Finite Group Databasebeta

← #11802007

Subgroups — #11802007

Order 1152.

2591 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C2×#63977C211yesmaximal, characteristic
3C2×#63952C211yesmaximal, characteristic, complemented
4C2×#63904C212yesmaximal, complemented
5#10592912C211yesmaximal, characteristic, complemented
6C3×#5210C211yesmaximal, characteristic, complemented
7#10591706C211yesmaximal, characteristic, complemented
8Dic3×#217C211yesmaximal, characteristic, complemented
9#10591382C212yesmaximal, complemented
10#10591277C212yesmaximal, complemented
11#10591237C212yesmaximal, complemented
12C4×#953—31nomaximal
13#74379—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×C4×D3—24no—
19C22×C3×C4×D3—28no—
20C22×C3×C4×D3C2212yes—
21C22×C3×C4×D3C2212yes—
22C22×#626C2212yes—
23C22×#624C2211yescharacteristic, complemented
24C2×#3757C2211yescharacteristic
25C2×#3752C2212yescomplemented
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×Dic3⋊C4C2212yescomplemented
29#63977C418yescomplemented
30C2×#3724C2211yescharacteristic, complemented
31C2×#3722C2211yescharacteristic, complemented
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×Dic32C2211yescharacteristic, complemented
36C2×Dic32C2212yescomplemented
37#63952—24no—
38#63904—28no—
39#63658C2212yescomplemented
40C3×C3⋊#95C2212yescomplemented
41#63579C2212yescomplemented
42C24×C3×C4—31no—
43C23×C4×D3D311yescharacteristic, complemented
44C2×#953—31no—
45C2×C4×#67—31no—
46C2×C4×#67—32no—
47C2×#893—32no—
48C2×#882—31no—
49C2×#67⋊C4—31no—
50C3×#385—31no—
51#5247—31no—
52#5213—31no—
53#5213—31no—
54#5213—32no—
55#5213—61no—
56#5210—32no—
57#5210D311yescharacteristic, complemented
58C4×#217—31no—
59C4×#217—32no—
60#4989—32no—
61#4955—31no—
62Dic3×C22⋊C4—31no—
63#4666—32no—
64#4665—32no—
65C24×C32C2311yescharacteristic
66C23×C3⋊D3C2311yescharacteristic
67C23×C3×D3—22no—
68C23×C3×D3—22no—
69C23×C3×D3—24no—
70C23×C3×D3—24no—
71C23×C3×D3C2×C414yescomplemented
72C23×C3×D3C2312yes—
73C22×C32×C4—22no—
74C22×C32×C4—24no—
75C22×C32×C4C2312yes—
76C2×#638—22no—
77C2×#638—22no—
78C2×#638C2×C414yescomplemented
79C22×C3⋊Dic3C2312yes—
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3×Dic3—24no—
82C22×C3×Dic3D414yescomplemented
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C2×C3×C4×D3—232no—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3D418yescomplemented
95C2×#626—24no—
96C2×#626—24no—
97C2×#626C2×C418yescomplemented
98C2×#624—24no—
99C2×#624—22no—
100#3757—22no—
101#3752—24no—
102C3×#217—22no—
103C3×#217C2×C414yescomplemented
104C3×Dic3⋊C4—24no—
105#3724—22no—
106#3722—22no—
107(C2×D3)⋊Dic3—24no—
108(C2×D3)⋊Dic3—24no—
109(C2×D3)⋊Dic3C2×C418yescomplemented
110Dic32—24no—
111Dic32—22no—
112C4×#120—91noSylow
113C25×C3—31no—
114C24×D3C2×D311yescharacteristic
115C23×C3×C4—21no—
116C23×C3×C4—31no—
117C23×C3×C4—32no—
118C23×C3×C4—32no—
119C23×C3×C4—64no—
120C23×C3×C4—68no—
121C23×C3×C4C2×D311yescharacteristic
122C23×C3×C4C2×D311yescharacteristic
123C22×#67—31no—
124C22×#67—31no—
125C22×#67—32no—
126C22×#67—61no—
127C23×Dic3C2×D311yescharacteristic
128C22×D12—32no—
129C22×C4×D3—24no—
130C22×C4×D3—28no—
131C22×C4×D3—31no—
132C22×C4×D3—31no—
133C22×C4×D3C2×D312yes—
134C22×C4×D3C2×D312yes—
135C2×C3×C4⋊C4—32no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138#953—38no—
139C2×#217—32no—
140C2×#217—31no—
141C2×#217—31no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—61no—
145C2×#217C2×D311yescharacteristic
146C2×#217C2×D311yescharacteristic
147C4×#67—68no—
148C4×#67—64no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—62no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4C2×D312yescomplemented
160C2×C4×Dic3—31no—
161C2×C4×Dic3—32no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—32no—
164#893—68no—
165#882—38no—
166#67⋊C4—64no—
167C3×#95—32no—
168C3⋊#95—32no—
169C3⋊#95—32no—
170C3⋊#95—32no—
171C3⋊#95—32no—
172C3⋊#95—62no—
173C3⋊#95C2×D312yescomplemented
174C23×C32—22no—
175C23×C32—22no—
176C23×C32C22×C412yes—
177C23×C32C2×D412yes—
178C23×C32#4112yes—
179C23×C32C2411yescharacteristic
180C22×C3⋊D3—21no—
181C22×C3⋊D3—22no—
182C22×C3⋊D3—22no—
183C22×C3⋊D3—21no—
184C22×C3⋊D3C22×C412yescomplemented
185C22×C3×D3—216no—
186C22×C3×D3—28no—
187C22×C3×D3—28no—
188C22×C3×D3—28no—
189C22×C3×D3—22no—
190C22×C3×D3—22no—
191C22×C3×D3—22no—
192C22×C3×D3—22no—
193C22×C3×D3—216no—
194C22×C3×D3C22×C414yes—
195C22×C3×D3C2×D414yes—
196C22×C3×D3#4114yes—
197C2×C32×C4—28no—
198C2×C32×C4—22no—
199C2×C32×C4—22no—
200C2×C32×C4C2×D414yes—
201#638—28no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3—22no—
206C2×C3⋊Dic3—22no—
207C2×C3⋊Dic3C22×C412yescomplemented
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—28no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3C22×C414yescomplemented
217C2×C3×Dic3C2×D412yes—
218C2×C3×Dic3C2×D412yes—
219C2×C3×Dic3C2×D414yes—
220C3×C4×D3—216no—
221C3×C4×D3—216no—
222#626—216no—
223#624—44no—
224C24×C4—31no—
225C2×#120—91no—
226C2×C4×D4—91no—
227C2×C4×D4—92no—
228#386—92no—
229#386—91no—
230#385—31no—
231#385—92no—
232#379—91no—
233C4×C22⋊C4—92no—
234C4×C22⋊C4—91no—
235C24×C3—21no—
236C24×C3—32no—
237C24×C3—34no—
238C24×C3—64no—
239C24×C3—64no—
240C24×C3—62no—
241C24×C3—62no—
242C24×C3C22×D311yescharacteristic
243C24×C3C22×D311yescharacteristic
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—24no—
247C23×D3—24no—
248C23×D3—31no—
249C23×D3—31no—
250C23×D3—61no—
251C23×D3C4×D314yescomplemented
252C23×D3C22×D312yes—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—24no—
256C22×C3×C4—24no—
257C22×C3×C4—22no—
258C22×C3×C4—31no—
259C22×C3×C4—34no—
260C22×C3×C4—31no—
261C22×C3×C4—32no—
262C22×C3×C4—38no—
263C22×C3×C4—31no—
264C22×C3×C4—31no—
265C22×C3×C4—44no—
266C22×C3×C4—42no—
267C22×C3×C4—64no—
268C22×C3×C4—64no—
269C22×C3×C4—64no—
270C22×C3×C4—64no—
271C22×C3×C4—632no—
272C22×C3×C4—64no—
273C22×C3×C4—64no—
274C22×C3×C4C22×D312yes—
275C22×C3×C4C22×D312yes—
276C2×#67—34no—
277C2×#67—34no—
278C2×#67—38no—
279C2×#67—64no—
280C2×#67—64no—
281C2×#67—64no—
282C2×#67—62no—
283C2×#67—62no—
284C2×#67—62no—
285C2×#67—62no—
286C2×#67—122no—
287C2×#67—122no—
288C22×Dic3—24no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—32no—
292C22×Dic3—32no—
293C22×Dic3—61no—
294C22×Dic3—62no—
295C22×Dic3#6714yescomplemented
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D312yes—
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D311yescharacteristic
301C2×D12—38no—
302C2×D12—64no—
303C2×D12—64no—
304C2×C4×D3—232no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—24no—
310C2×C4×D3—64no—
311C2×C4×D3—62no—
312C2×C4×D3—62no—
313C2×C4×D3—64no—
314C2×C4×D3#6718yescomplemented
315C3×C4⋊C4—64no—
316C3×C22⋊C4—34no—
317C3×C22⋊C4—62no—
318#217—22no—
319#217—38no—
320#217—64no—
321#217—64no—
322#217—62no—
323#217—62no—
324#217—122no—
325#217C4×D314yescomplemented
326(C2×D3)⋊C4—38no—
327(C2×D3)⋊C4—62no—
328(C2×D3)⋊C4—64no—
329(C2×D3)⋊C4—64no—
330(C2×D3)⋊C4—64no—
331(C2×D3)⋊C4—64no—
332(C2×D3)⋊C4—62no—
333(C2×D3)⋊C4—124no—
334Dic3⋊C4—24no—
335Dic3⋊C4—62no—
336Dic3⋊C4—62no—
337C4×Dic3—64no—
338C4×Dic3—62no—
339C4×Dic3—62no—
340C4×Dic3—64no—
341C22×C32—24no—
342C22×C32—22no—
343C22×C32—22no—
344C22×C32—24no—
345C22×C32C4×D414yescomplemented
346C22×C32C23×C411yescharacteristic
347C22×C32C22×D412yes—
348C22×C32C22×D411yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4112yes—
351C2×C3⋊D3—24no—
352C2×C3⋊D3—22no—
353C2×C3⋊D3—41no—
354C2×C3⋊D3—41no—
355C2×C3⋊D3—42no—
356C2×C3×D3—232no—
357C2×C3×D3—24no—
358C2×C3×D3—24no—
359C2×C3×D3—24no—
360C2×C3×D3—24no—
361C2×C3×D3—24no—
362C2×C3×D3—24no—
363C2×C3×D3C4×D418yescomplemented
364C32×C4—24no—
365C3⋊Dic3—22no—
366C3⋊Dic3—42no—
367C3×Dic3—24no—
368C3×Dic3—22no—
369C3×Dic3—41no—
370C3×Dic3—41no—
371C3×Dic3#12014yescomplemented
372C25—31no—
373C22×D4—92no—
374C22×D4—91no—
375C23×C4—31no—
376C23×C4—32no—
377C23×C4—32no—
378C23×C4—64no—
379C23×C4—68no—
380C23×C4—91no—
381C23×C4D3211yescharacteristic
382#120—98no—
383C4×D4—184no—
384C4×D4—188no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—91no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—31no—
389C2×C22⋊C4—92no—
390C2×C22⋊C4—91no—
391C2×C22⋊C4—92no—
392C2×C22⋊C4—92no—
393C2×C22⋊C4—91no—
394C2×C22⋊C4—92no—
395C2×C42—92no—
396C2×C42—91no—
397#95—32no—
398#95—92no—
399#95—92no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—21no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—34no—
409C23×C3—34no—
410C23×C3—34no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—616no—
414C23×C3—68no—
415C23×C3—68no—
416C23×C3—616no—
417C23×C3—68no—
418C23×C3—62no—
419C23×C3—62no—
420C23×C3—62no—
421C23×C3—62no—
422C23×C3C2×C4×D312yes—
423C23×C3C2×C4×D312yes—
424C23×C3#23512yes—
425C23×C3D3×D412yes—
426C23×C3#23912yes—
427C23×C3C2×#6712yes—
428C23×C3C23×D311yescharacteristic
429C23×C3C23×D311yescharacteristic
430C22×D3—28no—
431C22×D3—28no—
432C22×D3—216no—
433C22×D3—28no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—216no—
439C22×D3—32no—
440C22×D3—32no—
441C22×D3—62no—
442C22×D3—62no—
443C22×D3—61no—
444C22×D3—61no—
445C22×D3—62no—
446C22×D3—61no—
447C22×D3—62no—
448C22×D3—62no—
449C22×D3—61no—
450C22×D3—122no—
451C22×D3—121no—
452C22×D3—121no—
453C22×D3—122no—
454C22×D3C2×C4×D314yes—
455C22×D3#23514yes—
456C22×D3C2×#6714yes—
457C2×C3×C4—28no—
458C2×C3×C4—28no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—24no—
464C2×C3×C4—32no—
465C2×C3×C4—34no—
466C2×C3×C4—34no—
467C2×C3×C4—32no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—48no—
471C2×C3×C4—616no—
472C2×C3×C4—616no—
473C2×C3×C4—68no—
474C2×C3×C4—62no—
475C2×C3×C4—62no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—62no—
481C2×C3×C4D3×D414yes—
482C2×C3×C4C2×#6714yes—
483#67—616no—
484#67—68no—
485#67—68no—
486#67—128no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—28no—
491C2×Dic3—21no—
492C2×Dic3—22no—
493C2×Dic3—21no—
494C2×Dic3—22no—
495C2×Dic3—32no—
496C2×Dic3—32no—
497C2×Dic3—62no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—62no—
503C2×Dic3—62no—
504C2×Dic3—62no—
505C2×Dic3—62no—
506C2×Dic3—62no—
507C2×Dic3—62no—
508C2×Dic3—121no—
509C2×Dic3—121no—
510C2×Dic3—122no—
511C2×Dic3—122no—
512C2×Dic3—122no—
513C2×Dic3C2×C4×D314yescomplemented
514C2×Dic3C2×#6712yes—
515C2×Dic3C2×#6712yes—
516C2×Dic3C2×#6714yes—
517D12—616no—
518C4×D3—216no—
519C4×D3—216no—
520C4×D3—124no—
521C4×D3—124no—
522C2×C32—24no—
523C2×C32C2×C4×D411yescharacteristic
524C2×C32C2×C4×D412yes—
525C2×C32C2×#12011yescharacteristic
526C2×C32#52511yescharacteristic
527C2×C32#52512yes—
528C3⋊D3—42no—
529C3×D3—28no—
530C24—32no—
531C24—34no—
532C24—64no—
533C24—64no—
534C24—62no—
535C24—62no—
536C24—91no—
537C24C2×D3211yescharacteristic
538C2×D4—98no—
539C2×D4—94no—
540C2×D4—184no—
541C2×D4—184no—
542C2×D4—182no—
543C2×D4—182no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—31no—
547C22×C4—32no—
548C22×C4—31no—
549C22×C4—34no—
550C22×C4—38no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—64no—
554C22×C4—64no—
555C22×C4—64no—
556C22×C4—64no—
557C22×C4—632no—
558C22×C4—64no—
559C22×C4—64no—
560C22×C4—91no—
561C22×C4—92no—
562C22×C4—182no—
563C22×C4—184no—
564C22×C4C2×D3212yes—
565C4⋊C4—64no—
566C4⋊C4—182no—
567C22⋊C4—34no—
568C22⋊C4—62no—
569C22⋊C4—98no—
570C22⋊C4—182no—
571C22⋊C4—184no—
572C22⋊C4—184no—
573C22⋊C4—182no—
574C22⋊C4—184no—
575C42—184no—
576C42—182no—
577C22×C3—22no—
578C22×C3—24no—
579C22×C3—24no—
580C22×C3—22no—
581C22×C3—24no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—24no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—21no—
590C22×C3—24no—
591C22×C3—38no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—632no—
597C22×C3—64no—
598C22×C3—64no—
599C22×C3—64no—
600C22×C3—64no—
601C22×C3—64no—
602C22×C3—64no—
603C22×C3#89314yescomplemented
604C22×C3C4×#6714yescomplemented
605C22×C3C22×C4×D311yescharacteristic
606C22×C3C22×C4×D311yescharacteristic
607C22×C3C2×#23511yescharacteristic
608C22×C3C2×#23512yes—
609C22×C3C2×D3×D411yescharacteristic
610C22×C3C2×D3×D412yes—
611C22×C3C2×#23911yescharacteristic
612C22×C3D3×#4112yes—
613C22×C3C22×#6712yes—
614C22×C3C22×#6711yescharacteristic
615C2×D3—232no—
616C2×D3—24no—
617C2×D3—24no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—24no—
621C2×D3—24no—
622C2×D3—62no—
623C2×D3—64no—
624C2×D3—62no—
625C2×D3—64no—
626C2×D3—122no—
627C2×D3—124no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—122no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3—122no—
634C2×D3—241no—
635C2×D3—242no—
636C2×D3—241no—
637C2×D3C4×#6718yescomplemented
638C3×C4—24no—
639C3×C4—24no—
640C3×C4—34no—
641C3×C4—44no—
642C3×C4—64no—
643C3×C4—62no—
644C3×C4—121no—
645C3×C4—121no—
646Dic3—24no—
647Dic3—22no—
648Dic3—41no—
649Dic3—41no—
650Dic3—62no—
651Dic3—62no—
652Dic3—122no—
653Dic3—122no—
654Dic3—122no—
655Dic3—242no—
656Dic3#95314yescomplemented
657C32C4×#12011yescharacteristic, complemented, Sylow
658C23—22no—
659C23—22no—
660C23—34no—
661C23—34no—
662C23—34no—
663C23—616no—
664C23—68no—
665C23—68no—
666C23—616no—
667C23—62no—
668C23—62no—
669C23—62no—
670C23—62no—
671C23—68no—
672C23—92no—
673C23—181no—
674C23—182no—
675C23—181no—
676C23—182no—
677C23#379912yes—
678C23C4×D3212yes—
679C23D3×#6712yes—
680C23C22×D3211yescharacteristic
681D4—1816no—
682D4—188no—
683C2×C4—28no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—32no—
687C2×C4—34no—
688C2×C4—34no—
689C2×C4—32no—
690C2×C4—616no—
691C2×C4—616no—
692C2×C4—68no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—62no—
700C2×C4—92no—
701C2×C4—181no—
702C2×C4—181no—
703C2×C4—182no—
704C2×C4—182no—
705C2×C4—182no—
706C2×C4—364no—
707C2×C4D3×#6714yes—
708C2×C3—24no—
709C2×C3—24no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—22no—
713C2×C3—21no—
714C2×C3—22no—
715C2×C3—44no—
716C2×C3—68no—
717C2×C3C2×#89311yescharacteristic
718C2×C3C4×D3×D412yes—
719C2×C3D3×#12011yescharacteristic
720C2×C3#562712yes—
721C2×C3#565611yescharacteristic
722C2×C3C2×C4×#6711yescharacteristic
723C2×C3C2×C4×#6712yes—
724C2×C3#579111yescharacteristic
725C2×C3#579112yes—
726C2×C3C2×#95311yescharacteristic
727D3—28no—
728D3—122no—
729D3—122no—
730D3—242no—
731C22—22no—
732C22—24no—
733C22—22no—
734C22—24no—
735C22—38no—
736C22—632no—
737C22—64no—
738C22—64no—
739C22—64no—
740C22—64no—
741C22—64no—
742C22—64no—
743C22—182no—
744C22—184no—
745C22—361no—
746C22—362no—
747C22—361no—
748C22#6390414yescomplemented
749C22C2×#379911yescharacteristic
750C22C2×C4×D3211yescharacteristic
751C22D3×#23512yes—
752C22C2×D3×#6711yescharacteristic
753C22C2×D3×#6712yes—
754C4—24no—
755C4—34no—
756C4—62no—
757C4—64no—
758C4—121no—
759C4—121no—
760C4—182no—
761C4—362no—
762C3—21no—
763C3#7437911yescharacteristic, complemented
764C3C4×#95311yescharacteristic, complemented
765C2—24no—
766C2—68no—
767C2—362no—
768C2#1059489611yescharacteristic
769C2C2×#6390411yescharacteristic
770C2#1059500512yes—
771C2C4×D3×#6712yes—
772C2D3×#95311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63977C2
hypercenterC23×C4D32
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
3. C2×#63952C2semidirect
4. C2×#63904C2semidirect
5. #10592912C2semidirect
6. C3×#5210C2semidirect
7. #10591706C2semidirect
8. Dic3×#217C2semidirect
9. #10591382C2semidirect
10. #10591277C2semidirect
11. #10591237C2semidirect
23. C22×#624C22semidirect
25. C2×#3752C22semidirect
28. C2×C3×Dic3⋊C4C22semidirect
29. #63977C4semidirect
30. C2×#3724C22semidirect
31. C2×#3722C22semidirect
35. C2×Dic32C22semidirect
36. C2×Dic32C22semidirect
39. #63658C22semidirect
40. C3×C3⋊#95C22semidirect
41. #63579C22semidirect
43. C23×C4×D3D3semidirect
57. #5210D3semidirect
71. C23×C3×D3C2×C4semidirect
78. C2×#638C2×C4semidirect
82. C22×C3×Dic3D4semidirect
94. C2×C3×C4×D3D4semidirect
97. C2×#626C2×C4semidirect
103. C3×#217C2×C4semidirect
109. (C2×D3)⋊Dic3C2×C4semidirect
159. C2×Dic3⋊C4C2×D3semidirect
173. C3⋊#95C2×D3semidirect
184. C22×C3⋊D3C22×C4semidirect
207. C2×C3⋊Dic3C22×C4semidirect
216. C2×C3×Dic3C22×C4semidirect
251. C23×D3C4×D3semidirect
295. C22×Dic3#67semidirect
314. C2×C4×D3#67semidirect
325. #217C4×D3semidirect
345. C22×C32C4×D4semidirect
363. C2×C3×D3C4×D4semidirect
371. C3×Dic3#120semidirect
513. C2×Dic3C2×C4×D3semidirect
603. C22×C3#893semidirect
604. C22×C3C4×#67semidirect
637. C2×D3C4×#67semidirect
656. Dic3#953semidirect
657. C32C4×#120semidirect
748. C22#63904semidirect
763. C3#74379semidirect
764. C3C4×#953semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C2×#639772
C2×#639522
C2×#639042
#105929122
C3×#52102
#105917062
Dic3×#2172
#105913822
#105912772
#105912372
C4×#9533
#743793