Finite Group Databasebeta

← #10846320

Subgroups — #10846320

Order 768.

1120 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#469C211yesmaximal, characteristic, complemented
2C2×#5154C211yesmaximal, characteristic, complemented
3C2×#5134C211yesmaximal, characteristic, complemented
4#82648C211yesmaximal, characteristic, complemented
5#82646C211yesmaximal, characteristic, complemented
6C2×#4852C211yesmaximal, characteristic, complemented
7#72038C211yesmaximal, characteristic, complemented
8#71983C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#71684C211yesmaximal, characteristic, complemented
11#70562C211yesmaximal, characteristic, complemented
12#70213C211yesmaximal, characteristic, complemented
13#70208C211yesmaximal, characteristic, complemented
14#70178C211yesmaximal, characteristic, complemented
15#70177C211yesmaximal, characteristic, complemented
16#25416—31nomaximal, Sylow
17C22×C3×D8C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#940C2211yescharacteristic
22C2×#938—21no—
23C2×#936C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×#204C2211yescharacteristic
29C2×#893C2211yescharacteristic
30C2×#887C2211yescharacteristic
31C3×#469—24no—
32C2×C3×#106C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35#5223—21no—
36#5222—21no—
37#5221—21no—
38#5221C2211yescharacteristic
39#5221C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C4×#217C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5154—24no—
45#5134—24no—
46C2×#821C2211yescharacteristic
47C2×#818C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#815C2211yescharacteristic
50C2×C8×Dic3C2211yescharacteristic
51#4984C2211yescharacteristic
52#4984C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#809C2211yescharacteristic
55#4961—21no—
56#4956—21no—
57#4948—21no—
58#4944—21no—
59#4852—24no—
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#496—31no—
65C2×#469D311yescharacteristic, complemented
66C2×#468—31no—
67C2×C4×SD16—31no—
68#2428—31no—
69#2426—31no—
70#2042—31no—
71#2041—31no—
72#2000—31no—
73#1999—31no—
74#1970—31no—
75#1944—31no—
76#1880—31no—
77#1879—31no—
78#1753—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×Dic6C2311yescharacteristic
90C2×C3×D8—22no—
91C2×C3×D8—22no—
92C2×C3×D8—22no—
93C2×C3×M16—22no—
94C2×C3×M16—22no—
95C2×C3×M16—22no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×#121—22no—
99C3×#121—22no—
100C3×#121—41no—
101C3×#121—41no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217D411yescharacteristic
114C2×#217D411yescharacteristic
115#940—22no—
116#940—41no—
117#938—44no—
118#936—22no—
119#936—41no—
120C2×#214—22no—
121C2×#214—22no—
122C2×#214—41no—
123C2×#213—22no—
124C2×#213—22no—
125C2×#213—41no—
126#930—22no—
127#930—41no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134#924—22no—
135#924—41no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×C4×Dic3—21no—
139C2×C4×Dic3C2311yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×#204—22no—
144C2×#204—22no—
145C2×#204D414yescomplemented
146#893—22no—
147#893—41no—
148#887—22no—
149#887—41no—
150C3×#106D414yescomplemented
151C3×#102—22no—
152C3×#102—22no—
153#832—41no—
154#832—41no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95D411yescharacteristic
158C3⋊#95D411yescharacteristic
159#830—22no—
160#821—22no—
161#818—22no—
162#816—22no—
163#815—22no—
164C8×Dic3—22no—
165#810—22no—
166#809—22no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×D8—31no—
170C22×D8C2×D311yescharacteristic
171C22×M16C2×D311yescharacteristic
172C2×#127—31no—
173C2×#124—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—61no—
177C2×#121C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×Q8—31no—
180C2×C4×D4—31no—
181#496—64no—
182#469—24no—
183#468—64no—
184C4×SD16—64no—
185C2×#107—31no—
186C2×#106C2×D311yescharacteristic
187C2×#103—31no—
188C2×#103—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102C2×D311yescharacteristic
194C2×#102C2×D311yescharacteristic
195C2×C22⋊C8—31no—
196C2×#97—31no—
197C2×C4×C8—31no—
198#396—61no—
199#394—61no—
200#394—61no—
201#392—61no—
202#390—31no—
203#390—31no—
204#390—61no—
205#389—31no—
206#389—31no—
207#388—61no—
208#386—61no—
209C4×C22⋊C4—31no—
210#340—31no—
211#340—31no—
212#336—31no—
213#336—31no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3C2×D411yescharacteristic
217C23×D3—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
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—42no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—81no—
235C2×C3×D4—81no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2411yescharacteristic
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—81no—
253C2×#67—81no—
254C2×#67—81no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3C2×D411yescharacteristic
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12C2×D412yes—
268C2×C4×D3—42no—
269C2×C4×D3—42no—
270C2×C4×D3—81no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6C2×D412yes—
277C3×D8—44no—
278C3×M16—44no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8C2×D412yes—
283C2×C3×C8C2×D412yes—
284C2×C3×C8#4112yes—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4C2×D412yes—
288C3×C4⋊C4C2×D412yes—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291#217—22no—
292#217—41no—
293#217—42no—
294#217—42no—
295#217—42no—
296#217—42no—
297#217—42no—
298#217—81no—
299#217—81no—
300#214—44no—
301#213—44no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—42no—
309C4⋊Dic3—81no—
310Dic3⋊C4—42no—
311Dic3⋊C4—42no—
312C4×Dic3—21no—
313C4×Dic3—21no—
314C4×Dic3—21no—
315C4×Dic3—21no—
316C4×Dic3—42no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8#4112yes—
323#204—28no—
324C22×Q8—31no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4C22×D311yescharacteristic
332C22×D4C22×D311yescharacteristic
333C23×C4—61no—
334C23×C4C22×D311yescharacteristic
335C2×SD16—34no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—121no—
341C2×D8—22no—
342C2×D8—22no—
343C2×D8—22no—
344C2×D8—62no—
345C2×D8—62no—
346C2×D8—121no—
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—22no—
350C22×C8—31no—
351C22×C8—31no—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354#127—62no—
355#127—121no—
356#124—62no—
357#124—121no—
358C22⋊Q8—62no—
359C22⋊Q8—121no—
360#121—22no—
361#121—22no—
362#121—41no—
363#121—41no—
364#121—62no—
365#121—124no—
366#121—121no—
367C4×Q8—62no—
368C4×Q8—121no—
369C4×D4—62no—
370C4×D4—121no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
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×C42—31no—
393C2×C42—31no—
394C2×C42—61no—
395#107—62no—
396#106#6714yescomplemented
397#103—62no—
398#103—62no—
399#102—22no—
400#102—22no—
401#102—62no—
402#102—62no—
403#102—121no—
404#102—121no—
405C22⋊C8—62no—
406#97—62no—
407C4×C8—62no—
408#95—31no—
409#95—31no—
410#95—61no—
411#95—61no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3C22×D411yescharacteristic
434C22×D3—22no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—84no—
450C3×D4—84no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4H(5,𝔽2)11yescharacteristic
469C2×C3×C4H(5,𝔽2)11yescharacteristic
470#67—84no—
471#67—84no—
472#67—84no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
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×Dic3AGL(1,ℤ/8)12yes—
494D12—22no—
495D12—22no—
496D12—41no—
497D12—41no—
498C4×D3—84no—
499Dic6—22no—
500Dic6—22no—
501Dic6—41no—
502Dic6—41no—
503C3×C8—41no—
504C3×C8#12114yescomplemented
505C3⋊C8—22no—
506C3⋊C8—41no—
507C24—21no—
508C24—21no—
509C24—61no—
510C24D3×D411yescharacteristic
511C2×Q8—32no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—32no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4—61no—
538C2×D4—61no—
539C2×D4—81no—
540C2×D4—81no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—122no—
547C2×D4—241no—
548C2×D4—241no—
549C2×D4—241no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—122no—
566C22×C4—122no—
567C22×C4—241no—
568C22×C4D3×D411yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—68no—
571SD16—124no—
572D8—44no—
573D8—124no—
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—32no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8D3×D412yes—
585C2×C8#23712yes—
586C2×C8C2×#6712yes—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—122no—
594C4⋊C4—122no—
595C4⋊C4—122no—
596C4⋊C4—241no—
597C4⋊C4C2×#6712yes—
598C4⋊C4C2×#6712yes—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—62no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—121no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—241no—
611C22⋊C4—241no—
612C42—61no—
613C42—61no—
614C42—61no—
615C42—61no—
616C42—122no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3#53211yescharacteristic
639C22×C3D4211yescharacteristic
640C22×C3D4211yescharacteristic
641C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
642C22×C3#57511yescharacteristic
643C22×C3#57611yescharacteristic
644C22×C3#57711yescharacteristic
645C2×D3—42no—
646C2×D3—42no—
647C2×D3—42no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C3×C4—41no—
653C3×C4—42no—
654C3×C4—42no—
655C3×C4C2×#12111yescharacteristic
656C3×C4#54011yescharacteristic
657C3×C4#54611yescharacteristic
658C3×C4#55011yescharacteristic
659Dic3—22no—
660Dic3—42no—
661Dic3—41no—
662Dic3—41no—
663Dic3—41no—
664Dic3—81no—
665Dic3—81no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—62no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23C2×D3×D411yescharacteristic
695Q8—62no—
696Q8—62no—
697Q8—121no—
698Q8—121no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—62no—
708D4—62no—
709D4—84no—
710D4—84no—
711D4—121no—
712D4—121no—
713D4—244no—
714D4—244no—
715D4—244no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—32no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—62no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—244no—
751C2×C4C2×D3×D411yescharacteristic
752C2×C4C2×#23711yescharacteristic
753C2×C4#100411yescharacteristic
754C2×C4D3×#4111yescharacteristic
755C2×C4#100911yescharacteristic
756C2×C4C22×#6711yescharacteristic
757C8—41no—
758C8—62no—
759C8—121no—
760C8#93814yescomplemented
761C2×C3—81no—
762C2×C3—161no—
763C2×C3—161no—
764C2×C3#242811yescharacteristic
765C2×C3#317111yescharacteristic
766C2×C3#317911yescharacteristic
767C2×C3#326511yescharacteristic
768C2×C3#326811yescharacteristic
769C2×C3#327411yescharacteristic
770C2×C3#327511yescharacteristic
771D3—82no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—122no—
794C22—122no—
795C22—122no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22#559611yescharacteristic
801C22#560911yescharacteristic
802C22D3×AGL(1,ℤ/8)11yescharacteristic
803C22#577311yescharacteristic
804C22#577411yescharacteristic
805C22#577511yescharacteristic
806C22D4×#6711yescharacteristic
807C4—41no—
808C4—42no—
809C4—42no—
810C4—62no—
811C4—122no—
812C4—121no—
813C4—121no—
814C4—121no—
815C4—241no—
816C4—241no—
817C4#561211yescharacteristic
818C4#561911yescharacteristic
819C4C2×#93811yescharacteristic
820C4#583411yescharacteristic
821C3#2541611yescharacteristic, complemented, Sylow
822C2—81no—
823C2—161no—
824C2—161no—
825C2—242no—
826C2#8084811yescharacteristic
827C2#8085111yescharacteristic
828C2#8088211yescharacteristic
829C2#8088311yescharacteristic
830C2#8264811yescharacteristic
831C2#8395311yescharacteristic
832C2#8395511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#469C2
socleC23×C3C22×D4
hypercenterC2×#469D3
hypocenterC3#25416
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×C3×#469C2semidirect
2. C2×#5154C2semidirect
3. C2×#5134C2semidirect
4. #82648C2semidirect
5. #82646C2semidirect
6. C2×#4852C2semidirect
7. #72038C2semidirect
8. #71983C2semidirect
9. #71685C2semidirect
10. #71684C2semidirect
11. #70562C2semidirect
12. #70213C2semidirect
13. #70208C2semidirect
14. #70178C2semidirect
15. #70177C2semidirect
65. C2×#469D3semidirect
145. C2×#204D4semidirect
150. C3×#106D4semidirect
396. #106#67semidirect
504. C3×C8#121semidirect
760. C8#938semidirect
821. C3#25416semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4692
C2×#51542
C2×#51342
#826482
#826462
C2×#48522
#720382
#719832
#716852
#716842
#705622
#702132
#702082
#701782
#701772
#254163