Finite Group Databasebeta

← #10846097

Subgroups — #10846097

Order 768.

1034 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#464C211yesmaximal, characteristic, complemented
2C2×#5188C211yesmaximal, characteristic, complemented
3C2×#5174C211yesmaximal, characteristic, complemented
4#82998C211yesmaximal, characteristic
5#82500C211yesmaximal, characteristic, complemented
6C2×#4836C211yesmaximal, characteristic, complemented
7#72071C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#71726C211yesmaximal, characteristic, complemented
10#71631C211yesmaximal, characteristic, complemented
11#70453C211yesmaximal, characteristic, complemented
12#70271C211yesmaximal, characteristic, complemented
13#70244C211yesmaximal, characteristic, complemented
14#70202C211yesmaximal, characteristic, complemented
15#70175C211yesmaximal, characteristic, complemented
16#25399—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×#124C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C2×#938C2211yescharacteristic
27C22×ΓL(1,𝔽25)C2211yescharacteristic
28C22×D3×C8C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C3×#464—24no—
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5188—24no—
41#5174—24no—
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#818C2211yescharacteristic
45C2×#818C2211yescharacteristic
46#4994—21no—
47#4994—21no—
48#4987C2211yescharacteristic
49#4987C2211yescharacteristic
50#4960—21no—
51#4957—21no—
52#4957—21no—
53#4949—21no—
54#4939—21no—
55#4935C2211yescharacteristic
56C4×C4⋊Dic3C2211yescharacteristic
57#4928—21no—
58C2×#803C2211yescharacteristic
59#4836—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#467—31no—
66C2×#464D311yescharacteristic, complemented
67C2×#435—31no—
68#2540—31no—
69#2538—31no—
70#2036—31no—
71#2033—31no—
72#2001—31no—
73#2000—31no—
74#1959—31no—
75#1947—31no—
76#1894—31no—
77#1893—31no—
78#1763—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×D12D411yescharacteristic
85C22×C4×D3C2311yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C2×C3×Q16—22no—
88C2×C3×Q16—22no—
89C2×C3×Q16—41no—
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—41no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×#124—22no—
96C3×#124—22no—
97C3×C4×Q8—22no—
98C3×C4×Q8—22no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C42—21no—
104C2×C3×C42C2311yescharacteristic
105C2×#217—21no—
106C2×#217—21no—
107#946—22no—
108#946—22no—
109#946—22no—
110#946—22no—
111#946—41no—
112#946—41no—
113#946—41no—
114#946—41no—
115#938—22no—
116#938—22no—
117#938—41no—
118#938—41no—
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)⋊C4—21no—
125C2×(C2×D3)⋊C4D411yescharacteristic
126C2×(C2×D3)⋊C4D411yescharacteristic
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3D411yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×C4×Dic3—21no—
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C2×ΓL(1,𝔽25)—22no—
142C2×ΓL(1,𝔽25)—22no—
143C2×ΓL(1,𝔽25)—41no—
144C2×D3×C8—22no—
145C2×D3×C8—22no—
146C2×D3×C8—41no—
147C4×D12—22no—
148C4×D12—22no—
149C3×C4⋊C8D414yescomplemented
150C3×#103—22no—
151C3×#102—22no—
152#835—22no—
153#835—22no—
154#835—41no—
155#835D414yescomplemented
156#832—22no—
157#832—41no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161(C2×D3)⋊C8—22no—
162(C2×D3)⋊C8—22no—
163#818—22no—
164#818—22no—
165#803—22no—
166C22×Q16C2×D311yescharacteristic
167C22×SD16C2×D311yescharacteristic
168C22×M16—31no—
169C23×C8—31no—
170C2×#124C2×D311yescharacteristic
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×Q8C2×D311yescharacteristic
178C2×C4×D4—31no—
179#468—64no—
180#467—64no—
181#464—24no—
182#435—64no—
183C2×#107—31no—
184C2×#107—31no—
185C2×C4⋊C8C2×D311yescharacteristic
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C2×#102C2×D311yescharacteristic
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×#97—31no—
197#399—61no—
198#396—61no—
199#396—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#390—61no—
204#389—61no—
205#384—31no—
206#380—31no—
207#380—31no—
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213C24×C3—21no—
214C23×D3C2×D411yescharacteristic
215C23×D3C2×D411yescharacteristic
216C2×C3×Q8—21no—
217C2×C3×Q8—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×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8C2×D412yes—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—81no—
245C2×#67—81no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252C2×D12—22no—
253C2×D12—22no—
254C2×D12—41no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C3×Q16—44no—
268C3×SD16—44no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8C2×D412yes—
274C2×C3×C8C2×D412yes—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—42no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C42—42no—
281C3×C42C2×D412yes—
282C3×C42#4112yes—
283#217—42no—
284#217—42no—
285(C2×D3)⋊C4—22no—
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—81no—
292(C2×D3)⋊C4—81no—
293C4⋊Dic3—22no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—42no—
301C4⋊Dic3—81no—
302C4⋊Dic3C2×D412yes—
303C4⋊Dic3#4112yes—
304Dic3⋊C4—42no—
305Dic3⋊C4—42no—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308C4×Dic3—81no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8C2×D412yes—
315ΓL(1,𝔽25)—44no—
316D3×C8—44no—
317C22×Q8C22×D311yescharacteristic
318C22×Q8C22×D311yescharacteristic
319C22×D4—31no—
320C22×D4—61no—
321C22×D4—61no—
322C22×D4C22×D311yescharacteristic
323C23×C4—31no—
324C23×C4—31no—
325C2×Q16—22no—
326C2×Q16—22no—
327C2×Q16—41no—
328C2×SD16—22no—
329C2×SD16—22no—
330C2×SD16—41no—
331C2×M16—62no—
332C2×M16—62no—
333C2×M16—121no—
334C22×C8—31no—
335C22×C8—31no—
336C22×C8—62no—
337C22×C8—62no—
338C22×C8—121no—
339C22×C8C22×D311yescharacteristic
340C22×C8C22×D311yescharacteristic
341#124—22no—
342#124—22no—
343C22⋊Q8—62no—
344C22⋊Q8—62no—
345C22⋊Q8—62no—
346C22⋊Q8—62no—
347C22⋊Q8—121no—
348C22⋊Q8—121no—
349C22⋊Q8—121no—
350C22⋊Q8—121no—
351#121—62no—
352#121—62no—
353#121—121no—
354#121—121no—
355C4×Q8—22no—
356C4×Q8—22no—
357C4×D4—62no—
358C4×D4—62no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—31no—
375C2×C22⋊C4—31no—
376C2×C22⋊C4—61no—
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—21no—
385C2×C42—61no—
386C2×C42C22×D311yescharacteristic
387#107—62no—
388#107—62no—
389C4⋊C8#6714yescomplemented
390#103—22no—
391#103—34no—
392#103—62no—
393#103—62no—
394#103—121no—
395#102—22no—
396#102—62no—
397#102—121no—
398C22⋊C8—62no—
399C22⋊C8—62no—
400#97—62no—
401#95—61no—
402#95—61no—
403#95—61no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3C22×D411yescharacteristic
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3#13712yes—
426C3×Q8—22no—
427C3×Q8—22no—
428C3×Q8—41no—
429C3×Q8—41no—
430C3×Q8—41no—
431C3×Q8—41no—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×D4—41no—
435C3×D4—41no—
436C3×D4—41no—
437C3×D4—41no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4#12112yes—
452C2×C3×C4#12112yes—
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4H(5,𝔽2)11yescharacteristic
458C2×C3×C4H(5,𝔽2)11yescharacteristic
459#67—84no—
460#67—84no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—22no—
466C2×Dic3—21no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479D12—44no—
480C4×D3—41no—
481C4×D3—41no—
482C4×D3—41no—
483C4×D3—41no—
484C4×D3—41no—
485C4×D3—41no—
486C4×D3—41no—
487C4×D3—41no—
488C3×C8—22no—
489C3×C8—22no—
490C3⋊C8—22no—
491C3⋊C8—41no—
492C24—21no—
493C24—31no—
494C24—31no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8D3×D412yes—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—62no—
514C2×D4—62no—
515C2×D4—121no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4—241no—
521C2×D4—241no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4D3×D411yescharacteristic
544C22×C4D3×D411yescharacteristic
545C22×C4C23×D311yescharacteristic
546Q16—44no—
547SD16—44no—
548M16—124no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—32no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—124no—
560C2×C8C2×#6712yes—
561C2×C8C2×#6712yes—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—32no—
565C4⋊C4—32no—
566C4⋊C4—42no—
567C4⋊C4—62no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—122no—
575C4⋊C4—122no—
576C4⋊C4—122no—
577C4⋊C4—122no—
578C4⋊C4—122no—
579C4⋊C4—241no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—62no—
583C22⋊C4—62no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C22⋊C4—122no—
589C22⋊C4—122no—
590C22⋊C4—241no—
591C22⋊C4—241no—
592C42—42no—
593C42—241no—
594C42#23712yes—
595C42C2×#6712yes—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3C2×#12111yescharacteristic
604C22×C3D4211yescharacteristic
605C22×C3#54611yescharacteristic
606C22×C3C2×#13711yescharacteristic
607C22×C3#57511yescharacteristic
608C22×C3#57611yescharacteristic
609C22×C3#57811yescharacteristic
610C2×D3—22no—
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—41no—
622C2×D3—41no—
623C2×D3—41no—
624C3×C4—22no—
625C3×C4—22no—
626C3×C4—42no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4#53211yescharacteristic
630C3×C4#54011yescharacteristic
631C3×C4D4211yescharacteristic
632C3×C4#55011yescharacteristic
633Dic3—41no—
634Dic3—41no—
635Dic3—42no—
636Dic3—42no—
637Dic3—81no—
638Dic3—81no—
639C23—32no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23—61no—
657C23—61no—
658C23—61no—
659C23—61no—
660C23C2×D3×D411yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667Q8—41no—
668Q8—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—124no—
674D4—244no—
675D4—244no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—62no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—62no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4#93812yes—
716C2×C4#93812yes—
717C2×C4C2×D3×D411yescharacteristic
718C2×C4C2×#23711yescharacteristic
719C2×C4#100411yescharacteristic
720C2×C4D3×#4111yescharacteristic
721C2×C4#100911yescharacteristic
722C2×C4C22×#6711yescharacteristic
723C8—22no—
724C8—22no—
725C8—62no—
726C8—121no—
727C2×C3—161no—
728C2×C3#242811yescharacteristic
729C2×C3#305611yescharacteristic
730C2×C3#306111yescharacteristic
731C2×C3#326811yescharacteristic
732C2×C3#327011yescharacteristic
733C2×C3#331311yescharacteristic
734C2×C3#331411yescharacteristic
735D3—42no—
736D3—81no—
737C22—62no—
738C22—62no—
739C22—62no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22—121no—
758C22#560911yescharacteristic
759C22#561211yescharacteristic
760C22#576911yescharacteristic
761C22#577111yescharacteristic
762C22D3×#13711yescharacteristic
763C22#577711yescharacteristic
764C22C2×#93811yescharacteristic
765C4—22no—
766C4—22no—
767C4—42no—
768C4—81no—
769C4—81no—
770C4—121no—
771C4—121no—
772C4—122no—
773C4—122no—
774C4—241no—
775C4—241no—
776C4#559611yescharacteristic
777C4#561911yescharacteristic
778C4D4×#6711yescharacteristic
779C4#583411yescharacteristic
780C3#2539911yescharacteristic, complemented, Sylow
781C2—122no—
782C2—161no—
783C2—241no—
784C2#8061811yescharacteristic
785C2#8061911yescharacteristic
786C2#8062811yescharacteristic
787C2#8063111yescharacteristic
788C2#8264811yescharacteristic
789C2#8391711yescharacteristic
790C2#8398511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#464C2
socleC23×C3C22×D4
prime radical#82998C2
hypercenterC2×#464D3
hypocenterC3#25399
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×C3×#464C2semidirect
2. C2×#5188C2semidirect
3. C2×#5174C2semidirect
5. #82500C2semidirect
6. C2×#4836C2semidirect
7. #72071C2semidirect
8. #72054C2semidirect
9. #71726C2semidirect
10. #71631C2semidirect
11. #70453C2semidirect
12. #70271C2semidirect
13. #70244C2semidirect
14. #70202C2semidirect
15. #70175C2semidirect
66. C2×#464D3semidirect
149. C3×C4⋊C8D4semidirect
155. #835D4semidirect
389. C4⋊C8#67semidirect
780. C3#25399semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4642
C2×#51882
C2×#51742
#829982
#825002
C2×#48362
#720712
#720542
#717262
#716312
#704532
#702712
#702442
#702022
#701752
#253993