Finite Group Databasebeta

← #10944025

Subgroups — #10944025

Order 768.

1468 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#239C211yesmaximal, characteristic
2C2×#5187C211yesmaximal, characteristic
3C2×#5182C211yesmaximal, characteristic, complemented
4C2×#4818C211yesmaximal, characteristic, complemented
5C2×#4808C211yesmaximal, characteristic
6#76664C211yesmaximal, characteristic, complemented
7C3×#1878C211yesmaximal, characteristic, complemented
8#71632C211yesmaximal, characteristic, complemented
9#70269C211yesmaximal, characteristic, complemented
10#70221C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#68892C211yesmaximal, characteristic, complemented
13#68879C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68662C211yesmaximal, characteristic, complemented
16#32907—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C2×#944C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C22×#204C2211yescharacteristic
26C4×#239—24no—
27C4×#239—24no—
28C2×#897C2211yescharacteristic
29C2×#893—21no—
30C2×#893C2211yescharacteristic
31C2×#892—21no—
32C2×#892C2211yescharacteristic
33C2×C4×D12—21no—
34C2×C4×D12C2211yescharacteristic
35C2×C42×D3—21no—
36C2×C42×D3C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C3×#391C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42#5187—24no—
43#5182—24no—
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49C2×Dic3⋊C8C2211yescharacteristic
50#4975C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#809C2211yescharacteristic
53#4929C2211yescharacteristic
54#4818—24no—
55#4808—24no—
56#4667—21no—
57#4667—21no—
58#4647—21no—
59#4647—21no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65#4524C2211yescharacteristic
66C2×C4×#41—31no—
67C2×#462—31no—
68C2×#461—31no—
69C2×#452—31no—
70C2×#452—31no—
71#2857—31no—
72#1878—31no—
73#1878D311yescharacteristic, complemented
74#1877—31no—
75#1877—31no—
76#1873—31no—
77#1873—31no—
78#1803—31no—
79#1802—31no—
80#1797—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×D12C2311yescharacteristic
91C22×C4×D3—21no—
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×C4×D3D411yescharacteristic
95C22×C4×D3D411yescharacteristic
96C22×C4×D3C2311yescharacteristic
97C22×Dic6C2311yescharacteristic
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#946—22no—
111#946—22no—
112Q8×Dic3—22no—
113Q8×Dic3D414yes—
114#944—22no—
115#944—22no—
116C2×#216—22no—
117C2×#216—22no—
118C2×#216—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×C4⋊Dic3—21no—
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3—21no—
138C2×C4×Dic3D411yescharacteristic
139C2×C4×Dic3D411yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×#204—22no—
144C2×#204—22no—
145C2×#204—22no—
146#897—22no—
147#897—22no—
148#893—28no—
149#893—22no—
150#893D414yes—
151#892—28no—
152#892—22no—
153#892—22no—
154C4×D12—28no—
155C4×D12—22no—
156C4×D12—22no—
157C42×D3—28no—
158C42×D3—22no—
159C42×D3—22no—
160C3×#103—22no—
161C3×#103—22no—
162C3×#95—21no—
163C3×#95—21no—
164#835—22no—
165#835—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168#821—22no—
169(C2×D3)⋊C8—22no—
170(C2×D3)⋊C8—22no—
171#816—22no—
172Dic3⋊C8—22no—
173Dic3⋊C8—22no—
174#810—22no—
175#809—22no—
176C22×#41—31no—
177C22×Q16—31no—
178C22×Q16C2×D311yescharacteristic
179C22×SD16—31no—
180C22×SD16—31no—
181C2×C4⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—31no—
184C4×#41—64no—
185C4×#41—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×C42—31no—
195C22×C42—61no—
196#462—64no—
197#461—64no—
198#452—64no—
199#452—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#103C2×D311yescharacteristic
207C2×#103C2×D311yescharacteristic
208C2×#102—31no—
209C2×#102—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212#391—31no—
213#391C2×D311yescharacteristic
214#389—61no—
215#389—61no—
216#384—31no—
217#380—61no—
218#380—61no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340C2×D311yescharacteristic
223#336—31no—
224#336C2×D311yescharacteristic
225C23×D3—21no—
226C23×D3C2×D411yescharacteristic
227C2×C3×Q8—21no—
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×Q8C2×D412yes—
237C2×C3×Q8C2×D412yes—
238C2×C3×Q8#4112yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2411yescharacteristic
246C22×Dic3—21no—
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×D12C2×D412yes—
263C2×D12C2×D412yes—
264C2×D12#4112yes—
265C2×C4×D3—24no—
266C2×C4×D3—24no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—24no—
272C2×C4×D3—24no—
273C2×C4×D3—22no—
274C2×C4×D3—22no—
275C2×C4×D3—22no—
276C2×C4×D3—24no—
277C2×C4×D3—22no—
278C2×C4×D3—22no—
279C2×C4×D3—41no—
280C2×C4×D3—42no—
281C2×C4×D3—42no—
282C2×C4×D3—42no—
283C2×C4×D3—42no—
284C2×C4×D3C2×D412yes—
285C2×C4×D3#4112yes—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—21no—
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#216—44no—
308#215—44no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—24no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—42no—
314C4⋊Dic3—21no—
315C4⋊Dic3—24no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—42no—
319C4⋊Dic3C2×D412yes—
320Dic3⋊C4—42no—
321Dic3⋊C4—42no—
322Dic3⋊C4—42no—
323Dic3⋊C4—42no—
324Dic3⋊C4—42no—
325C4×Dic3—24no—
326C4×Dic3—22no—
327C4×Dic3—22no—
328C4×Dic3—24no—
329C4×Dic3C2×D412yes—
330C4×Dic3C2×D412yes—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337#204—44no—
338C2×#41—34no—
339C2×#41—62no—
340C2×#41—62no—
341C2×#41—62no—
342C2×#41—62no—
343C2×#41—62no—
344C22×Q8—31no—
345C22×Q8C22×D311yescharacteristic
346C22×Q8C22×D311yescharacteristic
347C22×D4—31no—
348C22×D4—61no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—61no—
353C23×C4—61no—
354C23×C4—61no—
355C2×Q16—22no—
356C2×Q16—22no—
357C2×Q16—22no—
358C2×Q16—62no—
359C2×Q16—62no—
360C2×Q16—62no—
361C2×SD16—62no—
362C2×SD16—62no—
363C2×SD16—62no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×SD16—62no—
367C22×C8—31no—
368C22×C8—31no—
369C22×C8C22×D311yescharacteristic
370C22×C8C22×D311yescharacteristic
371C4⋊Q8—62no—
372C4⋊Q8—62no—
373C22⋊Q8—62no—
374C22⋊Q8—62no—
375C22⋊Q8—62no—
376C22⋊Q8—62no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—34no—
380C4×Q8—62no—
381C4×D4—34no—
382C4×D4—62no—
383C4×D4—62no—
384C4×D4—68no—
385C4×D4—62no—
386C4×D4—68no—
387#117—62no—
388#117—68no—
389#117—62no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C42—21no—
408C2×C42—31no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—62no—
412C2×C42—62no—
413C2×C42—68no—
414C2×C42—61no—
415C2×C42—61no—
416C2×C42C22×D311yescharacteristic
417C4⋊C8—62no—
418C4⋊C8—62no—
419#103—22no—
420#103—22no—
421#103—62no—
422#103—62no—
423#103—62no—
424#103—62no—
425#102—62no—
426#102—62no—
427C22⋊C8—62no—
428C22⋊C8—62no—
429#95—21no—
430#95—21no—
431#95—61no—
432#95—61no—
433C23×C3C22×D411yescharacteristic
434C22×D3—21no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—21no—
438C22×D3—22no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3#12112yes—
448C3×Q8—22no—
449C3×Q8—22no—
450C3×Q8—22no—
451C3×Q8—41no—
452C3×Q8—41no—
453C3×Q8—41no—
454C3×Q8—41no—
455C3×Q8#12114yes—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4#13712yes—
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4C2×#4111yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—22no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3#12012yes—
494C2×Dic3#12012yes—
495C2×Dic3#12112yes—
496C2×Dic3#13512yes—
497C2×Dic3#13712yes—
498D12—216no—
499D12—22no—
500D12—22no—
501D12—22no—
502D12#12114yes—
503C4×D3—216no—
504C4×D3—22no—
505C4×D3—22no—
506C4×D3—22no—
507C4×D3—22no—
508C4×D3—44no—
509C4×D3—48no—
510C4×D3—44no—
511C4×D3—48no—
512Dic6—41no—
513Dic6—41no—
514Dic6—41no—
515Dic6—41no—
516C3×C8—41no—
517C3×C8—41no—
518C3⋊C8—41no—
519C3⋊C8—41no—
520C24—31no—
521C24—61no—
522#41—68no—
523#41—68no—
524#41—68no—
525#41—68no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8#23512yes—
542C2×Q8D3×D412yes—
543C2×Q8D3×D412yes—
544C2×D4—32no—
545C2×D4—32no—
546C2×D4—32no—
547C2×D4—64no—
548C2×D4—64no—
549C2×D4—64no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—64no—
563C22×C4—64no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—64no—
569C22×C4—64no—
570C22×C4—64no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—62no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—121no—
580C22×C4—122no—
581C22×C4—122no—
582C22×C4—122no—
583C22×C4—122no—
584C22×C4D3×D411yescharacteristic
585C22×C4D3×D411yescharacteristic
586C22×C4C23×D311yescharacteristic
587Q16—44no—
588Q16—124no—
589SD16—124no—
590SD16—124no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C2×C8—61no—
601C2×C8—61no—
602C2×C8—61no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—32no—
608C4⋊C4—64no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—122no—
613C4⋊C4—122no—
614C4⋊C4—122no—
615C4⋊C4—122no—
616C4⋊C4—122no—
617C4⋊C4—122no—
618C4⋊C4D3×D412yes—
619C22⋊C4—64no—
620C22⋊C4—64no—
621C22⋊C4—64no—
622C22⋊C4—122no—
623C22⋊C4—122no—
624C42—24no—
625C42—21no—
626C42—21no—
627C42—32no—
628C42—32no—
629C42—62no—
630C42—62no—
631C42—64no—
632C42—64no—
633C22×C3C2×#12011yescharacteristic
634C22×C3C2×#12111yescharacteristic
635C22×C3#52511yescharacteristic
636C22×C3C2×#13511yescharacteristic
637C22×C3C2×#13711yescharacteristic
638C22×C3C2×#13711yescharacteristic
639C22×C3#57511yescharacteristic
640C2×D3—22no—
641C2×D3—24no—
642C2×D3—22no—
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—42no—
646C2×D3—41no—
647C2×D3—42no—
648C2×D3—41no—
649C2×D3—42no—
650C2×D3—41no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C3×C4—24no—
655C3×C4—22no—
656C3×C4—41no—
657C3×C4—42no—
658C3×C4—81no—
659C3×C4—81no—
660C3×C4C2×#12111yescharacteristic
661C3×C4C2×#12111yescharacteristic
662C3×C4#52511yescharacteristic
663C3×C4#52511yescharacteristic
664Dic3—22no—
665Dic3—22no—
666Dic3—42no—
667Dic3—81no—
668Dic3—81no—
669Dic3#45214yescomplemented
670C23—32no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—62no—
676C23—61no—
677C23—62no—
678C23—61no—
679C23—62no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23C2×D3×D411yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—121no—
693Q8—121no—
694Q8—121no—
695Q8—121no—
696Q8#88414yes—
697D4—34no—
698D4—616no—
699D4—62no—
700D4—62no—
701D4—62no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—616no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—124no—
735C2×C4—128no—
736C2×C4—124no—
737C2×C4—128no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4#91812yes—
747C2×C4C2×#23511yescharacteristic
748C2×C4C2×D3×D411yescharacteristic
749C2×C4C2×D3×D411yescharacteristic
750C2×C4C2×D3×D411yescharacteristic
751C2×C4D3×#4111yescharacteristic
752C2×C4D3×#4111yescharacteristic
753C8—41no—
754C8—41no—
755C8—121no—
756C8—121no—
757C2×C3#284711yescharacteristic
758C2×C3C2×#45211yescharacteristic
759C2×C3#300711yescharacteristic
760C2×C3#303511yescharacteristic
761C2×C3#303911yescharacteristic
762C2×C3#310711yescharacteristic
763C2×C3#311611yescharacteristic
764D3—42no—
765D3—44no—
766C22—62no—
767C22—64no—
768C22—62no—
769C22—62no—
770C22—121no—
771C22—122no—
772C22—122no—
773C22—121no—
774C22—122no—
775C22—121no—
776C22—122no—
777C22—122no—
778C22—121no—
779C22—122no—
780C22#554711yescharacteristic
781C22D3×#12011yescharacteristic
782C22D3×#12111yescharacteristic
783C22C2×#91811yescharacteristic
784C22D3×#13511yescharacteristic
785C22D3×#13711yescharacteristic
786C22#577711yescharacteristic
787C4—22no—
788C4—24no—
789C4—34no—
790C4—41no—
791C4—42no—
792C4—62no—
793C4—62no—
794C4—81no—
795C4—81no—
796C4—122no—
797C4—241no—
798C4—241no—
799C4C2×#88411yescharacteristic
800C4#554711yescharacteristic
801C4D3×#12111yescharacteristic
802C4#565611yescharacteristic
803C3#3290711yescharacteristic, complemented, Sylow
804C2—122no—
805C2—124no—
806C2#7493511yescharacteristic
807C2#7974711yescharacteristic
808C2#7984811yescharacteristic
809C2#8018411yescharacteristic
810C2D3×#45211yescharacteristic
811C2#8047711yescharacteristic
812C2#8059711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1878C2
socleC23×C3C22×D4
prime radicalC22×#239C22
hypercenter#1878D3
hypocenterC3#32907
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
3. C2×#5182C2semidirect
4. C2×#4818C2semidirect
6. #76664C2semidirect
7. C3×#1878C2semidirect
8. #71632C2semidirect
9. #70269C2semidirect
10. #70221C2semidirect
11. #69687C2semidirect
12. #68892C2semidirect
13. #68879C2semidirect
14. #68672C2semidirect
15. #68662C2semidirect
73. #1878D3semidirect
669. Dic3#452semidirect
803. C3#32907semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#2392
C2×#51872
C2×#51822
C2×#48182
C2×#48082
#766642
C3×#18782
#716322
#702692
#702212
#696872
#688922
#688792
#686722
#686622
#329073