Finite Group Databasebeta

← #10731721

Subgroups — #10731721

Order 768.

3458 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C22×#938C211yesmaximal, characteristic, complemented
3C22×C4×#67C211yesmaximal, characteristic, complemented
4C2×#5223C212yesmaximal, complemented
5C2×#5221C211yesmaximal, characteristic, complemented
6C2×#5212C211yesmaximal, characteristic, complemented
7C2×#4987C211yesmaximal, characteristic, complemented
8#72131C212yesmaximal, complemented
9#71563C211yesmaximal, characteristic, complemented
10#71550C212yesmaximal, complemented
11#71547C212yesmaximal, complemented
12#15123—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×C3×D4C2212yes—
15C24×C3×C4C2211yescharacteristic
16C23×#67C2211yescharacteristic
17C23×#67C2212yes—
18C23×C4×D3C2211yescharacteristic
19C2×C3×#121—24no—
20C2×C3×#121—24no—
21C2×C3×#121—24no—
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2212yes—
24C22×#217C2212yes—
25C22×#217C2212yes—
26C22×#217C2211yescharacteristic
27C22×#217C2212yes—
28C22×#217C2212yes—
29C2×#938—24no—
30C2×#938—24no—
31C2×#938—24no—
32C2×C4×#67—24no—
33C2×C4×#67—24no—
34C2×C4×#67—24no—
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2212yes—
37C22×C4⋊Dic3C2211yescharacteristic
38C22×C4⋊Dic3C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41#5223—28no—
42#5221—24no—
43#5212—24no—
44C2×C3⋊#95C2212yes—
45C2×C3⋊#95C2212yes—
46C2×C3⋊#95C2212yes—
47C2×C3⋊#95C2212yes—
48#4987—24no—
49C22×#121—31no—
50C22×#121D311yescharacteristic, complemented
51C22×C4×D4—31no—
52C2×#392—32no—
53C2×#390—31no—
54C2×#380—31no—
55C2×#380—31no—
56#1439—32no—
57#1438—32no—
58#1438—32no—
59C4⋊#95—31no—
60C25×C3C2312yes—
61C25×C3C2311yescharacteristic
62C24×D3C2311yescharacteristic
63C22×C3×D4—24no—
64C22×C3×D4—24no—
65C22×C3×D4—24no—
66C22×C3×D4—24no—
67C22×C3×D4—22no—
68C22×C3×D4—22no—
69C22×C3×D4—22no—
70C22×C3×D4—24no—
71C22×C3×D4—22no—
72C22×C3×D4—22no—
73C22×C3×D4—22no—
74C22×C3×D4—42no—
75C22×C3×D4—42no—
76C22×C3×D4D414yescomplemented
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4D414yescomplemented
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2312yes—
86C23×C3×C4C2311yescharacteristic
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—24no—
92C22×#67—24no—
93C22×#67—24no—
94C22×#67—24no—
95C22×#67—22no—
96C22×#67—24no—
97C22×#67—22no—
98C22×#67—42no—
99C22×#67—42no—
100C22×#67D414yescomplemented
101C23×Dic3C2312yes—
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2312yes—
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3D414yescomplemented
113C3×#121—232no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4D414yescomplemented
117C2×C3×C22⋊C4—24no—
118C2×C3×C22⋊C4—24no—
119C2×C3×C22⋊C4—24no—
120C2×#217—22no—
121C2×#217—24no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—24no—
125C2×#217—24no—
126C2×#217—24no—
127C2×#217—24no—
128C2×#217—24no—
129C2×#217—24no—
130C2×#217—24no—
131C2×#217—24no—
132C2×#217—42no—
133C2×#217—42no—
134C2×#217—42no—
135#938—232no—
136C4×#67—232no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—24no—
141C2×(C2×D3)⋊C4—24no—
142C2×(C2×D3)⋊C4—42no—
143C2×C4⋊Dic3—22no—
144C2×C4⋊Dic3—22no—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3—22no—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3D414yescomplemented
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×C4×Dic3—22no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3D414yescomplemented
155C3⋊#95—24no—
156C3⋊#95—24no—
157C3⋊#95—24no—
158C3⋊#95—42no—
159C23×D4—31no—
160C23×D4—32no—
161C23×D4C2×D311yescharacteristic
162C23×D4C2×D312yes—
163C24×C4—31no—
164C24×C4C2×D311yescharacteristic
165C2×#121—24no—
166C2×#121—24no—
167C2×#121—24no—
168C2×#121—64no—
169C2×#121—64no—
170C2×#121—64no—
171C2×C4×D4—64no—
172C2×C4×D4—64no—
173C2×C4×D4—64no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4C2×D311yescharacteristic
178C22×C22⋊C4—32no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—32no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—32no—
183C22×C22⋊C4—32no—
184C22×C22⋊C4—32no—
185C22×C22⋊C4C2×D312yes—
186C22×C42—31no—
187#392—68no—
188#390—64no—
189#380—64no—
190#380—64no—
191C2×#95—32no—
192C2×#95—32no—
193C2×#95—32no—
194C2×#95—32no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—22no—
208C24×C3—22no—
209C24×C3—22no—
210C24×C3—22no—
211C24×C3—22no—
212C24×C3—22no—
213C24×C3—22no—
214C24×C3—22no—
215C24×C3—22no—
216C24×C3—22no—
217C24×C3—22no—
218C24×C3—22no—
219C24×C3—22no—
220C24×C3—22no—
221C24×C3C2×D412yes—
222C24×C3C2×D414yes—
223C24×C3C2×D412yes—
224C24×C3#4112yes—
225C24×C3C2411yescharacteristic
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3C2×D412yes—
239C23×D3C2×D412yes—
240C23×D3#4112yes—
241C2×C3×D4—216no—
242C2×C3×D4—28no—
243C2×C3×D4—28no—
244C2×C3×D4—28no—
245C2×C3×D4—48no—
246C2×C3×D4—48no—
247C2×C3×D4—48no—
248C2×C3×D4—48no—
249C2×C3×D4—48no—
250C2×C3×D4—48no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C2×C3×D4—44no—
254C2×C3×D4—44no—
255C22×C3×C4—21no—
256C22×C3×C4—22no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—21no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—28no—
268C22×C3×C4—28no—
269C22×C3×C4—28no—
270C22×C3×C4—44no—
271C22×C3×C4—44no—
272C22×C3×C4—44no—
273C22×C3×C4—44no—
274C22×C3×C4C2×D412yes—
275C22×C3×C4C2×D412yes—
276C22×C3×C4C2×D412yes—
277C22×C3×C4C2×D414yes—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4#4112yes—
283C2×#67—28no—
284C2×#67—28no—
285C2×#67—28no—
286C2×#67—28no—
287C2×#67—28no—
288C2×#67—28no—
289C2×#67—216no—
290C2×#67—28no—
291C2×#67—48no—
292C2×#67—48no—
293C2×#67—48no—
294C2×#67—48no—
295C2×#67—48no—
296C2×#67—48no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—22no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—22no—
313C22×Dic3—21no—
314C22×Dic3—22no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—22no—
318C22×Dic3—21no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3C2×D414yes—
327C22×Dic3C2×D412yes—
328C22×Dic3C2×D412yes—
329C22×Dic3C2×D412yes—
330C22×Dic3C2×D412yes—
331C22×Dic3#4112yes—
332C2×C4×D3—28no—
333C2×C4×D3—28no—
334C2×C4×D3—28no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C2×C4×D3—44no—
339C3×C4⋊C4—28no—
340C3×C22⋊C4—216no—
341#217—28no—
342#217—216no—
343#217—48no—
344#217—48no—
345#217—48no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—48no—
348C4⋊Dic3—28no—
349C4⋊Dic3—44no—
350Dic3⋊C4—28no—
351C4×Dic3—28no—
352C25—31no—
353C25C22×D312yes—
354C25C22×D311yescharacteristic
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—24no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—34no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—62no—
370C22×D4—62no—
371C22×D4—64no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—62no—
375C22×D4—62no—
376C22×D4—64no—
377C22×D4—64no—
378C22×D4—64no—
379C22×D4—64no—
380C22×D4—122no—
381C22×D4—122no—
382C22×D4#6714yescomplemented
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—32no—
393C23×C4—34no—
394C23×C4—32no—
395C23×C4—62no—
396C23×C4—62no—
397C23×C4—62no—
398C23×C4—62no—
399C23×C4—62no—
400C23×C4—62no—
401C23×C4#6714yescomplemented
402C23×C4C22×D311yescharacteristic
403C23×C4C22×D312yes—
404C23×C4C22×D311yescharacteristic
405#121—232no—
406#121—632no—
407C4×D4—632no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—62no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4—62no—
418C2×C4⋊C4—62no—
419C2×C4⋊C4#6714yescomplemented
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—64no—
428C2×C22⋊C4—64no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—64no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—64no—
437C2×C22⋊C4—64no—
438C2×C22⋊C4—64no—
439C2×C22⋊C4—64no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4—122no—
443C2×C22⋊C4—122no—
444C2×C42—34no—
445C2×C42—62no—
446C2×C42—62no—
447#95—64no—
448#95—64no—
449#95—64no—
450#95—122no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—24no—
470C23×C3—24no—
471C23×C3—24no—
472C23×C3—24no—
473C23×C3—24no—
474C23×C3—24no—
475C23×C3—24no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—42no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3—42no—
496C23×C3—42no—
497C23×C3—42no—
498C23×C3—42no—
499C23×C3—42no—
500C23×C3—42no—
501C23×C3—42no—
502C23×C3—42no—
503C23×C3—42no—
504C23×C3—42no—
505C23×C3—42no—
506C23×C3—42no—
507C23×C3—42no—
508C23×C3—42no—
509C23×C3—42no—
510C23×C3—42no—
511C23×C3—42no—
512C23×C3—42no—
513C23×C3—42no—
514C23×C3—42no—
515C23×C3—42no—
516C23×C3—42no—
517C23×C3—42no—
518C23×C3—42no—
519C23×C3—42no—
520C23×C3#12114yescomplemented
521C23×C3C22×D411yescharacteristic
522C23×C3C22×D411yescharacteristic
523C23×C3C22×D411yescharacteristic
524C23×C3C22×D411yescharacteristic
525C23×C3C22×D411yescharacteristic
526C23×C3C22×D411yescharacteristic
527C23×C3C22×D411yescharacteristic
528C23×C3C2×#4111yescharacteristic
529C23×C3C2×#4111yescharacteristic
530C23×C3C2×#4111yescharacteristic
531C23×C3C2×#4111yescharacteristic
532C23×C3H(5,𝔽2)11yescharacteristic
533C23×C3H(5,𝔽2)11yescharacteristic
534C23×C3H(5,𝔽2)11yescharacteristic
535C23×C32−1+411yescharacteristic
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3#12114yescomplemented
571C3×D4—432no—
572C3×D4—416no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—24no—
576C2×C3×C4—22no—
577C2×C3×C4—24no—
578C2×C3×C4—24no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—42no—
583C2×C3×C4—41no—
584C2×C3×C4—42no—
585C2×C3×C4—42no—
586C2×C3×C4—42no—
587C2×C3×C4—416no—
588C2×C3×C4#12014yes—
589C2×C3×C4#12014yes—
590C2×C3×C4#12014yes—
591C2×C3×C4#12114yes—
592C2×C3×C4#12114yes—
593C2×C3×C4#12114yes—
594C2×C3×C4#12714yes—
595#67—232no—
596#67—432no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—24no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—24no—
611C2×Dic3—24no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—42no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—42no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—42no—
623C2×Dic3—42no—
624C2×Dic3—42no—
625C2×Dic3—42no—
626C2×Dic3—42no—
627C2×Dic3—42no—
628C2×Dic3—42no—
629C2×Dic3—42no—
630C2×Dic3—42no—
631C2×Dic3#12114yescomplemented
632C4×D3—416no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—32no—
660C24—32no—
661C24—32no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24D3×D412yes—
675C24#23712yes—
676C24C2×#6714yes—
677C24C2×#6712yes—
678C24C23×D311yescharacteristic
679C2×D4—216no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—68no—
694C2×D4—68no—
695C2×D4—68no—
696C2×D4—68no—
697C2×D4—68no—
698C2×D4—68no—
699C2×D4—68no—
700C2×D4—616no—
701C2×D4—128no—
702C2×D4—128no—
703C2×D4—128no—
704C2×D4—128no—
705C2×D4—128no—
706C2×D4—128no—
707C22×C4—21no—
708C22×C4—22no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—28no—
720C22×C4—28no—
721C22×C4—28no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—34no—
726C22×C4—32no—
727C22×C4—32no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—62no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—62no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—62no—
744C22×C4—61no—
745C22×C4—62no—
746C22×C4—61no—
747C22×C4—62no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—62no—
754C22×C4—68no—
755C22×C4—68no—
756C22×C4—68no—
757C22×C4—62no—
758C22×C4—62no—
759C22×C4—62no—
760C22×C4—62no—
761C22×C4—62no—
762C22×C4—62no—
763C22×C4—62no—
764C22×C4—124no—
765C22×C4—124no—
766C22×C4—124no—
767C22×C4—124no—
768C22×C4D3×D412yes—
769C22×C4D3×D412yes—
770C22×C4D3×D412yes—
771C22×C4#23712yes—
772C22×C4C2×#6714yes—
773C22×C4C2×#6712yes—
774C22×C4C2×#6712yes—
775C22×C4C2×#6712yes—
776C22×C4C2×#6712yes—
777C4⋊C4—28no—
778C4⋊C4—68no—
779C4⋊C4—68no—
780C4⋊C4—124no—
781C22⋊C4—216no—
782C22⋊C4—68no—
783C22⋊C4—68no—
784C22⋊C4—616no—
785C22⋊C4—128no—
786C22⋊C4—128no—
787C22⋊C4—128no—
788C22⋊C4—128no—
789C42—68no—
790C22×C3—24no—
791C22×C3—24no—
792C22×C3—24no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—44no—
806C22×C3—44no—
807C22×C3—44no—
808C22×C3—44no—
809C22×C3—44no—
810C22×C3—44no—
811C22×C3—44no—
812C22×C3—82no—
813C22×C3—82no—
814C22×C3—82no—
815C22×C3—82no—
816C22×C3—82no—
817C22×C3—82no—
818C22×C3—82no—
819C22×C3—82no—
820C22×C3C2×#12011yescharacteristic
821C22×C3C2×#12011yescharacteristic
822C22×C3C2×#12011yescharacteristic
823C22×C3C2×#12111yescharacteristic
824C22×C3C2×#12111yescharacteristic
825C22×C3C2×#12111yescharacteristic
826C22×C3C2×#12111yescharacteristic
827C22×C3C2×#12111yescharacteristic
828C22×C3C2×#12111yescharacteristic
829C22×C3#52511yescharacteristic
830C22×C3#52511yescharacteristic
831C22×C3#52511yescharacteristic
832C22×C3C2×#12711yescharacteristic
833C22×C3#53511yescharacteristic
834C22×C3#53511yescharacteristic
835C22×C3#53511yescharacteristic
836C22×C3#53711yescharacteristic
837C22×C3#53711yescharacteristic
838C22×C3#53711yescharacteristic
839C22×C3D4211yescharacteristic
840C22×C3D4211yescharacteristic
841C22×C3D4211yescharacteristic
842C22×C3#54611yescharacteristic
843C22×C3#54611yescharacteristic
844C22×C3#54611yescharacteristic
845C22×C3#54611yescharacteristic
846C22×C3#54711yescharacteristic
847C22×C3#54711yescharacteristic
848C22×C3#54811yescharacteristic
849C22×C3#54811yescharacteristic
850C22×C3#55011yescharacteristic
851C22×C3#55011yescharacteristic
852C22×C3#55311yescharacteristic
853C22×C3#55311yescharacteristic
854C22×C3#55511yescharacteristic
855C2×D3—24no—
856C2×D3—24no—
857C2×D3—24no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—42no—
862C2×D3—42no—
863C2×D3—42no—
864C2×D3—42no—
865C2×D3—42no—
866C2×D3—42no—
867C2×D3—42no—
868C2×D3—42no—
869C2×D3—42no—
870C3×C4—42no—
871C3×C4—44no—
872C3×C4#39218yescomplemented
873Dic3—24no—
874Dic3—42no—
875Dic3—42no—
876Dic3—44no—
877Dic3—82no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—24no—
897C23—24no—
898C23—24no—
899C23—24no—
900C23—24no—
901C23—24no—
902C23—24no—
903C23—34no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—42no—
921C23—42no—
922C23—42no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—42no—
930C23—42no—
931C23—42no—
932C23—42no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—42no—
939C23—42no—
940C23—42no—
941C23—42no—
942C23—42no—
943C23—42no—
944C23—42no—
945C23—42no—
946C23—42no—
947C23—42no—
948C23—62no—
949C23—62no—
950C23—62no—
951C23—62no—
952C23—62no—
953C23—62no—
954C23—62no—
955C23—62no—
956C23—62no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23—121no—
977C23—121no—
978C23—121no—
979C23—121no—
980C23—121no—
981C23—121no—
982C23#93814yescomplemented
983C23C2×D3×D411yescharacteristic
984C23C2×D3×D411yescharacteristic
985C23C2×D3×D411yescharacteristic
986C23C2×D3×D411yescharacteristic
987C23C2×#23711yescharacteristic
988C23C2×#23711yescharacteristic
989C23#100411yescharacteristic
990C23#100411yescharacteristic
991C23D3×#4111yescharacteristic
992C23D3×#4111yescharacteristic
993C23#100911yescharacteristic
994C23#101011yescharacteristic
995C23C22×#6711yescharacteristic
996C23C22×#6711yescharacteristic
997C23C22×#6711yescharacteristic
998D4—432no—
999D4—416no—
1000D4—632no—
1001D4—1232no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—34no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—416no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—64no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—64no—
1032C2×C4—64no—
1033C2×C4—122no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—122no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—122no—
1042C2×C4—122no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—1216no—
1046C2×C4—122no—
1047C2×C4—122no—
1048C2×C4—122no—
1049C2×C4—122no—
1050C2×C4—122no—
1051C2×C4—122no—
1052C2×C4—122no—
1053C2×C4#93714yes—
1054C2×C4#93714yes—
1055C2×C4#93814yes—
1056C2×C4#93914yes—
1057C2×C4#93914yes—
1058C2×C4#94014yes—
1059C2×C4#95314yes—
1060C2×C3—44no—
1061C2×C3—84no—
1062C2×C3C2×#39211yescharacteristic
1063C2×C3#240711yescharacteristic
1064C2×C3#240711yescharacteristic
1065C2×C3#240811yescharacteristic
1066C2×C3#240811yescharacteristic
1067C2×C3#241411yescharacteristic
1068C2×C3#241411yescharacteristic
1069C2×C3#241611yescharacteristic
1070C2×C3#241611yescharacteristic
1071C2×C3#253511yescharacteristic
1072C2×C3#253711yescharacteristic
1073C2×C3#254011yescharacteristic
1074C2×C3#254111yescharacteristic
1075C2×C3#261511yescharacteristic
1076C2×C3#284711yescharacteristic
1077D3—44no—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—44no—
1094C22—44no—
1095C22—44no—
1096C22—44no—
1097C22—44no—
1098C22—44no—
1099C22—44no—
1100C22—64no—
1101C22—64no—
1102C22—64no—
1103C22—82no—
1104C22—82no—
1105C22—82no—
1106C22—82no—
1107C22—82no—
1108C22—82no—
1109C22—82no—
1110C22—82no—
1111C22—122no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22—122no—
1116C22—122no—
1117C22—122no—
1118C22—122no—
1119C22—122no—
1120C22—122no—
1121C22—122no—
1122C22—122no—
1123C22#559811yescharacteristic
1124C22#559911yescharacteristic
1125C22D3×#12111yescharacteristic
1126C22D3×#12111yescharacteristic
1127C22#560611yescharacteristic
1128C22#560611yescharacteristic
1129C22#560711yescharacteristic
1130C22#560711yescharacteristic
1131C22#560811yescharacteristic
1132C22#560811yescharacteristic
1133C22#560911yescharacteristic
1134C22#561111yescharacteristic
1135C22#561211yescharacteristic
1136C22#561411yescharacteristic
1137C22#561611yescharacteristic
1138C22#561811yescharacteristic
1139C22C2×#93711yescharacteristic
1140C22C2×#93711yescharacteristic
1141C22C2×#93811yescharacteristic
1142C22C2×#93811yescharacteristic
1143C22D4×#6711yescharacteristic
1144C22D4×#6711yescharacteristic
1145C22C2×#93911yescharacteristic
1146C22C2×#93911yescharacteristic
1147C22C2×#94011yescharacteristic
1148C22#580511yescharacteristic
1149C22#580611yescharacteristic
1150C22#580611yescharacteristic
1151C22#582411yescharacteristic
1152C22#582811yescharacteristic
1153C22#582911yescharacteristic
1154C22#583111yescharacteristic
1155C22#583311yescharacteristic
1156C22#583411yescharacteristic
1157C22C2×#95311yescharacteristic
1158C4—42no—
1159C4—44no—
1160C4—64no—
1161C4—122no—
1162C4—122no—
1163C4—124no—
1164C4—242no—
1165C4#522318yescomplemented
1166C3#1512311yescharacteristic, complemented, Sylow
1167C2—44no—
1168C2—84no—
1169C2—124no—
1170C2#8264011yescharacteristic
1171C2#8264111yescharacteristic
1172C2#8266611yescharacteristic
1173C2#8266711yescharacteristic
1174C2#8266811yescharacteristic
1175C2#8266911yescharacteristic
1176C2#8270111yescharacteristic
1177C2#8270311yescharacteristic
1178C2#8270411yescharacteristic
1179C2#8270511yescharacteristic
1180C2#8270911yescharacteristic
1181C2#8272311yescharacteristic
1182C2C2×#522311yescharacteristic
1183C2#8405311yescharacteristic
1184C2#8409711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#121C2
hypercenterC22×#121D3
hypocenterC3#15123
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C22×#938C2semidirect
3. C22×C4×#67C2semidirect
4. C2×#5223C2semidirect
5. C2×#5221C2semidirect
6. C2×#5212C2semidirect
7. C2×#4987C2semidirect
8. #72131C2semidirect
9. #71563C2semidirect
10. #71550C2semidirect
11. #71547C2semidirect
50. C22×#121D3semidirect
76. C22×C3×D4D4semidirect
83. C23×C3×C4D4semidirect
100. C22×#67D4semidirect
112. C22×C4×D3D4semidirect
116. C2×C3×C4⋊C4D4semidirect
148. C2×C4⋊Dic3D4semidirect
154. C2×C4×Dic3D4semidirect
382. C22×D4#67semidirect
401. C23×C4#67semidirect
419. C2×C4⋊C4#67semidirect
520. C23×C3#121semidirect
570. C22×D3#121semidirect
631. C2×Dic3#121semidirect
872. C3×C4#392semidirect
982. C23#938semidirect
1165. C4#5223semidirect
1166. C3#15123semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C22×#9382
C22×C4×#672
C2×#52232
C2×#52212
C2×#52122
C2×#49872
#721312
#715632
#715502
#715472
#151233