Finite Group Databasebeta

← #10830618

Subgroups — #10830618

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×#5576C211yesmaximal, characteristic, complemented
2C2×C4×#215C211yesmaximal, characteristic, complemented
3C2×#4844C211yesmaximal, characteristic, complemented
4C2×#4810C211yesmaximal, characteristic, complemented
5C2×#4806C211yesmaximal, characteristic, complemented
6#74239C211yesmaximal, characteristic, complemented
7C3×#1805C211yesmaximal, characteristic, complemented
8#70470C211yesmaximal, characteristic, complemented
9#70267C211yesmaximal, characteristic, complemented
10#70266C211yesmaximal, characteristic, complemented
11#69551C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68824C211yesmaximal, characteristic, complemented
15#68823C211yesmaximal, characteristic, complemented
16#24244—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C22×D24C2211yescharacteristic
22C22×#204C2211yescharacteristic
23#5576—24no—
24#5576—24no—
25C2×#897—21no—
26C2×#897C2211yescharacteristic
27C2×#895—21no—
28C2×#895C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#895C2211yescharacteristic
31C2×#875—21no—
32C2×#875C2211yescharacteristic
33C2×C4×D12—21no—
34C2×C4×D12C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic
36C2×C3×C4⋊C8C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C3×#382C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C4×#215—24no—
48#4987C2211yescharacteristic
49#4987C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#808C2211yescharacteristic
56C2×C4×C3⋊C8C2211yescharacteristic
57#4844—24no—
58#4810—24no—
59#4806—24no—
60#4674—21no—
61#4671—21no—
62#4665—21no—
63#4665—21no—
64C3×#340C2211yescharacteristic
65C3×#340C2211yescharacteristic
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#1805D311yescharacteristic, complemented
79#1788—31no—
80#1787—31no—
81C22×C3×Q8C2311yescharacteristic
82C2×#239—22no—
83C2×#239—22no—
84C2×#239—22no—
85C2×#239—22no—
86C2×#239—41no—
87C2×#239—41no—
88C2×D3×Q8—22no—
89C2×D3×Q8—22no—
90C2×D3×Q8—22no—
91C2×D3×Q8—22no—
92C2×D3×Q8—41no—
93C2×D3×Q8—41no—
94C22×D12—21no—
95C22×D12—21no—
96C22×D12—21no—
97C22×D12—21no—
98C22×D12D411yescharacteristic
99C22×D12C2311yescharacteristic
100C22×D12C2311yescharacteristic
101C22×C4×D3—21no—
102C22×C4×D3—21no—
103C22×C4×D3—21no—
104C22×C4×D3C2311yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C22×Dic6—21no—
107C22×Dic6C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×C4×Q8—22no—
111C3×C4×Q8D414yescomplemented
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C42—21no—
117C2×C3×C42C2311yescharacteristic
118C2×#215—22no—
119C2×#215—22no—
120C2×#215D414yescomplemented
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
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)⋊C4D411yescharacteristic
131C2×(C2×D3)⋊C4D411yescharacteristic
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3D411yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C2×D24—22no—
138C2×D24—22no—
139C2×D24—41no—
140C2×#204—22no—
141C2×#204—22no—
142C2×#204—41no—
143#897—28no—
144#897—22no—
145#897—22no—
146#895—28no—
147#895—22no—
148#895—22no—
149#895—22no—
150#895—22no—
151#895—41no—
152#895—41no—
153#875—28no—
154#875—22no—
155#875D414yescomplemented
156C4×D12—28no—
157C4×D12—22no—
158C4×D12—22no—
159C4×D12—22no—
160C4×D12—22no—
161C3×C4⋊C8—22no—
162C3×#103—22no—
163C3×#103—22no—
164C3×#95—21no—
165C3×#95—21no—
166#835—22no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169#821—22no—
170(C2×D3)⋊C8—22no—
171(C2×D3)⋊C8—22no—
172(C2×D3)⋊C8—41no—
173(C2×D3)⋊C8—41no—
174#816—22no—
175#810—22no—
176#810—41no—
177#809—22no—
178#809—22no—
179#809—41no—
180#808—22no—
181C4×C3⋊C8—22no—
182C22×#41—31no—
183C23×Q8—31no—
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×Q8C2×D311yescharacteristic
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⋊C8C2×D311yescharacteristic
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⋊C8—31no—
221C2×C4×C8—31no—
222#397—61no—
223#392—61no—
224#386—61no—
225#386—61no—
226#382C2×D311yescharacteristic
227#380—31no—
228#380—31no—
229#340C2×D311yescharacteristic
230#340C2×D311yescharacteristic
231C23×D3—21no—
232C23×D3—21no—
233C23×D3C2×D411yescharacteristic
234C23×D3C2×D411yescharacteristic
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8C2×D412yes—
239C2×C3×Q8C2×D412yes—
240C2×C3×Q8#4112yes—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2411yescharacteristic
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252#239—44no—
253#239—44no—
254#239—44no—
255#239—44no—
256D3×Q8—44no—
257D3×Q8—44no—
258D3×Q8—44no—
259D3×Q8—44no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—24no—
269C2×D12—24no—
270C2×D12—22no—
271C2×D12—22no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—41no—
275C2×D12—42no—
276C2×D12—42no—
277C2×D12—42no—
278C2×D12—42no—
279C2×D12—42no—
280C2×D12—42no—
281C2×D12—42no—
282C2×D12—42no—
283C2×D12—81no—
284C2×D12—81no—
285C2×D12C2×D412yes—
286C2×D12C2×D412yes—
287C2×C4×D3—24no—
288C2×C4×D3—24no—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—42no—
302C2×C4×D3—42no—
303C2×C4×D3—42no—
304C2×C4×D3—42no—
305C2×C4×D3—42no—
306C2×C4×D3—81no—
307C2×C4×D3—81no—
308C2×Dic6—21no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—24no—
313C2×Dic6—21no—
314C2×Dic6—42no—
315C2×Dic6—42no—
316C2×Dic6C2×D412yes—
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—24no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4C2×D412yes—
330C3×C42—24no—
331C3×C42C2×D412yes—
332C3×C42C2×D412yes—
333#215—28no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—22no—
337(C2×D3)⋊C4—22no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—42no—
341(C2×D3)⋊C4—42no—
342(C2×D3)⋊C4—42no—
343(C2×D3)⋊C4—81no—
344(C2×D3)⋊C4—81no—
345C4⋊Dic3—24no—
346C4⋊Dic3—22no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8C2×D412yes—
355D24—44no—
356#204—44no—
357C2×#41—62no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C2×#41—121no—
362C2×#41—121no—
363C22×Q8—31no—
364C22×Q8—61no—
365C22×Q8—62no—
366C22×Q8—62no—
367C22×Q8—62no—
368C22×Q8—62no—
369C22×Q8—121no—
370C22×Q8—121no—
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—31no—
380C23×C4—31no—
381C23×C4—61no—
382C23×C4—61no—
383C23×C4—61no—
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—68no—
399#124—62no—
400C22⋊Q8—62no—
401C22⋊Q8—68no—
402C22⋊Q8—62no—
403#121—62no—
404#121—68no—
405#121—62no—
406#121—62no—
407#121—62no—
408#121—121no—
409#121—121no—
410C4×Q8—22no—
411C4×Q8D1214yescomplemented
412C4×D4—68no—
413C4×D4—62no—
414C4×D4—62no—
415C4×D4—62no—
416C4×D4—62no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4C22×D311yescharacteristic
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C4⋊C4C22×D311yescharacteristic
424C2×C22⋊C4—31no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4—61no—
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—21no—
436C2×C42C22×D311yescharacteristic
437#106—62no—
438C4⋊C8—22no—
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—62no—
450C22⋊C8—62no—
451C22⋊C8—121no—
452C22⋊C8—121no—
453C4×C8—62no—
454#95—21no—
455#95—21no—
456#95—61no—
457#95—61no—
458C23×C3C22×D411yescharacteristic
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—41no—
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#13512yes—
487C3×Q8—22no—
488C3×Q8—22no—
489C3×Q8—22no—
490C3×Q8#12114yes—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—22no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4#12012yes—
508C2×C3×C4#12012yes—
509C2×C3×C4C22×D411yescharacteristic
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C22×D411yescharacteristic
512C2×C3×C4C2×#4111yescharacteristic
513C2×C3×C4H(5,𝔽2)11yescharacteristic
514C2×C3×C4H(5,𝔽2)11yescharacteristic
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—22no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527D12—22no—
528D12—22no—
529D12—22no—
530D12—22no—
531D12—44no—
532D12—48no—
533D12—48no—
534D12—41no—
535D12—41no—
536D12—41no—
537D12—41no—
538D12—84no—
539D12—84no—
540C4×D3—48no—
541C4×D3—48no—
542C4×D3—41no—
543C4×D3—41no—
544C4×D3—41no—
545C4×D3—41no—
546C4×D3—41no—
547C4×D3—41no—
548C4×D3—41no—
549C4×D3—41no—
550C4×D3—84no—
551Dic6—22no—
552Dic6—22no—
553Dic6—48no—
554Dic6—41no—
555Dic6—41no—
556C3×C8—41no—
557C3×C8—41no—
558C3⋊C8—22no—
559C3⋊C8—41no—
560C24—31no—
561C24—31no—
562C24—61no—
563C24—61no—
564#41—124no—
565#41—124no—
566#41—124no—
567#41—124no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—32no—
572C2×Q8—64no—
573C2×Q8—61no—
574C2×Q8—61no—
575C2×Q8—61no—
576C2×Q8—61no—
577C2×Q8—61no—
578C2×Q8—122no—
579C2×Q8—122no—
580C2×Q8—124no—
581C2×Q8—124no—
582C2×Q8—124no—
583C2×Q8—124no—
584C2×Q8C2×D1212yes—
585C2×Q8D3×D412yes—
586C2×Q8#23912yes—
587C2×D4—32no—
588C2×D4—32no—
589C2×D4—62no—
590C2×D4—64no—
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—121no—
604C2×D4—122no—
605C2×D4—122no—
606C2×D4—122no—
607C2×D4—122no—
608C2×D4—122no—
609C2×D4—122no—
610C2×D4—122no—
611C2×D4—122no—
612C2×D4—241no—
613C2×D4—241no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—64no—
621C22×C4—64no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
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—122no—
637C22×C4—122no—
638C22×C4—122no—
639C22×C4—122no—
640C22×C4—122no—
641C22×C4—241no—
642C22×C4—241no—
643C22×C4D3×D411yescharacteristic
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—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—64no—
668C4⋊C4—62no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4C2×D1212yes—
672C22⋊C4—64no—
673C22⋊C4—64no—
674C22⋊C4—62no—
675C22⋊C4—62no—
676C22⋊C4—64no—
677C22⋊C4—64no—
678C22⋊C4—122no—
679C22⋊C4—122no—
680C22⋊C4—122no—
681C22⋊C4—241no—
682C22⋊C4—241no—
683C42—24no—
684C42C2×D1212yes—
685C42D3×D412yes—
686C22×C3C2×#12011yescharacteristic
687C22×C3D4211yescharacteristic
688C22×C3#54611yescharacteristic
689C22×C3C2×#13511yescharacteristic
690C22×C3#57511yescharacteristic
691C22×C3#57711yescharacteristic
692C22×C3#57711yescharacteristic
693C2×D3—22no—
694C2×D3—22no—
695C2×D3—22no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
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—22no—
723C3×C4—22no—
724C3×C4—42no—
725C3×C4—81no—
726C3×C4—81no—
727C3×C4C2×#12111yescharacteristic
728C3×C4#53511yescharacteristic
729C3×C4D4211yescharacteristic
730C3×C4#54611yescharacteristic
731Dic3—42no—
732Dic3—41no—
733Dic3—41no—
734Dic3—81no—
735C23—32no—
736C23—61no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—62no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—62no—
749C23—61no—
750C23—61no—
751C23—121no—
752C23—121no—
753C23—121no—
754C23—121no—
755C23—121no—
756C23—121no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—121no—
761C23—121no—
762C23—121no—
763C23C2×D3×D411yescharacteristic
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—62no—
768Q8—62no—
769Q8—128no—
770Q8—121no—
771Q8—121no—
772Q8#89514yes—
773D4—62no—
774D4—62no—
775D4—62no—
776D4—62no—
777D4—124no—
778D4—128no—
779D4—128no—
780D4—121no—
781D4—121no—
782D4—121no—
783D4—121no—
784D4—244no—
785D4—244no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
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—62no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—128no—
810C2×C4—128no—
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—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—244no—
825C2×C4#88212yes—
826C2×C4#88212yes—
827C2×C4C22×D1211yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×D3×D411yescharacteristic
830C2×C4C2×#23911yescharacteristic
831C2×C4#100911yescharacteristic
832C2×C4#100911yescharacteristic
833C8—41no—
834C8—41no—
835C8—62no—
836C8—121no—
837C2×C3#240811yescharacteristic
838C2×C3#300211yescharacteristic
839C2×C3#301011yescharacteristic
840C2×C3#327511yescharacteristic
841C2×C3#328211yescharacteristic
842C2×C3#330111yescharacteristic
843C2×C3#332611yescharacteristic
844D3—42no—
845D3—81no—
846D3—82no—
847D3—82no—
848C22—62no—
849C22—62no—
850C22—62no—
851C22—121no—
852C22—121no—
853C22—121no—
854C22—121no—
855C22—122no—
856C22—121no—
857C22—122no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—122no—
862C22—121no—
863C22—122no—
864C22—121no—
865C22—122no—
866C22—122no—
867C22—121no—
868C22—241no—
869C22—241no—
870C22—241no—
871C22—241no—
872C22—241no—
873C22—241no—
874C22—241no—
875C22—241no—
876C22C2×#88211yescharacteristic
877C22#560911yescharacteristic
878C22#563011yescharacteristic
879C22D3×#13511yescharacteristic
880C22#576811yescharacteristic
881C22#577811yescharacteristic
882C22#577811yescharacteristic
883C4—24no—
884C4—22no—
885C4—22no—
886C4—42no—
887C4—81no—
888C4—81no—
889C4—121no—
890C4—121no—
891C4—122no—
892C4—241no—
893C4C2×#89511yescharacteristic
894C4#552511yescharacteristic
895C4#560911yescharacteristic
896C4#563011yescharacteristic
897C3#2424411yescharacteristic, complemented, Sylow
898C2—122no—
899C2—241no—
900C2—242no—
901C2—242no—
902C2#7401611yescharacteristic
903C2#7883311yescharacteristic
904C2#7896011yescharacteristic
905C2#8062911yescharacteristic
906C2#8063011yescharacteristic
907C2#8124611yescharacteristic
908C2#8125111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1805C2
socleC23×C3C22×D4
hypercenter#1805D3
hypocenterC3#24244
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
1. C2×#5576C2semidirect
2. C2×C4×#215C2semidirect
3. C2×#4844C2semidirect
4. C2×#4810C2semidirect
5. C2×#4806C2semidirect
6. #74239C2semidirect
7. C3×#1805C2semidirect
8. #70470C2semidirect
9. #70267C2semidirect
10. #70266C2semidirect
11. #69551C2semidirect
12. #68887C2semidirect
13. #68886C2semidirect
14. #68824C2semidirect
15. #68823C2semidirect
78. #1805D3semidirect
111. C3×C4×Q8D4semidirect
120. C2×#215D4semidirect
155. #875D4semidirect
411. C4×Q8D12semidirect
897. C3#24244semidirect

Maximal subgroups

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

subgroupindex
C2×#55762
C2×C4×#2152
C2×#48442
C2×#48102
C2×#48062
#742392
C3×#18052
#704702
#702672
#702662
#695512
#688872
#688862
#688242
#688232
#242443