Finite Group Databasebeta

← #10944157

Subgroups — #10944157

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×#5574C211yesmaximal, characteristic, complemented
2C2×#5187C211yesmaximal, characteristic, complemented
3C2×#5185C211yesmaximal, characteristic, complemented
4C2×#4819C211yesmaximal, characteristic, complemented
5C2×#4810C211yesmaximal, characteristic
6#76640C211yesmaximal, characteristic, complemented
7C3×#1878C211yesmaximal, characteristic, complemented
8#71633C211yesmaximal, characteristic, complemented
9#70268C211yesmaximal, characteristic, complemented
10#70221C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#68892C211yesmaximal, characteristic, complemented
13#68880C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68663C211yesmaximal, characteristic, complemented
16#32919—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C22×D24C2211yescharacteristic
26#5574—24no—
27#5574—24no—
28C2×#895C2211yescharacteristic
29C2×#893—21no—
30C2×#893C2211yescharacteristic
31C2×D3×C4⋊C4—21no—
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×C4×D12—21no—
34C2×C4×D12C2211yescharacteristic
35C2×#872—21no—
36C2×#872C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C3×#391C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42#5187—24no—
43#5185—24no—
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49C2×Dic3⋊C8C2211yescharacteristic
50#4975C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53#4939C2211yescharacteristic
54#4819—24no—
55#4810—24no—
56#4676—21no—
57#4676—21no—
58#4672—21no—
59#4672—21no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65#4524C2211yescharacteristic
66C2×#520—31no—
67C2×#464—31no—
68C2×#463—31no—
69C2×#452—31no—
70C2×#449—31no—
71#2620—31no—
72#1880—31no—
73#1879—31no—
74#1878D311yescharacteristic, complemented
75#1877—31no—
76#1874—31no—
77#1872—31no—
78#1803—31no—
79#1802—31no—
80#1798—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C2×#239—22no—
84C2×#239—22no—
85C2×#239—22no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239D414yes—
89C22×D12—21no—
90C22×D12—21no—
91C22×D12C2311yescharacteristic
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×C4×D3C2311yescharacteristic
98C2×C3×Q16—22no—
99C2×C3×Q16—22no—
100C2×C3×Q16—22no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×C4×Q8—22no—
104C3×C4×Q8—22no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C42—21no—
109C2×C3×C42C2311yescharacteristic
110#947—22no—
111#947—22no—
112#946—22no—
113#946—22no—
114Q8×Dic3—22no—
115Q8×Dic3D414yescomplemented
116C2×#215—22no—
117C2×#215—22no—
118C2×#215—22no—
119C2×#215—22no—
120C2×#215—22no—
121C2×#215—22no—
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⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4D411yescharacteristic
140C2×Dic3⋊C4D411yescharacteristic
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×D24—22no—
146C2×D24—22no—
147C2×D24—22no—
148#895—22no—
149#895—22no—
150#893—28no—
151#893—22no—
152#893D414yescomplemented
153D3×C4⋊C4—28no—
154D3×C4⋊C4—22no—
155D3×C4⋊C4—22no—
156C4×D12—28no—
157C4×D12—22no—
158C4×D12—22no—
159#872—28no—
160#872—22no—
161#872—22no—
162C3×#103—22no—
163C3×#103—22no—
164C3×#95—21no—
165C3×#95—21no—
166#835—22no—
167#835—22no—
168#821—22no—
169#821—22no—
170(C2×D3)⋊C8—22no—
171(C2×D3)⋊C8—22no—
172Dic3⋊C8—22no—
173Dic3⋊C8—22no—
174#809—22no—
175#809—22no—
176C22×#41—31no—
177C22×Q16C2×D311yescharacteristic
178C22×SD16—31no—
179C22×SD16—31no—
180C22×D8—31no—
181C2×#124—31no—
182C2×C22⋊Q8—31no—
183C2×#121—31no—
184#520—64no—
185#520—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8C2×D311yescharacteristic
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—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103C2×D311yescharacteristic
205C2×#103C2×D311yescharacteristic
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212#396—61no—
213#396—61no—
214#394—61no—
215#394—61no—
216#391C2×D311yescharacteristic
217#390—31no—
218#384—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340C2×D311yescharacteristic
223#336—31no—
224#336C2×D311yescharacteristic
225C23×D3—21no—
226C23×D3—21no—
227C23×D3C2×D411yescharacteristic
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8C2×D412yes—
238C2×C3×Q8C2×D412yes—
239C2×C3×Q8#4112yes—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2411yescharacteristic
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3C2×D411yescharacteristic
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252#239—28no—
253#239—28no—
254#239—28no—
255#239—28no—
256C2×D12—24no—
257C2×D12—24no—
258C2×D12—24no—
259C2×D12—21no—
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—42no—
269C2×D12—81no—
270C2×D12—81no—
271C2×D12C2×D412yes—
272C2×D12C2×D412yes—
273C2×D12#4112yes—
274C2×C4×D3—24no—
275C2×C4×D3—24no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—24no—
281C2×C4×D3—24no—
282C2×C4×D3—24no—
283C2×C4×D3—24no—
284C2×C4×D3—81no—
285C2×C4×D3—81no—
286C2×C4×D3—81no—
287C2×C4×D3—81no—
288C2×C4×D3—81no—
289C2×C4×D3—81no—
290C2×C4×D3C2×D412yes—
291C2×C4×D3#4112yes—
292C3×Q16—44no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C3×C4⋊C4—24no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4C2×D412yes—
304C3×C42—24no—
305C3×C42—21no—
306C3×C42—21no—
307#215—44no—
308#215—44no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—22no—
311(C2×D3)⋊C4—22no—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—42no—
314(C2×D3)⋊C4—42no—
315(C2×D3)⋊C4—42no—
316(C2×D3)⋊C4—42no—
317(C2×D3)⋊C4—81no—
318(C2×D3)⋊C4—81no—
319C4⋊Dic3—21no—
320C4⋊Dic3—24no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3C2×D412yes—
324Dic3⋊C4—24no—
325Dic3⋊C4—22no—
326Dic3⋊C4—22no—
327Dic3⋊C4—42no—
328Dic3⋊C4—81no—
329Dic3⋊C4—81no—
330C4×Dic3—24no—
331C4×Dic3C2×D412yes—
332C4×Dic3C2×D412yes—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339D24—44no—
340C2×#41—34no—
341C2×#41—62no—
342C2×#41—62no—
343C2×#41—62no—
344C2×#41—62no—
345C2×#41—62no—
346C22×Q8C22×D311yescharacteristic
347C22×Q8C22×D311yescharacteristic
348C22×D4—31no—
349C22×D4—31no—
350C22×D4—61no—
351C22×D4—61no—
352C23×C4—31no—
353C23×C4—61no—
354C23×C4—61no—
355C23×C4—61no—
356C23×C4—61no—
357C2×Q16—22no—
358C2×Q16—22no—
359C2×Q16—22no—
360C2×SD16—62no—
361C2×SD16—62no—
362C2×SD16—62no—
363C2×SD16—62no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×D8—62no—
367C2×D8—62no—
368C2×D8—62no—
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—62no—
378#121—62no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—34no—
382C4×Q8—62no—
383C4×D4—34no—
384C4×D4—62no—
385C4×D4—62no—
386C4×D4—68no—
387C4×D4—62no—
388C4×D4—68no—
389#117—62no—
390#117—62no—
391#117—68no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—68no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4—61no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—61no—
403C2×C4⋊C4—61no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4C22×D311yescharacteristic
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C22⋊C4—31no—
408C2×C22⋊C4—31no—
409C2×C22⋊C4—61no—
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—21no—
418C2×C42—31no—
419C2×C42—61no—
420C2×C42C22×D311yescharacteristic
421C4⋊C8—62no—
422C4⋊C8—62no—
423#103—22no—
424#103—22no—
425#103—62no—
426#103—62no—
427#102—62no—
428#102—62no—
429#102—62no—
430#102—62no—
431C22⋊C8—62no—
432C22⋊C8—62no—
433#95—21no—
434#95—21no—
435C23×C3C22×D411yescharacteristic
436C22×D3—21no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—21no—
440C22×D3—22no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3#12112yes—
457C3×Q8—22no—
458C3×Q8—22no—
459C3×Q8—22no—
460C3×Q8—41no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—41no—
464C3×Q8#12114yes—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4C22×D411yescharacteristic
484C2×C3×C4C22×D411yescharacteristic
485C2×C3×C4C22×D411yescharacteristic
486C2×C3×C4C2×#4111yescharacteristic
487C2×C3×C4C2×#4111yescharacteristic
488C2×C3×C4C2×#4111yescharacteristic
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—22no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3#12012yes—
502C2×Dic3#12012yes—
503C2×Dic3#12112yes—
504D12—216no—
505D12—22no—
506D12—22no—
507D12—22no—
508D12—41no—
509D12—41no—
510D12—41no—
511D12—41no—
512D12—84no—
513D12#12114yes—
514C4×D3—216no—
515C4×D3—22no—
516C4×D3—22no—
517C4×D3—22no—
518C4×D3—22no—
519C4×D3—84no—
520C4×D3—84no—
521C4×D3—84no—
522C3×C8—41no—
523C3×C8—41no—
524C3⋊C8—41no—
525C3⋊C8—41no—
526C24—31no—
527C24—61no—
528C24—61no—
529#41—68no—
530#41—68no—
531#41—68no—
532#41—68no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8#23512yes—
543C2×Q8D3×D412yes—
544C2×Q8D3×D412yes—
545C2×D4—32no—
546C2×D4—32no—
547C2×D4—32no—
548C2×D4—64no—
549C2×D4—64no—
550C2×D4—64no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—61no—
557C2×D4—61no—
558C2×D4—61no—
559C2×D4—61no—
560C2×D4—122no—
561C2×D4—241no—
562C2×D4—241no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—32no—
571C22×C4—32no—
572C22×C4—64no—
573C22×C4—64no—
574C22×C4—64no—
575C22×C4—64no—
576C22×C4—64no—
577C22×C4—64no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—241no—
585C22×C4—241no—
586C22×C4—241no—
587C22×C4—241no—
588C22×C4—241no—
589C22×C4—241no—
590C22×C4D3×D411yescharacteristic
591C22×C4D3×D411yescharacteristic
592C22×C4C23×D311yescharacteristic
593Q16—44no—
594SD16—124no—
595SD16—124no—
596D8—124no—
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—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—32no—
614C4⋊C4—62no—
615C4⋊C4—62no—
616C4⋊C4—64no—
617C4⋊C4—64no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—122no—
622C4⋊C4—241no—
623C4⋊C4—241no—
624C4⋊C4D3×D412yes—
625C22⋊C4—62no—
626C22⋊C4—62no—
627C22⋊C4—64no—
628C22⋊C4—64no—
629C22⋊C4—122no—
630C22⋊C4—122no—
631C22⋊C4—122no—
632C22⋊C4—122no—
633C22⋊C4—241no—
634C22⋊C4—241no—
635C42—24no—
636C42—21no—
637C42—21no—
638C42—32no—
639C42—32no—
640C42—64no—
641C22×C3C2×#12011yescharacteristic
642C22×C3C2×#12111yescharacteristic
643C22×C3#52511yescharacteristic
644C22×C3#57611yescharacteristic
645C22×C3#57711yescharacteristic
646C22×C3#57711yescharacteristic
647C22×C3#57811yescharacteristic
648C2×D3—22no—
649C2×D3—24no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—41no—
653C2×D3—42no—
654C2×D3—41no—
655C2×D3—42no—
656C2×D3—41no—
657C2×D3—42no—
658C2×D3—41no—
659C2×D3—42no—
660C2×D3—42no—
661C2×D3—42no—
662C2×D3—81no—
663C2×D3—81no—
664C2×D3—81no—
665C2×D3—81no—
666C2×D3—81no—
667C2×D3—81no—
668C2×D3—81no—
669C3×C4—24no—
670C3×C4—41no—
671C3×C4—42no—
672C3×C4—41no—
673C3×C4—81no—
674C3×C4—81no—
675C3×C4C2×#12111yescharacteristic
676C3×C4C2×#12111yescharacteristic
677C3×C4#52511yescharacteristic
678C3×C4#52511yescharacteristic
679Dic3—22no—
680Dic3—22no—
681Dic3—22no—
682Dic3—42no—
683Dic3—81no—
684C23—32no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—62no—
690C23—61no—
691C23—62no—
692C23—61no—
693C23—62no—
694C23—121no—
695C23—121no—
696C23—121no—
697C23—121no—
698C23—121no—
699C23—121no—
700C23—121no—
701C23—121no—
702C23—121no—
703C23—121no—
704C23—121no—
705C23C2×D3×D411yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8#88414yes—
714D4—34no—
715D4—616no—
716D4—62no—
717D4—62no—
718D4—62no—
719D4—121no—
720D4—121no—
721D4—121no—
722D4—121no—
723D4—244no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—616no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—244no—
763C2×C4—244no—
764C2×C4—244no—
765C2×C4C2×#23511yescharacteristic
766C2×C4C2×D3×D411yescharacteristic
767C2×C4C2×D3×D411yescharacteristic
768C2×C4C2×D3×D411yescharacteristic
769C2×C4D3×#4111yescharacteristic
770C2×C4D3×#4111yescharacteristic
771C8—41no—
772C8—41no—
773C8—121no—
774C8—121no—
775C2×C3#284711yescharacteristic
776C2×C3#301211yescharacteristic
777C2×C3#301311yescharacteristic
778C2×C3#304511yescharacteristic
779C2×C3#304611yescharacteristic
780C2×C3#312411yescharacteristic
781C2×C3#312511yescharacteristic
782D3—42no—
783D3—44no—
784D3—161no—
785C22—62no—
786C22—64no—
787C22—62no—
788C22—62no—
789C22—121no—
790C22—122no—
791C22—122no—
792C22—121no—
793C22—122no—
794C22—121no—
795C22—122no—
796C22—122no—
797C22—121no—
798C22—122no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22—241no—
803C22—241no—
804C22—241no—
805C22—241no—
806C22#554711yescharacteristic
807C22D3×#12011yescharacteristic
808C22D3×#12111yescharacteristic
809C22#576611yescharacteristic
810C22#576911yescharacteristic
811C22#577811yescharacteristic
812C22#577811yescharacteristic
813C4—24no—
814C4—41no—
815C4—41no—
816C4—42no—
817C4—62no—
818C4—62no—
819C4—62no—
820C4—81no—
821C4—81no—
822C4—122no—
823C4—241no—
824C4C2×#88411yescharacteristic
825C4#554711yescharacteristic
826C4D3×#12111yescharacteristic
827C4#565611yescharacteristic
828C3#3291911yescharacteristic, complemented, Sylow
829C2—122no—
830C2—124no—
831C2—481no—
832C2#7493511yescharacteristic
833C2#7974911yescharacteristic
834C2#7985011yescharacteristic
835C2#8018611yescharacteristic
836C2#8023111yescharacteristic
837C2#8047911yescharacteristic
838C2#8060211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1878C2
socleC23×C3C22×D4
prime radicalC2×#4810C2
hypercenter#1878D3
hypocenterC3#32919
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
1. C2×#5574C2semidirect
2. C2×#5187C2semidirect
3. C2×#5185C2semidirect
4. C2×#4819C2semidirect
6. #76640C2semidirect
7. C3×#1878C2semidirect
8. #71633C2semidirect
9. #70268C2semidirect
10. #70221C2semidirect
11. #69687C2semidirect
12. #68892C2semidirect
13. #68880C2semidirect
14. #68673C2semidirect
15. #68663C2semidirect
74. #1878D3semidirect
115. Q8×Dic3D4semidirect
152. #893D4semidirect
828. C3#32919semidirect

Maximal subgroups

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

subgroupindex
C2×#55742
C2×#51872
C2×#51852
C2×#48192
C2×#48102
#766402
C3×#18782
#716332
#702682
#702212
#696872
#688922
#688802
#686732
#686632
#329193