Finite Group Databasebeta

← C2×#10591390 #11808166

Subgroups — C2×#10591390 #11808166

Order 1152.

2669 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#625C211yesmaximal, characteristic
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
6C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63658C211yesmaximal, characteristic, complemented
8#10591390C218yesmaximal, direct product factor
9C2×#4959—31nomaximal
10C2×#4961—31nomaximal
11C24×C3×D3C2211yescharacteristic
12C24×C3×D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×#625—24no—
19C22×#625—24no—
20C22×#625—24no—
21C22×#625C2214yes—
22C2×C3×(C2×D3)⋊C4—24no—
23C2×C3×(C2×D3)⋊C4—24no—
24C2×C3×(C2×D3)⋊C4C2214yescomplemented
25C2×C3×(C2×D3)⋊C4C2214yescomplemented
26C2×Dic3⋊Dic3—24no—
27C2×Dic3⋊Dic3C2214yescomplemented
28C2×(C2×D3)⋊Dic3—24no—
29C2×(C2×D3)⋊Dic3—24no—
30C2×(C2×D3)⋊Dic3C2214yescomplemented
31C2×(C2×D3)⋊Dic3C2214yescomplemented
32#63658C2214yescomplemented
33C23×#67—31no—
34C23×#67—31no—
35C22×C3×C22⋊C4—31no—
36C22×C3×C22⋊C4—31no—
37C22×#217—31no—
38C22×#217—31no—
39C22×(C2×D3)⋊C4—31no—
40C22×(C2×D3)⋊C4—31no—
41C22×(C2×D3)⋊C4D311yescharacteristic, complemented
42C22×(C2×D3)⋊C4D311yescharacteristic, complemented
43C22×C4⋊Dic3—31no—
44C22×Dic3⋊C4—31no—
45C2×C3⋊#95—31no—
46C2×C3⋊#95—31no—
47C2×C3⋊#95—61no—
48#4961—38no—
49#4959—38no—
50C24×C32C2311yescharacteristic
51C23×C3×D3—22no—
52C23×C3×D3—22no—
53C23×C3×D3—22no—
54C23×C3×D3—22no—
55C23×C3×D3—22no—
56C23×C3×D3—22no—
57C23×C3×D3—22no—
58C23×C3×D3—22no—
59C23×C3×D3—22no—
60C23×C3×D3—22no—
61C23×C3×D3—22no—
62C23×C3×D3—22no—
63C23×C3×D3D414yes—
64C23×C3×D3D414yes—
65C23×C3×D3C2312yes—
66C23×C3×D3C2312yes—
67C22×C32×C4—22no—
68C22×C32×C4—22no—
69C22×C32×C4—22no—
70C22×C32×C4C2312yes—
71C22×C3⋊Dic3—22no—
72C22×C3⋊Dic3—22no—
73C22×C3⋊Dic3—22no—
74C22×C3⋊Dic3—22no—
75C22×C3⋊Dic3—22no—
76C22×C3⋊Dic3D414yes—
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2312yes—
79C22×C3×Dic3—22no—
80C22×C3×Dic3—22no—
81C22×C3×Dic3—22no—
82C22×C3×Dic3—22no—
83C22×C3×Dic3—22no—
84C22×C3×Dic3D414yescomplemented
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C2×#625—232no—
88C2×#625—28no—
89C2×#625—28no—
90C2×#625—28no—
91C3×(C2×D3)⋊C4—28no—
92C3×(C2×D3)⋊C4—28no—
93Dic3⋊Dic3—28no—
94(C2×D3)⋊Dic3—28no—
95(C2×D3)⋊Dic3—28no—
96C2×#394—91noSylow
97C25×C3—31no—
98C25×C3—31no—
99C24×D3C2×D311yescharacteristic
100C24×D3C2×D311yescharacteristic
101C23×C3×C4—21no—
102C23×C3×C4—31no—
103C23×C3×C4—31no—
104C23×C3×C4C2×D311yescharacteristic
105C23×C3×C4C2×D311yescharacteristic
106C22×#67—34no—
107C22×#67—34no—
108C22×#67—64no—
109C22×#67—64no—
110C22×#67—64no—
111C22×#67—64no—
112C22×#67—64no—
113C22×#67—64no—
114C23×Dic3—31no—
115C23×Dic3—31no—
116C23×Dic3—31no—
117C23×Dic3—31no—
118C23×Dic3—61no—
119C23×Dic3—61no—
120C23×Dic3C2×D311yescharacteristic
121C23×Dic3C2×D311yescharacteristic
122C2×C3×C22⋊C4—34no—
123C2×C3×C22⋊C4—34no—
124C2×C3×C22⋊C4—64no—
125C2×C3×C22⋊C4—64no—
126C2×#217—34no—
127C2×#217—34no—
128C2×#217—64no—
129C2×#217—64no—
130C2×(C2×D3)⋊C4—24no—
131C2×(C2×D3)⋊C4—24no—
132C2×(C2×D3)⋊C4—34no—
133C2×(C2×D3)⋊C4—34no—
134C2×(C2×D3)⋊C4—64no—
135C2×(C2×D3)⋊C4—64no—
136C2×(C2×D3)⋊C4C2×D314yescomplemented
137C2×(C2×D3)⋊C4C2×D314yescomplemented
138C2×C4⋊Dic3—34no—
139C2×C4⋊Dic3—64no—
140C2×Dic3⋊C4—34no—
141C2×Dic3⋊C4—64no—
142C3⋊#95—34no—
143C3⋊#95—34no—
144C3⋊#95—64no—
145C23×C32C2×D412yes—
146C23×C32C2×D412yes—
147C23×C32C2×D412yes—
148C23×C32C2×D412yes—
149C23×C32#4112yes—
150C23×C32#4112yes—
151C23×C32#4112yes—
152C23×C32C2411yescharacteristic
153C22×C3×D3—28no—
154C22×C3×D3—28no—
155C22×C3×D3—28no—
156C22×C3×D3—28no—
157C22×C3×D3—28no—
158C22×C3×D3—28no—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3—22no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3—44no—
172C22×C3×D3—44no—
173C22×C3×D3—44no—
174C22×C3×D3—44no—
175C22×C3×D3—44no—
176C22×C3×D3—44no—
177C22×C3×D3—44no—
178C22×C3×D3—44no—
179C22×C3×D3C2×D414yes—
180C22×C3×D3C2×D414yes—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4—44no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—28no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—22no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—44no—
192C2×C3⋊Dic3C2×D414yes—
193C2×C3×Dic3—28no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—44no—
200C2×C3×Dic3C2×D414yescomplemented
201#625—232no—
202C23×D4—91no—
203C22×C4⋊C4—91no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—91no—
207C22×C22⋊C4—91no—
208#394—98no—
209C2×#95—91no—
210C24×C3—21no—
211C24×C3—34no—
212C24×C3—34no—
213C24×C3—32no—
214C24×C3—32no—
215C24×C3—62no—
216C24×C3—62no—
217C24×C3—62no—
218C24×C3—62no—
219C24×C3—62no—
220C24×C3—62no—
221C24×C3—62no—
222C24×C3—62no—
223C24×C3—62no—
224C24×C3—62no—
225C24×C3—62no—
226C24×C3—62no—
227C24×C3C22×D311yescharacteristic
228C24×C3C22×D311yescharacteristic
229C23×D3—22no—
230C23×D3—22no—
231C23×D3—22no—
232C23×D3—22no—
233C23×D3—22no—
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—22no—
237C23×D3—22no—
238C23×D3—22no—
239C23×D3—22no—
240C23×D3—22no—
241C23×D3D1214yes—
242C23×D3#6714yes—
243C23×D3C22×D312yes—
244C23×D3C22×D312yes—
245C22×C3×C4—24no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—34no—
254C22×C3×C4—32no—
255C22×C3×C4—32no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4—62no—
259C22×C3×C4—62no—
260C22×C3×C4—62no—
261C22×C3×C4—62no—
262C22×C3×C4—62no—
263C22×C3×C4C22×D312yes—
264C22×C3×C4C22×D312yes—
265C2×#67—68no—
266C2×#67—68no—
267C2×#67—68no—
268C2×#67—68no—
269C2×#67—632no—
270C2×#67—632no—
271C2×#67—68no—
272C2×#67—68no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—34no—
279C22×Dic3—34no—
280C22×Dic3—32no—
281C22×Dic3—32no—
282C22×Dic3—32no—
283C22×Dic3—32no—
284C22×Dic3—62no—
285C22×Dic3—62no—
286C22×Dic3—64no—
287C22×Dic3—62no—
288C22×Dic3—62no—
289C22×Dic3—62no—
290C22×Dic3—62no—
291C22×Dic3—64no—
292C22×Dic3—62no—
293C22×Dic3—62no—
294C22×Dic3—62no—
295C22×Dic3—62no—
296C22×Dic3—62no—
297C22×Dic3—62no—
298C22×Dic3—122no—
299C22×Dic3—122no—
300C22×Dic3—122no—
301C22×Dic3—122no—
302C22×Dic3#6714yescomplemented
303C22×Dic3C22×D312yes—
304C22×Dic3C22×D312yes—
305C3×C22⋊C4—68no—
306C3×C22⋊C4—68no—
307#217—68no—
308#217—68no—
309(C2×D3)⋊C4—28no—
310(C2×D3)⋊C4—28no—
311(C2×D3)⋊C4—68no—
312(C2×D3)⋊C4—68no—
313C4⋊Dic3—68no—
314Dic3⋊C4—68no—
315C22×C32#12014yes—
316C22×C32#12114yes—
317C22×C32#12114yes—
318C22×C32#12114yes—
319C22×C32#12314yes—
320C22×C32#12314yes—
321C22×C32#12414yes—
322C22×C32C22×D411yescharacteristic
323C22×C32C22×D411yescharacteristic
324C22×C32C22×D411yescharacteristic
325C22×C32C22×D411yescharacteristic
326C22×C32C2×#4111yescharacteristic
327C22×C32C2×#4111yescharacteristic
328C22×C32C2×#4111yescharacteristic
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—24no—
332C2×C3×D3—24no—
333C2×C3×D3—24no—
334C2×C3×D3—24no—
335C2×C3×D3—42no—
336C2×C3×D3—42no—
337C2×C3×D3—42no—
338C2×C3×D3—42no—
339C2×C3×D3—42no—
340C2×C3×D3—42no—
341C2×C3×D3—42no—
342C2×C3×D3—42no—
343C2×C3×D3—416no—
344C2×C3×D3—416no—
345C32×C4—42no—
346C3⋊Dic3—24no—
347C3⋊Dic3—42no—
348C3×Dic3—24no—
349C3×Dic3—42no—
350C25—31no—
351C25—31no—
352C22×D4—94no—
353C22×D4—184no—
354C22×D4—184no—
355C22×D4—184no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—91no—
359C23×C4—91no—
360C23×C4D3211yescharacteristic
361C2×C4⋊C4—94no—
362C2×C4⋊C4—184no—
363C2×C22⋊C4—34no—
364C2×C22⋊C4—34no—
365C2×C22⋊C4—64no—
366C2×C22⋊C4—64no—
367C2×C22⋊C4—94no—
368C2×C22⋊C4—94no—
369C2×C22⋊C4—184no—
370C2×C22⋊C4—184no—
371#95—94no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—34no—
381C23×C3—34no—
382C23×C3—68no—
383C23×C3—68no—
384C23×C3—68no—
385C23×C3—68no—
386C23×C3—68no—
387C23×C3—68no—
388C23×C3—62no—
389C23×C3—62no—
390C23×C3—62no—
391C23×C3—62no—
392C23×C3—62no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3—62no—
397C23×C3—62no—
398C23×C3—62no—
399C23×C3—62no—
400C23×C3—124no—
401C23×C3—124no—
402C23×C3—124no—
403C23×C3—124no—
404C23×C3—124no—
405C23×C3—124no—
406C23×C3—124no—
407C23×C3—124no—
408C23×C3C2×D1212yes—
409C23×C3#23512yes—
410C23×C3#23512yes—
411C23×C3#23512yes—
412C23×C3D3×D412yes—
413C23×C3D3×D412yes—
414C23×C3D3×D412yes—
415C23×C3D3×D412yes—
416C23×C3D3×D412yes—
417C23×C3#23712yes—
418C23×C3#23712yes—
419C23×C3#23712yes—
420C23×C3C2×#6712yes—
421C23×C3C2×#6712yes—
422C23×C3C23×D311yescharacteristic
423C23×C3C23×D311yescharacteristic
424C22×D3—28no—
425C22×D3—28no—
426C22×D3—28no—
427C22×D3—28no—
428C22×D3—28no—
429C22×D3—28no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—44no—
443C22×D3—44no—
444C22×D3—44no—
445C22×D3—44no—
446C22×D3—44no—
447C22×D3—44no—
448C22×D3—44no—
449C22×D3—44no—
450C22×D3C2×D1214yes—
451C22×D3C2×#6714yes—
452C2×C3×C4—24no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—34no—
460C2×C3×C4—42no—
461C2×C3×C4—42no—
462C2×C3×C4—48no—
463C2×C3×C4—44no—
464C2×C3×C4—44no—
465C2×C3×C4—68no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—62no—
470C2×C3×C4—62no—
471C2×C3×C4—124no—
472#67—632no—
473#67—632no—
474C2×Dic3—28no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—34no—
481C2×Dic3—34no—
482C2×Dic3—44no—
483C2×Dic3—64no—
484C2×Dic3—68no—
485C2×Dic3—68no—
486C2×Dic3—62no—
487C2×Dic3—62no—
488C2×Dic3—62no—
489C2×Dic3—62no—
490C2×Dic3—64no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3—62no—
495C2×Dic3—62no—
496C2×Dic3—62no—
497C2×Dic3—122no—
498C2×Dic3—122no—
499C2×Dic3—128no—
500C2×Dic3—122no—
501C2×Dic3—122no—
502C2×Dic3—128no—
503C2×Dic3—124no—
504C2×Dic3—124no—
505C2×Dic3C2×#6714yescomplemented
506C2×C32#39418yescomplemented
507C2×C32C2×#12011yescharacteristic
508C2×C32C2×#12111yescharacteristic
509C2×C32C2×#12111yescharacteristic
510C2×C32C2×#12111yescharacteristic
511C2×C32C2×#12311yescharacteristic
512C2×C32C2×#12311yescharacteristic
513C2×C32C2×#12411yescharacteristic
514C3×D3—44no—
515C3×D3—44no—
516C24—32no—
517C24—32no—
518C24—34no—
519C24—34no—
520C24—62no—
521C24—62no—
522C24—62no—
523C24—62no—
524C24—62no—
525C24—62no—
526C24—62no—
527C24—62no—
528C24—62no—
529C24—62no—
530C24—62no—
531C24—62no—
532C24C2×D3211yescharacteristic
533C2×D4—188no—
534C2×D4—188no—
535C2×D4—188no—
536C2×D4—1832no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—32no—
541C22×C4—34no—
542C22×C4—32no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—92no—
549C22×C4—94no—
550C22×C4—92no—
551C22×C4—182no—
552C22×C4—182no—
553C22×C4—182no—
554C22×C4—182no—
555C22×C4—182no—
556C22×C4C2×D3212yes—
557C4⋊C4—188no—
558C22⋊C4—68no—
559C22⋊C4—68no—
560C22⋊C4—188no—
561C22⋊C4—188no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—24no—
570C22×C3—24no—
571C22×C3—24no—
572C22×C3—24no—
573C22×C3—24no—
574C22×C3—24no—
575C22×C3—24no—
576C22×C3—64no—
577C22×C3—64no—
578C22×C3—64no—
579C22×C3—64no—
580C22×C3—64no—
581C22×C3—64no—
582C22×C3—1216no—
583C22×C3—1216no—
584C22×C3—122no—
585C22×C3—122no—
586C22×C3—122no—
587C22×C3—122no—
588C22×C3—122no—
589C22×C3—122no—
590C22×C3—122no—
591C22×C3—122no—
592C22×C3#88214yes—
593C22×C3#88314yes—
594C22×C3#88314yes—
595C22×C3#88414yes—
596C22×C3#88414yes—
597C22×C3#88514yes—
598C22×C3#88514yes—
599C22×C3#88614yes—
600C22×C3#92914yes—
601C22×C3#93014yes—
602C22×C3#93714yes—
603C22×C3#93814yes—
604C22×C3#93914yes—
605C22×C3#93914yes—
606C22×C3C22×D1211yescharacteristic
607C22×C3C2×#23511yescharacteristic
608C22×C3C2×#23511yescharacteristic
609C22×C3C2×#23511yescharacteristic
610C22×C3C2×D3×D411yescharacteristic
611C22×C3C2×D3×D411yescharacteristic
612C22×C3C2×D3×D411yescharacteristic
613C22×C3C2×D3×D411yescharacteristic
614C22×C3C2×D3×D411yescharacteristic
615C22×C3C2×#23711yescharacteristic
616C22×C3C2×#23711yescharacteristic
617C22×C3C2×#23711yescharacteristic
618C22×C3C22×#6711yescharacteristic
619C22×C3C22×#6711yescharacteristic
620C2×D3—24no—
621C2×D3—24no—
622C2×D3—24no—
623C2×D3—24no—
624C2×D3—24no—
625C2×D3—24no—
626C2×D3—416no—
627C2×D3—416no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C3×C4—44no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—64no—
640C3×C4—122no—
641Dic3—24no—
642Dic3—42no—
643Dic3—64no—
644Dic3—64no—
645Dic3—124no—
646Dic3—124no—
647Dic3—122no—
648Dic3—122no—
649C32C2×#39411yescharacteristic, complemented, Sylow
650C23—34no—
651C23—34no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23—62no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23—62no—
662C23—62no—
663C23—62no—
664C23—68no—
665C23—68no—
666C23—68no—
667C23—68no—
668C23—68no—
669C23—68no—
670C23—124no—
671C23—124no—
672C23—124no—
673C23—124no—
674C23—124no—
675C23—124no—
676C23—124no—
677C23—124no—
678C23#379512yes—
679C23#379812yes—
680C23D3×D1212yes—
681C23#380212yes—
682C23#380512yes—
683C23D3×#6712yes—
684C23D3×#6712yes—
685C23C22×D3211yescharacteristic
686D4—1832no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—34no—
691C2×C4—44no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—68no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—94no—
699C2×C4—124no—
700C2×C4—182no—
701C2×C4—182no—
702C2×C4—188no—
703C2×C4—182no—
704C2×C4—182no—
705C2×C4—182no—
706C2×C4—364no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—28no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—124no—
716C2×C3—124no—
717C2×C3#495918yescomplemented
718C2×C3#496118yescomplemented
719C2×C3C2×#88211yescharacteristic
720C2×C3C2×#88311yescharacteristic
721C2×C3C2×#88311yescharacteristic
722C2×C3C2×#88411yescharacteristic
723C2×C3C2×#88411yescharacteristic
724C2×C3C2×#88511yescharacteristic
725C2×C3C2×#88511yescharacteristic
726C2×C3C2×#88611yescharacteristic
727C2×C3C2×#92911yescharacteristic
728C2×C3C2×#93011yescharacteristic
729C2×C3C2×#93711yescharacteristic
730C2×C3C2×#93811yescharacteristic
731C2×C3C2×#93911yescharacteristic
732C2×C3C2×#93911yescharacteristic
733D3—44no—
734D3—44no—
735C22—64no—
736C22—64no—
737C22—64no—
738C22—64no—
739C22—64no—
740C22—64no—
741C22—122no—
742C22—122no—
743C22—122no—
744C22—1216no—
745C22—1216no—
746C22—122no—
747C22—122no—
748C22—122no—
749C22—122no—
750C22—122no—
751C22#6388514yes—
752C22#6389114yes—
753C22#6390514yes—
754C22#6390614yes—
755C22#6391514yes—
756C22#6392214yes—
757C22#6397014yes—
758C22C2×#379511yescharacteristic
759C22C2×#379811yescharacteristic
760C22C2×D3×D1211yescharacteristic
761C22C2×#380211yescharacteristic
762C22C2×#380511yescharacteristic
763C22C2×D3×#6711yescharacteristic
764C22C2×D3×#6711yescharacteristic
765C4—42no—
766C4—64no—
767C4—122no—
768C4—184no—
769C4—362no—
770C3—21no—
771C3C2×#496111yescharacteristic, complemented
772C3C2×#495911yescharacteristic, complemented
773C2—124no—
774C2—124no—
775C2#1059139018yesdirect product factor
776C2C2×#6388511yescharacteristic
777C2C2×#6389111yescharacteristic
778C2C2×#6390511yescharacteristic
779C2C2×#6390611yescharacteristic
780C2C2×#6391511yescharacteristic
781C2C2×#6392211yescharacteristic
782C2C2×#6397011yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC23×#625C2
hypercenterC23×C4D32
hypocenterC32C2×#394
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×(C2×D3)⋊C4C2semidirect
3. C22×C3×(C2×D3)⋊C4C2semidirect
4. C22×Dic3⋊Dic3C2semidirect
5. C22×(C2×D3)⋊Dic3C2semidirect
6. C22×(C2×D3)⋊Dic3C2semidirect
7. C2×#63658C2semidirect
8. #10591390C2direct (N × H)
24. C2×C3×(C2×D3)⋊C4C22semidirect
25. C2×C3×(C2×D3)⋊C4C22semidirect
27. C2×Dic3⋊Dic3C22semidirect
30. C2×(C2×D3)⋊Dic3C22semidirect
31. C2×(C2×D3)⋊Dic3C22semidirect
32. #63658C22semidirect
41. C22×(C2×D3)⋊C4D3semidirect
42. C22×(C2×D3)⋊C4D3semidirect
84. C22×C3×Dic3D4semidirect
136. C2×(C2×D3)⋊C4C2×D3semidirect
137. C2×(C2×D3)⋊C4C2×D3semidirect
200. C2×C3×Dic3C2×D4semidirect
302. C22×Dic3#67semidirect
505. C2×Dic3C2×#67semidirect
506. C2×C32#394semidirect
649. C32C2×#394semidirect
717. C2×C3#4959semidirect
718. C2×C3#4961semidirect
771. C3C2×#4961semidirect
772. C3C2×#4959semidirect
775. C2#10591390direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6252
C22×C3×(C2×D3)⋊C42
C22×Dic3⋊Dic32
C22×(C2×D3)⋊Dic32
C2×#636582
#105913902
C2×#49593
C2×#49613