Finite Group Databasebeta

← #10823494

Subgroups — #10823494

Order 768.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5619C211yesmaximal, characteristic, complemented
2C2×Dic3×D8C211yesmaximal, characteristic, complemented
3#82633C211yesmaximal, 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#70164C211yesmaximal, characteristic, complemented
11#70152C211yesmaximal, characteristic, complemented
12#69934C211yesmaximal, characteristic, complemented
13#69907C211yesmaximal, characteristic, complemented
14#68829C211yesmaximal, characteristic, complemented
15#68780C211yesmaximal, characteristic, complemented
16#23580—31nomaximal, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#940C2211yescharacteristic
21C2×#939—21no—
22C2×#938—21no—
23C2×D4×Dic3C2211yescharacteristic
24C2×D4×Dic3C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×#926C2211yescharacteristic
28#5619—24no—
29#5619—24no—
30C2×#893C2211yescharacteristic
31C2×#890C2211yescharacteristic
32C2×#886—21no—
33C2×#883—21no—
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37#5221—21no—
38#5221C2211yescharacteristic
39#5220—21no—
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45Dic3×D8—24no—
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic
48C2×#818C2211yescharacteristic
49C2×#815C2211yescharacteristic
50C2×C8×Dic3C2211yescharacteristic
51#4984C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#808C2211yescharacteristic
55#4951—21no—
56#4950—21no—
57#4785—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#540—31no—
65C2×#442—31no—
66C2×C4×D8—31no—
67#2324—31no—
68#2059—31no—
69#2041—31no—
70#2034—31no—
71#2033—31no—
72#2025—31no—
73#2011—31no—
74#1999—31no—
75#1999D311yescharacteristic, complemented
76#1762—31no—
77C4×#102—31no—
78#1750—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—
89C22×D12C2311yescharacteristic
90C22×C4×D3—21no—
91C2×C3×D8—22no—
92C2×C3×D8—22no—
93C2×C3×D8—22no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×#121—22no—
97C3×#121—22no—
98C3×#121—22no—
99C3×#121—22no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217D411yescharacteristic
110C2×#217D411yescharacteristic
111#940—22no—
112#940—22no—
113#939—28no—
114#938—28no—
115D4×Dic3—22no—
116D4×Dic3—22no—
117D4×Dic3—22no—
118D4×Dic3D414yescomplemented
119C2×#213—22no—
120C2×#213—22no—
121C2×#213—22no—
122#930—22no—
123#930—22no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126#926—22no—
127#926—22no—
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3D411yescharacteristic
131C2×C4⋊Dic3D411yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3C2311yescharacteristic
138C2×C4×Dic3C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141#893—22no—
142#893D414yescomplemented
143#890—22no—
144#890—22no—
145#886—28no—
146#883—28no—
147C3×#102—22no—
148C3×#102—22no—
149C3×C22⋊C8—22no—
150#832—22no—
151#832—22no—
152#832—22no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#830—22no—
157#821—22no—
158#821—22no—
159#818—22no—
160#815—22no—
161C8×Dic3—22no—
162#809—22no—
163#808—22no—
164C22×D8—31no—
165C22×D8C2×D311yescharacteristic
166#540—64no—
167#540—64no—
168C2×#127—31no—
169C2×#125—31no—
170C2×#123—61no—
171C2×#123—61no—
172C2×#121—31no—
173C2×#121—61no—
174C2×#121—61no—
175C2×#121C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×#117—31no—
181#442—64no—
182C4×D8—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×#102—31no—
186C2×#102—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102C2×D311yescharacteristic
192C2×#102C2×D311yescharacteristic
193C2×C22⋊C8—31no—
194C2×C22⋊C8C2×D311yescharacteristic
195C2×#97—31no—
196C2×C4×C8—31no—
197#390—31no—
198#390—61no—
199#389—31no—
200#388—61no—
201#386—61no—
202#385—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340C2×D311yescharacteristic
209#336—31no—
210#336—31no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C2×C3×D4—24no—
216C2×C3×D4—24no—
217C2×C3×D4—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—81no—
228C2×C3×D4—81no—
229C2×C3×D4—81no—
230C2×C3×D4—81no—
231C2×C3×D4C2×D412yes—
232C2×C3×D4#4112yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C2×#67—24no—
244C2×#67—24no—
245C2×#67—24no—
246C2×#67—81no—
247C2×#67—81no—
248C2×#67—81no—
249C2×#67—81no—
250C2×#67—81no—
251C2×#67—81no—
252C22×Dic3—21no—
253C22×Dic3—24no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—42no—
257C22×Dic3—81no—
258C22×Dic3—81no—
259C22×Dic3—81no—
260C22×Dic3—81no—
261C22×Dic3C2×D411yescharacteristic
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12C2×D412yes—
271C2×C4×D3—24no—
272C2×C4×D3—81no—
273C2×C4×D3—81no—
274C3×D8—28no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8#4112yes—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4C2×D412yes—
284C3×C4⋊C4#4112yes—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—24no—
287#217—24no—
288#217—22no—
289#217—22no—
290#217—42no—
291#217—81no—
292#217—81no—
293#217—81no—
294#213—28no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—24no—
297C4⋊Dic3—24no—
298C4⋊Dic3—21no—
299C4⋊Dic3—22no—
300C4⋊Dic3—22no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—81no—
306C4⋊Dic3C2×D412yes—
307Dic3⋊C4—24no—
308C4×Dic3—21no—
309C4×Dic3—21no—
310C4×Dic3—81no—
311C4×Dic3C2×D412yes—
312C4×Dic3C2×D412yes—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8#4112yes—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—31no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4C22×D311yescharacteristic
326C22×D4C22×D311yescharacteristic
327C23×C4—61no—
328C23×C4—61no—
329C23×C4—61no—
330C23×C4C22×D311yescharacteristic
331C2×D8—22no—
332C2×D8—22no—
333C2×D8—22no—
334C2×D8—62no—
335C2×D8—62no—
336C2×D8—62no—
337C22×C8—31no—
338C22×C8—31no—
339C22×C8C22×D311yescharacteristic
340C22×C8C22×D311yescharacteristic
341#127—62no—
342#127—62no—
343#125—62no—
344#125—62no—
345#123—68no—
346#123—68no—
347#121—22no—
348#121—22no—
349#121—22no—
350#121—22no—
351#121—62no—
352#121—62no—
353#121—68no—
354#121—68no—
355C4×D4—34no—
356C4×D4—34no—
357C4×D4—62no—
358C4×D4—62no—
359C4×D4—62no—
360C4×D4—62no—
361#117—62no—
362#117—62no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—31no—
376C2×C22⋊C4—31no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C42—31no—
385C2×C42—31no—
386C2×C42—61no—
387#107—62no—
388#106—62no—
389#102—22no—
390#102—22no—
391#102—62no—
392#102—62no—
393#102—62no—
394#102—62no—
395#102—62no—
396#102—62no—
397C22⋊C8—22no—
398C22⋊C8—62no—
399#97—62no—
400C4×C8—62no—
401#95—61no—
402#95—61no—
403#95—61no—
404C23×C3—21no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3C22×D411yescharacteristic
426C22×D3—22no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C3×D4—22no—
434C3×D4—22no—
435C3×D4—22no—
436C3×D4—22no—
437C3×D4—41no—
438C3×D4—41no—
439C3×D4—41no—
440C3×D4—41no—
441C3×D4—84no—
442C3×D4—84no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—21no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462#67—84no—
463#67—84no—
464#67—84no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—84no—
485C2×Dic3—84no—
486C2×Dic3#12012yes—
487C2×Dic3#12012yes—
488D12—22no—
489D12—22no—
490D12—41no—
491D12—41no—
492C4×D3—84no—
493C3×C8—22no—
494C3×C8—41no—
495C3⋊C8—22no—
496C3⋊C8—41no—
497C24—21no—
498C24—21no—
499C24—61no—
500C24D3×D411yescharacteristic
501C2×D4—24no—
502C2×D4—24no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—32no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4—64no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—81no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4—241no—
527C2×D4—241no—
528C2×D4—241no—
529C2×D4—241no—
530C2×D4—241no—
531C2×D4—241no—
532C2×D4D3×D412yes—
533C2×D4#23712yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—64no—
547C22×C4—64no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—122no—
552C22×C4—241no—
553C22×C4—241no—
554C22×C4—241no—
555C22×C4—241no—
556C22×C4—241no—
557C22×C4—241no—
558C22×C4D3×D411yescharacteristic
559C22×C4C23×D311yescharacteristic
560D8—28no—
561D8—68no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—32no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8#23712yes—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—32no—
577C4⋊C4—62no—
578C4⋊C4—62no—
579C4⋊C4—64no—
580C4⋊C4—64no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—241no—
587C4⋊C4D3×D412yes—
588C4⋊C4#23712yes—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—64no—
592C22⋊C4—64no—
593C22⋊C4—62no—
594C22⋊C4—62no—
595C22⋊C4—64no—
596C22⋊C4—122no—
597C22⋊C4—241no—
598C22⋊C4—241no—
599C22⋊C4—241no—
600C42—32no—
601C42—32no—
602C42—61no—
603C42—61no—
604C42—241no—
605C22×C3—41no—
606C22×C3—42no—
607C22×C3—41no—
608C22×C3—42no—
609C22×C3—41no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—42no—
615C22×C3—41no—
616C22×C3—42no—
617C22×C3—41no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3C2×#12011yescharacteristic
627C22×C3#52511yescharacteristic
628C22×C3#53211yescharacteristic
629C22×C3#57611yescharacteristic
630C22×C3#57611yescharacteristic
631C22×C3#57611yescharacteristic
632C22×C3#57711yescharacteristic
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C3×C4—42no—
641C3×C4—41no—
642C3×C4—42no—
643C3×C4#52511yescharacteristic
644C3×C4#52511yescharacteristic
645C3×C4#53211yescharacteristic
646C3×C4#53211yescharacteristic
647Dic3—22no—
648Dic3—22no—
649Dic3—41no—
650Dic3—42no—
651Dic3—41no—
652Dic3—81no—
653Dic3—81no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—21no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—62no—
676C23—121no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23C2×D3×D411yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—62no—
692D4—62no—
693D4—84no—
694D4—84no—
695D4—121no—
696D4—121no—
697D4—244no—
698D4—244no—
699D4—244no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—62no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—244no—
735C2×C4—244no—
736C2×C4—244no—
737C2×C4C2×D3×D411yescharacteristic
738C2×C4C2×D3×D411yescharacteristic
739C2×C4C2×#23711yescharacteristic
740C2×C4C2×#23711yescharacteristic
741C2×C4C2×#23711yescharacteristic
742C2×C4D3×#4111yescharacteristic
743C8—22no—
744C8—41no—
745C8—62no—
746C8—121no—
747C2×C3—81no—
748C2×C3—82no—
749C2×C3—82no—
750C2×C3#238811yescharacteristic
751C2×C3#300811yescharacteristic
752C2×C3#301211yescharacteristic
753C2×C3#311911yescharacteristic
754C2×C3#312211yescharacteristic
755C2×C3#317611yescharacteristic
756C2×C3#317911yescharacteristic
757D3—82no—
758C22—41no—
759C22—41no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—122no—
780C22—122no—
781C22—122no—
782C22—241no—
783C22—241no—
784C22—241no—
785C22—241no—
786C22#558611yescharacteristic
787C22D3×#12011yescharacteristic
788C22#559611yescharacteristic
789C22#575711yescharacteristic
790C22#576911yescharacteristic
791C22#577411yescharacteristic
792C22#577511yescharacteristic
793C4—41no—
794C4—42no—
795C4—42no—
796C4—62no—
797C4—62no—
798C4—121no—
799C4—121no—
800C4—122no—
801C4—241no—
802C4—241no—
803C4#558611yescharacteristic
804C4#559611yescharacteristic
805C4#560611yescharacteristic
806C4#571611yescharacteristic
807C3#2358011yescharacteristic, complemented, Sylow
808C2—81no—
809C2—82no—
810C2—82no—
811C2—242no—
812C2#7666511yescharacteristic
813C2#7999311yescharacteristic
814C2#8000511yescharacteristic
815C2#8007211yescharacteristic
816C2#8008511yescharacteristic
817C2#8069911yescharacteristic
818C2#8085111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1999C2
socleC23×C3C22×D4
hypercenter#1999D3
hypocenterC3#23580
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×#5619C2semidirect
2. C2×Dic3×D8C2semidirect
3. #82633C2semidirect
4. C2×#4785C2semidirect
5. C3×#1999C2semidirect
6. #72044C2semidirect
7. #71684C2semidirect
8. #71680C2semidirect
9. #70177C2semidirect
10. #70164C2semidirect
11. #70152C2semidirect
12. #69934C2semidirect
13. #69907C2semidirect
14. #68829C2semidirect
15. #68780C2semidirect
75. #1999D3semidirect
118. D4×Dic3D4semidirect
142. #893D4semidirect
807. C3#23580semidirect

Maximal subgroups

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

subgroupindex
C2×#56192
C2×Dic3×D82
#826332
C2×#47852
C3×#19992
#720442
#716842
#716802
#701772
#701642
#701522
#699342
#699072
#688292
#687802
#235803