C2×D8—62no—
381C2×D8—62no—
382C2×D8—62no—
383C2×D8—62no—
384C2×D8—62no—
385C2×D8—62no—
386C2×M16—34no—
387C2×M16—62no—
388C2×M16—62no—
389C2×M16—62no—
390C2×M16—62no—
391C2×M16—62no—
392C22×C8—31no—
393C22×C8—31no—
394C22×C8C22×D311yescharacteristic
395C22×C8C22×D311yescharacteristic
396#117—62no—
397#117—62no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—61no—
403C2×C4⋊C4C22×D311yescharacteristic
404C2×C4⋊C4C22×D311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
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×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—124no—
419C2×C22⋊C4—124no—
420C2×C42—31no—
421C2×C42—31no—
422C2×C42—31no—
423C2×C42—62no—
424C2×C42—62no—
425C2×C42—61no—
426C2×C42C22×D311yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—62no—
429C4⋊C8—62no—
430C4⋊C8—62no—
431#103—22no—
432#103—62no—
433#102—22no—
434#102—62no—
435#102—62no—
436#102—62no—
437#102—62no—
438#102—62no—
439#95—21no—
440#95—21no—
441#95—61no—
442#95—61no—
443C23×C3—22no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3C22×D411yescharacteristic
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—48no—
458C22×D3—48no—
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—
470C22×D3—41no—
471C22×D3—48no—
472C22×D3—84no—
473C22×D3—84no—
474C22×D3—84no—
475C22×D3—84no—
476C22×D3#12112yes—
477C22×D3#12112yes—
478C22×D3#12112yes—
479C3×Q8—22no—
480C3×Q8—22no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×D4—22no—
484C3×D4—22no—
485C3×D4—41no—
486C3×D4—41no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—22no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4AGL(1,ℤ/8)12yescomplemented
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4C22×D411yescharacteristic
504C2×C3×C4C22×D411yescharacteristic
505C2×C3×C4C2×#4111yescharacteristic
506C2×C3×C4C2×#4111yescharacteristic
507C2×C3×C4C2×#4111yescharacteristic
508#67—48no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3#12112yes—
521C2×Dic3#12112yes—
522C2×Dic3#12112yes—
523C2×Dic3AGL(1,ℤ/8)12yescomplemented
524D12—22no—
525D12—22no—
526D12—22no—
527D12—22no—
528D12—48no—
529D12—41no—
530D12—41no—
531D12—41no—
532D12—41no—
533C4×D3—44no—
534C4×D3—44no—
535C4×D3—48no—
536C4×D3—84no—
537C4×D3#12014yes—
538C4×D3#12314yes—
539C4×D3#12314yes—
540C4×D3#12414yes—
541C3×C8—22no—
542C3×C8—41no—
543C3⋊C8—22no—
544C3⋊C8—41no—
545C24—21no—
546C24—31no—
547C24—64no—
548C24—61no—
549C24—61no—
550C24—122no—
551C24—122no—
552C24—122no—
553C24—122no—
554C24—122no—
555C24—122no—
556#41—68no—
557#41—68no—
558#41—124no—
559#41—124no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8D3×D412yes—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—32no—
572C2×D4—32no—
573C2×D4—64no—
574C2×D4—68no—
575C2×D4—68no—
576C2×D4—64no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—124no—
588C2×D4—124no—
589C2×D4—122no—
590C2×D4—122no—
591C2×D4—122no—
592C2×D4—122no—
593C2×D4D3×D412yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—31no—
598C22×C4—32no—
599C22×C4—32no—
600C22×C4—32no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—32no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—62no—
607C22×C4—64no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—121no—
614C22×C4—121no—
615C22×C4—122no—
616C22×C4—122no—
617C22×C4—122no—
618C22×C4—122no—
619C22×C4—122no—
620C22×C4D3×D411yescharacteristic
621C22×C4D3×D411yescharacteristic
622C22×C4C23×D311yescharacteristic
623SD16—28no—
624SD16—68no—
625D8—68no—
626D8—68no—
627M16—68no—
628M16—124no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—32no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—61no—
638C2×C8—61no—
639C2×C8—61no—
640C2×C8D3×D412yes—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—122no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—122no—
653C22⋊C4—122no—
654C22⋊C4—122no—
655C22⋊C4—122no—
656C22⋊C4—122no—
657C22⋊C4—122no—
658C22⋊C4—122no—
659C22⋊C4—122no—
660C22⋊C4—122no—
661C22⋊C4—122no—
662C22⋊C4—122no—
663C42—21no—
664C42—21no—
665C42—62no—
666C42—62no—
667C42—61no—
668C42—61no—
669C42—122no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3C2×#12111yescharacteristic
678C22×C3C2×#12111yescharacteristic
679C22×C3C2×#12111yescharacteristic
680C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
681C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
682C22×C3#57511yescharacteristic
683C22×C3#57511yescharacteristic
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—42no—
691C2×D3—42no—
692C2×D3—42no—
693C2×D3—42no—
694C2×D3—42no—
695C2×D3—42no—
696C2×D3—816no—
697C2×D3—81no—
698C2×D3—81no—
699C2×D3—81no—
700C2×D3—81no—
701C2×D3—81no—
702C2×D3—81no—
703C2×D3—81no—
704C2×D3—81no—
705C2×D3#39414yes—
706C3×C4—22no—
707C3×C4—42no—
708C3×C4—41no—
709C3×C4—81no—
710C3×C4—81no—
711C3×C4C2×#12011yescharacteristic
712C3×C4C2×#12311yescharacteristic
713C3×C4C2×#12311yescharacteristic
714C3×C4C2×#12411yescharacteristic
715Dic3—22no—
716Dic3—41no—
717Dic3—81no—
718Dic3—81no—
719Dic3#39414yes—
720C23—22no—
721C23—32no—
722C23—32no—
723C23—32no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—61no—
731C23—61no—
732C23—61no—
733C23—61no—
734C23—62no—
735C23—62no—
736C23—128no—
737C23—128no—
738C23—128no—
739C23—121no—
740C23—121no—
741C23—121no—
742C23—121no—
743C23—121no—
744C23—121no—
745C23—121no—
746C23—121no—
747C23—121no—
748C23—121no—
749C23—121no—
750C23—121no—
751C23—244no—
752C23—244no—
753C23—244no—
754C23—244no—
755C23C2×D3×D411yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—41no—
759Q8—41no—
760D4—22no—
761D4—22no—
762D4—41no—
763D4—41no—
764D4—62no—
765D4—62no—
766D4—62no—
767D4—62no—
768D4—128no—
769D4—128no—
770D4—121no—
771D4—121no—
772D4—121no—
773D4—121no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—34no—
784C2×C4—34no—
785C2×C4—34no—
786C2×C4—34no—
787C2×C4—32no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—124no—
802C2×C4—128no—
803C2×C4—124no—
804C2×C4—121no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4—121no—
809C2×C4—121no—
810C2×C4—244no—
811C2×C4#91412yescomplemented
812C2×C4C2×D3×D411yescharacteristic
813C2×C4C2×D3×D411yescharacteristic
814C2×C4C2×D3×D411yescharacteristic
815C2×C4D3×#4111yescharacteristic
816C2×C4D3×#4111yescharacteristic
817C2×C4D3×#4111yescharacteristic
818C8—22no—
819C8—41no—
820C8—62no—
821C8—121no—
822C2×C3—82no—
823C2×C3C2×#39411yescharacteristic
824C2×C3#303611yescharacteristic
825C2×C3#303611yescharacteristic
826C2×C3#303811yescharacteristic
827C2×C3#304011yescharacteristic
828C2×C3#305511yescharacteristic
829C2×C3#305511yescharacteristic
830D3—24no—
831D3—82no—
832D3—82no—
833C22—34no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—62no—
838C22—62no—
839C22—62no—
840C22—62no—
841C22—62no—
842C22—62no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—122no—
848C22—122no—
849C22—122no—
850C22—122no—
851C22—122no—
852C22—122no—
853C22—2416no—
854C22—241no—
855C22—241no—
856C22—241no—
857C22—241no—
858C22—241no—
859C22—241no—
860C22—241no—
861C22—241no—
862C22D3×#12111yescharacteristic
863C22D3×#12111yescharacteristic
864C22D3×#12111yescharacteristic
865C22C2×#91411yescharacteristic
866C22#576811yescharacteristic
867C22D3×AGL(1,ℤ/8)11yescharacteristic
868C22#577711yescharacteristic
869C4—22no—
870C4—34no—
871C4—42no—
872C4—41no—
873C4—62no—
874C4—81no—
875C4—81no—
876C4—121no—
877C4—241no—
878C4—241no—
879C4D3×#12011yescharacteristic
880C4D3×#12311yescharacteristic
881C4D3×#12311yescharacteristic
882C4D3×#12411yescharacteristic
883C3#2354611yescharacteristic, complemented, Sylow
884C2—64no—
885C2—82no—
886C2—242no—
887C2—242no—
888C2D3×#39411yescharacteristic
889C2#8038411yescharacteristic
890C2#8042811yescharacteristic
891C2#8053411yescharacteristic
892C2#8059911yescharacteristic
893C2#8065711yescharacteristic
894C2#8080511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2055C2
socleC23×C3C22×D4
prime radicalC22×#914C2
hypercenter#2055D3
hypocenterC3#23546
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×#4837C2semidirect
3. C2×#4803C2semidirect
4. C2×#4770C2semidirect
5. #76478C2semidirect
6. D3×#390C2semidirect
7. C3×#2055C2semidirect
8. #72051C2semidirect
9. #70481C2semidirect
10. #70280C2semidirect
11. #70212C2semidirect
12. #69680C2semidirect
13. #69650C2semidirect
14. #68867C2semidirect
15. #68862C2semidirect
33. C2×C3×C4⋊C8C22semidirect
34. C2×C3×#103C22semidirect
36. C3×#391C22semidirect
38. #5229C22semidirect
39. C2×#835C22semidirect
43. C2×#821C22semidirect
44. C2×Dic3⋊C8C22semidirect
45. C2×Dic3⋊C8C22semidirect
47. #4988C22semidirect
49. C2×#809C22semidirect
53. #4939C22semidirect
54. C2×C4⋊(C3⋊C8)C22semidirect
62. C3×#340C22semidirect
63. #4551C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
75. #2055D3semidirect
195. C2×C4⋊C8C2×D3semidirect
199. C2×#103C2×D3semidirect
207. #391C2×D3semidirect
223. #340C2×D3semidirect
501. C2×C3×C4AGL(1,ℤ/8)semidirect
523. C2×Dic3AGL(1,ℤ/8)semidirect
811. C2×C4#914semidirect
883. C3#23546semidirect

Maximal subgroups

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

subgroupindex
C22×#9142
C2×#48372
C2×#48032
C2×#47702
#764782
D3×#3902
C3×#20552
#720512
#704812
#702802
#702122
#696802
#696502
#688672
#688622
#235463