Finite Group Databasebeta

← #10801000

Subgroups — #10801000

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×#5523C211yesmaximal, characteristic, complemented
2#82236C211yesmaximal, characteristic, complemented
3C2×#4734C211yesmaximal, characteristic
4C2×#4711C211yesmaximal, characteristic, complemented
5C2×C4×#204C211yesmaximal, characteristic, complemented
6C3×#1750C211yesmaximal, characteristic, complemented
7#69960C211yesmaximal, characteristic, complemented
8#69932C211yesmaximal, characteristic, complemented
9#69928C211yesmaximal, characteristic, complemented
10#69813C211yesmaximal, characteristic, complemented
11C4×#821C211yesmaximal, characteristic, complemented
12#68686C211yesmaximal, characteristic, complemented
13#68684C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68671C211yesmaximal, characteristic, complemented
16#21464—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×#117C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C22×D24C2211yescharacteristic
22C22×#204C2211yescharacteristic
23#5523—24no—
24#5523—24no—
25C2×#892—21no—
26C2×D3×C4⋊C4—21no—
27C2×#67⋊C4—21no—
28C2×#67⋊C4—21no—
29C2×C4×D12C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C2×C4×Dic6C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C2×C3×C22⋊C8C2211yescharacteristic
35C2×C3×C22⋊C8C2211yescharacteristic
36C2×C3×#97C2211yescharacteristic
37C2×C3×C4×C8C2211yescharacteristic
38#5212C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#817C2211yescharacteristic
45C2×#817C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49#4990—21no—
50#4989—21no—
51#4957—21no—
52#4956—21no—
53#4939C2211yescharacteristic
54C4×C4⋊Dic3C2211yescharacteristic
55#4928C2211yescharacteristic
56#4734C418yescomplemented
57#4711—24no—
58C4×#204—24no—
59C3×#336C2211yescharacteristic
60C3×#336C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64#4551C2211yescharacteristic
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#1853—31no—
76#1788—31no—
77#1763—31no—
78C4×#102—31no—
79#1750D311yescharacteristic, complemented
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—21no—
83C23×Dic3—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
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×#117—22no—
102C3×#117—22no—
103C2×C3×C4⋊C4D411yescharacteristic
104C2×C3×C4⋊C4D411yescharacteristic
105C2×C3×C22⋊C4D411yescharacteristic
106C2×C3×C22⋊C4D411yescharacteristic
107C2×C3×C42C2311yescharacteristic
108C2×C3×C42C2311yescharacteristic
109C2×#217—21no—
110#930—22no—
111#930C2×C414yescomplemented
112C2×(C2×D3)⋊C4—21no—
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×C4⋊Dic3—21no—
119C2×C4⋊Dic3—22no—
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×C4×Dic3—21no—
130C2×C4×Dic3—21no—
131C2×C4×Dic3—21no—
132C2×D24—22no—
133C2×D24—22no—
134C2×D24C2×C414yescomplemented
135C2×#204—22no—
136C2×#204—22no—
137C2×#204C2×C414yescomplemented
138#892—28no—
139D3×C4⋊C4—28no—
140#67⋊C4—28no—
141#67⋊C4—28no—
142C4×D12—22no—
143C4×D12—22no—
144C4×D12—22no—
145C4×D12—22no—
146C4×D12—22no—
147C4×D12D414yescomplemented
148C4×Dic6—22no—
149C4×Dic6—22no—
150C4×Dic6—22no—
151C4×Dic6D414yescomplemented
152C3×C22⋊C8—22no—
153C3×C22⋊C8C2×C414yescomplemented
154C3×#97—22no—
155C3×C4×C8—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#821—22no—
160#821—22no—
161#821—22no—
162#821—22no—
163#821C2×C414yescomplemented
164#817—22no—
165#817—22no—
166#816—22no—
167#816—22no—
168#816C2×C414yescomplemented
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—61no—
183C2×#117C2×D311yescharacteristic
184C22×C4⋊C4—31no—
185C22×C4⋊C4—61no—
186#449—38no—
187#442—64no—
188C4×SD16—64no—
189C2×#106—31no—
190C2×#106—31no—
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⋊C8C2×D311yescharacteristic
200C2×C22⋊C8C2×D311yescharacteristic
201C2×#97C2×D311yescharacteristic
202C2×C4×C8C2×D311yescharacteristic
203#390—31no—
204#390—61no—
205#389—31no—
206#388—61no—
207#386—61no—
208#385—61no—
209#380—31no—
210C4×C4⋊C4—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336C2×D311yescharacteristic
216#336C2×D311yescharacteristic
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×C4C22×C412yes—
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4#4112yes—
231C22×C3×C4C2411yescharacteristic
232C2×#67—24no—
233C2×#67—24no—
234C2×#67—24no—
235C2×#67—24no—
236C2×#67—81no—
237C2×#67—81no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—24no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—81no—
246C22×Dic3—81no—
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×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8C22×C412yes—
292C2×C3×C8C22×C412yes—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—22no—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—22no—
297C3×C42—21no—
298C3×C42—21no—
299C3×C42C2×D412yes—
300C3×C42C2×D412yes—
301#217—81no—
302(C2×D3)⋊C4—24no—
303(C2×D3)⋊C4—24no—
304(C2×D3)⋊C4—24no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—81no—
307(C2×D3)⋊C4—81no—
308C4⋊Dic3—24no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315C4⋊Dic3—21no—
316C4⋊Dic3C22×C412yes—
317C4⋊Dic3C2×D412yes—
318C4⋊Dic3C2×D412yes—
319Dic3⋊C4—24no—
320Dic3⋊C4—24no—
321Dic3⋊C4—81no—
322C4×Dic3—24no—
323C4×Dic3—24no—
324C4×Dic3—81no—
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—61no—
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×C8C22×D311yescharacteristic
351C22×C8C22×D311yescharacteristic
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—68no—
364C4×D4—68no—
365C4×D4—62no—
366C4×D4—62no—
367C4×D4—62no—
368#117—22no—
369#117—22no—
370#117—68no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—68no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4—61no—
383C2×C4⋊C4D1211yescharacteristic
384C2×C4⋊C4D1211yescharacteristic
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4D1211yescharacteristic
393C2×C22⋊C4D1211yescharacteristic
394C2×C42—61no—
395C2×C42—61no—
396C2×C42—61no—
397C2×C42C22×D311yescharacteristic
398C2×C42C22×D311yescharacteristic
399#106—62no—
400#106—62no—
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—22no—
410C22⋊C8C4×D314yescomplemented
411#97—22no—
412C4×C8—22no—
413#95—61no—
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—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4C4×D412yes—
455C2×C3×C4#12012yes—
456C2×C3×C4#12012yes—
457C2×C3×C4C23×C411yescharacteristic
458C2×C3×C4C22×D411yescharacteristic
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463#67—216no—
464#67—84no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—41no—
472C2×Dic3—41no—
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—41no—
482C2×Dic3—41no—
483C2×Dic3—84no—
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—
506C24C2×D1211yescharacteristic
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—64no—
540C22×C4—64no—
541C22×C4—64no—
542C22×C4—61no—
543C22×C4—64no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—64no—
548C22×C4—64no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—122no—
552C22×C4—241no—
553C22×C4—241no—
554C22×C4—241no—
555C22×C4—241no—
556C22×C4—241no—
557C22×C4—241no—
558C22×C4—241no—
559C22×C4—241no—
560C22×C4C2×C4×D312yes—
561C22×C4C2×D1211yescharacteristic
562C22×C4C2×D1211yescharacteristic
563C22×C4C2×D1211yescharacteristic
564C22×C4C2×D1211yescharacteristic
565C22×C4C2×D1211yescharacteristic
566C22×C4#23512yes—
567C22×C4C23×D311yescharacteristic
568SD16—68no—
569D8—68no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8C2×C4×D312yes—
581C2×C8C2×C4×D312yes—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—32no—
585C4⋊C4—32no—
586C4⋊C4—32no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—64no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—241no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—64no—
601C22⋊C4—64no—
602C22⋊C4—64no—
603C22⋊C4—122no—
604C22⋊C4—241no—
605C22⋊C4—241no—
606C22⋊C4—241no—
607C42—21no—
608C42—21no—
609C42—64no—
610C42—64no—
611C42—241no—
612C42D3×D412yes—
613C42D3×D412yes—
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—22no—
644C3×C4—22no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4C2×C4×D411yescharacteristic
648C3×C4C2×C4×D411yescharacteristic
649C3×C4#52511yescharacteristic
650C3×C4#52511yescharacteristic
651Dic3—24no—
652Dic3—42no—
653Dic3—42no—
654Dic3—42no—
655Dic3—81no—
656Dic3—81no—
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—
677C23C4×D1212yes—
678C23C22×D1211yescharacteristic
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—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—616no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—244no—
729C2×C4—244no—
730C2×C4—244no—
731C2×C4—244no—
732C2×C4C4×D1212yes—
733C2×C4#88212yes—
734C2×C4#88212yes—
735C2×C4C22×C4×D311yescharacteristic
736C2×C4C2×#23511yescharacteristic
737C2×C4C2×D3×D411yescharacteristic
738C2×C4C2×D3×D411yescharacteristic
739C2×C4D3×#4111yescharacteristic
740C2×C4D3×#4111yescharacteristic
741C8—22no—
742C8—22no—
743C8—41no—
744C8—41no—
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×C4×D1211yescharacteristic
777C22C2×#88211yescharacteristic
778C22#552411yescharacteristic
779C22#575111yescharacteristic
780C22#575111yescharacteristic
781C22#575111yescharacteristic
782C22#575211yescharacteristic
783C4—22no—
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—64no—
789C4—122no—
790C4—122no—
791C4—122no—
792C4—241no—
793C4—241no—
794C4C4×D3×D411yescharacteristic
795C4C4×D3×D411yescharacteristic
796C4#554711yescharacteristic
797C4#554711yescharacteristic
798C3#2146411yescharacteristic, complemented, Sylow
799C2—42no—
800C2—124no—
801C2—242no—
802C2C4×#88211yescharacteristic
803C2#7856011yescharacteristic
804C2#7857411yescharacteristic
805C2#7867211yescharacteristic
806C2#7867811yescharacteristic
807C2#7938411yescharacteristic
808C2#7938911yescharacteristic
subgroupG/H
centerC23C22×D12
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1750C2
socleC23×C3C22×D4
prime radicalC2×#4734C2
cosocleC22×C3×C4C24
hypercenter#1750D3
hypocenterC3#21464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. C2×#5523C2semidirect
2. #82236C2semidirect
4. C2×#4711C2semidirect
5. C2×C4×#204C2semidirect
6. C3×#1750C2semidirect
7. #69960C2semidirect
8. #69932C2semidirect
9. #69928C2semidirect
10. #69813C2semidirect
11. C4×#821C2semidirect
12. #68686C2semidirect
13. #68684C2semidirect
14. #68673C2semidirect
15. #68671C2semidirect
56. #4734C4semidirect
79. #1750D3semidirect
89. C2×#235C2×C4semidirect
111. #930C2×C4semidirect
134. C2×D24C2×C4semidirect
137. C2×#204C2×C4semidirect
147. C4×D12D4semidirect
151. C4×Dic6D4semidirect
153. C3×C22⋊C8C2×C4semidirect
163. #821C2×C4semidirect
168. #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×#55232
#822362
C2×#47342
C2×#47112
C2×C4×#2042
C3×#17502
#699602
#699322
#699282
#698132
C4×#8212
#686862
#686842
#686732
#686712
#214643