Finite Group Databasebeta

← #10830621

Subgroups — #10830621

Order 768.

1488 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5817C211yesmaximal, characteristic, complemented
2C2×C3×#448C211yesmaximal, characteristic, complemented
3C2×#5172C211yesmaximal, characteristic, complemented
4C2×#5165C211yesmaximal, characteristic, complemented
5C2×Dic3×SD16C211yesmaximal, characteristic, complemented
6#82666C211yesmaximal, characteristic, complemented
7#72132C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#70267C211yesmaximal, characteristic, complemented
11#70243C211yesmaximal, characteristic, complemented
12#70226C211yesmaximal, characteristic, complemented
13#70222C211yesmaximal, characteristic, complemented
14#69935C211yesmaximal, characteristic, complemented
15#69916C211yesmaximal, characteristic, complemented
16#24244—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×#239C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22#5817—24no—
23#5817—24no—
24C2×#947—21no—
25C2×#947C2211yescharacteristic
26C2×#946—21no—
27C2×#946C2211yescharacteristic
28C2×Q8×Dic3C2211yescharacteristic
29C2×#938C2211yescharacteristic
30C2×D4×Dic3C2211yescharacteristic
31C22×#213C2211yescharacteristic
32C2×#930—21no—
33C2×#930C2211yescharacteristic
34C2×C4×#67—21no—
35C2×C4×#67C2211yescharacteristic
36C3×#448—24no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44#5223—21no—
45#5220—21no—
46C2×#832C2211yescharacteristic
47#5212C2211yescharacteristic
48C2×#830C2211yescharacteristic
49#5172—24no—
50#5165—24no—
51Dic3×SD16—24no—
52C2×#821C2211yescharacteristic
53C2×#821C2211yescharacteristic
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×(C2×D3)⋊C8C2211yescharacteristic
56C2×#817C2211yescharacteristic
57C2×Dic3⋊C8C2211yescharacteristic
58C2×C8×Dic3C2211yescharacteristic
59#4987C2211yescharacteristic
60#4977C2211yescharacteristic
61C2×#809C2211yescharacteristic
62#4958—21no—
63#4952—21no—
64#4551C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#548—31no—
67C2×#463—31no—
68C2×#449—31no—
69C2×#448D311yescharacteristic, complemented
70C2×C4×SD16—31no—
71#2535—31no—
72#2035—31no—
73#2034—31no—
74#2000—31no—
75#1999—31no—
76#1958—31no—
77#1954—31no—
78#1805—31no—
79#1788—31no—
80#1787—31no—
81C22×C3×Q8—22no—
82C22×C3×Q8—22no—
83C22×C3×Q8—21no—
84C22×C3×Q8—22no—
85C22×C3×Q8—22no—
86C22×C3×Q8—41no—
87C22×C3×Q8—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×Q8C2311yescharacteristic
90C22×C3×D4—21no—
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C22×#67—21no—
95C22×#67—21no—
96C22×#67D411yescharacteristic
97C23×Dic3—21no—
98C2×#239—22no—
99C2×#239—22no—
100C2×#239—22no—
101C2×#239—22no—
102C2×#239—41no—
103C2×#239—41no—
104C22×D12—21no—
105C22×D12C2311yescharacteristic
106C22×C4×D3—21no—
107C22×C4×D3C2311yescharacteristic
108C2×C3×SD16—22no—
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—41no—
113C2×C3×SD16D414yescomplemented
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C3×#121—22no—
117C3×#121—41no—
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C22⋊C4—21no—
120C2×#217—21no—
121C2×#217—21no—
122C2×#217—21no—
123C2×#217D411yescharacteristic
124#947—28no—
125#947—22no—
126#947D414yescomplemented
127#946—28no—
128#946—22no—
129#946—22no—
130Q8×Dic3—22no—
131Q8×Dic3D414yescomplemented
132#938—22no—
133#938—41no—
134D4×Dic3—22no—
135D4×Dic3—22no—
136C2×#213—22no—
137C2×#213—22no—
138C2×#213—41no—
139#930—28no—
140#930—22no—
141#930—22no—
142C4×#67—28no—
143C4×#67—22no—
144C4×#67—22no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4—21no—
147C2×(C2×D3)⋊C4—21no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4—21no—
150C2×(C2×D3)⋊C4D411yescharacteristic
151C2×C4⋊Dic3—21no—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2311yescharacteristic
155C2×Dic3⋊C4—21no—
156C2×Dic3⋊C4D411yescharacteristic
157C2×C4×Dic3—21no—
158C2×C4×Dic3C2311yescharacteristic
159C22×C3⋊C8C2311yescharacteristic
160C22×C3⋊C8C2311yescharacteristic
161C3×#103—22no—
162C3×#103—22no—
163C3×C22⋊C8—22no—
164#835—22no—
165#835—22no—
166#835—22no—
167#835—41no—
168#832—22no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172C3⋊#95—21no—
173#830—41no—
174#821—22no—
175#821—22no—
176(C2×D3)⋊C8—22no—
177(C2×D3)⋊C8—41no—
178#817—22no—
179Dic3⋊C8—22no—
180C8×Dic3—22no—
181#809—41no—
182C22×#41—31no—
183C23×Q8C2×D311yescharacteristic
184C22×SD16C2×D311yescharacteristic
185C22×SD16C2×D311yescharacteristic
186C22×D8—31no—
187#548—64no—
188#548—64no—
189C2×#124—31no—
190C2×#124—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—61no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#121C2×D311yescharacteristic
197C2×C4×Q8—31no—
198C2×C4×D4—31no—
199C2×C4×D4—31no—
200C2×C4×D4—61no—
201#463—64no—
202#449—64no—
203#448—24no—
204C4×SD16—64no—
205C2×#106—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103—31no—
211C2×#103C2×D311yescharacteristic
212C2×#103C2×D311yescharacteristic
213C2×#102—31no—
214C2×#102—31no—
215C2×#102—31no—
216C2×#102—31no—
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8C2×D311yescharacteristic
221C2×C4×C8—31no—
222#397—61no—
223#392—61no—
224#386—61no—
225#386—61no—
226#382—31no—
227#380—31no—
228#380—31no—
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C24×C3C2×D411yescharacteristic
233C23×D3—21no—
234C23×D3C2×D411yescharacteristic
235C2×C3×Q8—24no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—42no—
245C2×C3×Q8—42no—
246C2×C3×Q8—44no—
247C2×C3×Q8—44no—
248C2×C3×Q8—44no—
249C2×C3×Q8—44no—
250C2×C3×Q8C2×D412yes—
251C2×C3×Q8C2×D412yes—
252C2×C3×Q8C2×D412yes—
253C2×C3×Q8#4112yes—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—42no—
260C2×C3×D4—42no—
261C2×C3×D4—81no—
262C2×C3×D4C2×D412yes—
263C22×C3×C4—21no—
264C22×C3×C4—24no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—24no—
278C2×#67—22no—
279C2×#67—22no—
280C2×#67—41no—
281C2×#67—42no—
282C2×#67—42no—
283C2×#67—42no—
284C2×#67—42no—
285C2×#67—81no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—42no—
290C22×Dic3—81no—
291C22×Dic3—81no—
292C22×Dic3C2×D411yescharacteristic
293C22×Dic3C2×D411yescharacteristic
294C22×Dic3C2×D411yescharacteristic
295#239—44no—
296#239—44no—
297#239—44no—
298#239—44no—
299C2×D12—21no—
300C2×D12—21no—
301C2×D12—21no—
302C2×D12—21no—
303C2×D12—24no—
304C2×D12—21no—
305C2×D12—42no—
306C2×D12—42no—
307C2×D12C2×D412yes—
308C2×C4×D3—24no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—42no—
316C2×C4×D3—42no—
317C3×SD16—28no—
318C3×SD16—44no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8C2×D412yes—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C22⋊C4—42no—
328#217—22no—
329#217—42no—
330#217—42no—
331#217—81no—
332#213—44no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—22no—
338(C2×D3)⋊C4—81no—
339C4⋊Dic3—21no—
340C4⋊Dic3—24no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345C4⋊Dic3C2×D412yes—
346Dic3⋊C4—24no—
347Dic3⋊C4—22no—
348C4×Dic3—24no—
349C4×Dic3C2×D412yes—
350C4×Dic3C2×D412yes—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×#41—62no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C2×#41—121no—
362C2×#41—121no—
363C22×Q8—22no—
364C22×Q8—22no—
365C22×Q8—21no—
366C22×Q8—22no—
367C22×Q8—22no—
368C22×Q8—41no—
369C22×Q8—41no—
370C22×Q8C22×D311yescharacteristic
371C22×Q8C22×D311yescharacteristic
372C22×D4—21no—
373C22×D4—31no—
374C22×D4—31no—
375C22×D4—61no—
376C22×D4—61no—
377C22×D4—61no—
378C22×D4C22×D311yescharacteristic
379C23×C4—21no—
380C23×C4—31no—
381C23×C4—61no—
382C23×C4—61no—
383C23×C4C22×D311yescharacteristic
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—41no—
389C2×SD16#6714yescomplemented
390C2×D8—62no—
391C2×D8—62no—
392C2×D8—121no—
393C22×C8—31no—
394C22×C8—31no—
395C22×C8C22×D311yescharacteristic
396C22×C8C22×D311yescharacteristic
397#124—34no—
398#124—62no—
399#124—68no—
400C22⋊Q8—62no—
401C22⋊Q8—68no—
402C22⋊Q8—62no—
403#121—22no—
404#121—41no—
405#121—62no—
406#121—62no—
407#121—68no—
408#121—62no—
409#121—121no—
410C4×Q8—34no—
411C4×Q8—62no—
412C4×D4—62no—
413C4×D4—62no—
414C4×D4—62no—
415C4×D4—62no—
416C4×D4—68no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4—61no—
423C2×C4⋊C4C22×D311yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4—31no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—61no—
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—31no—
436C2×C42—61no—
437#106—62no—
438C4⋊C8—62no—
439#103—22no—
440#103—22no—
441#103—62no—
442#103—62no—
443#103—62no—
444#103—121no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—121no—
449C22⋊C8—22no—
450C22⋊C8—62no—
451C22⋊C8—121no—
452C22⋊C8—121no—
453C4×C8—62no—
454#95—61no—
455#95—61no—
456#95—61no—
457#95—61no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—22no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3#13512yes—
472C23×C3C22×D411yescharacteristic
473C22×D3—21no—
474C22×D3—22no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—41no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C3×Q8—22no—
488C3×Q8—22no—
489C3×Q8—22no—
490C3×Q8—22no—
491C3×Q8—22no—
492C3×Q8—48no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×Q8#12114yes—
496C3×D4—22no—
497C3×D4—22no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—84no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—48no—
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—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
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—44no—
525#67—48no—
526#67—84no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—22no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—84no—
544C2×Dic3#12012yes—
545C2×Dic3#12012yes—
546D12—22no—
547D12—22no—
548D12—48no—
549D12—41no—
550D12—41no—
551C4×D3—48no—
552C4×D3—41no—
553C4×D3—41no—
554C4×D3—41no—
555C4×D3—41no—
556C3×C8—22no—
557C3×C8—41no—
558C3⋊C8—41no—
559C3⋊C8—41no—
560C24—21no—
561C24—31no—
562C24—61no—
563C24D3×D411yescharacteristic
564#41—124no—
565#41—124no—
566#41—124no—
567#41—124no—
568C2×Q8—24no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—42no—
578C2×Q8—42no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—44no—
583C2×Q8D3×D412yes—
584C2×Q8D3×D412yes—
585C2×Q8#23712yes—
586C2×Q8C2×#6712yes—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—32no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—64no—
596C2×D4—62no—
597C2×D4—64no—
598C2×D4—62no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—81no—
605C2×D4—122no—
606C2×D4—122no—
607C2×D4—121no—
608C2×D4—122no—
609C2×D4—122no—
610C2×D4—122no—
611C2×D4—122no—
612C2×D4—241no—
613C2×D4C2×#6712yes—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—64no—
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—122no—
640C22×C4—122no—
641C22×C4—122no—
642C22×C4—241no—
643C22×C4—241no—
644C22×C4D3×D411yescharacteristic
645C22×C4C23×D311yescharacteristic
646SD16—28no—
647SD16—44no—
648D8—124no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—61no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8C2×#6712yes—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—32no—
664C4⋊C4—62no—
665C4⋊C4—64no—
666C4⋊C4—64no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C22⋊C4—42no—
673C22⋊C4—62no—
674C22⋊C4—64no—
675C22⋊C4—64no—
676C22⋊C4—64no—
677C22⋊C4—64no—
678C22⋊C4—62no—
679C22⋊C4—122no—
680C22⋊C4—122no—
681C22⋊C4—241no—
682C22⋊C4—241no—
683C42—32no—
684C42—32no—
685C42—64no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3C2×#12011yescharacteristic
701C22×C3D4211yescharacteristic
702C22×C3#54611yescharacteristic
703C22×C3C2×#13511yescharacteristic
704C22×C3#57511yescharacteristic
705C22×C3#57711yescharacteristic
706C22×C3#57711yescharacteristic
707C2×D3—42no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—42no—
711C2×D3—41no—
712C2×D3—42no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—81no—
718C2×D3—81no—
719C2×D3—81no—
720C2×D3—81no—
721C3×C4—24no—
722C3×C4—41no—
723C3×C4—42no—
724C3×C4—81no—
725C3×C4C2×#12111yescharacteristic
726C3×C4#53511yescharacteristic
727C3×C4D4211yescharacteristic
728C3×C4#54611yescharacteristic
729Dic3—22no—
730Dic3—22no—
731Dic3—41no—
732Dic3—42no—
733Dic3—81no—
734Dic3—81no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—61no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—62no—
754C23—61no—
755C23—61no—
756C23—121no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—121no—
761C23—121no—
762C23#91612yes—
763C23C2×D3×D411yescharacteristic
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—48no—
770Q8—41no—
771Q8—41no—
772Q8#93914yes—
773D4—22no—
774D4—22no—
775D4—41no—
776D4—41no—
777D4—62no—
778D4—62no—
779D4—84no—
780D4—128no—
781D4—124no—
782D4—128no—
783D4—121no—
784D4—121no—
785D4—244no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—32no—
794C2×C4—32no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—62no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—128no—
814C2×C4—121no—
815C2×C4—121no—
816C2×C4—121no—
817C2×C4—121no—
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—244no—
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×#23711yescharacteristic
830C2×C4#100411yescharacteristic
831C2×C4#100411yescharacteristic
832C2×C4C22×#6711yescharacteristic
833C8—22no—
834C8—41no—
835C8—121no—
836C8—121no—
837C2×C3—42no—
838C2×C3—82no—
839C2×C3#240811yescharacteristic
840C2×C3#300211yescharacteristic
841C2×C3#301011yescharacteristic
842C2×C3#327511yescharacteristic
843C2×C3#328211yescharacteristic
844C2×C3#330111yescharacteristic
845C2×C3#332611yescharacteristic
846D3—81no—
847D3—82no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—121no—
863C22—122no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—122no—
868C22—121no—
869C22—122no—
870C22—121no—
871C22—121no—
872C22—241no—
873C22—241no—
874C22—241no—
875C22—241no—
876C22D3×#12011yescharacteristic
877C22#559111yescharacteristic
878C22C2×#91611yescharacteristic
879C22#576211yescharacteristic
880C22#577711yescharacteristic
881C22#577811yescharacteristic
882C22D4×#6711yescharacteristic
883C4—24no—
884C4—41no—
885C4—42no—
886C4—62no—
887C4—62no—
888C4—81no—
889C4—121no—
890C4—122no—
891C4—241no—
892C4—241no—
893C4#559111yescharacteristic
894C4#559211yescharacteristic
895C4D4×#6711yescharacteristic
896C4C2×#93911yescharacteristic
897C3#2424411yescharacteristic, complemented, Sylow
898C2—42no—
899C2—82no—
900C2—241no—
901C2—242no—
902C2#8003811yescharacteristic
903C2#8004111yescharacteristic
904C2#8005011yescharacteristic
905C2#8005511yescharacteristic
906C2#8258211yescharacteristic
907C2#8386711yescharacteristic
908C2#8399111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#448C2
socleC23×C3C22×D4
hypercenterC2×#448D3
hypocenterC3#24244
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#5817C2semidirect
2. C2×C3×#448C2semidirect
3. C2×#5172C2semidirect
4. C2×#5165C2semidirect
5. C2×Dic3×SD16C2semidirect
6. #82666C2semidirect
7. #72132C2semidirect
8. #72054C2semidirect
9. #71684C2semidirect
10. #70267C2semidirect
11. #70243C2semidirect
12. #70226C2semidirect
13. #70222C2semidirect
14. #69935C2semidirect
15. #69916C2semidirect
69. C2×#448D3semidirect
113. C2×C3×SD16D4semidirect
126. #947D4semidirect
131. Q8×Dic3D4semidirect
389. C2×SD16#67semidirect
897. C3#24244semidirect

Maximal subgroups

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

subgroupindex
C2×#58172
C2×C3×#4482
C2×#51722
C2×#51652
C2×Dic3×SD162
#826662
#721322
#720542
#716842
#702672
#702432
#702262
#702222
#699352
#699162
#242443