Finite Group Databasebeta

← #10823431

Subgroups — #10823431

Order 768.

1260 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5680C211yesmaximal, characteristic, complemented
2C2×#5164C211yesmaximal, characteristic, complemented
3C2×#5152C211yesmaximal, characteristic, complemented
4#76291C211yesmaximal, characteristic, complemented
5C3×#2012C211yesmaximal, characteristic, complemented
6#72054C211yesmaximal, characteristic, complemented
7#72043C211yesmaximal, characteristic
8#71722C211yesmaximal, characteristic, complemented
9#70243C211yesmaximal, characteristic, complemented
10#70220C211yesmaximal, characteristic, complemented
11#70175C211yesmaximal, characteristic, complemented
12#70152C211yesmaximal, characteristic, complemented
13#69639C211yesmaximal, characteristic, complemented
14#68634C211yesmaximal, characteristic, complemented
15#68600C211yesmaximal, characteristic, complemented
16#23575—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×#124C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C2×D4×Dic3C2211yescharacteristic
25C2×D4×Dic3C2211yescharacteristic
26#5680—24no—
27#5680—24no—
28C2×#883—21no—
29C2×#67⋊C4—21no—
30C2×#67⋊C4—21no—
31C2×#879—21no—
32C2×#877—21no—
33C2×C42×D3C2211yescharacteristic
34C2×#870C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C3×#390C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44#5164—24no—
45#5152—24no—
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×#818C2211yescharacteristic
49C2×#817C2211yescharacteristic
50C2×#815C2211yescharacteristic
51C2×#815C2211yescharacteristic
52#4987C2211yescharacteristic
53Dic3×C4⋊C4C2211yescharacteristic
54#4956—21no—
55#4945—21no—
56Dic3×C22⋊C4—21no—
57#4928C2211yescharacteristic
58C3×#336C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529—31no—
65C2×#442—31no—
66C2×#440—31no—
67C4×#121—31no—
68#2059—31no—
69#2042—31no—
70#2035—31no—
71#2033—31no—
72#2025—31no—
73#2012D311yescharacteristic, complemented
74#2000—31no—
75#1999—31no—
76#1763—31no—
77#1762—31no—
78#1749—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C23×Dic3—21no—
85C23×Dic3—21no—
86C22×C4×D3D411yescharacteristic
87C22×C4×D3D411yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×D8—22no—
93C2×C3×D8—22no—
94C2×C3×D8—22no—
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×#124—22no—
98C3×#124—22no—
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C42C2311yescharacteristic
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109#946—22no—
110#946—22no—
111Q8×Dic3—22no—
112Q8×Dic3D414yescomplemented
113#938—22no—
114#938—22no—
115#938—22no—
116#938—22no—
117D4×Dic3—22no—
118D4×Dic3—22no—
119D4×Dic3—22no—
120D4×Dic3D414yescomplemented
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3—21no—
134C2×C4×Dic3D411yescharacteristic
135C2×C4×Dic3D411yescharacteristic
136C2×C4×Dic3C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139#883—28no—
140#67⋊C4—28no—
141#67⋊C4—44no—
142#879—28no—
143#877—28no—
144C42×D3—22no—
145C42×D3—22no—
146#870—22no—
147#870—22no—
148C3×#103—22no—
149C3×#102—22no—
150#835—22no—
151#835—22no—
152#832—22no—
153#832—22no—
154#832—22no—
155#832—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159(C2×D3)⋊C8—22no—
160(C2×D3)⋊C8—22no—
161#818—22no—
162#817—22no—
163#815—22no—
164#815—22no—
165C22×SD16C2×D311yescharacteristic
166C22×D8C2×D311yescharacteristic
167#529—64no—
168#529—64no—
169C2×#126—61no—
170C2×#125—31no—
171C2×#124C2×D311yescharacteristic
172C2×#123—61no—
173C2×C22⋊Q8—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—61no—
180C2×C4×D4—61no—
181C2×#117—61no—
182C22×C42—31no—
183#442—64no—
184#440—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×#97—31no—
198C2×#97—31no—
199#390C2×D311yescharacteristic
200#389—31no—
201#388—61no—
202#386—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205C4×C22⋊C4—61no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#336—31no—
211#336C2×D311yescharacteristic
212C24×C3—21no—
213C24×C3—21no—
214C23×D3C2×D411yescharacteristic
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8C2×D412yes—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4C2×D412yes—
232C2×C3×D4#4112yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C2×#67—24no—
239C2×#67—24no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—24no—
248C22×Dic3—21no—
249C22×Dic3—42no—
250C22×Dic3—42no—
251C22×Dic3—42no—
252C22×Dic3—42no—
253C22×Dic3—42no—
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256C22×Dic3C2×D411yescharacteristic
257C2×C4×D3—22no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—22no—
265C2×C4×D3—22no—
266C2×C4×D3—41no—
267C2×C4×D3—41no—
268C2×C4×D3—41no—
269C3×SD16—28no—
270C3×D8—28no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8#4112yes—
276C2×C3×C8#4112yes—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—42no—
282C3×C22⋊C4—42no—
283C3×C42—21no—
284C3×C42—21no—
285#217—24no—
286#217—24no—
287#217—24no—
288#217—42no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—42no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—24no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3C2×D412yes—
298C4⋊Dic3C2×D412yes—
299C4⋊Dic3#4112yes—
300Dic3⋊C4—24no—
301Dic3⋊C4—24no—
302Dic3⋊C4—24no—
303Dic3⋊C4—42no—
304C4×Dic3—22no—
305C4×Dic3—22no—
306C4×Dic3—24no—
307C4×Dic3—42no—
308C4×Dic3C2×D412yes—
309C4×Dic3C2×D412yes—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—61no—
318C22×D4—61no—
319C22×D4C22×D311yescharacteristic
320C22×D4C22×D311yescharacteristic
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—61no—
325C23×C4—61no—
326C2×SD16—22no—
327C2×SD16—22no—
328C2×SD16—22no—
329C2×D8—22no—
330C2×D8—22no—
331C2×D8—22no—
332C22×C8—31no—
333C22×C8—31no—
334C22×C8C22×D311yescharacteristic
335C22×C8C22×D311yescharacteristic
336#126—68no—
337#125—62no—
338#125—62no—
339#124—22no—
340#124—22no—
341#123—68no—
342C22⋊Q8—62no—
343C22⋊Q8—62no—
344#121—62no—
345#121—62no—
346#121—62no—
347#121—62no—
348C4×Q8—34no—
349C4×Q8—62no—
350C4×D4—34no—
351C4×D4—62no—
352C4×D4—62no—
353C4×D4—62no—
354C4×D4—68no—
355C4×D4—124no—
356#117—68no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C42—31no—
378C2×C42—31no—
379C2×C42—31no—
380C2×C42—62no—
381C2×C42—62no—
382C2×C42—61no—
383C2×C42—61no—
384C2×C42C22×D311yescharacteristic
385#107—62no—
386#106—62no—
387#103—22no—
388#103—62no—
389#103—62no—
390#102—22no—
391#102—62no—
392#102—62no—
393#102—62no—
394#102—62no—
395C22⋊C8—62no—
396C22⋊C8—62no—
397#97—62no—
398#97—62no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3C22×D411yescharacteristic
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3AGL(1,ℤ/8)12yes—
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×D4—22no—
429C3×D4—22no—
430C3×D4—22no—
431C3×D4—22no—
432C3×D4—41no—
433C3×D4—41no—
434C3×D4—41no—
435C3×D4—41no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454#67—48no—
455#67—48no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—48no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—84no—
477C2×Dic3#12012yes—
478C2×Dic3#12012yes—
479C4×D3—44no—
480C4×D3—44no—
481C4×D3—41no—
482C4×D3—41no—
483C4×D3—41no—
484C4×D3—41no—
485C3×C8—22no—
486C3×C8—22no—
487C3⋊C8—41no—
488C3⋊C8—41no—
489C24—21no—
490C24—21no—
491C24—31no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8D3×D412yes—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—64no—
509C2×D4—64no—
510C2×D4—122no—
511C2×D4—122no—
512C2×D4—122no—
513C2×D4—122no—
514C2×D4D3×D412yes—
515C2×D4#23712yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—64no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—121no—
536C22×C4—121no—
537C22×C4—121no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4—122no—
541C22×C4—122no—
542C22×C4—122no—
543C22×C4D3×D411yescharacteristic
544C22×C4D3×D411yescharacteristic
545C22×C4C23×D311yescharacteristic
546SD16—28no—
547D8—28no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8#23712yes—
559C2×C8#23712yes—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—32no—
563C4⋊C4—32no—
564C4⋊C4—32no—
565C4⋊C4—64no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—64no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—122no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—64no—
580C22⋊C4—64no—
581C22⋊C4—64no—
582C22⋊C4—64no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C42—21no—
586C42—21no—
587C42—32no—
588C42—32no—
589C42—62no—
590C42—62no—
591C42—64no—
592C42—122no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3C2×#12011yescharacteristic
608C22×C3#52511yescharacteristic
609C22×C3#53211yescharacteristic
610C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
611C22×C3#57511yescharacteristic
612C22×C3#57511yescharacteristic
613C22×C3#57511yescharacteristic
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—22no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C3×C4—42no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—81no—
625C3×C4#52511yescharacteristic
626C3×C4#52511yescharacteristic
627C3×C4#53211yescharacteristic
628C3×C4#53211yescharacteristic
629Dic3—22no—
630Dic3—22no—
631Dic3—42no—
632Dic3—41no—
633Dic3—42no—
634Dic3—42no—
635Dic3—81no—
636C23—22no—
637C23—22no—
638C23—32no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23—61no—
657C23C2×D3×D411yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—128no—
671D4—128no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—61no—
695C2×C4—62no—
696C2×C4—124no—
697C2×C4—124no—
698C2×C4—128no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—244no—
713C2×C4C2×D3×D411yescharacteristic
714C2×C4C2×D3×D411yescharacteristic
715C2×C4C2×#23711yescharacteristic
716C2×C4C2×#23711yescharacteristic
717C2×C4C2×#23711yescharacteristic
718C2×C4D3×#4111yescharacteristic
719C8—22no—
720C8—22no—
721C8—121no—
722C8—121no—
723C2×C3—82no—
724C2×C3—82no—
725C2×C3#238811yescharacteristic
726C2×C3#300511yescharacteristic
727C2×C3#300611yescharacteristic
728C2×C3#311111yescharacteristic
729C2×C3#311411yescharacteristic
730C2×C3#318011yescharacteristic
731C2×C3#318311yescharacteristic
732D3—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—62no—
740C22—62no—
741C22—62no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22D3×#12011yescharacteristic
755C22#560611yescharacteristic
756C22#571611yescharacteristic
757C22#576811yescharacteristic
758C22#576811yescharacteristic
759C22D3×AGL(1,ℤ/8)11yescharacteristic
760C22#577311yescharacteristic
761C4—42no—
762C4—41no—
763C4—41no—
764C4—62no—
765C4—62no—
766C4—81no—
767C4—121no—
768C4—122no—
769C4—122no—
770C4—122no—
771C4—241no—
772C4#558611yescharacteristic
773C4#558611yescharacteristic
774C4#559611yescharacteristic
775C4#559611yescharacteristic
776C3#2357511yescharacteristic, complemented, Sylow
777C2—82no—
778C2—82no—
779C2—122no—
780C2#7666511yescharacteristic
781C2#8008311yescharacteristic
782C2#8008411yescharacteristic
783C2#8050611yescharacteristic
784C2#8050711yescharacteristic
785C2#8181211yescharacteristic
786C2#8183811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2012C2
socleC23×C3C22×D4
prime radical#72043C2
hypercenter#2012D3
hypocenterC3#23575
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2012

Complements

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

NH ≅ G/Ntype
1. C2×#5680C2semidirect
2. C2×#5164C2semidirect
3. C2×#5152C2semidirect
4. #76291C2semidirect
5. C3×#2012C2semidirect
6. #72054C2semidirect
8. #71722C2semidirect
9. #70243C2semidirect
10. #70220C2semidirect
11. #70175C2semidirect
12. #70152C2semidirect
13. #69639C2semidirect
14. #68634C2semidirect
15. #68600C2semidirect
73. #2012D3semidirect
112. Q8×Dic3D4semidirect
120. D4×Dic3D4semidirect
776. C3#23575semidirect

Maximal subgroups

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

subgroupindex
C2×#56802
C2×#51642
C2×#51522
#762912
C3×#20122
#720542
#720432
#717222
#702432
#702202
#701752
#701522
#696392
#686342
#686002
#235753