Finite Group Databasebeta

← #10800993

Subgroups — #10800993

Order 768.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5504C211yesmaximal, characteristic, complemented
2C2×#4869C211yesmaximal, characteristic, complemented
3C2×#4852C211yesmaximal, characteristic, complemented
4C2×#4734C211yesmaximal, characteristic
5#73872C211yesmaximal, characteristic, complemented
6C3×#1853C211yesmaximal, characteristic, complemented
7#71560C211yesmaximal, characteristic, complemented
8#70588C211yesmaximal, characteristic, complemented
9#70584C211yesmaximal, characteristic, complemented
10#69907C211yesmaximal, characteristic, complemented
11#69522C211yesmaximal, characteristic, complemented
12#68909C211yesmaximal, characteristic, complemented
13#68897C211yesmaximal, characteristic, complemented
14#68783C211yesmaximal, characteristic, complemented
15#68780C211yesmaximal, characteristic, complemented
16#21464—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×C4×#67—21no—
21C2×C4×#67—21no—
22C2×#926C2211yescharacteristic
23C22×D24C2211yescharacteristic
24C22×#204C2211yescharacteristic
25#5504—24no—
26#5504—24no—
27C2×#893C2211yescharacteristic
28C2×#893C2211yescharacteristic
29C2×#893C2211yescharacteristic
30C2×#892—21no—
31C2×D3×C4⋊C4—21no—
32C2×#887C2211yescharacteristic
33C2×#887C2211yescharacteristic
34C2×C3×#106C2211yescharacteristic
35C2×C3×#106C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#830C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#816C2211yescharacteristic
41C2×#815C2211yescharacteristic
42C2×C8×Dic3C2211yescharacteristic
43#4988C2211yescharacteristic
44Dic3×C4⋊C4C2211yescharacteristic
45#4972C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4957—21no—
53#4956—21no—
54#4869—24no—
55#4852—24no—
56#4734C418yescomplemented
57#4670—21no—
58#4668—21no—
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#520—31no—
66C2×#449—31no—
67C2×#442—31no—
68C2×C4×SD16—31no—
69#2324—31no—
70#1880—31no—
71#1879—31no—
72#1874—31no—
73#1865—31no—
74#1864—31no—
75#1853D311yescharacteristic, complemented
76#1788—31no—
77#1763—31no—
78C4×#102—31no—
79#1750—31no—
80C23×C3×C4—21no—
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C2×#235—22no—
85C2×#235—22no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235C2×C414yescomplemented
90C22×D12C2311yescharacteristic
91C22×D12C2311yescharacteristic
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×Dic6C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×#217D411yescharacteristic
108C2×#217D411yescharacteristic
109#930—22no—
110#930C2×C414yescomplemented
111C4×#67—28no—
112C4×#67—28no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119#926—22no—
120#926—22no—
121C2×C4⋊Dic3D411yescharacteristic
122C2×C4⋊Dic3D411yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×C4×Dic3—21no—
128C2×C4×Dic3—21no—
129C2×C4×Dic3—21no—
130C2×C4×Dic3C2311yescharacteristic
131C2×C4×Dic3C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C2×D24—22no—
135C2×D24—22no—
136C2×D24C2×C414yescomplemented
137C2×#204—22no—
138C2×#204—22no—
139C2×#204C2×C414yescomplemented
140#893—22no—
141#893—22no—
142#893—22no—
143#893—22no—
144#893—22no—
145#893D414yescomplemented
146#892—28no—
147D3×C4⋊C4—28no—
148#887—22no—
149#887—22no—
150#887—22no—
151#887D414yescomplemented
152C3×#106—22no—
153C3×#106—22no—
154C3×C22⋊C8C2×C414yescomplemented
155C3×#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#830—22no—
159#821C2×C414yescomplemented
160#816C2×C414yescomplemented
161#815—22no—
162C8×Dic3—22no—
163#810—22no—
164#810—22no—
165#809—22no—
166#809—22no—
167#809—22no—
168#809—22no—
169C22×#41—31no—
170C22×SD16—31no—
171C22×D8—31no—
172C2×#121—31no—
173#520—64no—
174#520—64no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C2×C4×D4—61no—
182C2×#117—31no—
183C2×#117—61no—
184C22×C4⋊C4—61no—
185C22×C4⋊C4C2×D311yescharacteristic
186#449—38no—
187#442—64no—
188C4×SD16—64no—
189C2×#106C2×D311yescharacteristic
190C2×#106C2×D311yescharacteristic
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8C2×D311yescharacteristic
201C2×#97—31no—
202C2×C4×C8—31no—
203#390—31no—
204#390—61no—
205#389—31no—
206#388—61no—
207#386—61no—
208#385—61no—
209#380C2×D311yescharacteristic
210C4×C4⋊C4—31no—
211#340—31no—
212#340—31no—
213#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C23×D3—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—24no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—81no—
230C22×C3×C4—81no—
231C22×C3×C4C22×C412yes—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4#4112yes—
234C22×C3×C4C2411yescharacteristic
235C2×#67—24no—
236C2×#67—24no—
237C2×#67—24no—
238C2×#67—24no—
239C2×#67—81no—
240C2×#67—81no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3C2×D411yescharacteristic
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247#235—28no—
248#235—28no—
249#235—28no—
250#235—28no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12C22×C412yes—
260C2×D12C22×C412yes—
261C2×D12C2×D412yes—
262C2×D12#4112yes—
263C2×C4×D3—24no—
264C2×C4×D3—24no—
265C2×C4×D3—24no—
266C2×C4×D3—24no—
267C2×C4×D3—24no—
268C2×C4×D3—42no—
269C2×C4×D3—81no—
270C2×C4×D3—81no—
271C2×C4×D3—81no—
272C2×C4×D3—81no—
273C2×C4×D3—81no—
274C2×C4×D3—81no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6C22×C412yes—
279C2×Dic6C2×D412yes—
280C2×Dic6#4112yes—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8C22×C412yes—
286C2×C3×C8C22×C412yes—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4C2×D412yes—
295C3×C4⋊C4C2×D412yes—
296C3×C22⋊C4—81no—
297#217—22no—
298#217—22no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—24no—
301(C2×D3)⋊C4—24no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—81no—
304(C2×D3)⋊C4—81no—
305C4⋊Dic3—21no—
306C4⋊Dic3—22no—
307C4⋊Dic3—22no—
308C4⋊Dic3C22×C412yes—
309Dic3⋊C4—24no—
310Dic3⋊C4—24no—
311Dic3⋊C4—81no—
312C4×Dic3—24no—
313C4×Dic3—21no—
314C4×Dic3—21no—
315C4×Dic3—24no—
316C4×Dic3—81no—
317C4×Dic3C2×D412yes—
318C4×Dic3C2×D412yes—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325D24—28no—
326#204—28no—
327C2×#41—34no—
328C2×#41—62no—
329C2×#41—62no—
330C2×#41—62no—
331C2×#41—62no—
332C2×#41—62no—
333C22×Q8—31no—
334C22×D4—31no—
335C22×D4—31no—
336C22×D4—61no—
337C22×D4—61no—
338C23×C4—21no—
339C23×C4—61no—
340C23×C4—61no—
341C23×C4—61no—
342C23×C4—61no—
343C23×C4C22×D311yescharacteristic
344C2×SD16—34no—
345C2×SD16—62no—
346C2×SD16—62no—
347C2×D8—34no—
348C2×D8—62no—
349C2×D8—62no—
350C22×C8—31no—
351C22×C8—31no—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354#121—34no—
355#121—62no—
356C4×Q8—34no—
357C4×Q8—62no—
358C4×Q8—62no—
359C4×Q8—62no—
360C4×D4—34no—
361C4×D4—62no—
362C4×D4—62no—
363C4×D4—62no—
364C4×D4—62no—
365C4×D4—68no—
366C4×D4—68no—
367C4×D4—62no—
368#117—62no—
369#117—62no—
370#117—68no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—68no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4C22×D311yescharacteristic
382C2×C4⋊C4C22×D311yescharacteristic
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C42—31no—
395C2×C42—31no—
396C2×C42—61no—
397C2×C42—61no—
398C2×C42—61no—
399#106—22no—
400#106—22no—
401#103—34no—
402#103—62no—
403#103—62no—
404#102—34no—
405#102—62no—
406#102—62no—
407#102—62no—
408#102—62no—
409C22⋊C8—62no—
410C22⋊C8C4×D314yescomplemented
411#97—62no—
412C4×C8—62no—
413#95—21no—
414#95—61no—
415#95—61no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3C4×D412yes—
423C23×C3C22×D411yescharacteristic
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
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×C4C4×D412yes—
458C2×C3×C4C23×C411yescharacteristic
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464#67—216no—
465#67—84no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—22no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3#12012yes—
483C2×Dic3#12012yes—
484D12—22no—
485D12—22no—
486D12—22no—
487D12—22no—
488D12—22no—
489D12—41no—
490D12—41no—
491D12C4×D414yes—
492C4×D3—216no—
493C4×D3—84no—
494C4×D3—84no—
495C4×D3—84no—
496Dic6—22no—
497Dic6—22no—
498Dic6—22no—
499Dic6C4×D414yes—
500C3×C8—22no—
501C3×C8—22no—
502C3⋊C8—41no—
503C3⋊C8—41no—
504C24—61no—
505C24—61no—
506C24D3×D411yescharacteristic
507#41—68no—
508#41—68no—
509#41—68no—
510#41—68no—
511C2×Q8—32no—
512C2×Q8—32no—
513C2×Q8—32no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×D4—32no—
518C2×D4—32no—
519C2×D4—32no—
520C2×D4—32no—
521C2×D4—64no—
522C2×D4—64no—
523C2×D4—64no—
524C2×D4—64no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—241no—
534C2×D4—241no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—64no—
549C22×C4—64no—
550C22×C4—64no—
551C22×C4—64no—
552C22×C4—61no—
553C22×C4—64no—
554C22×C4—61no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—122no—
558C22×C4—241no—
559C22×C4—241no—
560C22×C4—241no—
561C22×C4—241no—
562C22×C4—241no—
563C22×C4—241no—
564C22×C4C2×C4×D312yes—
565C22×C4D3×D411yescharacteristic
566C22×C4#23912yes—
567C22×C4C23×D311yescharacteristic
568SD16—68no—
569D8—68no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8C2×C4×D312yes—
581C2×C8C2×C4×D312yes—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—32no—
590C4⋊C4—62no—
591C4⋊C4—62no—
592C4⋊C4—64no—
593C4⋊C4—64no—
594C4⋊C4—61no—
595C4⋊C4—241no—
596C4⋊C4D3×D412yes—
597C4⋊C4D3×D412yes—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—62no—
601C22⋊C4—62no—
602C22⋊C4—64no—
603C22⋊C4—81no—
604C22⋊C4—122no—
605C22⋊C4—241no—
606C22⋊C4—241no—
607C42—32no—
608C42—32no—
609C42—64no—
610C42—64no—
611C42—61no—
612C42—61no—
613C42—241no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3C2×C4×D411yescharacteristic
622C22×C3C2×#12011yescharacteristic
623C22×C3#52511yescharacteristic
624C22×C3#57611yescharacteristic
625C22×C3#57711yescharacteristic
626C22×C3#57711yescharacteristic
627C22×C3#57711yescharacteristic
628C2×D3—24no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C3×C4—22no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—81no—
646C3×C4—81no—
647C3×C4C2×C4×D411yescharacteristic
648C3×C4C2×C4×D411yescharacteristic
649C3×C4#52511yescharacteristic
650C3×C4#52511yescharacteristic
651Dic3—22no—
652Dic3—22no—
653Dic3—24no—
654Dic3—42no—
655Dic3—41no—
656Dic3—41no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—62no—
664C23—62no—
665C23—62no—
666C23—62no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23#89312yes—
678C23C2×D3×D411yescharacteristic
679Q8—34no—
680Q8—62no—
681Q8—62no—
682Q8—62no—
683D4—34no—
684D4—616no—
685D4—62no—
686D4—62no—
687D4—62no—
688D4—62no—
689D4—62no—
690D4—121no—
691D4—121no—
692D4—244no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—616no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—84no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—244no—
732C2×C4—244no—
733C2×C4—244no—
734C2×C4#89312yes—
735C2×C4C22×C4×D311yescharacteristic
736C2×C4C2×D3×D411yescharacteristic
737C2×C4C2×D3×D411yescharacteristic
738C2×C4C2×#23911yescharacteristic
739C2×C4D3×#4111yescharacteristic
740C2×C4D3×#4111yescharacteristic
741C8—22no—
742C8—22no—
743C8—121no—
744C8—121no—
745C2×C3—42no—
746C2×C3C4×#12011yescharacteristic
747C2×C3#294611yescharacteristic
748C2×C3#295211yescharacteristic
749C2×C3#301011yescharacteristic
750C2×C3#301211yescharacteristic
751C2×C3#311911yescharacteristic
752C2×C3#312511yescharacteristic
753D3—44no—
754D3—82no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—64no—
763C22—122no—
764C22—122no—
765C22—122no—
766C22—122no—
767C22—122no—
768C22—122no—
769C22—122no—
770C22—122no—
771C22—122no—
772C22—241no—
773C22—241no—
774C22—241no—
775C22—241no—
776C22C2×#89311yescharacteristic
777C22D3×#12011yescharacteristic
778C22#565611yescharacteristic
779C22#576211yescharacteristic
780C22#576211yescharacteristic
781C22#577411yescharacteristic
782C22#577811yescharacteristic
783C4—22no—
784C4—42no—
785C4—42no—
786C4—62no—
787C4—64no—
788C4—62no—
789C4—81no—
790C4—81no—
791C4—121no—
792C4—122no—
793C4—121no—
794C4C4×D3×D411yescharacteristic
795C4C4×D3×D411yescharacteristic
796C4#562711yescharacteristic
797C4#562711yescharacteristic
798C3#2146411yescharacteristic, complemented, Sylow
799C2—42no—
800C2—124no—
801C2—242no—
802C2#7437911yescharacteristic
803C2#7910611yescharacteristic
804C2#7920111yescharacteristic
805C2#8004111yescharacteristic
806C2#8014911yescharacteristic
807C2#8131211yescharacteristic
808C2#8141711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1853C2
socleC23×C3C22×D4
prime radicalC2×#4734C2
cosocleC22×C3×C4C24
hypercenter#1853D3
hypocenterC3#21464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
1. C2×#5504C2semidirect
2. C2×#4869C2semidirect
3. C2×#4852C2semidirect
5. #73872C2semidirect
6. C3×#1853C2semidirect
7. #71560C2semidirect
8. #70588C2semidirect
9. #70584C2semidirect
10. #69907C2semidirect
11. #69522C2semidirect
12. #68909C2semidirect
13. #68897C2semidirect
14. #68783C2semidirect
15. #68780C2semidirect
56. #4734C4semidirect
75. #1853D3semidirect
89. C2×#235C2×C4semidirect
110. #930C2×C4semidirect
136. C2×D24C2×C4semidirect
139. C2×#204C2×C4semidirect
145. #893D4semidirect
151. #887D4semidirect
154. C3×C22⋊C8C2×C4semidirect
159. #821C2×C4semidirect
160. #816C2×C4semidirect
410. C22⋊C8C4×D3semidirect
798. C3#21464semidirect

Maximal subgroups

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

subgroupindex
C2×#55042
C2×#48692
C2×#48522
C2×#47342
#738722
C3×#18532
#715602
#705882
#705842
#699072
#695222
#689092
#688972
#687832
#687802
#214643