Finite Group Databasebeta

← #10823186

Subgroups — #10823186

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×#911C211yesmaximal, characteristic
2C2×#4837C211yesmaximal, characteristic, complemented
3C2×#4771C211yesmaximal, characteristic, complemented
4C2×#4770C211yesmaximal, characteristic, complemented
5D3×#390C211yesmaximal, characteristic, complemented
6#76290C211yesmaximal, 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#23546—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×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×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic, complemented
36C3×#390C2211yescharacteristic
37C3×#390C2211yescharacteristic, complemented
38#5221C2211yescharacteristic
39#5221C2211yescharacteristic, complemented
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic, complemented
42C2×#821C2211yescharacteristic
43C2×#816C2211yescharacteristic, complemented
44C2×Dic3⋊C8C2211yescharacteristic, complemented
45C2×Dic3⋊C8C2211yescharacteristic, complemented
46#4988C2211yescharacteristic
47#4973C2211yescharacteristic, complemented
48C2×#810C2211yescharacteristic, complemented
49C2×#809C2211yescharacteristic
50#4957—21no—
51#4957—21no—
52#4956—21no—
53#4956—21no—
54Dic3×C22⋊C4—21no—
55Dic3×C22⋊C4—21no—
56#4939C2211yescharacteristic
57#4929C2211yescharacteristic, complemented
58C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#4837—24no—
60#4771—24no—
61#4770—24no—
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#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×D3D411yescharacteristic
102C22×C4×D3D411yescharacteristic
103C22×C4×D3C2311yescharacteristic
104C22×Dic6C2311yescharacteristic
105C2×C3×D8—22no—
106C2×C3×D8—22no—
107C2×C3×D8—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×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C42C2311yescharacteristic
117C2×#217—21no—
118C2×#217—21no—
119C2×#217—21no—
120C2×#217—21no—
121C2×#214—22no—
122C2×#214—22no—
123C2×#214—22no—
124C2×#213—22no—
125C2×#213—22no—
126C2×#213—22no—
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#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)—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×#102—22no—
161C3×#102—22no—
162#832—22no—
163#832—22no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168#821—22no—
169#816—22no—
170Dic3⋊C8—22no—
171Dic3⋊C8—22no—
172#810—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×SD16—31no—
182C22×D8—31no—
183C22×D8C2×D311yescharacteristic
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×#103—31no—
200C2×#102—31no—
201C2×#102—31no—
202C2×#102—31no—
203C2×#102—31no—
204C2×#102C2×D311yescharacteristic
205C2×#102C2×D311yescharacteristic, complemented
206#391—31no—
207#391—31no—
208#390—31no—
209#390—31no—
210#390—31no—
211#390—31no—
212#390—61no—
213#390—61no—
214#390C2×D311yescharacteristic
215#390C2×D311yescharacteristic, complemented
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—
225C24×C3—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×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×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4C2×D412yes—
246C2×C3×D4C2×D412yes—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2411yescharacteristic
252C2×#67—24no—
253C2×#67—24no—
254C2×#67—42no—
255C2×#67—42no—
256C2×#67—42no—
257C2×#67—42no—
258C22×Dic3—21no—
259C22×Dic3—24no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—42no—
263C22×Dic3—42no—
264C22×Dic3C2×D411yescharacteristic
265C22×Dic3C2×D411yescharacteristic
266C22×Dic3C2×D411yescharacteristic
267#237—28no—
268#237—28no—
269#237—44no—
270#237—44no—
271D3×D4—28no—
272D3×D4—28no—
273D3×D4—44no—
274D3×D4—44no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12C2×D412yes—
281C2×C4×D3—22no—
282C2×C4×D3—22no—
283C2×C4×D3—22no—
284C2×C4×D3—22no—
285C2×C4×D3—41no—
286C2×C4×D3—41no—
287C2×C4×D3—42no—
288C2×C4×D3—42no—
289C2×C4×D3—42no—
290C2×C4×D3C2×D412yes—
291C2×C4×D3C2×D412yes—
292C2×C4×D3C2×D412yes—
293C2×C4×D3#4112yes—
294C2×C4×D3#4112yes—
295C2×C4×D3#4112yes—
296C2×Dic6—21no—
297C2×Dic6—21no—
298C2×Dic6—21no—
299C2×Dic6—21no—
300C2×Dic6—21no—
301C2×Dic6C2×D412yes—
302C3×D8—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×C22⋊C4—42no—
316C3×C22⋊C4—42no—
317C3×C42—21no—
318C3×C42—21no—
319#217—42no—
320#217—42no—
321#217—42no—
322#217—42no—
323#214—28no—
324#213—28no—
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—
346#204—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×Q8—31no—
357C22×D4—34no—
358C22×D4—31no—
359C22×D4—62no—
360C22×D4—62no—
361C22×D4—62no—
362C22×D4—62no—
363C22×D4—62no—
364C22×D4—61no—
365C22×D4—61no—
366C22×D4C22×D311yescharacteristic
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—62no—
375C2×SD16—62no—
376C2×SD16—62no—
377C2×SD16—62no—
378C2×SD16—62no—
379C2×SD16—62no—
380C2×D8—22no—
381C2×D8—22no—
382C2×D8—22no—
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—21no—
408C2×C22⋊C4—21no—
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—62no—
432#103—62no—
433#102—22no—
434#102—22no—
435#102—62no—
436#102—62no—
437#102—62no—
438#102—62no—
439#95—61no—
440#95—61no—
441#95—61no—
442#95—61no—
443C23×C3—22no—
444C23×C3—22no—
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×C3—41no—
456C23×C3—41no—
457C23×C3C22×D411yescharacteristic
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—22no—
463C22×D3—48no—
464C22×D3—48no—
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×D4—22no—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—22no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—41no—
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—41no—
498C2×C3×C4AGL(1,ℤ/8)12yescomplemented
499C2×C3×C4C22×D411yescharacteristic
500C2×C3×C4C22×D411yescharacteristic
501C2×C3×C4C22×D411yescharacteristic
502C2×C3×C4C2×#4111yescharacteristic
503C2×C3×C4C2×#4111yescharacteristic
504C2×C3×C4C2×#4111yescharacteristic
505#67—48no—
506#67—48no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—22no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—48no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3#12112yes—
523C2×Dic3#12112yes—
524C2×Dic3#12112yes—
525C2×Dic3AGL(1,ℤ/8)12yescomplemented
526D12—22no—
527D12—22no—
528D12—41no—
529D12—41no—
530C4×D3—44no—
531C4×D3—44no—
532C4×D3—84no—
533C4×D3#12014yes—
534C4×D3#12314yes—
535C4×D3#12314yes—
536C4×D3#12414yes—
537Dic6—22no—
538Dic6—22no—
539Dic6—41no—
540Dic6—41no—
541C3×C8—22no—
542C3×C8—41no—
543C3⋊C8—22no—
544C3⋊C8—41no—
545C24—21no—
546C24—21no—
547C24—31no—
548C24—64no—
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—32no—
561C2×Q8—61no—
562C2×Q8—61no—
563C2×Q8—61no—
564C2×Q8—61no—
565C2×Q8—61no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—32no—
577C2×D4—68no—
578C2×D4—68no—
579C2×D4—64no—
580C2×D4—64no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—124no—
587C2×D4—124no—
588C2×D4—122no—
589C2×D4—122no—
590C2×D4—122no—
591C2×D4—122no—
592C2×D4D3×D412yes—
593C2×D4D3×D412yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—31no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—32no—
600C22×C4—32no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—64no—
609C22×C4—61no—
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—68no—
624SD16—68no—
625D8—28no—
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—42no—
653C22⋊C4—42no—
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—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3C2×#12111yescharacteristic
685C22×C3C2×#12111yescharacteristic
686C22×C3C2×#12111yescharacteristic
687C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
688C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
689C22×C3#57511yescharacteristic
690C22×C3#57511yescharacteristic
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—22no—
694C2×D3—22no—
695C2×D3—22no—
696C2×D3—22no—
697C2×D3—42no—
698C2×D3—42no—
699C2×D3—42no—
700C2×D3—816no—
701C2×D3—81no—
702C2×D3—81no—
703C2×D3—81no—
704C2×D3—81no—
705C2×D3#39414yes—
706C3×C4—22no—
707C3×C4—41no—
708C3×C4—81no—
709C3×C4—81no—
710C3×C4C2×#12011yescharacteristic
711C3×C4C2×#12311yescharacteristic
712C3×C4C2×#12311yescharacteristic
713C3×C4C2×#12411yescharacteristic
714Dic3—22no—
715Dic3—42no—
716Dic3—41no—
717Dic3—81no—
718Dic3—81no—
719Dic3#39414yes—
720C23—22no—
721C23—22no—
722C23—32no—
723C23—32no—
724C23—32no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—62no—
742C23—128no—
743C23—128no—
744C23—128no—
745C23—121no—
746C23—121no—
747C23—121no—
748C23—121no—
749C23—121no—
750C23—121no—
751C23—244no—
752C23—244no—
753C23—244no—
754C23—244no—
755C23C2×D3×D411yescharacteristic
756Q8—62no—
757Q8—62no—
758Q8—121no—
759Q8—121no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—62no—
769D4—62no—
770D4—128no—
771D4—128no—
772D4—121no—
773D4—121no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—34no—
783C2×C4—34no—
784C2×C4—34no—
785C2×C4—34no—
786C2×C4—32no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—62no—
799C2×C4—124no—
800C2×C4—128no—
801C2×C4—124no—
802C2×C4—121no—
803C2×C4—121no—
804C2×C4—121no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4—121no—
809C2×C4—121no—
810C2×C4—244no—
811C2×C4#91112yescomplemented
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×C3—82no—
824C2×C3C2×#39411yescharacteristic
825C2×C3#303611yescharacteristic
826C2×C3#303611yescharacteristic
827C2×C3#303811yescharacteristic
828C2×C3#304011yescharacteristic
829C2×C3#305511yescharacteristic
830C2×C3#305511yescharacteristic
831D3—24no—
832D3—82no—
833C22—34no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—62no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—62no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—122no—
855C22—122no—
856C22—122no—
857C22—2416no—
858C22—241no—
859C22—241no—
860C22—241no—
861C22—241no—
862C22D3×#12111yescharacteristic
863C22D3×#12111yescharacteristic
864C22D3×#12111yescharacteristic
865C22C2×#91111yescharacteristic
866C22#576811yescharacteristic
867C22D3×AGL(1,ℤ/8)11yescharacteristic
868C22#577311yescharacteristic
869C4—22no—
870C4—34no—
871C4—41no—
872C4—62no—
873C4—81no—
874C4—81no—
875C4—122no—
876C4—121no—
877C4—241no—
878C4—241no—
879C4D3×#12011yescharacteristic
880C4D3×#12311yescharacteristic
881C4D3×#12311yescharacteristic
882C4D3×#12411yescharacteristic
883C3#2354611yescharacteristic, complemented, Sylow
884C2—64no—
885C2—82no—
886C2—82no—
887C2—242no—
888C2D3×#39411yescharacteristic
889C2#8033211yescharacteristic
890C2#8033311yescharacteristic
891C2#8053411yescharacteristic
892C2#8053511yescharacteristic
893C2#8071511yescharacteristic
894C2#8086411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2054C2
socleC23×C3C22×D4
prime radicalC22×#911C2
hypercenter#2054D3
hypocenterC3#23546
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×#4837C2semidirect
3. C2×#4771C2semidirect
4. C2×#4770C2semidirect
5. D3×#390C2semidirect
6. #76290C2semidirect
7. C3×#2054C2semidirect
8. #72040C2semidirect
9. #70482C2semidirect
10. #70217C2semidirect
11. #70212C2semidirect
12. #69651C2semidirect
13. #69650C2semidirect
14. #68867C2semidirect
15. #68863C2semidirect
33. C2×C3×C4⋊C8C22semidirect
35. C2×C3×#102C22semidirect
37. C3×#390C22semidirect
39. #5221C22semidirect
41. C2×#832C22semidirect
43. C2×#816C22semidirect
44. C2×Dic3⋊C8C22semidirect
45. C2×Dic3⋊C8C22semidirect
47. #4973C22semidirect
48. C2×#810C22semidirect
57. #4929C22semidirect
58. C2×C4⋊(C3⋊C8)C22semidirect
62. C3×#340C22semidirect
63. #4551C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
79. #2054D3semidirect
195. C2×C4⋊C8C2×D3semidirect
205. C2×#102C2×D3semidirect
215. #390C2×D3semidirect
223. #340C2×D3semidirect
498. C2×C3×C4AGL(1,ℤ/8)semidirect
525. C2×Dic3AGL(1,ℤ/8)semidirect
811. C2×C4#911semidirect
883. C3#23546semidirect

Maximal subgroups

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

subgroupindex
C22×#9112
C2×#48372
C2×#47712
C2×#47702
D3×#3902
#762902
C3×#20542
#720402
#704822
#702172
#702122
#696512
#696502
#688672
#688632
#235463