Finite Group Databasebeta

← #10846062

Subgroups — #10846062

Order 768.

1184 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2541C211yesmaximal, characteristic, complemented
2C2×#5072C211yesmaximal, characteristic, complemented
3C2×#5039C211yesmaximal, characteristic, complemented
4C2×#5038C211yesmaximal, characteristic, complemented
5#82415C211yesmaximal, characteristic, complemented
6C2×#5011C211yesmaximal, characteristic, complemented
7#71765C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#71682C211yesmaximal, characteristic, complemented
11#71681C211yesmaximal, characteristic, complemented
12#71680C211yesmaximal, characteristic, complemented
13#71679C211yesmaximal, characteristic, complemented
14#69474C211yesmaximal, characteristic, complemented
15#69468C211yesmaximal, characteristic, complemented
16#25396—31nomaximal, Sylow
17C2×C3×#127—21no—
18C2×C3×#127C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C22×#208C2211yescharacteristic
29C23×C3⋊C8C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C3×#392—21no—
32C3×#392—21no—
33C3×#390—21no—
34C3×C4×C4⋊C4C2211yescharacteristic
35#5223—21no—
36C2×#832C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42#5212C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5072—24no—
47#5039—24no—
48#5038—24no—
49#5011—24no—
50#4992—21no—
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4956—21no—
56#4956—21no—
57#4936C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×#803C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#469—31no—
65C2×#466—31no—
66C2×#459—31no—
67C2×#435—31no—
68#2541D311yescharacteristic, complemented
69#2535—31no—
70#2034—31no—
71#2033—31no—
72#1999—31no—
73#1999—31no—
74#1961—31no—
75#1949—31no—
76#1895—31no—
77#1893—31no—
78#1762—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4—21no—
85C22×C3×D4D411yescharacteristic
86C22×C3×D4C2311yescharacteristic
87C22×C3×D4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C22×#67—21no—
91C22×#67—21no—
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C3×#127—22no—
95C3×#127—22no—
96C3×#127—44no—
97C3×#121—22no—
98C3×#121—22no—
99C3×#121—22no—
100C3×#121—22no—
101C3×#121—41no—
102C3×#121—41no—
103C3×#121—41no—
104C3×#121—41no—
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C2×C3×C4⋊C4D411yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4D411yescharacteristic
115C2×C3×C22⋊C4D411yescharacteristic
116C2×C3×C42—21no—
117C2×C3×C42C2311yescharacteristic
118C2×#217—21no—
119C2×#217—21no—
120C2×#213—22no—
121C2×#213—22no—
122C2×#213—22no—
123C2×#213—22no—
124C2×#213—41no—
125C2×#213—41no—
126#930—22no—
127#930—22no—
128#930—41no—
129#930—41no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×#208—22no—
137C2×#208—22no—
138C2×#208—41no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8—22no—
141C22×C3⋊C8—41no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C4×D12—22no—
147C4×D12—22no—
148C3×#95—21no—
149#832—22no—
150#832—22no—
151#832—22no—
152#832—22no—
153#832—41no—
154#832—41no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#830—22no—
160#830—22no—
161#809—22no—
162#809D414yescomplemented
163#808—22no—
164#807—22no—
165C4⋊(C3⋊C8)D414yescomplemented
166#803—22no—
167C22×D8—31no—
168C22×D8—31no—
169C22×M16—31no—
170C23×C8—31no—
171C2×#127—21no—
172C2×#127C2×D311yescharacteristic
173C2×#121—31no—
174C2×#121—31no—
175C2×#121C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×#121C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×D4—31no—
180C2×C4×D4C2×D311yescharacteristic
181#469—64no—
182#466—64no—
183#459—64no—
184#435—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×C4⋊C8—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×#97—31no—
199#397—61no—
200#392—21no—
201#392—21no—
202#392—61no—
203#390—21no—
204#386—61no—
205#386—61no—
206#382—31no—
207#380—31no—
208#380—31no—
209C4×C4⋊C4C2×D311yescharacteristic
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3C2×D411yescharacteristic
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C2×C3×D4—22no—
220C2×C3×D4—22no—
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—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—41no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4—42no—
246C2×C3×D4—81no—
247C2×C3×D4—81no—
248C2×C3×D4—81no—
249C2×C3×D4—81no—
250C2×C3×D4—81no—
251C2×C3×D4—81no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2×D411yescharacteristic
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2411yescharacteristic
271C2×#67—42no—
272C2×#67—42no—
273C2×#67—42no—
274C2×#67—42no—
275C2×#67—81no—
276C2×#67—81no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12C2×D412yes—
286C2×C4×D3—42no—
287C2×C4×D3—81no—
288C2×C4×D3—81no—
289C3×C4⋊C4—22no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4C2×D412yes—
293C3×C4⋊C4#4112yes—
294C3×C22⋊C4—22no—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—42no—
297C3×C22⋊C4—42no—
298C3×C22⋊C4—42no—
299C3×C22⋊C4—42no—
300C3×C42—42no—
301C3×C42C2×D412yes—
302C3×C42#4112yes—
303#217—81no—
304#217—81no—
305#213—44no—
306#213—44no—
307(C2×D3)⋊C4—42no—
308(C2×D3)⋊C4—42no—
309(C2×D3)⋊C4—42no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315C4⋊Dic3—21no—
316#208—44no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—44no—
327C2×C3⋊C8C2×D412yes—
328C2×C3⋊C8C2×D412yes—
329C2×C3⋊C8C2×D412yes—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—31no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4#6711yescharacteristic
340C22×D4C22×D311yescharacteristic
341C22×D4C22×D311yescharacteristic
342C23×C4—61no—
343C23×C4C22×D311yescharacteristic
344C23×C4C22×D311yescharacteristic
345C2×D8—62no—
346C2×D8—62no—
347C2×D8—62no—
348C2×D8—62no—
349C2×D8—121no—
350C2×D8—121no—
351C2×M16—62no—
352C2×M16—62no—
353C2×M16—121no—
354C22×C8—31no—
355C22×C8—31no—
356C22×C8—31no—
357C22×C8—31no—
358C22×C8—62no—
359C22×C8—62no—
360C22×C8—121no—
361#127—22no—
362#127—22no—
363#127—44no—
364#121—22no—
365#121—22no—
366#121—22no—
367#121—22no—
368#121—41no—
369#121—41no—
370#121—41no—
371#121—41no—
372#121—62no—
373#121—62no—
374#121—121no—
375#121—121no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—62no—
379C4×D4—62no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4#6711yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C4⋊C4C22×D311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4#6711yescharacteristic
396C2×C22⋊C4#6711yescharacteristic
397C2×C42—21no—
398C2×C42C22×D311yescharacteristic
399#107—62no—
400#106—62no—
401C4⋊C8—34no—
402#102—34no—
403#102—62no—
404#102—62no—
405#102—62no—
406#102—62no—
407#102—62no—
408#102—121no—
409#102—121no—
410C22⋊C8—62no—
411C22⋊C8—62no—
412#97—62no—
413#95—21no—
414#95—61no—
415#95—61no—
416#95—61no—
417#95—61no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3AGL(1,ℤ/8)12yes—
446C23×C3C22×D411yescharacteristic
447C22×D3—22no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C3×D4—44no—
455C3×D4—41no—
456C3×D4—41no—
457C3×D4—41no—
458C3×D4—41no—
459C3×D4—41no—
460C3×D4—41no—
461C3×D4—41no—
462C3×D4—41no—
463C3×D4—84no—
464C3×D4—84no—
465C3×D4—84no—
466C3×D4—84no—
467C3×D4—84no—
468C3×D4—84no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4#12112yes—
494C2×C3×C4#12112yes—
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499C2×C3×C4H(5,𝔽2)11yescharacteristic
500C2×C3×C4H(5,𝔽2)11yescharacteristic
501#67—84no—
502#67—84no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512D12—22no—
513D12—22no—
514D12—41no—
515D12—41no—
516C4×D3—84no—
517C3⋊C8—22no—
518C3⋊C8—22no—
519C3⋊C8—22no—
520C3⋊C8—41no—
521C24—21no—
522C24—21no—
523C24—61no—
524C24C2×#6711yescharacteristic
525C24C2×#6711yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—32no—
541C2×D4—41no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—61no—
557C2×D4—61no—
558C2×D4—61no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—122no—
566C2×D4—122no—
567C2×D4—122no—
568C2×D4—122no—
569C2×D4—241no—
570C2×D4—241no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—122no—
589C22×C4—241no—
590C22×C4—241no—
591C22×C4C2×#6711yescharacteristic
592C22×C4C2×#6711yescharacteristic
593C22×C4C2×#6711yescharacteristic
594C22×C4C2×#6711yescharacteristic
595C22×C4C23×D311yescharacteristic
596D8—124no—
597D8—124no—
598M16—124no—
599C2×C8—32no—
600C2×C8—32no—
601C2×C8—32no—
602C2×C8—61no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C2×C8—61no—
610C2×C8—61no—
611C2×C8—124no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4D3×D412yes—
622C4⋊C4#23712yes—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—122no—
630C22⋊C4—122no—
631C22⋊C4—122no—
632C22⋊C4—241no—
633C22⋊C4—241no—
634C42—42no—
635C42D3×D412yes—
636C42#23712yes—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3C2×#12111yescharacteristic
666C22×C3D4211yescharacteristic
667C22×C3#54611yescharacteristic
668C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
669C22×C3#57511yescharacteristic
670C22×C3#57611yescharacteristic
671C22×C3#57611yescharacteristic
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—81no—
676C2×D3—81no—
677C2×D3—81no—
678C2×D3—81no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4#53211yescharacteristic
686C3×C4#54011yescharacteristic
687C3×C4D4211yescharacteristic
688C3×C4#55011yescharacteristic
689Dic3—81no—
690Dic3—81no—
691Dic3—81no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—62no—
720C23—121no—
721C23—121no—
722C23—121no—
723C23—121no—
724C23—121no—
725C23—121no—
726C23#93212yes—
727C23C22×#6711yescharacteristic
728D4—44no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—62no—
738D4—62no—
739D4—84no—
740D4—84no—
741D4—84no—
742D4—84no—
743D4—84no—
744D4—84no—
745D4—121no—
746D4—121no—
747D4—244no—
748D4—244no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—121no—
774C2×C4—121no—
775C2×C4—121no—
776C2×C4—121no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—244no—
783C2×C4#93912yes—
784C2×C4#93912yes—
785C2×C4C2×D3×D411yescharacteristic
786C2×C4C2×D3×D411yescharacteristic
787C2×C4C2×#23711yescharacteristic
788C2×C4C2×#23711yescharacteristic
789C2×C4#100411yescharacteristic
790C2×C4#100411yescharacteristic
791C8—62no—
792C8—62no—
793C8—62no—
794C8—121no—
795C2×C3—42no—
796C2×C3—81no—
797C2×C3—161no—
798C2×C3—161no—
799C2×C3#242811yescharacteristic
800C2×C3#305511yescharacteristic
801C2×C3#305811yescharacteristic
802C2×C3#326411yescharacteristic
803C2×C3#326811yescharacteristic
804C2×C3#330911yescharacteristic
805C2×C3#331811yescharacteristic
806D3—82no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—122no—
836C22—122no—
837C22—122no—
838C22—241no—
839C22—241no—
840C22—241no—
841C22—241no—
842C22C2×#93211yescharacteristic
843C22D4×#6711yescharacteristic
844C22C2×#93911yescharacteristic
845C22#580611yescharacteristic
846C22#582211yescharacteristic
847C22#583511yescharacteristic
848C22#583511yescharacteristic
849C4—22no—
850C4—22no—
851C4—42no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—241no—
856C4—241no—
857C4—241no—
858C4#571611yescharacteristic
859C4#571711yescharacteristic
860C4#571811yescharacteristic
861C4#571911yescharacteristic
862C3#2539611yescharacteristic, complemented, Sylow
863C2—42no—
864C2—81no—
865C2—161no—
866C2—161no—
867C2—242no—
868C2#8262111yescharacteristic
869C2#8318611yescharacteristic
870C2#8337811yescharacteristic
871C2#8348511yescharacteristic
872C2#8348811yescharacteristic
873C2#8357211yescharacteristic
874C2#8357711yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2541C2
socleC23×C3C22×D4
hypercenter#2541D3
hypocenterC3#25396
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C3×#2541C2semidirect
2. C2×#5072C2semidirect
3. C2×#5039C2semidirect
4. C2×#5038C2semidirect
5. #82415C2semidirect
6. C2×#5011C2semidirect
7. #71765C2semidirect
8. #71684C2semidirect
9. #71684C2semidirect
10. #71682C2semidirect
11. #71681C2semidirect
12. #71680C2semidirect
13. #71679C2semidirect
14. #69474C2semidirect
15. #69468C2semidirect
68. #2541D3semidirect
162. #809D4semidirect
165. C4⋊(C3⋊C8)D4semidirect
862. C3#25396semidirect

Maximal subgroups

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

subgroupindex
C3×#25412
C2×#50722
C2×#50392
C2×#50382
#824152
C2×#50112
#717652
#716842
#716822
#716812
#716802
#716792
#694742
#694682
#253963