Finite Group Databasebeta

← #10944263

Subgroups — #10944263

Order 768.

1580 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×M16C211yesmaximal, characteristic, complemented
2C2×C3×#468C211yesmaximal, characteristic, complemented
3C2×#5174C211yesmaximal, characteristic, complemented
4C2×#5171C211yesmaximal, characteristic, complemented
5#82834C211yesmaximal, characteristic, complemented
6#82723C211yesmaximal, characteristic
7#71988C211yesmaximal, characteristic, complemented
8#71697C211yesmaximal, characteristic, complemented
9#71682C211yesmaximal, characteristic, complemented
10#70631C211yesmaximal, characteristic, complemented
11#70630C211yesmaximal, characteristic, complemented
12#70271C211yesmaximal, characteristic, complemented
13#70270C211yesmaximal, characteristic, complemented
14#70203C211yesmaximal, characteristic, complemented
15#70202C211yesmaximal, characteristic, complemented
16#32935—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic, complemented
19C22×C3×M16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C2×#937—21no—
27C22×#208C2211yescharacteristic
28C2×D3×M16—24no—
29C2×D3×M16—24no—
30C2×D3×M16—24no—
31C22×ΓL(1,𝔽25)C2211yescharacteristic
32C22×ΓL(1,𝔽25)C2211yescharacteristic
33C22×D3×C8C2211yescharacteristic
34C22×D3×C8C2211yescharacteristic
35C3×#468—24no—
36C2×C3×#107C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic, complemented
39C2×#835C2211yescharacteristic, complemented
40C2×#835C2211yescharacteristic, complemented
41#5220—21no—
42C2×#832C2211yescharacteristic, complemented
43C2×#832C2211yescharacteristic, complemented
44#5212C2211yescharacteristic
45#5212C2211yescharacteristic
46#5174—24no—
47#5171—24no—
48C2×#818C2211yescharacteristic, complemented
49C2×#817C2211yescharacteristic, complemented
50#4989—21no—
51#4989—21no—
52#4987C2211yescharacteristic
53#4987C2211yescharacteristic
54#4987C2211yescharacteristic
55#4987C2211yescharacteristic
56#4956—21no—
57#4956—21no—
58#4955—21no—
59#4946—21no—
60#4551C2211yescharacteristic, complemented
61#4551C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C23×M16—31no—
67C2×#468—31no—
68C2×#468D311yescharacteristic, complemented
69C2×#465—31no—
70#2848—31no—
71#2847—31no—
72#1895—31no—
73#1895—31no—
74#1894—31no—
75#1894—31no—
76#1893—31no—
77#1892—31no—
78#1809—31no—
79#1809—31no—
80#1808—31no—
81C24×D3D411yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4—21no—
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C23×Dic3D411yescharacteristic
89C22×C4×D3—22no—
90C22×C4×D3—22no—
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3D411yescharacteristic
96C22×C4×D3D411yescharacteristic
97C22×C4×D3C2311yescharacteristic
98C22×C4×D3C2311yescharacteristic
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×M16—22no—
103C2×C3×M16—22no—
104C2×C3×M16D414yescomplemented
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C3×#121—22no—
110C3×#121—22no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×#217—21no—
117C2×#217—21no—
118C2×#217—21no—
119C2×#217—21no—
120#946—22no—
121#946—22no—
122#946—22no—
123#946—22no—
124#938—22no—
125#938—22no—
126#938—22no—
127#938—22no—
128#937—44no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×#208—22no—
142C2×#208—22no—
143C2×#208—22no—
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146D3×M16—232no—
147C2×ΓL(1,𝔽25)—22no—
148C2×ΓL(1,𝔽25)—22no—
149C2×ΓL(1,𝔽25)—22no—
150C2×ΓL(1,𝔽25)—22no—
151C2×ΓL(1,𝔽25)—22no—
152C2×ΓL(1,𝔽25)D414yescomplemented
153C2×D3×C8—22no—
154C2×D3×C8—22no—
155C2×D3×C8—22no—
156C2×D3×C8—22no—
157C2×D3×C8—22no—
158C2×D3×C8D414yescomplemented
159C3×#107—22no—
160C3×#103—22no—
161C3×#102—22no—
162#835—22no—
163#835—22no—
164#832—22no—
165#832—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172#818—22no—
173#817—22no—
174C24×C4—31no—
175C22×SD16C2×D311yescharacteristic, complemented
176C22×M16—31no—
177C22×M16—31no—
178C22×M16—31no—
179C22×M16—64no—
180C22×M16—64no—
181C22×M16—64no—
182C22×M16C2×D311yescharacteristic
183C23×C8—31no—
184C23×C8—31no—
185C2×C22⋊Q8—31no—
186C2×C22⋊Q8—31no—
187C2×C22⋊Q8C2×D311yescharacteristic
188C2×#121—31no—
189C2×#121—31no—
190C2×#121C2×D311yescharacteristic
191C2×#120—61no—
192#468—24no—
193#468—64no—
194#465—64no—
195C2×#107—31no—
196C2×#107C2×D311yescharacteristic, complemented
197C2×#106—31no—
198C2×#103—31no—
199C2×#103—31no—
200C2×#103C2×D311yescharacteristic, complemented
201C2×#102—31no—
202C2×#102—31no—
203C2×#102C2×D311yescharacteristic, complemented
204#386—61no—
205#386—61no—
206#386—61no—
207#385—61no—
208#385—61no—
209#385—61no—
210#380—31no—
211#380—31no—
212#380—31no—
213#380—31no—
214#380—31no—
215#380—31no—
216#379—61no—
217#340—31no—
218#340—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223C24×C3—21no—
224C24×C3C2×D411yescharacteristic
225C23×D3—22no—
226C23×D3—22no—
227C23×D3—22no—
228C23×D3—22no—
229C23×D3—22no—
230C23×D3—41no—
231C23×D3—41no—
232C23×D3C2×D411yescharacteristic
233C23×D3C2×D411yescharacteristic
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—42no—
247C2×C3×D4—42no—
248C2×C3×D4—42no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D412yes—
258C22×C3×C4#4112yes—
259C22×C3×C4C2411yescharacteristic
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—42no—
265C2×#67—42no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—22no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3C2×D411yescharacteristic
274C22×Dic3C2×D411yescharacteristic
275C2×C4×D3—28no—
276C2×C4×D3—28no—
277C2×C4×D3—28no—
278C2×C4×D3—28no—
279C2×C4×D3—22no—
280C2×C4×D3—22no—
281C2×C4×D3—22no—
282C2×C4×D3—22no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—22no—
292C2×C4×D3—22no—
293C2×C4×D3C2×D412yes—
294C2×C4×D3C2×D412yes—
295C2×C4×D3#4112yes—
296C2×C4×D3#4112yes—
297C3×SD16—44no—
298C3×M16—28no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8C2×D412yes—
302C2×C3×C8C2×D412yes—
303C2×C3×C8C2×D412yes—
304C2×C3×C8C2×D412yes—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—42no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—42no—
312#217—42no—
313#217—42no—
314#217—42no—
315#217—42no—
316(C2×D3)⋊C4—42no—
317(C2×D3)⋊C4—42no—
318(C2×D3)⋊C4—42no—
319(C2×D3)⋊C4—42no—
320(C2×D3)⋊C4—42no—
321(C2×D3)⋊C4—42no—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3—21no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330Dic3⋊C4—42no—
331Dic3⋊C4—42no—
332#208—28no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8C2×D412yes—
338C2×C3⋊C8C2×D412yes—
339ΓL(1,𝔽25)—28no—
340ΓL(1,𝔽25)—28no—
341D3×C8—28no—
342D3×C8—28no—
343C25—31no—
344C22×Q8C22×D311yescharacteristic
345C22×D4—21no—
346C22×D4—61no—
347C22×D4—61no—
348C22×D4C22×D311yescharacteristic
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—62no—
355C23×C4—62no—
356C23×C4—62no—
357C23×C4—62no—
358C23×C4—62no—
359C23×C4—62no—
360C23×C4C22×D311yescharacteristic
361C2×SD16—22no—
362C2×SD16—22no—
363C2×SD16—22no—
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—34no—
367C2×M16—62no—
368C2×M16—62no—
369C2×M16—62no—
370C2×M16—62no—
371C2×M16—632no—
372C2×M16—62no—
373C2×M16—62no—
374C2×M16—62no—
375C2×M16—62no—
376C2×M16#6714yescomplemented
377C22×C8—31no—
378C22×C8—31no—
379C22×C8—34no—
380C22×C8—62no—
381C22×C8—62no—
382C22×C8—62no—
383C22×C8—62no—
384C22×C8—62no—
385C22×C8C22×D311yescharacteristic
386C22×C8C22×D311yescharacteristic
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—62no—
390C22⋊Q8—62no—
391C22⋊Q8—62no—
392C22⋊Q8—62no—
393#121—22no—
394#121—22no—
395#121—62no—
396#121—62no—
397#121—62no—
398#121—62no—
399#120—124no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—31no—
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—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—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421#107—22no—
422#107—62no—
423#106—62no—
424#103—22no—
425#103—62no—
426#103—62no—
427#102—22no—
428#102—62no—
429#102—62no—
430#95—61no—
431#95—61no—
432#95—61no—
433#95—61no—
434#95—61no—
435#95—61no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3#12112yes—
450C23×C3C22×D411yescharacteristic
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—28no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—44no—
463C22×D3—44no—
464C22×D3—44no—
465C22×D3—44no—
466C22×D3—44no—
467C22×D3—44no—
468C22×D3#12112yes—
469C22×D3#12112yes—
470C22×D3AGL(1,ℤ/8)12yes—
471C22×D3#13712yes—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×Q8—41no—
476C3×D4—41no—
477C3×D4—41no—
478C3×D4—41no—
479C3×D4—41no—
480C3×D4—84no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
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×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4#12112yes—
497C2×C3×C4C22×D411yescharacteristic
498C2×C3×C4C22×D411yescharacteristic
499C2×C3×C4C22×D411yescharacteristic
500C2×C3×C4C2×#4111yescharacteristic
501C2×C3×C4C2×#4111yescharacteristic
502C2×C3×C4C2×#4111yescharacteristic
503#67—84no—
504#67—84no—
505C2×Dic3—28no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
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—41no—
522C2×Dic3#12112yes—
523C2×Dic3#12112yes—
524C4×D3—28no—
525C4×D3—28no—
526C4×D3—22no—
527C4×D3—22no—
528C4×D3—22no—
529C4×D3—22no—
530C4×D3—22no—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—22no—
534C3×C8—22no—
535C3×C8#12014yescomplemented
536C3⋊C8—22no—
537C3⋊C8—22no—
538C24—21no—
539C24—31no—
540C24—31no—
541C24—62no—
542C24—62no—
543C24—62no—
544C24—62no—
545C24—62no—
546C24—121no—
547C24—121no—
548C24D3×D411yescharacteristic
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—122no—
565C2×D4—122no—
566C2×D4—122no—
567C2×D4—122no—
568C2×D4—122no—
569C2×D4—122no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—32no—
580C22×C4—32no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—68no—
588C22×C4—68no—
589C22×C4—68no—
590C22×C4—68no—
591C22×C4—62no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4D3×D411yescharacteristic
609C22×C4#23712yes—
610C22×C4C2×#6712yes—
611C22×C4C23×D311yescharacteristic
612SD16—44no—
613M16—28no—
614M16—68no—
615M16—68no—
616M16—68no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—32no—
620C2×C8—32no—
621C2×C8—68no—
622C2×C8—61no—
623C2×C8—61no—
624C2×C8—61no—
625C2×C8—61no—
626C2×C8—68no—
627C2×C8D3×D412yes—
628C2×C8D3×D412yes—
629C2×C8C2×#6712yes—
630C2×C8C2×#6712yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—42no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—122no—
645C4⋊C4—122no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—122no—
649C22⋊C4—122no—
650C22⋊C4—122no—
651C22⋊C4—122no—
652C22⋊C4—122no—
653C22⋊C4—122no—
654C22⋊C4—122no—
655C22⋊C4—122no—
656C22⋊C4—122no—
657C22⋊C4—122no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3C2×#12111yescharacteristic
673C22×C3C2×#12111yescharacteristic
674C22×C3C2×#12111yescharacteristic
675C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
676C22×C3C2×#13711yescharacteristic
677C22×C3#57511yescharacteristic
678C22×C3#57511yescharacteristic
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—22no—
688C2×D3—416no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3#46814yescomplemented
694C3×C4—22no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—81no—
698C3×C4C2×#12011yescharacteristic
699C3×C4#52511yescharacteristic
700C3×C4#52511yescharacteristic
701C3×C4#52511yescharacteristic
702Dic3—22no—
703Dic3—22no—
704Dic3—81no—
705Dic3—81no—
706Dic3—81no—
707Dic3—81no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—32no—
715C23—32no—
716C23—32no—
717C23—32no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—68no—
726C23—61no—
727C23—61no—
728C23—61no—
729C23—61no—
730C23—61no—
731C23—61no—
732C23—61no—
733C23—61no—
734C23—61no—
735C23—61no—
736C23—124no—
737C23—124no—
738C23—124no—
739C23—124no—
740C23—124no—
741C23—124no—
742C23#93812yes—
743C23C2×D3×D411yescharacteristic
744Q8—41no—
745Q8—41no—
746Q8—41no—
747Q8—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—244no—
754D4—244no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—68no—
773C2×C4—68no—
774C2×C4—68no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
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—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4#93812yes—
800C2×C4C2×D3×D411yescharacteristic
801C2×C4C2×D3×D411yescharacteristic
802C2×C4C2×#23711yescharacteristic
803C2×C4D3×#4111yescharacteristic
804C2×C4D3×#4111yescharacteristic
805C2×C4C22×#6711yescharacteristic
806C8—22no—
807C8—62no—
808C8—62no—
809C8#93714yescomplemented
810C2×C3—42no—
811C2×C3—161no—
812C2×C3#284711yescharacteristic
813C2×C3C2×#46811yescharacteristic
814C2×C3#305411yescharacteristic
815C2×C3#305511yescharacteristic
816C2×C3#305511yescharacteristic
817C2×C3#305611yescharacteristic
818C2×C3#305611yescharacteristic
819D3—24no—
820D3—42no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—34no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—62no—
830C22—62no—
831C22—62no—
832C22—62no—
833C22—62no—
834C22—62no—
835C22—62no—
836C22—62no—
837C22—62no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—1216no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22D3×#12111yescharacteristic
851C22D3×#12111yescharacteristic
852C22D3×AGL(1,ℤ/8)11yescharacteristic
853C22#577311yescharacteristic
854C22D3×#13711yescharacteristic
855C22#577711yescharacteristic
856C22C2×#93811yescharacteristic
857C4—22no—
858C4—62no—
859C4—62no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—241no—
864C4—241no—
865C4—241no—
866C4—241no—
867C4#560611yescharacteristic
868C4#560611yescharacteristic
869C4C2×#93711yescharacteristic
870C4#582811yescharacteristic
871C3#3293511yescharacteristic, complemented, Sylow
872C2—42no—
873C2—64no—
874C2—122no—
875C2—161no—
876C2D3×#46811yescharacteristic
877C2#8080411yescharacteristic
878C2#8080511yescharacteristic
879C2#8080611yescharacteristic
880C2#8272311yescharacteristic
881C2#8395011yescharacteristic
882C2#8398511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#468C2
socleC23×C3C22×D4
prime radical#82723C2
hypercenterC2×#468D3
hypocenterC3#32935
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C22×D3×M16C2semidirect
2. C2×C3×#468C2semidirect
3. C2×#5174C2semidirect
4. C2×#5171C2semidirect
5. #82834C2semidirect
7. #71988C2semidirect
8. #71697C2semidirect
9. #71682C2semidirect
10. #70631C2semidirect
11. #70630C2semidirect
12. #70271C2semidirect
13. #70270C2semidirect
14. #70203C2semidirect
15. #70202C2semidirect
18. C22×C3×SD16C22semidirect
36. C2×C3×#107C22semidirect
37. C2×C3×#103C22semidirect
38. C2×C3×#102C22semidirect
39. C2×#835C22semidirect
40. C2×#835C22semidirect
42. C2×#832C22semidirect
43. C2×#832C22semidirect
48. C2×#818C22semidirect
49. C2×#817C22semidirect
60. #4551C22semidirect
61. #4551C22semidirect
62. #4529C22semidirect
63. #4529C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
68. C2×#468D3semidirect
104. C2×C3×M16D4semidirect
152. C2×ΓL(1,𝔽25)D4semidirect
158. C2×D3×C8D4semidirect
175. C22×SD16C2×D3semidirect
196. C2×#107C2×D3semidirect
200. C2×#103C2×D3semidirect
203. C2×#102C2×D3semidirect
376. C2×M16#67semidirect
535. C3×C8#120semidirect
693. C2×D3#468semidirect
809. C8#937semidirect
871. C3#32935semidirect

Maximal subgroups

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

subgroupindex
C22×D3×M162
C2×C3×#4682
C2×#51742
C2×#51712
#828342
#827232
#719882
#716972
#716822
#706312
#706302
#702712
#702702
#702032
#702022
#329353