Finite Group Databasebeta

← #10830661

Subgroups — #10830661

Order 768.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5554C211yesmaximal, characteristic
2C2×C3×C4×SD16C211yesmaximal, characteristic, complemented
3C2×#5173C211yesmaximal, characteristic, complemented
4C2×#5169C211yesmaximal, characteristic, complemented
5#82499C211yesmaximal, characteristic, complemented
6C2×#5028C211yesmaximal, characteristic, complemented
7#71605C211yesmaximal, characteristic, complemented
8#70582C211yesmaximal, characteristic, complemented
9#70581C211yesmaximal, characteristic, complemented
10#70273C211yesmaximal, characteristic, complemented
11#70272C211yesmaximal, characteristic, complemented
12#70199C211yesmaximal, characteristic, complemented
13#70198C211yesmaximal, characteristic, complemented
14#69787C211yesmaximal, characteristic, complemented
15#69773C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic, complemented
21C2×C3×C4×D4C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#946C2211yescharacteristic, complemented
24C22×#216C2211yescharacteristic, complemented
25C22×#215C2211yescharacteristic
26C2×#930—21no—
27C22×(C2×D3)⋊C4—21no—
28#5554—24no—
29#5554—24no—
30C2×#897C2211yescharacteristic
31C2×#895C2211yescharacteristic
32C2×#886—21no—
33C2×#882—21no—
34C2×#875C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic
36C3×C4×SD16—24no—
37C2×C3×#106C2211yescharacteristic, complemented
38C2×C3×#103C2211yescharacteristic, complemented
39C2×C3×#102C2211yescharacteristic
40C2×C3×C4×C8C2211yescharacteristic, complemented
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5173—24no—
44#5169—24no—
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C2×#816C2211yescharacteristic, complemented
52C2×#816C2211yescharacteristic, complemented
53#5028—24no—
54#4991—21no—
55#4987C2211yescharacteristic
56#4987C2211yescharacteristic, complemented
57#4981—21no—
58C2×#810C2211yescharacteristic, complemented
59C2×#809C2211yescharacteristic
60#4940—21no—
61#4940—21no—
62#4936C2211yescharacteristic, complemented
63C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#464—31no—
68C2×#452—31no—
69C2×#450—31no—
70C2×C4×SD16D311yescharacteristic, complemented
71#2536—31no—
72#2035—31no—
73#2034—31no—
74#2001—31no—
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C22×#67—21no—
86C22×#67—21no—
87C23×Dic3—21no—
88C2×#237—22no—
89C2×#237—22no—
90C2×#237—22no—
91C2×#237—22no—
92C2×#237—41no—
93C2×#237—41no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4—22no—
97C2×D3×D4—22no—
98C2×D3×D4—41no—
99C2×D3×D4—41no—
100C22×D12—21no—
101C22×D12D411yescharacteristic
102C22×D12C2311yescharacteristic
103C22×C4×D3C2311yescharacteristic
104C22×C4×D3C2311yescharacteristic
105C22×Dic6C2311yescharacteristic
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C2×C3×SD16D414yescomplemented
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C3×C4×Q8—22no—
112C3×C4×Q8—22no—
113C3×C4×D4—22no—
114C3×C4×D4D414yes—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C22⋊C4—21no—
119C2×C3×C42—21no—
120C2×C3×C42C2311yescharacteristic
121#946—22no—
122#946—22no—
123#946—41no—
124#946—41no—
125C2×#216—22no—
126C2×#216—22no—
127C2×#216—41no—
128C2×#215—22no—
129C2×#215—22no—
130C2×#215—41no—
131#930—28no—
132C2×(C2×D3)⋊C4—28no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4D411yescharacteristic
142C2×(C2×D3)⋊C4D411yescharacteristic
143C2×C4⋊Dic3—21no—
144C2×C4⋊Dic3D411yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C22×C3⋊C8C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151#897—22no—
152#897—22no—
153#895—22no—
154#895—22no—
155#886—28no—
156#882—28no—
157#875—22no—
158#875D414yes—
159C4×D12—22no—
160C4×D12—22no—
161C3×#106—22no—
162C3×#103—22no—
163C3×#102—22no—
164C3×C4×C8—22no—
165#832—22no—
166#832—22no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#821—22no—
172#821—41no—
173(C2×D3)⋊C8—22no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—41no—
176(C2×D3)⋊C8—41no—
177#816—22no—
178#816—41no—
179#810—22no—
180#809—22no—
181C4⋊(C3⋊C8)—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×Q16—31no—
185C22×SD16—31no—
186C22×SD16C2×D311yescharacteristic
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×Q8C2×D311yescharacteristic, complemented
198C2×C4×D4—31no—
199C2×C4×D4C2×D311yescharacteristic
200C22×C22⋊C4—61no—
201#464—64no—
202#452—64no—
203#450—64no—
204C4×SD16—24no—
205C2×#106C2×D311yescharacteristic, complemented
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103C2×D311yescharacteristic, complemented
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102—31no—
216C2×#102C2×D311yescharacteristic
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8—31no—
221C2×C4×C8C2×D311yescharacteristic, complemented
222#398—61no—
223#394—61no—
224#388—61no—
225#388—61no—
226#382—31no—
227#380—31no—
228#380—31no—
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C23×D3—21no—
233C23×D3—24no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—81no—
239C23×D3—81no—
240C23×D3C2×D411yescharacteristic
241C23×D3C2×D411yescharacteristic
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8C2×D412yes—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4C2×D412yes—
252C2×C3×D4C2×D412yes—
253C2×C3×D4#4112yes—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—24no—
257C22×C3×C4—21no—
258C22×C3×C4—81no—
259C22×C3×C4—81no—
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2411yescharacteristic
263C2×#67—24no—
264C2×#67—24no—
265C2×#67—42no—
266C2×#67—42no—
267C2×#67—42no—
268C2×#67—42no—
269C22×Dic3—24no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—42no—
274C22×Dic3—42no—
275C22×Dic3C2×D411yescharacteristic
276C22×Dic3C2×D411yescharacteristic
277#237—44no—
278#237—44no—
279#237—44no—
280#237—44no—
281D3×D4—44no—
282D3×D4—44no—
283D3×D4—44no—
284D3×D4—44no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—22no—
290C2×D12—22no—
291C2×D12—21no—
292C2×D12—24no—
293C2×D12—41no—
294C2×D12—81no—
295C2×D12—81no—
296C2×D12C2×D412yes—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—21no—
313C2×Dic6—21no—
314C2×Dic6C2×D412yes—
315C3×SD16—28no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8C2×D412yes—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—42no—
326C3×C4⋊C4C2×D412yes—
327C3×C22⋊C4—24no—
328C3×C42—42no—
329C3×C42C2×D412yes—
330C3×C42C2×D412yes—
331#216—44no—
332#215—44no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—22no—
336(C2×D3)⋊C4—22no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—42no—
341(C2×D3)⋊C4—42no—
342(C2×D3)⋊C4—42no—
343C4⋊Dic3—24no—
344C4⋊Dic3—22no—
345C4⋊Dic3—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349Dic3⋊C4—42no—
350Dic3⋊C4—42no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C25—61no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C2×#41—62no—
362C2×#41—121no—
363C2×#41—121no—
364C22×Q8—31no—
365C22×Q8C22×D311yescharacteristic
366C22×D4—31no—
367C22×D4—31no—
368C22×D4—61no—
369C22×D4—61no—
370C22×D4—62no—
371C22×D4—61no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—62no—
375C22×D4—121no—
376C22×D4—121no—
377C22×D4C22×D311yescharacteristic
378C23×C4—21no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—61no—
382C2×Q16—62no—
383C2×Q16—62no—
384C2×Q16—121no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—62no—
388C2×SD16—62no—
389C2×SD16—121no—
390C2×SD16D1214yescomplemented
391C22×C8—31no—
392C22×C8—31no—
393C22×C8C22×D311yescharacteristic
394C22×C8C22×D311yescharacteristic
395#124—34no—
396#124—62no—
397#123—68no—
398C22⋊Q8—62no—
399C22⋊Q8—62no—
400C22⋊Q8—62no—
401C22⋊Q8—62no—
402C22⋊Q8—121no—
403C22⋊Q8—121no—
404#121—62no—
405#121—68no—
406#121—62no—
407#120—68no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×D4—22no—
411C4×D4—62no—
412C4×D4—62no—
413C4×D4#6714yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4C22×D311yescharacteristic
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—31no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—68no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C42—21no—
436C2×C42C22×D311yescharacteristic
437#106—22no—
438C4⋊C8—62no—
439#103—22no—
440#103—62no—
441#103—62no—
442#103—121no—
443#102—22no—
444#102—62no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—121no—
449C22⋊C8—62no—
450C22⋊C8—62no—
451C22⋊C8—121no—
452C22⋊C8—121no—
453C4×C8—22no—
454#95—61no—
455#95—61no—
456#95—61no—
457#95—61no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3C22×D411yescharacteristic
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—22no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—48no—
481C22×D3—48no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—84no—
489C22×D3—84no—
490C22×D3—84no—
491C22×D3—84no—
492C22×D3—84no—
493C22×D3#13512yes—
494C3×Q8—22no—
495C3×Q8—22no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—22no—
501C3×D4#12114yes—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—84no—
516C2×C3×C4#12012yes—
517C2×C3×C4#12012yes—
518C2×C3×C4C22×D411yescharacteristic
519C2×C3×C4C22×D411yescharacteristic
520C2×C3×C4C22×D411yescharacteristic
521C2×C3×C4C2×#4111yescharacteristic
522C2×C3×C4H(5,𝔽2)11yescharacteristic
523C2×C3×C4H(5,𝔽2)11yescharacteristic
524#67—48no—
525#67—48no—
526C2×Dic3—21no—
527C2×Dic3—22no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—48no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542D12—22no—
543D12—22no—
544D12—44no—
545D12—41no—
546D12—41no—
547D12—84no—
548C4×D3—41no—
549C4×D3—41no—
550C4×D3—41no—
551C4×D3—41no—
552C4×D3—41no—
553C4×D3—41no—
554C4×D3—41no—
555C4×D3—41no—
556Dic6—22no—
557Dic6—22no—
558Dic6—41no—
559Dic6—41no—
560C3×C8—22no—
561C3×C8—41no—
562C3⋊C8—41no—
563C3⋊C8—41no—
564C24—21no—
565C24—31no—
566C24—31no—
567C24—64no—
568C24—61no—
569C24—122no—
570C24—122no—
571C24—122no—
572C24—122no—
573C24—241no—
574C24—241no—
575#41—124no—
576#41—124no—
577#41—124no—
578#41—124no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—32no—
585C2×Q8—61no—
586C2×Q8—61no—
587C2×Q8—61no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8C2×D1212yes—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—32no—
595C2×D4—62no—
596C2×D4—64no—
597C2×D4—64no—
598C2×D4—64no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—121no—
606C2×D4—122no—
607C2×D4—122no—
608C2×D4—124no—
609C2×D4—124no—
610C2×D4—124no—
611C2×D4—122no—
612C2×D4—122no—
613C2×D4—124no—
614C2×D4—241no—
615C2×D4—241no—
616C2×D4C2×D1212yes—
617C2×D4#23512yes—
618C2×D4C2×#6712yes—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—21no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—64no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—81no—
642C22×C4—81no—
643C22×C4—122no—
644C22×C4—122no—
645C22×C4D3×D411yescharacteristic
646C22×C4D3×D411yescharacteristic
647C22×C4C23×D311yescharacteristic
648Q16—124no—
649SD16—28no—
650SD16—124no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8C2×D1212yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—64no—
668C4⋊C4—62no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—61no—
673C4⋊C4—122no—
674C4⋊C4—122no—
675C4⋊C4C2×#6712yes—
676C22⋊C4—24no—
677C22⋊C4—64no—
678C22⋊C4—64no—
679C22⋊C4—62no—
680C22⋊C4—62no—
681C22⋊C4—64no—
682C22⋊C4—64no—
683C22⋊C4—122no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C42—42no—
688C42D3×D412yes—
689C42C2×#6712yes—
690C22×C3—24no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3C2×#12011yescharacteristic
698C22×C3D4211yescharacteristic
699C22×C3#54611yescharacteristic
700C22×C3C2×#13511yescharacteristic
701C22×C3#57511yescharacteristic
702C22×C3#57711yescharacteristic
703C22×C3#57711yescharacteristic
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—42no—
713C2×D3—41no—
714C2×D3—42no—
715C2×D3—41no—
716C2×D3—42no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—816no—
722C2×D3—81no—
723C2×D3—81no—
724C2×D3—81no—
725C2×D3—81no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—81no—
731C3×C4C2×#12111yescharacteristic
732C3×C4#53511yescharacteristic
733C3×C4D4211yescharacteristic
734C3×C4#54611yescharacteristic
735Dic3—42no—
736Dic3—41no—
737Dic3—41no—
738Dic3—81no—
739Dic3—81no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—32no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—61no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—62no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23—128no—
763C23—128no—
764C23—121no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—244no—
771C23—244no—
772C23—244no—
773C23—244no—
774C23—244no—
775C23C2×D3×D411yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—41no—
779Q8—41no—
780Q8—62no—
781Q8—62no—
782Q8—121no—
783Q8—121no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—62no—
788D4—62no—
789D4—124no—
790D4—128no—
791D4—128no—
792D4—121no—
793D4—121no—
794D4—244no—
795D4#93014yes—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—61no—
810C2×C4—62no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—84no—
817C2×C4—128no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—121no—
825C2×C4—121no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—121no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—121no—
834C2×C4#93712yes—
835C2×C4#93712yes—
836C2×C4C22×D1211yescharacteristic
837C2×C4C2×#23511yescharacteristic
838C2×C4C2×D3×D411yescharacteristic
839C2×C4#100911yescharacteristic
840C2×C4#100911yescharacteristic
841C2×C4C22×#6711yescharacteristic
842C8—22no—
843C8—41no—
844C8—121no—
845C8—121no—
846C2×C3—44no—
847C2×C3#240811yescharacteristic
848C2×C3#300211yescharacteristic
849C2×C3#300911yescharacteristic
850C2×C3#327511yescharacteristic
851C2×C3#328211yescharacteristic
852C2×C3#329611yescharacteristic
853C2×C3#332311yescharacteristic
854D3—42no—
855D3—81no—
856D3—82no—
857C22—24no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—62no—
865C22—62no—
866C22—62no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—122no—
877C22—121no—
878C22—122no—
879C22—121no—
880C22—122no—
881C22—2416no—
882C22—241no—
883C22—241no—
884C22—241no—
885C22—241no—
886C22D4×D1211yescharacteristic
887C22#555011yescharacteristic
888C22#576211yescharacteristic
889C22#576211yescharacteristic
890C22D3×#13511yescharacteristic
891C22#576811yescharacteristic
892C22C2×#93711yescharacteristic
893C4—22no—
894C4—22no—
895C4—42no—
896C4—42no—
897C4—81no—
898C4—121no—
899C4—121no—
900C4—122no—
901C4—241no—
902C4—241no—
903C4D4×D1211yescharacteristic
904C4#555011yescharacteristic
905C4C2×#93011yescharacteristic
906C4#583011yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—44no—
909C2—122no—
910C2—241no—
911C2—242no—
912C2#7967111yescharacteristic
913C2#7967411yescharacteristic
914C2#7967711yescharacteristic
915C2#7968211yescharacteristic
916C2#8240311yescharacteristic
917C2#8385911yescharacteristic
918C2#8391111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×C4×SD16C2
socleC23×C3C22×D4
prime radicalC2×#5554C2
hypercenterC2×C4×SD16D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×SD16C2semidirect
3. C2×#5173C2semidirect
4. C2×#5169C2semidirect
5. #82499C2semidirect
6. C2×#5028C2semidirect
7. #71605C2semidirect
8. #70582C2semidirect
9. #70581C2semidirect
10. #70273C2semidirect
11. #70272C2semidirect
12. #70199C2semidirect
13. #70198C2semidirect
14. #69787C2semidirect
15. #69773C2semidirect
20. C2×C3×C4×Q8C22semidirect
23. C2×#946C22semidirect
24. C22×#216C22semidirect
37. C2×C3×#106C22semidirect
38. C2×C3×#103C22semidirect
40. C2×C3×C4×C8C22semidirect
49. C2×(C2×D3)⋊C8C22semidirect
50. C2×(C2×D3)⋊C8C22semidirect
51. C2×#816C22semidirect
52. C2×#816C22semidirect
56. #4987C22semidirect
58. C2×#810C22semidirect
62. #4936C22semidirect
63. C2×C4⋊(C3⋊C8)C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
70. C2×C4×SD16D3semidirect
108. C2×C3×SD16D4semidirect
197. C2×C4×Q8C2×D3semidirect
205. C2×#106C2×D3semidirect
210. C2×#103C2×D3semidirect
221. C2×C4×C8C2×D3semidirect
390. C2×SD16D12semidirect
907. C3#24247semidirect

Maximal subgroups

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

subgroupindex
C2×#55542
C2×C3×C4×SD162
C2×#51732
C2×#51692
#824992
C2×#50282
#716052
#705822
#705812
#702732
#702722
#701992
#701982
#697872
#697732
#242473