Finite Group Databasebeta

← #10945041

Subgroups — #10945041

Order 768.

1432 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5545C211yesmaximal, characteristic
2C2×#5169C211yesmaximal, characteristic
3C2×#4815C211yesmaximal, characteristic, complemented
4#76642C211yesmaximal, characteristic, complemented
5C3×#1877C211yesmaximal, characteristic, complemented
6#72047C211yesmaximal, characteristic, complemented
7#71606C211yesmaximal, characteristic, complemented
8#70276C211yesmaximal, characteristic, complemented
9#70198C211yesmaximal, characteristic
10#70170C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#68894C211yesmaximal, characteristic, complemented
13#68813C211yesmaximal, characteristic, complemented
14#68671C211yesmaximal, characteristic, complemented
15#68665C211yesmaximal, characteristic, complemented
16#33018—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×D4×Dic3C2211yescharacteristic
23C2×C4×#67—21no—
24C22×(C2×D3)⋊C4—21no—
25#5545—24no—
26#5545—24no—
27C2×#893C2211yescharacteristic
28C2×#892C2211yescharacteristic
29C2×#67⋊C4—21no—
30C2×D3×C22⋊C4—21no—
31C2×C4×D12C2211yescharacteristic
32C2×#872C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic, complemented
34C2×C3×#102C2211yescharacteristic
35C3×#391C2211yescharacteristic, complemented
36#5229C2211yescharacteristic, complemented
37C2×#835C2211yescharacteristic, complemented
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5169—24no—
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×#817C2211yescharacteristic, complemented
46#4987C2211yescharacteristic
47#4984C2211yescharacteristic, complemented
48C2×#809C2211yescharacteristic
49C2×#807C2211yescharacteristic, complemented
50#4928C2211yescharacteristic, complemented
51#4815—24no—
52#4675—21no—
53#4674—21no—
54#4658—21no—
55#4657—21no—
56C3×#340C2211yescharacteristic, complemented
57C3×#336C2211yescharacteristic, complemented
58#4551C2211yescharacteristic, complemented
59#4550C2211yescharacteristic, complemented
60#4550C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4524C2211yescharacteristic, complemented
64C2×#518—31no—
65C2×#485—31no—
66C2×#450—31no—
67#2625—31no—
68#1877—31no—
69#1877—31no—
70#1877—31no—
71#1877D311yescharacteristic, complemented
72#1864—31no—
73#1864—31no—
74#1862—31no—
75#1862—31no—
76#1825—31no—
77#1818—31no—
78#1786—31no—
79C24×D3—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C22×#67—21no—
84C23×Dic3—21no—
85C2×D3×D4—22no—
86C2×D3×D4—22no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4D414yes—
91C22×D12C2311yescharacteristic
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×C4×D3C2311yescharacteristic
95C2×C3×SD16—22no—
96C2×C3×SD16—22no—
97C2×C3×SD16—22no—
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×C3×C42C2311yescharacteristic
106C2×#217—21no—
107#946—22no—
108#946—22no—
109C2×#215—22no—
110C2×#215—22no—
111C2×#215—22no—
112D4×Dic3—22no—
113D4×Dic3—22no—
114C4×#67—28no—
115C2×(C2×D3)⋊C4—28no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×(C2×D3)⋊C4D411yescharacteristic
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4D411yescharacteristic
130C2×Dic3⋊C4D411yescharacteristic
131C2×C4×Dic3—21no—
132C2×C4×Dic3C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135#893—22no—
136#893—22no—
137#892—22no—
138#892D414yes—
139#67⋊C4—28no—
140D3×C22⋊C4—28no—
141C4×D12—22no—
142C4×D12—22no—
143#872—22no—
144#872—22no—
145C3×#103—22no—
146C3×#102—22no—
147C3×#95—21no—
148C3×#95—21no—
149#835—22no—
150#832—22no—
151#832—22no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#821—22no—
158#821—22no—
159(C2×D3)⋊C8—22no—
160(C2×D3)⋊C8—22no—
161#817—22no—
162#809—22no—
163#807—22no—
164C23×D4—31no—
165C22×SD16—31no—
166C22×SD16C2×D311yescharacteristic
167C2×C22⋊Q8—31no—
168#518—64no—
169#518—64no—
170C2×C4×D4—31no—
171C2×C4×D4—31no—
172C2×C4×D4—31no—
173C2×C4×D4—61no—
174C2×C4×D4—61no—
175C2×C4×D4C2×D311yescharacteristic
176C2×#117—31no—
177C2×#117—31no—
178C22×C22⋊C4—61no—
179C22×C22⋊C4—61no—
180#485—64no—
181#450—64no—
182C2×#107—31no—
183C2×#106—31no—
184C2×#103—31no—
185C2×#103C2×D311yescharacteristic, complemented
186C2×#102—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102C2×D311yescharacteristic
192C2×C22⋊C8—31no—
193C2×C22⋊C8—31no—
194#400—61no—
195#398—61no—
196#397—61no—
197#397—61no—
198#391—31no—
199#391C2×D311yescharacteristic, complemented
200#389—31no—
201#389—31no—
202#380—31no—
203#340—31no—
204#340—31no—
205#340—31no—
206#340C2×D311yescharacteristic, complemented
207#336—31no—
208#336—31no—
209#336—31no—
210#336C2×D311yescharacteristic, complemented
211C24×C3—21no—
212C23×D3—21no—
213C23×D3—24no—
214C23×D3—24no—
215C23×D3—24no—
216C23×D3—81no—
217C23×D3—81no—
218C23×D3—81no—
219C23×D3—81no—
220C23×D3C2×D411yescharacteristic
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4C2×D412yes—
231C2×C3×D4#4112yes—
232C2×C3×D4#4112yes—
233C22×C3×C4—21no—
234C22×C3×C4—24no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—81no—
238C22×C3×C4—81no—
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C2×#67—24no—
243C2×#67—24no—
244C2×#67—24no—
245C22×Dic3—21no—
246C22×Dic3—24no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—81no—
250C22×Dic3—81no—
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254D3×D4—28no—
255D3×D4—28no—
256D3×D4—28no—
257D3×D4—28no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12C2×D412yes—
262C2×D12#4112yes—
263C2×D12#4112yes—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—24no—
269C2×C4×D3—24no—
270C2×C4×D3—81no—
271C2×C4×D3—81no—
272C2×C4×D3—81no—
273C2×C4×D3—81no—
274C2×C4×D3C2×D412yes—
275C2×C4×D3C2×D412yes—
276C3×SD16—44no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4C2×D412yes—
287C3×C22⋊C4—24no—
288C3×C42—21no—
289C3×C42—21no—
290#217—24no—
291#215—44no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—22no—
296(C2×D3)⋊C4—24no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—81no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—81no—
305C4⋊Dic3C2×D412yes—
306Dic3⋊C4—22no—
307Dic3⋊C4—22no—
308Dic3⋊C4—42no—
309Dic3⋊C4—81no—
310C4×Dic3—21no—
311C4×Dic3—21no—
312C4×Dic3—24no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C25—61no—
320C22×Q8C22×D311yescharacteristic
321C22×D4—34no—
322C22×D4—31no—
323C22×D4—62no—
324C22×D4—61no—
325C22×D4—62no—
326C22×D4—62no—
327C22×D4—62no—
328C22×D4—62no—
329C22×D4C22×D311yescharacteristic
330C23×C4—21no—
331C23×C4—31no—
332C23×C4—61no—
333C23×C4—61no—
334C23×C4—61no—
335C2×SD16—22no—
336C2×SD16—22no—
337C2×SD16—22no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—62no—
341C22×C8—31no—
342C22×C8—31no—
343C22×C8C22×D311yescharacteristic
344C22×C8C22×D311yescharacteristic
345C22⋊Q8—62no—
346C22⋊Q8—62no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—62no—
350C4×D4—62no—
351C4×D4—68no—
352C4×D4—62no—
353C4×D4—62no—
354C4×D4—68no—
355C4×D4—62no—
356C4×D4—62no—
357#117—34no—
358#117—62no—
359#117—62no—
360#117—62no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—31no—
374C2×C22⋊C4—68no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—68no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C42—31no—
383C2×C42—61no—
384C2×C42C22×D311yescharacteristic
385#107—62no—
386#106—62no—
387#103—22no—
388#103—62no—
389#102—22no—
390#102—62no—
391#102—62no—
392#102—62no—
393#102—62no—
394#102—62no—
395C22⋊C8—62no—
396C22⋊C8—62no—
397#95—21no—
398#95—21no—
399#95—61no—
400#95—61no—
401#95—61no—
402#95—61no—
403#95—61no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3C22×D411yescharacteristic
412C22×D3—22no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—216no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—84no—
427C22×D3—84no—
428C22×D3—84no—
429C22×D3—84no—
430C22×D3—84no—
431C22×D3—84no—
432C22×D3#12012yes—
433C3×Q8—41no—
434C3×Q8—41no—
435C3×Q8—41no—
436C3×Q8—41no—
437C3×D4—22no—
438C3×D4—22no—
439C3×D4—22no—
440C3×D4#12314yes—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—84no—
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C22×D411yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463#67—216no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—22no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—84no—
482C2×Dic3#12012yes—
483D12—22no—
484D12—22no—
485D12—22no—
486D12#12314yes—
487C4×D3—22no—
488C4×D3—22no—
489C4×D3—22no—
490C4×D3—22no—
491C4×D3—84no—
492C4×D3—84no—
493C3×C8—41no—
494C3×C8—41no—
495C3⋊C8—41no—
496C3⋊C8—41no—
497C24—21no—
498C24—31no—
499C24—64no—
500C24—64no—
501C24—64no—
502C24—61no—
503C24—241no—
504C24—241no—
505C24—241no—
506C24—241no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—32no—
517C2×D4—32no—
518C2×D4—32no—
519C2×D4—64no—
520C2×D4—68no—
521C2×D4—68no—
522C2×D4—68no—
523C2×D4—64no—
524C2×D4—64no—
525C2×D4—68no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4#23512yes—
530C2×D4D3×D412yes—
531C2×D4#23712yes—
532C22×C4—21no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—31no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—64no—
542C22×C4—64no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—64no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—241no—
554C22×C4—241no—
555C22×C4—241no—
556C22×C4—241no—
557C22×C4—241no—
558C22×C4—241no—
559C22×C4D3×D411yescharacteristic
560C22×C4D3×D411yescharacteristic
561C22×C4C23×D311yescharacteristic
562SD16—44no—
563SD16—124no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—32no—
580C4⋊C4—62no—
581C4⋊C4—62no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—122no—
588C4⋊C4—241no—
589C4⋊C4—241no—
590C4⋊C4D3×D412yes—
591C22⋊C4—24no—
592C22⋊C4—62no—
593C22⋊C4—62no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—122no—
599C22⋊C4—241no—
600C42—21no—
601C42—21no—
602C42—64no—
603C42—61no—
604C42—61no—
605C22×C3—24no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3C2×#12011yescharacteristic
613C22×C3#52511yescharacteristic
614C22×C3#52511yescharacteristic
615C22×C3#57611yescharacteristic
616C22×C3#57711yescharacteristic
617C22×C3#57711yescharacteristic
618C22×C3#57711yescharacteristic
619C2×D3—22no—
620C2×D3—24no—
621C2×D3—22no—
622C2×D3—22no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—816no—
634C3×C4—41no—
635C3×C4—42no—
636C3×C4—41no—
637C3×C4—81no—
638C3×C4—81no—
639C3×C4C2×#12311yescharacteristic
640C3×C4C2×#12311yescharacteristic
641C3×C4#52511yescharacteristic
642C3×C4#52511yescharacteristic
643Dic3—22no—
644Dic3—42no—
645Dic3—41no—
646Dic3—41no—
647Dic3—81no—
648Dic3—81no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—32no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—616no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23—61no—
662C23—61no—
663C23—62no—
664C23—62no—
665C23—61no—
666C23—62no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—244no—
672C23—244no—
673C23—244no—
674C23—244no—
675C23—244no—
676C23—244no—
677C23C2×D3×D411yescharacteristic
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—34no—
686D4—616no—
687D4—62no—
688D4—62no—
689D4—62no—
690D4#88314yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—32no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—62no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—84no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—244no—
730C2×C4—244no—
731C2×C4—244no—
732C2×C4C2×#23511yescharacteristic
733C2×C4C2×D3×D411yescharacteristic
734C2×C4C2×D3×D411yescharacteristic
735C2×C4C2×#23711yescharacteristic
736C2×C4D3×#4111yescharacteristic
737C2×C4D3×#4111yescharacteristic
738C8—41no—
739C8—41no—
740C8—121no—
741C8—121no—
742C2×C3—44no—
743C2×C3#284911yescharacteristic
744C2×C3#300911yescharacteristic
745C2×C3#301211yescharacteristic
746C2×C3#311811yescharacteristic
747C2×C3#311811yescharacteristic
748C2×C3#312311yescharacteristic
749C2×C3#312311yescharacteristic
750D3—42no—
751D3—44no—
752C22—24no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—62no—
760C22—62no—
761C22—62no—
762C22—64no—
763C22—122no—
764C22—121no—
765C22—122no—
766C22—121no—
767C22—122no—
768C22—122no—
769C22—121no—
770C22—122no—
771C22—121no—
772C22—122no—
773C22—2416no—
774C22#554711yescharacteristic
775C22D3×#12011yescharacteristic
776C22#560611yescharacteristic
777C22#576211yescharacteristic
778C22#577011yescharacteristic
779C22#577411yescharacteristic
780C22#577811yescharacteristic
781C4—41no—
782C4—42no—
783C4—41no—
784C4—62no—
785C4—81no—
786C4—81no—
787C4—121no—
788C4—121no—
789C4—122no—
790C4—241no—
791C4—241no—
792C4C2×#88311yescharacteristic
793C4#554711yescharacteristic
794C4#560611yescharacteristic
795C4D3×#12311yescharacteristic
796C3#3301811yescharacteristic, complemented, Sylow
797C2—44no—
798C2—122no—
799C2—124no—
800C2#7493611yescharacteristic
801C2#7965911yescharacteristic
802C2#7978511yescharacteristic
803C2#8014911yescharacteristic
804C2#8022911yescharacteristic
805C2#8041311yescharacteristic
806C2#8050911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1877C2
socleC23×C3C22×D4
prime radicalC22×D3×D4C22
hypercenter#1877D3
hypocenterC3#33018
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
3. C2×#4815C2semidirect
4. #76642C2semidirect
5. C3×#1877C2semidirect
6. #72047C2semidirect
7. #71606C2semidirect
8. #70276C2semidirect
10. #70170C2semidirect
11. #69687C2semidirect
12. #68894C2semidirect
13. #68813C2semidirect
14. #68671C2semidirect
15. #68665C2semidirect
33. C2×C3×#103C22semidirect
35. C3×#391C22semidirect
36. #5229C22semidirect
37. C2×#835C22semidirect
45. C2×#817C22semidirect
47. #4984C22semidirect
49. C2×#807C22semidirect
50. #4928C22semidirect
56. C3×#340C22semidirect
57. C3×#336C22semidirect
58. #4551C22semidirect
59. #4550C22semidirect
60. #4550C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4524C22semidirect
71. #1877D3semidirect
185. C2×#103C2×D3semidirect
199. #391C2×D3semidirect
206. #340C2×D3semidirect
210. #336C2×D3semidirect
796. C3#33018semidirect

Maximal subgroups

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

subgroupindex
C2×#55452
C2×#51692
C2×#48152
#766422
C3×#18772
#720472
#716062
#702762
#701982
#701702
#696872
#688942
#688132
#686712
#686652
#330183