Finite Group Databasebeta

← #10846077

Subgroups — #10846077

Order 768.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2540C211yesmaximal, characteristic, complemented
2C2×#5057C211yesmaximal, characteristic, complemented
3C2×#5049C211yesmaximal, characteristic, complemented
4C2×#5038C211yesmaximal, characteristic, complemented
5#82417C211yesmaximal, characteristic, complemented
6C2×#5011C211yesmaximal, characteristic, complemented
7#71726C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71696C211yesmaximal, characteristic, complemented
10#71695C211yesmaximal, characteristic, complemented
11#71684C211yesmaximal, characteristic, complemented
12#71682C211yesmaximal, characteristic, complemented
13#71679C211yesmaximal, characteristic, complemented
14#69474C211yesmaximal, characteristic, complemented
15#69466C211yesmaximal, characteristic, complemented
16#25397—31nomaximal, Sylow
17C2×C3×#124C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C2×#938—21no—
25C22×#213C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C22×#208C2211yescharacteristic
29C23×C3⋊C8C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C3×#399—21no—
32C3×#392—21no—
33C3×#390—21no—
34C3×#390—21no—
35C3×C4×C4⋊C4C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42#5212C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5057—24no—
47#5049—24no—
48#5038—24no—
49#5011—24no—
50#4987—21no—
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#807C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4961—21no—
56#4961—21no—
57#4935C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×#803C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#466—31no—
66C2×#463—31no—
67C2×#435—31no—
68#2540D311yescharacteristic, complemented
69#2537—31no—
70#2036—31no—
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1959—31no—
75#1947—31no—
76#1895—31no—
77#1892—31no—
78#1762—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4D411yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3—21no—
90C3×#124—22no—
91C3×#124—22no—
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—41no—
95C3×C22⋊Q8—41no—
96C3×#121—22no—
97C3×#121—22no—
98C3×#121—41no—
99C3×#121—41no—
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4D411yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4D411yescharacteristic
114C2×C3×C22⋊C4D411yescharacteristic
115C2×C3×C42—21no—
116C2×C3×C42C2311yescharacteristic
117C2×#217—21no—
118C2×#217—21no—
119C2×#215—22no—
120C2×#215—22no—
121C2×#215—41no—
122#938—44no—
123C2×#213—22no—
124C2×#213—22no—
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⋊Dic3—21no—
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×#208—22no—
139C2×#208—22no—
140C2×#208—41no—
141C22×C3⋊C8—22no—
142C22×C3⋊C8—22no—
143C22×C3⋊C8—41no—
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C4×D12—22no—
149C4×D12—22no—
150C3×#95—21no—
151#835—22no—
152#835—22no—
153#835—41no—
154#832—22no—
155#832—22no—
156#832—41no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#830—22no—
160#830—22no—
161#809—22no—
162#809D414yescomplemented
163#807—22no—
164#807—22no—
165C4⋊(C3⋊C8)D414yescomplemented
166#803—22no—
167C22×SD16—31no—
168C22×D8—31no—
169C22×M16—31no—
170C23×C8—31no—
171C2×#124C2×D311yescharacteristic
172C2×C22⋊Q8C2×D311yescharacteristic
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—61no—
177C2×#121C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×D4—31no—
180C2×C4×D4C2×D311yescharacteristic
181#468—64no—
182#466—64no—
183#463—64no—
184#435—64no—
185C2×#107—31no—
186C2×#107—31no—
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—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#399—21no—
200#394—61no—
201#394—61no—
202#392—21no—
203#390—21no—
204#390—21no—
205#384—31no—
206#380—31no—
207#380—31no—
208#380—61no—
209C4×C4⋊C4C2×D311yescharacteristic
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
216C24×C3C2×D411yescharacteristic
217C23×D3—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×D4—22no—
225C2×C3×D4—22no—
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—41no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—81no—
238C2×C3×D4—81no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—81no—
264C2×#67—81no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12C2×D412yes—
274C2×C4×D3—42no—
275C2×C4×D3—42no—
276C2×C4×D3—42no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—42no—
281C3×C4⋊C4—42no—
282C3×C4⋊C4C2×D412yes—
283C3×C4⋊C4#4112yes—
284C3×C22⋊C4—22no—
285C3×C22⋊C4—22no—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4—42no—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291C3×C22⋊C4—42no—
292C3×C42—81no—
293C3×C42C2×D412yes—
294C3×C42#4112yes—
295#217—42no—
296#217—42no—
297#215—44no—
298#213—44no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—42no—
309C4⋊Dic3—81no—
310#208—44no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—44no—
321C2×C3⋊C8C2×D412yes—
322C2×C3⋊C8C2×D412yes—
323C2×C3⋊C8C2×D412yes—
324C22×Q8C22×D311yescharacteristic
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4#6711yescharacteristic
331C22×D4C22×D311yescharacteristic
332C23×C4—61no—
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—121no—
338C2×D8—62no—
339C2×D8—62no—
340C2×D8—121no—
341C2×M16—62no—
342C2×M16—62no—
343C2×M16—121no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8—62no—
349C22×C8—62no—
350C22×C8—121no—
351#124—22no—
352#124—22no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8—41no—
356C22⋊Q8—41no—
357#121—22no—
358#121—22no—
359#121—41no—
360#121—41no—
361#121—62no—
362#121—62no—
363#121—121no—
364#121—121no—
365#121—124no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—62no—
369C4×D4—62no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4#6711yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
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#6711yescharacteristic
392C2×C22⋊C4#6711yescharacteristic
393C2×C42—21no—
394C2×C42C22×D311yescharacteristic
395#107—62no—
396#107—62no—
397C4⋊C8—34no—
398#103—62no—
399#103—62no—
400#103—121no—
401#102—34no—
402#102—62no—
403#102—62no—
404#102—62no—
405#102—121no—
406C22⋊C8—62no—
407C22⋊C8—62no—
408#97—62no—
409#95—21no—
410#95—61no—
411#95—61no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3AGL(1,ℤ/8)12yes—
433C23×C3C22×D411yescharacteristic
434C22×D3—22no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C3×Q8—41no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—44no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—84no—
451C3×D4—84no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
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—41no—
478C2×C3×C4—41no—
479C2×C3×C4#12112yes—
480C2×C3×C4#12112yes—
481C2×C3×C4C22×D411yescharacteristic
482C2×C3×C4C22×D411yescharacteristic
483C2×C3×C4C2×#4111yescharacteristic
484C2×C3×C4C2×#4111yescharacteristic
485C2×C3×C4H(5,𝔽2)11yescharacteristic
486C2×C3×C4H(5,𝔽2)11yescharacteristic
487#67—84no—
488#67—84no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498D12—22no—
499D12—22no—
500D12—41no—
501D12—41no—
502C4×D3—84no—
503C3⋊C8—22no—
504C3⋊C8—22no—
505C3⋊C8—22no—
506C3⋊C8—41no—
507C24—21no—
508C24—61no—
509C24C2×#6711yescharacteristic
510C24C2×#6711yescharacteristic
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—32no—
526C2×D4—41no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—81no—
537C2×D4—81no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—241no—
543C2×D4—241no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4—122no—
565C22×C4C2×#6711yescharacteristic
566C22×C4C2×#6711yescharacteristic
567C22×C4C2×#6711yescharacteristic
568C22×C4C2×#6711yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—124no—
571D8—124no—
572M16—124no—
573C2×C8—32no—
574C2×C8—32no—
575C2×C8—32no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—124no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—122no—
598C4⋊C4—241no—
599C4⋊C4D3×D412yes—
600C4⋊C4#23712yes—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—81no—
615C42D3×D412yes—
616C42#23712yes—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3C2×#12111yescharacteristic
639C22×C3D4211yescharacteristic
640C22×C3#54611yescharacteristic
641C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
642C22×C3#57511yescharacteristic
643C22×C3#57611yescharacteristic
644C22×C3#57811yescharacteristic
645C2×D3—42no—
646C2×D3—42no—
647C2×D3—42no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—81no—
659C3×C4#53211yescharacteristic
660C3×C4#54011yescharacteristic
661C3×C4D4211yescharacteristic
662C3×C4#55011yescharacteristic
663Dic3—81no—
664Dic3—81no—
665Dic3—81no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—62no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23#94912yes—
694C23C22×#6711yescharacteristic
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—41no—
699D4—44no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—62no—
705D4—62no—
706D4—84no—
707D4—84no—
708D4—121no—
709D4—121no—
710D4—244no—
711D4—244no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—244no—
749C2×C4#93912yes—
750C2×C4#93912yes—
751C2×C4C2×D3×D411yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4C2×#23711yescharacteristic
754C2×C4C2×#23711yescharacteristic
755C2×C4#100411yescharacteristic
756C2×C4#100411yescharacteristic
757C8—62no—
758C8—62no—
759C8—62no—
760C8—121no—
761C2×C3—42no—
762C2×C3—81no—
763C2×C3—161no—
764C2×C3#242811yescharacteristic
765C2×C3#305511yescharacteristic
766C2×C3#306111yescharacteristic
767C2×C3#326411yescharacteristic
768C2×C3#326911yescharacteristic
769C2×C3#330811yescharacteristic
770C2×C3#331911yescharacteristic
771D3—82no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—122no—
794C22—122no—
795C22—122no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22D4×#6711yescharacteristic
801C22C2×#93911yescharacteristic
802C22#580611yescharacteristic
803C22C2×#94911yescharacteristic
804C22#582211yescharacteristic
805C22#583511yescharacteristic
806C22#583811yescharacteristic
807C4—22no—
808C4—22no—
809C4—42no—
810C4—42no—
811C4—41no—
812C4—41no—
813C4—81no—
814C4—241no—
815C4—241no—
816C4—241no—
817C4#571611yescharacteristic
818C4#571711yescharacteristic
819C4#571811yescharacteristic
820C4#571911yescharacteristic
821C3#2539711yescharacteristic, complemented, Sylow
822C2—42no—
823C2—81no—
824C2—161no—
825C2—242no—
826C2#8292411yescharacteristic
827C2#8318611yescharacteristic
828C2#8342111yescharacteristic
829C2#8349911yescharacteristic
830C2#8350211yescharacteristic
831C2#8353611yescharacteristic
832C2#8354311yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2540C2
socleC23×C3C22×D4
hypercenter#2540D3
hypocenterC3#25397
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C3×#2540C2semidirect
2. C2×#5057C2semidirect
3. C2×#5049C2semidirect
4. C2×#5038C2semidirect
5. #82417C2semidirect
6. C2×#5011C2semidirect
7. #71726C2semidirect
8. #71699C2semidirect
9. #71696C2semidirect
10. #71695C2semidirect
11. #71684C2semidirect
12. #71682C2semidirect
13. #71679C2semidirect
14. #69474C2semidirect
15. #69466C2semidirect
68. #2540D3semidirect
162. #809D4semidirect
165. C4⋊(C3⋊C8)D4semidirect
821. C3#25397semidirect

Maximal subgroups

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

subgroupindex
C3×#25402
C2×#50572
C2×#50492
C2×#50382
#824172
C2×#50112
#717262
#716992
#716962
#716952
#716842
#716822
#716792
#694742
#694662
#253973