Finite Group Databasebeta

← #11801996

Subgroups — #11801996

Order 1152.

2779 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#624C211yesmaximal, characteristic, complemented
2C2×#64146C211yesmaximal, characteristic
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63952C212yesmaximal, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6#10591722C212yesmaximal, complemented
7#10591714C211yesmaximal, characteristic, complemented
8Dic3×#217C211yesmaximal, characteristic, complemented
9#10591693C211yesmaximal, characteristic, complemented
10#10591378C212yesmaximal, complemented
11#10591233C212yesmaximal, complemented
12C4×#937—31nomaximal
13#74659—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C22×#638C2212yes—
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic, complemented
20C22×#624—24no—
21C22×#624—28no—
22C22×#624C2212yes—
23C22×#624C2212yes—
24C2×#3757C2211yescharacteristic
25#64146C418yescomplemented
26C2×#3752C2212yes—
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic, complemented
30C2×C3×#217C2212yescomplemented
31C3×D4×Dic3—24no—
32C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
33C2×C3×C4×Dic3C2211yescharacteristic, complemented
34C2×#3724C2212yescomplemented
35C2×#3722C2212yes—
36C2×#3722C2212yes—
37C2×Dic32C2212yescomplemented
38#63952—28no—
39C3×C3⋊#95C2212yescomplemented
40#63579C2212yescomplemented
41#63579C2212yescomplemented
42C23×C4×D3—31no—
43C23×C4×D3—31no—
44C2×C3×C4×D4—31no—
45C2×#937—31no—
46C2×#937—31no—
47C2×#937—61no—
48C2×D4×Dic3D311yescharacteristic, complemented
49C2×C4×#67—32no—
50C2×#67⋊C4—32no—
51C3×#386—31no—
52#5220D311yescharacteristic, complemented
53#5210—31no—
54C4×#217—31no—
55#4989—32no—
56#4956—32no—
57#4956—32no—
58#4955—31no—
59#4955—31no—
60#4946—31no—
61Dic3×C22⋊C4—31no—
62C4×(C2×D3)⋊C4—32no—
63#4668—32no—
64#4666—32no—
65C24×C32C2311yescharacteristic
66C24×C32C2311yescharacteristic
67C23×C3⋊D3—22no—
68C23×C3⋊D3—22no—
69C23×C3⋊D3—24no—
70C23×C3⋊D3—24no—
71C23×C3⋊D3C2×C414yescomplemented
72C23×C3⋊D3C2312yes—
73C2×C32×D4—22no—
74C2×C32×D4—22no—
75C2×C32×D4C2×C414yescomplemented
76C22×C32×C4C2311yescharacteristic
77C2×#638—24no—
78C2×#638—24no—
79C2×#638C2×C418yescomplemented
80C22×C3⋊Dic3C2312yes—
81C22×C3×Dic3—22no—
82C22×C3×Dic3—24no—
83C22×C3×Dic3—24no—
84C22×C3×Dic3—22no—
85C22×C3×Dic3—24no—
86C22×C3×Dic3D414yescomplemented
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C2×#624—232no—
94C2×#624—24no—
95C2×#624—24no—
96C2×#624—24no—
97C2×#624—24no—
98C2×#624—24no—
99C2×#624D418yescomplemented
100#3757C2×C414yescomplemented
101#3752C2×C418yescomplemented
102C3×#217—22no—
103C3×#217—22no—
104C3×#217—22no—
105C3×#217—24no—
106C3×C4⋊Dic3—22no—
107C3×C4×Dic3—22no—
108#3724—24no—
109#3722—24no—
110#3722—24no—
111Dic32—24no—
112C4×#120—91noSylow
113C24×D3—31no—
114C24×D3—31no—
115C24×D3—61no—
116C22×C3×D4—21no—
117C22×C3×D4C2×D311yescharacteristic
118C22×C3×D4C2×D311yescharacteristic
119C23×C3×C4—31no—
120C23×C3×C4—31no—
121C23×C3×C4—31no—
122C22×#67—32no—
123C22×#67—32no—
124C22×#67—62no—
125C23×Dic3C2×D311yescharacteristic
126C23×Dic3C2×D311yescharacteristic
127C23×Dic3C2×D311yescharacteristic, complemented
128C22×C4×D3—32no—
129C22×C4×D3—32no—
130C22×C4×D3—32no—
131C22×C4×D3—32no—
132C22×C4×D3—68no—
133C22×C4×D3—68no—
134C22×C4×D3—64no—
135C22×C4×D3—64no—
136C3×C4×D4—64no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—32no—
142C2×C3×C42—31no—
143C2×#217—31no—
144C2×#217—31no—
145C2×#217—61no—
146C2×#217C2×D311yescharacteristic
147C2×#217C2×D311yescharacteristic
148C2×#217C2×D311yescharacteristic, complemented
149C2×#217C2×D312yescomplemented
150#937—38no—
151#937—38no—
152#937—68no—
153D4×Dic3—24no—
154C4×#67—68no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—32no—
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4—32no—
160C2×(C2×D3)⋊C4—32no—
161C2×(C2×D3)⋊C4—62no—
162C2×C4⋊Dic3C2×D311yescharacteristic, complemented
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×C4×Dic3—32no—
166C2×C4×Dic3—32no—
167C2×C4×Dic3C2×D311yescharacteristic, complemented
168#67⋊C4—68no—
169C3×#95—32no—
170C3⋊#95—32no—
171C3⋊#95—32no—
172C3⋊#95—32no—
173C3⋊#95—32no—
174C3⋊#95C2×D312yescomplemented
175C23×C32—22no—
176C23×C32—22no—
177C23×C32—22no—
178C23×C32—21no—
179C23×C32—22no—
180C23×C32—21no—
181C23×C32C22×C412yes—
182C23×C32C22×C412yescomplemented
183C23×C32C2×D412yes—
184C23×C32#4112yes—
185C23×C32C2411yescharacteristic
186C22×C3⋊D3—216no—
187C22×C3⋊D3—28no—
188C22×C3⋊D3—28no—
189C22×C3⋊D3—28no—
190C22×C3⋊D3—22no—
191C22×C3⋊D3—22no—
192C22×C3⋊D3—22no—
193C22×C3⋊D3—22no—
194C22×C3⋊D3—216no—
195C22×C3⋊D3C22×C414yes—
196C22×C3⋊D3C2×D414yes—
197C22×C3⋊D3#4114yes—
198C32×D4—28no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4C22×C412yescomplemented
202#638—216no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3C22×C414yescomplemented
206C2×C3×Dic3—28no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—28no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—44no—
219C2×C3×Dic3C2×D414yes—
220C2×C3×Dic3C2×D414yes—
221C2×C3×Dic3C2×D412yes—
222C2×C3×Dic3C2×D412yes—
223#624—216no—
224#624—216no—
225C24×C4—91no—
226C2×#120—91no—
227C2×C4×D4—31no—
228C2×C4×D4—92no—
229#386—31no—
230#386—92no—
231#385—92no—
232#385—91no—
233#379—91no—
234C4×C22⋊C4—92no—
235C4×C22⋊C4—91no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3C22×D311yescharacteristic
239C24×C3C22×D311yescharacteristic
240C24×C3C22×D311yescharacteristic
241C24×C3C22×D311yescharacteristic
242C23×D3—32no—
243C23×D3—32no—
244C23×D3—34no—
245C23×D3—34no—
246C23×D3—62no—
247C23×D3—64no—
248C23×D3—64no—
249C23×D3—64no—
250C23×D3—64no—
251C23×D3—64no—
252C23×D3—62no—
253C23×D3—62no—
254C23×D3—62no—
255C23×D3—62no—
256C23×D3—124no—
257C23×D3—124no—
258C23×D3—122no—
259C23×D3—122no—
260C2×C3×D4—22no—
261C2×C3×D4—22no—
262C2×C3×D4—22no—
263C2×C3×D4—22no—
264C2×C3×D4—24no—
265C2×C3×D4—42no—
266C2×C3×D4—42no—
267C2×C3×D4C4×D314yescomplemented
268C2×C3×D4C4×D314yescomplemented
269C22×C3×C4—21no—
270C22×C3×C4—31no—
271C22×C3×C4—34no—
272C22×C3×C4—31no—
273C22×C3×C4—32no—
274C22×C3×C4—31no—
275C22×C3×C4—32no—
276C22×C3×C4—31no—
277C22×C3×C4—64no—
278C22×C3×C4—64no—
279C22×C3×C4—64no—
280C22×C3×C4—62no—
281C22×C3×C4—62no—
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C2×#67—38no—
285C2×#67—38no—
286C2×#67—68no—
287C2×#67—64no—
288C2×#67—64no—
289C2×#67—64no—
290C2×#67—64no—
291C2×#67—124no—
292C2×#67—124no—
293C22×Dic3—22no—
294C22×Dic3—24no—
295C22×Dic3—24no—
296C22×Dic3—24no—
297C22×Dic3—22no—
298C22×Dic3—32no—
299C22×Dic3—32no—
300C22×Dic3—62no—
301C22×Dic3#6714yescomplemented
302C22×Dic3C22×D311yescharacteristic
303C22×Dic3C22×D312yes—
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D312yes—
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C2×C4×D3—38no—
309C2×C4×D3—38no—
310C2×C4×D3—64no—
311C2×C4×D3—64no—
312C2×C4×D3—64no—
313C2×C4×D3—64no—
314C2×C4×D3—64no—
315C2×C4×D3—64no—
316C2×C4×D3—632no—
317C2×C4×D3—632no—
318C2×C4×D3—64no—
319C2×C4×D3—64no—
320C2×C4×D3—64no—
321C2×C4×D3—64no—
322C3×C4⋊C4—62no—
323C3×C22⋊C4—64no—
324C3×C22⋊C4—62no—
325C3×C22⋊C4—62no—
326C3×C22⋊C4—62no—
327C3×C42—62no—
328#217—22no—
329#217—22no—
330#217—24no—
331#217—22no—
332#217—34no—
333#217—34no—
334#217—64no—
335(C2×D3)⋊C4—38no—
336(C2×D3)⋊C4—38no—
337(C2×D3)⋊C4—68no—
338(C2×D3)⋊C4—64no—
339(C2×D3)⋊C4—64no—
340(C2×D3)⋊C4—64no—
341(C2×D3)⋊C4—64no—
342C4⋊Dic3—22no—
343Dic3⋊C4—64no—
344Dic3⋊C4—64no—
345C4×Dic3—22no—
346C4×Dic3—64no—
347C4×Dic3—64no—
348C22×C32—24no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32—24no—
352C22×C32—24no—
353C22×C32—22no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32—42no—
357C22×C32C4×D414yescomplemented
358C22×C32C23×C411yescharacteristic
359C22×C32C22×D412yes—
360C22×C32C22×D411yescharacteristic
361C22×C32C2×#4111yescharacteristic
362C22×C32C2×#4112yes—
363C2×C3⋊D3—232no—
364C2×C3⋊D3—24no—
365C2×C3⋊D3—24no—
366C2×C3⋊D3—24no—
367C2×C3⋊D3—24no—
368C2×C3⋊D3—24no—
369C2×C3⋊D3—24no—
370C2×C3⋊D3C4×D418yescomplemented
371C32×C4—22no—
372C3⋊Dic3—24no—
373C3×Dic3—22no—
374C3×Dic3—24no—
375C3×Dic3—41no—
376C3×Dic3—41no—
377C3×Dic3—42no—
378C3×Dic3#12014yescomplemented
379C25—91no—
380C22×D4—92no—
381C22×D4D3211yescharacteristic
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—92no—
386C23×C4—92no—
387C23×C4—184no—
388C23×C4—188no—
389#120—98no—
390C4×D4—64no—
391C4×D4—188no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—92no—
394C2×C22⋊C4—31no—
395C2×C22⋊C4—31no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—31no—
398C2×C22⋊C4—91no—
399C2×C22⋊C4—92no—
400C2×C22⋊C4—92no—
401C2×C22⋊C4—92no—
402C2×C42—31no—
403C2×C42—92no—
404#95—32no—
405#95—92no—
406#95—92no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—21no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—42no—
425C23×C3—42no—
426C23×C3—42no—
427C23×C3—42no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3C2×C4×D312yes—
431C23×C3C2×C4×D312yes—
432C23×C3C2×C4×D312yescomplemented
433C23×C3C2×C4×D312yescomplemented
434C23×C3#23512yes—
435C23×C3D3×D412yes—
436C23×C3#23712yes—
437C23×C3C2×#6712yes—
438C23×C3C23×D311yescharacteristic
439C23×C3C23×D311yescharacteristic
440C22×D3—34no—
441C22×D3—34no—
442C22×D3—34no—
443C22×D3—34no—
444C22×D3—34no—
445C22×D3—34no—
446C22×D3—64no—
447C22×D3—64no—
448C22×D3—64no—
449C22×D3—616no—
450C22×D3—616no—
451C22×D3—68no—
452C22×D3—68no—
453C22×D3—68no—
454C22×D3—616no—
455C22×D3—68no—
456C22×D3—616no—
457C22×D3—68no—
458C22×D3—68no—
459C22×D3—62no—
460C22×D3—62no—
461C22×D3—62no—
462C22×D3—62no—
463C22×D3—62no—
464C22×D3—62no—
465C22×D3—62no—
466C22×D3—62no—
467C22×D3—1216no—
468C22×D3—122no—
469C22×D3—122no—
470C22×D3—122no—
471C22×D3—122no—
472C22×D3—128no—
473C22×D3—128no—
474C22×D3—1216no—
475C22×D3—128no—
476C3×D4—28no—
477C3×D4—28no—
478C3×D4—48no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—34no—
485C2×C3×C4—32no—
486C2×C3×C4—34no—
487C2×C3×C4—32no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—68no—
491C2×C3×C4—68no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—124no—
503C2×C3×C4C2×C4×D312yescomplemented
504C2×C3×C4C2×C4×D312yescomplemented
505#67—616no—
506#67—616no—
507#67—1216no—
508C2×Dic3—28no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—28no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—34no—
521C2×Dic3—34no—
522C2×Dic3—44no—
523C2×Dic3—64no—
524C2×Dic3—62no—
525C2×Dic3—62no—
526C2×Dic3—62no—
527C2×Dic3—62no—
528C2×Dic3—122no—
529C2×Dic3—122no—
530C2×Dic3D3×D414yes—
531C2×Dic3D3×D414yes—
532C2×Dic3C2×#6712yes—
533C2×Dic3C2×#6712yes—
534C4×D3—616no—
535C4×D3—616no—
536C4×D3—616no—
537C4×D3—616no—
538C2×C32—24no—
539C2×C32—42no—
540C2×C32C2×C4×D411yescharacteristic
541C2×C32C2×C4×D412yes—
542C2×C32C2×#12011yescharacteristic
543C2×C32#52511yescharacteristic
544C2×C32#52512yes—
545C3⋊D3—28no—
546C24—92no—
547C24—94no—
548C24—184no—
549C24—184no—
550C24—182no—
551C24—182no—
552C24C2×D3211yescharacteristic
553C24C2×D3211yescharacteristic
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—98no—
557C2×D4—184no—
558C2×D4—184no—
559C2×D4#62414yescomplemented
560C22×C4—31no—
561C22×C4—32no—
562C22×C4—31no—
563C22×C4—34no—
564C22×C4—32no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—64no—
568C22×C4—64no—
569C22×C4—62no—
570C22×C4—64no—
571C22×C4—62no—
572C22×C4—98no—
573C22×C4—92no—
574C22×C4—184no—
575C22×C4—184no—
576C22×C4—184no—
577C22×C4—184no—
578C22×C4—184no—
579C22×C4—1832no—
580C22×C4C2×D3211yescharacteristic
581C4⋊C4—62no—
582C4⋊C4—184no—
583C22⋊C4—62no—
584C22⋊C4—64no—
585C22⋊C4—62no—
586C22⋊C4—62no—
587C22⋊C4—94no—
588C22⋊C4—98no—
589C22⋊C4—184no—
590C22⋊C4—184no—
591C42—62no—
592C42—184no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—24no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—24no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—24no—
604C22×C3—24no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—24no—
611C22×C3—44no—
612C22×C3—44no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—44no—
616C22×C3—42no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—42no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—42no—
623C22×C3—82no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3#67⋊C414yescomplemented
627C22×C3C4×#6714yescomplemented
628C22×C3C22×C4×D311yescharacteristic
629C22×C3C22×C4×D311yescharacteristic
630C22×C3C2×#23511yescharacteristic
631C22×C3C2×D3×D412yes—
632C22×C3C2×D3×D412yes—
633C22×C3C2×D3×D411yescharacteristic
634C22×C3C2×#23711yescharacteristic
635C22×C3D3×#4112yes—
636C22×C3D3×#4112yes—
637C22×C3C22×#6711yescharacteristic
638C2×D3—38no—
639C2×D3—38no—
640C2×D3—68no—
641C2×D3—632no—
642C2×D3—632no—
643C2×D3—64no—
644C2×D3—64no—
645C2×D3—64no—
646C2×D3—64no—
647C2×D3—64no—
648C2×D3—64no—
649C2×D3—64no—
650C2×D3—64no—
651C2×D3—64no—
652C2×D3—64no—
653C2×D3—64no—
654C2×D3—64no—
655C2×D3—124no—
656C2×D3—124no—
657C2×D3—124no—
658C2×D3—124no—
659C2×D3—124no—
660C2×D3—124no—
661C2×D3—1232no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—34no—
665C3×C4—42no—
666C3×C4—64no—
667C3×C4—62no—
668C3×C4—121no—
669C3×C4—122no—
670C3×C4—121no—
671Dic3—22no—
672Dic3—24no—
673Dic3—41no—
674Dic3—41no—
675Dic3—42no—
676Dic3—64no—
677Dic3—64no—
678Dic3—124no—
679Dic3#93714yescomplemented
680C32C4×#12011yescharacteristic, complemented, Sylow
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—21no—
686C23—21no—
687C23—94no—
688C23—94no—
689C23—94no—
690C23—1816no—
691C23—188no—
692C23—1816no—
693C23—188no—
694C23—182no—
695C23—182no—
696C23—182no—
697C23—182no—
698C23—188no—
699C23#380412yes—
700C23C2×#62412yes—
701C23C2×#62412yescomplemented
702C23D3×#6712yes—
703C23C22×D3211yescharacteristic
704D4—28no—
705D4—1816no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—34no—
709C2×C4—32no—
710C2×C4—34no—
711C2×C4—32no—
712C2×C4—68no—
713C2×C4—68no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—94no—
725C2×C4—124no—
726C2×C4—1816no—
727C2×C4—1816no—
728C2×C4—182no—
729C2×C4—182no—
730C2×C4C2×#62412yescomplemented
731C2×C3—24no—
732C2×C3—24no—
733C2×C3—22no—
734C2×C3—22no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—44no—
739C2×C3—42no—
740C2×C3—42no—
741C2×C3—82no—
742C2×C3C2×#67⋊C411yescharacteristic
743C2×C3C4×D3×D412yes—
744C2×C3C4×D3×D412yes—
745C2×C3#554712yes—
746C2×C3D3×#12011yescharacteristic
747C2×C3#560612yes—
748C2×C3#565611yescharacteristic
749C2×C3C2×C4×#6711yescharacteristic
750C2×C3C2×#93711yescharacteristic
751C2×C3#582811yescharacteristic
752D3—68no—
753D3—68no—
754D3—128no—
755C22—24no—
756C22—24no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—22no—
761C22—42no—
762C22—41no—
763C22—41no—
764C22—98no—
765C22—1832no—
766C22—184no—
767C22—184no—
768C22—184no—
769C22—184no—
770C22—184no—
771C22—184no—
772C22#6395214yescomplemented
773C22D32×D412yes—
774C22#6431212yes—
775C22C2×#380411yescharacteristic
776C22C22×#62411yescharacteristic
777C22C2×D3×#6711yescharacteristic
778C4—22no—
779C4—34no—
780C4—64no—
781C4—62no—
782C4—122no—
783C4—121no—
784C4—121no—
785C4—184no—
786C3—21no—
787C3#7465911yescharacteristic, complemented
788C3C4×#93711yescharacteristic, complemented
789C2—24no—
790C2—42no—
791C2—188no—
792C2D4×#62412yes—
793C2#1059513812yes—
794C2#1059515911yescharacteristic
795C2D3×#93711yescharacteristic
796C2C2×#6395211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×#64146C2
hypercenterC22×D4D32
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C23×#624C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×#63952C2semidirect
5. C3×#5220C2semidirect
6. #10591722C2semidirect
7. #10591714C2semidirect
8. Dic3×#217C2semidirect
9. #10591693C2semidirect
10. #10591378C2semidirect
11. #10591233C2semidirect
19. C23×C3×Dic3C22semidirect
25. #64146C4semidirect
29. C2×C3×#217C22semidirect
30. C2×C3×#217C22semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C2×C3×C4×Dic3C22semidirect
34. C2×#3724C22semidirect
37. C2×Dic32C22semidirect
39. C3×C3⋊#95C22semidirect
40. #63579C22semidirect
41. #63579C22semidirect
48. C2×D4×Dic3D3semidirect
52. #5220D3semidirect
71. C23×C3⋊D3C2×C4semidirect
75. C2×C32×D4C2×C4semidirect
79. C2×#638C2×C4semidirect
86. C22×C3×Dic3D4semidirect
99. C2×#624D4semidirect
100. #3757C2×C4semidirect
101. #3752C2×C4semidirect
127. C23×Dic3C2×D3semidirect
148. C2×#217C2×D3semidirect
149. C2×#217C2×D3semidirect
162. C2×C4⋊Dic3C2×D3semidirect
167. C2×C4×Dic3C2×D3semidirect
174. C3⋊#95C2×D3semidirect
182. C23×C32C22×C4semidirect
201. C2×C32×C4C22×C4semidirect
205. C2×C3⋊Dic3C22×C4semidirect
267. C2×C3×D4C4×D3semidirect
268. C2×C3×D4C4×D3semidirect
301. C22×Dic3#67semidirect
357. C22×C32C4×D4semidirect
370. C2×C3⋊D3C4×D4semidirect
378. C3×Dic3#120semidirect
432. C23×C3C2×C4×D3semidirect
433. C23×C3C2×C4×D3semidirect
503. C2×C3×C4C2×C4×D3semidirect
504. C2×C3×C4C2×C4×D3semidirect
559. C2×D4#624semidirect
626. C22×C3#67⋊C4semidirect
627. C22×C3C4×#67semidirect
679. Dic3#937semidirect
680. C32C4×#120semidirect
701. C23C2×#624semidirect
730. C2×C4C2×#624semidirect
772. C22#63952semidirect
787. C3#74659semidirect
788. C3C4×#937semidirect

Maximal subgroups

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

subgroupindex
C23×#6242
C2×#641462
C2×C3×D4×Dic32
C2×#639522
C3×#52202
#105917222
#105917142
Dic3×#2172
#105916932
#105913782
#105912332
C4×#9373
#746593