Finite Group Databasebeta

← #10827373

Subgroups — #10827373

Order 768.

1500 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5558C211yesmaximal, characteristic, complemented
2C2×#5156C211yesmaximal, characteristic, complemented
3C2×D3×#102C211yesmaximal, characteristic, complemented
4#76436C211yesmaximal, characteristic, complemented
5C3×#1879C211yesmaximal, characteristic, complemented
6#72043C211yesmaximal, characteristic, complemented
7#71613C211yesmaximal, characteristic, complemented
8#70204C211yesmaximal, characteristic, complemented
9#70202C211yesmaximal, characteristic, complemented
10#70201C211yesmaximal, characteristic, complemented
11#69639C211yesmaximal, characteristic, complemented
12#68881C211yesmaximal, characteristic, complemented
13#68872C211yesmaximal, characteristic, complemented
14#68679C211yesmaximal, characteristic, complemented
15#68668C211yesmaximal, characteristic, complemented
16#23963—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic, complemented
20C2×#938C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×#938C2211yescharacteristic, complemented
23C22×#213C2211yescharacteristic
24C2×#929—21no—
25C2×C4×#67—21no—
26C22×D3×C8C2211yescharacteristic
27#5558—24no—
28#5558—24no—
29C2×#895C2211yescharacteristic
30C2×#892C2211yescharacteristic, complemented
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×#884—21no—
33C2×#882—21no—
34C2×#879—21no—
35C2×C4×D12C2211yescharacteristic
36C2×#870C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic, complemented
39C3×#390C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic, complemented
43#5156—24no—
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
48C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
49#4987C2211yescharacteristic
50C2×#809C2211yescharacteristic
51#4961—21no—
52#4960—21no—
53#4955—21no—
54#4939C2211yescharacteristic
55D3×#102—24no—
56C3×#340C2211yescharacteristic, complemented
57C3×#336C2211yescharacteristic, complemented
58#4551C2211yescharacteristic, complemented
59#4551C2211yescharacteristic, complemented
60#4529C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4524C2211yescharacteristic, complemented
64C2×#553—31no—
65C2×#447—31no—
66C22×#102—31no—
67#2408—31no—
68#2025—31no—
69#2025—31no—
70#1999—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1879D311yescharacteristic, complemented
75#1875—31no—
76#1875—31no—
77#1869—31no—
78#1824—31no—
79C24×D3—21no—
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—41no—
92C2×D3×D4—41no—
93C22×D12—21no—
94C22×D12D411yescharacteristic
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C22×C4×D3C2311yescharacteristic
98C22×C4×D3C2311yescharacteristic
99C2×C3×D8—22no—
100C2×C3×D8—22no—
101C2×C3×D8—41no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×C4×D4—22no—
105C3×C4×D4—22no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C42C2311yescharacteristic
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115#938—22no—
116#938—22no—
117#938—22no—
118#938—22no—
119#938—41no—
120#938D414yescomplemented
121C2×#213—22no—
122C2×#213—22no—
123C2×#213—41no—
124#929—28no—
125C4×#67—28no—
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)⋊C4D411yescharacteristic
132C2×(C2×D3)⋊C4D411yescharacteristic
133C2×C4⋊Dic3D411yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×C4×Dic3—21no—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×D3×C8—22no—
144C2×D3×C8—41no—
145C2×D3×C8—41no—
146#895—22no—
147#895—41no—
148#892—22no—
149#892—22no—
150D3×C4⋊C4—22no—
151D3×C4⋊C4D414yescomplemented
152#884—28no—
153#882—44no—
154#879—28no—
155C4×D12—22no—
156C4×D12—22no—
157#870—22no—
158#870—22no—
159C3×#102—22no—
160C3×#102—41no—
161#832—22no—
162#832—22no—
163#832—41no—
164C3⋊#95—21no—
165#821—22no—
166#821—22no—
167(C2×D3)⋊C8—22no—
168(C2×D3)⋊C8—41no—
169(C2×D3)⋊C8—41no—
170#809—22no—
171C23×D4—31no—
172C22×D8—31no—
173C22×D8C2×D311yescharacteristic
174C23×C8—31no—
175#553—64no—
176#553—64no—
177C2×#126—61no—
178C2×#125—31no—
179C2×#123—61no—
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—31no—
183C2×#121—31no—
184C2×#121—61no—
185C2×#120—61no—
186C2×C4×D4—31no—
187C2×C4×D4—61no—
188C2×C4×D4C2×D311yescharacteristic, complemented
189C2×#117—31no—
190C22×C4⋊C4—31no—
191#447—64no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—64no—
199C2×#102C2×D311yescharacteristic
200C2×#102C2×D311yescharacteristic, complemented
201C2×C22⋊C8—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8—31no—
204#394—61no—
205#392—61no—
206#390—31no—
207#390C2×D311yescharacteristic
208#380—31no—
209#379—61no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#340C2×D311yescharacteristic, complemented
216#336—31no—
217#336C2×D311yescharacteristic, complemented
218C24×C3—21no—
219C24×C3—21no—
220C23×D3—21no—
221C23×D3—42no—
222C23×D3—42no—
223C23×D3—42no—
224C23×D3—42no—
225C23×D3—42no—
226C23×D3—81no—
227C23×D3—81no—
228C23×D3C2×D411yescharacteristic
229C23×D3C2×D411yescharacteristic
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
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×D4C2×D412yes—
241C2×C3×D4#4112yes—
242C22×C3×C4—21no—
243C22×C3×C4—24no—
244C22×C3×C4—21no—
245C22×C3×C4—81no—
246C22×C3×C4—81no—
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—
256C2×#67—42no—
257C2×#67—42no—
258C2×#67—42no—
259C2×#67—81no—
260C2×#67—81no—
261C2×#67—81no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3C2×D411yescharacteristic
266C22×Dic3C2×D411yescharacteristic
267D3×D4—28no—
268D3×D4—44no—
269D3×D4—44no—
270D3×D4—44no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—22no—
276C2×D12—22no—
277C2×D12—22no—
278C2×D12—21no—
279C2×D12—42no—
280C2×D12—42no—
281C2×D12—81no—
282C2×D12#4112yes—
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—21no—
292C2×C4×D3—21no—
293C2×C4×D3—24no—
294C2×C4×D3—81no—
295C2×C4×D3—81no—
296C2×C4×D3C2×D412yes—
297C2×C4×D3C2×D412yes—
298C3×D8—44no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4C2×D412yes—
309C3×C22⋊C4—24no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—81no—
312C3×C42—21no—
313C3×C42—21no—
314#217—24no—
315#217—24no—
316#217—42no—
317#213—44no—
318(C2×D3)⋊C4—24no—
319(C2×D3)⋊C4—22no—
320(C2×D3)⋊C4—22no—
321(C2×D3)⋊C4—42no—
322(C2×D3)⋊C4—42no—
323(C2×D3)⋊C4—42no—
324(C2×D3)⋊C4—81no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—22no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3C2×D412yes—
331C4⋊Dic3C2×D412yes—
332Dic3⋊C4—24no—
333Dic3⋊C4—24no—
334Dic3⋊C4—24no—
335C4×Dic3—24no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342D3×C8—44no—
343C25—61no—
344C22×D4—31no—
345C22×D4—31no—
346C22×D4—61no—
347C22×D4—62no—
348C22×D4—62no—
349C22×D4—61no—
350C22×D4—62no—
351C22×D4—62no—
352C22×D4—61no—
353C22×D4—61no—
354C22×D4—61no—
355C22×D4—121no—
356C22×D4—121no—
357C22×D4C22×D311yescharacteristic
358C22×D4C22×D311yescharacteristic
359C23×C4—21no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—61no—
363C2×D8—22no—
364C2×D8—22no—
365C2×D8—41no—
366C2×D8—62no—
367C2×D8—62no—
368C2×D8—121no—
369C22×C8—31no—
370C22×C8—31no—
371C22×C8—62no—
372C22×C8—121no—
373C22×C8—121no—
374C22×C8C22×D311yescharacteristic
375C22×C8C22×D311yescharacteristic
376#126—68no—
377#125—62no—
378#125—62no—
379#123—68no—
380#121—34no—
381#121—68no—
382#121—62no—
383#121—62no—
384#121—62no—
385#121—62no—
386#121—62no—
387#121—121no—
388#121—121no—
389#120—124no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—62no—
393C4×D4—62no—
394C4×D4—68no—
395#117—62no—
396#117—62no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—61no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4—61no—
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—31no—
412C2×C22⋊C4—31no—
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—
421C2×C42—61no—
422C2×C42C22×D311yescharacteristic
423#102—22no—
424#102—41no—
425#102—62no—
426#102—62no—
427#102—62no—
428#102—62no—
429#102—62no—
430#102—121no—
431C22⋊C8—62no—
432C22⋊C8—121no—
433C22⋊C8—121no—
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—21no—
455C22×D3—22no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—48no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—84no—
470C22×D3—84no—
471C22×D3—84no—
472C22×D3—84no—
473C22×D3—84no—
474C22×D3—84no—
475C22×D3#12012yes—
476C22×D3#13512yes—
477C22×D3AGL(1,ℤ/8)12yes—
478C3×D4—22no—
479C3×D4—22no—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—41no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—41no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
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—84no—
499C2×C3×C4C22×D411yescharacteristic
500C2×C3×C4C22×D411yescharacteristic
501C2×C3×C4C2×#4111yescharacteristic
502C2×C3×C4C2×#4111yescharacteristic
503C2×C3×C4H(5,𝔽2)11yescharacteristic
504C2×C3×C4H(5,𝔽2)11yescharacteristic
505#67—48no—
506#67—48no—
507#67—84no—
508#67—84no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3#12012yes—
524D12—22no—
525D12—22no—
526D12—44no—
527D12—41no—
528D12—41no—
529D12—84no—
530C4×D3—22no—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—22no—
534C4×D3—41no—
535C4×D3—41no—
536C4×D3—41no—
537C4×D3—41no—
538C4×D3—84no—
539C3×C8—41no—
540C3×C8—41no—
541C3⋊C8—41no—
542C3⋊C8—41no—
543C24—21no—
544C24—21no—
545C24—31no—
546C24—31no—
547C24—61no—
548C24—122no—
549C24—122no—
550C24—122no—
551C24—122no—
552C24—122no—
553C24—241no—
554C24—241no—
555C2×D4—21no—
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—32no—
566C2×D4—62no—
567C2×D4—62no—
568C2×D4—62no—
569C2×D4—68no—
570C2×D4—64no—
571C2×D4—64no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—122no—
578C2×D4—122no—
579C2×D4—122no—
580C2×D4—124no—
581C2×D4—124no—
582C2×D4—124no—
583C2×D4—122no—
584C2×D4—122no—
585C2×D4—122no—
586C2×D4—122no—
587C2×D4—122no—
588C2×D4—122no—
589C2×D4—241no—
590C2×D4—241no—
591C2×D4—241no—
592C2×D4—241no—
593C2×D4#23512yes—
594C2×D4D3×D412yes—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—31no—
599C22×C4—32no—
600C22×C4—32no—
601C22×C4—31no—
602C22×C4—64no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4—241no—
619C22×C4—241no—
620C22×C4D3×D411yescharacteristic
621C22×C4D3×D411yescharacteristic
622C22×C4C23×D311yescharacteristic
623D8—44no—
624D8—124no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—61no—
632C2×C8—61no—
633C2×C8—61no—
634C2×C8—61no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—124no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—32no—
642C4⋊C4—32no—
643C4⋊C4—64no—
644C4⋊C4—62no—
645C4⋊C4—64no—
646C4⋊C4—64no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4D3×D412yes—
652C22⋊C4—24no—
653C22⋊C4—42no—
654C22⋊C4—62no—
655C22⋊C4—62no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—81no—
660C22⋊C4—122no—
661C22⋊C4—122no—
662C22⋊C4—122no—
663C22⋊C4—122no—
664C22⋊C4—241no—
665C42—21no—
666C42—21no—
667C42—64no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3—81no—
682C22×C3C2×#12011yescharacteristic
683C22×C3#54611yescharacteristic
684C22×C3#54611yescharacteristic
685C22×C3C2×#13511yescharacteristic
686C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
687C22×C3#57611yescharacteristic
688C22×C3#57611yescharacteristic
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—22no—
694C2×D3—22no—
695C2×D3—41no—
696C2×D3—42no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—42no—
702C2×D3—41no—
703C2×D3—42no—
704C2×D3—41no—
705C2×D3—816no—
706C2×D3—81no—
707C2×D3—81no—
708C2×D3—81no—
709C2×D3—81no—
710C2×D3#44914yes—
711C3×C4—41no—
712C3×C4—42no—
713C3×C4—41no—
714C3×C4—81no—
715C3×C4#52511yescharacteristic
716C3×C4#53511yescharacteristic
717C3×C4#54611yescharacteristic
718C3×C4#54611yescharacteristic
719Dic3—22no—
720Dic3—41no—
721Dic3—42no—
722Dic3—42no—
723Dic3—81no—
724C23—22no—
725C23—22no—
726C23—32no—
727C23—32no—
728C23—32no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—61no—
749C23—61no—
750C23—61no—
751C23—62no—
752C23—61no—
753C23—128no—
754C23—121no—
755C23—121no—
756C23—121no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—244no—
761C23—244no—
762C23—244no—
763C23—244no—
764C23—244no—
765C23—244no—
766C23C2×D3×D411yescharacteristic
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—62no—
776D4—62no—
777D4—124no—
778D4—128no—
779D4—128no—
780D4—121no—
781D4—121no—
782D4—244no—
783D4—244no—
784D4—244no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—32no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—62no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—61no—
809C2×C4—84no—
810C2×C4—121no—
811C2×C4—121no—
812C2×C4—121no—
813C2×C4—121no—
814C2×C4—121no—
815C2×C4—121no—
816C2×C4—121no—
817C2×C4—121no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—244no—
822C2×C4C2×#23511yescharacteristic
823C2×C4C2×D3×D411yescharacteristic
824C2×C4C2×D3×D411yescharacteristic
825C2×C4#100411yescharacteristic
826C2×C4D3×#4111yescharacteristic
827C2×C4#100911yescharacteristic
828C8—41no—
829C8—41no—
830C8—121no—
831C8—121no—
832C2×C3—82no—
833C2×C3—82no—
834C2×C3#240411yescharacteristic
835C2×C3C2×#44911yescharacteristic
836C2×C3#300811yescharacteristic
837C2×C3#329711yescharacteristic
838C2×C3#329711yescharacteristic
839C2×C3#331811yescharacteristic
840C2×C3#331811yescharacteristic
841D3—24no—
842D3—81no—
843D3—82no—
844C22—34no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—62no—
852C22—62no—
853C22—62no—
854C22—62no—
855C22—62no—
856C22—62no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—122no—
869C22—121no—
870C22—122no—
871C22—121no—
872C22—121no—
873C22—122no—
874C22—121no—
875C22—2416no—
876C22—241no—
877C22—241no—
878C22—241no—
879C22—241no—
880C22#555011yescharacteristic
881C22D3×#12011yescharacteristic
882C22#561211yescharacteristic
883C22#575711yescharacteristic
884C22D3×#13511yescharacteristic
885C22D3×AGL(1,ℤ/8)11yescharacteristic
886C22#577411yescharacteristic
887C4—41no—
888C4—42no—
889C4—41no—
890C4—62no—
891C4—81no—
892C4—122no—
893C4—121no—
894C4—122no—
895C4—241no—
896C4#549011yescharacteristic
897C4#554711yescharacteristic
898C4#560711yescharacteristic
899C4#565411yescharacteristic
900C3#2396311yescharacteristic, complemented, Sylow
901C2—64no—
902C2—82no—
903C2—82no—
904C2—241no—
905C2—242no—
906C2#7488611yescharacteristic
907C2#7960911yescharacteristic
908C2#7988211yescharacteristic
909C2#8000411yescharacteristic
910C2D3×#44911yescharacteristic
911C2#8035511yescharacteristic
912C2#8055911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1879C2
socleC23×C3C22×D4
hypercenter#1879D3
hypocenterC3#23963
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×#5558C2semidirect
2. C2×#5156C2semidirect
3. C2×D3×#102C2semidirect
4. #76436C2semidirect
5. C3×#1879C2semidirect
6. #72043C2semidirect
7. #71613C2semidirect
8. #70204C2semidirect
9. #70202C2semidirect
10. #70201C2semidirect
11. #69639C2semidirect
12. #68881C2semidirect
13. #68872C2semidirect
14. #68679C2semidirect
15. #68668C2semidirect
19. C2×C3×C4×D4C22semidirect
22. C2×#938C22semidirect
30. C2×#892C22semidirect
36. C2×#870C22semidirect
38. C2×C3×#102C22semidirect
42. C2×#832C22semidirect
47. C2×(C2×D3)⋊C8C22semidirect
48. C2×(C2×D3)⋊C8C22semidirect
56. C3×#340C22semidirect
57. C3×#336C22semidirect
58. #4551C22semidirect
59. #4551C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4524C22semidirect
74. #1879D3semidirect
120. #938D4semidirect
151. D3×C4⋊C4D4semidirect
188. C2×C4×D4C2×D3semidirect
200. C2×#102C2×D3semidirect
215. #340C2×D3semidirect
217. #336C2×D3semidirect
900. C3#23963semidirect

Maximal subgroups

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

subgroupindex
C2×#55582
C2×#51562
C2×D3×#1022
#764362
C3×#18792
#720432
#716132
#702042
#702022
#702012
#696392
#688812
#688722
#686792
#686682
#239633