Finite Group Databasebeta

← #10826968

Subgroups — #10826968

Order 768.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5828C211yesmaximal, characteristic, complemented
2C2×#5606C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic, complemented
4C2×#5239C211yesmaximal, characteristic, complemented
5C2×#5173C211yesmaximal, characteristic, complemented
6C2×#5158C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#72043C211yesmaximal, characteristic, complemented
9#71678C211yesmaximal, characteristic, complemented
10#70273C211yesmaximal, characteristic, complemented
11#70269C211yesmaximal, characteristic, complemented
12#70205C211yesmaximal, characteristic, complemented
13#70201C211yesmaximal, characteristic, complemented
14#69955C211yesmaximal, characteristic, complemented
15#69931C211yesmaximal, characteristic, complemented
16#23923—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×#237C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic, complemented
21C22×C3×D8C2211yescharacteristic, complemented
22C2×C3×#121C2211yescharacteristic
23#5828—24no—
24#5828—24no—
25C2×#946C2211yescharacteristic
26C2×#946C2211yescharacteristic
27C22×#216C2211yescharacteristic, complemented
28C2×#938C2211yescharacteristic
29C2×#938C2211yescharacteristic
30C2×#938C2211yescharacteristic
31C2×#937—21no—
32C2×#937—21no—
33C2×#935—21no—
34C2×D4×Dic3—21no—
35C22×#214C2211yescharacteristic, complemented
36C2×C4×#67—21no—
37C2×C4×#67—21no—
38C2×#926C2211yescharacteristic
39C2×#924C2211yescharacteristic
40#5606—24no—
41#5606—24no—
42C2×#897C2211yescharacteristic
43C2×#892C2211yescharacteristic
44C2×#883—21no—
45C2×#67⋊C4—21no—
46C3×#449—24no—
47C2×C3×#103C2211yescharacteristic, complemented
48C2×C3×#102C2211yescharacteristic, complemented
49C2×C3×C22⋊C8C2211yescharacteristic
50#5239—24no—
51C2×#835C2211yescharacteristic, complemented
52C2×#832C2211yescharacteristic, complemented
53C2×#832C2211yescharacteristic, complemented
54C2×#832C2211yescharacteristic, complemented
55C2×#830C2211yescharacteristic
56#5173—24no—
57#5158—24no—
58C2×(C2×D3)⋊C8C2211yescharacteristic
59C2×(C2×D3)⋊C8C2211yescharacteristic
60C2×(C2×D3)⋊C8C2211yescharacteristic
61C2×(C2×D3)⋊C8C2211yescharacteristic
62C2×#816C2211yescharacteristic, complemented
63C2×#816C2211yescharacteristic, complemented
64#4551C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C2×#525—31no—
69C2×#525—31no—
70C2×#452—31no—
71C2×#452—31no—
72C2×#449—31no—
73C2×#449D311yescharacteristic, complemented
74#2001—31no—
75#2000—31no—
76#2000—31no—
77#1999—31no—
78#1875—31no—
79#1875—31no—
80#1873—31no—
81#1873—31no—
82#1779—31no—
83C24×D3D411yescharacteristic
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—41no—
89C2×C3×#41—41no—
90C22×C3×Q8C2311yescharacteristic
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4C2311yescharacteristic
94C22×C3×D4C2311yescharacteristic
95C23×C3×C4—21no—
96C23×C3×C4C2311yescharacteristic
97C22×#67—21no—
98C22×#67—21no—
99C22×#67—21no—
100C22×#67—21no—
101C23×Dic3—21no—
102C23×Dic3D411yescharacteristic
103C2×#237—22no—
104C2×#237—22no—
105C2×#237—22no—
106C2×#237—22no—
107C2×#237—41no—
108C2×#237—41no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3—22no—
113C22×C4×D3—41no—
114C22×C4×D3—41no—
115C22×C4×D3D411yescharacteristic
116C22×C4×D3D411yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×C4×D3C2311yescharacteristic
119C22×Dic6C2311yescharacteristic
120C2×C3×SD16—22no—
121C2×C3×SD16—22no—
122C2×C3×SD16—41no—
123C2×C3×D8—22no—
124C2×C3×D8—22no—
125C2×C3×D8—41no—
126C22×C3×C8C2311yescharacteristic
127C22×C3×C8C2311yescharacteristic
128C3×#121—22no—
129C3×#121D414yescomplemented
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C22⋊C4—21no—
132C2×#217—21no—
133C2×#217—21no—
134C2×#217—21no—
135C2×#217—21no—
136C2×#217—21no—
137#946—22no—
138#946—22no—
139#946—22no—
140#946D414yescomplemented
141C2×#216—22no—
142C2×#216—22no—
143C2×#216—41no—
144#938—22no—
145#938—22no—
146#938—22no—
147#938—22no—
148#938—22no—
149#938D414yescomplemented
150#937—28no—
151#937—28no—
152#935—28no—
153D4×Dic3—28no—
154C2×#214—22no—
155C2×#214—22no—
156C2×#214—41no—
157C4×#67—28no—
158C4×#67—28no—
159C2×(C2×D3)⋊C4—21no—
160C2×(C2×D3)⋊C4—21no—
161C2×(C2×D3)⋊C4—21no—
162C2×(C2×D3)⋊C4—21no—
163#926—22no—
164#926—22no—
165C2×C4⋊Dic3—21no—
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2311yescharacteristic
168C2×C4⋊Dic3C2311yescharacteristic
169#924—22no—
170#924D414yescomplemented
171C2×Dic3⋊C4—21no—
172C2×Dic3⋊C4—21no—
173C2×Dic3⋊C4—21no—
174C2×C4×Dic3—21no—
175C2×C4×Dic3—21no—
176C22×C3⋊C8C2311yescharacteristic
177C22×C3⋊C8C2311yescharacteristic
178#897—22no—
179#897—22no—
180#892—22no—
181#892—22no—
182#883—28no—
183#67⋊C4—28no—
184C3×#103—22no—
185C3×#102—22no—
186C3×C22⋊C8—22no—
187#835—22no—
188#832—22no—
189#832—22no—
190#832—22no—
191#830—22no—
192(C2×D3)⋊C8—22no—
193(C2×D3)⋊C8—22no—
194(C2×D3)⋊C8—41no—
195(C2×D3)⋊C8—41no—
196#816—22no—
197#816—22no—
198C22×#41—31no—
199C22×#41C2×D311yescharacteristic
200C24×C4—31no—
201C22×Q16—31no—
202C22×SD16—31no—
203C22×SD16C2×D311yescharacteristic, complemented
204C22×D8C2×D311yescharacteristic, complemented
205#525—64no—
206#525—64no—
207#525—64no—
208#525—64no—
209C2×#123—61no—
210C2×#123—61no—
211C2×C22⋊Q8—31no—
212C2×C22⋊Q8—31no—
213C2×C22⋊Q8—31no—
214C2×C22⋊Q8—31no—
215C2×#121—31no—
216C2×#121—31no—
217C2×#121—31no—
218C2×#121C2×D311yescharacteristic
219C2×#120—61no—
220C2×#120—61no—
221C2×C4×D4—61no—
222C2×C4×D4—61no—
223C2×C4×D4—61no—
224C2×C4×D4—61no—
225C2×#117—31no—
226C2×#117—31no—
227#452—64no—
228#452—64no—
229#449—24no—
230#449—64no—
231C2×#103—31no—
232C2×#103—31no—
233C2×#103—31no—
234C2×#103C2×D311yescharacteristic, complemented
235C2×#102—31no—
236C2×#102—31no—
237C2×#102—31no—
238C2×#102C2×D311yescharacteristic, complemented
239C2×C22⋊C8—31no—
240C2×C22⋊C8—31no—
241C2×C22⋊C8—31no—
242C2×C22⋊C8—31no—
243C2×C22⋊C8—31no—
244C2×C22⋊C8C2×D311yescharacteristic
245#340—31no—
246#340—31no—
247#340—31no—
248#340—31no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3C2×D411yescharacteristic
252C23×D3—22no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—41no—
256C23×D3—41no—
257C23×D3—41no—
258C23×D3—41no—
259C23×D3C2×D411yescharacteristic
260C23×D3C2×D411yescharacteristic
261C3×#41—44no—
262C3×#41—44no—
263C3×#41—44no—
264C3×#41—44no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
267C2×C3×Q8—21no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8C2×D412yes—
271C2×C3×D4—24no—
272C2×C3×D4—24no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—42no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4—42no—
287C2×C3×D4C2×D412yes—
288C2×C3×D4C2×D412yes—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—24no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2411yescharacteristic
302C2×#67—24no—
303C2×#67—24no—
304C2×#67—24no—
305C2×#67—24no—
306C2×#67—42no—
307C2×#67—42no—
308C2×#67—42no—
309C2×#67—42no—
310C2×#67—42no—
311C2×#67—42no—
312C2×#67—42no—
313C2×#67—42no—
314C22×Dic3—24no—
315C22×Dic3—22no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—22no—
321C22×Dic3—41no—
322C22×Dic3—42no—
323C22×Dic3—42no—
324C22×Dic3C2×D411yescharacteristic
325C22×Dic3C2×D411yescharacteristic
326#237—44no—
327#237—44no—
328#237—44no—
329#237—44no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—22no—
335C2×C4×D3—22no—
336C2×C4×D3—22no—
337C2×C4×D3—21no—
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—21no—
341C2×C4×D3—21no—
342C2×C4×D3—21no—
343C2×C4×D3—22no—
344C2×C4×D3—44no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C2×C4×D3—44no—
348C2×C4×D3—41no—
349C2×C4×D3—41no—
350C2×C4×D3C2×D412yes—
351C2×C4×D3C2×D412yes—
352C2×Dic6—21no—
353C2×Dic6—21no—
354C2×Dic6—21no—
355C2×Dic6—21no—
356C2×Dic6—21no—
357C2×Dic6C2×D412yes—
358C3×SD16—44no—
359C3×D8—44no—
360C2×C3×C8—21no—
361C2×C3×C8—21no—
362C2×C3×C8—21no—
363C2×C3×C8—21no—
364C2×C3×C8—21no—
365C2×C3×C8—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4C2×D412yes—
368C3×C22⋊C4—24no—
369#217—24no—
370#217—24no—
371#217—24no—
372#217—24no—
373#217—24no—
374#216—44no—
375#214—44no—
376(C2×D3)⋊C4—24no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379(C2×D3)⋊C4—24no—
380C4⋊Dic3—24no—
381C4⋊Dic3—21no—
382C4⋊Dic3—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3C2×D412yes—
385C4⋊Dic3C2×D412yes—
386C4⋊Dic3C2×D412yes—
387Dic3⋊C4—24no—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390C4×Dic3—24no—
391C4×Dic3—24no—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—21no—
394C2×C3⋊C8—21no—
395C2×C3⋊C8—21no—
396C2×C3⋊C8—21no—
397C2×C3⋊C8—21no—
398C25—31no—
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—41no—
404C2×#41—41no—
405C2×#41—62no—
406C2×#41—62no—
407C2×#41—62no—
408C2×#41—62no—
409C2×#41—121no—
410C2×#41—121no—
411C22×Q8—31no—
412C22×Q8C22×D311yescharacteristic
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—61no—
416C22×D4—61no—
417C22×D4—61no—
418C22×D4—61no—
419C22×D4C22×D311yescharacteristic
420C22×D4C22×D311yescharacteristic
421C23×C4—21no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—31no—
427C23×C4—62no—
428C23×C4—62no—
429C23×C4—61no—
430C23×C4—62no—
431C23×C4—62no—
432C23×C4—121no—
433C23×C4—121no—
434C23×C4C22×D311yescharacteristic
435C2×Q16—62no—
436C2×Q16—62no—
437C2×Q16—121no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—41no—
441C2×SD16—62no—
442C2×SD16—62no—
443C2×SD16—121no—
444C2×D8—22no—
445C2×D8—22no—
446C2×D8—41no—
447C22×C8—31no—
448C22×C8—31no—
449C22×C8C22×D311yescharacteristic
450C22×C8C22×D311yescharacteristic
451#123—68no—
452#123—68no—
453C22⋊Q8—34no—
454C22⋊Q8—34no—
455C22⋊Q8—62no—
456C22⋊Q8—62no—
457C22⋊Q8—62no—
458C22⋊Q8—62no—
459C22⋊Q8—62no—
460C22⋊Q8—62no—
461#121—22no—
462#121—34no—
463#121—62no—
464#121—62no—
465#121—62no—
466#121—62no—
467#121—62no—
468#121#6714yescomplemented
469#120—68no—
470#120—68no—
471C4×D4—68no—
472C4×D4—68no—
473C4×D4—68no—
474C4×D4—68no—
475#117—62no—
476#117—62no—
477#117—62no—
478#117—62no—
479C2×C4⋊C4—31no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—61no—
483C2×C4⋊C4—61no—
484C2×C4⋊C4—61no—
485C2×C4⋊C4—61no—
486C2×C4⋊C4C22×D311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—61no—
489C2×C22⋊C4—61no—
490C2×C22⋊C4—61no—
491C2×C22⋊C4—61no—
492C2×C22⋊C4—61no—
493C2×C22⋊C4—61no—
494C2×C22⋊C4—61no—
495C2×C22⋊C4—61no—
496C2×C22⋊C4—61no—
497C2×C42—61no—
498C2×C42—61no—
499#103—22no—
500#103—62no—
501#103—62no—
502#103—62no—
503#102—22no—
504#102—62no—
505#102—62no—
506#102—62no—
507C22⋊C8—22no—
508C22⋊C8—62no—
509C22⋊C8—62no—
510C22⋊C8—62no—
511C22⋊C8—121no—
512C22⋊C8—121no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3#12012yes—
534C23×C3C22×D411yescharacteristic
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—44no—
548C22×D3—44no—
549C22×D3—44no—
550C22×D3—44no—
551C22×D3—44no—
552C22×D3—44no—
553C22×D3—44no—
554C22×D3#12012yes—
555C22×D3#13512yes—
556C3×Q8—22no—
557C3×Q8—22no—
558C3×Q8—41no—
559C3×Q8—41no—
560C3×D4—22no—
561C3×D4—22no—
562C3×D4—22no—
563C3×D4—22no—
564C3×D4—48no—
565C3×D4—48no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4—41no—
569C3×D4—41no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—48no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4#12012yes—
584C2×C3×C4C22×D411yescharacteristic
585C2×C3×C4C22×D411yescharacteristic
586C2×C3×C4C22×D411yescharacteristic
587C2×C3×C4C22×D411yescharacteristic
588C2×C3×C4H(5,𝔽2)11yescharacteristic
589C2×C3×C4H(5,𝔽2)11yescharacteristic
590#67—48no—
591#67—48no—
592#67—48no—
593#67—48no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—21no—
600C2×Dic3—22no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—44no—
604C2×Dic3—48no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3#12012yes—
614C4×D3—22no—
615C4×D3—22no—
616C4×D3—22no—
617C4×D3—22no—
618C4×D3—44no—
619C4×D3—44no—
620C4×D3—41no—
621C4×D3—41no—
622C4×D3—41no—
623C4×D3—41no—
624Dic6—22no—
625Dic6—22no—
626Dic6—41no—
627Dic6—41no—
628C3×C8—41no—
629C3×C8—41no—
630C3⋊C8—41no—
631C3⋊C8—41no—
632C24—21no—
633C24—21no—
634C24—31no—
635C24—31no—
636C24—62no—
637C24—62no—
638C24—62no—
639C24—121no—
640C24—121no—
641C24—121no—
642C24—121no—
643C24D3×D411yescharacteristic
644#41—44no—
645#41—44no—
646#41—44no—
647#41—44no—
648#41—124no—
649#41—124no—
650#41—124no—
651#41—124no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—32no—
658C2×Q8—61no—
659C2×Q8—61no—
660C2×Q8—61no—
661C2×Q8—61no—
662C2×Q8—61no—
663C2×Q8D3×D412yes—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—64no—
681C2×D4—64no—
682C2×D4—64no—
683C2×D4—64no—
684C2×D4—122no—
685C2×D4—122no—
686C2×D4—122no—
687C2×D4—122no—
688C2×D4—122no—
689C2×D4—122no—
690C2×D4—122no—
691C2×D4—122no—
692C2×D4D3×D412yes—
693C2×D4C2×#6712yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—31no—
702C22×C4—32no—
703C22×C4—32no—
704C22×C4—31no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—62no—
708C22×C4—62no—
709C22×C4—62no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—64no—
715C22×C4—62no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—62no—
721C22×C4—62no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—121no—
729C22×C4—121no—
730C22×C4—124no—
731C22×C4—124no—
732C22×C4—124no—
733C22×C4—124no—
734C22×C4—122no—
735C22×C4—121no—
736C22×C4—122no—
737C22×C4D3×D411yescharacteristic
738C22×C4D3×D412yes—
739C22×C4C2×#6712yes—
740C22×C4C23×D311yescharacteristic
741Q16—124no—
742SD16—44no—
743SD16—124no—
744D8—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—61no—
752C2×C8—61no—
753C2×C8—61no—
754C2×C8—61no—
755C2×C8—61no—
756C2×C8—61no—
757C4⋊C4—21no—
758C4⋊C4—32no—
759C4⋊C4—32no—
760C4⋊C4—32no—
761C4⋊C4—64no—
762C4⋊C4—64no—
763C4⋊C4—64no—
764C4⋊C4—64no—
765C4⋊C4—61no—
766C4⋊C4—61no—
767C4⋊C4—61no—
768C4⋊C4C2×#6712yes—
769C22⋊C4—24no—
770C22⋊C4—64no—
771C22⋊C4—64no—
772C22⋊C4—64no—
773C22⋊C4—64no—
774C22⋊C4—64no—
775C22⋊C4—64no—
776C22⋊C4—64no—
777C22⋊C4—64no—
778C22⋊C4—64no—
779C42—64no—
780C42—64no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—42no—
789C22×C3—42no—
790C22×C3—42no—
791C22×C3—42no—
792C22×C3—42no—
793C22×C3—42no—
794C22×C3—81no—
795C22×C3—81no—
796C22×C3—81no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3—81no—
800C22×C3—81no—
801C22×C3—81no—
802C22×C3C2×#12011yescharacteristic
803C22×C3C2×#12011yescharacteristic
804C22×C3#53411yescharacteristic
805C22×C3C2×#13511yescharacteristic
806C22×C3#57511yescharacteristic
807C22×C3#57511yescharacteristic
808C22×C3#57511yescharacteristic
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—416no—
816C2×D3—41no—
817C2×D3—41no—
818C2×D3—41no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—41no—
823C2×D3—41no—
824C3×C4—22no—
825C3×C4—42no—
826C3×C4—42no—
827C3×C4D4211yescharacteristic
828C3×C4D4211yescharacteristic
829C3×C4D4211yescharacteristic
830C3×C4D4211yescharacteristic
831Dic3—22no—
832Dic3—42no—
833Dic3—41no—
834Dic3—42no—
835Dic3—42no—
836Dic3—42no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—22no—
844C23—22no—
845C23—32no—
846C23—32no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—61no—
866C23—61no—
867C23—61no—
868C23—61no—
869C23—61no—
870C23—61no—
871C23—124no—
872C23—124no—
873C23—124no—
874C23—124no—
875C23—124no—
876C23—124no—
877C23—124no—
878C23#93712yes—
879C23C2×D3×D411yescharacteristic
880Q8—22no—
881Q8—22no—
882Q8—41no—
883Q8—41no—
884Q8—62no—
885Q8—62no—
886Q8—121no—
887Q8—121no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—48no—
893D4—48no—
894D4—41no—
895D4—41no—
896D4—41no—
897D4—41no—
898D4—128no—
899D4—128no—
900D4—128no—
901D4—128no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—32no—
911C2×C4—48no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—61no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—62no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—124no—
930C2×C4—124no—
931C2×C4—124no—
932C2×C4—128no—
933C2×C4—121no—
934C2×C4—121no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—121no—
943C2×C4—121no—
944C2×C4—121no—
945C2×C4#93712yes—
946C2×C4C2×D3×D411yescharacteristic
947C2×C4C2×D3×D411yescharacteristic
948C2×C4C2×D3×D411yescharacteristic
949C2×C4#100411yescharacteristic
950C2×C4#100411yescharacteristic
951C2×C4C22×#6711yescharacteristic
952C8—41no—
953C8—41no—
954C8—121no—
955C8—121no—
956C2×C3—42no—
957C2×C3—82no—
958C2×C3—82no—
959C2×C3#240311yescharacteristic
960C2×C3#300211yescharacteristic
961C2×C3#300211yescharacteristic
962C2×C3#300511yescharacteristic
963C2×C3#300511yescharacteristic
964C2×C3#319111yescharacteristic
965C2×C3#319711yescharacteristic
966D3—42no—
967D3—42no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—1216no—
996C22—121no—
997C22—121no—
998C22—121no—
999C22—121no—
1000C22—121no—
1001C22—121no—
1002C22—121no—
1003C22—121no—
1004C22D3×#12011yescharacteristic
1005C22#558911yescharacteristic
1006C22D3×#13511yescharacteristic
1007C22#576811yescharacteristic
1008C22#577311yescharacteristic
1009C22#577311yescharacteristic
1010C22C2×#93711yescharacteristic
1011C4—22no—
1012C4—42no—
1013C4—42no—
1014C4—62no—
1015C4—121no—
1016C4—122no—
1017C4—122no—
1018C4—122no—
1019C4—122no—
1020C4#559011yescharacteristic
1021C4#559011yescharacteristic
1022C4D4×#6711yescharacteristic
1023C4D4×#6711yescharacteristic
1024C3#2392311yescharacteristic, complemented, Sylow
1025C2—42no—
1026C2—82no—
1027C2—82no—
1028C2—122no—
1029C2—122no—
1030C2#8008211yescharacteristic
1031C2#8008311yescharacteristic
1032C2#8009011yescharacteristic
1033C2#8009211yescharacteristic
1034C2#8260411yescharacteristic
1035C2#8391111yescharacteristic
1036C2#8394511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3#23923
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×#5606C2semidirect
3. C2×C3×#449C2semidirect
4. C2×#5239C2semidirect
5. C2×#5173C2semidirect
6. C2×#5158C2semidirect
7. #72054C2semidirect
8. #72043C2semidirect
9. #71678C2semidirect
10. #70273C2semidirect
11. #70269C2semidirect
12. #70205C2semidirect
13. #70201C2semidirect
14. #69955C2semidirect
15. #69931C2semidirect
20. C22×C3×SD16C22semidirect
21. C22×C3×D8C22semidirect
27. C22×#216C22semidirect
35. C22×#214C22semidirect
47. C2×C3×#103C22semidirect
48. C2×C3×#102C22semidirect
51. C2×#835C22semidirect
52. C2×#832C22semidirect
53. C2×#832C22semidirect
54. C2×#832C22semidirect
62. C2×#816C22semidirect
63. C2×#816C22semidirect
64. #4551C22semidirect
65. #4551C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
73. C2×#449D3semidirect
129. C3×#121D4semidirect
140. #946D4semidirect
149. #938D4semidirect
170. #924D4semidirect
203. C22×SD16C2×D3semidirect
204. C22×D8C2×D3semidirect
234. C2×#103C2×D3semidirect
238. C2×#102C2×D3semidirect
468. #121#67semidirect
1024. C3#23923semidirect

Maximal subgroups

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

subgroupindex
C2×#58282
C2×#56062
C2×C3×#4492
C2×#52392
C2×#51732
C2×#51582
#720542
#720432
#716782
#702732
#702692
#702052
#702012
#699552
#699312
#239233