Finite Group Databasebeta

← #10827603

Subgroups — #10827603

Order 768.

1300 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5543C211yesmaximal, characteristic, complemented
2C3×#2407C211yesmaximal, characteristic
3C2×#5239C211yesmaximal, characteristic, complemented
4C2×#5232C211yesmaximal, characteristic, complemented
5#71700C211yesmaximal, characteristic, complemented
6#71692C211yesmaximal, characteristic, complemented
7#71685C211yesmaximal, characteristic, complemented
8#71677C211yesmaximal, characteristic, complemented
9#71611C211yesmaximal, characteristic, complemented
10#69690C211yesmaximal, characteristic, complemented
11#69668C211yesmaximal, characteristic, complemented
12#69660C211yesmaximal, characteristic, complemented
13#69638C211yesmaximal, characteristic, complemented
14#69516C211yesmaximal, characteristic, complemented
15#69501C211yesmaximal, characteristic, complemented
16#23981—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C2×D4×Dic3—21no—
23C22×#214C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×#208C2211yescharacteristic
29#5543—24no—
30#5543—24no—
31C2×#890—21no—
32C2×#878—21no—
33C2×#878—21no—
34C2×#869C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C3×#394—21no—
37C3×#392—21no—
38C3×#391C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C3×#386—21no—
41C3×#385—21no—
42C3×#380C2211yescharacteristic
43#5239—24no—
44#5232—24no—
45C2×#835C2211yescharacteristic
46C2×#835C2211yescharacteristic
47C2×#835C2211yescharacteristic
48C2×#832C2211yescharacteristic
49C2×#832C2211yescharacteristic
50C2×#832C2211yescharacteristic
51C2×#830C2211yescharacteristic
52C2×#830C2211yescharacteristic
53C2×#830C2211yescharacteristic
54C2×#810C2211yescharacteristic
55C2×#810C2211yescharacteristic
56#4529C2211yescharacteristic
57#4529C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#554—31no—
65C2×#452—31no—
66C2×#417—31no—
67#2407D311yescharacteristic
68#2024—31no—
69#2023—31no—
70#2001—31no—
71#2000—31no—
72#1894—31no—
73#1880—31no—
74#1878—31no—
75#1874—31no—
76#1872—31no—
77#1870—31no—
78#1823—31no—
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4—21no—
88C22×C3×D4D411yescharacteristic
89C22×C3×D4C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×Dic3—21no—
94C23×Dic3—21no—
95C22×Dic6—21no—
96C22×Dic6C2311yescharacteristic
97C3×C22⋊Q8—22no—
98C3×C22⋊Q8—41no—
99C3×#121—22no—
100C3×#121—41no—
101C3×C4×D4—22no—
102C3×C4×D4—22no—
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⋊C4D411yescharacteristic
113C2×C3×C22⋊C4D411yescharacteristic
114C2×C3×C42C2311yescharacteristic
115C2×#217—21no—
116C2×#217—21no—
117C2×#216—22no—
118C2×#216—22no—
119C2×#216—41no—
120D4×Dic3—28no—
121C2×#214—22no—
122C2×#214—22no—
123C2×#214—41no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3—22no—
128C2×C4⋊Dic3—22no—
129C2×C4⋊Dic3—22no—
130C2×C4⋊Dic3D414yescomplemented
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134#924—22no—
135#924—22no—
136#924—22no—
137#924D414yescomplemented
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×C4×Dic3—21no—
142C2×#208—22no—
143C2×#208—41no—
144C2×#208—41no—
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149#890—28no—
150#878—28no—
151#878—28no—
152#869—22no—
153#869—22no—
154C4×Dic6—22no—
155C4×Dic6—22no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159#835—22no—
160#835—22no—
161#835—22no—
162#832—22no—
163#832—22no—
164#832—22no—
165#830—22no—
166#830—41no—
167#830—41no—
168#810—41no—
169#810—41no—
170C22×#41C2×D311yescharacteristic
171C22×Q16—31no—
172C22×SD16—31no—
173C22×M16—31no—
174#554—64no—
175#554—64no—
176C2×C4⋊Q8—31no—
177C2×#125—61no—
178C2×C22⋊Q8—31no—
179C2×C22⋊Q8—31no—
180C2×C22⋊Q8—61no—
181C2×C22⋊Q8—61no—
182C2×C22⋊Q8C2×D311yescharacteristic
183C2×#121C2×D311yescharacteristic
184C2×C4×Q8—31no—
185C2×C4×D4—61no—
186C2×C4×D4C2×D311yescharacteristic
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189#452—64no—
190#417—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202#394—21no—
203#392—21no—
204#391C2×D311yescharacteristic
205#390C2×D311yescharacteristic
206#386—21no—
207#385—21no—
208#380C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C24×C3C2×D411yescharacteristic
220C3×#41—28no—
221C3×#41—44no—
222C3×#41—44no—
223C3×#41—44no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8#4112yes—
230C2×C3×D4—22no—
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C2×C3×D4—81no—
244C2×C3×D4#4112yes—
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×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—42no—
259C22×C3×C4—42no—
260C22×C3×C4—42no—
261C22×C3×C4C2×D412yes—
262C22×C3×C4C2×D412yes—
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—24no—
273C22×Dic3—24no—
274C22×Dic3—81no—
275C22×Dic3—81no—
276C22×Dic3—81no—
277C22×Dic3—81no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—24no—
284C2×Dic6—81no—
285C2×Dic6—81no—
286C2×Dic6C2×D412yes—
287C3×C4⋊C4—22no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—42no—
293C3×C22⋊C4—22no—
294C3×C22⋊C4—22no—
295C3×C22⋊C4—42no—
296C3×C22⋊C4—42no—
297C3×C22⋊C4—42no—
298C3×C22⋊C4—81no—
299C3×C22⋊C4—81no—
300C3×C42—21no—
301C3×C42—21no—
302#217—24no—
303#217—24no—
304#216—44no—
305#214—44no—
306C4⋊Dic3—24no—
307C4⋊Dic3—24no—
308C4⋊Dic3—24no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3C2×D412yes—
313C4⋊Dic3C2×D412yes—
314C4⋊Dic3C2×D412yes—
315Dic3⋊C4—24no—
316Dic3⋊C4—24no—
317Dic3⋊C4—24no—
318C4×Dic3—24no—
319#208—44no—
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—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—41no—
337C2×#41—41no—
338C22×Q8—31no—
339C22×Q8—61no—
340C22×Q8C22×D311yescharacteristic
341C22×D4—21no—
342C22×D4—21no—
343C22×D4#6711yescharacteristic
344C22×D4C22×D311yescharacteristic
345C23×C4—21no—
346C23×C4—61no—
347C23×C4—61no—
348C23×C4C22×D311yescharacteristic
349C23×C4C22×D311yescharacteristic
350C2×Q16—62no—
351C2×Q16—62no—
352C2×Q16—121no—
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—121no—
356C2×M16—62no—
357C2×M16—121no—
358C2×M16—121no—
359C22×C8—31no—
360C22×C8—31no—
361C22×C8—31no—
362C22×C8—31no—
363C4⋊Q8—62no—
364C4⋊Q8—62no—
365#125—68no—
366C22⋊Q8—22no—
367C22⋊Q8—34no—
368C22⋊Q8—41no—
369C22⋊Q8—68no—
370C22⋊Q8—68no—
371C22⋊Q8—62no—
372C22⋊Q8—62no—
373C22⋊Q8—62no—
374#121—22no—
375#121—41no—
376C4×Q8—62no—
377C4×Q8—62no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—68no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4#6711yescharacteristic
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4#6711yescharacteristic
406C2×C22⋊C4#6711yescharacteristic
407C2×C42—61no—
408C2×C42C22×D311yescharacteristic
409#103—62no—
410#103—62no—
411#103—62no—
412#103—121no—
413#103—121no—
414#102—62no—
415#102—62no—
416#102—62no—
417C22⋊C8—62no—
418C22⋊C8—121no—
419C22⋊C8—121no—
420#95—21no—
421#95—21no—
422#95—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—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—22no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3#12012yes—
443C23×C3#13712yes—
444C23×C3C22×D411yescharacteristic
445C3×Q8—22no—
446C3×Q8—22no—
447C3×Q8—41no—
448C3×Q8—41no—
449C3×D4—28no—
450C3×D4—22no—
451C3×D4—22no—
452C3×D4—48no—
453C3×D4—41no—
454C3×D4—41no—
455C3×D4—84no—
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—22no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—48no—
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—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4#12012yes—
485C2×C3×C4#13712yes—
486C2×C3×C4C22×D411yescharacteristic
487C2×C3×C4C22×D411yescharacteristic
488C2×C3×C4C2×#4111yescharacteristic
489C2×C3×C4C2×#4111yescharacteristic
490C2×C3×C4H(5,𝔽2)11yescharacteristic
491C2×C3×C4H(5,𝔽2)11yescharacteristic
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—84no—
505C2×Dic3—84no—
506Dic6—22no—
507Dic6—22no—
508Dic6—41no—
509Dic6—41no—
510Dic6—84no—
511C3⋊C8—41no—
512C3⋊C8—41no—
513C3⋊C8—41no—
514C3⋊C8—41no—
515C24—21no—
516C24C2×#6711yescharacteristic
517C24C2×#6711yescharacteristic
518#41—28no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—32no—
528C2×Q8—64no—
529C2×Q8—61no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—241no—
535C2×Q8—241no—
536C2×Q8#23712yes—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—81no—
551C2×D4#23712yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—64no—
573C22×C4—64no—
574C22×C4—241no—
575C22×C4—241no—
576C22×C4—241no—
577C22×C4—241no—
578C22×C4D3×D412yes—
579C22×C4D3×D412yes—
580C22×C4C2×#6711yescharacteristic
581C22×C4C2×#6711yescharacteristic
582C22×C4C2×#6711yescharacteristic
583C22×C4C2×#6711yescharacteristic
584C22×C4C23×D311yescharacteristic
585Q16—124no—
586SD16—124no—
587M16—124no—
588C2×C8—61no—
589C2×C8—61no—
590C2×C8—61no—
591C2×C8—61no—
592C2×C8—61no—
593C2×C8—61no—
594C2×C8—61no—
595C2×C8—61no—
596C2×C8—61no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—32no—
606C4⋊C4—32no—
607C4⋊C4—32no—
608C4⋊C4—42no—
609C4⋊C4—64no—
610C4⋊C4—64no—
611C4⋊C4—64no—
612C4⋊C4—64no—
613C4⋊C4—64no—
614C4⋊C4—64no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—64no—
624C22⋊C4—64no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C42—21no—
628C42—21no—
629C42—64no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—42no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3C2×#12011yescharacteristic
652C22×C3#54611yescharacteristic
653C22×C3#54611yescharacteristic
654C22×C3C2×#13711yescharacteristic
655C22×C3C2×#13711yescharacteristic
656C22×C3#57611yescharacteristic
657C22×C3#57711yescharacteristic
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—41no—
661C3×C4—42no—
662C3×C4—41no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4#52511yescharacteristic
666C3×C4#53511yescharacteristic
667C3×C4#54611yescharacteristic
668C3×C4#54611yescharacteristic
669Dic3—42no—
670Dic3—42no—
671Dic3—42no—
672Dic3—42no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23#93712yes—
693C23#95112yes—
694C23C22×#6711yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—41no—
698Q8—41no—
699Q8—62no—
700Q8—62no—
701Q8—121no—
702Q8—121no—
703Q8—244no—
704D4—28no—
705D4—22no—
706D4—22no—
707D4—48no—
708D4—41no—
709D4—41no—
710D4—84no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—48no—
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—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4—244no—
752C2×C4—244no—
753C2×C4#93712yes—
754C2×C4#95112yes—
755C2×C4C2×D3×D411yescharacteristic
756C2×C4C2×D3×D411yescharacteristic
757C2×C4C2×#23711yescharacteristic
758C2×C4C2×#23711yescharacteristic
759C2×C4#100411yescharacteristic
760C2×C4#100411yescharacteristic
761C8—121no—
762C8—121no—
763C8—121no—
764C8—121no—
765C2×C3—42no—
766C2×C3—42no—
767C2×C3—82no—
768C2×C3#240411yescharacteristic
769C2×C3#300411yescharacteristic
770C2×C3#301211yescharacteristic
771C2×C3#331411yescharacteristic
772C2×C3#331611yescharacteristic
773C2×C3#333111yescharacteristic
774C2×C3#333311yescharacteristic
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22C2×#93711yescharacteristic
797C22#580611yescharacteristic
798C22#580611yescharacteristic
799C22C2×#95111yescharacteristic
800C22C2×#95111yescharacteristic
801C22#583511yescharacteristic
802C22#583711yescharacteristic
803C4—22no—
804C4—22no—
805C4—41no—
806C4—42no—
807C4—41no—
808C4—81no—
809C4—81no—
810C4—122no—
811C4—122no—
812C4—122no—
813C4—122no—
814C4#558611yescharacteristic
815C4#559111yescharacteristic
816C4#559111yescharacteristic
817C4#559211yescharacteristic
818C3#2398111yescharacteristic, complemented, Sylow
819C2—42no—
820C2—42no—
821C2—82no—
822C2#8258111yescharacteristic
823C2#8293311yescharacteristic
824C2#8342411yescharacteristic
825C2#8349811yescharacteristic
826C2#8351511yescharacteristic
827C2#8353811yescharacteristic
828C2#8357511yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#2407C2
socleC23×C3C22×D4
hypercenter#2407D3
hypocenterC3#23981
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#5543C2semidirect
3. C2×#5239C2semidirect
4. C2×#5232C2semidirect
5. #71700C2semidirect
6. #71692C2semidirect
7. #71685C2semidirect
8. #71677C2semidirect
9. #71611C2semidirect
10. #69690C2semidirect
11. #69668C2semidirect
12. #69660C2semidirect
13. #69638C2semidirect
14. #69516C2semidirect
15. #69501C2semidirect
130. C2×C4⋊Dic3D4semidirect
137. #924D4semidirect
818. C3#23981semidirect

Maximal subgroups

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

subgroupindex
C2×#55432
C3×#24072
C2×#52392
C2×#52322
#717002
#716922
#716852
#716772
#716112
#696902
#696682
#696602
#696382
#695162
#695012
#239813