Finite Group Databasebeta

← #10826941

Subgroups — #10826941

Order 768.

2272 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5828C211yesmaximal, characteristic, complemented
2C2×D3×#121C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic, complemented
4C2×#5238C211yesmaximal, characteristic, complemented
5C2×#5169C211yesmaximal, characteristic, complemented
6C2×#5156C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#72043C211yesmaximal, characteristic, complemented
9#71678C211yesmaximal, characteristic, complemented
10#70272C211yesmaximal, characteristic, complemented
11#70268C211yesmaximal, characteristic, complemented
12#70204C211yesmaximal, characteristic, complemented
13#70200C211yesmaximal, characteristic, complemented
14#69955C211yesmaximal, characteristic, complemented
15#69933C211yesmaximal, characteristic, complemented
16#23920—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic, complemented
18C22×D3×D4—21no—
19C22×D3×D4C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic, complemented
22C22×C3×D8C2211yescharacteristic, complemented
23C2×C3×#121C2211yescharacteristic
24#5828—24no—
25#5828—24no—
26C2×#946C2211yescharacteristic
27C2×#946C2211yescharacteristic, complemented
28C22×#215C2211yescharacteristic, complemented
29C2×#939—21no—
30C2×#938C2211yescharacteristic
31C2×#938C2211yescharacteristic
32C2×#938C2211yescharacteristic, complemented
33C2×#937—21no—
34C2×#935—21no—
35C22×#213C2211yescharacteristic, complemented
36C2×#930C2211yescharacteristic
37C2×C4×#67—21no—
38C2×C4×#67—21no—
39C2×#926C2211yescharacteristic, complemented
40D3×#121—24no—
41D3×#121—24no—
42C2×#895C2211yescharacteristic
43C2×D3×C4⋊C4C2211yescharacteristic
44C2×#884—21no—
45C2×D3×C22⋊C4—21no—
46C3×#449—24no—
47C2×C3×#103C2211yescharacteristic, complemented
48C2×C3×#102C2211yescharacteristic, complemented
49C2×C3×C22⋊C8C2211yescharacteristic, complemented
50#5238—24no—
51C2×#835C2211yescharacteristic, complemented
52C2×#832C2211yescharacteristic, complemented
53C2×#832C2211yescharacteristic, complemented
54C2×#832C2211yescharacteristic, complemented
55C2×#830C2211yescharacteristic, complemented
56#5169—24no—
57#5156—24no—
58C2×#821C2211yescharacteristic, complemented
59C2×#821C2211yescharacteristic, complemented
60C2×(C2×D3)⋊C8C2211yescharacteristic
61C2×(C2×D3)⋊C8C2211yescharacteristic
62C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
64#4551C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C2×#525—31no—
69C22×#121—31no—
70C2×#449—31no—
71C2×#449D311yescharacteristic, complemented
72C2×#450—31no—
73C2×#447—31no—
74#2000—31no—
75#2000—31no—
76#1999—31no—
77#1999—31no—
78#1875—31no—
79#1875—31no—
80#1874—31no—
81#1872—31no—
82#1779—31no—
83C24×D3—21no—
84C24×D3D411yescharacteristic
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—22no—
89C2×C3×#41—41no—
90C2×C3×#41—41no—
91C22×C3×Q8C2311yescharacteristic
92C22×C3×D4—21no—
93C22×C3×D4—21no—
94C22×C3×D4C2311yescharacteristic
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C22×#67—21no—
99C22×#67—21no—
100C22×#67—21no—
101C22×#67—21no—
102C22×#67—21no—
103C23×Dic3D411yescharacteristic
104C2×D3×D4—28no—
105C2×D3×D4—22no—
106C2×D3×D4—22no—
107C2×D3×D4—22no—
108C2×D3×D4—22no—
109C2×D3×D4—41no—
110C2×D3×D4—41no—
111C2×D3×D4—44no—
112C2×D3×D4—44no—
113C22×D12—21no—
114C22×D12C2311yescharacteristic
115C22×C4×D3—21no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3—22no—
120C22×C4×D3—41no—
121C22×C4×D3—41no—
122C22×C4×D3D411yescharacteristic
123C22×C4×D3D411yescharacteristic
124C22×C4×D3C2311yescharacteristic
125C22×C4×D3C2311yescharacteristic
126C2×C3×SD16—22no—
127C2×C3×SD16—22no—
128C2×C3×SD16—41no—
129C2×C3×D8—22no—
130C2×C3×D8—22no—
131C2×C3×D8—41no—
132C22×C3×C8C2311yescharacteristic
133C22×C3×C8C2311yescharacteristic
134C3×#121—22no—
135C3×#121D414yescomplemented
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C22⋊C4—21no—
138C2×#217—21no—
139C2×#217—21no—
140C2×#217—21no—
141C2×#217—21no—
142#946—22no—
143#946—22no—
144#946—22no—
145#946D414yescomplemented
146C2×#215—22no—
147C2×#215—22no—
148C2×#215—41no—
149#939—28no—
150#938—22no—
151#938—22no—
152#938—22no—
153#938—22no—
154#938—22no—
155#938D414yescomplemented
156#937—28no—
157#935—28no—
158C2×#213—22no—
159C2×#213—22no—
160C2×#213—41no—
161#930—22no—
162#930D414yescomplemented
163C4×#67—28no—
164C4×#67—28no—
165C2×(C2×D3)⋊C4—21no—
166C2×(C2×D3)⋊C4—21no—
167C2×(C2×D3)⋊C4—21no—
168C2×(C2×D3)⋊C4—21no—
169#926—22no—
170#926—22no—
171C2×C4⋊Dic3C2311yescharacteristic
172C2×C4⋊Dic3C2311yescharacteristic
173C2×C4⋊Dic3C2311yescharacteristic
174C2×Dic3⋊C4—21no—
175C2×Dic3⋊C4—21no—
176C2×Dic3⋊C4—21no—
177C2×C4×Dic3—21no—
178C22×C3⋊C8C2311yescharacteristic
179C22×C3⋊C8C2311yescharacteristic
180#895—22no—
181#895—22no—
182D3×C4⋊C4—22no—
183D3×C4⋊C4—22no—
184#884—28no—
185D3×C22⋊C4—28no—
186C3×#103—22no—
187C3×#102—22no—
188C3×C22⋊C8—22no—
189#835—22no—
190#832—22no—
191#832—22no—
192#832—22no—
193#830—22no—
194#821—22no—
195#821—22no—
196(C2×D3)⋊C8—22no—
197(C2×D3)⋊C8—22no—
198(C2×D3)⋊C8—41no—
199(C2×D3)⋊C8—41no—
200C22×#41C2×D311yescharacteristic, complemented
201C23×D4—31no—
202C23×D4—61no—
203C24×C4—31no—
204C22×SD16—31no—
205C22×SD16C2×D311yescharacteristic, complemented
206C22×D8—31no—
207C22×D8C2×D311yescharacteristic, complemented
208#525—64no—
209#525—64no—
210C2×#123—61no—
211C2×C22⋊Q8—31no—
212C2×C22⋊Q8—31no—
213C2×#121—31no—
214C2×#121—31no—
215C2×#121—31no—
216C2×#121—31no—
217C2×#121—31no—
218C2×#121—61no—
219C2×#121—64no—
220C2×#121—61no—
221C2×#121—64no—
222C2×#121C2×D311yescharacteristic
223C2×#120—61no—
224C2×C4×D4—61no—
225C2×C4×D4—61no—
226C2×#117—31no—
227C22×C4⋊C4—31no—
228C22×C22⋊C4—61no—
229#450—64no—
230#449—24no—
231#449—64no—
232#447—64no—
233C2×#103—31no—
234C2×#103C2×D311yescharacteristic, complemented
235C2×#102—31no—
236C2×#102—31no—
237C2×#102—31no—
238C2×#102—31no—
239C2×#102—31no—
240C2×#102C2×D311yescharacteristic, complemented
241C2×C22⋊C8—31no—
242C2×C22⋊C8—31no—
243C2×C22⋊C8—31no—
244C2×C22⋊C8—31no—
245C2×C22⋊C8—31no—
246C2×C22⋊C8C2×D311yescharacteristic, complemented
247#340—31no—
248#340—31no—
249#340—31no—
250#340—31no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3C2×D411yescharacteristic
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—24no—
258C23×D3—21no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3—41no—
262C23×D3—41no—
263C23×D3—42no—
264C23×D3—42no—
265C23×D3—42no—
266C23×D3—42no—
267C23×D3—42no—
268C23×D3—42no—
269C23×D3C2×D411yescharacteristic
270C23×D3C2×D411yescharacteristic
271C3×#41—44no—
272C3×#41—44no—
273C3×#41—44no—
274C3×#41—44no—
275C2×C3×Q8—21no—
276C2×C3×Q8—21no—
277C2×C3×Q8—21no—
278C2×C3×Q8—21no—
279C2×C3×Q8—21no—
280C2×C3×Q8C2×D412yescomplemented
281C2×C3×D4—24no—
282C2×C3×D4—24no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—42no—
294C2×C3×D4—42no—
295C2×C3×D4—42no—
296C2×C3×D4—42no—
297C2×C3×D4C2×D412yes—
298C2×C3×D4C2×D412yescomplemented
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—24no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—42no—
307C22×C3×C4—42no—
308C22×C3×C4C2×D411yescharacteristic
309C22×C3×C4C2×D412yes—
310C22×C3×C4C2×D412yes—
311C22×C3×C4C2411yescharacteristic
312C2×#67—24no—
313C2×#67—24no—
314C2×#67—24no—
315C2×#67—24no—
316C2×#67—24no—
317C2×#67—42no—
318C2×#67—42no—
319C2×#67—42no—
320C2×#67—42no—
321C2×#67—42no—
322C2×#67—42no—
323C2×#67—42no—
324C2×#67—42no—
325C2×#67—42no—
326C2×#67—42no—
327C22×Dic3—22no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—22no—
332C22×Dic3—41no—
333C22×Dic3C2×D411yescharacteristic
334C22×Dic3C2×D411yescharacteristic
335D3×D4—44no—
336D3×D4—44no—
337D3×D4—44no—
338D3×D4—44no—
339D3×D4—432no—
340C2×D12—21no—
341C2×D12—21no—
342C2×D12—21no—
343C2×D12—21no—
344C2×D12—24no—
345C2×D12—21no—
346C2×D12—42no—
347C2×D12—42no—
348C2×D12C2×D412yes—
349C2×C4×D3—21no—
350C2×C4×D3—21no—
351C2×C4×D3—21no—
352C2×C4×D3—21no—
353C2×C4×D3—24no—
354C2×C4×D3—22no—
355C2×C4×D3—22no—
356C2×C4×D3—22no—
357C2×C4×D3—21no—
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×C4×D3—21no—
361C2×C4×D3—21no—
362C2×C4×D3—21no—
363C2×C4×D3—22no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C2×C4×D3—44no—
367C2×C4×D3—44no—
368C2×C4×D3—41no—
369C2×C4×D3—41no—
370C2×C4×D3—42no—
371C2×C4×D3—42no—
372C2×C4×D3C2×D412yes—
373C2×C4×D3C2×D412yes—
374C3×SD16—44no—
375C3×D8—44no—
376C2×C3×C8—21no—
377C2×C3×C8—21no—
378C2×C3×C8—21no—
379C2×C3×C8—21no—
380C2×C3×C8—21no—
381C2×C3×C8—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4C2×D412yes—
384C3×C22⋊C4—24no—
385#217—24no—
386#217—24no—
387#217—24no—
388#217—24no—
389#215—44no—
390#213—44no—
391(C2×D3)⋊C4—24no—
392(C2×D3)⋊C4—24no—
393(C2×D3)⋊C4—24no—
394(C2×D3)⋊C4—24no—
395C4⋊Dic3—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3C2×D412yes—
399C4⋊Dic3C2×D412yescomplemented
400C4⋊Dic3C2×D412yescomplemented
401Dic3⋊C4—24no—
402Dic3⋊C4—24no—
403Dic3⋊C4—24no—
404C4×Dic3—24no—
405C2×C3⋊C8—21no—
406C2×C3⋊C8—21no—
407C2×C3⋊C8—21no—
408C2×C3⋊C8—21no—
409C2×C3⋊C8—21no—
410C2×C3⋊C8—21no—
411C25—31no—
412C25—61no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—22no—
416C2×#41—22no—
417C2×#41—41no—
418C2×#41—41no—
419C22×Q8C22×D311yescharacteristic
420C22×D4—21no—
421C22×D4—21no—
422C22×D4—31no—
423C22×D4—61no—
424C22×D4—62no—
425C22×D4—62no—
426C22×D4—61no—
427C22×D4—62no—
428C22×D4—68no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—62no—
434C22×D4—121no—
435C22×D4—121no—
436C22×D4—124no—
437C22×D4—124no—
438C22×D4C22×D311yescharacteristic
439C22×D4C22×D311yescharacteristic
440C23×C4—21no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—62no—
447C23×C4—62no—
448C23×C4—61no—
449C23×C4—62no—
450C23×C4—62no—
451C23×C4—121no—
452C23×C4—121no—
453C23×C4C22×D311yescharacteristic
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16—41no—
457C2×SD16—62no—
458C2×SD16—62no—
459C2×SD16—121no—
460C2×D8—22no—
461C2×D8—22no—
462C2×D8—41no—
463C2×D8—62no—
464C2×D8—62no—
465C2×D8—121no—
466C22×C8—31no—
467C22×C8—31no—
468C22×C8C22×D311yescharacteristic
469C22×C8C22×D311yescharacteristic
470#123—68no—
471C22⋊Q8—34no—
472C22⋊Q8—62no—
473C22⋊Q8—62no—
474C22⋊Q8—62no—
475#121—22no—
476#121—34no—
477#121—34no—
478#121—68no—
479#121—62no—
480#121—62no—
481#121—62no—
482#121—62no—
483#121—68no—
484#121—62no—
485#121—62no—
486#121—62no—
487#121—62no—
488#121#6714yescomplemented
489#120—68no—
490C4×D4—68no—
491C4×D4—68no—
492#117—62no—
493#117—62no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—62no—
498C2×C4⋊C4—61no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4—61no—
501C2×C4⋊C4—62no—
502C2×C4⋊C4C22×D311yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—68no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
512C2×C22⋊C4—61no—
513C2×C42—61no—
514#103—22no—
515#103—62no—
516#102—22no—
517#102—62no—
518#102—62no—
519#102—62no—
520#102—62no—
521#102—62no—
522C22⋊C8—22no—
523C22⋊C8—62no—
524C22⋊C8—62no—
525C22⋊C8—62no—
526C22⋊C8—121no—
527C22⋊C8—121no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3#12012yes—
549C23×C3C22×D411yescharacteristic
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—28no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—22no—
562C22×D3—44no—
563C22×D3—44no—
564C22×D3—44no—
565C22×D3—44no—
566C22×D3—44no—
567C22×D3—48no—
568C22×D3—48no—
569C22×D3—48no—
570C22×D3—44no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—84no—
578C22×D3—84no—
579C22×D3—84no—
580C22×D3—84no—
581C22×D3#12012yes—
582C22×D3#13512yes—
583C22×D3AGL(1,ℤ/8)12yes—
584C22×D3AGL(1,ℤ/8)12yes—
585C3×Q8—22no—
586C3×Q8—22no—
587C3×Q8—41no—
588C3×Q8—41no—
589C3×D4—22no—
590C3×D4—22no—
591C3×D4—22no—
592C3×D4—22no—
593C3×D4—48no—
594C3×D4—48no—
595C3×D4—41no—
596C3×D4—41no—
597C3×D4—41no—
598C3×D4—41no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—48no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4#12012yes—
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4C22×D411yescharacteristic
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C22×D411yescharacteristic
617C2×C3×C4H(5,𝔽2)11yescharacteristic
618C2×C3×C4H(5,𝔽2)11yescharacteristic
619#67—48no—
620#67—48no—
621#67—48no—
622#67—48no—
623#67—48no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—21no—
629C2×Dic3—22no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—44no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3#12012yes—
640D12—22no—
641D12—22no—
642D12—48no—
643D12—41no—
644D12—41no—
645C4×D3—22no—
646C4×D3—22no—
647C4×D3—22no—
648C4×D3—22no—
649C4×D3—44no—
650C4×D3—44no—
651C4×D3—48no—
652C4×D3—41no—
653C4×D3—41no—
654C4×D3—41no—
655C4×D3—41no—
656C3×C8—41no—
657C3×C8—41no—
658C3⋊C8—41no—
659C3⋊C8—41no—
660C24—21no—
661C24—21no—
662C24—31no—
663C24—31no—
664C24—62no—
665C24—62no—
666C24—62no—
667C24—62no—
668C24—64no—
669C24—62no—
670C24—61no—
671C24—121no—
672C24—121no—
673C24—122no—
674C24—122no—
675C24—122no—
676C24—122no—
677C24—122no—
678C24—122no—
679C24D3×D411yescharacteristic
680#41—44no—
681#41—44no—
682#41—44no—
683#41—44no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8D3×D412yescomplemented
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—32no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—42no—
707C2×D4—64no—
708C2×D4—64no—
709C2×D4—64no—
710C2×D4—64no—
711C2×D4—64no—
712C2×D4—64no—
713C2×D4—61no—
714C2×D4—61no—
715C2×D4—61no—
716C2×D4—61no—
717C2×D4—61no—
718C2×D4—122no—
719C2×D4—122no—
720C2×D4—122no—
721C2×D4—124no—
722C2×D4—124no—
723C2×D4—124no—
724C2×D4—124no—
725C2×D4—122no—
726C2×D4—1232no—
727C2×D4—122no—
728C2×D4—122no—
729C2×D4—122no—
730C2×D4—122no—
731C2×D4—122no—
732C2×D4—122no—
733C2×D4—122no—
734C2×D4—122no—
735C2×D4D3×D412yescomplemented
736C2×D4C2×#6712yes—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—24no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—31no—
745C22×C4—32no—
746C22×C4—32no—
747C22×C4—31no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—62no—
751C22×C4—62no—
752C22×C4—64no—
753C22×C4—62no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—62no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—62no—
763C22×C4—62no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—121no—
771C22×C4—121no—
772C22×C4—124no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4—124no—
776C22×C4—122no—
777C22×C4—122no—
778C22×C4—121no—
779C22×C4D3×D411yescharacteristic
780C22×C4D3×D412yes—
781C22×C4C2×#6712yes—
782C22×C4C23×D311yescharacteristic
783SD16—44no—
784SD16—124no—
785D8—44no—
786D8—124no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—61no—
794C2×C8—61no—
795C2×C8—61no—
796C2×C8—61no—
797C2×C8—61no—
798C2×C8—61no—
799C4⋊C4—21no—
800C4⋊C4—32no—
801C4⋊C4—32no—
802C4⋊C4—32no—
803C4⋊C4—64no—
804C4⋊C4—64no—
805C4⋊C4—64no—
806C4⋊C4—61no—
807C4⋊C4—61no—
808C4⋊C4—61no—
809C4⋊C4C2×#6712yes—
810C22⋊C4—24no—
811C22⋊C4—64no—
812C22⋊C4—64no—
813C22⋊C4—64no—
814C22⋊C4—64no—
815C22⋊C4—64no—
816C22⋊C4—64no—
817C22⋊C4—64no—
818C22⋊C4—64no—
819C42—64no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3C2×#12011yescharacteristic
842C22×C3C2×#12011yescharacteristic
843C22×C3#53411yescharacteristic
844C22×C3C2×#13511yescharacteristic
845C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
846C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
847C22×C3#57511yescharacteristic
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—416no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—42no—
863C2×D3—42no—
864C2×D3—42no—
865C2×D3—816no—
866C2×D3—81no—
867C2×D3—81no—
868C2×D3—81no—
869C2×D3—81no—
870C2×D3#44914yescomplemented
871C3×C4—22no—
872C3×C4—42no—
873C3×C4—42no—
874C3×C4D4211yescharacteristic
875C3×C4D4211yescharacteristic
876C3×C4D4211yescharacteristic
877C3×C4D4211yescharacteristic
878Dic3—22no—
879Dic3—41no—
880Dic3—42no—
881Dic3—42no—
882Dic3—42no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—22no—
890C23—22no—
891C23—32no—
892C23—32no—
893C23—32no—
894C23—32no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—68no—
908C23—61no—
909C23—61no—
910C23—61no—
911C23—61no—
912C23—61no—
913C23—61no—
914C23—61no—
915C23—61no—
916C23—61no—
917C23—61no—
918C23—62no—
919C23—124no—
920C23—124no—
921C23—124no—
922C23—124no—
923C23—124no—
924C23—124no—
925C23—128no—
926C23—128no—
927C23—128no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—244no—
935C23—244no—
936C23—244no—
937C23—244no—
938C23#93712yes—
939C23C2×D3×D411yescharacteristic
940Q8—22no—
941Q8—22no—
942Q8—41no—
943Q8—41no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—48no—
949D4—48no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—41no—
954D4—62no—
955D4—62no—
956D4—128no—
957D4—128no—
958D4—128no—
959D4—128no—
960D4—128no—
961D4—128no—
962D4—121no—
963D4—121no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—32no—
973C2×C4—48no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—62no—
981C2×C4—62no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—61no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—124no—
991C2×C4—124no—
992C2×C4—128no—
993C2×C4—124no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4#93712yes—
1005C2×C4C2×D3×D411yescharacteristic
1006C2×C4C2×D3×D411yescharacteristic
1007C2×C4C2×D3×D411yescharacteristic
1008C2×C4#100411yescharacteristic
1009C2×C4#100411yescharacteristic
1010C2×C4C22×#6711yescharacteristic
1011C8—41no—
1012C8—41no—
1013C8—121no—
1014C8—121no—
1015C2×C3—42no—
1016C2×C3—82no—
1017C2×C3—82no—
1018C2×C3#240311yescharacteristic
1019C2×C3C2×#44911yescharacteristic
1020C2×C3#300211yescharacteristic
1021C2×C3#300311yescharacteristic
1022C2×C3#300611yescharacteristic
1023C2×C3#318811yescharacteristic
1024C2×C3#319411yescharacteristic
1025D3—24no—
1026D3—42no—
1027D3—82no—
1028C22—22no—
1029C22—22no—
1030C22—22no—
1031C22—34no—
1032C22—41no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—1216no—
1060C22—121no—
1061C22—121no—
1062C22—121no—
1063C22—121no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—2416no—
1068C22—241no—
1069C22—241no—
1070C22—241no—
1071C22—241no—
1072C22D3×#12011yescharacteristic
1073C22#558911yescharacteristic
1074C22D3×#13511yescharacteristic
1075C22#576811yescharacteristic
1076C22D3×AGL(1,ℤ/8)11yescharacteristic
1077C22D3×AGL(1,ℤ/8)11yescharacteristic
1078C22C2×#93711yescharacteristic
1079C4—22no—
1080C4—42no—
1081C4—42no—
1082C4—62no—
1083C4—121no—
1084C4—122no—
1085C4—122no—
1086C4—122no—
1087C4#559011yescharacteristic
1088C4#559011yescharacteristic
1089C4D4×#6711yescharacteristic
1090C4D4×#6711yescharacteristic
1091C3#2392011yescharacteristic, complemented, Sylow
1092C2—42no—
1093C2—64no—
1094C2—82no—
1095C2—82no—
1096C2—122no—
1097C2—242no—
1098C2D3×#44911yescharacteristic
1099C2#8008411yescharacteristic
1100C2#8008911yescharacteristic
1101C2#8009111yescharacteristic
1102C2#8260411yescharacteristic
1103C2#8391111yescharacteristic
1104C2#8394411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3#23920
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#5828C2semidirect
2. C2×D3×#121C2semidirect
3. C2×C3×#449C2semidirect
4. C2×#5238C2semidirect
5. C2×#5169C2semidirect
6. C2×#5156C2semidirect
7. #72054C2semidirect
8. #72043C2semidirect
9. #71678C2semidirect
10. #70272C2semidirect
11. #70268C2semidirect
12. #70204C2semidirect
13. #70200C2semidirect
14. #69955C2semidirect
15. #69933C2semidirect
17. C22×C3×#41C22semidirect
21. C22×C3×SD16C22semidirect
22. C22×C3×D8C22semidirect
27. C2×#946C22semidirect
28. C22×#215C22semidirect
32. C2×#938C22semidirect
35. C22×#213C22semidirect
39. C2×#926C22semidirect
47. C2×C3×#103C22semidirect
48. C2×C3×#102C22semidirect
49. C2×C3×C22⋊C8C22semidirect
51. C2×#835C22semidirect
52. C2×#832C22semidirect
53. C2×#832C22semidirect
54. C2×#832C22semidirect
55. C2×#830C22semidirect
58. C2×#821C22semidirect
59. C2×#821C22semidirect
62. C2×(C2×D3)⋊C8C22semidirect
63. C2×(C2×D3)⋊C8C22semidirect
64. #4551C22semidirect
65. #4551C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
71. C2×#449D3semidirect
135. C3×#121D4semidirect
145. #946D4semidirect
155. #938D4semidirect
162. #930D4semidirect
200. C22×#41C2×D3semidirect
205. C22×SD16C2×D3semidirect
207. C22×D8C2×D3semidirect
234. C2×#103C2×D3semidirect
240. C2×#102C2×D3semidirect
246. C2×C22⋊C8C2×D3semidirect
280. C2×C3×Q8C2×D4semidirect
298. C2×C3×D4C2×D4semidirect
399. C4⋊Dic3C2×D4semidirect
400. C4⋊Dic3C2×D4semidirect
488. #121#67semidirect
689. C2×Q8D3×D4semidirect
735. C2×D4D3×D4semidirect
870. C2×D3#449semidirect
1091. C3#23920semidirect

Maximal subgroups

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

subgroupindex
C2×#58282
C2×D3×#1212
C2×C3×#4492
C2×#52382
C2×#51692
C2×#51562
#720542
#720432
#716782
#702722
#702682
#702042
#702002
#699552
#699332
#239203