Finite Group Databasebeta

← #10827379

Subgroups — #10827379

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×#5530C211yesmaximal, characteristic, complemented
2#82640C211yesmaximal, characteristic, complemented
3C2×#4773C211yesmaximal, characteristic, complemented
4C2×D3×#102C211yesmaximal, characteristic, complemented
5C3×#1875C211yesmaximal, characteristic, complemented
6#71684C211yesmaximal, characteristic, complemented
7#71586C211yesmaximal, characteristic, complemented
8#70208C211yesmaximal, characteristic, complemented
9#70164C211yesmaximal, characteristic, complemented
10#69961C211yesmaximal, characteristic, complemented
11#69957C211yesmaximal, characteristic, complemented
12#68899C211yesmaximal, characteristic, complemented
13#68897C211yesmaximal, characteristic, complemented
14#68883C211yesmaximal, characteristic, complemented
15#68872C211yesmaximal, characteristic, complemented
16#23963—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic, complemented
20C2×#937—21no—
21C22×#213C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#930C2211yescharacteristic, complemented
24C2×C4×#67C2211yescharacteristic
25C22×D24C2211yescharacteristic
26C22×D3×C8C2211yescharacteristic
27#5530—24no—
28#5530—24no—
29C2×#895C2211yescharacteristic
30C2×#893C2211yescharacteristic, complemented
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×#890C2211yescharacteristic, complemented
33C2×#884—21no—
34C2×#883—21no—
35C2×#876—21no—
36C2×C4×D12—21no—
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40#5223—21no—
41#5221C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#830C2211yescharacteristic, complemented
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic, complemented
46C2×(C2×D3)⋊C8C2211yescharacteristic
47#4988C2211yescharacteristic
48#4987C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic, complemented
52#4959—21no—
53#4955—21no—
54#4773—24no—
55D3×#102—24no—
56C3×#340C2211yescharacteristic, complemented
57C3×#340C2211yescharacteristic, complemented
58#4551C2211yescharacteristic, complemented
59#4550C2211yescharacteristic, complemented
60#4550C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, 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#1879—31no—
75#1875—31no—
76#1875D311yescharacteristic, complemented
77#1869—31no—
78#1824—31no—
79C24×D3—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×#67D411yescharacteristic
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×D12C2311yescharacteristic
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C22×C4×D3—21no—
98C22×C4×D3C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×#121—22no—
102C3×#121—41no—
103C3×#117—22no—
104C3×#117—22no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C42—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217D411yescharacteristic
114#937—44no—
115C2×#213—22no—
116C2×#213—22no—
117C2×#213—41no—
118#930—22no—
119#930—22no—
120#930—22no—
121#930—41no—
122C4×#67—22no—
123C4×#67—22no—
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)⋊C4D411yescharacteristic
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4D411yescharacteristic
138C2×C4×Dic3C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C2×D24—22no—
142C2×D24—22no—
143C2×D24—41no—
144C2×D3×C8—22no—
145C2×D3×C8—41no—
146C2×D3×C8—41no—
147#895—22no—
148#895D414yescomplemented
149#893—22no—
150#893—22no—
151D3×C4⋊C4—22no—
152D3×C4⋊C4D414yescomplemented
153#890—22no—
154#890—22no—
155#884—28no—
156#883—28no—
157#876—28no—
158C4×D12—28no—
159C3×#102—22no—
160C3×#102—22no—
161C3×C22⋊C8—41no—
162#832—22no—
163C3⋊#95—21no—
164#830—41no—
165#821—22no—
166#821—41no—
167(C2×D3)⋊C8—22no—
168#809—22no—
169#809—22no—
170#809—41no—
171C23×D4—31no—
172C22×D8—31no—
173C22×D8—31no—
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—61no—
184C2×#121C2×D311yescharacteristic
185C2×#120—61no—
186C2×C4×D4—31no—
187C2×C4×D4—31no—
188C2×C4×D4—61no—
189C2×#117C2×D311yescharacteristic, complemented
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
201C2×C22⋊C8—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8C2×D311yescharacteristic, complemented
204#394—61no—
205#392—61no—
206#390—31no—
207#390—31no—
208#380—31no—
209#379—61no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic, complemented
215#340C2×D311yescharacteristic, complemented
216#336—31no—
217#336—31no—
218C24×C3—21no—
219C24×C3C2×D411yescharacteristic
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—42no—
223C23×D3—42no—
224C23×D3—42no—
225C23×D3—42no—
226C23×D3—42no—
227C23×D3—81no—
228C23×D3—81no—
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—42no—
236C2×C3×D4—42no—
237C2×C3×D4—81no—
238C2×C3×D4#4112yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2411yescharacteristic
250C2×#67—22no—
251C2×#67—22no—
252C2×#67—22no—
253C2×#67—24no—
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×Dic3C2×D411yescharacteristic
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—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—24no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—42no—
283C2×D12—42no—
284C2×D12C2×D412yes—
285C2×D12#4112yes—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—24no—
291C2×C4×D3—24no—
292C2×C4×D3—81no—
293C2×C4×D3—81no—
294C2×C4×D3—81no—
295C2×C4×D3—81no—
296C2×C4×D3C2×D412yes—
297C2×C4×D3C2×D412yes—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4C2×D412yes—
309C3×C4⋊C4C2×D412yes—
310C3×C22⋊C4—24no—
311C3×C22⋊C4—42no—
312C3×C42—24no—
313#217—22no—
314#217—42no—
315#217—81no—
316#213—44no—
317(C2×D3)⋊C4—24no—
318(C2×D3)⋊C4—24no—
319(C2×D3)⋊C4—22no—
320(C2×D3)⋊C4—24no—
321(C2×D3)⋊C4—42no—
322(C2×D3)⋊C4—42no—
323(C2×D3)⋊C4—42no—
324(C2×D3)⋊C4—81no—
325C4⋊Dic3—24no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3C2×D412yes—
330Dic3⋊C4—24no—
331Dic3⋊C4—22no—
332Dic3⋊C4—24no—
333C4×Dic3—21no—
334C4×Dic3—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341D24—44no—
342D3×C8—44no—
343C25—61no—
344C22×D4—21no—
345C22×D4—31no—
346C22×D4—31no—
347C22×D4—31no—
348C22×D4—61no—
349C22×D4—62no—
350C22×D4—62no—
351C22×D4—61no—
352C22×D4—62no—
353C22×D4—62no—
354C22×D4—61no—
355C22×D4—61no—
356C22×D4—121no—
357C22×D4—121no—
358C22×D4C22×D311yescharacteristic
359C23×C4—31no—
360C23×C4—61no—
361C23×C4—61no—
362C23×C4C22×D311yescharacteristic
363C2×D8—62no—
364C2×D8—62no—
365C2×D8—62no—
366C2×D8—62no—
367C2×D8—121no—
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—22no—
381#121—34no—
382#121—41no—
383#121—68no—
384#121—62no—
385#121—62no—
386#121—62no—
387#121—62no—
388#121—121no—
389#120—124no—
390C4×D4—68no—
391C4×D4—62no—
392C4×D4—62no—
393C4×D4—62no—
394C4×D4—62no—
395#117—22no—
396#117—22no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—61no—
403C2×C4⋊C4—61no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4C22×D311yescharacteristic
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—31no—
411C2×C22⋊C4—31no—
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—
421C2×C42—21no—
422C2×C42—31no—
423#102—22no—
424#102—22no—
425#102—62no—
426#102—62no—
427#102—62no—
428#102—62no—
429#102—121no—
430#102—121no—
431C22⋊C8—41no—
432C22⋊C8—62no—
433C22⋊C8—121no—
434#95—61no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
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—22no—
456C22×D3—48no—
457C22×D3—41no—
458C22×D3—41no—
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—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—41no—
481C3×D4—41no—
482C3×D4—84no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
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—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
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—44no—
507#67—84no—
508#67—84no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—22no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3#12012yes—
524D12—22no—
525D12—22no—
526D12—22no—
527D12—22no—
528D12—48no—
529D12—41no—
530D12—41no—
531D12—41no—
532D12—41no—
533C4×D3—22no—
534C4×D3—22no—
535C4×D3—22no—
536C4×D3—22no—
537C4×D3—84no—
538C4×D3—84no—
539C3×C8—41no—
540C3×C8—41no—
541C3⋊C8—41no—
542C3⋊C8—41no—
543C24—21no—
544C24—31no—
545C24—61no—
546C24—61no—
547C24—122no—
548C24—122no—
549C24—122no—
550C24—122no—
551C24—122no—
552C24—241no—
553C24—241no—
554C24D3×D411yescharacteristic
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—32no—
561C2×D4—32no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—64no—
565C2×D4—68no—
566C2×D4—62no—
567C2×D4—62no—
568C2×D4—62no—
569C2×D4—64no—
570C2×D4—61no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—81no—
581C2×D4—122no—
582C2×D4—122no—
583C2×D4—122no—
584C2×D4—124no—
585C2×D4—124no—
586C2×D4—124no—
587C2×D4—122no—
588C2×D4—122no—
589C2×D4—122no—
590C2×D4—122no—
591C2×D4—241no—
592C2×D4—241no—
593C2×D4—241no—
594C2×D4#23512yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—32no—
606C22×C4—32no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—64no—
610C22×C4—64no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—241no—
618C22×C4—241no—
619C22×C4—241no—
620C22×C4—241no—
621C22×C4D3×D411yescharacteristic
622C22×C4C23×D311yescharacteristic
623D8—124no—
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—21no—
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⋊C4D3×D412yes—
651C4⋊C4D3×D412yes—
652C22⋊C4—24no—
653C22⋊C4—42no—
654C22⋊C4—64no—
655C22⋊C4—62no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—62no—
659C22⋊C4—122no—
660C22⋊C4—122no—
661C22⋊C4—122no—
662C22⋊C4—122no—
663C22⋊C4—241no—
664C22⋊C4—241no—
665C42—24no—
666C42—61no—
667C42—61no—
668C22×C3—42no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—42no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—42no—
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—42no—
696C2×D3—42no—
697C2×D3—42no—
698C2×D3—42no—
699C2×D3—42no—
700C2×D3—42no—
701C2×D3—816no—
702C2×D3—81no—
703C2×D3—81no—
704C2×D3—81no—
705C2×D3—81no—
706C2×D3—81no—
707C2×D3—81no—
708C2×D3—81no—
709C2×D3—81no—
710C2×D3#44914yes—
711C3×C4—41no—
712C3×C4—42no—
713C3×C4—42no—
714C3×C4—81no—
715C3×C4#52511yescharacteristic
716C3×C4#53511yescharacteristic
717C3×C4#54611yescharacteristic
718C3×C4#54611yescharacteristic
719Dic3—22no—
720Dic3—41no—
721Dic3—41no—
722Dic3—42no—
723Dic3—81no—
724C23—21no—
725C23—22no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—32no—
733C23—32no—
734C23—32no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—62no—
746C23—62no—
747C23—128no—
748C23—121no—
749C23—121no—
750C23—121no—
751C23—121no—
752C23—121no—
753C23—121no—
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—41no—
770D4—41no—
771D4—62no—
772D4—62no—
773D4—62no—
774D4—62no—
775D4—84no—
776D4—128no—
777D4—128no—
778D4—124no—
779D4—121no—
780D4—121no—
781D4—121no—
782D4—121no—
783D4—244no—
784D4—244no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—32no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—62no—
815C2×C4—121no—
816C2×C4—121no—
817C2×C4—121no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—244no—
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—81no—
834C2×C3#240411yescharacteristic
835C2×C3C2×#44911yescharacteristic
836C2×C3#300811yescharacteristic
837C2×C3#329711yescharacteristic
838C2×C3#329711yescharacteristic
839C2×C3#331811yescharacteristic
840C2×C3#331811yescharacteristic
841D3—24no—
842D3—82no—
843D3—82no—
844C22—34no—
845C22—41no—
846C22—42no—
847C22—41no—
848C22—42no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—42no—
855C22—62no—
856C22—62no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—62no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—122no—
866C22—122no—
867C22—122no—
868C22—122no—
869C22—122no—
870C22—122no—
871C22—2416no—
872C22—241no—
873C22—241no—
874C22—241no—
875C22—241no—
876C22—241no—
877C22—241no—
878C22—241no—
879C22—241no—
880C22#549011yescharacteristic
881C22D3×#12011yescharacteristic
882C22#565411yescharacteristic
883C22D3×#13511yescharacteristic
884C22#576911yescharacteristic
885C22D3×AGL(1,ℤ/8)11yescharacteristic
886C22#577411yescharacteristic
887C4—41no—
888C4—42no—
889C4—42no—
890C4—62no—
891C4—81no—
892C4—121no—
893C4—121no—
894C4—122no—
895C4—241no—
896C4#554711yescharacteristic
897C4#555011yescharacteristic
898C4#560711yescharacteristic
899C4#561211yescharacteristic
900C3#2396311yescharacteristic, complemented, Sylow
901C2—64no—
902C2—81no—
903C2—82no—
904C2—242no—
905C2—242no—
906C2#7488611yescharacteristic
907C2#7884611yescharacteristic
908C2#7893611yescharacteristic
909C2D3×#44911yescharacteristic
910C2#8008511yescharacteristic
911C2#8138211yescharacteristic
912C2#8138511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1875C2
socleC23×C3C22×D4
hypercenter#1875D3
hypocenterC3#23963
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. C2×#5530C2semidirect
2. #82640C2semidirect
3. C2×#4773C2semidirect
4. C2×D3×#102C2semidirect
5. C3×#1875C2semidirect
6. #71684C2semidirect
7. #71586C2semidirect
8. #70208C2semidirect
9. #70164C2semidirect
10. #69961C2semidirect
11. #69957C2semidirect
12. #68899C2semidirect
13. #68897C2semidirect
14. #68883C2semidirect
15. #68872C2semidirect
19. C2×C3×#117C22semidirect
23. C2×#930C22semidirect
30. C2×#893C22semidirect
32. C2×#890C22semidirect
39. C2×C3×C22⋊C8C22semidirect
43. C2×#830C22semidirect
45. C2×#821C22semidirect
51. C2×#809C22semidirect
56. C3×#340C22semidirect
57. C3×#340C22semidirect
58. #4551C22semidirect
59. #4550C22semidirect
60. #4550C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4529C22semidirect
76. #1875D3semidirect
148. #895D4semidirect
152. D3×C4⋊C4D4semidirect
189. C2×#117C2×D3semidirect
203. C2×C22⋊C8C2×D3semidirect
214. #340C2×D3semidirect
215. #340C2×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×#55302
#826402
C2×#47732
C2×D3×#1022
C3×#18752
#716842
#715862
#702082
#701642
#699612
#699572
#688992
#688972
#688832
#688722
#239633