Finite Group Databasebeta

← #10830620

Subgroups — #10830620

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×#5552C211yesmaximal, characteristic, complemented
2C3×#2535C211yesmaximal, characteristic, complemented
3C2×#5040C211yesmaximal, characteristic, complemented
4C2×#5037C211yesmaximal, characteristic, complemented
5C2×C4×#214C211yesmaximal, characteristic, complemented
6C2×#5016C211yesmaximal, characteristic, complemented
7#71685C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9#71614C211yesmaximal, characteristic, complemented
10#69559C211yesmaximal, characteristic, complemented
11#69551C211yesmaximal, characteristic, complemented
12#69526C211yesmaximal, characteristic, complemented
13#69525C211yesmaximal, characteristic, complemented
14#69524C211yesmaximal, characteristic, complemented
15#69522C211yesmaximal, characteristic, complemented
16#24244—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×Dic6C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C2×#939—21no—
24C22×#214C2211yescharacteristic
25C22×#214C2211yescharacteristic
26C22×#213C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C2×#924C2211yescharacteristic
29#5552—24no—
30#5552—24no—
31C2×#896—21no—
32C2×#885—21no—
33C2×#67⋊C4—21no—
34C2×#875C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C3×#397—21no—
37C3×#392—21no—
38C3×#386—21no—
39C3×#386—21no—
40C3×#382C2211yescharacteristic
41C3×#380C2211yescharacteristic
42C3×#380C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46C2×#830C2211yescharacteristic
47C2×#830C2211yescharacteristic
48#5040—24no—
49#5037—24no—
50C4×#214—24no—
51#5016—24no—
52C2×#810C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#810C2211yescharacteristic
55C2×#810C2211yescharacteristic
56C2×#810C2211yescharacteristic
57C2×#810C2211yescharacteristic
58C2×#809C2211yescharacteristic
59C2×#809C2211yescharacteristic
60C2×#809C2211yescharacteristic
61C2×#808C2211yescharacteristic
62C2×C4⋊(C3⋊C8)C2211yescharacteristic
63C2×C4×C3⋊C8C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#548—31no—
67C2×#463—31no—
68C2×#449—31no—
69C2×#448—31no—
70C2×C4×SD16—31no—
71#2535D311yescharacteristic, complemented
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×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4D411yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C22×#67—21no—
89C22×#67—21no—
90C23×Dic3—21no—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235—22no—
94C2×#235—22no—
95C2×#235—41no—
96C2×#235—41no—
97C22×D12C2311yescharacteristic
98C22×C4×D3—21no—
99C22×Dic6—21no—
100C22×Dic6—22no—
101C22×Dic6—22no—
102C22×Dic6—22no—
103C22×Dic6—22no—
104C22×Dic6—41no—
105C22×Dic6—41no—
106C22×Dic6C2311yescharacteristic
107C22×Dic6C2311yescharacteristic
108C3×#121—22no—
109C3×#121—22no—
110C3×#121—41no—
111C3×#121—41no—
112C3×C4×D4—22no—
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C2×C3×C4⋊C4D411yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4D411yescharacteristic
126C2×C3×C22⋊C4D411yescharacteristic
127C2×C3×C42C2311yescharacteristic
128C2×#217—21no—
129#939—28no—
130C2×#214—22no—
131C2×#214—22no—
132C2×#214—22no—
133C2×#214—22no—
134C2×#214—41no—
135C2×#214D414yescomplemented
136C2×#213—22no—
137C2×#213—22no—
138C2×#213—41no—
139#930—22no—
140#930—22no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×C4⋊Dic3C2311yescharacteristic
145#924—22no—
146#924—22no—
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×C4×Dic3—21no—
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154#896—28no—
155#885—28no—
156#67⋊C4—28no—
157#875—22no—
158#875D414yescomplemented
159C4×Dic6—22no—
160C4×Dic6D414yescomplemented
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—21no—
165#832—22no—
166#830—22no—
167#830—22no—
168#830—41no—
169#830—41no—
170#810—22no—
171#810—22no—
172#810—22no—
173#810—22no—
174#810—22no—
175#810—41no—
176#809—22no—
177#809—22no—
178#809—41no—
179#808—22no—
180C4⋊(C3⋊C8)—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—61no—
195C2×#121C2×D311yescharacteristic
196C2×#121C2×D311yescharacteristic
197C2×C4×Q8—31no—
198C2×C4×D4—61no—
199C2×C4×D4C2×D311yescharacteristic
200C2×C4×D4C2×D311yescharacteristic
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×#103—31no—
210C2×#103—31no—
211C2×#103—31no—
212C2×#103—31no—
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—21no—
223#392—21no—
224#386—21no—
225#386—21no—
226#382C2×D311yescharacteristic
227#380C2×D311yescharacteristic
228#380C2×D311yescharacteristic
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C24×C3C2×D411yescharacteristic
233C24×C3C2×D411yescharacteristic
234C23×D3—21no—
235C2×C3×D4—22no—
236C2×C3×D4—22no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—41no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4—42no—
246C2×C3×D4—42no—
247C2×C3×D4—81no—
248C2×C3×D4—81no—
249C2×C3×D4C2×D412yes—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
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—81no—
267C22×C3×C4—81no—
268C22×C3×C4C2×D411yescharacteristic
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2411yescharacteristic
273C2×#67—24no—
274C2×#67—24no—
275C2×#67—42no—
276C2×#67—42no—
277C2×#67—42no—
278C2×#67—42no—
279C22×Dic3—21no—
280C22×Dic3—24no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—42no—
284C22×Dic3—42no—
285#235—44no—
286#235—44no—
287#235—44no—
288#235—44no—
289C2×D12—21no—
290C2×D12—21no—
291C2×D12—21no—
292C2×D12—21no—
293C2×D12—21no—
294C2×D12C2×D412yes—
295C2×C4×D3—24no—
296C2×C4×D3—42no—
297C2×C4×D3—42no—
298C2×Dic6—21no—
299C2×Dic6—21no—
300C2×Dic6—21no—
301C2×Dic6—21no—
302C2×Dic6—21no—
303C2×Dic6—21no—
304C2×Dic6—21no—
305C2×Dic6—24no—
306C2×Dic6—21no—
307C2×Dic6—44no—
308C2×Dic6—44no—
309C2×Dic6—44no—
310C2×Dic6—42no—
311C2×Dic6—42no—
312C2×Dic6—44no—
313C2×Dic6C2×D412yes—
314C2×Dic6C2×D412yes—
315C2×Dic6C2×D412yes—
316C2×Dic6#4112yes—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C22⋊C4—22no—
325C3×C22⋊C4—22no—
326C3×C22⋊C4—42no—
327C3×C22⋊C4—42no—
328C3×C22⋊C4—42no—
329C3×C22⋊C4—81no—
330C3×C22⋊C4—81no—
331C3×C42C2×D412yes—
332C3×C42C2×D412yes—
333#217—24no—
334#214—28no—
335#214—44no—
336#213—44no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—24no—
340C4⋊Dic3—21no—
341C4⋊Dic3C2×D412yes—
342Dic3⋊C4—24no—
343Dic3⋊C4—24no—
344C4×Dic3—24no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8C2×D412yes—
357C2×#41—62no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C2×#41—121no—
362C2×#41—121no—
363C22×Q8—31no—
364C22×Q8—31no—
365C22×Q8—62no—
366C22×Q8—62no—
367C22×Q8—62no—
368C22×Q8—62no—
369C22×Q8—61no—
370C22×Q8—121no—
371C22×Q8—121no—
372C22×D4—21no—
373C22×D4—21no—
374C22×D4—31no—
375C22×D4—61no—
376C22×D4—61no—
377C22×D4#6711yescharacteristic
378C22×D4C22×D311yescharacteristic
379C23×C4—21no—
380C23×C4—61no—
381C23×C4—61no—
382C23×C4C22×D311yescharacteristic
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×C8—31no—
396C22×C8—31no—
397#124—34no—
398#124—68no—
399#124—62no—
400C22⋊Q8—68no—
401C22⋊Q8—62no—
402C22⋊Q8—62no—
403#121—22no—
404#121—22no—
405#121—41no—
406#121—41no—
407#121—62no—
408#121—62no—
409#121—68no—
410C4×Q8—34no—
411C4×Q8—62no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—68no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4#6711yescharacteristic
421C2×C4⋊C4C22×D311yescharacteristic
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C4⋊C4C22×D311yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4#6711yescharacteristic
434C2×C22⋊C4#6711yescharacteristic
435C2×C42—61no—
436C2×C42C22×D311yescharacteristic
437#106—62no—
438C4⋊C8—62no—
439#103—62no—
440#103—62no—
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—21no—
457#95—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—22no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3#13512yes—
479C23×C3C22×D411yescharacteristic
480C22×D3—22no—
481C22×D3—41no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—44no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—84no—
493C3×D4—84no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
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×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—84no—
522C2×C3×C4#12012yes—
523C2×C3×C4#12012yes—
524C2×C3×C4C22×D411yescharacteristic
525C2×C3×C4C22×D411yescharacteristic
526C2×C3×C4C22×D411yescharacteristic
527C2×C3×C4C2×#4111yescharacteristic
528C2×C3×C4H(5,𝔽2)11yescharacteristic
529C2×C3×C4H(5,𝔽2)11yescharacteristic
530#67—48no—
531#67—48no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—48no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542D12—22no—
543D12—22no—
544D12—41no—
545D12—41no—
546C4×D3—48no—
547Dic6—22no—
548Dic6—22no—
549Dic6—22no—
550Dic6—22no—
551Dic6—22no—
552Dic6—48no—
553Dic6—41no—
554Dic6—41no—
555Dic6#12114yes—
556C3⋊C8—22no—
557C3⋊C8—41no—
558C3⋊C8—41no—
559C3⋊C8—41no—
560C24—21no—
561C24—61no—
562C24C2×#6711yescharacteristic
563C24C2×#6711yescharacteristic
564#41—124no—
565#41—124no—
566#41—124no—
567#41—124no—
568C2×Q8—32no—
569C2×Q8—32no—
570C2×Q8—32no—
571C2×Q8—32no—
572C2×Q8—64no—
573C2×Q8—61no—
574C2×Q8—61no—
575C2×Q8—61no—
576C2×Q8—61no—
577C2×Q8—61no—
578C2×Q8—61no—
579C2×Q8—61no—
580C2×Q8—61no—
581C2×Q8—122no—
582C2×Q8—122no—
583C2×Q8—124no—
584C2×Q8—124no—
585C2×Q8—124no—
586C2×Q8—124no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—32no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—64no—
601C2×D4—64no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—122no—
610C2×D4—122no—
611C2×D4—122no—
612C2×D4—122no—
613C2×D4D3×D412yes—
614C22×C4—21no—
615C22×C4—21no—
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—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—42no—
630C22×C4—64no—
631C22×C4—61no—
632C22×C4—64no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—122no—
638C22×C4—122no—
639C22×C4—122no—
640C22×C4—122no—
641C22×C4C2×#6711yescharacteristic
642C22×C4C2×#6711yescharacteristic
643C22×C4C2×#6711yescharacteristic
644C22×C4C2×#6711yescharacteristic
645C22×C4C23×D311yescharacteristic
646SD16—68no—
647SD16—124no—
648D8—124no—
649C2×C8—32no—
650C2×C8—61no—
651C2×C8—61no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—32no—
669C4⋊C4—64no—
670C4⋊C4—64no—
671C4⋊C4—61no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—64no—
678C22⋊C4—64no—
679C22⋊C4—64no—
680C22⋊C4—64no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—64no—
684C42D3×D412yes—
685C42D3×D412yes—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—42no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3C2×#12011yescharacteristic
708C22×C3D4211yescharacteristic
709C22×C3#54611yescharacteristic
710C22×C3C2×#13511yescharacteristic
711C22×C3#57511yescharacteristic
712C22×C3#57711yescharacteristic
713C22×C3#57711yescharacteristic
714C2×D3—42no—
715C2×D3—42no—
716C2×D3—42no—
717C2×D3—81no—
718C2×D3—81no—
719C2×D3—81no—
720C2×D3—81no—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—81no—
726C3×C4—81no—
727C3×C4—81no—
728C3×C4C2×#12111yescharacteristic
729C3×C4#53511yescharacteristic
730C3×C4D4211yescharacteristic
731C3×C4#54611yescharacteristic
732Dic3—24no—
733Dic3—42no—
734Dic3—42no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—62no—
756C23—121no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—121no—
761C23—121no—
762C23#95012yes—
763C23C22×#6711yescharacteristic
764Q8—34no—
765Q8—62no—
766Q8—62no—
767Q8—62no—
768Q8—62no—
769Q8—62no—
770Q8—128no—
771Q8—121no—
772Q8—121no—
773D4—22no—
774D4—22no—
775D4—44no—
776D4—41no—
777D4—41no—
778D4—62no—
779D4—62no—
780D4—84no—
781D4—84no—
782D4—128no—
783D4—128no—
784D4—121no—
785D4—121no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
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—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—84no—
819C2×C4—128no—
820C2×C4—128no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—121no—
825C2×C4#93712yes—
826C2×C4#93712yes—
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×D3×D411yescharacteristic
830C2×C4#100411yescharacteristic
831C2×C4D3×#4111yescharacteristic
832C2×C4#100911yescharacteristic
833C8—62no—
834C8—121no—
835C8—121no—
836C8—121no—
837C2×C3—42no—
838C2×C3—81no—
839C2×C3—82no—
840C2×C3#240811yescharacteristic
841C2×C3#300211yescharacteristic
842C2×C3#301011yescharacteristic
843C2×C3#327511yescharacteristic
844C2×C3#328211yescharacteristic
845C2×C3#330111yescharacteristic
846C2×C3#332611yescharacteristic
847D3—82no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—42no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—42no—
864C22—41no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—122no—
870C22—122no—
871C22—122no—
872C22—241no—
873C22—241no—
874C22—241no—
875C22—241no—
876C22C2×#93711yescharacteristic
877C22D4×#6711yescharacteristic
878C22C2×#95011yescharacteristic
879C22#582211yescharacteristic
880C22#582911yescharacteristic
881C22#583611yescharacteristic
882C22#583611yescharacteristic
883C4—22no—
884C4—22no—
885C4—41no—
886C4—41no—
887C4—64no—
888C4—81no—
889C4—81no—
890C4—81no—
891C4—122no—
892C4—122no—
893C4D3×#12111yescharacteristic
894C4#560711yescharacteristic
895C4#560911yescharacteristic
896C4#561211yescharacteristic
897C3#2424411yescharacteristic, complemented, Sylow
898C2—42no—
899C2—81no—
900C2—82no—
901C2—242no—
902C2#8264011yescharacteristic
903C2#8292611yescharacteristic
904C2#8339011yescharacteristic
905C2#8350811yescharacteristic
906C2#8350911yescharacteristic
907C2#8361811yescharacteristic
908C2#8362111yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2535C2
socleC23×C3C22×D4
hypercenter#2535D3
hypocenterC3#24244
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#5552C2semidirect
2. C3×#2535C2semidirect
3. C2×#5040C2semidirect
4. C2×#5037C2semidirect
5. C2×C4×#214C2semidirect
6. C2×#5016C2semidirect
7. #71685C2semidirect
8. #71684C2semidirect
9. #71614C2semidirect
10. #69559C2semidirect
11. #69551C2semidirect
12. #69526C2semidirect
13. #69525C2semidirect
14. #69524C2semidirect
15. #69522C2semidirect
71. #2535D3semidirect
135. C2×#214D4semidirect
158. #875D4semidirect
160. C4×Dic6D4semidirect
897. C3#24244semidirect

Maximal subgroups

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

subgroupindex
C2×#55522
C3×#25352
C2×#50402
C2×#50372
C2×C4×#2142
C2×#50162
#716852
#716842
#716142
#695592
#695512
#695262
#695252
#695242
#695222
#242443