Finite Group Databasebeta

← #11856291

Subgroups — #11856291

Order 1152.

2321 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#882C211yesmaximal, characteristic
3C2×#63884C212yesmaximal, complemented
4#10592645C211yesmaximal, characteristic, complemented
5C3×#4946C211yesmaximal, characteristic, complemented
6#10591713C211yesmaximal, characteristic, complemented
7#10591710C211yesmaximal, characteristic, complemented
8#10591706C211yesmaximal, characteristic, complemented
9#10591376C212yesmaximal, complemented
10#10591372C212yesmaximal, complemented
11#10591362C212yesmaximal, complemented
12#82602—31nomaximal
13#74656—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×D3×Dic3—28no—
21C22×D3×Dic3—24no—
22C22×D3×Dic3C2212yes—
23C22×D3×Dic3C2212yes—
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3750C2212yescomplemented
27C2×C3×#217C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2212yescomplemented
31C3×#882—24no—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yescomplemented
35C2×(C2×D3)⋊Dic3C2212yescomplemented
36#63884—28no—
37#63658C2212yescomplemented
38C3×C3⋊#95C2212yescomplemented
39#63579C2212yescomplemented
40#63579C2212yescomplemented
41C24×Dic3—31no—
42C23×C4×D3—31no—
43C2×C3×#120—31no—
44C2×#935—32no—
45C2×#894—32no—
46C2×#882D311yescharacteristic
47C3×#385—31no—
48#5247—31no—
49#5220—31no—
50#5220—31no—
51#5220—32no—
52#5213—31no—
53#4989—32no—
54#4958—31no—
55#4955—31no—
56#4946—31no—
57#4946—31no—
58#4946—32no—
59#4946—61no—
60#4946D311yescharacteristic, complemented
61#4943—32no—
62#4665—32no—
63#4664—32no—
64C24×C32C2311yescharacteristic
65C23×C3×D3—22no—
66C23×C3×D3—22no—
67C23×C3×D3—24no—
68C23×C3×D3—24no—
69C23×C3×D3D414yes—
70C23×C3×D3C2311yescharacteristic
71C23×C3×D3C2311yescharacteristic
72C23×C3×D3C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3—22no—
76C22×C3⋊Dic3—24no—
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2312yes—
79C2×C3×#67—22no—
80C2×C3×#67—22no—
81C2×C3×#67—22no—
82C22×C3×Dic3—22no—
83C22×C3×Dic3—24no—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C2×C3×D12—22no—
88C2×C3×D12—22no—
89C2×C3×D12—24no—
90C2×C3×D12—24no—
91C2×D3×Dic3—232no—
92C2×D3×Dic3—24no—
93C2×D3×Dic3—24no—
94C2×D3×Dic3—24no—
95C2×D3×Dic3—24no—
96C2×D3×Dic3—24no—
97C2×D3×Dic3D418yescomplemented
98C32×C22⋊C4—22no—
99#3757—22no—
100#3750—24no—
101C3×#217—22no—
102C3×(C2×D3)⋊C4—22no—
103C3×(C2×D3)⋊C4—22no—
104C3×Dic3⋊C4—24no—
105(C2×D3)⋊Dic3—24no—
106(C2×D3)⋊Dic3—24no—
107(C2×D3)⋊Dic3—24no—
108(C2×D3)⋊Dic3—24no—
109#2849—91noSylow
110C25×C3—31no—
111C24×D3C2×D311yescharacteristic
112C22×C3×D4—31no—
113C22×C3×D4—31no—
114C22×C3×D4—31no—
115C23×C3×C4—31no—
116C22×#67C2×D311yescharacteristic
117C23×Dic3—32no—
118C23×Dic3—31no—
119C23×Dic3—31no—
120C23×Dic3—32no—
121C23×Dic3—61no—
122C23×Dic3—68no—
123C23×Dic3—64no—
124C23×Dic3C2×D311yescharacteristic
125C22×D12C2×D311yescharacteristic
126C22×D12C2×D311yescharacteristic
127C22×C4×D3—32no—
128C22×C4×D3—32no—
129C22×C4×D3—68no—
130C22×C4×D3—64no—
131C3×#120—64no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4C2×D311yescharacteristic
138C2×C3×C22⋊C4C2×D311yescharacteristic
139C2×#217—31no—
140C2×#217—31no—
141C2×#217—32no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—32no—
145C2×#217—61no—
146C2×#217C2×D311yescharacteristic
147#935—68no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4C2×D311yescharacteristic
153C2×(C2×D3)⋊C4C2×D311yescharacteristic
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—62no—
157C2×Dic3⋊C4C2×D312yescomplemented
158#894—68no—
159#882—24no—
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—216no—
176C22×C3×D3—216no—
177C22×C3×D3—28no—
178C22×C3×D3—22no—
179C22×C3×D3—21no—
180C22×C3×D3—21no—
181C22×C3×D3—21no—
182C22×C3×D3—21no—
183C22×C3×D3—22no—
184C22×C3×D3—28no—
185C22×C3×D3—28no—
186C22×C3×D3—22no—
187C22×C3×D3—21no—
188C22×C3×D3—22no—
189C22×C3×D3—21no—
190C22×C3×D3—21no—
191C22×C3×D3C2×D414yes—
192C22×C3×D3C2×D412yes—
193C22×C3×D3C2×D412yes—
194C22×C3×D3#4114yes—
195C2×C32×C4—22no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—22no—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3—28no—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3C2×D414yes—
206C3×#67—44no—
207C2×C3×Dic3—28no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3C2×D414yes—
217C3×D12—44no—
218C3×D12—44no—
219D3×Dic3—216no—
220D3×Dic3—216no—
221C24×C4—91no—
222C2×#123—92no—
223C2×#120—31no—
224#386—92no—
225#386—91no—
226#386—91no—
227#385—31no—
228#385—92no—
229#385—91no—
230#381—92no—
231#379—91no—
232C24×C3—21no—
233C24×C3—31no—
234C24×C3—31no—
235C24×C3—34no—
236C24×C3—31no—
237C24×C3—64no—
238C24×C3—64no—
239C24×C3—62no—
240C24×C3—62no—
241C24×C3C22×D311yescharacteristic
242C24×C3C22×D311yescharacteristic
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—24no—
246C23×D3—24no—
247C23×D3#6714yes—
248C23×D3C22×D311yescharacteristic
249C23×D3C22×D311yescharacteristic
250C23×D3C22×D311yescharacteristic
251C2×C3×D4—64no—
252C2×C3×D4—62no—
253C2×C3×D4—62no—
254C2×C3×D4—64no—
255C2×C3×D4—62no—
256C2×C3×D4—62no—
257C2×C3×D4—62no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—32no—
261C22×C3×C4—31no—
262C22×C3×C4—32no—
263C22×C3×C4—64no—
264C22×C3×C4—62no—
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D311yescharacteristic
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C22×D311yescharacteristic
269C2×#67—22no—
270C2×#67—22no—
271C2×#67—22no—
272C22×Dic3—22no—
273C22×Dic3—24no—
274C22×Dic3—32no—
275C22×Dic3—32no—
276C22×Dic3—38no—
277C22×Dic3—32no—
278C22×Dic3—32no—
279C22×Dic3—62no—
280C22×Dic3—62no—
281C22×Dic3—64no—
282C22×Dic3—64no—
283C22×Dic3—64no—
284C22×Dic3—64no—
285C22×Dic3—632no—
286C22×Dic3—64no—
287C22×Dic3—64no—
288C22×Dic3—62no—
289C22×Dic3—62no—
290C22×Dic3—64no—
291C22×Dic3—124no—
292C22×Dic3—122no—
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D312yes—
295C22×Dic3C22×D312yes—
296C2×D12—24no—
297C2×D12—24no—
298C2×D12—22no—
299C2×D12—22no—
300C2×C4×D3—38no—
301C2×C4×D3—64no—
302C2×C4×D3—64no—
303C2×C4×D3—632no—
304C2×C4×D3—64no—
305C2×C4×D3—64no—
306C2×C4×D3—64no—
307C3×C4⋊C4—64no—
308C3×C22⋊C4—22no—
309C3×C22⋊C4—22no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—62no—
312C3×C22⋊C4—62no—
313C3×C22⋊C4—62no—
314#217—22no—
315#217—64no—
316#217—64no—
317#217—64no—
318#217—64no—
319#217—62no—
320#217—62no—
321#217—64no—
322(C2×D3)⋊C4—22no—
323(C2×D3)⋊C4—22no—
324(C2×D3)⋊C4—64no—
325(C2×D3)⋊C4—64no—
326(C2×D3)⋊C4—64no—
327(C2×D3)⋊C4—64no—
328Dic3⋊C4—24no—
329Dic3⋊C4—64no—
330Dic3⋊C4—64no—
331Dic3⋊C4—124no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—24no—
335C22×C32—24no—
336C22×C32#12314yescomplemented
337C22×C32C22×D412yes—
338C22×C32C22×D411yescharacteristic
339C22×C32C2×#4111yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C22×C32C2×#4112yes—
342C2×C3×D3—232no—
343C2×C3×D3—22no—
344C2×C3×D3—22no—
345C2×C3×D3—22no—
346C2×C3×D3—22no—
347C2×C3×D3—24no—
348C2×C3×D3—24no—
349C2×C3×D3—24no—
350C2×C3×D3—24no—
351C2×C3×D3—41no—
352C2×C3×D3—41no—
353C2×C3×D3—41no—
354C2×C3×D3—42no—
355C2×C3×D3—42no—
356C2×C3×D3#12014yes—
357C2×C3×D3#12314yescomplemented
358C32×C4—41no—
359C32×C4—41no—
360C3⋊Dic3—24no—
361C3⋊Dic3—42no—
362C3×Dic3—24no—
363C3×Dic3—41no—
364C3×Dic3—42no—
365C25—31no—
366C22×D4—31no—
367C22×D4—31no—
368C22×D4—31no—
369C23×C4—31no—
370C23×C4—92no—
371C23×C4—92no—
372C23×C4—91no—
373C23×C4—188no—
374C23×C4—184no—
375#123—188no—
376#120—64no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4—92no—
379C2×C22⋊C4—31no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—92no—
383C2×C22⋊C4—92no—
384C2×C22⋊C4—92no—
385C2×C22⋊C4—92no—
386C2×C22⋊C4—91no—
387C2×C22⋊C4D3211yescharacteristic
388#95—32no—
389#95—92no—
390#95—92no—
391#95—92no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—21no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—34no—
401C23×C3—32no—
402C23×C3—32no—
403C23×C3—34no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—68no—
407C23×C3—68no—
408C23×C3—616no—
409C23×C3—616no—
410C23×C3—68no—
411C23×C3—61no—
412C23×C3—61no—
413C23×C3—62no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3—62no—
417C23×C3—61no—
418C23×C3—62no—
419C23×C3—61no—
420C23×C3—61no—
421C23×C3—62no—
422C23×C3#23512yes—
423C23×C3D3×D412yes—
424C23×C3#23712yes—
425C23×C3#23712yes—
426C23×C3#23912yes—
427C23×C3C2×#6712yes—
428C23×C3C23×D311yescharacteristic
429C23×C3C23×D311yescharacteristic
430C22×D3—216no—
431C22×D3—216no—
432C22×D3—28no—
433C22×D3—22no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—22no—
439C22×D3—28no—
440C22×D3—28no—
441C22×D3—22no—
442C22×D3—22no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3D3×D414yes—
447C22×D3#23714yes—
448C22×D3C2×#6712yes—
449C22×D3C2×#6712yes—
450C3×D4—124no—
451C3×D4—124no—
452C3×D4—124no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—34no—
462C2×C3×C4—42no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—42no—
466C2×C3×C4—68no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—61no—
470C2×C3×C4—62no—
471C2×C3×C4—61no—
472C2×C3×C4—62no—
473C2×C3×C4—62no—
474C2×C3×C4—61no—
475#67—44no—
476C2×Dic3—28no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—21no—
485C2×Dic3—34no—
486C2×Dic3—34no—
487C2×Dic3—64no—
488C2×Dic3—616no—
489C2×Dic3—616no—
490C2×Dic3—68no—
491C2×Dic3—68no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3—62no—
495C2×Dic3—62no—
496C2×Dic3—64no—
497C2×Dic3—62no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3—122no—
504C2×Dic3—122no—
505C2×Dic3—122no—
506C2×Dic3—122no—
507C2×Dic3—128no—
508C2×Dic3D3×D414yes—
509D12—44no—
510D12—44no—
511C4×D3—616no—
512C4×D3—616no—
513C2×C32—24no—
514C2×C32C2×#12011yescharacteristic
515C2×C32C2×#12311yescharacteristic
516C2×C32C2×#12311yescharacteristic
517C2×C32#52512yes—
518C2×C32#52512yes—
519C3×D3—24no—
520C3×D3—24no—
521C3×D3—81no—
522C24—31no—
523C24—31no—
524C24—34no—
525C24—31no—
526C24—64no—
527C24—64no—
528C24—62no—
529C24—62no—
530C24C2×D3211yescharacteristic
531C2×D4—62no—
532C2×D4—62no—
533C2×D4—64no—
534C2×D4—64no—
535C2×D4—62no—
536C2×D4—62no—
537C2×D4—62no—
538C22×C4—32no—
539C22×C4—32no—
540C22×C4—31no—
541C22×C4—64no—
542C22×C4—62no—
543C22×C4—98no—
544C22×C4—92no—
545C22×C4—92no—
546C22×C4—184no—
547C22×C4—184no—
548C22×C4—184no—
549C22×C4—184no—
550C22×C4—184no—
551C22×C4—1832no—
552C22×C4—184no—
553C22×C4—182no—
554C22×C4C2×D3211yescharacteristic
555C22×C4C2×D3211yescharacteristic
556C4⋊C4—64no—
557C4⋊C4—184no—
558C22⋊C4—22no—
559C22⋊C4—62no—
560C22⋊C4—62no—
561C22⋊C4—62no—
562C22⋊C4—184no—
563C22⋊C4—184no—
564C22⋊C4—184no—
565C22⋊C4—184no—
566C22⋊C4—182no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—24no—
571C22×C3—24no—
572C22×C3—24no—
573C22×C3—22no—
574C22×C3—24no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—21no—
580C22×C3—24no—
581C22×C3—34no—
582C22×C3—34no—
583C22×C3—42no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—42no—
587C22×C3—632no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—62no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—62no—
594C22×C3—64no—
595C22×C3—64no—
596C22×C3—121no—
597C22×C3—121no—
598C22×C3—122no—
599C22×C3—121no—
600C22×C3—122no—
601C22×C3#89414yescomplemented
602C22×C3#93514yescomplemented
603C22×C3C2×#23511yescharacteristic
604C22×C3C2×D3×D412yes—
605C22×C3C2×D3×D412yes—
606C22×C3C2×D3×D411yescharacteristic
607C22×C3C2×#23711yescharacteristic
608C22×C3C2×#23711yescharacteristic
609C22×C3C2×#23712yes—
610C22×C3C2×#23911yescharacteristic
611C22×C3D3×#4112yes—
612C22×C3C22×#6711yescharacteristic
613C2×D3—232no—
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—22no—
617C2×D3—22no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—24no—
621C2×D3—24no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3#93514yescomplemented
628C2×D3#93714yes—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—64no—
634C3×C4—81no—
635C3×C4—81no—
636C3×C4—121no—
637C3×C4—122no—
638Dic3—24no—
639Dic3—41no—
640Dic3—42no—
641Dic3—64no—
642Dic3—64no—
643Dic3—124no—
644Dic3—124no—
645Dic3—122no—
646Dic3—122no—
647C32#284911yescharacteristic, complemented, Sylow
648C23—22no—
649C23—22no—
650C23—34no—
651C23—34no—
652C23—32no—
653C23—32no—
654C23—68no—
655C23—68no—
656C23—616no—
657C23—616no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23—61no—
662C23—62no—
663C23—62no—
664C23—68no—
665C23—61no—
666C23—61no—
667C23—62no—
668C23—62no—
669C23—61no—
670C23#379512yes—
671C23#379612yes—
672C23D3×#6712yes—
673C23C22×D3211yescharacteristic
674D4—124no—
675D4—124no—
676D4—124no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—34no—
682C2×C4—68no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—61no—
691C2×C4—94no—
692C2×C4—1816no—
693C2×C4—1816no—
694C2×C4—188no—
695C2×C4—182no—
696C2×C4—182no—
697C2×C4—182no—
698C2×C4—182no—
699C2×C4—182no—
700C2×C3—24no—
701C2×C3—24no—
702C2×C3—22no—
703C2×C3—22no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—44no—
708C2×C3—64no—
709C2×C3—64no—
710C2×C3—241no—
711C2×C3C2×#89411yescharacteristic
712C2×C3#554712yes—
713C2×C3#558612yes—
714C2×C3#558612yes—
715C2×C3D3×#12011yescharacteristic
716C2×C3#562712yes—
717C2×C3D3×#12311yescharacteristic
718C2×C3C2×#93511yescharacteristic
719C2×C3C2×#93511yescharacteristic
720C2×C3C2×#93711yescharacteristic
721D3—24no—
722D3—24no—
723D3—81no—
724C22—24no—
725C22—24no—
726C22—22no—
727C22—22no—
728C22—34no—
729C22—34no—
730C22—632no—
731C22—64no—
732C22—64no—
733C22—64no—
734C22—64no—
735C22—62no—
736C22—62no—
737C22—62no—
738C22—62no—
739C22—122no—
740C22—122no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22#6388414yescomplemented
745C22C2×#379511yescharacteristic
746C22C2×#379611yescharacteristic
747C22D32×D412yes—
748C22D3×#23712yes—
749C22C2×D3×#6711yescharacteristic
750C4—41no—
751C4—41no—
752C4—64no—
753C4—122no—
754C4—121no—
755C4—184no—
756C4—362no—
757C3—21no—
758C3#7465611yescharacteristic, complemented
759C3#8260211yescharacteristic, complemented
760C2—24no—
761C2—64no—
762C2—64no—
763C2—241no—
764C2#1059405412yes—
765C2#1059405512yes—
766C2C2×#6388411yescharacteristic
767C2D3×#93511yescharacteristic
768C2D3×#93711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×C3×#882C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D3×Dic3C2semidirect
3. C2×#63884C2semidirect
4. #10592645C2semidirect
5. C3×#4946C2semidirect
6. #10591713C2semidirect
7. #10591710C2semidirect
8. #10591706C2semidirect
9. #10591376C2semidirect
10. #10591372C2semidirect
11. #10591362C2semidirect
26. C2×#3750C22semidirect
30. C2×C3×Dic3⋊C4C22semidirect
34. C2×(C2×D3)⋊Dic3C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
37. #63658C22semidirect
38. C3×C3⋊#95C22semidirect
39. #63579C22semidirect
40. #63579C22semidirect
60. #4946D3semidirect
97. C2×D3×Dic3D4semidirect
157. C2×Dic3⋊C4C2×D3semidirect
168. C3⋊#95C2×D3semidirect
336. C22×C32#123semidirect
357. C2×C3×D3#123semidirect
601. C22×C3#894semidirect
602. C22×C3#935semidirect
627. C2×D3#935semidirect
647. C32#2849semidirect
744. C22#63884semidirect
758. C3#74656semidirect
759. C3#82602semidirect

Maximal subgroups

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

subgroupindex
C23×D3×Dic32
C2×C3×#8822
C2×#638842
#105926452
C3×#49462
#105917132
#105917102
#105917062
#105913762
#105913722
#105913622
#826023
#746563