Finite Group Databasebeta

← #10944146

Subgroups — #10944146

Order 768.

1448 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5827C211yesmaximal, characteristic, complemented
2C2×C3×#449C211yesmaximal, characteristic
3C2×#5239C211yesmaximal, characteristic, complemented
4C2×#5166C211yesmaximal, characteristic, complemented
5C2×#5153C211yesmaximal, characteristic, complemented
6#82677C211yesmaximal, characteristic, complemented
7#72048C211yesmaximal, characteristic, complemented
8#72037C211yesmaximal, characteristic, complemented
9#71677C211yesmaximal, characteristic, complemented
10#70239C211yesmaximal, characteristic, complemented
11#70221C211yesmaximal, characteristic, complemented
12#70171C211yesmaximal, characteristic, complemented
13#70153C211yesmaximal, characteristic, complemented
14#69930C211yesmaximal, characteristic, complemented
15#69909C211yesmaximal, characteristic, complemented
16#32919—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21#5827—24no—
22#5827—24no—
23C2×Q8×Dic3C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C22×#216C2211yescharacteristic
26C2×#936C2211yescharacteristic
27C2×D4×Dic3—21no—
28C2×D4×Dic3—21no—
29C2×D4×Dic3C2211yescharacteristic
30C2×D4×Dic3C2211yescharacteristic
31C22×#214C2211yescharacteristic
32C2×#926—21no—
33C2×#926C2211yescharacteristic
34C22×C4⋊Dic3—21no—
35C22×C4⋊Dic3C2211yescharacteristic
36C2×#924C2211yescharacteristic
37C3×#449—24no—
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41#5239—24no—
42C2×#835C2211yescharacteristic
43#5222—21no—
44#5222—21no—
45#5221C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#832C2211yescharacteristic
48C2×#832C2211yescharacteristic
49C2×#830C2211yescharacteristic
50#5166—24no—
51#5153—24no—
52C2×#816C2211yescharacteristic
53C2×#816C2211yescharacteristic
54C2×Dic3⋊C8C2211yescharacteristic
55C2×Dic3⋊C8C2211yescharacteristic
56#4975C2211yescharacteristic
57#4973C2211yescharacteristic
58#4948—21no—
59#4948—21no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#520—31no—
67C2×#464—31no—
68C2×#463—31no—
69C2×#452—31no—
70C2×#449D311yescharacteristic
71#2620—31no—
72#1880—31no—
73#1879—31no—
74#1878—31no—
75#1877—31no—
76#1874—31no—
77#1872—31no—
78#1803—31no—
79#1802—31no—
80#1798—31no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41D414yes—
87C22×C3×Q8C2311yescharacteristic
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4C2311yescharacteristic
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C23×Dic3—21no—
95C23×Dic3—21no—
96C23×Dic3—21no—
97C22×Dic6C2311yescharacteristic
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C2×C3×D8—22no—
102C2×C3×D8—22no—
103C2×C3×D8—22no—
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×#121—22no—
107C3×#121—22no—
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#217—21no—
117C2×#217D411yescharacteristic
118C2×#217D411yescharacteristic
119Q8×Dic3—22no—
120Q8×Dic3—22no—
121Q8×Dic3—22no—
122Q8×Dic3D414yescomplemented
123C2×#216—22no—
124C2×#216—22no—
125C2×#216—22no—
126#936—22no—
127#936—22no—
128D4×Dic3—28no—
129D4×Dic3—28no—
130D4×Dic3—22no—
131D4×Dic3—22no—
132D4×Dic3—22no—
133D4×Dic3D414yescomplemented
134C2×#214—22no—
135C2×#214—22no—
136C2×#214—22no—
137#926—28no—
138#926—22no—
139#926—22no—
140C2×C4⋊Dic3—28no—
141C2×C4⋊Dic3—21no—
142C2×C4⋊Dic3—21no—
143C2×C4⋊Dic3—21no—
144C2×C4⋊Dic3—22no—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3D411yescharacteristic
147C2×C4⋊Dic3D411yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2311yescharacteristic
151#924—22no—
152#924—22no—
153C2×Dic3⋊C4—21no—
154C2×Dic3⋊C4—21no—
155C2×Dic3⋊C4—21no—
156C2×C4×Dic3—21no—
157C2×C4×Dic3—21no—
158C2×C4×Dic3C2311yescharacteristic
159C2×C4×Dic3C2311yescharacteristic
160C22×C3⋊C8C2311yescharacteristic
161C22×C3⋊C8C2311yescharacteristic
162C3×#103—22no—
163C3×#102—22no—
164C3×C22⋊C8—22no—
165#835—22no—
166#832—22no—
167#832—22no—
168#832—22no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#830—22no—
172#816—22no—
173#816—22no—
174Dic3⋊C8—22no—
175Dic3⋊C8—22no—
176C22×#41C2×D311yescharacteristic
177C22×Q16—31no—
178C22×SD16—31no—
179C22×SD16C2×D311yescharacteristic
180C22×D8C2×D311yescharacteristic
181C2×#124—31no—
182C2×C22⋊Q8—31no—
183C2×#121C2×D311yescharacteristic
184#520—64no—
185#520—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×#117—31no—
193C2×#117—61no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—61no—
196#464—64no—
197#463—64no—
198#452—64no—
199#449—24no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103C2×D311yescharacteristic
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102C2×D311yescharacteristic
210C2×C22⋊C8—31no—
211C2×C22⋊C8C2×D311yescharacteristic
212#396—61no—
213#396—61no—
214#394—61no—
215#394—61no—
216#391—31no—
217#390—31no—
218#384—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223#336—31no—
224#336—31no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3C2×D411yescharacteristic
228C3×#41—28no—
229C3×#41—28no—
230C3×#41—28no—
231C3×#41—28no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8C2×D412yes—
236C2×C3×Q8C2×D412yes—
237C2×C3×Q8#4112yes—
238C2×C3×D4—24no—
239C2×C3×D4—24no—
240C2×C3×D4—24no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—42no—
251C2×C3×D4—81no—
252C2×C3×D4—81no—
253C2×C3×D4C2×D412yes—
254C2×C3×D4C2×D412yes—
255C2×C3×D4#4112yes—
256C22×C3×C4—24no—
257C22×C3×C4—24no—
258C22×C3×C4—21no—
259C22×C3×C4—24no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D412yes—
267C22×C3×C4#4112yes—
268C22×C3×C4C2411yescharacteristic
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—24no—
272C22×Dic3—24no—
273C22×Dic3—24no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—81no—
277C22×Dic3—81no—
278C22×Dic3—81no—
279C22×Dic3—81no—
280C22×Dic3—81no—
281C22×Dic3—81no—
282C22×Dic3C2×D411yescharacteristic
283C22×Dic3C2×D411yescharacteristic
284C22×Dic3C2×D411yescharacteristic
285C22×Dic3C2×D411yescharacteristic
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C3×SD16—44no—
293C3×D8—44no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C22⋊C4—42no—
303#217—24no—
304#217—22no—
305#217—22no—
306#217—24no—
307#217—42no—
308#217—42no—
309#217—42no—
310#217—81no—
311#217—81no—
312#216—44no—
313#214—44no—
314C4⋊Dic3—24no—
315C4⋊Dic3—24no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—22no—
319C4⋊Dic3—24no—
320C4⋊Dic3—22no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3C2×D412yes—
324C4⋊Dic3C2×D412yes—
325Dic3⋊C4—42no—
326Dic3⋊C4—81no—
327Dic3⋊C4—81no—
328C4×Dic3—24no—
329C4×Dic3—21no—
330C4×Dic3—21no—
331C4×Dic3—24no—
332C4×Dic3C2×D412yes—
333C4×Dic3C2×D412yes—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41#6714yes—
346C22×Q8—31no—
347C22×Q8C22×D311yescharacteristic
348C22×D4—21no—
349C22×D4—21no—
350C22×D4C22×D311yescharacteristic
351C22×D4C22×D311yescharacteristic
352C23×C4—21no—
353C23×C4—61no—
354C23×C4—61no—
355C23×C4—61no—
356C23×C4C22×D311yescharacteristic
357C2×Q16—62no—
358C2×Q16—62no—
359C2×Q16—62no—
360C2×SD16—22no—
361C2×SD16—22no—
362C2×SD16—22no—
363C2×SD16—62no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×D8—22no—
367C2×D8—22no—
368C2×D8—22no—
369C22×C8—31no—
370C22×C8—31no—
371C22×C8C22×D311yescharacteristic
372C22×C8C22×D311yescharacteristic
373#124—62no—
374#124—62no—
375C22⋊Q8—62no—
376C22⋊Q8—62no—
377#121—22no—
378#121—22no—
379C4×Q8—34no—
380C4×Q8—62no—
381C4×Q8—62no—
382C4×Q8—62no—
383C4×D4—34no—
384C4×D4—62no—
385C4×D4—62no—
386C4×D4—68no—
387C4×D4—68no—
388C4×D4—62no—
389#117—62no—
390#117—62no—
391#117—68no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4—61no—
401C2×C4⋊C4—68no—
402C2×C4⋊C4—61no—
403C2×C4⋊C4—61no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4—61no—
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—31no—
409C2×C22⋊C4—31no—
410C2×C22⋊C4—61no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C42—31no—
418C2×C42—31no—
419C2×C42—61no—
420C2×C42—61no—
421C4⋊C8—62no—
422C4⋊C8—62no—
423#103—22no—
424#103—62no—
425#103—62no—
426#103—62no—
427#102—22no—
428#102—62no—
429#102—62no—
430#102—62no—
431C22⋊C8—22no—
432C22⋊C8—62no—
433#95—61no—
434#95—61no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—21no—
439C23×C3—22no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3#12112yes—
456C23×C3C22×D411yescharacteristic
457C3×Q8—22no—
458C3×Q8—22no—
459C3×Q8—22no—
460C3×Q8#12114yes—
461C3×D4—216no—
462C3×D4—22no—
463C3×D4—22no—
464C3×D4—22no—
465C3×D4—41no—
466C3×D4—41no—
467C3×D4—41no—
468C3×D4—41no—
469C3×D4—84no—
470C3×D4#12114yes—
471C2×C3×C4—216no—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4#12112yes—
485C2×C3×C4C22×D411yescharacteristic
486C2×C3×C4C22×D411yescharacteristic
487C2×C3×C4C22×D411yescharacteristic
488C2×C3×C4C2×#4111yescharacteristic
489C2×C3×C4C2×#4111yescharacteristic
490C2×C3×C4C2×#4111yescharacteristic
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—84no—
514C2×Dic3—84no—
515C2×Dic3—84no—
516C2×Dic3#12012yes—
517C2×Dic3#12012yes—
518Dic6—41no—
519Dic6—41no—
520Dic6—41no—
521Dic6—41no—
522C3×C8—41no—
523C3×C8—41no—
524C3⋊C8—41no—
525C3⋊C8—41no—
526C24—21no—
527C24—21no—
528C24D3×D411yescharacteristic
529#41—28no—
530#41—28no—
531#41—28no—
532#41—28no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8—61no—
542C2×Q8D3×D412yes—
543C2×Q8#23712yes—
544C2×Q8C2×#6712yes—
545C2×D4—24no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4D3×D412yes—
561C2×D4#23712yes—
562C2×D4C2×#6712yes—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—64no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—64no—
580C22×C4—64no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—241no—
584C22×C4—241no—
585C22×C4—241no—
586C22×C4—241no—
587C22×C4—241no—
588C22×C4—241no—
589C22×C4D3×D411yescharacteristic
590C22×C4#23712yes—
591C22×C4C2×#6712yes—
592C22×C4C23×D311yescharacteristic
593Q16—124no—
594SD16—44no—
595SD16—124no—
596D8—44no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—32no—
612C4⋊C4—32no—
613C4⋊C4—62no—
614C4⋊C4—62no—
615C4⋊C4—64no—
616C4⋊C4—64no—
617C4⋊C4—64no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—122no—
623C4⋊C4—241no—
624C4⋊C4—241no—
625C22⋊C4—42no—
626C22⋊C4—62no—
627C22⋊C4—62no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—122no—
631C22⋊C4—122no—
632C22⋊C4—122no—
633C22⋊C4—241no—
634C22⋊C4—241no—
635C42—32no—
636C42—32no—
637C42—64no—
638C42—64no—
639C42—61no—
640C42—61no—
641C22×C3—22no—
642C22×C3—24no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—42no—
647C22×C3—41no—
648C22×C3—42no—
649C22×C3—41no—
650C22×C3—42no—
651C22×C3—41no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3C2×#12011yescharacteristic
663C22×C3C2×#12111yescharacteristic
664C22×C3#52511yescharacteristic
665C22×C3#57611yescharacteristic
666C22×C3#57711yescharacteristic
667C22×C3#57711yescharacteristic
668C22×C3#57811yescharacteristic
669C3×C4—22no—
670C3×C4—24no—
671C3×C4—81no—
672C3×C4C2×#12111yescharacteristic
673C3×C4C2×#12111yescharacteristic
674C3×C4#52511yescharacteristic
675C3×C4#52511yescharacteristic
676Dic3—22no—
677Dic3—22no—
678Dic3—41no—
679Dic3—42no—
680Dic3—42no—
681Dic3—41no—
682Dic3—81no—
683Dic3—81no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—22no—
691C23—21no—
692C23—22no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23#93912yes—
705C23C2×D3×D411yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—121no—
710Q8—121no—
711Q8—121no—
712Q8—121no—
713Q8#93914yes—
714D4—216no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—84no—
723D4#93914yes—
724C2×C4—216no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—61no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—244no—
762C2×C4—244no—
763C2×C4—244no—
764C2×C4#93912yes—
765C2×C4C2×D3×D411yescharacteristic
766C2×C4C2×D3×D411yescharacteristic
767C2×C4C2×#23711yescharacteristic
768C2×C4C2×#23711yescharacteristic
769C2×C4C2×#23711yescharacteristic
770C2×C4C22×#6711yescharacteristic
771C8—41no—
772C8—41no—
773C8—121no—
774C8—121no—
775C2×C3—42no—
776C2×C3—44no—
777C2×C3—161no—
778C2×C3#284711yescharacteristic
779C2×C3#301211yescharacteristic
780C2×C3#301311yescharacteristic
781C2×C3#304511yescharacteristic
782C2×C3#304611yescharacteristic
783C2×C3#312411yescharacteristic
784C2×C3#312511yescharacteristic
785C22—22no—
786C22—24no—
787C22—22no—
788C22—22no—
789C22—42no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—42no—
794C22—41no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—42no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22#558611yescharacteristic
807C22D3×#12011yescharacteristic
808C22#577011yescharacteristic
809C22#577111yescharacteristic
810C22#577411yescharacteristic
811C22#577511yescharacteristic
812C22C2×#93911yescharacteristic
813C4—22no—
814C4—24no—
815C4—62no—
816C4—62no—
817C4—81no—
818C4—121no—
819C4—122no—
820C4—122no—
821C4—121no—
822C4—241no—
823C4—241no—
824C4#558611yescharacteristic
825C4#558611yescharacteristic
826C4C2×#93911yescharacteristic
827C4C2×#93911yescharacteristic
828C3#3291911yescharacteristic, complemented, Sylow
829C2—42no—
830C2—44no—
831C2—161no—
832C2#8007411yescharacteristic
833C2#8007511yescharacteristic
834C2#8008711yescharacteristic
835C2#8008811yescharacteristic
836C2#8260111yescharacteristic
837C2#8390211yescharacteristic
838C2#8393611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3#32919
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#5827C2semidirect
3. C2×#5239C2semidirect
4. C2×#5166C2semidirect
5. C2×#5153C2semidirect
6. #82677C2semidirect
7. #72048C2semidirect
8. #72037C2semidirect
9. #71677C2semidirect
10. #70239C2semidirect
11. #70221C2semidirect
12. #70171C2semidirect
13. #70153C2semidirect
14. #69930C2semidirect
15. #69909C2semidirect
122. Q8×Dic3D4semidirect
133. D4×Dic3D4semidirect
828. C3#32919semidirect

Maximal subgroups

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

subgroupindex
C2×#58272
C2×C3×#4492
C2×#52392
C2×#51662
C2×#51532
#826772
#720482
#720372
#716772
#702392
#702212
#701712
#701532
#699302
#699092
#329193