Finite Group Databasebeta

← #10811314

Subgroups — #10811314

Order 768.

1696 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5806C211yesmaximal, characteristic
2C3×D4×C22⋊C4C211yesmaximal, characteristic, complemented
3D4×#217C211yesmaximal, characteristic, complemented
4#71543C212yesmaximal, complemented
5C2×#4527C212yesmaximal, complemented
6#69530C211yesmaximal, characteristic, complemented
7#69529C211yesmaximal, characteristic, complemented
8#69496C212yesmaximal, complemented
9#69495C212yesmaximal, complemented
10#69457C211yesmaximal, characteristic, complemented
11C4×#806C211yesmaximal, characteristic, complemented
12#22476—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C22×#237C411yescharacteristic, complemented
15C2×C3×C4×D4—21no—
16C22×C3×C22⋊C4C2212yes—
17C2×#953C2212yes—
18C22×#217C2212yes—
19C22×#217C2212yes—
20#5806—21no—
21#5806—22no—
22#5806—21no—
23#5806—21no—
24#5806—22no—
25#5806—21no—
26C2×#939C412yescomplemented
27C2×#938C411yescharacteristic, complemented
28C2×#936C411yescharacteristic, complemented
29C2×#935C412yescomplemented
30C2×D4×Dic3—21no—
31C2×D4×Dic3C411yescharacteristic, complemented
32C2×C4×#67C2211yescharacteristic
33C2×#924C2211yescharacteristic
34C3×#390—21no—
35C3×#386—22no—
36C3×#380C2211yescharacteristic
37C3×#379C2212yes—
38C3×C4×C22⋊C4C2211yescharacteristic
39#5247C2212yes—
40#5221—21no—
41#5220—22no—
42#5212C2211yescharacteristic
43C4×#217C2211yescharacteristic
44C2×#806C2211yescharacteristic
45C2×#806C2211yescharacteristic
46C2×#806C2212yes—
47#4527C2211yescharacteristic
48#4527C2211yescharacteristic
49#4527C2212yes—
50#4527C2212yes—
51#4527C2212yes—
52#4527C2212yes—
53#4527C2212yes—
54C2×#546—31no—
55D4×C22⋊C4—31no—
56D4×C22⋊C4D311yescharacteristic, complemented
57#1996—31no—
58#1996—31no—
59#1898—32no—
60#1898—32no—
61#1819—32no—
62#1799—31no—
63C4×#99—31no—
64C2×#342—32no—
65C25×C3C2312yes—
66C22×C3×D4—44no—
67C22×C3×D4C2×C411yescharacteristic
68C22×C3×D4C2×C412yes—
69C22×C3×D4C2×C411yescharacteristic
70C22×C3×D4D411yescharacteristic
71C22×C3×D4D412yes—
72C22×C3×D4D411yescharacteristic
73C22×C3×D4D411yescharacteristic
74C22×C3×D4D412yes—
75C22×C3×D4D411yescharacteristic
76C23×C3×C4—22no—
77C23×C3×C4C2311yescharacteristic
78C22×#67C2×C412yescomplemented
79C22×#67C2×C412yescomplemented
80C22×#67C2311yescharacteristic
81C23×Dic3—22no—
82C23×Dic3C2×C412yescomplemented
83C23×Dic3C2×C412yescomplemented
84C2×#237—22no—
85C2×#237—21no—
86C2×#237—21no—
87C2×#237—44no—
88C22×C4×D3C2×C411yescharacteristic, complemented
89C22×Dic6C2×C411yescharacteristic, complemented
90C3×C4×D4—44no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—42no—
97C2×C3×C22⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4C2312yes—
99C2×C3×C22⋊C4C2311yescharacteristic
100C2×C3×C42—21no—
101#953—22no—
102#953—22no—
103#953—22no—
104#953—22no—
105C2×#217—22no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—24no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—42no—
114C2×#217C2×C412yescomplemented
115C2×#217C2×C412yescomplemented
116C2×#217C2×C412yescomplemented
117C2×#217C2×C412yescomplemented
118C2×#217C2311yescharacteristic
119C2×#217C2312yes—
120C2×#217C2312yes—
121C2×#217C2311yescharacteristic
122C2×#217C2311yescharacteristic
123#939—22no—
124#939—22no—
125#939—22no—
126#939—22no—
127#938—21no—
128#938—21no—
129#938—22no—
130#936—21no—
131#936—21no—
132#936—22no—
133#935—22no—
134#935—22no—
135#935—22no—
136#935—22no—
137D4×Dic3—22no—
138D4×Dic3—21no—
139D4×Dic3—21no—
140D4×Dic3—44no—
141C4×#67—21no—
142C4×#67—21no—
143C4×#67—21no—
144C4×#67—21no—
145C2×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
146C2×C4⋊Dic3—21no—
147C2×C4⋊Dic3C2×C411yescharacteristic, complemented
148#924—21no—
149#924—21no—
150#924—21no—
151#924—21no—
152C2×Dic3⋊C4C2×C412yescomplemented
153C2×Dic3⋊C4C2×C411yescharacteristic, complemented
154C2×C4×Dic3—21no—
155C2×C4×Dic3C2×C411yescharacteristic, complemented
156C3×#95—21no—
157C3×#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160#806—22no—
161#806—22no—
162#806—42no—
163C22×#41—31no—
164C23×D4C2×D311yescharacteristic
165#546—61no—
166#546—62no—
167#546—61no—
168#546—61no—
169#546—62no—
170#546—61no—
171C2×#124—31no—
172C2×#123—32no—
173C2×C22⋊Q8—31no—
174C2×#121—31no—
175C2×#121—32no—
176C2×#120—32no—
177C2×C4×D4—21no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C22×C22⋊C4—32no—
182C22×C22⋊C4—32no—
183C22×C22⋊C4C2×D312yes—
184C2×#99—31no—
185C2×#99—31no—
186C2×#99—32no—
187#390—21no—
188#390—61no—
189#386—22no—
190#386—62no—
191#380—31no—
192#380C2×D311yescharacteristic
193#379—32no—
194#379C2×D312yes—
195C4×C22⋊C4—31no—
196C4×C22⋊C4C2×D311yescharacteristic
197#342—32no—
198#342—31no—
199#342—32no—
200#342—32no—
201#342—32no—
202#342—32no—
203#342—31no—
204C24×C3—22no—
205C24×C3—22no—
206C24×C3—22no—
207C24×C3—22no—
208C24×C3—44no—
209C24×C3—82no—
210C24×C3C22×C412yes—
211C24×C3C22×C412yes—
212C24×C3C2×D412yes—
213C24×C3C2×D412yes—
214C24×C3C2×D412yes—
215C24×C3C2×D412yes—
216C24×C3C2411yescharacteristic
217C23×D3C22×C411yescharacteristic
218C2×C3×D4—24no—
219C2×C3×D4—24no—
220C2×C3×D4—24no—
221C2×C3×D4—42no—
222C2×C3×D4—42no—
223C2×C3×D4—42no—
224C2×C3×D4—44no—
225C2×C3×D4—44no—
226C2×C3×D4—44no—
227C2×C3×D4C22⋊C412yes—
228C2×C3×D4C22⋊C411yescharacteristic
229C2×C3×D4C22⋊C412yes—
230C2×C3×D4C22⋊C412yes—
231C2×C3×D4C22⋊C411yescharacteristic
232C2×C3×D4C22⋊C411yescharacteristic
233C2×C3×D4C22⋊C412yes—
234C2×C3×D4C22⋊C412yes—
235C2×C3×D4C22⋊C412yes—
236C2×C3×D4C22⋊C411yescharacteristic
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—22no—
240C22×C3×C4—42no—
241C22×C3×C4—44no—
242C22×C3×C4—44no—
243C22×C3×C4—82no—
244C22×C3×C4C22×C411yescharacteristic
245C22×C3×C4C22×C411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C2×#67—22no—
251C2×#67—22no—
252C2×#67—21no—
253C2×#67—21no—
254C2×#67—21no—
255C2×#67—21no—
256C2×#67—21no—
257C2×#67—21no—
258C2×#67—22no—
259C2×#67—22no—
260C2×#67—44no—
261C2×#67—82no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—21no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—21no—
268C22×Dic3—22no—
269C22×Dic3—44no—
270C22×Dic3—44no—
271C22×Dic3—44no—
272C22×Dic3—82no—
273C22×Dic3—82no—
274C22×Dic3C22×C411yescharacteristic
275C22×Dic3C22×C411yescharacteristic
276C22×Dic3C22×C412yes—
277C22×Dic3C22×C412yes—
278C22×Dic3C22×C411yescharacteristic
279#237—48no—
280#237—44no—
281#237—44no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—42no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—42no—
288C3×C4⋊C4—42no—
289C3×C22⋊C4—21no—
290C3×C22⋊C4—21no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—22no—
293C3×C22⋊C4—21no—
294C3×C22⋊C4—44no—
295C3×C22⋊C4—44no—
296C3×C22⋊C4—82no—
297C3×C22⋊C4#4112yescomplemented
298C3×C42—42no—
299#217—22no—
300#217—22no—
301#217—22no—
302#217—22no—
303#217—22no—
304#217—22no—
305#217—22no—
306#217—22no—
307#217—22no—
308#217—22no—
309#217—21no—
310#217—21no—
311#217—21no—
312#217—21no—
313#217—22no—
314#217—22no—
315#217—21no—
316#217—44no—
317#217—44no—
318#217—82no—
319#217#4112yescomplemented
320(C2×D3)⋊C4—21no—
321(C2×D3)⋊C4—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3—42no—
325Dic3⋊C4—22no—
326Dic3⋊C4—22no—
327Dic3⋊C4—21no—
328Dic3⋊C4—21no—
329C4×Dic3—21no—
330C4×Dic3—21no—
331C4×Dic3—42no—
332C25C22×D312yes—
333C2×#41—61no—
334C2×#41—62no—
335C2×#41—61no—
336C2×#41—124no—
337C22×Q8—31no—
338C22×D4—31no—
339C22×D4—32no—
340C22×D4—32no—
341C22×D4—44no—
342C22×D4C4×D311yescharacteristic
343C22×D4C4×D312yes—
344C22×D4C4×D311yescharacteristic
345C22×D4D1211yescharacteristic
346C22×D4D1212yes—
347C22×D4D1211yescharacteristic
348C22×D4#6711yescharacteristic
349C22×D4#6712yes—
350C22×D4#6711yescharacteristic
351C23×C4—22no—
352C23×C4—32no—
353C23×C4—32no—
354C23×C4—31no—
355C23×C4—62no—
356C23×C4C22×D311yescharacteristic
357#124—61no—
358#124—61no—
359#124—62no—
360#123—62no—
361#123—62no—
362#123—62no—
363#123—62no—
364C22⋊Q8—61no—
365C22⋊Q8—61no—
366C22⋊Q8—61no—
367C22⋊Q8—61no—
368#121—61no—
369#121—61no—
370#121—62no—
371#121—62no—
372#121—62no—
373#121—62no—
374#121—62no—
375#120—62no—
376#120—62no—
377#120—62no—
378#120—62no—
379C4×D4—44no—
380C4×D4—62no—
381C4×D4—61no—
382C4×D4—61no—
383C4×D4—61no—
384C4×D4—61no—
385C4×D4—61no—
386C4×D4—61no—
387C4×D4—124no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—61no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—31no—
398C2×C22⋊C4—32no—
399C2×C22⋊C4—32no—
400C2×C22⋊C4—32no—
401C2×C22⋊C4—32no—
402C2×C22⋊C4—31no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—122no—
417C2×C22⋊C4C22×D312yes—
418C2×C22⋊C4C22×D311yescharacteristic
419C2×C22⋊C4C22×D311yescharacteristic
420C2×C42—21no—
421C2×C42—31no—
422C2×C42—61no—
423#99—62no—
424#99—62no—
425#99—122no—
426#95—21no—
427#95—21no—
428#95—61no—
429#95—61no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—24no—
437C23×C3—24no—
438C23×C3—24no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—42no—
446C23×C3—42no—
447C23×C3—41no—
448C23×C3—42no—
449C23×C3—41no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—42no—
453C23×C3—42no—
454C23×C3—42no—
455C23×C3—42no—
456C23×C3—84no—
457C23×C3—84no—
458C23×C3—84no—
459C23×C3—84no—
460C23×C3C2×C22⋊C412yes—
461C23×C3C2×C22⋊C412yes—
462C23×C3C2×C22⋊C412yes—
463C23×C3C2×C22⋊C412yes—
464C23×C3C23×C411yescharacteristic
465C23×C3C22×D411yescharacteristic
466C23×C3C22×D411yescharacteristic
467C23×C3C2×#4111yescharacteristic
468C23×C3C2×#4111yescharacteristic
469C23×C3H(5,𝔽2)11yescharacteristic
470C23×C32−1+411yescharacteristic
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—41no—
475C22×D3—41no—
476C3×D4—24no—
477C3×D4—24no—
478C3×D4—24no—
479C3×D4—22no—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—42no—
483C3×D4—42no—
484C3×D4—42no—
485C3×D4#9914yescomplemented
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—42no—
497C2×C3×C4—41no—
498C2×C3×C4—42no—
499C2×C3×C4—42no—
500C2×C3×C4—41no—
501C2×C3×C4—88no—
502C2×C3×C4C2×C22⋊C411yescharacteristic
503C2×C3×C4C2×C22⋊C411yescharacteristic
504C2×C3×C4C2×C22⋊C411yescharacteristic
505C2×C3×C4C2×C22⋊C411yescharacteristic
506#67—44no—
507#67—41no—
508#67—41no—
509#67—41no—
510#67—41no—
511#67—44no—
512#67—82no—
513#67—82no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—22no—
522C2×Dic3—41no—
523C2×Dic3—44no—
524C2×Dic3—41no—
525C2×Dic3—44no—
526C2×Dic3—42no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—42no—
530C2×Dic3—41no—
531C2×Dic3—42no—
532C2×Dic3—41no—
533C2×Dic3—42no—
534C2×Dic3—42no—
535C2×Dic3—41no—
536C2×Dic3—82no—
537C2×Dic3—82no—
538C2×Dic3—88no—
539C4×D3—42no—
540C4×D3—42no—
541Dic6—42no—
542Dic6—42no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—31no—
548C24—44no—
549C24—82no—
550C24C2×C4×D312yes—
551C24C2×C4×D312yes—
552C24C2×D1212yes—
553C24C2×D1212yes—
554C24C2×#6712yes—
555C24C2×#6712yes—
556C24C23×D311yescharacteristic
557#41—128no—
558#41—124no—
559#41—124no—
560C2×Q8—61no—
561C2×Q8—61no—
562C2×Q8—122no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—62no—
573C2×D4—62no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—62no—
581C2×D4—62no—
582C2×D4—124no—
583C2×D4—242no—
584C2×D4(C2×D3)⋊C412yes—
585C2×D4(C2×D3)⋊C411yescharacteristic
586C2×D4(C2×D3)⋊C412yes—
587C2×D4(C2×D3)⋊C412yes—
588C2×D4(C2×D3)⋊C411yescharacteristic
589C2×D4(C2×D3)⋊C411yescharacteristic
590C2×D4(C2×D3)⋊C412yes—
591C2×D4(C2×D3)⋊C412yes—
592C2×D4(C2×D3)⋊C412yes—
593C2×D4(C2×D3)⋊C411yescharacteristic
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—32no—
600C22×C4—31no—
601C22×C4—32no—
602C22×C4—42no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—61no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—62no—
614C22×C4—82no—
615C22×C4—122no—
616C22×C4—124no—
617C22×C4—124no—
618C22×C4—124no—
619C22×C4—242no—
620C22×C4—242no—
621C22×C4C2×C4×D311yescharacteristic
622C22×C4C2×C4×D311yescharacteristic
623C22×C4C2×D1211yescharacteristic
624C22×C4C2×D1211yescharacteristic
625C22×C4C2×#6711yescharacteristic
626C22×C4C2×#6711yescharacteristic
627C4⋊C4—42no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—62no—
633C4⋊C4—62no—
634C4⋊C4—122no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—32no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—62no—
644C22⋊C4—62no—
645C22⋊C4—62no—
646C22⋊C4—62no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—62no—
650C22⋊C4—62no—
651C22⋊C4—61no—
652C22⋊C4—62no—
653C22⋊C4—61no—
654C22⋊C4—61no—
655C22⋊C4—62no—
656C22⋊C4—61no—
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—62no—
660C22⋊C4—62no—
661C22⋊C4—61no—
662C22⋊C4—82no—
663C22⋊C4—124no—
664C22⋊C4—124no—
665C22⋊C4—242no—
666C22⋊C4#23712yescomplemented
667C42—42no—
668C42—61no—
669C42—61no—
670C42—122no—
671C22×C3—22no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—22no—
678C22×C3—21no—
679C22×C3—22no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—44no—
693C22×C3—44no—
694C22×C3—44no—
695C22×C3—44no—
696C22×C3—44no—
697C22×C3—44no—
698C22×C3—82no—
699C22×C3—82no—
700C22×C3—82no—
701C22×C3—82no—
702C22×C3—82no—
703C22×C3—82no—
704C22×C3C2×#9914yes—
705C22×C3C22×C22⋊C411yescharacteristic
706C22×C3C4×#4111yescharacteristic
707C22×C3#52011yescharacteristic
708C22×C3#54611yescharacteristic
709C22×C3#54611yescharacteristic
710C22×C3#54711yescharacteristic
711C22×C3#54711yescharacteristic
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—81no—
716C2×D3—81no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—42no—
721C3×C4—81no—
722C3×C4—82no—
723C3×C4C2×#9912yes—
724Dic3—42no—
725Dic3—41no—
726Dic3—42no—
727Dic3—41no—
728Dic3—41no—
729Dic3—42no—
730Dic3—81no—
731Dic3—82no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—41no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—41no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—84no—
762C23—84no—
763C23—84no—
764C23—84no—
765C23—121no—
766C23—121no—
767C23C2×(C2×D3)⋊C412yes—
768C23C2×(C2×D3)⋊C412yes—
769C23C2×(C2×D3)⋊C412yes—
770C23C2×(C2×D3)⋊C412yes—
771C23C22×C4×D311yescharacteristic
772C23C22×D1211yescharacteristic
773C23C2×#23711yescharacteristic
774C23#100411yescharacteristic
775C23D3×#4111yescharacteristic
776C23#101011yescharacteristic
777C23C22×#6711yescharacteristic
778Q8—122no—
779Q8—122no—
780D4—24no—
781D4—24no—
782D4—24no—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—42no—
787D4—42no—
788D4—42no—
789D4—124no—
790D4—124no—
791D4—121no—
792D4—121no—
793D4—121no—
794D4—121no—
795D4—242no—
796D4—242no—
797D4#80614yescomplemented
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—62no—
816C2×C4—61no—
817C2×C4—62no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—62no—
821C2×C4—88no—
822C2×C4—122no—
823C2×C4—121no—
824C2×C4—124no—
825C2×C4—121no—
826C2×C4—124no—
827C2×C4—122no—
828C2×C4—121no—
829C2×C4—122no—
830C2×C4—121no—
831C2×C4—122no—
832C2×C4—121no—
833C2×C4—122no—
834C2×C4—121no—
835C2×C4—122no—
836C2×C4—122no—
837C2×C4—121no—
838C2×C4—242no—
839C2×C4—242no—
840C2×C4—248no—
841C2×C4C2×(C2×D3)⋊C411yescharacteristic
842C2×C4C2×(C2×D3)⋊C411yescharacteristic
843C2×C4C2×(C2×D3)⋊C411yescharacteristic
844C2×C4C2×(C2×D3)⋊C411yescharacteristic
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—24no—
852C2×C3—42no—
853C2×C3—42no—
854C2×C3—42no—
855C2×C3#233911yescharacteristic
856C2×C3C22×#9911yescharacteristic
857C2×C3#288311yescharacteristic
858D3—81no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—22no—
863C22—22no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—82no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—241no—
896C22—241no—
897C22C2×#80614yes—
898C22C4×#23711yescharacteristic
899C22#554611yescharacteristic
900C22#555411yescharacteristic
901C22#555511yescharacteristic
902C22C22×(C2×D3)⋊C411yescharacteristic
903C22#580611yescharacteristic
904C22#582411yescharacteristic
905C4—21no—
906C4—21no—
907C4—21no—
908C4—42no—
909C4—82no—
910C4—81no—
911C4—122no—
912C4—121no—
913C4—122no—
914C4—121no—
915C4—121no—
916C4—122no—
917C4—242no—
918C4—241no—
919C4C2×#80612yes—
920C3#2247611yescharacteristic, complemented, Sylow
921C2—21no—
922C2—21no—
923C2—21no—
924C2—21no—
925C2—21no—
926C2—21no—
927C2—24no—
928C2—42no—
929C2—42no—
930C2—42no—
931C2—241no—
932C2C22×#80611yescharacteristic
933C2#8233011yescharacteristic
934C2#8254611yescharacteristic
subgroupG/H
centerC22C22×(C2×D3)⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×D4×C22⋊C4C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5806C2
cosocleC24×C3C24
hypercenterD4×C22⋊C4D3
hypocenterC3#22476
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×D4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×D4×C22⋊C4C2semidirect
3. D4×#217C2semidirect
4. #71543C2semidirect
5. C2×#4527C2semidirect
6. #69530C2semidirect
7. #69529C2semidirect
8. #69496C2semidirect
9. #69495C2semidirect
10. #69457C2semidirect
11. C4×#806C2semidirect
14. C22×#237C4semidirect
26. C2×#939C4semidirect
27. C2×#938C4semidirect
28. C2×#936C4semidirect
29. C2×#935C4semidirect
31. C2×D4×Dic3C4semidirect
56. D4×C22⋊C4D3semidirect
78. C22×#67C2×C4semidirect
79. C22×#67C2×C4semidirect
82. C23×Dic3C2×C4semidirect
83. C23×Dic3C2×C4semidirect
88. C22×C4×D3C2×C4semidirect
89. C22×Dic6C2×C4semidirect
114. C2×#217C2×C4semidirect
115. C2×#217C2×C4semidirect
116. C2×#217C2×C4semidirect
117. C2×#217C2×C4semidirect
145. C2×(C2×D3)⋊C4C2×C4semidirect
147. C2×C4⋊Dic3C2×C4semidirect
152. C2×Dic3⋊C4C2×C4semidirect
153. C2×Dic3⋊C4C2×C4semidirect
155. C2×C4×Dic3C2×C4semidirect
297. C3×C22⋊C4#41semidirect
319. #217#41semidirect
485. C3×D4#99semidirect
666. C22⋊C4#237semidirect
797. D4#806semidirect
920. C3#22476semidirect

Maximal subgroups

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

subgroupindex
C2×#58062
C3×D4×C22⋊C42
D4×#2172
#715432
C2×#45272
#695302
#695292
#694962
#694952
#694572
C4×#8062
#224763