Finite Group Databasebeta

← #10846248

Subgroups — #10846248

Order 768.

1104 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4864C211yesmaximal, characteristic, complemented
2C2×#4864C211yesmaximal, characteristic, complemented
3C2×#4852C211yesmaximal, characteristic, complemented
4C2×#4693C211yesmaximal, characteristic, complemented
5#76221C211yesmaximal, characteristic, complemented
6#76220C211yesmaximal, characteristic
7C3×#1941C211yesmaximal, characteristic, complemented
8#70574C211yesmaximal, characteristic, complemented
9C8×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#69633C211yesmaximal, characteristic, complemented
11#69627C211yesmaximal, characteristic, complemented
12#68909C211yesmaximal, characteristic, complemented
13#68896C211yesmaximal, characteristic, complemented
14#68887C211yesmaximal, characteristic, complemented
15#68887C211yesmaximal, characteristic, complemented
16#25410—31nomaximal, Sylow
17C22×#204C2211yescharacteristic
18C22×#204C2211yescharacteristic
19C22×#204C2211yescharacteristic
20C22×#204C2211yescharacteristic
21C22×D3×C8C2211yescharacteristic
22C2×#897C2211yescharacteristic
23C2×#897C2211yescharacteristic
24C2×#895—21no—
25C2×#895C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#893C2211yescharacteristic
28C2×#887C2211yescharacteristic
29C2×#874C2211yescharacteristic
30C2×#869C2211yescharacteristic
31C2×C3×#106C2211yescharacteristic
32C2×C3×#106C2211yescharacteristic
33C2×C3×C4×C8C2211yescharacteristic
34C3×#389C2211yescharacteristic
35C3×#389C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×C8×Dic3C2211yescharacteristic
38#4994—21no—
39#4991—21no—
40#4988C2211yescharacteristic
41#4984—21no—
42#4973C2211yescharacteristic
43C2×#810C2211yescharacteristic
44C2×#810C2211yescharacteristic
45C2×#810C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C4×(C2×D3)⋊C4C2211yescharacteristic
52#4864—24no—
53#4864—24no—
54#4852—24no—
55#4693—24no—
56#4671—21no—
57#4670—21no—
58#4665—21no—
59#4661—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4550C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#492—31no—
65C2×#465—31no—
66C2×#465—31no—
67C2×C4×SD16—31no—
68#2429—31no—
69#2428—31no—
70#2043—31no—
71#2041—31no—
72#2000—31no—
73#2000—31no—
74#1968—31no—
75#1941D311yescharacteristic, complemented
76#1880—31no—
77#1877—31no—
78C8×C22⋊C4—31no—
79C22×D12—21no—
80C22×D12—21no—
81C22×D12—21no—
82C22×D12—21no—
83C22×D12C2311yescharacteristic
84C22×D12C2311yescharacteristic
85C22×C4×D3—21no—
86C22×C4×D3C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C22×Dic6C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C42C2311yescharacteristic
98C2×(C2×D3)⋊C4—21no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4—21no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4D411yescharacteristic
106C2×(C2×D3)⋊C4D411yescharacteristic
107C2×C4⋊Dic3—21no—
108C2×C4⋊Dic3—21no—
109C2×C4⋊Dic3—21no—
110C2×C4⋊Dic3—21no—
111C2×Dic3⋊C4—21no—
112C2×C4×Dic3—21no—
113C2×C4×Dic3C2311yescharacteristic
114C22×C3⋊C8C2311yescharacteristic
115C22×C3⋊C8C2311yescharacteristic
116C2×#204—22no—
117C2×#204—22no—
118C2×#204—22no—
119C2×#204—22no—
120C2×#204—22no—
121C2×#204—22no—
122C2×#204—22no—
123C2×#204—22no—
124C2×#204—22no—
125C2×#204—41no—
126C2×#204—41no—
127C2×#204D414yescomplemented
128C2×D3×C8—22no—
129C2×D3×C8—22no—
130C2×D3×C8—22no—
131#897—22no—
132#897—22no—
133#897—41no—
134#897—41no—
135#895—22no—
136#895—22no—
137#895—41no—
138#895—41no—
139#895—44no—
140#893—22no—
141#893—41no—
142#887—22no—
143#887—41no—
144#874—22no—
145#874—41no—
146#869—22no—
147#869—41no—
148C3×#106—22no—
149C3×#106D414yescomplemented
150C3×C4×C8—22no—
151C3×#95—21no—
152C3×#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95D411yescharacteristic
156C3⋊#95D411yescharacteristic
157(C2×D3)⋊C8—22no—
158C8×Dic3—22no—
159#810—22no—
160#810—22no—
161#810—22no—
162#810—41no—
163#809—22no—
164#809—22no—
165#809—22no—
166#809—41no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×SD16—31no—
170C22×SD16—31no—
171C23×C8—31no—
172C2×C4⋊Q8—31no—
173C2×#127—31no—
174C2×C22⋊Q8—31no—
175C2×C22⋊Q8—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—61no—
179C2×C4×Q8—31no—
180C2×C4×D4—31no—
181#492—64no—
182#465—64no—
183#465—64no—
184C4×SD16—64no—
185C2×#106C2×D311yescharacteristic
186C2×#106C2×D311yescharacteristic
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8—31no—
197C2×C4×C8C2×D311yescharacteristic
198#398—61no—
199#396—61no—
200#394—61no—
201#392—61no—
202#391—31no—
203#390—31no—
204#389—61no—
205#389C2×D311yescharacteristic
206#389C2×D311yescharacteristic
207#388—61no—
208#386—61no—
209C4×C22⋊C4—31no—
210#340C2×D311yescharacteristic
211#340C2×D311yescharacteristic
212#336—31no—
213#336—31no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3C2×D411yescharacteristic
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2411yescharacteristic
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3C2×D411yescharacteristic
227C22×Dic3C2×D411yescharacteristic
228C22×Dic3C2×D411yescharacteristic
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—42no—
241C2×D12—42no—
242C2×D12—42no—
243C2×D12—42no—
244C2×D12—42no—
245C2×D12—42no—
246C2×D12—42no—
247C2×D12—42no—
248C2×D12—81no—
249C2×D12—81no—
250C2×D12—81no—
251C2×D12—81no—
252C2×D12C2×D412yes—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—42no—
260C2×C4×D3—42no—
261C2×C4×D3—81no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6C2×D412yes—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8C2×D412yes—
277C2×C3×C8C2×D412yes—
278C2×C3×C8#4112yes—
279C2×C3×C8#4112yes—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—42no—
287C3×C4⋊C4—42no—
288C3×C4⋊C4C2×D412yes—
289C3×C4⋊C4C2×D412yes—
290C3×C42—21no—
291C3×C42—21no—
292(C2×D3)⋊C4—22no—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—81no—
300(C2×D3)⋊C4SD1614yescomplemented
301C4⋊Dic3—42no—
302C4⋊Dic3—42no—
303C4⋊Dic3—42no—
304C4⋊Dic3—42no—
305Dic3⋊C4—42no—
306C4×Dic3—21no—
307C4×Dic3—21no—
308C4×Dic3—42no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315#204—28no—
316#204—44no—
317#204—44no—
318#204—44no—
319D3×C8—44no—
320C22×Q8—31no—
321C22×Q8—31no—
322C22×D4—31no—
323C22×D4—31no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4—61no—
328C23×C4—31no—
329C23×C4—61no—
330C2×SD16—34no—
331C2×SD16—62no—
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—62no—
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—121no—
341C2×SD16—121no—
342C22×C8—31no—
343C22×C8—31no—
344C22×C8—62no—
345C22×C8—62no—
346C22×C8—62no—
347C22×C8C22×D311yescharacteristic
348C22×C8C22×D311yescharacteristic
349C4⋊Q8—62no—
350C4⋊Q8—121no—
351#127—62no—
352#127—121no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355C22⋊Q8—121no—
356C22⋊Q8—121no—
357#121—62no—
358#121—62no—
359#121—124no—
360#121—121no—
361#121—121no—
362C4×Q8—62no—
363C4×Q8—121no—
364C4×D4—62no—
365C4×D4—121no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C4⋊C4C22×D311yescharacteristic
375C2×C4⋊C4C22×D311yescharacteristic
376C2×C4⋊C4C22×D311yescharacteristic
377C2×C22⋊C4—31no—
378C2×C22⋊C4—31no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C42—31no—
387C2×C42—61no—
388C2×C42C22×D311yescharacteristic
389#106—22no—
390#106D1214yescomplemented
391#103—62no—
392#103—62no—
393#103—62no—
394#103—121no—
395#102—62no—
396#102—62no—
397#102—62no—
398#102—121no—
399C22⋊C8—62no—
400C4×C8—22no—
401C4×C8—62no—
402#95—21no—
403#95—21no—
404#95—31no—
405#95—31no—
406#95—61no—
407#95—61no—
408C23×C3C22×D411yescharacteristic
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—22no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3C2×SD1612yes—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4C2×SD1612yes—
447C2×C3×C4#13512yes—
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4H(5,𝔽2)11yescharacteristic
453C2×C3×C4H(5,𝔽2)11yescharacteristic
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—22no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3C2×SD1612yes—
469D12—22no—
470D12—22no—
471D12—41no—
472D12—41no—
473D12—41no—
474D12—41no—
475D12—41no—
476D12—41no—
477D12—84no—
478D12—84no—
479D12—84no—
480D12—84no—
481C4×D3—41no—
482C4×D3—41no—
483C4×D3—41no—
484C4×D3—41no—
485C4×D3—84no—
486Dic6—22no—
487Dic6—22no—
488Dic6—41no—
489Dic6—41no—
490Dic6—41no—
491Dic6—41no—
492Dic6—41no—
493Dic6—41no—
494C3×C8—22no—
495C3×C8#12114yescomplemented
496C3⋊C8—41no—
497C3⋊C8—41no—
498C24—31no—
499C24—61no—
500C24—61no—
501C2×Q8—32no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×D4—32no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—122no—
526C2×D4—122no—
527C2×D4—122no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—241no—
534C2×D4—241no—
535C2×D4—241no—
536C2×D4—241no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—122no—
553C22×C4—122no—
554C22×C4—241no—
555C22×C4D3×D411yescharacteristic
556C22×C4D3×D411yescharacteristic
557C22×C4C23×D311yescharacteristic
558SD16—68no—
559SD16—124no—
560SD16—124no—
561SD16—124no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—61no—
565C2×C8—61no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—124no—
571C2×C8C2×D1212yes—
572C2×C8D3×D412yes—
573C2×C8#23912yes—
574C2×C8#23912yes—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—122no—
584C4⋊C4—122no—
585C4⋊C4—122no—
586C4⋊C4—122no—
587C4⋊C4—122no—
588C4⋊C4C2×D1212yes—
589C4⋊C4C2×D1212yes—
590C22⋊C4—34no—
591C22⋊C4—62no—
592C22⋊C4—122no—
593C22⋊C4—122no—
594C22⋊C4—122no—
595C22⋊C4—122no—
596C22⋊C4—122no—
597C22⋊C4—122no—
598C22⋊C4—241no—
599C42—21no—
600C42—21no—
601C42—61no—
602C42—61no—
603C42—122no—
604C22×C3#53211yescharacteristic
605C22×C3D4211yescharacteristic
606C22×C3D4211yescharacteristic
607C22×C3C22×SD1611yescharacteristic
608C22×C3C2×#13511yescharacteristic
609C22×C3#57711yescharacteristic
610C22×C3#57711yescharacteristic
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—42no—
621C2×D3—81no—
622C2×D3—81no—
623C2×D3—81no—
624C2×D3—81no—
625C2×D3—81no—
626C2×D3—81no—
627C2×D3—81no—
628C2×D3—81no—
629C2×D3—81no—
630C2×D3—81no—
631C2×D3—81no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—81no—
637C3×C4—81no—
638C3×C4C2×#12111yescharacteristic
639C3×C4#54011yescharacteristic
640C3×C4#54611yescharacteristic
641C3×C4#55011yescharacteristic
642Dic3—22no—
643Dic3—42no—
644Dic3—41no—
645Dic3—41no—
646Dic3—81no—
647C23—32no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—62no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—121no—
661C23—121no—
662C23—121no—
663C23—121no—
664C23—121no—
665C23—121no—
666C23—121no—
667C23—121no—
668C23C2×D3×D411yescharacteristic
669Q8—62no—
670Q8—62no—
671Q8—121no—
672Q8—121no—
673Q8—121no—
674Q8—121no—
675Q8—121no—
676Q8—121no—
677D4—62no—
678D4—62no—
679D4—121no—
680D4—121no—
681D4—121no—
682D4—121no—
683D4—121no—
684D4—121no—
685D4—244no—
686D4—244no—
687D4—244no—
688D4—244no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—32no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—62no—
715C2×C4—121no—
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—244no—
725C2×C4D3×SD1612yes—
726C2×C4#91612yes—
727C2×C4C22×D1211yescharacteristic
728C2×C4C2×D3×D411yescharacteristic
729C2×C4C2×#23911yescharacteristic
730C2×C4C2×#23911yescharacteristic
731C2×C4#100911yescharacteristic
732C2×C4#100911yescharacteristic
733C8—22no—
734C8—121no—
735C8—121no—
736C8#89514yescomplemented
737C2×C3#242811yescharacteristic
738C2×C3#316711yescharacteristic
739C2×C3#317411yescharacteristic
740C2×C3D4×SD1611yescharacteristic
741C2×C3D4×SD1611yescharacteristic
742C2×C3#328211yescharacteristic
743C2×C3#328411yescharacteristic
744D3—42no—
745D3—82no—
746D3—161no—
747C22—62no—
748C22—62no—
749C22—62no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—122no—
755C22—122no—
756C22—122no—
757C22—241no—
758C22—241no—
759C22—241no—
760C22—241no—
761C22—241no—
762C22—241no—
763C22—241no—
764C22—241no—
765C22—241no—
766C22—241no—
767C22—241no—
768C22D4×D1211yescharacteristic
769C22#560911yescharacteristic
770C22#572511yescharacteristic
771C22C2×D3×SD1611yescharacteristic
772C22C2×#91611yescharacteristic
773C22#577011yescharacteristic
774C22#577011yescharacteristic
775C4—22no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—62no—
780C4—81no—
781C4—81no—
782C4—121no—
783C4—121no—
784C4—122no—
785C4—241no—
786C4C2×#89511yescharacteristic
787C4#557711yescharacteristic
788C4#563011yescharacteristic
789C4#569711yescharacteristic
790C3#2541011yescharacteristic, complemented, Sylow
791C2—122no—
792C2—242no—
793C2—481no—
794C2#7622011yescharacteristic
795C2SD16×D1211yescharacteristic
796C2#7967511yescharacteristic
797C2#8067611yescharacteristic
798C2#8067711yescharacteristic
799C2#8188611yescharacteristic
800C2#8190811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1941C2
socleC23×C3C22×D4
prime radical#76220C2
hypercenter#1941D3
hypocenterC3#25410
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

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

NH ≅ G/Ntype
1. C2×#4864C2semidirect
2. C2×#4864C2semidirect
3. C2×#4852C2semidirect
4. C2×#4693C2semidirect
5. #76221C2semidirect
7. C3×#1941C2semidirect
8. #70574C2semidirect
9. C8×(C2×D3)⋊C4C2semidirect
10. #69633C2semidirect
11. #69627C2semidirect
12. #68909C2semidirect
13. #68896C2semidirect
14. #68887C2semidirect
15. #68887C2semidirect
75. #1941D3semidirect
127. C2×#204D4semidirect
149. C3×#106D4semidirect
300. (C2×D3)⋊C4SD16semidirect
390. #106D12semidirect
495. C3×C8#121semidirect
736. C8#895semidirect
790. C3#25410semidirect

Maximal subgroups

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

subgroupindex
C2×#48642
C2×#48522
C2×#46932
#762212
#762202
C3×#19412
#705742
C8×(C2×D3)⋊C42
#696332
#696272
#689092
#688962
#688872
#254103