Finite Group Databasebeta

← #10728001

Subgroups — #10728001

Order 768.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4668C211yesmaximal, characteristic
2C2×#4667C211yesmaximal, characteristic
3C2×D3×#95C211yesmaximal, characteristic
4C2×#4660C211yesmaximal, characteristic, complemented
5C3×#1443C211yesmaximal, characteristic, complemented
6(C2×D3)⋊#95C211yesmaximal, characteristic
7(C2×D3)⋊#95C211yesmaximal, characteristic
8(C2×D3)⋊#95C211yesmaximal, characteristic
9(C2×D3)⋊#95C211yesmaximal, characteristic
10#69421C211yesmaximal, characteristic, complemented
11#69417C211yesmaximal, characteristic, complemented
12#69414C211yesmaximal, characteristic, complemented
13#69413C211yesmaximal, characteristic, complemented
14#69413C211yesmaximal, characteristic, complemented
15#69411C211yesmaximal, characteristic, complemented
16#14826—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
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
52#4668—24no—
53#4667—24no—
54D3×#95—24no—
55#4660—24no—
56C2×#400—31no—
57C2×#385—31no—
58C2×#380—31no—
59C22×#95—31no—
60#1445—31no—
61#1443—31no—
62#1443D311yescharacteristic, complemented
63#1442—31no—
64#1442—31no—
65#1442—31no—
66#1441—31no—
67C22⋊#95—31no—
68C22⋊#95—31no—
69C22⋊#95—31no—
70C22⋊#95—31no—
71C24×D3C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C22×C4×D3—22no—
87C22×C4×D3—22no—
88C22×C4×D3—22no—
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—41no—
101C22×C4×D3—41no—
102C22×C4×D3—41no—
103C22×C4×D3—41no—
104C22×C4×D3—41no—
105C22×C4×D3—41no—
106C22×C4×D3D414yes—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4Q814yes—
119C2×C4⋊Dic3—22no—
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3—22no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—41no—
128C2×Dic3⋊C4—41no—
129C2×Dic3⋊C4—41no—
130C2×Dic3⋊C4—41no—
131C3×#95—22no—
132C3×#95—22no—
133C3×#95—22no—
134C3×#95—22no—
135C3×#95—22no—
136C3×#95—41no—
137C3×#95—41no—
138C3⋊#95—22no—
139C3⋊#95—22no—
140C3⋊#95—22no—
141C3⋊#95—22no—
142C3⋊#95—22no—
143C3⋊#95—22no—
144C3⋊#95—22no—
145C3⋊#95—22no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—41no—
149C3⋊#95—41no—
150C3⋊#95—41no—
151C3⋊#95—41no—
152C3⋊#95—41no—
153C3⋊#95—41no—
154C3⋊#95D414yes—
155C24×C4—31no—
156C24×C4—31no—
157C24×C4—31no—
158C22×C4⋊C4—31no—
159C22×C4⋊C4—31no—
160C22×C4⋊C4—31no—
161C22×C4⋊C4—31no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—31no—
164C22×C22⋊C4—31no—
165C22×C22⋊C4—31no—
166#400—64no—
167#385—64no—
168#380—64no—
169C2×#95—31no—
170C2×#95—31no—
171C2×#95—31no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—64no—
187C2×#95C2×D311yescharacteristic
188C2×#95C2×D311yescharacteristic
189C2×#95C2×D311yescharacteristic
190C2×#95C2×D311yescharacteristic
191C2×#95C2×D311yescharacteristic
192C2×#95C2×D311yescharacteristic
193C2×#95C2×D311yescharacteristic
194C24×C3C2411yescharacteristic
195C23×D3—21no—
196C23×D3—21no—
197C23×D3—21no—
198C23×D3—21no—
199C23×D3—21no—
200C23×D3—21no—
201C23×D3—21no—
202C23×D3—21no—
203C23×D3C2×D412yes—
204C23×D3C2×Q812yes—
205C23×D3#4112yes—
206C23×D3#4112yes—
207C23×D3#4112yes—
208C23×D3#4112yes—
209C23×D3#4112yes—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
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×C4C2×D412yes—
256C22×C3×C4C2×D412yes—
257C22×C3×C4C2×Q812yes—
258C22×C3×C4#4112yes—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
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×Dic3C2×D412yes—
303C22×Dic3C2×D412yes—
304C22×Dic3C2×D412yes—
305C22×Dic3C2×Q812yes—
306C22×Dic3#4112yes—
307C22×Dic3#4112yes—
308C2×C4×D3—28no—
309C2×C4×D3—28no—
310C2×C4×D3—28no—
311C2×C4×D3—28no—
312C2×C4×D3—44no—
313C2×C4×D3—44no—
314C2×C4×D3—44no—
315C2×C4×D3—44no—
316C2×C4×D3—44no—
317C2×C4×D3—44no—
318C2×C4×D3—44no—
319C2×C4×D3—44no—
320C2×C4×D3—44no—
321C2×C4×D3—44no—
322C2×C4×D3—44no—
323C2×C4×D3—44no—
324C2×C4×D3—44no—
325C2×C4×D3—44no—
326C2×C4×D3—44no—
327C2×C4×D3—44no—
328C2×C4×D3—44no—
329(C2×D3)⋊C4—28no—
330(C2×D3)⋊C4—44no—
331(C2×D3)⋊C4—44no—
332(C2×D3)⋊C4—44no—
333C4⋊Dic3—44no—
334Dic3⋊C4—44no—
335Dic3⋊C4—44no—
336Dic3⋊C4—44no—
337C25—31no—
338C23×C4—31no—
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—34no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—62no—
347C23×C4—62no—
348C23×C4—62no—
349C23×C4—62no—
350C23×C4—62no—
351C23×C4—62no—
352C23×C4—62no—
353C23×C4—62no—
354C23×C4—62no—
355C23×C4—62no—
356C23×C4—62no—
357C23×C4—62no—
358C23×C4—62no—
359C23×C4—62no—
360C23×C4—121no—
361C23×C4—121no—
362C23×C4—121no—
363C23×C4—121no—
364C23×C4—121no—
365C23×C4—121no—
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C23×C4C22×D311yescharacteristic
372C23×C4C22×D311yescharacteristic
373C2×C4⋊C4—62no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—62no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4—62no—
380C2×C4⋊C4—62no—
381C2×C4⋊C4—121no—
382C2×C4⋊C4—121no—
383C2×C4⋊C4—121no—
384C2×C4⋊C4—121no—
385C2×C22⋊C4—34no—
386C2×C22⋊C4—62no—
387C2×C22⋊C4—62no—
388C2×C22⋊C4—62no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—62no—
391C2×C22⋊C4—62no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4—62no—
394C2×C22⋊C4—62no—
395C2×C22⋊C4—62no—
396C2×C22⋊C4—62no—
397#95—22no—
398#95—22no—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—34no—
403#95—41no—
404#95—41no—
405#95—62no—
406#95—62no—
407#95—62no—
408#95—62no—
409#95—62no—
410#95—62no—
411#95—62no—
412#95—62no—
413#95—62no—
414#95—62no—
415#95—121no—
416#95—121no—
417#95—121no—
418#95—121no—
419#95—121no—
420#95—121no—
421C23×C3C22×D411yescharacteristic
422C23×C3C22×D411yescharacteristic
423C23×C3C22×Q811yescharacteristic
424C23×C3C2×#4111yescharacteristic
425C23×C3C2×#4111yescharacteristic
426C23×C3C2×#4111yescharacteristic
427C23×C3C2×#4111yescharacteristic
428C23×C3C2×#4111yescharacteristic
429C23×C3C2×#4111yescharacteristic
430C23×C3C2×#4111yescharacteristic
431C23×C3C2×#4111yescharacteristic
432C23×C3H(5,𝔽2)11yescharacteristic
433C23×C3H(5,𝔽2)11yescharacteristic
434C23×C3H(5,𝔽2)11yescharacteristic
435C23×C32−1+411yescharacteristic
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3C22⋊Q814yes—
465C22×D3#12314yes—
466C22×D3#12414yes—
467C22×D3#12514yes—
468C22×D3#12514yes—
469C22×D3#12614yes—
470C22×D3#12614yes—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—41no—
566C2×Dic3—41no—
567C2×Dic3—41no—
568C2×Dic3#12114yes—
569C4×D3—416no—
570C4×D3—416no—
571C4×D3—416no—
572C24—32no—
573C24—32no—
574C24—32no—
575C24—32no—
576C24—32no—
577C24—32no—
578C24—32no—
579C24—61no—
580C24—61no—
581C24—61no—
582C24—61no—
583C24—61no—
584C24—61no—
585C24—61no—
586C24—61no—
587C24C23×D311yescharacteristic
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
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—32no—
634C22×C4—32no—
635C22×C4—32no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—32no—
639C22×C4—68no—
640C22×C4—68no—
641C22×C4—68no—
642C22×C4—68no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—124no—
687C22×C4—124no—
688C22×C4—124no—
689C22×C4—124no—
690C22×C4—124no—
691C22×C4—124no—
692C22×C4—124no—
693C22×C4—124no—
694C22×C4—124no—
695C22×C4—124no—
696C22×C4—124no—
697C22×C4—124no—
698C22×C4—124no—
699C22×C4—124no—
700C22×C4—124no—
701C22×C4—124no—
702C22×C4—124no—
703C22×C4#23512yes—
704C22×C4D3×D412yes—
705C22×C4D3×D412yes—
706C22×C4D3×Q812yes—
707C4⋊C4—124no—
708C4⋊C4—124no—
709C4⋊C4—124no—
710C4⋊C4—124no—
711C22⋊C4—68no—
712C22⋊C4—124no—
713C22⋊C4—124no—
714C22⋊C4—124no—
715C22×C3C2×#12111yescharacteristic
716C22×C3C2×C22⋊Q811yescharacteristic
717C22×C3C2×#12311yescharacteristic
718C22×C3#52511yescharacteristic
719C22×C3#52511yescharacteristic
720C22×C3C2×#12411yescharacteristic
721C22×C3C2×#12511yescharacteristic
722C22×C3C2×#12511yescharacteristic
723C22×C3C2×#12611yescharacteristic
724C22×C3C2×#12611yescharacteristic
725C22×C3#52911yescharacteristic
726C22×C3#52911yescharacteristic
727C22×C3#53211yescharacteristic
728C22×C3#53411yescharacteristic
729C22×C3#53711yescharacteristic
730C22×C3#53811yescharacteristic
731C22×C3#53811yescharacteristic
732C22×C3#53911yescharacteristic
733C22×C3#53911yescharacteristic
734C22×C3#54611yescharacteristic
735C22×C3#54611yescharacteristic
736C22×C3#54611yescharacteristic
737C22×C3D4×Q811yescharacteristic
738C22×C3#55111yescharacteristic
739C22×C3#55111yescharacteristic
740C22×C3#55111yescharacteristic
741C22×C3#55111yescharacteristic
742C22×C3#55111yescharacteristic
743C22×C3#55111yescharacteristic
744C22×C3#55211yescharacteristic
745C22×C3#55211yescharacteristic
746C22×C3#55211yescharacteristic
747C22×C3#55411yescharacteristic
748C22×C3#55411yescharacteristic
749C22×C3#55411yescharacteristic
750C2×D3—24no—
751C2×D3—24no—
752C2×D3—24no—
753C2×D3—24no—
754C2×D3—24no—
755C2×D3—24no—
756C2×D3—24no—
757C2×D3—24no—
758C2×D3—24no—
759C2×D3—24no—
760C2×D3—24no—
761C2×D3—24no—
762C2×D3—24no—
763C2×D3—24no—
764C2×D3#40018yescomplemented
765C3×C4—42no—
766C3×C4—42no—
767C3×C4—42no—
768C3×C4—42no—
769C3×C4—81no—
770C3×C4—81no—
771C3×C4—81no—
772Dic3—24no—
773Dic3—42no—
774Dic3—42no—
775Dic3—42no—
776Dic3—81no—
777Dic3—81no—
778Dic3—81no—
779C23—34no—
780C23—34no—
781C23—34no—
782C23—34no—
783C23—34no—
784C23—34no—
785C23—34no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23—62no—
809C23—62no—
810C23—62no—
811C23—62no—
812C23—62no—
813C23—62no—
814C23C2×#23511yescharacteristic
815C23C2×D3×D411yescharacteristic
816C23C2×D3×D411yescharacteristic
817C23#100411yescharacteristic
818C23C2×D3×Q811yescharacteristic
819C23D3×#4111yescharacteristic
820C23D3×#4111yescharacteristic
821C23D3×#4111yescharacteristic
822C23D3×#4111yescharacteristic
823C23D3×#4111yescharacteristic
824C23D3×#4111yescharacteristic
825C23D3×#4111yescharacteristic
826C23#100911yescharacteristic
827C23#100911yescharacteristic
828C23#101011yescharacteristic
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—34no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—1216no—
895C2×C4—1216no—
896C2×C4—1216no—
897C2×C4—121no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4—121no—
901C2×C4—121no—
902C2×C4—121no—
903C2×C4—121no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—121no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C4—121no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—121no—
930C2×C3C2×#40011yescharacteristic
931C2×C3#241211yescharacteristic
932C2×C3#241711yescharacteristic
933C2×C3#247311yescharacteristic
934C2×C3#247311yescharacteristic
935C2×C3#248011yescharacteristic
936C2×C3#248011yescharacteristic
937C2×C3#249311yescharacteristic
938C2×C3#249311yescharacteristic
939C2×C3#249811yescharacteristic
940C2×C3#250511yescharacteristic
941C2×C3#250511yescharacteristic
942C2×C3#256411yescharacteristic
943C2×C3#263911yescharacteristic
944C2×C3#285011yescharacteristic
945D3—28no—
946C22—38no—
947C22—64no—
948C22—64no—
949C22—64no—
950C22—64no—
951C22—64no—
952C22—64no—
953C22—64no—
954C22—64no—
955C22—64no—
956C22—64no—
957C22—64no—
958C22—64no—
959C22—64no—
960C22—64no—
961C22#552711yescharacteristic
962C22#552811yescharacteristic
963C22#552911yescharacteristic
964C22#554711yescharacteristic
965C22#554811yescharacteristic
966C22#555611yescharacteristic
967C22#557911yescharacteristic
968C22D3×#12111yescharacteristic
969C22#560811yescharacteristic
970C22#561011yescharacteristic
971C22D3×C22⋊Q811yescharacteristic
972C22#563211yescharacteristic
973C22#563611yescharacteristic
974C22D3×#12311yescharacteristic
975C22#565311yescharacteristic
976C22#565411yescharacteristic
977C22#565611yescharacteristic
978C22#565711yescharacteristic
979C22#565711yescharacteristic
980C22D3×#12411yescharacteristic
981C22#567611yescharacteristic
982C22#567911yescharacteristic
983C22D3×#12511yescharacteristic
984C22D3×#12511yescharacteristic
985C22#569011yescharacteristic
986C22D3×#12611yescharacteristic
987C22D3×#12611yescharacteristic
988C22#570511yescharacteristic
989C22#570511yescharacteristic
990C22#570511yescharacteristic
991C22#570611yescharacteristic
992C22#570711yescharacteristic
993C22#570711yescharacteristic
994C22#570811yescharacteristic
995C22#570811yescharacteristic
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—64no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—122no—
1005C4—122no—
1006C4—122no—
1007C4—241no—
1008C4—241no—
1009C4—241no—
1010C3#1482611yescharacteristic, complemented, Sylow
1011C2—68no—
1012C2#7430011yescharacteristic
1013C2#7500811yescharacteristic
1014C2#7534111yescharacteristic
1015C2#7536011yescharacteristic
1016C2#7554111yescharacteristic
1017C2#7586911yescharacteristic
1018C2#7595711yescharacteristic
1019C2#7728511yescharacteristic
1020C2#7748011yescharacteristic
1021C2#7766811yescharacteristic
1022C2#7768711yescharacteristic
1023C2#7814111yescharacteristic
1024C2D3×#40011yescharacteristic
1025C2#7835311yescharacteristic
1026C2#7843011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1443C2
prime radicalC24×D3C23
hypercenter#1443D3
hypocenterC3#14826
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
4. C2×#4660C2semidirect
5. C3×#1443C2semidirect
10. #69421C2semidirect
11. #69417C2semidirect
12. #69414C2semidirect
13. #69413C2semidirect
14. #69413C2semidirect
15. #69411C2semidirect
62. #1443D3semidirect
764. C2×D3#400semidirect
1010. C3#14826semidirect

Maximal subgroups

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

subgroupindex
C2×#46682
C2×#46672
C2×D3×#952
C2×#46602
C3×#14432
(C2×D3)⋊#952
#694212
#694172
#694142
#694132
#694112
#148263