Finite Group Databasebeta

← #10724523

Subgroups — #10724523

Order 768.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#392C211yesmaximal, characteristic
2C2×#5221C211yesmaximal, characteristic, complemented
3C2×#5220C211yesmaximal, characteristic, complemented
4C2×#5220C211yesmaximal, characteristic, complemented
5C2×#5220C211yesmaximal, characteristic, complemented
6C2×#5220C211yesmaximal, characteristic, complemented
7C2×#4950C211yesmaximal, characteristic, complemented
8#72131C211yesmaximal, characteristic, complemented
9#71548C211yesmaximal, characteristic, complemented
10#71546C211yesmaximal, characteristic, complemented
11#71546C211yesmaximal, characteristic, complemented
12#71545C211yesmaximal, characteristic, complemented
13#71544C211yesmaximal, characteristic, complemented
14#69412C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14519—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C3×#392C418yescomplemented
39C2×C3×#95C2211yescharacteristic
40#5221—24no—
41#5220—24no—
42#5220—24no—
43#5220—24no—
44#5220—24no—
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4950—24no—
59C2×#392D311yescharacteristic
60C2×#390—31no—
61C2×#386—31no—
62C2×#386—31no—
63C2×#386—31no—
64C2×#386—31no—
65C2×#385—31no—
66#1442—31no—
67#1440—31no—
68#1439—31no—
69#1439—31no—
70#1438—31no—
71#1437—31no—
72#1434—31no—
73C22⋊#95—31no—
74C25×C3C2311yescharacteristic
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—22no—
86C22×C3×D4—22no—
87C22×C3×D4—41no—
88C22×C3×D4—41no—
89C22×C3×D4—41no—
90C22×C3×D4—41no—
91C22×C3×D4—41no—
92C22×C3×D4—41no—
93C22×C3×D4—41no—
94C22×C3×D4—41no—
95C22×C3×D4C2×C414yes—
96C22×C3×D4C2×C414yescomplemented
97C22×C3×D4C2×C414yescomplemented
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×Dic3—22no—
103C23×Dic3—22no—
104C23×Dic3—22no—
105C23×Dic3—22no—
106C23×Dic3—22no—
107C23×Dic3—22no—
108C23×Dic3—41no—
109C23×Dic3—41no—
110C23×Dic3—41no—
111C23×Dic3—41no—
112C23×Dic3—41no—
113C23×Dic3—41no—
114C23×Dic3—41no—
115C23×Dic3—41no—
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C22⋊C4—41no—
128C2×C3×C22⋊C4—41no—
129C2×C3×C22⋊C4—41no—
130C2×C3×C22⋊C4C2×C414yescomplemented
131C2×C3×C22⋊C4C2×C414yescomplemented
132C2×C3×C22⋊C4C2×C414yescomplemented
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—22no—
145C2×#217—22no—
146C2×#217—22no—
147C2×#217—41no—
148C2×#217—41no—
149C2×#217—41no—
150C2×#217—41no—
151C2×#217—41no—
152C2×#217—41no—
153C2×#217—41no—
154C2×#217—41no—
155C2×#217—41no—
156C2×#217—41no—
157C2×#217—41no—
158C2×#217—41no—
159C2×#217—41no—
160C2×#217—41no—
161C2×#217D414yescomplemented
162C2×#217D414yescomplemented
163C2×C4⋊Dic3—22no—
164C2×C4⋊Dic3—22no—
165C2×C4⋊Dic3—22no—
166C2×C4⋊Dic3—41no—
167C2×C4⋊Dic3—41no—
168C2×C4⋊Dic3—41no—
169C2×C4×Dic3—22no—
170C2×C4×Dic3—22no—
171C2×C4×Dic3—41no—
172C3×#95C2×C414yescomplemented
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—41no—
182C3⋊#95—41no—
183C3⋊#95—41no—
184C3⋊#95—41no—
185C3⋊#95D414yescomplemented
186C23×D4C2×D311yescharacteristic
187C23×D4C2×D311yescharacteristic
188C23×D4C2×D311yescharacteristic
189C24×C4—31no—
190C24×C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4C2×D311yescharacteristic
204C22×C22⋊C4C2×D311yescharacteristic
205C22×C22⋊C4C2×D311yescharacteristic
206C22×C42—31no—
207#392Dic318yescomplemented
208#390—64no—
209#386—64no—
210#386—64no—
211#386—64no—
212#386—64no—
213#385—64no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95C2×D311yescharacteristic
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—21no—
258C24×C3—21no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—21no—
263C24×C3—21no—
264C24×C3—21no—
265C24×C3—21no—
266C24×C3C22×C412yes—
267C24×C3C22×C412yes—
268C24×C3C22×C412yes—
269C24×C3C2×D412yes—
270C24×C3C2×D412yes—
271C24×C3#4112yes—
272C24×C3#4112yes—
273C24×C3C2411yescharacteristic
274C2×C3×D4—28no—
275C2×C3×D4—28no—
276C2×C3×D4—28no—
277C2×C3×D4—28no—
278C2×C3×D4—28no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
284C2×C3×D4—44no—
285C2×C3×D4—44no—
286C2×C3×D4—44no—
287C2×C3×D4—44no—
288C2×C3×D4—44no—
289C2×C3×D4—44no—
290C2×C3×D4—44no—
291C2×C3×D4—44no—
292C2×C3×D4—44no—
293C2×C3×D4—44no—
294C2×C3×D4—44no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4C22×C412yes—
318C22×C3×C4C22×C412yes—
319C22×C3×C4C22×C412yes—
320C22×C3×C4C22×C412yes—
321C22×C3×C4C2×D412yes—
322C22×C3×C4#4112yes—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—44no—
374C22×Dic3—44no—
375C22×Dic3—44no—
376C22×Dic3—44no—
377C22×Dic3—44no—
378C22×Dic3—44no—
379C22×Dic3—44no—
380C22×Dic3—44no—
381C22×Dic3—44no—
382C22×Dic3—44no—
383C22×Dic3—44no—
384C22×Dic3—44no—
385C22×Dic3—44no—
386C22×Dic3—44no—
387C22×Dic3C2×D412yes—
388C22×Dic3C2×D412yes—
389C22×Dic3C2×D412yes—
390C22×Dic3C2×D412yes—
391C22×Dic3C2×D412yes—
392C22×Dic3C2×D412yes—
393C3×C22⋊C4—28no—
394C3×C22⋊C4—44no—
395C3×C22⋊C4—44no—
396#217—44no—
397#217—44no—
398#217—44no—
399#217—44no—
400#217—44no—
401#217—44no—
402#217—44no—
403#217—44no—
404#217—44no—
405#217—44no—
406C4⋊Dic3—44no—
407C4⋊Dic3—44no—
408C4×Dic3—44no—
409C25C22×D311yescharacteristic
410C25C22×D311yescharacteristic
411C25C22×D311yescharacteristic
412C22×D4—22no—
413C22×D4—22no—
414C22×D4—22no—
415C22×D4—22no—
416C22×D4—22no—
417C22×D4—22no—
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—22no—
422C22×D4—41no—
423C22×D4—41no—
424C22×D4—41no—
425C22×D4—41no—
426C22×D4—41no—
427C22×D4—41no—
428C22×D4—41no—
429C22×D4—41no—
430C22×D4C2×Dic314yes—
431C22×D4C2×Dic314yescomplemented
432C22×D4C2×Dic314yescomplemented
433C23×C4—31no—
434C23×C4—31no—
435C23×C4—31no—
436C23×C4—31no—
437C23×C4—31no—
438C23×C4—31no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—62no—
442C23×C4—62no—
443C23×C4—62no—
444C23×C4—62no—
445C23×C4—62no—
446C23×C4—62no—
447C23×C4—121no—
448C23×C4—121no—
449C23×C4—121no—
450C23×C4—121no—
451C23×C4—121no—
452C23×C4—121no—
453C23×C4—121no—
454C23×C4—121no—
455C23×C4C22×D311yescharacteristic
456C23×C4C22×D311yescharacteristic
457C23×C4C22×D311yescharacteristic
458C23×C4C22×D311yescharacteristic
459C2×C4⋊C4—62no—
460C2×C4⋊C4—62no—
461C2×C4⋊C4—62no—
462C2×C4⋊C4—121no—
463C2×C4⋊C4—121no—
464C2×C4⋊C4—121no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—34no—
468C2×C22⋊C4—34no—
469C2×C22⋊C4—41no—
470C2×C22⋊C4—41no—
471C2×C22⋊C4—41no—
472C2×C22⋊C4—41no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—121no—
488C2×C22⋊C4—121no—
489C2×C22⋊C4—121no—
490C2×C22⋊C4—121no—
491C2×C22⋊C4—121no—
492C2×C22⋊C4—121no—
493C2×C22⋊C4—121no—
494C2×C22⋊C4—121no—
495C2×C22⋊C4—121no—
496C2×C22⋊C4—121no—
497C2×C22⋊C4—121no—
498C2×C22⋊C4—121no—
499C2×C22⋊C4—121no—
500C2×C22⋊C4—121no—
501C2×C22⋊C4C2×Dic314yescomplemented
502C2×C22⋊C4C2×Dic314yescomplemented
503C2×C22⋊C4C2×Dic314yescomplemented
504C2×C42—62no—
505C2×C42—62no—
506C2×C42—121no—
507#95—34no—
508#95—62no—
509#95—62no—
510#95—62no—
511#95—62no—
512#95—62no—
513#95—62no—
514#95—62no—
515#95—62no—
516#95—121no—
517#95—121no—
518#95—121no—
519#95—121no—
520#95C2×Dic314yescomplemented
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—22no—
558C23×C3—22no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3—41no—
600C23×C3—41no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—41no—
610C23×C3—41no—
611C23×C3—41no—
612C23×C3—41no—
613C23×C3—41no—
614C23×C3—41no—
615C23×C3—41no—
616C23×C3—41no—
617C23×C3—41no—
618C23×C3—41no—
619C23×C3—41no—
620C23×C3—41no—
621C23×C3—41no—
622C23×C3—41no—
623C23×C3—41no—
624C23×C3C4×D414yes—
625C23×C3C4×D414yes—
626C23×C3C23×C411yescharacteristic
627C23×C3C22×D411yescharacteristic
628C23×C3C22×D411yescharacteristic
629C23×C3C22×D411yescharacteristic
630C23×C3C2×#4111yescharacteristic
631C23×C3C2×#4111yescharacteristic
632C23×C3C2×#4111yescharacteristic
633C23×C3H(5,𝔽2)11yescharacteristic
634C23×C3H(5,𝔽2)11yescharacteristic
635C23×C3H(5,𝔽2)11yescharacteristic
636C23×C3H(5,𝔽2)11yescharacteristic
637C23×C3H(5,𝔽2)11yescharacteristic
638C23×C3H(5,𝔽2)11yescharacteristic
639C23×C3H(5,𝔽2)11yescharacteristic
640C23×C32−1+411yescharacteristic
641C3×D4—416no—
642C3×D4—416no—
643C3×D4—416no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4C4×D414yes—
672C2×Dic3—22no—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—416no—
691C2×Dic3—416no—
692C2×Dic3—41no—
693C2×Dic3—41no—
694C2×Dic3—41no—
695C2×Dic3—41no—
696C2×Dic3—41no—
697C2×Dic3—41no—
698C2×Dic3—41no—
699C2×Dic3—41no—
700C2×Dic3—41no—
701C2×Dic3—41no—
702C2×Dic3—41no—
703C2×Dic3—41no—
704C2×Dic3—41no—
705C2×Dic3—41no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—41no—
709C2×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3—41no—
718C2×Dic3—41no—
719C2×Dic3—41no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24D3×D412yes—
769C24D3×D412yes—
770C24#23712yes—
771C24#23712yes—
772C24C22×Dic312yes—
773C24C22×Dic312yes—
774C24C22×Dic312yes—
775C24C23×D311yescharacteristic
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—32no—
820C22×C4—32no—
821C22×C4—32no—
822C22×C4—32no—
823C22×C4—32no—
824C22×C4—32no—
825C22×C4—61no—
826C22×C4—61no—
827C22×C4—61no—
828C22×C4—61no—
829C22×C4—61no—
830C22×C4—61no—
831C22×C4—61no—
832C22×C4—61no—
833C22×C4—61no—
834C22×C4—61no—
835C22×C4—61no—
836C22×C4—61no—
837C22×C4—61no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—61no—
844C22×C4—61no—
845C22×C4—61no—
846C22×C4—61no—
847C22×C4—61no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—61no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—124no—
876C22×C4—124no—
877C22×C4—124no—
878C22×C4—124no—
879C22×C4—124no—
880C22×C4—124no—
881C22×C4—124no—
882C22×C4—124no—
883C22×C4—124no—
884C22×C4—124no—
885C22×C4—124no—
886C22×C4—124no—
887C22×C4—124no—
888C22×C4—124no—
889C22×C4D3×D412yes—
890C22×C4#23712yes—
891C22×C4C22×Dic312yes—
892C22×C4C22×Dic312yes—
893C22×C4C22×Dic312yes—
894C22×C4C22×Dic312yes—
895C4⋊C4—124no—
896C4⋊C4—124no—
897C22⋊C4—28no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—124no—
901C22⋊C4—124no—
902C22⋊C4—124no—
903C22⋊C4—124no—
904C22⋊C4—124no—
905C22⋊C4—124no—
906C22⋊C4—124no—
907C22⋊C4—124no—
908C22⋊C4—124no—
909C22⋊C4—124no—
910C42—124no—
911C22×C3—24no—
912C22×C3—24no—
913C22×C3—24no—
914C22×C3—24no—
915C22×C3—24no—
916C22×C3—24no—
917C22×C3—42no—
918C22×C3—42no—
919C22×C3—42no—
920C22×C3—42no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—42no—
925C22×C3—42no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—42no—
930C22×C3—42no—
931C22×C3—42no—
932C22×C3—42no—
933C22×C3—42no—
934C22×C3—42no—
935C22×C3—42no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3—42no—
939C22×C3—42no—
940C22×C3—42no—
941C22×C3—42no—
942C22×C3—42no—
943C22×C3—42no—
944C22×C3—42no—
945C22×C3—42no—
946C22×C3—42no—
947C22×C3—42no—
948C22×C3—81no—
949C22×C3—81no—
950C22×C3—81no—
951C22×C3—81no—
952C22×C3—81no—
953C22×C3—81no—
954C22×C3—81no—
955C22×C3—81no—
956C22×C3C2×C4×D411yescharacteristic
957C22×C3C2×C4×D411yescharacteristic
958C22×C3C2×C4×D411yescharacteristic
959C22×C3#51811yescharacteristic
960C22×C3#51811yescharacteristic
961C22×C3#51811yescharacteristic
962C22×C3#52011yescharacteristic
963C22×C3#53411yescharacteristic
964C22×C3#53411yescharacteristic
965C22×C3#53511yescharacteristic
966C22×C3#53511yescharacteristic
967C22×C3#53511yescharacteristic
968C22×C3#53711yescharacteristic
969C22×C3#53811yescharacteristic
970C22×C3#53811yescharacteristic
971C22×C3#53811yescharacteristic
972C22×C3#53911yescharacteristic
973C22×C3#54011yescharacteristic
974C22×C3#54011yescharacteristic
975C22×C3D4211yescharacteristic
976C22×C3D4211yescharacteristic
977C22×C3D4211yescharacteristic
978C22×C3#54611yescharacteristic
979C22×C3#54611yescharacteristic
980C22×C3#54611yescharacteristic
981C22×C3#54611yescharacteristic
982C22×C3#54711yescharacteristic
983C22×C3#54811yescharacteristic
984C22×C3#55111yescharacteristic
985C22×C3#55111yescharacteristic
986C22×C3#55311yescharacteristic
987C22×C3#56011yescharacteristic
988C22×C3#56011yescharacteristic
989C22×C3#56211yescharacteristic
990C22×C3#56211yescharacteristic
991C3×C4—24no—
992C3×C4—42no—
993C3×C4—42no—
994C3×C4—42no—
995Dic3—42no—
996Dic3—42no—
997Dic3—42no—
998Dic3—42no—
999Dic3—42no—
1000Dic3—42no—
1001Dic3—81no—
1002Dic3—81no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23D4×Dic314yes—
1107C23D4×Dic314yes—
1108C23C2×D3×D411yescharacteristic
1109C23C2×D3×D411yescharacteristic
1110C23C2×D3×D411yescharacteristic
1111C23C2×#23711yescharacteristic
1112C23C2×#23711yescharacteristic
1113C23C2×#23711yescharacteristic
1114C23#100411yescharacteristic
1115C23#100411yescharacteristic
1116C23#100411yescharacteristic
1117C23#100411yescharacteristic
1118C23#100411yescharacteristic
1119C23#100411yescharacteristic
1120C23#100911yescharacteristic
1121C23#101011yescharacteristic
1122C23C23×Dic311yescharacteristic
1123D4—416no—
1124D4—416no—
1125D4—416no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—62no—
1154C2×C4—62no—
1155C2×C4—62no—
1156C2×C4—62no—
1157C2×C4—62no—
1158C2×C4—62no—
1159C2×C4—62no—
1160C2×C4—62no—
1161C2×C4—62no—
1162C2×C4—62no—
1163C2×C4—62no—
1164C2×C4—62no—
1165C2×C4—62no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—1216no—
1172C2×C4—1216no—
1173C2×C4—121no—
1174C2×C4—121no—
1175C2×C4—121no—
1176C2×C4—121no—
1177C2×C4—121no—
1178C2×C4—121no—
1179C2×C4—121no—
1180C2×C4—121no—
1181C2×C4—121no—
1182C2×C4—121no—
1183C2×C4—121no—
1184C2×C4—121no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4—121no—
1188C2×C4—121no—
1189C2×C4—121no—
1190C2×C4—121no—
1191C2×C4—121no—
1192C2×C4—121no—
1193C2×C4—121no—
1194C2×C4—121no—
1195C2×C4—121no—
1196C2×C4—121no—
1197C2×C4—121no—
1198C2×C4—121no—
1199C2×C4—121no—
1200C2×C4—121no—
1201C2×C4—121no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4—121no—
1205C2×C4—121no—
1206C2×C4—121no—
1207C2×C4—121no—
1208C2×C4—121no—
1209C2×C4—121no—
1210C2×C4—121no—
1211C2×C4D4×Dic314yes—
1212C2×C3—44no—
1213C2×C3—44no—
1214C2×C3—82no—
1215C2×C3#232111yescharacteristic
1216C2×C3#232511yescharacteristic
1217C2×C3#232811yescharacteristic
1218C2×C3#235811yescharacteristic
1219C2×C3#235811yescharacteristic
1220C2×C3#236111yescharacteristic
1221C2×C3#237711yescharacteristic
1222C2×C3#266911yescharacteristic
1223C2×C3#267111yescharacteristic
1224C2×C3#267611yescharacteristic
1225C2×C3#267811yescharacteristic
1226C2×C3#268811yescharacteristic
1227C2×C3#269611yescharacteristic
1228C2×C3#270611yescharacteristic
1229C2×C3#274911yescharacteristic
1230C22—24no—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22#558711yescharacteristic
1276C22#558711yescharacteristic
1277C22#558911yescharacteristic
1278C22#559011yescharacteristic
1279C22#559011yescharacteristic
1280C22#559111yescharacteristic
1281C22#559111yescharacteristic
1282C22#559111yescharacteristic
1283C22#559111yescharacteristic
1284C22#559211yescharacteristic
1285C22#559311yescharacteristic
1286C22#559311yescharacteristic
1287C22#559711yescharacteristic
1288C22#559811yescharacteristic
1289C22#560211yescharacteristic
1290C22#560511yescharacteristic
1291C22#560911yescharacteristic
1292C22#561111yescharacteristic
1293C22#561711yescharacteristic
1294C22#561811yescharacteristic
1295C22#562011yescharacteristic
1296C22#562011yescharacteristic
1297C22#562111yescharacteristic
1298C22#562111yescharacteristic
1299C22#571511yescharacteristic
1300C22#571511yescharacteristic
1301C22#571911yescharacteristic
1302C22#571911yescharacteristic
1303C22C2×D4×Dic311yescharacteristic
1304C22C2×D4×Dic311yescharacteristic
1305C22C2×D4×Dic311yescharacteristic
1306C22#579811yescharacteristic
1307C22#579811yescharacteristic
1308C22#579811yescharacteristic
1309C22#582711yescharacteristic
1310C4—24no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—122no—
1315C4—122no—
1316C4—122no—
1317C4—122no—
1318C4—122no—
1319C4—122no—
1320C4—241no—
1321C4—241no—
1322C3#1451911yescharacteristic, complemented, Sylow
1323C2—44no—
1324C2—44no—
1325C2—82no—
1326C2#7671011yescharacteristic
1327C2#7671411yescharacteristic
1328C2#7671911yescharacteristic
1329C2#7672511yescharacteristic
1330C2#7673311yescharacteristic
1331C2#7676411yescharacteristic
1332C2#7677211yescharacteristic
1333C2#7677311yescharacteristic
1334C2#8257811yescharacteristic
1335C2#8257911yescharacteristic
1336C2#8257911yescharacteristic
1337C2#8263411yescharacteristic
1338C2#8263611yescharacteristic
1339C2#8263911yescharacteristic
1340C2#8317211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
Fitting, prime radicalC2×C3×#392C2
socle, cosocleC24×C3C24
hypercenterC2×#392D3
hypocenterC3#14519
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
2. C2×#5221C2semidirect
3. C2×#5220C2semidirect
4. C2×#5220C2semidirect
5. C2×#5220C2semidirect
6. C2×#5220C2semidirect
7. C2×#4950C2semidirect
8. #72131C2semidirect
9. #71548C2semidirect
10. #71546C2semidirect
11. #71546C2semidirect
12. #71545C2semidirect
13. #71544C2semidirect
14. #69412C2semidirect
15. #69401C2semidirect
38. C3×#392C4semidirect
96. C22×C3×D4C2×C4semidirect
97. C22×C3×D4C2×C4semidirect
130. C2×C3×C22⋊C4C2×C4semidirect
131. C2×C3×C22⋊C4C2×C4semidirect
132. C2×C3×C22⋊C4C2×C4semidirect
161. C2×#217D4semidirect
162. C2×#217D4semidirect
172. C3×#95C2×C4semidirect
185. C3⋊#95D4semidirect
207. #392Dic3semidirect
431. C22×D4C2×Dic3semidirect
432. C22×D4C2×Dic3semidirect
501. C2×C22⋊C4C2×Dic3semidirect
502. C2×C22⋊C4C2×Dic3semidirect
503. C2×C22⋊C4C2×Dic3semidirect
520. #95C2×Dic3semidirect
1322. C3#14519semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3922
C2×#52212
C2×#52202
C2×#49502
#721312
#715482
#715462
#715452
#715442
#694122
#694012
#145193