Finite Group Databasebeta

← #11773311

Subgroups — #11773311

Order 1152.

1725 conjugacy classes of subgroups.

The subgroup lattice has 753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C22×(C2×D3)⋊Dic3C212yesmaximal
4C2×#63658C211yesmaximal, characteristic, complemented
5C2×#63579C212yesmaximal, complemented
6#71570—31nomaximal
7#71546—31nomaximal
8C24×C3×D3C2211yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2212yes—
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C2×C3×(C2×D3)⋊C4—22no—
14C2×C3×(C2×D3)⋊C4—22no—
15C2×C3×(C2×D3)⋊C4C414yescomplemented
16C2×C3×C4⋊Dic3—22no—
17C2×C3×C4⋊Dic3—24no—
18C2×(C2×D3)⋊Dic3—24no—
19C2×(C2×D3)⋊Dic3—24no—
20C2×(C2×D3)⋊Dic3—24no—
21#63658—22no—
22#63579—24no—
23C22×C3×C4⋊C4—31no—
24C22×C3×C22⋊C4—31no—
25C22×#217—32no—
26C22×(C2×D3)⋊C4—32no—
27C22×(C2×D3)⋊C4D311yescharacteristic
28C22×C4⋊Dic3D311yescharacteristic, complemented
29C2×C3⋊#95—31no—
30C2×C3⋊#95—31no—
31C2×C3⋊#95—32no—
32C2×C3⋊#95—32no—
33C2×C3⋊#95—61no—
34C24×C32C2311yescharacteristic
35C23×C3×D3—21no—
36C23×C3×D3—21no—
37C23×C3×D3—22no—
38C23×C3×D3—22no—
39C23×C3×D3—21no—
40C23×C3×D3—21no—
41C23×C3×D3—22no—
42C23×C3×D3—22no—
43C23×C3×D3C2×C412yes—
44C23×C3×D3D412yes—
45C23×C3×D3Q812yes—
46C22×C32×C4—22no—
47C22×C32×C4—22no—
48C22×C32×C4C2×C412yes—
49C22×C32×C4D412yes—
50C22×C32×C4D412yes—
51C22×C3⋊Dic3—22no—
52C22×C3⋊Dic3—22no—
53C22×C3⋊Dic3—22no—
54C22×C3⋊Dic3—22no—
55C22×C3⋊Dic3—22no—
56C22×C3⋊Dic3—22no—
57C22×C3⋊Dic3D414yes—
58C22×C3×Dic3—22no—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3—22no—
64C22×C3×Dic3—22no—
65C22×C3×Dic3—22no—
66C22×C3×Dic3—22no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3C2×C412yes—
69C22×C3×Dic3D414yes—
70C3×(C2×D3)⋊C4—28no—
71C3×C4⋊Dic3—28no—
72(C2×D3)⋊Dic3—216no—
73#1439—91noSylow
74C25×C3—31no—
75C24×D3C2×D311yescharacteristic
76C23×C3×C4—21no—
77C23×C3×C4—31no—
78C23×C3×C4—32no—
79C23×C3×C4C2×D311yescharacteristic
80C23×C3×C4C2×D311yescharacteristic
81C23×Dic3—32no—
82C23×Dic3—32no—
83C23×Dic3—62no—
84C23×Dic3C2×D311yescharacteristic
85C23×Dic3C2×D312yes—
86C2×C3×C4⋊C4—64no—
87C2×C3×C4⋊C4—62no—
88C2×C3×C22⋊C4—34no—
89C2×C3×C22⋊C4—62no—
90C2×C3×C22⋊C4—62no—
91C2×#217—64no—
92C2×#217—64no—
93C2×#217—64no—
94C2×(C2×D3)⋊C4—22no—
95C2×(C2×D3)⋊C4—22no—
96C2×(C2×D3)⋊C4—64no—
97C2×(C2×D3)⋊C4—64no—
98C2×(C2×D3)⋊C4—64no—
99C2×(C2×D3)⋊C4Dic314yescomplemented
100C2×C4⋊Dic3—22no—
101C2×C4⋊Dic3—24no—
102C3⋊#95—64no—
103C3⋊#95—64no—
104C3⋊#95—64no—
105C3⋊#95—62no—
106C3⋊#95—62no—
107C23×C32C22×C411yescharacteristic
108C23×C32C2×D411yescharacteristic
109C23×C32C2×D411yescharacteristic
110C23×C32C2×D412yes—
111C23×C32C2×D412yes—
112C23×C32C2×D411yescharacteristic
113C23×C32C2×Q811yescharacteristic
114C23×C32#4111yescharacteristic
115C23×C32#4112yes—
116C23×C32#4111yescharacteristic
117C23×C32#4112yes—
118C22×C3×D3—22no—
119C22×C3×D3—22no—
120C22×C3×D3—24no—
121C22×C3×D3—24no—
122C22×C3×D3—24no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—24no—
126C22×C3×D3—24no—
127C22×C3×D3—22no—
128C22×C3×D3—22no—
129C22×C3×D3—24no—
130C22×C3×D3—41no—
131C22×C3×D3—42no—
132C22×C3×D3—42no—
133C22×C3×D3—42no—
134C22×C3×D3—42no—
135C22×C3×D3—41no—
136C22×C3×D3—42no—
137C22×C3×D3—41no—
138C22×C3×D3—42no—
139C22×C3×D3—41no—
140C22×C3×D3C4⋊C414yescomplemented
141C2×C32×C4—24no—
142C2×C32×C4—22no—
143C2×C32×C4—24no—
144C2×C32×C4—22no—
145C2×C32×C4C22⋊C414yescomplemented
146C2×C3⋊Dic3—24no—
147C2×C3⋊Dic3—24no—
148C2×C3⋊Dic3—24no—
149C2×C3⋊Dic3—42no—
150C2×C3⋊Dic3—42no—
151C2×C3⋊Dic3—42no—
152C2×C3⋊Dic3—42no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—24no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—24no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3—42no—
160C2×C3×Dic3—42no—
161C2×C3×Dic3—42no—
162C2×C3×Dic3—41no—
163C2×C3×Dic3—41no—
164C2×C3×Dic3—42no—
165C22×C4⋊C4—31no—
166C22×C22⋊C4—31no—
167C22×C22⋊C4—92no—
168C2×#95—92no—
169C2×#95—91no—
170C24×C3—21no—
171C24×C3—32no—
172C24×C3—32no—
173C24×C3—32no—
174C24×C3—61no—
175C24×C3—62no—
176C24×C3—62no—
177C24×C3—61no—
178C24×C3—62no—
179C24×C3—61no—
180C24×C3—62no—
181C24×C3—61no—
182C24×C3C22×D311yescharacteristic
183C24×C3C22×D311yescharacteristic
184C23×D3—21no—
185C23×D3—21no—
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—22no—
189C23×D3—22no—
190C23×D3—21no—
191C23×D3—21no—
192C23×D3Dic612yes—
193C23×D3D1212yes—
194C23×D3C2×Dic312yes—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—32no—
203C22×C3×C4—34no—
204C22×C3×C4—42no—
205C22×C3×C4—42no—
206C22×C3×C4—62no—
207C22×C3×C4—61no—
208C22×C3×C4—62no—
209C22×C3×C4—62no—
210C22×C3×C4—62no—
211C22×C3×C4—62no—
212C22×C3×C4—62no—
213C22×C3×C4—62no—
214C22×C3×C4—61no—
215C22×C3×C4—62no—
216C22×C3×C4C4×D312yes—
217C22×C3×C4D1212yes—
218C22×C3×C4C2×Dic312yes—
219C22×C3×C4#6712yes—
220C22×C3×C4#6712yes—
221C22×C3×C4#6712yes—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—34no—
233C22×Dic3—34no—
234C22×Dic3—64no—
235C22×Dic3—64no—
236C22×Dic3—64no—
237C22×Dic3—62no—
238C22×Dic3—62no—
239C22×Dic3—62no—
240C22×Dic3—62no—
241C22×Dic3—62no—
242C22×Dic3—62no—
243C22×Dic3—62no—
244C22×Dic3—62no—
245C22×Dic3—62no—
246C22×Dic3—62no—
247C22×Dic3—62no—
248C22×Dic3—62no—
249C22×Dic3—122no—
250C22×Dic3—122no—
251C22×Dic3—122no—
252C22×Dic3—122no—
253C22×Dic3C2×Dic312yes—
254C22×Dic3#6714yes—
255C3×C4⋊C4—68no—
256C3×C22⋊C4—68no—
257#217—616no—
258(C2×D3)⋊C4—28no—
259(C2×D3)⋊C4—616no—
260C4⋊Dic3—28no—
261C22×C32C2×C22⋊C411yescharacteristic
262C22×C32C2×C4⋊C411yescharacteristic
263C22×C32#11711yescharacteristic
264C22×C32C4×D412yes—
265C22×C32C4×D412yes—
266C22×C32#12012yes—
267C22×C32#12011yescharacteristic
268C22×C32#12112yes—
269C22×C32#12111yescharacteristic
270C22×C32#12112yes—
271C22×C32#12111yescharacteristic
272C22×C32#12112yes—
273C22×C32C22⋊Q812yes—
274C22×C32C22⋊Q812yes—
275C22×C32C22⋊Q811yescharacteristic
276C22×C32C22⋊Q811yescharacteristic
277C22×C32#12312yes—
278C22×C32#12312yes—
279C22×C32#12311yescharacteristic
280C22×C32#12412yes—
281C22×C32#12411yescharacteristic
282C22×C32#12612yes—
283C22×C32#12711yescharacteristic
284C2×C3×D3—24no—
285C2×C3×D3—28no—
286C2×C3×D3—42no—
287C2×C3×D3—44no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—44no—
292C2×C3×D3—44no—
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C32×C4—24no—
296C3⋊Dic3—44no—
297C3×Dic3—42no—
298C3×Dic3—44no—
299C25—31no—
300C23×C4—31no—
301C23×C4—32no—
302C23×C4—92no—
303C23×C4D3211yescharacteristic
304C2×C4⋊C4—64no—
305C2×C4⋊C4—62no—
306C2×C22⋊C4—34no—
307C2×C22⋊C4—62no—
308C2×C22⋊C4—62no—
309C2×C22⋊C4—184no—
310C2×C22⋊C4—184no—
311C2×C22⋊C4—184no—
312#95—184no—
313#95—182no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—22no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—22no—
320C23×C3—21no—
321C23×C3—22no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—22no—
325C23×C3—34no—
326C23×C3—62no—
327C23×C3—64no—
328C23×C3—64no—
329C23×C3—62no—
330C23×C3—64no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—64no—
334C23×C3—64no—
335C23×C3—62no—
336C23×C3—62no—
337C23×C3—64no—
338C23×C3—122no—
339C23×C3—122no—
340C23×C3—122no—
341C23×C3—121no—
342C23×C3—122no—
343C23×C3—122no—
344C23×C3—121no—
345C23×C3—121no—
346C23×C3—122no—
347C23×C3—121no—
348C23×C3C2×Dic611yescharacteristic
349C23×C3C2×C4×D311yescharacteristic
350C23×C3C2×D1211yescharacteristic
351C23×C3C2×D1211yescharacteristic
352C23×C3#23511yescharacteristic
353C23×C3#23511yescharacteristic
354C23×C3#23512yes—
355C23×C3D3×D411yescharacteristic
356C23×C3D3×D412yes—
357C23×C3D3×D412yes—
358C23×C3D3×D412yes—
359C23×C3#23711yescharacteristic
360C23×C3#23712yes—
361C23×C3#23712yes—
362C23×C3D3×Q811yescharacteristic
363C23×C3#23912yes—
364C23×C3#23911yescharacteristic
365C23×C3C22×Dic311yescharacteristic
366C23×C3C2×#6711yescharacteristic
367C23×C3C2×#6711yescharacteristic
368C23×C3C2×#6711yescharacteristic
369C23×C3C2×#6712yes—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—24no—
373C22×D3—24no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—22no—
378C22×D3—22no—
379C22×D3—24no—
380C22×D3—24no—
381C22×D3—22no—
382C22×D3—42no—
383C22×D3—42no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—41no—
387C22×D3—41no—
388C22×D3—41no—
389C22×D3—42no—
390C22×D3—42no—
391C22×D3—41no—
392C22×D3C4⋊Dic314yescomplemented
393C2×C3×C4—24no—
394C2×C3×C4—22no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—22no—
401C2×C3×C4—24no—
402C2×C3×C4—42no—
403C2×C3×C4—44no—
404C2×C3×C4—42no—
405C2×C3×C4—44no—
406C2×C3×C4—64no—
407C2×C3×C4—64no—
408C2×C3×C4—64no—
409C2×C3×C4—62no—
410C2×C3×C4—64no—
411C2×C3×C4—122no—
412C2×C3×C4—122no—
413C2×C3×C4—122no—
414C2×C3×C4—122no—
415C2×C3×C4—122no—
416C2×C3×C4—121no—
417C2×C3×C4—121no—
418C2×C3×C4(C2×D3)⋊C414yescomplemented
419C2×C3×C4#21714yescomplemented
420C2×Dic3—24no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—22no—
424C2×Dic3—24no—
425C2×Dic3—41no—
426C2×Dic3—42no—
427C2×Dic3—42no—
428C2×Dic3—42no—
429C2×Dic3—42no—
430C2×Dic3—41no—
431C2×Dic3—42no—
432C2×Dic3—68no—
433C2×Dic3—64no—
434C2×Dic3—64no—
435C2×Dic3—64no—
436C2×Dic3—64no—
437C2×Dic3—64no—
438C2×Dic3—64no—
439C2×Dic3—124no—
440C2×Dic3—124no—
441C2×Dic3—124no—
442C2×Dic3—124no—
443C2×Dic3—124no—
444C2×Dic3—124no—
445C2×Dic3—122no—
446C2×Dic3—122no—
447C2×Dic3—122no—
448C2×Dic3—122no—
449C2×Dic3—122no—
450C2×Dic3—122no—
451C2×Dic3—122no—
452C2×Dic3—122no—
453C2×C32#38011yescharacteristic
454C2×C32#38512yes—
455C2×C32#38611yescharacteristic
456C2×C32#38812yes—
457C2×C32#39011yescharacteristic
458C2×C32#39211yescharacteristic
459C2×C32#39311yescharacteristic
460C2×C32#39412yes—
461C2×C32#39612yes—
462C2×C32#39711yescharacteristic
463C2×C32#39911yescharacteristic
464C3×D3—44no—
465C24—32no—
466C24—32no—
467C24—32no—
468C24—61no—
469C24—62no—
470C24—61no—
471C24—62no—
472C24—62no—
473C24—61no—
474C24—61no—
475C24—62no—
476C24C2×D3211yescharacteristic
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—32no—
480C22×C4—34no—
481C22×C4—62no—
482C22×C4—62no—
483C22×C4—62no—
484C22×C4—62no—
485C22×C4—62no—
486C22×C4—62no—
487C22×C4—61no—
488C22×C4—62no—
489C22×C4—61no—
490C22×C4—62no—
491C22×C4—94no—
492C22×C4—182no—
493C22×C4—182no—
494C22×C4—182no—
495C22×C4—182no—
496C22×C4—182no—
497C22×C4—182no—
498C22×C4D3×Dic312yes—
499C22×C4#62512yes—
500C22×C4#62612yes—
501C4⋊C4—68no—
502C22⋊C4—68no—
503C22⋊C4—1816no—
504C22×C3—21no—
505C22×C3—22no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—22no—
509C22×C3—21no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—22no—
525C22×C3—21no—
526C22×C3—22no—
527C22×C3—64no—
528C22×C3—68no—
529C22×C3—122no—
530C22×C3—122no—
531C22×C3—122no—
532C22×C3—122no—
533C22×C3—124no—
534C22×C3—124no—
535C22×C3—122no—
536C22×C3—122no—
537C22×C3—124no—
538C22×C3#87812yes—
539C22×C3#87812yes—
540C22×C3#87912yes—
541C22×C3#88212yes—
542C22×C3#88312yes—
543C22×C3#88412yes—
544C22×C3#88512yes—
545C22×C3#88612yes—
546C22×C3D3×C4⋊C411yescharacteristic
547C22×C3#89211yescharacteristic
548C22×C3#89312yes—
549C22×C3#89412yes—
550C22×C3#89412yes—
551C22×C3#89511yescharacteristic
552C22×C3#89512yes—
553C22×C3#89612yes—
554C22×C3#89711yescharacteristic
555C22×C3#89812yes—
556C22×C3#92411yescharacteristic
557C22×C3#92411yescharacteristic
558C22×C3C2×C4⋊Dic311yescharacteristic
559C22×C3#92611yescharacteristic
560C22×C3C2×(C2×D3)⋊C411yescharacteristic
561C22×C3C4×#6712yes—
562C22×C3#92911yescharacteristic
563C22×C3#93011yescharacteristic
564C22×C3#93011yescharacteristic
565C22×C3#93012yes—
566C22×C3D4×Dic312yes—
567C22×C3D4×Dic312yes—
568C22×C3#93511yescharacteristic
569C22×C3#93611yescharacteristic
570C22×C3#93712yes—
571C22×C3#93711yescharacteristic
572C22×C3#93811yescharacteristic
573C22×C3#93812yes—
574C22×C3#93912yes—
575C22×C3#93912yes—
576C22×C3#94011yescharacteristic
577C22×C3#94011yescharacteristic
578C22×C3#94611yescharacteristic
579C22×C3#94612yes—
580C22×C3#94711yescharacteristic
581C22×C3#94712yes—
582C22×C3C2×#21711yescharacteristic
583C22×C3#95311yescharacteristic
584C2×D3—28no—
585C2×D3—24no—
586C2×D3—42no—
587C2×D3—44no—
588C2×D3—42no—
589C2×D3—44no—
590C2×D3—42no—
591C2×D3—42no—
592C2×D3—44no—
593C2×D3—42no—
594C2×D3—42no—
595C3×C4—24no—
596C3×C4—24no—
597C3×C4—44no—
598C3×C4—124no—
599C3×C4—122no—
600Dic3—42no—
601Dic3—44no—
602Dic3—128no—
603Dic3—124no—
604Dic3—124no—
605C32#143911yescharacteristic, complemented, Sylow
606C23—34no—
607C23—62no—
608C23—62no—
609C23—62no—
610C23—64no—
611C23—64no—
612C23—64no—
613C23—64no—
614C23—62no—
615C23—62no—
616C23—64no—
617C23—62no—
618C23—64no—
619C23—122no—
620C23—122no—
621C23—121no—
622C23—122no—
623C23—122no—
624C23—121no—
625C23—122no—
626C23—121no—
627C23—121no—
628C23—122no—
629C23D3×Dic611yescharacteristic
630C23#379511yescharacteristic
631C23#379612yes—
632C23#379911yescharacteristic
633C23D3×D1211yescharacteristic
634C23#380212yes—
635C23C2×D3×Dic311yescharacteristic
636C23#380412yes—
637C23C2×#62511yescharacteristic
638C23C2×#62611yescharacteristic
639C23D3×#6712yes—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—64no—
645C2×C4—64no—
646C2×C4—64no—
647C2×C4—62no—
648C2×C4—64no—
649C2×C4—121no—
650C2×C4—122no—
651C2×C4—122no—
652C2×C4—121no—
653C2×C4—122no—
654C2×C4—122no—
655C2×C4—122no—
656C2×C4—184no—
657C2×C4—184no—
658C2×C4—184no—
659C2×C4—362no—
660C2×C4—362no—
661C2×C4—362no—
662C2×C4—362no—
663C2×C4(C2×D3)⋊Dic314yescomplemented
664C2×C3—21no—
665C2×C3—22no—
666C2×C3—22no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—22no—
672C2×C3—21no—
673C2×C3—22no—
674C2×C3—21no—
675C2×C3—124no—
676C2×C3#494711yescharacteristic
677C2×C3#494812yes—
678C2×C3#494911yescharacteristic
679C2×C3#495012yes—
680C2×C3#495112yes—
681C2×C3#495311yescharacteristic
682C2×C3#496011yescharacteristic
683C2×C3#496112yes—
684C2×C3#498711yescharacteristic
685C2×C3#498811yescharacteristic
686C2×C3#498912yes—
687C2×C3#499012yes—
688C2×C3#499112yes—
689C2×C3#499211yescharacteristic
690C2×C3#499311yescharacteristic
691C2×C3#499412yes—
692C2×C3#521211yescharacteristic
693C2×C3#521311yescharacteristic
694C2×C3#522011yescharacteristic
695C2×C3#522111yescharacteristic
696C2×C3#522311yescharacteristic
697C2×C3#523111yescharacteristic
698D3—44no—
699C22—64no—
700C22—68no—
701C22—122no—
702C22—124no—
703C22—124no—
704C22—122no—
705C22—122no—
706C22—122no—
707C22—122no—
708C22—124no—
709C22—122no—
710C22#6384111yescharacteristic
711C22#6385412yes—
712C22#6385611yescharacteristic
713C22#6385711yescharacteristic
714C22#6385812yes—
715C22#6386311yescharacteristic
716C22#6388512yes—
717C22#6388712yes—
718C22D3×C4⋊Dic311yescharacteristic
719C22#6389012yes—
720C22#6389812yes—
721C22#6389912yes—
722C22#6390712yes—
723C22#6390811yescharacteristic
724C22#6390911yescharacteristic
725C22#6391411yescharacteristic
726C22#6391612yes—
727C22#6392212yes—
728C22C2×(C2×D3)⋊Dic311yescharacteristic
729C22#6396111yescharacteristic
730C22Dic3×#6712yes—
731C22#6397611yescharacteristic
732C22#6397812yes—
733C4—24no—
734C4—122no—
735C4—124no—
736C4—364no—
737C3—21no—
738C3#7154611yescharacteristic, complemented
739C3#7157011yescharacteristic, complemented
740C2—124no—
741C2#1059130411yescharacteristic
742C2#1059130712yes—
743C2#1059130812yes—
744C2#1059131311yescharacteristic
745C2#1059131411yescharacteristic
746C2#1059132311yescharacteristic
747C2#1059132411yescharacteristic
748C2#1059137712yes—
749C2#1059138911yescharacteristic
750C2#1059139212yes—
751C2#1059171011yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, cosocleC24×C32C23
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32#1439
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊Dic3C2semidirect
4. C2×#63658C2semidirect
5. C2×#63579C2semidirect
15. C2×C3×(C2×D3)⋊C4C4semidirect
28. C22×C4⋊Dic3D3semidirect
99. C2×(C2×D3)⋊C4Dic3semidirect
140. C22×C3×D3C4⋊C4semidirect
145. C2×C32×C4C22⋊C4semidirect
392. C22×D3C4⋊Dic3semidirect
418. C2×C3×C4(C2×D3)⋊C4semidirect
419. C2×C3×C4#217semidirect
605. C32#1439semidirect
663. C2×C4(C2×D3)⋊Dic3semidirect
738. C3#71546semidirect
739. C3#71570semidirect

Maximal subgroups

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

subgroupindex
C22×C3×(C2×D3)⋊C42
C22×C3×C4⋊Dic32
C22×(C2×D3)⋊Dic32
C2×#636582
C2×#635792
#715703
#715463