Finite Group Databasebeta

← #10733617

Subgroups — #10733617

Order 768.

2458 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic
2C2×C3×#386C211yesmaximal, characteristic, complemented
3C2×#5222C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic, complemented
5C2×#4953C211yesmaximal, characteristic, complemented
6C2×#4961C211yesmaximal, characteristic, complemented
7#72127C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71544C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#69429C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14#69420C211yesmaximal, characteristic, complemented
15#69413C211yesmaximal, characteristic, complemented
16#15312—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C2×#939—24no—
31C2×#939—24no—
32C2×#939—24no—
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×C4⋊Dic3C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C3×#386—24no—
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44#5222—24no—
45#5213—24no—
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#4961—24no—
59#4953—24no—
60C22×#121—31no—
61C2×#397—31no—
62C2×#394—31no—
63C2×#394—31no—
64C2×#386—31no—
65C2×#386D311yescharacteristic, complemented
66#1444—31no—
67#1442—31no—
68#1440—31no—
69#1439—31no—
70#1438—31no—
71#1438—31no—
72C22⋊#95—31no—
73C22⋊#95—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—41no—
83C22×C3×D4—41no—
84C22×C3×D4D414yes—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—41no—
89C23×C3×C4—41no—
90C23×C3×C4—41no—
91C23×C3×C4—41no—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—22no—
102C22×#67—22no—
103C22×#67—22no—
104C22×#67—22no—
105C22×#67—22no—
106C22×#67—41no—
107C22×#67—41no—
108C22×#67—41no—
109C22×#67—41no—
110C22×#67D414yes—
111C23×Dic3—22no—
112C23×Dic3—22no—
113C23×Dic3—22no—
114C23×Dic3—22no—
115C23×Dic3—22no—
116C23×Dic3—41no—
117C23×Dic3—41no—
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—41no—
130C2×C3×C22⋊C4—41no—
131C2×C3×C22⋊C4—41no—
132C2×C3×C22⋊C4—41no—
133C2×C3×C22⋊C4D414yescomplemented
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—41no—
147C2×#217—41no—
148C2×#217D414yes—
149#939—232no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—41no—
160C2×(C2×D3)⋊C4—41no—
161C2×(C2×D3)⋊C4—41no—
162C2×(C2×D3)⋊C4—41no—
163C2×(C2×D3)⋊C4—41no—
164C2×(C2×D3)⋊C4—41no—
165C2×C4⋊Dic3—22no—
166C2×C4⋊Dic3—22no—
167C2×C4⋊Dic3—41no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—41no—
173C2×Dic3⋊C4—41no—
174C3×#95—22no—
175C3×#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—22no—
185C3⋊#95—41no—
186C3⋊#95—41no—
187C3⋊#95—41no—
188C23×D4—31no—
189C23×D4—31no—
190C23×D4C2×D311yescharacteristic
191C24×C4—31no—
192C24×C4C2×D311yescharacteristic
193C2×#121—64no—
194C2×#121—64no—
195C2×#121—64no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C22⋊C4C2×D311yescharacteristic
212#397—64no—
213#394—64no—
214#394—64no—
215#386—24no—
216#386—64no—
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×#95—31no—
228C2×#95—31no—
229C2×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
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×C3C2×D412yes—
256C24×C3C2×D412yes—
257C24×C3C2×D412yes—
258C24×C3C2×D412yes—
259C24×C3C2×D412yes—
260C24×C3#4112yes—
261C24×C3C2411yescharacteristic
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3C2×D412yes—
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—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
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—44no—
316C22×C3×C4—44no—
317C22×C3×C4—44no—
318C22×C3×C4—44no—
319C22×C3×C4—44no—
320C22×C3×C4—44no—
321C22×C3×C4—44no—
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2×D412yes—
325C22×C3×C4#4112yes—
326C2×#67—28no—
327C2×#67—28no—
328C2×#67—28no—
329C2×#67—44no—
330C2×#67—44no—
331C2×#67—44no—
332C2×#67—44no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—44no—
336C2×#67—44no—
337C2×#67—44no—
338C2×#67—44no—
339C2×#67—44no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—28no—
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—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3—44no—
385C22×Dic3—44no—
386C22×Dic3—44no—
387C22×Dic3—44no—
388C22×Dic3—44no—
389C22×Dic3—44no—
390C22×Dic3C2×D412yes—
391C22×Dic3C2×D412yes—
392C22×Dic3C2×D412yes—
393C22×Dic3#4112yes—
394C22×Dic3#4112yes—
395C22×Dic3#4112yes—
396C3×C22⋊C4—44no—
397C3×C22⋊C4—44no—
398C3×C22⋊C4—44no—
399#217—28no—
400#217—44no—
401#217—44no—
402#217—44no—
403#217—44no—
404(C2×D3)⋊C4—28no—
405(C2×D3)⋊C4—44no—
406(C2×D3)⋊C4—44no—
407(C2×D3)⋊C4—44no—
408(C2×D3)⋊C4—44no—
409C4⋊Dic3—44no—
410Dic3⋊C4—28no—
411Dic3⋊C4—44no—
412C25—31no—
413C25C22×D311yescharacteristic
414C25C22×D311yescharacteristic
415C22×D4—22no—
416C22×D4—22no—
417C22×D4—22no—
418C22×D4—22no—
419C22×D4—34no—
420C22×D4—41no—
421C22×D4—41no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—62no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—62no—
429C22×D4—62no—
430C22×D4—62no—
431C22×D4—121no—
432C22×D4—121no—
433C22×D4—121no—
434C22×D4—121no—
435C22×D4D1214yes—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—41no—
447C23×C4—41no—
448C23×C4—41no—
449C23×C4—41no—
450C23×C4—62no—
451C23×C4—62no—
452C23×C4—62no—
453C23×C4—62no—
454C23×C4—62no—
455C23×C4—121no—
456C23×C4—121no—
457C23×C4C22×D311yescharacteristic
458C23×C4C22×D311yescharacteristic
459C23×C4C22×D311yescharacteristic
460C23×C4C22×D311yescharacteristic
461C23×C4C22×D311yescharacteristic
462#121—632no—
463C2×C4⋊C4—62no—
464C2×C4⋊C4—62no—
465C2×C4⋊C4—62no—
466C2×C4⋊C4—62no—
467C2×C4⋊C4—62no—
468C2×C4⋊C4—62no—
469C2×C4⋊C4—121no—
470C2×C4⋊C4—121no—
471C2×C4⋊C4—121no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—34no—
477C2×C22⋊C4—41no—
478C2×C22⋊C4—41no—
479C2×C22⋊C4—41no—
480C2×C22⋊C4—41no—
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—62no—
488C2×C22⋊C4—62no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—62no—
491C2×C22⋊C4—62no—
492C2×C22⋊C4—62no—
493C2×C22⋊C4—62no—
494C2×C22⋊C4—62no—
495C2×C22⋊C4—62no—
496C2×C22⋊C4—62no—
497C2×C22⋊C4—62no—
498C2×C22⋊C4—62no—
499C2×C22⋊C4—62no—
500C2×C22⋊C4—62no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—121no—
503C2×C22⋊C4—121no—
504C2×C22⋊C4—121no—
505C2×C22⋊C4—121no—
506C2×C22⋊C4—121no—
507C2×C22⋊C4—121no—
508C2×C22⋊C4—121no—
509C2×C22⋊C4—121no—
510C2×C22⋊C4#6714yescomplemented
511#95—22no—
512#95—22no—
513#95—62no—
514#95—62no—
515#95—62no—
516#95—62no—
517#95—62no—
518#95—62no—
519#95—62no—
520#95—62no—
521#95—62no—
522#95—121no—
523#95—121no—
524#95—121no—
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—41no—
562C23×C3—41no—
563C23×C3—41no—
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#12014yes—
594C23×C3#12114yes—
595C23×C3C22×D411yescharacteristic
596C23×C3C22×D411yescharacteristic
597C23×C3C22×D411yescharacteristic
598C23×C3C22×D411yescharacteristic
599C23×C3C2×#4111yescharacteristic
600C23×C3C2×#4111yescharacteristic
601C23×C3C2×#4111yescharacteristic
602C23×C3C2×#4111yescharacteristic
603C23×C3C2×#4111yescharacteristic
604C23×C3H(5,𝔽2)11yescharacteristic
605C23×C3H(5,𝔽2)11yescharacteristic
606C23×C3H(5,𝔽2)11yescharacteristic
607C23×C3H(5,𝔽2)11yescharacteristic
608C23×C3H(5,𝔽2)11yescharacteristic
609C23×C32−1+411yescharacteristic
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—41no—
618C22×D3—41no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—41no—
622C22×D3—41no—
623C22×D3—41no—
624C22×D3—41no—
625C22×D3—41no—
626C22×D3—41no—
627C22×D3—41no—
628C22×D3—41no—
629C22×D3—41no—
630C22×D3—41no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3—41no—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
644C22×D3—41no—
645C3×D4—416no—
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—416no—
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×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682#67—416no—
683#67—416no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—416no—
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—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3#12314yes—
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—32no—
759C24—61no—
760C24—61no—
761C24—61no—
762C24—61no—
763C24—61no—
764C24—61no—
765C24—61no—
766C24—61no—
767C24—61no—
768C24—61no—
769C24—61no—
770C24—61no—
771C24—61no—
772C24—61no—
773C24C2×D1212yes—
774C24C2×D1212yes—
775C24#23512yes—
776C24D3×D412yes—
777C24D3×D412yes—
778C24C2×#6712yes—
779C24C23×D311yescharacteristic
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—68no—
788C2×D4—68no—
789C2×D4—68no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—124no—
793C2×D4—124no—
794C2×D4—124no—
795C2×D4—124no—
796C2×D4—124no—
797C2×D4—124no—
798C2×D4—124no—
799C2×D4—124no—
800C2×D4—124no—
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—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—32no—
833C22×C4—32no—
834C22×C4—32no—
835C22×C4—32no—
836C22×C4—32no—
837C22×C4—32no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—61no—
846C22×C4—61no—
847C22×C4—61no—
848C22×C4—61no—
849C22×C4—68no—
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—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—61no—
883C22×C4—61no—
884C22×C4—61no—
885C22×C4—61no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—61no—
889C22×C4—124no—
890C22×C4—124no—
891C22×C4—124no—
892C22×C4—124no—
893C22×C4—124no—
894C22×C4—124no—
895C22×C4C2×D1212yes—
896C22×C4#23712yes—
897C22×C4C2×#6712yes—
898C22×C4C2×#6712yes—
899C4⋊C4—68no—
900C4⋊C4—124no—
901C4⋊C4—124no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—68no—
906C22⋊C4—68no—
907C22⋊C4—124no—
908C22⋊C4—124no—
909C22⋊C4—124no—
910C22⋊C4—124no—
911C22⋊C4—124no—
912C22⋊C4—124no—
913C22⋊C4—124no—
914C22⋊C4—124no—
915C22×C3—24no—
916C22×C3—24no—
917C22×C3—24no—
918C22×C3—24no—
919C22×C3—24no—
920C22×C3—24no—
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×C3C2×#12011yescharacteristic
946C22×C3C2×#12111yescharacteristic
947C22×C3C2×#12311yescharacteristic
948C22×C3#52911yescharacteristic
949C22×C3#53211yescharacteristic
950C22×C3#53211yescharacteristic
951C22×C3#53411yescharacteristic
952C22×C3#53411yescharacteristic
953C22×C3#53411yescharacteristic
954C22×C3#53711yescharacteristic
955C22×C3#53811yescharacteristic
956C22×C3#53811yescharacteristic
957C22×C3#53911yescharacteristic
958C22×C3#54011yescharacteristic
959C22×C3#54211yescharacteristic
960C22×C3D4211yescharacteristic
961C22×C3D4211yescharacteristic
962C22×C3#54611yescharacteristic
963C22×C3#54611yescharacteristic
964C22×C3#54611yescharacteristic
965C22×C3#54611yescharacteristic
966C22×C3#54611yescharacteristic
967C22×C3#54611yescharacteristic
968C22×C3#54611yescharacteristic
969C22×C3#54611yescharacteristic
970C22×C3#54611yescharacteristic
971C22×C3#54711yescharacteristic
972C22×C3#54711yescharacteristic
973C22×C3#54711yescharacteristic
974C22×C3#55311yescharacteristic
975C22×C3#55311yescharacteristic
976C22×C3#55311yescharacteristic
977C22×C3#55511yescharacteristic
978C22×C3#56011yescharacteristic
979C22×C3#56211yescharacteristic
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—81no—
988C2×D3—81no—
989C2×D3—81no—
990C2×D3—81no—
991C2×D3—81no—
992C2×D3—81no—
993C2×D3—81no—
994C2×D3—81no—
995C3×C4—42no—
996C3×C4—42no—
997C3×C4—42no—
998C3×C4—42no—
999C3×C4—81no—
1000Dic3—24no—
1001Dic3—42no—
1002Dic3—42no—
1003Dic3—42no—
1004Dic3—81no—
1005Dic3—81no—
1006Dic3—81no—
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—41no—
1044C23—41no—
1045C23—41no—
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—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
1080C23—62no—
1081C23—62no—
1082C23—121no—
1083C23—121no—
1084C23—121no—
1085C23—121no—
1086C23—121no—
1087C23—121no—
1088C23—121no—
1089C23—121no—
1090C23—121no—
1091C23—121no—
1092C23—121no—
1093C23—121no—
1094C23—121no—
1095C23—121no—
1096C23—121no—
1097C23—121no—
1098C23—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23—121no—
1108C23—121no—
1109C23—121no—
1110C23#88214yes—
1111C23#93014yes—
1112C23C22×D1211yescharacteristic
1113C23C2×#23511yescharacteristic
1114C23C2×D3×D411yescharacteristic
1115C23C2×D3×D411yescharacteristic
1116C23C2×#23711yescharacteristic
1117C23#100411yescharacteristic
1118C23#100411yescharacteristic
1119C23#100411yescharacteristic
1120C23#100411yescharacteristic
1121C23#100411yescharacteristic
1122C23D3×#4111yescharacteristic
1123C23D3×#4111yescharacteristic
1124C23D3×#4111yescharacteristic
1125C23#101011yescharacteristic
1126C23C22×#6711yescharacteristic
1127D4—416no—
1128D4—1216no—
1129D4—1216no—
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—22no—
1142C2×C4—34no—
1143C2×C4—416no—
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—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—62no—
1174C2×C4—62no—
1175C2×C4—62no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—1216no—
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×C4—121no—
1212C2×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4—121no—
1216C2×C3—44no—
1217C2×C3—44no—
1218C2×C3#240511yescharacteristic
1219C2×C3#241011yescharacteristic
1220C2×C3#242011yescharacteristic
1221C2×C3#242211yescharacteristic
1222C2×C3#242511yescharacteristic
1223C2×C3#243011yescharacteristic
1224C2×C3#254311yescharacteristic
1225C2×C3#255511yescharacteristic
1226C2×C3#255911yescharacteristic
1227C2×C3#266811yescharacteristic
1228C2×C3#267111yescharacteristic
1229C2×C3#268611yescharacteristic
1230C2×C3#268811yescharacteristic
1231C2×C3#269111yescharacteristic
1232C2×C3#270811yescharacteristic
1233D3—82no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
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—122no—
1265C22—122no—
1266C22—122no—
1267C22—122no—
1268C22—122no—
1269C22—122no—
1270C22—122no—
1271C22—241no—
1272C22—241no—
1273C22—241no—
1274C22—241no—
1275C22—241no—
1276C22—241no—
1277C22—241no—
1278C22—241no—
1279C22C2×#88211yescharacteristic
1280C22#549011yescharacteristic
1281C22#549011yescharacteristic
1282C22#549311yescharacteristic
1283C22#553811yescharacteristic
1284C22#554011yescharacteristic
1285C22#554011yescharacteristic
1286C22#555411yescharacteristic
1287C22#555411yescharacteristic
1288C22#555411yescharacteristic
1289C22#555511yescharacteristic
1290C22#556411yescharacteristic
1291C22#558911yescharacteristic
1292C22#559111yescharacteristic
1293C22#559311yescharacteristic
1294C22#559511yescharacteristic
1295C22#559611yescharacteristic
1296C22#559711yescharacteristic
1297C22#561011yescharacteristic
1298C22#561011yescharacteristic
1299C22#561311yescharacteristic
1300C22#561511yescharacteristic
1301C22#561611yescharacteristic
1302C22#562111yescharacteristic
1303C22D3×#12311yescharacteristic
1304C22#565511yescharacteristic
1305C22#566111yescharacteristic
1306C22#566211yescharacteristic
1307C22C2×#93011yescharacteristic
1308C22D4×#6711yescharacteristic
1309C22D4×#6711yescharacteristic
1310C22#580411yescharacteristic
1311C22#580611yescharacteristic
1312C22#582411yescharacteristic
1313C22#583211yescharacteristic
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—64no—
1319C4—81no—
1320C4—122no—
1321C4—122no—
1322C4—122no—
1323C4—241no—
1324C4—241no—
1325C4—241no—
1326C3#1531211yescharacteristic, complemented, Sylow
1327C2—44no—
1328C2—44no—
1329C2—242no—
1330C2#7468611yescharacteristic
1331C2#7469511yescharacteristic
1332C2#7469911yescharacteristic
1333C2#7476011yescharacteristic
1334C2#7479611yescharacteristic
1335C2#7479911yescharacteristic
1336C2#7480011yescharacteristic
1337C2#7492611yescharacteristic
1338C2#8212711yescharacteristic
1339C2#8235511yescharacteristic
1340C2#8238011yescharacteristic
1341C2#8260811yescharacteristic
1342C2#8267211yescharacteristic
1343C2#8268111yescharacteristic
1344C2#8284511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC22×#939C2
hypercenterC2×#386D3
hypocenterC3#15312
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×C3×#386C2semidirect
3. C2×#5222C2semidirect
4. C2×#5213C2semidirect
5. C2×#4953C2semidirect
6. C2×#4961C2semidirect
7. #72127C2semidirect
8. #71550C2semidirect
9. #71550C2semidirect
10. #71544C2semidirect
11. #71544C2semidirect
12. #69429C2semidirect
13. #69428C2semidirect
14. #69420C2semidirect
15. #69413C2semidirect
65. C2×#386D3semidirect
133. C2×C3×C22⋊C4D4semidirect
510. C2×C22⋊C4#67semidirect
1326. C3#15312semidirect

Maximal subgroups

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

subgroupindex
C22×#9392
C2×C3×#3862
C2×#52222
C2×#52132
C2×#49532
C2×#49612
#721272
#715502
#715442
#694292
#694282
#694202
#694132
#153123