Finite Group Databasebeta

← #10819899

Subgroups — #10819899

Order 768.

1126 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2367C211yesmaximal, characteristic, complemented
2C2×#5058C211yesmaximal, characteristic
3C2×#5026C211yesmaximal, characteristic, complemented
4C2×C4×#213C211yesmaximal, characteristic, complemented
5#73653C211yesmaximal, characteristic, complemented
6#71721C211yesmaximal, characteristic, complemented
7#71633C211yesmaximal, characteristic, complemented
8#71613C211yesmaximal, characteristic, complemented
9#69687C211yesmaximal, characteristic, complemented
10#69676C211yesmaximal, characteristic, complemented
11#69657C211yesmaximal, characteristic, complemented
12#69648C211yesmaximal, characteristic, complemented
13#69487C211yesmaximal, characteristic, complemented
14#69481C211yesmaximal, characteristic, complemented
15#69478C211yesmaximal, characteristic, complemented
16#23195—31nomaximal, Sylow
17C2×C3×#124C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×#893—21no—
25C2×#874C2211yescharacteristic
26C2×C4×D12C2211yescharacteristic
27C2×C4×D12C2211yescharacteristic
28C3×#391C2211yescharacteristic
29C3×#390C2211yescharacteristic
30C3×#388—21no—
31C3×#388—21no—
32C3×#385—21no—
33C3×C4×C4⋊C4C2211yescharacteristic
34C3×C4×C4⋊C4C2211yescharacteristic
35C3×C4×C22⋊C4—21no—
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5058C418yescomplemented
41#5026—24no—
42C4×#213—24no—
43#4988—21no—
44C2×#809C2211yescharacteristic
45C2×#809C2211yescharacteristic
46C2×#809C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#808C2211yescharacteristic
49C2×#807C2211yescharacteristic
50#4939C2211yescharacteristic
51#4939C2211yescharacteristic
52C4×C4⋊Dic3C2211yescharacteristic
53C2×C4⋊(C3⋊C8)C2211yescharacteristic
54C2×#803C2211yescharacteristic
55C2×#803C2211yescharacteristic
56C2×C4×C3⋊C8C2211yescharacteristic
57#4665—21no—
58#4665—21no—
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4524C2211yescharacteristic
62#4524C2211yescharacteristic
63C2×#496—31no—
64C2×#440—31no—
65C2×C4×D8—31no—
66#2367D311yescharacteristic, complemented
67#2366—31no—
68#1983—31no—
69#1982—31no—
70#1972—31no—
71#1968—31no—
72#1880—31no—
73#1879—31no—
74#1879—31no—
75#1877—31no—
76#1776—31no—
77#1771—31no—
78C22×C3×Q8C2311yescharacteristic
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×D12—21no—
82C22×D12—21no—
83C22×D12C2311yescharacteristic
84C22×D12C2311yescharacteristic
85C22×C4×D3—21no—
86C22×C4×D3—21no—
87C3×#124—22no—
88C3×#124C2×C414yescomplemented
89C3×C4×Q8—22no—
90C3×C4×Q8—41no—
91C3×C4×D4—22no—
92C3×C4×D4—41no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4D411yescharacteristic
95C2×C3×C4⋊C4D411yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C42—21no—
104C2×C3×C42—21no—
105C2×C3×C42C2311yescharacteristic
106C2×C3×C42C2311yescharacteristic
107C2×C3×C42C2311yescharacteristic
108C2×#215—22no—
109C2×#215—22no—
110C2×#215—41no—
111C2×#215—41no—
112C2×#215C2×C414yescomplemented
113C2×#215C2×C414yescomplemented
114C2×#213—22no—
115C2×#213—22no—
116C2×#213—41no—
117C2×#213—41no—
118C2×#213C2×C414yescomplemented
119C2×#213C2×C414yescomplemented
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4×Dic3—21no—
129C22×C3⋊C8C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133#893—44no—
134#874—22no—
135#874C2×C414yescomplemented
136C4×D12—22no—
137C4×D12—22no—
138C4×D12—41no—
139C4×D12—41no—
140C3×#95—21no—
141C3×#95—21no—
142C3×#95—21no—
143C3×#95D411yescharacteristic
144C3×#95D411yescharacteristic
145#835—22no—
146#835—41no—
147#832—22no—
148#832—41no—
149C3⋊#95—21no—
150#809—22no—
151#809—22no—
152#809—41no—
153#809—41no—
154#808—22no—
155#807D414yescomplemented
156C4⋊(C3⋊C8)—22no—
157#803—22no—
158#803C2×C414yescomplemented
159C4×C3⋊C8—22no—
160C22×SD16—31no—
161C22×SD16—31no—
162C22×D8—31no—
163C22×D8—31no—
164C2×#127—31no—
165C2×#124C2×D311yescharacteristic
166C2×C4×Q8C2×D311yescharacteristic
167C2×C4×D4—31no—
168C2×C4×D4—31no—
169C2×C4×D4—61no—
170C2×C4×D4C2×D311yescharacteristic
171#496—38no—
172#440—64no—
173C4×D8—64no—
174C2×#107—31no—
175C2×#106—31no—
176C2×C4⋊C8—31no—
177C2×#103—31no—
178C2×#103—31no—
179C2×#102—31no—
180C2×#102—31no—
181C2×#102—31no—
182C2×#102—31no—
183C2×#102—31no—
184C2×#102—31no—
185C2×#97—31no—
186C2×#97—31no—
187C2×C4×C8—31no—
188#391C2×D311yescharacteristic
189#390—31no—
190#390—31no—
191#390—61no—
192#390C2×D311yescharacteristic
193#388—21no—
194#388—21no—
195#386—61no—
196#386—61no—
197#385—21no—
198C4×C4⋊C4—31no—
199C4×C4⋊C4C2×D311yescharacteristic
200C4×C4⋊C4C2×D311yescharacteristic
201C4×C22⋊C4—21no—
202#340—31no—
203#340—31no—
204#336—31no—
205#336—31no—
206C24×C3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8C22×C412yes—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4C22×C412yes—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—42no—
225C22×C3×C4—42no—
226C22×C3×C4—81no—
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2411yescharacteristic
234C22×Dic3—21no—
235C22×Dic3—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—24no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—24no—
248C2×D12—42no—
249C2×D12—42no—
250C2×D12—81no—
251C2×D12—81no—
252C2×D12C22×C412yes—
253C2×D12C22×C412yes—
254C2×C4×D3—42no—
255C2×C4×D3—42no—
256C2×C4×D3—42no—
257C2×C4×D3—42no—
258C2×C4×D3—81no—
259C2×C4×D3—81no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—41no—
265C3×C4⋊C4—42no—
266C3×C4⋊C4C2×D412yes—
267C3×C22⋊C4—24no—
268C3×C22⋊C4—24no—
269C3×C22⋊C4—42no—
270C3×C22⋊C4—42no—
271C3×C22⋊C4—81no—
272C3×C42—21no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—42no—
277C3×C42—81no—
278C3×C42C22×C412yes—
279C3×C42#4112yes—
280#215—28no—
281#215—44no—
282#213—28no—
283#213—44no—
284(C2×D3)⋊C4—42no—
285(C2×D3)⋊C4—42no—
286(C2×D3)⋊C4—42no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—81no—
289(C2×D3)⋊C4—81no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3C2×D412yes—
294C4×Dic3—42no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8C22×C412yes—
304C2×C3⋊C8C22×C412yes—
305C2×C3⋊C8C2×D412yes—
306C2×C3⋊C8#4112yes—
307C22×Q8C22×D311yescharacteristic
308C22×D4—31no—
309C22×D4—31no—
310C22×D4—61no—
311C22×D4—61no—
312C22×D4C22×D311yescharacteristic
313C23×C4—21no—
314C23×C4—61no—
315C23×C4—61no—
316C2×SD16—34no—
317C2×SD16—34no—
318C2×SD16—62no—
319C2×SD16—62no—
320C2×SD16—121no—
321C2×SD16—121no—
322C2×D8—34no—
323C2×D8—34no—
324C2×D8—62no—
325C2×D8—62no—
326C2×D8—121no—
327C2×D8—121no—
328C22×C8—31no—
329C22×C8—31no—
330C22×C8—31no—
331C22×C8—31no—
332#127—34no—
333#127—62no—
334#124—22no—
335#124C4×D314yescomplemented
336C4×Q8—22no—
337C4×Q8—41no—
338C4×D4—22no—
339C4×D4—41no—
340C4×D4—62no—
341C4×D4—62no—
342C4×D4—121no—
343C4×D4—121no—
344C4×D4—124no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4#6711yescharacteristic
349C2×C4⋊C4#6711yescharacteristic
350C2×C4⋊C4C22×D311yescharacteristic
351C2×C4⋊C4C22×D311yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—61no—
358C2×C22⋊C4—61no—
359C2×C22⋊C4—61no—
360C2×C22⋊C4—61no—
361C2×C22⋊C4—61no—
362C2×C22⋊C4—61no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—61no—
366C2×C42C22×D311yescharacteristic
367C2×C42C22×D311yescharacteristic
368C2×C42C22×D311yescharacteristic
369#107—34no—
370#106—62no—
371C4⋊C8—62no—
372#103—62no—
373#103—121no—
374#102—62no—
375#102—62no—
376#102—62no—
377#102—121no—
378#102—121no—
379#102—121no—
380#97—34no—
381#97—62no—
382C4×C8—62no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—61no—
387#95#6711yescharacteristic
388#95#6711yescharacteristic
389C23×C3—22no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3C22×D411yescharacteristic
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—41no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—41no—
408C22×D3—41no—
409C22×D3—41no—
410C22×D3—41no—
411C3×Q8—22no—
412C3×Q8—22no—
413C3×Q8—41no—
414C3×Q8—41no—
415C3×D4—22no—
416C3×D4—22no—
417C3×D4—41no—
418C3×D4—41no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
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—84no—
444C2×C3×C4C4×D412yes—
445C2×C3×C4C4×D412yes—
446C2×C3×C4AGL(1,ℤ/8)12yes—
447C2×C3×C4C23×C411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×C3×C4H(5,𝔽2)11yescharacteristic
453C2×Dic3—22no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459D12—22no—
460D12—22no—
461D12—22no—
462D12—22no—
463D12—48no—
464D12—41no—
465D12—41no—
466D12—41no—
467D12—41no—
468D12—84no—
469C4×D3—84no—
470C4×D3—84no—
471C3⋊C8—22no—
472C3⋊C8—41no—
473C3⋊C8—41no—
474C3⋊C8C4×D414yescomplemented
475C24—21no—
476C24—61no—
477C24—61no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8C2×C4×D312yes—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—32no—
490C2×D4—32no—
491C2×D4—64no—
492C2×D4—64no—
493C2×D4—61no—
494C2×D4—61no—
495C2×D4—61no—
496C2×D4—61no—
497C2×D4—61no—
498C2×D4—61no—
499C2×D4—61no—
500C2×D4—61no—
501C2×D4—61no—
502C2×D4—61no—
503C2×D4—122no—
504C2×D4—122no—
505C2×D4—241no—
506C2×D4—241no—
507C2×D4C2×C4×D312yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—81no—
516C22×C4—122no—
517C22×C4—122no—
518C22×C4—122no—
519C22×C4—122no—
520C22×C4—241no—
521C22×C4—241no—
522C22×C4C2×#6711yescharacteristic
523C22×C4C2×#6711yescharacteristic
524C22×C4C2×#6711yescharacteristic
525C22×C4C2×#6711yescharacteristic
526C22×C4C2×#6711yescharacteristic
527C22×C4C2×#6711yescharacteristic
528C22×C4C23×D311yescharacteristic
529SD16—68no—
530SD16—124no—
531D8—68no—
532D8—124no—
533C2×C8—32no—
534C2×C8—32no—
535C2×C8—32no—
536C2×C8—32no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C4⋊C4—22no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—32no—
550C4⋊C4—41no—
551C4⋊C4—42no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4D3×D412yes—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4—122no—
562C22⋊C4—122no—
563C22⋊C4—122no—
564C22⋊C4—122no—
565C22⋊C4—241no—
566C22⋊C4—241no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—81no—
573C42—122no—
574C42C2×C4×D312yes—
575C42#23512yes—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—81no—
580C22×C3—81no—
581C22×C3—81no—
582C22×C3—81no—
583C22×C3C2×C4×D411yescharacteristic
584C22×C3D4211yescharacteristic
585C22×C3#55011yescharacteristic
586C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
587C22×C3#57511yescharacteristic
588C22×C3#57611yescharacteristic
589C22×C3#57711yescharacteristic
590C2×D3—42no—
591C2×D3—42no—
592C2×D3—42no—
593C2×D3—42no—
594C2×D3—42no—
595C2×D3—42no—
596C2×D3—81no—
597C2×D3—81no—
598C2×D3—81no—
599C2×D3—81no—
600C2×D3—81no—
601C2×D3—81no—
602C2×D3—81no—
603C2×D3—81no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—42no—
608C3×C4—41no—
609C3×C4—42no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—81no—
613C3×C4C2×C4×D411yescharacteristic
614C3×C4#51811yescharacteristic
615C3×C4#55011yescharacteristic
616C3×C4#55911yescharacteristic
617Dic3—42no—
618Dic3—81no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—62no—
627C23—62no—
628C23—121no—
629C23—121no—
630C23—121no—
631C23—121no—
632C23—121no—
633C23—121no—
634C23—121no—
635C23—121no—
636C23—121no—
637C23—121no—
638C23—121no—
639C23—121no—
640C23C22×#6711yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—62no—
650D4—62no—
651D4—62no—
652D4—62no—
653D4—128no—
654D4—121no—
655D4—121no—
656D4—121no—
657D4—121no—
658D4—244no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—62no—
684C2×C4—84no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—244no—
691C2×C4—244no—
692C2×C4C4×#6712yes—
693C2×C4C4×#6712yes—
694C2×C4#94912yes—
695C2×C4C22×C4×D311yescharacteristic
696C2×C4C2×#23511yescharacteristic
697C2×C4C2×D3×D411yescharacteristic
698C2×C4#100411yescharacteristic
699C2×C4D3×#4111yescharacteristic
700C2×C4#100911yescharacteristic
701C8—34no—
702C8—62no—
703C8—121no—
704C8—121no—
705C2×C3—82no—
706C2×C3#236611yescharacteristic
707C2×C3C4×AGL(1,ℤ/8)11yescharacteristic
708C2×C3#294611yescharacteristic
709C2×C3#326411yescharacteristic
710C2×C3#327111yescharacteristic
711C2×C3#339711yescharacteristic
712C2×C3#340311yescharacteristic
713D3—82no—
714D3—82no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—122no—
723C22—122no—
724C22—122no—
725C22—122no—
726C22—122no—
727C22—122no—
728C22—241no—
729C22—241no—
730C22—241no—
731C22—241no—
732C22—241no—
733C22—241no—
734C22—241no—
735C22—241no—
736C22C2×C4×#6711yescharacteristic
737C22D4×#6711yescharacteristic
738C22C2×#94911yescharacteristic
739C22#582211yescharacteristic
740C22#583411yescharacteristic
741C22#583511yescharacteristic
742C22#583711yescharacteristic
743C4—22no—
744C4—22no—
745C4—22no—
746C4—41no—
747C4—42no—
748C4—41no—
749C4—41no—
750C4—42no—
751C4—81no—
752C4—122no—
753C4—241no—
754C4C4×D3×D411yescharacteristic
755C4#554511yescharacteristic
756C4#555311yescharacteristic
757C4#555911yescharacteristic
758C3#2319511yescharacteristic, complemented, Sylow
759C2—82no—
760C2—242no—
761C2—242no—
762C2#8234311yescharacteristic
763C2C4×#94911yescharacteristic
764C2#8256411yescharacteristic
765C2#8350211yescharacteristic
766C2#8354711yescharacteristic
767C2#8367111yescharacteristic
768C2#8371611yescharacteristic
subgroupG/H
centerC23C22×#67
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#2367C2
socleC23×C3C22×D4
prime radicalC2×#5058C2
cosocleC22×C3×C4C24
hypercenter#2367D3
hypocenterC3#23195
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
1. C3×#2367C2semidirect
3. C2×#5026C2semidirect
4. C2×C4×#213C2semidirect
5. #73653C2semidirect
6. #71721C2semidirect
7. #71633C2semidirect
8. #71613C2semidirect
9. #69687C2semidirect
10. #69676C2semidirect
11. #69657C2semidirect
12. #69648C2semidirect
13. #69487C2semidirect
14. #69481C2semidirect
15. #69478C2semidirect
40. #5058C4semidirect
66. #2367D3semidirect
88. C3×#124C2×C4semidirect
112. C2×#215C2×C4semidirect
113. C2×#215C2×C4semidirect
118. C2×#213C2×C4semidirect
119. C2×#213C2×C4semidirect
135. #874C2×C4semidirect
155. #807D4semidirect
158. #803C2×C4semidirect
335. #124C4×D3semidirect
474. C3⋊C8C4×D4semidirect
758. C3#23195semidirect

Maximal subgroups

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

subgroupindex
C3×#23672
C2×#50582
C2×#50262
C2×C4×#2132
#736532
#717212
#716332
#716132
#696872
#696762
#696572
#696482
#694872
#694812
#694782
#231953