Finite Group Databasebeta

← #11856282

Subgroups — #11856282

Order 1152.

2347 conjugacy classes of subgroups.

The subgroup lattice has 782 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×#63850C212yesmaximal, complemented
4#10592912C211yesmaximal, characteristic, complemented
5C3×#5210C211yesmaximal, characteristic, complemented
6#10591711C211yesmaximal, characteristic, complemented
7#10591706C211yesmaximal, characteristic, complemented
8#10591693C211yesmaximal, characteristic, complemented
9#10591382C212yesmaximal, complemented
10#10591294C212yesmaximal, complemented
11#10591277C212yesmaximal, complemented
12#84033—31nomaximal
13#74656—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×C4×D3—28no—
19C22×C3×C4×D3—24no—
20C22×C3×C4×D3C2212yes—
21C22×C3×C4×D3C2212yes—
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3752C2212yescomplemented
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×Dic3⋊C4C2212yescomplemented
29#63977—24no—
30C2×#3724C2212yescomplemented
31C2×#3722C2212yescomplemented
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36#63850—28no—
37#63658C2212yescomplemented
38C3×C3⋊#95C2212yescomplemented
39#63579C2212yescomplemented
40#63579C2212yescomplemented
41C24×C3×C4—31no—
42C23×C4×D3D311yescharacteristic, complemented
43C2×#953—31no—
44C2×#929—32no—
45C2×#894—32no—
46C2×#882—31no—
47C3×#385—31no—
48#5247—31no—
49#5213—31no—
50#5213—31no—
51#5213—31no—
52#5213—32no—
53#5213—61no—
54#5211—32no—
55#5210—31no—
56#5210—32no—
57#5210D311yescharacteristic, complemented
58#4989—32no—
59#4958—31no—
60#4955—31no—
61#4946—31no—
62#4665—32no—
63#4664—32no—
64C24×C32C2311yescharacteristic
65C23×C3⋊D3C2311yescharacteristic
66C23×C3×D3—22no—
67C23×C3×D3—22no—
68C23×C3×D3—24no—
69C23×C3×D3—24no—
70C23×C3×D3D414yes—
71C23×C3×D3C2311yescharacteristic
72C23×C3×D3C2311yescharacteristic
73C22×C32×C4—22no—
74C22×C32×C4—24no—
75C22×C32×C4C2312yes—
76C2×#638—22no—
77C2×#638—22no—
78C2×#638—22no—
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3×Dic3—22no—
82C22×C3×Dic3—24no—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C2×C3×C4×D3—232no—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3D418yescomplemented
94C2×#626—24no—
95C2×#626—22no—
96C2×#626—22no—
97C2×#626—24no—
98#3757—22no—
99#3752—24no—
100C3×#217—22no—
101C3×#217—22no—
102C3×Dic3⋊C4—24no—
103#3724—24no—
104#3722—24no—
105(C2×D3)⋊Dic3—24no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108(C2×D3)⋊Dic3—24no—
109#2849—91noSylow
110C25×C3—31no—
111C24×D3C2×D311yescharacteristic
112C23×C3×C4—21no—
113C23×C3×C4—32no—
114C23×C3×C4—31no—
115C23×C3×C4—32no—
116C23×C3×C4—68no—
117C23×C3×C4—64no—
118C23×C3×C4C2×D311yescharacteristic
119C23×C3×C4C2×D311yescharacteristic
120C22×#67—31no—
121C22×#67—31no—
122C22×#67—31no—
123C22×#67—31no—
124C22×#67—61no—
125C23×Dic3C2×D311yescharacteristic
126C22×D12—31no—
127C22×D12—31no—
128C22×C4×D3—24no—
129C22×C4×D3—28no—
130C22×C4×D3C2×D312yes—
131C22×C4×D3C2×D312yes—
132C2×C3×C4⋊C4—32no—
133C2×C3×C22⋊C4—31no—
134C2×C3×C22⋊C4—31no—
135#953—64no—
136C2×#217—31no—
137C2×#217—31no—
138C2×#217—31no—
139C2×#217—32no—
140C2×#217—31no—
141C2×#217—32no—
142C2×#217—61no—
143C2×#217C2×D311yescharacteristic
144C2×#217C2×D311yescharacteristic
145#929—68no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—62no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4C2×D312yescomplemented
158#894—68no—
159#882—64no—
160C3×#95—32no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—32no—
164C3⋊#95—32no—
165C3⋊#95—32no—
166C3⋊#95—32no—
167C3⋊#95—62no—
168C3⋊#95C2×D312yescomplemented
169C23×C32—22no—
170C23×C32—22no—
171C23×C32C2×D412yes—
172C23×C32#4112yes—
173C23×C32#4112yes—
174C23×C32C2411yescharacteristic
175C22×C3⋊D3—21no—
176C22×C3⋊D3—22no—
177C22×C3⋊D3—21no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—21no—
180C22×C3×D3—216no—
181C22×C3×D3—216no—
182C22×C3×D3—28no—
183C22×C3×D3—22no—
184C22×C3×D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C22×C3×D3—22no—
189C22×C3×D3—28no—
190C22×C3×D3—28no—
191C22×C3×D3C2×D414yes—
192C22×C3×D3C2×D412yes—
193C22×C3×D3C2×D412yes—
194C22×C3×D3#4114yes—
195C2×C32×C4—28no—
196C2×C32×C4—22no—
197C2×C32×C4—22no—
198C2×C32×C4C2×D414yes—
199#638—44no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3—21no—
206C2×C3×Dic3—28no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—22no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3C2×D414yes—
217C3×C4×D3—216no—
218C3×C4×D3—216no—
219#626—44no—
220#626—44no—
221C24×C4—31no—
222C2×#123—92no—
223C2×#120—91no—
224#386—92no—
225#386—91no—
226#386—91no—
227#385—31no—
228#385—91no—
229#385—92no—
230#381—92no—
231#379—91no—
232C24×C3—21no—
233C24×C3—31no—
234C24×C3—31no—
235C24×C3—34no—
236C24×C3—64no—
237C24×C3—64no—
238C24×C3—62no—
239C24×C3—62no—
240C24×C3C22×D311yescharacteristic
241C24×C3C22×D311yescharacteristic
242C23×D3—22no—
243C23×D3—22no—
244C23×D3—24no—
245C23×D3—24no—
246C23×D3—31no—
247C23×D3—31no—
248C23×D3—61no—
249C23×D3#6714yes—
250C23×D3C22×D311yescharacteristic
251C23×D3C22×D311yescharacteristic
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—24no—
255C22×C3×C4—24no—
256C22×C3×C4—22no—
257C22×C3×C4—32no—
258C22×C3×C4—38no—
259C22×C3×C4—31no—
260C22×C3×C4—32no—
261C22×C3×C4—31no—
262C22×C3×C4—44no—
263C22×C3×C4—42no—
264C22×C3×C4—64no—
265C22×C3×C4—64no—
266C22×C3×C4—64no—
267C22×C3×C4—64no—
268C22×C3×C4—632no—
269C22×C3×C4—64no—
270C22×C3×C4—62no—
271C22×C3×C4—64no—
272C22×C3×C4C22×D312yes—
273C22×C3×C4C22×D312yes—
274C2×#67—64no—
275C2×#67—62no—
276C2×#67—62no—
277C2×#67—64no—
278C2×#67—64no—
279C2×#67—62no—
280C2×#67—62no—
281C2×#67—62no—
282C2×#67—62no—
283C2×#67—62no—
284C2×#67—62no—
285C2×#67—122no—
286C2×#67—122no—
287C22×Dic3—22no—
288C22×Dic3—24no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—32no—
292C22×Dic3—32no—
293C22×Dic3—61no—
294C22×Dic3—62no—
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D312yes—
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D312yes—
299C2×D12—64no—
300C2×D12—62no—
301C2×D12—62no—
302C2×D12—64no—
303C2×C4×D3—232no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3#6718yescomplemented
310C3×C4⋊C4—64no—
311C3×C22⋊C4—62no—
312C3×C22⋊C4—62no—
313#217—22no—
314#217—22no—
315#217—64no—
316#217—64no—
317#217—62no—
318#217—62no—
319#217—62no—
320#217—62no—
321#217—122no—
322(C2×D3)⋊C4—64no—
323(C2×D3)⋊C4—64no—
324(C2×D3)⋊C4—62no—
325(C2×D3)⋊C4—62no—
326(C2×D3)⋊C4—64no—
327(C2×D3)⋊C4—64no—
328(C2×D3)⋊C4—64no—
329(C2×D3)⋊C4—64no—
330(C2×D3)⋊C4—124no—
331Dic3⋊C4—24no—
332Dic3⋊C4—64no—
333Dic3⋊C4—64no—
334C22×C32—22no—
335C22×C32—22no—
336C22×C32—24no—
337C22×C32—24no—
338C22×C32#12314yescomplemented
339C22×C32C22×D411yescharacteristic
340C22×C32C22×D412yes—
341C22×C32C2×#4111yescharacteristic
342C22×C32C2×#4111yescharacteristic
343C22×C32C2×#4112yes—
344C2×C3⋊D3—41no—
345C2×C3⋊D3—42no—
346C2×C3⋊D3—41no—
347C2×C3⋊D3—41no—
348C2×C3⋊D3—42no—
349C2×C3×D3—232no—
350C2×C3×D3—22no—
351C2×C3×D3—22no—
352C2×C3×D3—22no—
353C2×C3×D3—22no—
354C2×C3×D3—24no—
355C2×C3×D3—24no—
356C2×C3×D3—24no—
357C2×C3×D3—24no—
358C2×C3×D3#12014yes—
359C2×C3×D3#12314yescomplemented
360C32×C4—24no—
361C3⋊Dic3—41no—
362C3⋊Dic3—42no—
363C3×Dic3—24no—
364C3×Dic3—41no—
365C3×Dic3—41no—
366C3×Dic3—42no—
367C25—31no—
368C22×D4—91no—
369C22×D4—91no—
370C22×D4—91no—
371C23×C4—32no—
372C23×C4—31no—
373C23×C4—32no—
374C23×C4—68no—
375C23×C4—64no—
376C23×C4D3211yescharacteristic
377#123—188no—
378#120—184no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—92no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—92no—
384C2×C22⋊C4—91no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4—92no—
387C2×C22⋊C4—92no—
388C2×C22⋊C4—91no—
389C2×C22⋊C4—92no—
390#95—32no—
391#95—92no—
392#95—92no—
393#95—92no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—21no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—34no—
403C23×C3—32no—
404C23×C3—32no—
405C23×C3—34no—
406C23×C3—42no—
407C23×C3—42no—
408C23×C3—68no—
409C23×C3—68no—
410C23×C3—616no—
411C23×C3—616no—
412C23×C3—68no—
413C23×C3—61no—
414C23×C3—61no—
415C23×C3—62no—
416C23×C3—61no—
417C23×C3—61no—
418C23×C3—62no—
419C23×C3#23512yes—
420C23×C3#23512yes—
421C23×C3#23512yes—
422C23×C3D3×D412yes—
423C23×C3#23912yes—
424C23×C3C2×#6712yes—
425C23×C3C23×D311yescharacteristic
426C23×C3C23×D311yescharacteristic
427C22×D3—216no—
428C22×D3—216no—
429C22×D3—28no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—28no—
437C22×D3—28no—
438C22×D3—62no—
439C22×D3—62no—
440C22×D3—61no—
441C22×D3—61no—
442C22×D3—61no—
443C22×D3—62no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—62no—
447C22×D3—62no—
448C22×D3—61no—
449C22×D3—122no—
450C22×D3—121no—
451C22×D3—121no—
452C22×D3—122no—
453C22×D3#23514yes—
454C22×D3C2×#6712yes—
455C22×D3C2×#6712yes—
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—34no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—48no—
468C2×C3×C4—616no—
469C2×C3×C4—616no—
470C2×C3×C4—68no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—62no—
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×C4D3×D414yes—
481C2×C3×C4C2×#6714yes—
482#67—124no—
483#67—124no—
484#67—128no—
485#67—124no—
486#67—124no—
487C2×Dic3—28no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—62no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—62no—
504C2×Dic3—61no—
505C2×Dic3—62no—
506C2×Dic3—61no—
507C2×Dic3—62no—
508C2×Dic3—62no—
509C2×Dic3—61no—
510C2×Dic3—121no—
511C2×Dic3—121no—
512C2×Dic3—122no—
513C2×Dic3—122no—
514C2×Dic3—122no—
515C2×Dic3C2×#6714yes—
516D12—124no—
517D12—124no—
518C4×D3—216no—
519C4×D3—216no—
520C2×C32—24no—
521C2×C32C2×#12011yescharacteristic
522C2×C32C2×#12311yescharacteristic
523C2×C32C2×#12311yescharacteristic
524C2×C32#52512yes—
525C2×C32#52512yes—
526C3⋊D3—81no—
527C3×D3—24no—
528C3×D3—24no—
529C24—31no—
530C24—31no—
531C24—34no—
532C24—64no—
533C24—64no—
534C24—62no—
535C24—62no—
536C24—91no—
537C24C2×D3211yescharacteristic
538C2×D4—182no—
539C2×D4—182no—
540C2×D4—184no—
541C2×D4—184no—
542C2×D4—182no—
543C2×D4—182no—
544C2×D4—182no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—32no—
548C22×C4—38no—
549C22×C4—31no—
550C22×C4—32no—
551C22×C4—31no—
552C22×C4—64no—
553C22×C4—64no—
554C22×C4—64no—
555C22×C4—64no—
556C22×C4—632no—
557C22×C4—64no—
558C22×C4—62no—
559C22×C4—64no—
560C22×C4—91no—
561C22×C4—92no—
562C22×C4C2×D3212yes—
563C4⋊C4—64no—
564C4⋊C4—184no—
565C22⋊C4—62no—
566C22⋊C4—62no—
567C22⋊C4—184no—
568C22⋊C4—182no—
569C22⋊C4—182no—
570C22⋊C4—184no—
571C22⋊C4—184no—
572C22⋊C4—182no—
573C22⋊C4—184no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—24no—
577C22×C3—24no—
578C22×C3—24no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—24no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—21no—
587C22×C3—24no—
588C22×C3—34no—
589C22×C3—34no—
590C22×C3—42no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—42no—
594C22×C3—632no—
595C22×C3—62no—
596C22×C3—62no—
597C22×C3—62no—
598C22×C3—64no—
599C22×C3—64no—
600C22×C3—62no—
601C22×C3—64no—
602C22×C3—64no—
603C22×C3#89414yescomplemented
604C22×C3#92914yescomplemented
605C22×C3C2×#23511yescharacteristic
606C22×C3C2×#23511yescharacteristic
607C22×C3C2×#23511yescharacteristic
608C22×C3C2×#23512yes—
609C22×C3C2×D3×D411yescharacteristic
610C22×C3C2×D3×D412yes—
611C22×C3C2×#23911yescharacteristic
612C22×C3D3×#4112yes—
613C22×C3C22×#6711yescharacteristic
614C22×C3C22×#6712yes—
615C2×D3—232no—
616C2×D3—22no—
617C2×D3—22no—
618C2×D3—22no—
619C2×D3—24no—
620C2×D3—24no—
621C2×D3—24no—
622C2×D3—24no—
623C2×D3—22no—
624C2×D3—122no—
625C2×D3—124no—
626C2×D3—121no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—122no—
631C2×D3—122no—
632C2×D3—122no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—122no—
636C2×D3—242no—
637C2×D3—241no—
638C2×D3—241no—
639C2×D3#92914yescomplemented
640C2×D3#95314yes—
641C3×C4—24no—
642C3×C4—24no—
643C3×C4—44no—
644C3×C4—64no—
645C3×C4—121no—
646C3×C4—122no—
647C3×C4—121no—
648Dic3—24no—
649Dic3—41no—
650Dic3—42no—
651Dic3—41no—
652Dic3—122no—
653Dic3—121no—
654Dic3—121no—
655Dic3—122no—
656Dic3—122no—
657Dic3—242no—
658C32#284911yescharacteristic, complemented, Sylow
659C23—22no—
660C23—22no—
661C23—34no—
662C23—34no—
663C23—32no—
664C23—32no—
665C23—68no—
666C23—68no—
667C23—616no—
668C23—616no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—62no—
674C23—62no—
675C23—68no—
676C23—181no—
677C23—181no—
678C23—182no—
679C23—182no—
680C23—181no—
681C23#379812yes—
682C23#379912yes—
683C23D3×#6712yes—
684C23C22×D3211yescharacteristic
685D4—364no—
686D4—364no—
687D4—364no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—34no—
692C2×C4—616no—
693C2×C4—616no—
694C2×C4—68no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—181no—
705C2×C4—182no—
706C2×C4—181no—
707C2×C4—182no—
708C2×C4—182no—
709C2×C4—181no—
710C2×C4D3×#6714yes—
711C2×C3—24no—
712C2×C3—24no—
713C2×C3—21no—
714C2×C3—22no—
715C2×C3—22no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—44no—
719C2×C3—64no—
720C2×C3—64no—
721C2×C3C2×#89411yescharacteristic
722C2×C3#554712yes—
723C2×C3D3×#12011yescharacteristic
724C2×C3#562712yes—
725C2×C3D3×#12311yescharacteristic
726C2×C3C2×#92911yescharacteristic
727C2×C3C2×#92911yescharacteristic
728C2×C3#579112yes—
729C2×C3#579112yes—
730C2×C3C2×#95311yescharacteristic
731D3—24no—
732D3—24no—
733D3—242no—
734D3—241no—
735D3—241no—
736C22—24no—
737C22—24no—
738C22—22no—
739C22—22no—
740C22—34no—
741C22—34no—
742C22—632no—
743C22—62no—
744C22—62no—
745C22—64no—
746C22—64no—
747C22—64no—
748C22—64no—
749C22—62no—
750C22—62no—
751C22—361no—
752C22—362no—
753C22—362no—
754C22—361no—
755C22—361no—
756C22#6385014yescomplemented
757C22C2×#379811yescharacteristic
758C22C2×#379911yescharacteristic
759C22D3×#23512yes—
760C22C2×D3×#6711yescharacteristic
761C22C2×D3×#6712yes—
762C4—24no—
763C4—64no—
764C4—122no—
765C4—121no—
766C4—121no—
767C4—361no—
768C4—362no—
769C3—21no—
770C3#7465611yescharacteristic, complemented
771C3#8403311yescharacteristic, complemented
772C2—24no—
773C2—64no—
774C2—64no—
775C2—721no—
776C2C2×#6385011yescharacteristic
777C2#1059500212yes—
778C2#1059500512yes—
779C2D3×#92911yescharacteristic
780C2D3×#95311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC2×#63977C2
hypercenterC23×C4D32
hypocenterC32#2849
LCSG ▷ C23×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×#63850C2semidirect
4. #10592912C2semidirect
5. C3×#5210C2semidirect
6. #10591711C2semidirect
7. #10591706C2semidirect
8. #10591693C2semidirect
9. #10591382C2semidirect
10. #10591294C2semidirect
11. #10591277C2semidirect
25. C2×#3752C22semidirect
28. C2×C3×Dic3⋊C4C22semidirect
30. C2×#3724C22semidirect
31. C2×#3722C22semidirect
37. #63658C22semidirect
38. C3×C3⋊#95C22semidirect
39. #63579C22semidirect
40. #63579C22semidirect
42. C23×C4×D3D3semidirect
57. #5210D3semidirect
93. C2×C3×C4×D3D4semidirect
157. C2×Dic3⋊C4C2×D3semidirect
168. C3⋊#95C2×D3semidirect
309. C2×C4×D3#67semidirect
338. C22×C32#123semidirect
359. C2×C3×D3#123semidirect
603. C22×C3#894semidirect
604. C22×C3#929semidirect
639. C2×D3#929semidirect
658. C32#2849semidirect
756. C22#63850semidirect
770. C3#74656semidirect
771. C3#84033semidirect

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×#638502
#105929122
C3×#52102
#105917112
#105917062
#105916932
#105913822
#105912942
#105912772
#840333
#746563