Finite Group Databasebeta

← #10830623

Subgroups — #10830623

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×#5227C211yesmaximal, characteristic, complemented
3C2×#4819C211yesmaximal, characteristic, complemented
4C2×#4810C211yesmaximal, characteristic, complemented
5C2×#4788C211yesmaximal, characteristic, complemented
6#73933C211yesmaximal, characteristic, complemented
7C3×#1787C211yesmaximal, characteristic, complemented
8#70274C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70267C211yesmaximal, characteristic, complemented
11#70226C211yesmaximal, characteristic, complemented
12#70222C211yesmaximal, characteristic, complemented
13#69961C211yesmaximal, characteristic, complemented
14#69916C211yesmaximal, characteristic, complemented
15#69524C211yesmaximal, characteristic, complemented
16#24244—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×#239C2211yescharacteristic
19#5817—24no—
20#5817—24no—
21C2×#947—21no—
22C2×#947C2211yescharacteristic
23C2×#946—21no—
24C2×#946C2211yescharacteristic
25C2×Q8×Dic3C2211yescharacteristic
26C22×#215C2211yescharacteristic
27C22×#215C2211yescharacteristic
28C2×#930—21no—
29C2×#930C2211yescharacteristic
30C2×#930C2211yescharacteristic
31C2×C4×#67—21no—
32C2×C4×#67C2211yescharacteristic
33C22×D24C2211yescharacteristic
34C2×#895C2211yescharacteristic
35C2×#893C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C3×#380C2211yescharacteristic
42#5227—24no—
43C2×#835C2211yescharacteristic
44C2×#835C2211yescharacteristic
45C2×#830C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×Dic3⋊C8C2211yescharacteristic
51C2×C8×Dic3C2211yescharacteristic
52#4987C2211yescharacteristic
53#4977C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56C2×#808C2211yescharacteristic
57#4960—21no—
58#4956—21no—
59#4819—24no—
60#4810—24no—
61#4788—24no—
62#4675—21no—
63#4665—21no—
64#4551C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#548—31no—
67C2×#463—31no—
68C2×#449—31no—
69C2×#448—31no—
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#1787D311yescharacteristic, complemented
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
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C22×#67—21no—
93C22×#67—21no—
94C22×#67D411yescharacteristic
95C2×#239—22no—
96C2×#239—22no—
97C2×#239—22no—
98C2×#239—22no—
99C2×#239—41no—
100C2×#239—41no—
101C22×D12—21no—
102C22×D12—21no—
103C22×D12C2311yescharacteristic
104C22×D12C2311yescharacteristic
105C22×C4×D3—21no—
106C22×C4×D3—21no—
107C22×C4×D3C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×#217D411yescharacteristic
114#947—28no—
115#947—22no—
116#947D414yescomplemented
117#946—28no—
118#946—22no—
119#946—22no—
120Q8×Dic3—22no—
121Q8×Dic3D414yescomplemented
122C2×#215—22no—
123C2×#215—22no—
124C2×#215—22no—
125C2×#215—22no—
126C2×#215—41no—
127C2×#215D414yescomplemented
128#930—28no—
129#930—22no—
130#930—22no—
131#930—22no—
132#930—41no—
133C4×#67—28no—
134C4×#67—22no—
135C4×#67—22no—
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)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4D411yescharacteristic
145C2×C4⋊Dic3—21no—
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148C2×Dic3⋊C4—21no—
149C2×Dic3⋊C4D411yescharacteristic
150C2×C4×Dic3—21no—
151C2×C4×Dic3C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C2×D24—22no—
155C2×D24—22no—
156C2×D24—41no—
157#895—22no—
158#895—41no—
159#893—22no—
160#893—22no—
161C3×#103—22no—
162C3×#103—22no—
163C3×#103—22no—
164C3×#103—41no—
165C3×C22⋊C8—41no—
166C3×#95—21no—
167#835—22no—
168#835—22no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172#830—22no—
173#821—22no—
174#821—41no—
175(C2×D3)⋊C8—22no—
176(C2×D3)⋊C8—41no—
177Dic3⋊C8—22no—
178C8×Dic3—22no—
179#809—22no—
180#809—22no—
181#808—22no—
182C22×#41—31no—
183C23×Q8C2×D311yescharacteristic
184C22×SD16—31no—
185C22×SD16—31no—
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—31no—
196C2×#121—61no—
197C2×C4×Q8—31no—
198C2×C4×D4—31no—
199C2×C4×D4—31no—
200C2×C4×D4—61no—
201#463—64no—
202#449—64no—
203#448—64no—
204C4×SD16—64no—
205C2×#106—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103C2×D311yescharacteristic
210C2×#103C2×D311yescharacteristic
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#380C2×D311yescharacteristic
229#340—31no—
230#340—31no—
231C24×C3C2×D411yescharacteristic
232C23×D3—21no—
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—
254C22×C3×C4—21no—
255C22×C3×C4—24no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—42no—
266C22×C3×C4—42no—
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C2×#67—24no—
270C2×#67—22no—
271C2×#67—22no—
272C2×#67—41no—
273C2×#67—42no—
274C2×#67—42no—
275C2×#67—42no—
276C2×#67—42no—
277C2×#67—81no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3C2×D411yescharacteristic
281C22×Dic3C2×D411yescharacteristic
282C22×Dic3C2×D411yescharacteristic
283#239—44no—
284#239—44no—
285#239—44no—
286#239—44no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—21no—
290C2×D12—21no—
291C2×D12—21no—
292C2×D12—21no—
293C2×D12—21no—
294C2×D12—21no—
295C2×D12—24no—
296C2×D12—21no—
297C2×D12—21no—
298C2×D12—42no—
299C2×D12—42no—
300C2×D12—42no—
301C2×D12—42no—
302C2×D12—81no—
303C2×D12C2×D412yes—
304C2×D12C2×D412yes—
305C2×C4×D3—24no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—42no—
313C2×C4×D3—42no—
314C2×C4×D3—42no—
315C2×C4×D3—81no—
316C2×C4×D3—81no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C22⋊C4—81no—
328#217—22no—
329#215—28no—
330#215—44no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—22no—
336(C2×D3)⋊C4—42no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—81no—
340C4⋊Dic3—21no—
341C4⋊Dic3—24no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3C2×D412yes—
345Dic3⋊C4—24no—
346Dic3⋊C4—22no—
347C4×Dic3—24no—
348C4×Dic3C2×D412yes—
349C4×Dic3C2×D412yes—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8C2×D412yes—
356D24—44no—
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—31no—
373C22×D4—31no—
374C22×D4—31no—
375C22×D4—61no—
376C22×D4—61no—
377C22×D4—61no—
378C22×D4—61no—
379C23×C4—21no—
380C23×C4—31no—
381C23×C4—61no—
382C23×C4—61no—
383C23×C4C22×D311yescharacteristic
384C2×SD16—34no—
385C2×SD16—62no—
386C2×SD16—62no—
387C2×SD16—62no—
388C2×SD16—62no—
389C2×SD16—121no—
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—62no—
404#121—62no—
405#121—68no—
406#121—62no—
407#121—62no—
408#121—121no—
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—61no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4C22×D311yescharacteristic
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—22no—
442#103—41no—
443#103—62no—
444#103—62no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—121no—
449C22⋊C8—41no—
450C22⋊C8—62no—
451C22⋊C8—62no—
452C22⋊C8—121no—
453C4×C8—62no—
454#95—21no—
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#13512yes—
465C23×C3C22×D411yescharacteristic
466C22×D3—21no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
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—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—48no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
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—41no—
516C2×C3×C4C22×D411yescharacteristic
517C2×C3×C4C22×D411yescharacteristic
518C2×C3×C4C22×D411yescharacteristic
519C2×C3×C4C2×#4111yescharacteristic
520C2×C3×C4H(5,𝔽2)11yescharacteristic
521C2×C3×C4H(5,𝔽2)11yescharacteristic
522#67—44no—
523#67—48no—
524#67—84no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—22no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3#12012yes—
539C2×Dic3#12012yes—
540D12—22no—
541D12—22no—
542D12—22no—
543D12—22no—
544D12—48no—
545D12—41no—
546D12—41no—
547D12—41no—
548D12—41no—
549D12—84no—
550C4×D3—48no—
551C4×D3—41no—
552C4×D3—41no—
553C4×D3—41no—
554C4×D3—41no—
555C4×D3—84no—
556C3×C8—41no—
557C3×C8—41no—
558C3⋊C8—22no—
559C3⋊C8—41no—
560C24—31no—
561C24—61no—
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×Q8#23512yes—
584C2×Q8D3×D412yes—
585C2×Q8D3×D412yes—
586C2×Q8D3×D412yes—
587C2×D4—32no—
588C2×D4—32no—
589C2×D4—64no—
590C2×D4—62no—
591C2×D4—64no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—122no—
604C2×D4—122no—
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×D4—241no—
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—21no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—64no—
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—68no—
647SD16—124no—
648D8—124no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—32no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—32no—
666C4⋊C4—62no—
667C4⋊C4—64no—
668C4⋊C4—64no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C22⋊C4—62no—
673C22⋊C4—64no—
674C22⋊C4—64no—
675C22⋊C4—64no—
676C22⋊C4—64no—
677C22⋊C4—62no—
678C22⋊C4—81no—
679C22⋊C4—122no—
680C22⋊C4—122no—
681C22⋊C4—122no—
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×C3C2×#12011yescharacteristic
694C22×C3D4211yescharacteristic
695C22×C3#54611yescharacteristic
696C22×C3C2×#13511yescharacteristic
697C22×C3#57511yescharacteristic
698C22×C3#57711yescharacteristic
699C22×C3#57711yescharacteristic
700C2×D3—42no—
701C2×D3—41no—
702C2×D3—42no—
703C2×D3—41no—
704C2×D3—42no—
705C2×D3—41no—
706C2×D3—42no—
707C2×D3—41no—
708C2×D3—42no—
709C2×D3—42no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—81no—
714C2×D3—81no—
715C2×D3—81no—
716C2×D3—81no—
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×C4—81no—
726C3×C4C2×#12111yescharacteristic
727C3×C4#53511yescharacteristic
728C3×C4D4211yescharacteristic
729C3×C4#54611yescharacteristic
730Dic3—22no—
731Dic3—22no—
732Dic3—41no—
733Dic3—42no—
734Dic3—81no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—62no—
747C23—61no—
748C23—62no—
749C23—61no—
750C23—121no—
751C23—121no—
752C23—121no—
753C23—121no—
754C23—121no—
755C23—121no—
756C23—121no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—121no—
761C23—121no—
762C23#91912yes—
763C23C2×D3×D411yescharacteristic
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—48no—
770Q8—41no—
771Q8—41no—
772Q8#88414yes—
773D4—62no—
774D4—62no—
775D4—62no—
776D4—62no—
777D4—128no—
778D4—124no—
779D4—128no—
780D4—121no—
781D4—121no—
782D4—121no—
783D4—121no—
784D4—244no—
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—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—62no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—128no—
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×#23511yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×D3×D411yescharacteristic
830C2×C4C2×D3×D411yescharacteristic
831C2×C4#100411yescharacteristic
832C2×C4#100411yescharacteristic
833C8—41no—
834C8—41no—
835C8—62no—
836C8—121no—
837C2×C3—42no—
838C2×C3#240811yescharacteristic
839C2×C3#300211yescharacteristic
840C2×C3#301011yescharacteristic
841C2×C3#327511yescharacteristic
842C2×C3#328211yescharacteristic
843C2×C3#330111yescharacteristic
844C2×C3#332611yescharacteristic
845D3—81no—
846D3—82no—
847D3—82no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—121no—
856C22—122no—
857C22—122no—
858C22—121no—
859C22—122no—
860C22—121no—
861C22—122no—
862C22—121no—
863C22—121no—
864C22—122no—
865C22—121no—
866C22—122no—
867C22—121no—
868C22—241no—
869C22—241no—
870C22—241no—
871C22—241no—
872C22—241no—
873C22—241no—
874C22—241no—
875C22—241no—
876C22#549011yescharacteristic
877C22D3×#12011yescharacteristic
878C22#559011yescharacteristic
879C22#576211yescharacteristic
880C22C2×#91911yescharacteristic
881C22#577711yescharacteristic
882C22#577811yescharacteristic
883C4—24no—
884C4—41no—
885C4—42no—
886C4—62no—
887C4—62no—
888C4—81no—
889C4—81no—
890C4—122no—
891C4—121no—
892C4—241no—
893C4C2×#88411yescharacteristic
894C4#549011yescharacteristic
895C4#559011yescharacteristic
896C4#559211yescharacteristic
897C3#2424411yescharacteristic, complemented, Sylow
898C2—42no—
899C2—241no—
900C2—242no—
901C2—242no—
902C2#7382411yescharacteristic
903C2#7880811yescharacteristic
904C2#7897011yescharacteristic
905C2#8004111yescharacteristic
906C2#8006211yescharacteristic
907C2#8018211yescharacteristic
908C2#8020711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1787C2
socleC23×C3C22×D4
hypercenter#1787D3
hypocenterC3#24244
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
1. C2×#5817C2semidirect
2. C2×#5227C2semidirect
3. C2×#4819C2semidirect
4. C2×#4810C2semidirect
5. C2×#4788C2semidirect
6. #73933C2semidirect
7. C3×#1787C2semidirect
8. #70274C2semidirect
9. #70272C2semidirect
10. #70267C2semidirect
11. #70226C2semidirect
12. #70222C2semidirect
13. #69961C2semidirect
14. #69916C2semidirect
15. #69524C2semidirect
80. #1787D3semidirect
116. #947D4semidirect
121. Q8×Dic3D4semidirect
127. C2×#215D4semidirect
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×#52272
C2×#48192
C2×#48102
C2×#47882
#739332
C3×#17872
#702742
#702722
#702672
#702262
#702222
#699612
#699162
#695242
#242443