Finite Group Databasebeta

← #10800905

Subgroups — #10800905

Order 768.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5545C211yesmaximal, characteristic, complemented
2C2×#4872C211yesmaximal, characteristic, complemented
3C2×#4773C211yesmaximal, characteristic
4C2×#4785C211yesmaximal, characteristic, complemented
5#76198C211yesmaximal, characteristic, complemented
6C3×#1862C211yesmaximal, characteristic, complemented
7#71613C211yesmaximal, characteristic, complemented
8#70633C211yesmaximal, characteristic, complemented
9#70198C211yesmaximal, characteristic, complemented
10Dic3×#102C211yesmaximal, characteristic, complemented
11#69626C211yesmaximal, characteristic, complemented
12#68881C211yesmaximal, characteristic, complemented
13#68782C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68601C211yesmaximal, characteristic, complemented
16#21458—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×D4×Dic3C2211yescharacteristic
20C22×#213C2211yescharacteristic
21C2×C4×#67—21no—
22C22×(C2×D3)⋊C4—21no—
23C22×D24C2211yescharacteristic
24#5545—24no—
25#5545—24no—
26C2×#895C2211yescharacteristic
27C2×#893C2211yescharacteristic
28C2×#893C2211yescharacteristic, complemented
29C2×#892C2211yescharacteristic
30C2×#67⋊C4—21no—
31C2×D3×C22⋊C4—21no—
32C2×C4×D12C2211yescharacteristic
33C2×#872C2211yescharacteristic
34C2×C3×#107C2211yescharacteristic, complemented
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C3×#389C2211yescharacteristic, complemented
38C2×#832C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic, complemented
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#815C2211yescharacteristic, complemented
44C2×C8×Dic3C2211yescharacteristic, complemented
45#4989—21no—
46#4988—21no—
47#4987C2211yescharacteristic
48Dic3×C4⋊C4C2211yescharacteristic, complemented
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic, complemented
52C2×#808C2211yescharacteristic, complemented
53#4939C2211yescharacteristic, complemented
54#4872—24no—
55#4785—24no—
56#4773C418yescomplemented
57#4669—21no—
58#4665—21no—
59C3×#340C2211yescharacteristic, complemented
60C3×#336C2211yescharacteristic, complemented
61#4551C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64#4524C2211yescharacteristic, complemented
65C2×#518—31no—
66C2×#447—31no—
67C2×#442—31no—
68C2×C4×D8—31no—
69#2324—31no—
70#1879—31no—
71#1879—31no—
72#1875—31no—
73#1864—31no—
74#1862D311yescharacteristic, complemented
75#1854—31no—
76#1786—31no—
77#1762—31no—
78C4×#102—31no—
79#1750—31no—
80C24×D3—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C22×#67—21no—
84C23×Dic3—21no—
85C2×D3×D4—22no—
86C2×D3×D4—22no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4C2×C414yescomplemented
91C22×D12—21no—
92C22×D12C2311yescharacteristic
93C22×D12C2311yescharacteristic
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×C4×D3C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C42C2311yescharacteristic
108C2×#217—21no—
109D4×Dic3—22no—
110D4×Dic3D414yescomplemented
111C2×#213—22no—
112C2×#213—22no—
113C2×#213C2×C414yescomplemented
114C4×#67—28no—
115C2×(C2×D3)⋊C4—28no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4D411yescharacteristic
125C2×(C2×D3)⋊C4D411yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×Dic3⋊C4D411yescharacteristic
129C2×Dic3⋊C4D411yescharacteristic
130C2×C4×Dic3—21no—
131C2×C4×Dic3—21no—
132C2×C4×Dic3C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C2×D24—22no—
136C2×D24—22no—
137C2×D24C2×C414yescomplemented
138#895—22no—
139#895C2×C414yescomplemented
140#893—22no—
141#893—22no—
142#893—22no—
143#893D414yescomplemented
144#892—22no—
145#892—22no—
146#67⋊C4—28no—
147D3×C22⋊C4—28no—
148C4×D12—22no—
149C4×D12—22no—
150#872—22no—
151#872—22no—
152C3×#107—22no—
153C3×#102—22no—
154C3×#102C2×C414yescomplemented
155C3×#95—21no—
156#832—22no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#821—22no—
160#821—22no—
161(C2×D3)⋊C8—22no—
162(C2×D3)⋊C8C2×C414yescomplemented
163#815—22no—
164C8×Dic3—22no—
165#809—22no—
166#809—22no—
167#809C2×C414yescomplemented
168#808—22no—
169C23×D4—31no—
170C22×D8—31no—
171C22×D8—31no—
172C2×#121—31no—
173#518—64no—
174#518—64no—
175C2×C4×D4—31no—
176C2×C4×D4—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—61no—
180C2×C4×D4—61no—
181C2×C4×D4C2×D311yescharacteristic
182C2×#117—31no—
183C2×#117—31no—
184C22×C22⋊C4—61no—
185C22×C22⋊C4—61no—
186#447—38no—
187#442—64no—
188C4×D8—64no—
189C2×#107C2×D311yescharacteristic, complemented
190C2×#106—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102C2×D311yescharacteristic
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×#97—31no—
202C2×C4×C8—31no—
203#390—31no—
204#390—61no—
205#389C2×D311yescharacteristic, complemented
206#388—61no—
207#386—61no—
208#385—61no—
209#380—31no—
210C4×C4⋊C4—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic, complemented
215#336—31no—
216#336C2×D311yescharacteristic, complemented
217C24×C3—21no—
218C23×D3—21no—
219C23×D3—24no—
220C23×D3—24no—
221C23×D3—24no—
222C23×D3—21no—
223C23×D3—81no—
224C23×D3—81no—
225C23×D3—81no—
226C23×D3—81no—
227C23×D3C2×D411yescharacteristic
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4C22×C412yes—
232C2×C3×D4C2×D412yes—
233C2×C3×D4#4112yes—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—24no—
237C22×C3×C4—21no—
238C22×C3×C4—81no—
239C22×C3×C4—81no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C2×#67—24no—
244C2×#67—24no—
245C2×#67—24no—
246C22×Dic3—21no—
247C22×Dic3—24no—
248C22×Dic3—21no—
249C22×Dic3—81no—
250C22×Dic3—81no—
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254D3×D4—28no—
255D3×D4—28no—
256D3×D4—28no—
257D3×D4—28no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—24no—
267C2×D12—81no—
268C2×D12—81no—
269C2×D12C22×C412yes—
270C2×D12C22×C412yes—
271C2×D12C2×D412yes—
272C2×D12#4112yes—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—24no—
278C2×C4×D3—24no—
279C2×C4×D3—42no—
280C2×C4×D3—81no—
281C2×C4×D3—81no—
282C2×C4×D3—81no—
283C2×C4×D3—81no—
284C2×C4×D3—81no—
285C2×C4×D3—81no—
286C2×C4×D3C22×C412yes—
287C2×C4×D3#4112yes—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8C22×C412yes—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—81no—
299C3×C4⋊C4C22×C412yes—
300C3×C4⋊C4C2×D412yes—
301C3×C22⋊C4—24no—
302C3×C42—21no—
303C3×C42—21no—
304#217—24no—
305#213—28no—
306(C2×D3)⋊C4—24no—
307(C2×D3)⋊C4—24no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—22no—
310(C2×D3)⋊C4—22no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—81no—
314(C2×D3)⋊C4—81no—
315(C2×D3)⋊C4—81no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3C2×D412yes—
320Dic3⋊C4—22no—
321Dic3⋊C4—22no—
322C4×Dic3—24no—
323C4×Dic3—81no—
324C4×Dic3C2×D412yes—
325C4×Dic3C2×D412yes—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8C22×C412yes—
332D24—28no—
333C25—61no—
334C22×D4—34no—
335C22×D4—31no—
336C22×D4—31no—
337C22×D4—61no—
338C22×D4—62no—
339C22×D4—61no—
340C22×D4—62no—
341C22×D4—62no—
342C22×D4—62no—
343C22×D4—62no—
344C22×D4C22×D311yescharacteristic
345C23×C4—21no—
346C23×C4—31no—
347C23×C4—61no—
348C23×C4—61no—
349C23×C4—61no—
350C23×C4—61no—
351C2×D8—34no—
352C2×D8—34no—
353C2×D8—62no—
354C2×D8—62no—
355C2×D8—62no—
356C2×D8—62no—
357C22×C8—31no—
358C22×C8—31no—
359C22×C8C22×D311yescharacteristic
360C22×C8C22×D311yescharacteristic
361#121—34no—
362#121—62no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—34no—
366C4×D4—34no—
367C4×D4—62no—
368C4×D4—62no—
369C4×D4—62no—
370C4×D4—62no—
371C4×D4—62no—
372C4×D4—62no—
373C4×D4—68no—
374C4×D4—68no—
375#117—62no—
376#117—62no—
377#117—62no—
378#117—62no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C4⋊C4C22×D311yescharacteristic
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—31no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—68no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—68no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—61no—
401C2×C42—31no—
402C2×C42—61no—
403C2×C42—61no—
404C2×C42C22×D311yescharacteristic
405#107—22no—
406#106—62no—
407#102—22no—
408#102—34no—
409#102—62no—
410#102—62no—
411#102—62no—
412#102—62no—
413#102—62no—
414#102C4×D314yescomplemented
415C22⋊C8—34no—
416C22⋊C8—62no—
417#97—62no—
418C4×C8—62no—
419#95—21no—
420#95—61no—
421#95—61no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3C22×D411yescharacteristic
430C22×D3—22no—
431C22×D3—21no—
432C22×D3—22no—
433C22×D3—21no—
434C22×D3—22no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—216no—
440C22×D3—22no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—84no—
452C22×D3—84no—
453C22×D3—84no—
454C22×D3—84no—
455C22×D3—84no—
456C22×D3—84no—
457C22×D3C4×D412yes—
458C3×D4—22no—
459C3×D4—22no—
460C3×D4—22no—
461C3×D4C4×D414yes—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—84no—
478C2×C3×C4C23×C411yescharacteristic
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4C2×#4111yescharacteristic
483C2×C3×C4C2×#4111yescharacteristic
484#67—216no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—22no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—84no—
498C2×Dic3C4×D412yes—
499C2×Dic3#12012yes—
500C2×Dic3#12012yes—
501D12—22no—
502D12—22no—
503D12—22no—
504D12—22no—
505D12—22no—
506D12—41no—
507D12—41no—
508D12—84no—
509D12C4×D414yes—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—22no—
513C4×D3—22no—
514C4×D3—84no—
515C4×D3—84no—
516C4×D3—84no—
517C3×C8—22no—
518C3×C8—41no—
519C3⋊C8—22no—
520C3⋊C8—41no—
521C24—21no—
522C24—31no—
523C24—64no—
524C24—64no—
525C24—64no—
526C24—61no—
527C24—61no—
528C24—241no—
529C24—241no—
530C24—241no—
531C24—241no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—32no—
536C2×D4—32no—
537C2×D4—32no—
538C2×D4—32no—
539C2×D4—64no—
540C2×D4—64no—
541C2×D4—68no—
542C2×D4—68no—
543C2×D4—68no—
544C2×D4—64no—
545C2×D4—64no—
546C2×D4—68no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—241no—
556C2×D4—241no—
557C2×D4C2×C4×D312yes—
558C2×D4D3×D412yes—
559C2×D4#23912yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—21no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—32no—
568C22×C4—32no—
569C22×C4—64no—
570C22×C4—64no—
571C22×C4—64no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4—122no—
581C22×C4—241no—
582C22×C4—241no—
583C22×C4—241no—
584C22×C4—241no—
585C22×C4—241no—
586C22×C4—241no—
587C22×C4—241no—
588C22×C4—241no—
589C22×C4D3×D411yescharacteristic
590C22×C4D3×D411yescharacteristic
591C22×C4C23×D311yescharacteristic
592D8—68no—
593D8—68no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—32no—
600C2×C8—61no—
601C2×C8—61no—
602C2×C8—61no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8C2×C4×D312yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—32no—
611C4⋊C4—62no—
612C4⋊C4—62no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—81no—
617C4⋊C4C2×C4×D312yes—
618C4⋊C4D3×D412yes—
619C22⋊C4—24no—
620C22⋊C4—62no—
621C22⋊C4—62no—
622C22⋊C4—64no—
623C22⋊C4—64no—
624C22⋊C4—64no—
625C22⋊C4—64no—
626C22⋊C4—64no—
627C22⋊C4—122no—
628C22⋊C4—241no—
629C22⋊C4—241no—
630C22⋊C4—241no—
631C42—21no—
632C42—21no—
633C42—32no—
634C42—32no—
635C42—64no—
636C42—241no—
637C22×C3—24no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3C2×C4×D411yescharacteristic
645C22×C3C2×#12011yescharacteristic
646C22×C3#52511yescharacteristic
647C22×C3#57611yescharacteristic
648C22×C3#57611yescharacteristic
649C22×C3#57611yescharacteristic
650C22×C3#57711yescharacteristic
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—24no—
655C2×D3—41no—
656C2×D3—42no—
657C2×D3—41no—
658C2×D3—42no—
659C2×D3—42no—
660C2×D3—42no—
661C2×D3—42no—
662C2×D3—41no—
663C2×D3—42no—
664C2×D3—41no—
665C2×D3—42no—
666C2×D3—42no—
667C2×D3—42no—
668C2×D3—816no—
669C2×D3—81no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C3×C4—42no—
674C3×C4—42no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—81no—
678C3×C4C2×C4×D411yescharacteristic
679C3×C4C2×C4×D411yescharacteristic
680C3×C4#52511yescharacteristic
681C3×C4#52511yescharacteristic
682Dic3—22no—
683Dic3—22no—
684Dic3—22no—
685Dic3—42no—
686Dic3—81no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—32no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—616no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—62no—
701C23—61no—
702C23—62no—
703C23—61no—
704C23—62no—
705C23—62no—
706C23—121no—
707C23—121no—
708C23—121no—
709C23—121no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23—121no—
715C23—121no—
716C23—244no—
717C23—244no—
718C23—244no—
719C23—244no—
720C23—244no—
721C23—244no—
722C23C2×D3×D411yescharacteristic
723D4—22no—
724D4—22no—
725D4—22no—
726D4—34no—
727D4—616no—
728D4—62no—
729D4—62no—
730D4—62no—
731D4—62no—
732D4—62no—
733D4—121no—
734D4—121no—
735D4—244no—
736D4#89314yes—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—32no—
746C2×C4—32no—
747C2×C4—32no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—84no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—244no—
773C2×C4—244no—
774C2×C4—244no—
775C2×C4—244no—
776C2×C4C22×C4×D311yescharacteristic
777C2×C4C2×D3×D411yescharacteristic
778C2×C4C2×D3×D411yescharacteristic
779C2×C4C2×#23911yescharacteristic
780C2×C4D3×#4111yescharacteristic
781C2×C4D3×#4111yescharacteristic
782C8—22no—
783C8—41no—
784C8—62no—
785C8—121no—
786C2×C3—44no—
787C2×C3C4×#12011yescharacteristic
788C2×C3#294611yescharacteristic
789C2×C3#294811yescharacteristic
790C2×C3#300811yescharacteristic
791C2×C3#301211yescharacteristic
792C2×C3#311811yescharacteristic
793C2×C3#312211yescharacteristic
794D3—42no—
795D3—44no—
796D3—82no—
797C22—24no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—62no—
805C22—64no—
806C22—62no—
807C22—62no—
808C22—121no—
809C22—122no—
810C22—122no—
811C22—121no—
812C22—122no—
813C22—121no—
814C22—122no—
815C22—122no—
816C22—121no—
817C22—122no—
818C22—122no—
819C22—122no—
820C22—122no—
821C22—2416no—
822C22—241no—
823C22—241no—
824C22—241no—
825C22—241no—
826C22C4×D3×D411yescharacteristic
827C22D3×#12011yescharacteristic
828C22#562711yescharacteristic
829C22#575711yescharacteristic
830C22#576911yescharacteristic
831C22#577411yescharacteristic
832C22#577811yescharacteristic
833C4—41no—
834C4—41no—
835C4—42no—
836C4—42no—
837C4—62no—
838C4—62no—
839C4—62no—
840C4—81no—
841C4—122no—
842C4—241no—
843C4C2×#89311yescharacteristic
844C4C4×D3×D411yescharacteristic
845C4#562711yescharacteristic
846C4#565611yescharacteristic
847C3#2145811yescharacteristic, complemented, Sylow
848C2—44no—
849C2—122no—
850C2—124no—
851C2—242no—
852C2#7437911yescharacteristic
853C2#7958811yescharacteristic
854C2#7977511yescharacteristic
855C2#8000411yescharacteristic
856C2#8023111yescharacteristic
857C2#8095211yescharacteristic
858C2#8114611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1862C2
socleC23×C3C22×D4
prime radicalC2×#4773C2
cosocleC22×C3×C4C24
hypercenter#1862D3
hypocenterC3#21458
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
1. C2×#5545C2semidirect
2. C2×#4872C2semidirect
4. C2×#4785C2semidirect
5. #76198C2semidirect
6. C3×#1862C2semidirect
7. #71613C2semidirect
8. #70633C2semidirect
9. #70198C2semidirect
10. Dic3×#102C2semidirect
11. #69626C2semidirect
12. #68881C2semidirect
13. #68782C2semidirect
14. #68673C2semidirect
15. #68601C2semidirect
28. C2×#893C22semidirect
34. C2×C3×#107C22semidirect
37. C3×#389C22semidirect
40. C2×#821C22semidirect
43. C2×#815C22semidirect
44. C2×C8×Dic3C22semidirect
48. Dic3×C4⋊C4C22semidirect
51. C2×#809C22semidirect
52. C2×#808C22semidirect
53. #4939C22semidirect
56. #4773C4semidirect
59. C3×#340C22semidirect
60. C3×#336C22semidirect
61. #4551C22semidirect
62. #4529C22semidirect
63. #4529C22semidirect
64. #4524C22semidirect
74. #1862D3semidirect
90. C2×D3×D4C2×C4semidirect
110. D4×Dic3D4semidirect
113. C2×#213C2×C4semidirect
137. C2×D24C2×C4semidirect
139. #895C2×C4semidirect
143. #893D4semidirect
154. C3×#102C2×C4semidirect
162. (C2×D3)⋊C8C2×C4semidirect
167. #809C2×C4semidirect
189. C2×#107C2×D3semidirect
205. #389C2×D3semidirect
214. #340C2×D3semidirect
216. #336C2×D3semidirect
414. #102C4×D3semidirect
847. C3#21458semidirect

Maximal subgroups

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

subgroupindex
C2×#55452
C2×#48722
C2×#47732
C2×#47852
#761982
C3×#18622
#716132
#706332
#701982
Dic3×#1022
#696262
#688812
#687822
#686732
#686012
#214583