Finite Group Databasebeta

← #10726413

Subgroups — #10726413

Order 768.

2430 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D3C211yesmaximal, characteristic
2C2×#4989C211yesmaximal, characteristic
3C2×#4980C211yesmaximal, characteristic, complemented
4C2×#4668C211yesmaximal, characteristic
5C2×#4655C211yesmaximal, characteristic, complemented
6C3×#1436C211yesmaximal, characteristic, complemented
7#71536C211yesmaximal, characteristic, complemented
8(C2×D3)⋊#95C211yesmaximal, characteristic
9(C2×D3)⋊#95C211yesmaximal, characteristic
10(C2×D3)⋊#95C211yesmaximal, characteristic
11(C2×D3)⋊#95C211yesmaximal, characteristic
12#69406C211yesmaximal, characteristic, complemented
13#69405C211yesmaximal, characteristic, complemented
14#69403C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14695—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C22×C4×Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C2×C42×D3—24no—
33C2×C42×D3—24no—
34C2×C42×D3—24no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
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
55#4989C418yescomplemented
56#4980—24no—
57#4668—24no—
58#4655—24no—
59C23×C42—31no—
60C2×#387—31no—
61C2×#387—31no—
62C2×#385—31no—
63C2×#385—31no—
64#1436—31no—
65#1436—31no—
66#1436—31no—
67#1436D311yescharacteristic, complemented
68#1434—31no—
69#1434—31no—
70C22⋊#95—31no—
71C22⋊#95—31no—
72C22⋊#95—31no—
73C22⋊#95—31no—
74C24×D3C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C22×C4×D3—22no—
90C22×C4×D3—22no—
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3C2×C414yes—
108C22×C4×D3D414yes—
109C22×C4×D3Q814yes—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4C2×C414yescomplemented
113C2×C3×C42—22no—
114C2×C3×C42—22no—
115C2×C3×C42—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4C2×C414yes—
127C2×(C2×D3)⋊C4C2×C414yes—
128C2×C4⋊Dic3—22no—
129C2×C4⋊Dic3—22no—
130C2×C4⋊Dic3—22no—
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4—22no—
133C2×Dic3⋊C4—22no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4C2×C414yescomplemented
137C2×C4×Dic3—22no—
138C2×C4×Dic3—22no—
139C2×C4×Dic3—22no—
140C2×C4×Dic3—22no—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—22no—
144C2×C4×Dic3D414yes—
145C2×C4×Dic3D414yes—
146C42×D3—232no—
147C3×#95—22no—
148C3×#95—22no—
149C3×#95—22no—
150C3×#95—22no—
151C3×#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95C2×C414yescomplemented
166C3⋊#95C2×C414yescomplemented
167C24×C4—31no—
168C24×C4—31no—
169C24×C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4C2×D311yescharacteristic
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C42—31no—
179C22×C42—31no—
180C22×C42—31no—
181C22×C42—64no—
182C22×C42—64no—
183C22×C42—64no—
184C22×C42C2×D311yescharacteristic
185#387—64no—
186#387—64no—
187#385—38no—
188#385—64no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95C2×D311yescharacteristic
205C2×#95C2×D311yescharacteristic
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C2×#95C2×D311yescharacteristic
209C24×C3C2411yescharacteristic
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—21no—
218C23×D3C22×C412yes—
219C23×D3C2×D412yes—
220C23×D3C2×Q812yes—
221C23×D3#4112yes—
222C23×D3#4112yes—
223C23×D3#4112yes—
224C23×D3#4112yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4C22×C412yes—
264C22×C3×C4C22×C412yes—
265C22×C3×C4C22×C412yes—
266C22×C3×C4C2×D412yes—
267C22×C3×C4C2×D412yes—
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×Q812yes—
270C22×C3×C4#4112yes—
271C22×C3×C4#4112yes—
272C22×C3×C4#4112yes—
273C22×C3×C4#4112yes—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3C22×C412yes—
313C22×Dic3C22×C412yes—
314C22×Dic3C22×C412yes—
315C22×Dic3C2×D412yes—
316C22×Dic3C2×D412yes—
317C22×Dic3C2×D412yes—
318C22×Dic3C2×D412yes—
319C22×Dic3C2×D412yes—
320C22×Dic3C2×Q812yes—
321C22×Dic3#4112yes—
322C22×Dic3#4112yes—
323C2×C4×D3—28no—
324C2×C4×D3—28no—
325C2×C4×D3—28no—
326C2×C4×D3—28no—
327C2×C4×D3—28no—
328C2×C4×D3—28no—
329C2×C4×D3—28no—
330C2×C4×D3—28no—
331C2×C4×D3—28no—
332C2×C4×D3—28no—
333C2×C4×D3—28no—
334C2×C4×D3—28no—
335C2×C4×D3—28no—
336C2×C4×D3—28no—
337C2×C4×D3—28no—
338C2×C4×D3—28no—
339C2×C4×D3—28no—
340C2×C4×D3—28no—
341C2×C4×D3—28no—
342C2×C4×D3—28no—
343C2×C4×D3—28no—
344C3×C4⋊C4—28no—
345C3×C42—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350C4⋊Dic3—44no—
351Dic3⋊C4—28no—
352Dic3⋊C4—44no—
353C4×Dic3—28no—
354C4×Dic3—28no—
355C4×Dic3—28no—
356C25—31no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—34no—
363C23×C4—34no—
364C23×C4—34no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—62no—
368C23×C4—62no—
369C23×C4—62no—
370C23×C4—62no—
371C23×C4—62no—
372C23×C4—62no—
373C23×C4—62no—
374C23×C4—62no—
375C23×C4—62no—
376C23×C4—62no—
377C23×C4—62no—
378C23×C4—62no—
379C23×C4—62no—
380C23×C4—62no—
381C23×C4—62no—
382C23×C4—62no—
383C23×C4—62no—
384C23×C4—62no—
385C23×C4C22×D311yescharacteristic
386C23×C4C22×D311yescharacteristic
387C23×C4C22×D311yescharacteristic
388C23×C4C22×D311yescharacteristic
389C23×C4C22×D311yescharacteristic
390C23×C4C22×D311yescharacteristic
391C23×C4C22×D311yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4C4×D314yescomplemented
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—34no—
420C2×C42—34no—
421C2×C42—632no—
422C2×C42—62no—
423C2×C42—62no—
424C2×C42—62no—
425C2×C42—62no—
426C2×C42—62no—
427C2×C42—62no—
428C2×C42—62no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—34no—
435#95—34no—
436#95—62no—
437#95—62no—
438#95—62no—
439#95—62no—
440#95—62no—
441#95—62no—
442#95—62no—
443#95—62no—
444#95—62no—
445#95—62no—
446#95—62no—
447#95—62no—
448#95—62no—
449C23×C3C23×C411yescharacteristic
450C23×C3C22×D411yescharacteristic
451C23×C3C22×D411yescharacteristic
452C23×C3C22×D411yescharacteristic
453C23×C3C22×Q811yescharacteristic
454C23×C3C2×#4111yescharacteristic
455C23×C3C2×#4111yescharacteristic
456C23×C3C2×#4111yescharacteristic
457C23×C3C2×#4111yescharacteristic
458C23×C3C2×#4111yescharacteristic
459C23×C3C2×#4111yescharacteristic
460C23×C3C2×#4111yescharacteristic
461C23×C3C2×#4111yescharacteristic
462C23×C3C2×#4111yescharacteristic
463C23×C3C2×#4111yescharacteristic
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3#11714yes—
493C22×D3C4×D414yes—
494C22×D3C4×Q814yes—
495C22×D3C22⋊Q814yes—
496C22×D3#12314yes—
497C22×D3#12514yes—
498C22×D3#12614yes—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4C4×D414yes—
546C2×C3×C4C22⋊Q814yes—
547C2×C3×C4#12314yes—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—41no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3C4×D414yes—
595C2×Dic3#12014yes—
596C2×Dic3C22⋊Q814yes—
597C4×D3—232no—
598C4×D3—232no—
599C4×D3—232no—
600C24—32no—
601C24—32no—
602C24—32no—
603C24—32no—
604C24—32no—
605C24—32no—
606C24—32no—
607C24—61no—
608C24—61no—
609C24—61no—
610C24—61no—
611C24—61no—
612C24—61no—
613C24—61no—
614C24—61no—
615C24C23×D311yescharacteristic
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—32no—
657C22×C4—32no—
658C22×C4—32no—
659C22×C4—32no—
660C22×C4—32no—
661C22×C4—32no—
662C22×C4—32no—
663C22×C4—32no—
664C22×C4—32no—
665C22×C4—68no—
666C22×C4—68no—
667C22×C4—68no—
668C22×C4—68no—
669C22×C4—68no—
670C22×C4—68no—
671C22×C4—68no—
672C22×C4—68no—
673C22×C4—68no—
674C22×C4—68no—
675C22×C4—68no—
676C22×C4—68no—
677C22×C4—68no—
678C22×C4—68no—
679C22×C4—68no—
680C22×C4—68no—
681C22×C4—68no—
682C22×C4—68no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—68no—
696C22×C4—68no—
697C22×C4—68no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4C2×C4×D312yes—
725C22×C4C2×C4×D312yes—
726C22×C4C2×C4×D312yes—
727C22×C4#23512yes—
728C22×C4#23512yes—
729C22×C4D3×D412yes—
730C22×C4D3×D412yes—
731C22×C4D3×D412yes—
732C22×C4#23712yes—
733C22×C4D3×Q812yes—
734C22×C4#23912yes—
735C4⋊C4—28no—
736C4⋊C4—68no—
737C4⋊C4—124no—
738C4⋊C4—124no—
739C22⋊C4—68no—
740C22⋊C4—68no—
741C22⋊C4—124no—
742C22⋊C4—124no—
743C42—28no—
744C42—68no—
745C42—68no—
746C42—68no—
747C22×C3C2×#11711yescharacteristic
748C22×C3C2×C4×D411yescharacteristic
749C22×C3C2×C4×D411yescharacteristic
750C22×C3C2×C4×D411yescharacteristic
751C22×C3C2×C4×Q811yescharacteristic
752C22×C3C4×#4111yescharacteristic
753C22×C3C4×#4111yescharacteristic
754C22×C3C2×#12011yescharacteristic
755C22×C3C2×C22⋊Q811yescharacteristic
756C22×C3C2×C22⋊Q811yescharacteristic
757C22×C3C2×C22⋊Q811yescharacteristic
758C22×C3C2×#12311yescharacteristic
759C22×C3C2×#12311yescharacteristic
760C22×C3#52511yescharacteristic
761C22×C3#52511yescharacteristic
762C22×C3#52511yescharacteristic
763C22×C3#52511yescharacteristic
764C22×C3#52511yescharacteristic
765C22×C3#52511yescharacteristic
766C22×C3#52511yescharacteristic
767C22×C3#52511yescharacteristic
768C22×C3#52511yescharacteristic
769C22×C3#52511yescharacteristic
770C22×C3C2×#12511yescharacteristic
771C22×C3C2×#12611yescharacteristic
772C22×C3#52911yescharacteristic
773C22×C3#52911yescharacteristic
774C22×C3#52911yescharacteristic
775C22×C3#52911yescharacteristic
776C22×C3#52911yescharacteristic
777C22×C3#52911yescharacteristic
778C22×C3#52911yescharacteristic
779C22×C3#52911yescharacteristic
780C22×C3#53311yescharacteristic
781C22×C3#53311yescharacteristic
782C2×D3—24no—
783C2×D3—24no—
784C2×D3—24no—
785C2×D3—24no—
786C2×D3—24no—
787C2×D3—24no—
788C2×D3—24no—
789C2×D3—24no—
790C2×D3—24no—
791C2×D3—24no—
792C2×D3—24no—
793C2×D3—24no—
794C2×D3—24no—
795C2×D3—24no—
796C2×D3#38718yescomplemented
797C3×C4—24no—
798C3×C4—24no—
799C3×C4—24no—
800C3×C4—42no—
801C3×C4—42no—
802C3×C4—81no—
803C3×C4—81no—
804Dic3—24no—
805Dic3—24no—
806Dic3—24no—
807Dic3—42no—
808Dic3—42no—
809Dic3—81no—
810Dic3—81no—
811C23—34no—
812C23—34no—
813C23—34no—
814C23—34no—
815C23—34no—
816C23—34no—
817C23—34no—
818C23—62no—
819C23—62no—
820C23—62no—
821C23—62no—
822C23—62no—
823C23—62no—
824C23—62no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23—62no—
829C23—62no—
830C23—62no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—62no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—62no—
840C23—62no—
841C23—62no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—62no—
846C23C22×C4×D311yescharacteristic
847C23C2×#23511yescharacteristic
848C23C2×#23511yescharacteristic
849C23C2×D3×D411yescharacteristic
850C23C2×D3×D411yescharacteristic
851C23C2×D3×D411yescharacteristic
852C23C2×#23711yescharacteristic
853C23C2×D3×Q811yescharacteristic
854C23C2×#23911yescharacteristic
855C23D3×#4111yescharacteristic
856C23D3×#4111yescharacteristic
857C23D3×#4111yescharacteristic
858C23D3×#4111yescharacteristic
859C23D3×#4111yescharacteristic
860C23D3×#4111yescharacteristic
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—34no—
886C2×C4—34no—
887C2×C4—34no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—632no—
911C2×C4—632no—
912C2×C4—632no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—62no—
916C2×C4—62no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—62no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—62no—
930C2×C4—62no—
931C2×C4—62no—
932C2×C4—62no—
933C2×C4—62no—
934C2×C4—62no—
935C2×C4—62no—
936C2×C4—62no—
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—121no—
946C2×C4—121no—
947C2×C4—121no—
948C2×C4—121no—
949C2×C4—121no—
950C2×C4—121no—
951C2×C4—121no—
952C2×C4—121no—
953C2×C4—121no—
954C2×C4—121no—
955C2×C4—121no—
956C2×C4—121no—
957C2×C4—121no—
958C2×C4—121no—
959C2×C4#67⋊C414yes—
960C2×C4#89414yes—
961C2×C4#89614yes—
962C2×C3C2×#38711yescharacteristic
963C2×C3#229011yescharacteristic
964C2×C3#229011yescharacteristic
965C2×C3C4×#12011yescharacteristic
966C2×C3C4×#12311yescharacteristic
967C2×C3C4×C22⋊Q811yescharacteristic
968C2×C3C4×C22⋊Q811yescharacteristic
969C2×C3#284811yescharacteristic
970C2×C3#284911yescharacteristic
971C2×C3#285111yescharacteristic
972C2×C3#285111yescharacteristic
973C2×C3#285211yescharacteristic
974C2×C3#285211yescharacteristic
975C2×C3#285311yescharacteristic
976C2×C3#285511yescharacteristic
977D3—28no—
978C22—38no—
979C22—64no—
980C22—64no—
981C22—64no—
982C22—64no—
983C22—64no—
984C22—64no—
985C22—64no—
986C22—64no—
987C22—64no—
988C22—64no—
989C22—64no—
990C22—64no—
991C22—64no—
992C22—64no—
993C22C4×#23511yescharacteristic
994C22C2×#67⋊C411yescharacteristic
995C22C2×#89411yescharacteristic
996C22C2×#89611yescharacteristic
997C22D3×#11711yescharacteristic
998C22#552811yescharacteristic
999C22#552811yescharacteristic
1000C22C4×D3×D411yescharacteristic
1001C22C4×D3×D411yescharacteristic
1002C22#554711yescharacteristic
1003C22#554711yescharacteristic
1004C22#554711yescharacteristic
1005C22#554711yescharacteristic
1006C22#555711yescharacteristic
1007C22#555711yescharacteristic
1008C22C4×D3×Q811yescharacteristic
1009C22C4×#23911yescharacteristic
1010C22#557811yescharacteristic
1011C22#558011yescharacteristic
1012C22D3×#12011yescharacteristic
1013C22#560611yescharacteristic
1014C22#560611yescharacteristic
1015C22D3×C22⋊Q811yescharacteristic
1016C22D3×C22⋊Q811yescharacteristic
1017C22#562711yescharacteristic
1018C22#562711yescharacteristic
1019C22D3×#12311yescharacteristic
1020C22#565611yescharacteristic
1021C22#565611yescharacteristic
1022C22#568011yescharacteristic
1023C22D3×#12511yescharacteristic
1024C22#569111yescharacteristic
1025C22D3×#12611yescharacteristic
1026C22#570611yescharacteristic
1027C22#572811yescharacteristic
1028C4—24no—
1029C4—24no—
1030C4—24no—
1031C4—42no—
1032C4—42no—
1033C4—64no—
1034C4—64no—
1035C4—64no—
1036C4—81no—
1037C4—81no—
1038C4—122no—
1039C4—122no—
1040C4—241no—
1041C4—241no—
1042C3#1469511yescharacteristic, complemented, Sylow
1043C2—68no—
1044C2#7356211yescharacteristic
1045C2C4×#89411yescharacteristic
1046C2C4×#89611yescharacteristic
1047C2#7465511yescharacteristic
1048C2#7465611yescharacteristic
1049C2#7465911yescharacteristic
1050C2#7493711yescharacteristic
1051C2D3×#38711yescharacteristic
1052C2#7544511yescharacteristic
1053C2#7544611yescharacteristic
1054C2#7595811yescharacteristic
1055C2#7595911yescharacteristic
1056C2#7628511yescharacteristic
1057C2#7628711yescharacteristic
1058C2#7647911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenter#1436D3
hypocenterC3#14695
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×#4980C2semidirect
5. C2×#4655C2semidirect
6. C3×#1436C2semidirect
7. #71536C2semidirect
12. #69406C2semidirect
13. #69405C2semidirect
14. #69403C2semidirect
15. #69401C2semidirect
55. #4989C4semidirect
67. #1436D3semidirect
112. C2×C3×C4⋊C4C2×C4semidirect
136. C2×Dic3⋊C4C2×C4semidirect
165. C3⋊#95C2×C4semidirect
166. C3⋊#95C2×C4semidirect
403. C2×C4⋊C4C4×D3semidirect
796. C2×D3#387semidirect
1042. C3#14695semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D32
C2×#49892
C2×#49802
C2×#46682
C2×#46552
C3×#14362
#715362
(C2×D3)⋊#952
#694062
#694052
#694032
#694012
#146953