Finite Group Databasebeta

← #10901272

Subgroups — #10901272

Order 768.

1138 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5643C211yesmaximal, characteristic, complemented
2C2×#5185C211yesmaximal, characteristic, complemented
3#82821C211yesmaximal, characteristic, complemented
4C2×#4819C211yesmaximal, characteristic, complemented
5C3×#2001C211yesmaximal, characteristic, complemented
6#72072C211yesmaximal, characteristic, complemented
7#71699C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#70277C211yesmaximal, characteristic, complemented
10#70231C211yesmaximal, characteristic, complemented
11#70221C211yesmaximal, characteristic, complemented
12#69961C211yesmaximal, characteristic
13#69909C211yesmaximal, characteristic, complemented
14#68898C211yesmaximal, characteristic, complemented
15#68892C211yesmaximal, characteristic, complemented
16#29677—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C2×#947C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×#926C2211yescharacteristic
28C22×D24C2211yescharacteristic
29#5643—24no—
30#5643—24no—
31C2×#898—21no—
32C2×#897—21no—
33C2×#893C2211yescharacteristic
34C2×#888C2211yescharacteristic
35C2×#885—21no—
36C2×#883—21no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40#5229C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5185—24no—
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×Dic3⋊C8C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49#4994—21no—
50#4994—21no—
51#4988C2211yescharacteristic
52#4975C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55#4959—21no—
56#4959—21no—
57#4819—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#542—31no—
65C2×#464—31no—
66C2×#463—31no—
67#2620—31no—
68#2024—31no—
69#2023—31no—
70#2015—31no—
71#2012—31no—
72#2001D311yescharacteristic, complemented
73#2000—31no—
74#2000—31no—
75#1999—31no—
76#1803—31no—
77#1802—31no—
78#1798—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×D12C2311yescharacteristic
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C22×Dic6—21no—
88C2×C3×Q16—22no—
89C2×C3×Q16—41no—
90C2×C3×Q16—41no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—22no—
95C3×C22⋊Q8—41no—
96C3×C22⋊Q8—41no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×#217D411yescharacteristic
104C2×#217D411yescharacteristic
105#947—22no—
106#947—22no—
107#947—22no—
108#947—22no—
109Q8×Dic3—22no—
110Q8×Dic3D414yescomplemented
111C2×#215—22no—
112C2×#215—22no—
113C2×#215—41no—
114C2×#215—41no—
115C2×#215—41no—
116C2×#215—41no—
117#930—22no—
118#930—22no—
119#930—41no—
120#930—41no—
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×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130#926—22no—
131#926—22no—
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3D411yescharacteristic
134C2×C4⋊Dic3D411yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3C2311yescharacteristic
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×D24—22no—
146C2×D24—41no—
147C2×D24—41no—
148#898—28no—
149#897—28no—
150#893—22no—
151#893D414yescomplemented
152#888—22no—
153#888—22no—
154#885—28no—
155#883—28no—
156C3×#103—22no—
157C3×#103—41no—
158C3×C22⋊C8—41no—
159#835—22no—
160#835—41no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#830—41no—
164#821—22no—
165#821—41no—
166Dic3⋊C8—22no—
167Dic3⋊C8—22no—
168#809—22no—
169#809—41no—
170C22×Q16C2×D311yescharacteristic
171C22×SD16—31no—
172C22×SD16—31no—
173C22×D8—31no—
174#542—64no—
175#542—64no—
176C2×C4⋊Q8—31no—
177C2×#126—61no—
178C2×#124—31no—
179C2×#124—31no—
180C2×#124—61no—
181C2×#123—61no—
182C2×C22⋊Q8—61no—
183C2×C22⋊Q8C2×D311yescharacteristic
184C2×C22⋊Q8C2×D311yescharacteristic
185C2×#121—31no—
186C2×#121—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×#117—31no—
190#464—64no—
191#463—64no—
192C2×C4⋊C8—31no—
193C2×C4⋊C8—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103C2×D311yescharacteristic
197C2×#103C2×D311yescharacteristic
198C2×#102—31no—
199C2×#102—31no—
200C2×#102—31no—
201C2×#102—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8C2×D311yescharacteristic
204#396—61no—
205#396—61no—
206#394—61no—
207#394—61no—
208#391—31no—
209#390—31no—
210#384—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C23×D3—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×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8C2×D412yes—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C2×#67—24no—
245C2×#67—42no—
246C2×#67—81no—
247C2×#67—81no—
248C2×#67—81no—
249C2×#67—81no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256C2×D12—21no—
257C2×D12—21no—
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—21no—
267C2×D12C2×D412yes—
268C2×C4×D3—24no—
269C2×C4×D3—81no—
270C2×C4×D3—81no—
271C2×Dic6—24no—
272C2×Dic6—81no—
273C2×Dic6—81no—
274C3×Q16—44no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—42no—
286C3×C4⋊C4C2×D412yes—
287C3×C22⋊C4—24no—
288C3×C22⋊C4—42no—
289#217—22no—
290#217—22no—
291#215—44no—
292#215—44no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—24no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—81no—
301(C2×D3)⋊C4—81no—
302C4⋊Dic3—21no—
303C4⋊Dic3—24no—
304C4⋊Dic3—22no—
305C4⋊Dic3—22no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3C2×D412yes—
309Dic3⋊C4—24no—
310Dic3⋊C4—81no—
311Dic3⋊C4—81no—
312C4×Dic3—21no—
313C4×Dic3—21no—
314C4×Dic3—24no—
315C4×Dic3C2×D412yes—
316C4×Dic3C2×D412yes—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323D24—44no—
324C22×Q8—61no—
325C22×Q8C22×D311yescharacteristic
326C22×Q8C22×D311yescharacteristic
327C22×D4—31no—
328C22×D4—31no—
329C22×D4—61no—
330C22×D4—61no—
331C23×C4—61no—
332C23×C4C22×D311yescharacteristic
333C2×Q16—22no—
334C2×Q16—41no—
335C2×Q16—41no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—121no—
339C2×SD16—121no—
340C2×SD16—121no—
341C2×SD16—121no—
342C2×D8—62no—
343C2×D8—121no—
344C2×D8—121no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8C22×D311yescharacteristic
348C22×C8C22×D311yescharacteristic
349C4⋊Q8—62no—
350C4⋊Q8—62no—
351#126—68no—
352#124—62no—
353#124—62no—
354#124—68no—
355#124—62no—
356#124—62no—
357#123—68no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—41no—
361C22⋊Q8—41no—
362C22⋊Q8—68no—
363#121—62no—
364#121—62no—
365#121—121no—
366#121—121no—
367C4×Q8—34no—
368C4×Q8—62no—
369C4×D4—34no—
370C4×D4—62no—
371#117—62no—
372#117—62no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4—61no—
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—31no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C42—31no—
399C2×C42—31no—
400C2×C42—61no—
401C4⋊C8—62no—
402C4⋊C8—62no—
403#103—22no—
404#103—41no—
405#103—62no—
406#103—121no—
407#102—62no—
408#102—62no—
409#102—121no—
410#102—121no—
411C22⋊C8—41no—
412C22⋊C8—121no—
413#95—61no—
414#95—61no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3C22×D411yescharacteristic
423C22×D3—22no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C3×Q8—22no—
438C3×Q8—22no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×Q8—41no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4H(5,𝔽2)11yescharacteristic
467C2×C3×C4H(5,𝔽2)11yescharacteristic
468C2×C3×C4H(5,𝔽2)11yescharacteristic
469C2×C3×C42−1+411yescharacteristic
470#67—84no—
471#67—84no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3#12012yes—
489C2×Dic3#12012yes—
490D12—22no—
491D12—22no—
492D12—41no—
493D12—41no—
494D12—41no—
495D12—41no—
496D12—41no—
497D12—41no—
498C4×D3—84no—
499Dic6—84no—
500C3×C8—41no—
501C3×C8—41no—
502C3⋊C8—41no—
503C3⋊C8—41no—
504C24—61no—
505C24—61no—
506C24D3×D411yescharacteristic
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—64no—
519C2×Q8—241no—
520C2×Q8—241no—
521C2×Q8D3×D412yes—
522C2×D4—32no—
523C2×D4—64no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—122no—
536C2×D4—241no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4—241no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—64no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—241no—
558C22×C4—241no—
559C22×C4D3×D411yescharacteristic
560C22×C4C23×D311yescharacteristic
561Q16—44no—
562SD16—124no—
563SD16—124no—
564D8—124no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C4⋊C4—24no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—32no—
582C4⋊C4—42no—
583C4⋊C4—62no—
584C4⋊C4—62no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—241no—
591C4⋊C4—241no—
592C4⋊C4D3×D412yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—62no—
600C22⋊C4—62no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—241no—
605C22⋊C4—241no—
606C42—32no—
607C42—32no—
608C42—64no—
609C42—61no—
610C42—61no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3C2×#12011yescharacteristic
619C22×C3#53511yescharacteristic
620C22×C3#53711yescharacteristic
621C22×C3#57611yescharacteristic
622C22×C3#57711yescharacteristic
623C22×C3#57711yescharacteristic
624C22×C3#57811yescharacteristic
625C2×D3—42no—
626C2×D3—42no—
627C2×D3—42no—
628C2×D3—81no—
629C2×D3—81no—
630C2×D3—81no—
631C2×D3—81no—
632C2×D3—81no—
633C2×D3—81no—
634C2×D3—81no—
635C2×D3—81no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C3×C4—41no—
640C3×C4—42no—
641C3×C4—42no—
642C3×C4—81no—
643C3×C4—81no—
644C3×C4#53511yescharacteristic
645C3×C4#53511yescharacteristic
646C3×C4#53711yescharacteristic
647C3×C4#53711yescharacteristic
648Dic3—22no—
649Dic3—22no—
650Dic3—41no—
651Dic3—42no—
652Dic3—41no—
653Dic3—81no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—62no—
662C23—121no—
663C23—121no—
664C23—121no—
665C23—121no—
666C23—121no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23C2×D3×D411yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—244no—
685D4—62no—
686D4—62no—
687D4—121no—
688D4—121no—
689D4—121no—
690D4—121no—
691D4—121no—
692D4—121no—
693D4—244no—
694D4—244no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—32no—
701C2×C4—32no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—62no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—244no—
733C2×C4C2×D3×D411yescharacteristic
734C2×C4C2×D3×D411yescharacteristic
735C2×C4#100411yescharacteristic
736C2×C4#100411yescharacteristic
737C2×C4#100411yescharacteristic
738C2×C4#101011yescharacteristic
739C8—41no—
740C8—41no—
741C8—121no—
742C8—121no—
743C2×C3—81no—
744C2×C3#261511yescharacteristic
745C2×C3#301211yescharacteristic
746C2×C3#301311yescharacteristic
747C2×C3#322411yescharacteristic
748C2×C3#322511yescharacteristic
749C2×C3#326211yescharacteristic
750C2×C3#326311yescharacteristic
751D3—82no—
752D3—161no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—122no—
761C22—122no—
762C22—122no—
763C22—241no—
764C22—241no—
765C22—241no—
766C22—241no—
767C22—241no—
768C22—241no—
769C22—241no—
770C22—241no—
771C22—241no—
772C22—241no—
773C22—241no—
774C22D3×#12011yescharacteristic
775C22#559211yescharacteristic
776C22#559711yescharacteristic
777C22#576611yescharacteristic
778C22#576911yescharacteristic
779C22#577811yescharacteristic
780C22#577811yescharacteristic
781C4—42no—
782C4—41no—
783C4—42no—
784C4—62no—
785C4—62no—
786C4—81no—
787C4—81no—
788C4—121no—
789C4—121no—
790C4—122no—
791C4—241no—
792C4#559211yescharacteristic
793C4#559711yescharacteristic
794C4#560811yescharacteristic
795C4#571511yescharacteristic
796C3#2967711yescharacteristic, complemented, Sylow
797C2—81no—
798C2—242no—
799C2—481no—
800C2#7669711yescharacteristic
801C2#8018611yescharacteristic
802C2#8020311yescharacteristic
803C2#8023111yescharacteristic
804C2#8026311yescharacteristic
805C2#8075111yescharacteristic
806C2#8089911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2001C2
socleC23×C3C22×D4
prime radical#69961C2
hypercenter#2001D3
hypocenterC3#29677
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
1. C2×#5643C2semidirect
2. C2×#5185C2semidirect
3. #82821C2semidirect
4. C2×#4819C2semidirect
5. C3×#2001C2semidirect
6. #72072C2semidirect
7. #71699C2semidirect
8. #71699C2semidirect
9. #70277C2semidirect
10. #70231C2semidirect
11. #70221C2semidirect
13. #69909C2semidirect
14. #68898C2semidirect
15. #68892C2semidirect
72. #2001D3semidirect
110. Q8×Dic3D4semidirect
151. #893D4semidirect
796. C3#29677semidirect

Maximal subgroups

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

subgroupindex
C2×#56432
C2×#51852
#828212
C2×#48192
C3×#20012
#720722
#716992
#702772
#702312
#702212
#699612
#699092
#688982
#688922
#296773