Finite Group Databasebeta

← #10823405

Subgroups — #10823405

Order 768.

1508 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5596C211yesmaximal, characteristic, complemented
2C2×#5152C211yesmaximal, characteristic, complemented
3Dic3×#121C211yesmaximal, characteristic, complemented
4C2×#4785C211yesmaximal, characteristic, complemented
5C3×#1999C211yesmaximal, characteristic, complemented
6#72044C211yesmaximal, characteristic, complemented
7#71684C211yesmaximal, characteristic, complemented
8#71680C211yesmaximal, characteristic, complemented
9#70177C211yesmaximal, characteristic, complemented
10#70163C211yesmaximal, characteristic, complemented
11#70152C211yesmaximal, characteristic, complemented
12#69935C211yesmaximal, characteristic, complemented
13#69906C211yesmaximal, characteristic, complemented
14#68827C211yesmaximal, characteristic, complemented
15#68782C211yesmaximal, characteristic, complemented
16#23573—31nomaximal, Sylow
17C22×#237—21no—
18C22×C3×D8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#940C2211yescharacteristic
22C2×#939—21no—
23C2×D4×Dic3—21no—
24C2×D4×Dic3C2211yescharacteristic
25C2×D4×Dic3C2211yescharacteristic
26C22×#213C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29#5596—24no—
30#5596—24no—
31C2×#893C2211yescharacteristic
32C2×#888C2211yescharacteristic
33C2×#885—21no—
34C2×#67⋊C4—21no—
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38#5221C2211yescharacteristic
39#5220—21no—
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45#5152—24no—
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic
48C2×#817C2211yescharacteristic
49C2×#815C2211yescharacteristic
50C2×#815C2211yescharacteristic
51#4984C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#808C2211yescharacteristic
55#4951—21no—
56Dic3×C22⋊C4—21no—
57#4785—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#532—31no—
65C2×#442—31no—
66C2×#442—31no—
67C4×#121—31no—
68#2058—31no—
69#2041—31no—
70#2034—31no—
71#2034—31no—
72#2023—31no—
73#2011—31no—
74#1999—31no—
75#1999D311yescharacteristic, complemented
76#1762—31no—
77#1762—31no—
78#1749—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—
87C23×Dic3—21no—
88C23×Dic3—21no—
89C23×Dic3D411yescharacteristic
90C23×Dic3D411yescharacteristic
91C2×#237—28no—
92C2×#237—44no—
93C2×#237—44no—
94C22×D12C2311yescharacteristic
95C22×C4×D3—21no—
96C22×Dic6—21no—
97C2×C3×D8—22no—
98C2×C3×D8—22no—
99C2×C3×D8—22no—
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C3×#121—22no—
103C3×#121—22no—
104C3×#121—22no—
105C3×#121—22no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115#940—22no—
116#940—22no—
117#939—28no—
118D4×Dic3—22no—
119D4×Dic3—22no—
120D4×Dic3—22no—
121D4×Dic3—44no—
122D4×Dic3D414yescomplemented
123C2×#213—22no—
124C2×#213—22no—
125C2×#213—22no—
126#930—22no—
127#930—22no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×C4×Dic3—22no—
136C2×C4×Dic3—22no—
137C2×C4×Dic3—21no—
138C2×C4×Dic3D411yescharacteristic
139C2×C4×Dic3D411yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C2×C4×Dic3C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144#893—22no—
145#893D414yescomplemented
146#888—22no—
147#888—22no—
148#885—28no—
149#67⋊C4—28no—
150C3×#102—22no—
151C3×#102—22no—
152C3×C22⋊C8—22no—
153#832—22no—
154#832—22no—
155#832—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#830—22no—
160#821—22no—
161#821—22no—
162#817—22no—
163#815—22no—
164#815—22no—
165#809—22no—
166#808—22no—
167C22×#41—61no—
168C22×D8—31no—
169C22×D8C2×D311yescharacteristic
170#532—64no—
171#532—64no—
172C2×C4⋊Q8—31no—
173C2×#127—31no—
174C2×#124—61no—
175C2×#121—31no—
176C2×#121—61no—
177C2×#121C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×D4—31no—
180C2×C4×D4—31no—
181C2×C4×D4—31no—
182C2×C4×D4—61no—
183C2×C4×D4—61no—
184C22×C42—31no—
185#442—64no—
186#442—64no—
187C2×#106—31no—
188C2×#106—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102C2×D311yescharacteristic
196C2×#102C2×D311yescharacteristic
197C2×C22⋊C8—31no—
198C2×C22⋊C8C2×D311yescharacteristic
199C2×#97—31no—
200C2×#97—31no—
201#390—31no—
202#389—31no—
203#388—61no—
204#386—61no—
205#380—31no—
206C4×C4⋊C4—31no—
207C4×C22⋊C4—61no—
208#340—31no—
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#336—31no—
213#336—31no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3C2×D411yescharacteristic
217C23×D3—21no—
218C2×C3×D4—24no—
219C2×C3×D4—24no—
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×D4C2×D412yes—
235C2×C3×D4#4112yescomplemented
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—24no—
247C2×#67—24no—
248C2×#67—24no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—21no—
259C22×Dic3—24no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—41no—
265C22×Dic3—42no—
266C22×Dic3—42no—
267C22×Dic3—42no—
268C22×Dic3—42no—
269C22×Dic3—42no—
270C22×Dic3C2×D411yescharacteristic
271C22×Dic3C2×D411yescharacteristic
272C22×Dic3C2×D411yescharacteristic
273C22×Dic3C2×D411yescharacteristic
274#237—432no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12C2×D412yes—
281C2×C4×D3—24no—
282C2×C4×D3—42no—
283C2×C4×D3—42no—
284C2×Dic6—24no—
285C2×Dic6—42no—
286C2×Dic6—42no—
287C3×D8—28no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8#4112yescomplemented
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4C2×D412yes—
297C3×C4⋊C4#4112yescomplemented
298C3×C22⋊C4—24no—
299C3×C22⋊C4—24no—
300#217—24no—
301#217—42no—
302#217—42no—
303#217—42no—
304#217—42no—
305#213—28no—
306(C2×D3)⋊C4—24no—
307(C2×D3)⋊C4—24no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—42no—
314C4⋊Dic3C2×D412yes—
315Dic3⋊C4—24no—
316C4×Dic3—21no—
317C4×Dic3—21no—
318C4×Dic3—22no—
319C4×Dic3—22no—
320C4×Dic3—42no—
321C4×Dic3C2×D412yes—
322C4×Dic3C2×D412yes—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8#4112yescomplemented
329C2×#41—68no—
330C2×#41—124no—
331C2×#41—124no—
332C22×Q8—61no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—31no—
336C22×D4—61no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4C22×D311yescharacteristic
340C22×D4C22×D311yescharacteristic
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—61no—
344C23×C4—61no—
345C23×C4—61no—
346C23×C4C22×D311yescharacteristic
347C2×D8—22no—
348C2×D8—22no—
349C2×D8—22no—
350C2×D8—62no—
351C2×D8—62no—
352C2×D8—62no—
353C22×C8—31no—
354C22×C8—31no—
355C22×C8C22×D311yescharacteristic
356C22×C8C22×D311yescharacteristic
357C4⋊Q8—62no—
358C4⋊Q8—62no—
359#127—62no—
360#127—62no—
361#124—68no—
362#121—22no—
363#121—22no—
364#121—22no—
365#121—22no—
366#121—62no—
367#121—62no—
368#121—68no—
369C4×D4—34no—
370C4×D4—34no—
371C4×D4—62no—
372C4×D4—62no—
373C4×D4—62no—
374C4×D4—62no—
375C4×D4—68no—
376C4×D4—124no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4C22×D311yescharacteristic
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
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⋊C4—61no—
393C2×C42—31no—
394C2×C42—31no—
395C2×C42—31no—
396C2×C42—31no—
397C2×C42—62no—
398C2×C42—62no—
399C2×C42—61no—
400#106—62no—
401#106—62no—
402#102—22no—
403#102—22no—
404#102—62no—
405#102—62no—
406#102—62no—
407#102—62no—
408#102—62no—
409#102—62no—
410C22⋊C8—22no—
411C22⋊C8—62no—
412#97—62no—
413#97—62no—
414#95—61no—
415#95—61no—
416#95—61no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—22no—
424C23×C3—22no—
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×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3AGL(1,ℤ/8)12yes—
438C23×C3C22×D411yescharacteristic
439C22×D3—22no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—22no—
449C3×D4—22no—
450C3×D4—48no—
451C3×D4—48no—
452C3×D4—41no—
453C3×D4—41no—
454C3×D4—41no—
455C3×D4—41no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C22×D411yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4C2×#4111yescharacteristic
473C2×C3×C4C2×#4111yescharacteristic
474C2×C3×C4C2×#4111yescharacteristic
475#67—48no—
476#67—48no—
477#67—48no—
478C2×Dic3—28no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—22no—
488C2×Dic3—44no—
489C2×Dic3—48no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—84no—
499C2×Dic3#12012yes—
500C2×Dic3#12012yes—
501C2×Dic3AGL(1,ℤ/8)12yes—
502C2×Dic3AGL(1,ℤ/8)12yes—
503D12—22no—
504D12—22no—
505D12—41no—
506D12—41no—
507C4×D3—48no—
508Dic6—48no—
509C3×C8—22no—
510C3×C8—41no—
511C3⋊C8—22no—
512C3⋊C8—41no—
513C24—21no—
514C24—21no—
515C24—61no—
516C24D3×D411yescharacteristic
517#41—1232no—
518C2×Q8—64no—
519C2×Q8—122no—
520C2×Q8—122no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—32no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—64no—
539C2×D4—64no—
540C2×D4—64no—
541C2×D4—61no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—122no—
549C2×D4—122no—
550C2×D4—122no—
551C2×D4—122no—
552C2×D4D3×D412yes—
553C2×D4#23712yescomplemented
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—64no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—64no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—122no—
577C22×C4—122no—
578C22×C4—122no—
579C22×C4—121no—
580C22×C4—122no—
581C22×C4—122no—
582C22×C4—122no—
583C22×C4—122no—
584C22×C4D3×D411yescharacteristic
585C22×C4C23×D311yescharacteristic
586D8—28no—
587D8—68no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—32no—
594C2×C8—61no—
595C2×C8—61no—
596C2×C8—61no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8#23712yescomplemented
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—32no—
603C4⋊C4—64no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—122no—
610C4⋊C4D3×D412yes—
611C4⋊C4#23712yescomplemented
612C22⋊C4—24no—
613C22⋊C4—24no—
614C22⋊C4—64no—
615C22⋊C4—64no—
616C22⋊C4—64no—
617C22⋊C4—122no—
618C22⋊C4—122no—
619C22⋊C4—122no—
620C22⋊C4—122no—
621C42—32no—
622C42—32no—
623C42—62no—
624C42—62no—
625C42—61no—
626C42—61no—
627C42—122no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3C2×#12011yescharacteristic
650C22×C3#52511yescharacteristic
651C22×C3#53211yescharacteristic
652C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
653C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
654C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
655C22×C3#57511yescharacteristic
656C2×D3—42no—
657C2×D3—42no—
658C2×D3—42no—
659C2×D3—81no—
660C2×D3—81no—
661C2×D3—81no—
662C2×D3—81no—
663C3×C4—42no—
664C3×C4—41no—
665C3×C4—42no—
666C3×C4#52511yescharacteristic
667C3×C4#52511yescharacteristic
668C3×C4#53211yescharacteristic
669C3×C4#53211yescharacteristic
670Dic3—22no—
671Dic3—22no—
672Dic3—22no—
673Dic3—22no—
674Dic3—42no—
675Dic3—81no—
676Dic3—81no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—22no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—62no—
698C23—121no—
699C23—121no—
700C23—121no—
701C23—121no—
702C23—121no—
703C23—121no—
704C23#91112yes—
705C23C2×D3×D411yescharacteristic
706Q8—128no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—48no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—62no—
718D4—62no—
719D4—128no—
720D4—128no—
721D4—128no—
722D4—121no—
723D4—121no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—68no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—62no—
751C2×C4—128no—
752C2×C4—124no—
753C2×C4—128no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—244no—
763C2×C4C2×D3×D411yescharacteristic
764C2×C4C2×D3×D411yescharacteristic
765C2×C4C2×#23711yescharacteristic
766C2×C4C2×#23711yescharacteristic
767C2×C4C2×#23711yescharacteristic
768C2×C4D3×#4111yescharacteristic
769C8—22no—
770C8—41no—
771C8—62no—
772C8—121no—
773C2×C3—42no—
774C2×C3—82no—
775C2×C3—82no—
776C2×C3#238811yescharacteristic
777C2×C3#300311yescharacteristic
778C2×C3#300611yescharacteristic
779C2×C3#310911yescharacteristic
780C2×C3#311511yescharacteristic
781C2×C3#318011yescharacteristic
782C2×C3#318411yescharacteristic
783D3—82no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—122no—
806C22—122no—
807C22—122no—
808C22—241no—
809C22—241no—
810C22—241no—
811C22—241no—
812C22#558611yescharacteristic
813C22D3×#12011yescharacteristic
814C22#559611yescharacteristic
815C22C2×#91111yescharacteristic
816C22#576811yescharacteristic
817C22D3×AGL(1,ℤ/8)11yescharacteristic
818C22D3×AGL(1,ℤ/8)11yescharacteristic
819C4—42no—
820C4—41no—
821C4—42no—
822C4—62no—
823C4—62no—
824C4—62no—
825C4—62no—
826C4—122no—
827C4—241no—
828C4—241no—
829C4#558611yescharacteristic
830C4#559611yescharacteristic
831C4#560611yescharacteristic
832C4#571611yescharacteristic
833C3#2357311yescharacteristic, complemented, Sylow
834C2—42no—
835C2—82no—
836C2—82no—
837C2—242no—
838C2#7666511yescharacteristic
839C2#7999011yescharacteristic
840C2#8000211yescharacteristic
841C2#8007111yescharacteristic
842C2#8008411yescharacteristic
843C2#8070111yescharacteristic
844C2#8085311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1999C2
socleC23×C3C22×D4
hypercenter#1999D3
hypocenterC3#23573
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1999

Complements

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

NH ≅ G/Ntype
1. C2×#5596C2semidirect
2. C2×#5152C2semidirect
3. Dic3×#121C2semidirect
4. C2×#4785C2semidirect
5. C3×#1999C2semidirect
6. #72044C2semidirect
7. #71684C2semidirect
8. #71680C2semidirect
9. #70177C2semidirect
10. #70163C2semidirect
11. #70152C2semidirect
12. #69935C2semidirect
13. #69906C2semidirect
14. #68827C2semidirect
15. #68782C2semidirect
75. #1999D3semidirect
122. D4×Dic3D4semidirect
145. #893D4semidirect
235. C2×C3×D4#41semidirect
293. C2×C3×C8#41semidirect
297. C3×C4⋊C4#41semidirect
328. C2×C3⋊C8#41semidirect
553. C2×D4#237semidirect
599. C2×C8#237semidirect
611. C4⋊C4#237semidirect
833. C3#23573semidirect

Maximal subgroups

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

subgroupindex
C2×#55962
C2×#51522
Dic3×#1212
C2×#47852
C3×#19992
#720442
#716842
#716802
#701772
#701632
#701522
#699352
#699062
#688272
#687822
#235733