Finite Group Databasebeta

← #11809008

Subgroups — #11809008

Order 1152.

3459 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic, complemented
2C22×D3×#67C211yesmaximal, characteristic, complemented
3C2×#64162C211yesmaximal, characteristic, complemented
4C2×C3×#953C211yesmaximal, characteristic, complemented
5C2×#63983C212yesmaximal, complemented
6#10591724C212yesmaximal, complemented
7#10591723C212yesmaximal, complemented
8#10591721C212yesmaximal, complemented
9#10591711C211yesmaximal, characteristic, complemented
10#10591710C211yesmaximal, characteristic, complemented
11#10591706C211yesmaximal, characteristic, complemented
12#84052—31nomaximal
13#82604—31nomaximal
14C25×C32C2211yescharacteristic, complemented
15C24×C3×D3C2211yescharacteristic
16C23×D32C2211yescharacteristic, complemented
17C22×#638C2211yescharacteristic
18C22×#638C2212yescomplemented
19C22×C3×#67—28no—
20C22×C3×#67—24no—
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2212yes—
23C22×C3×#67C2212yescomplemented
24C22×C3×#67C2212yescomplemented
25C23×C3×Dic3C2211yescharacteristic, complemented
26C2×D3×#67—24no—
27C2×D3×#67—24no—
28C2×D3×#67—24no—
29C22×#626C2211yescharacteristic, complemented
30C22×#625C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic, complemented
32#64162—24no—
33C2×#3757C2211yescharacteristic, complemented
34C2×#3757C2212yescomplemented
35C3×#953—24no—
36C2×C3×#217C2211yescharacteristic, complemented
37C2×C3×#217C2212yescomplemented
38#63983—28no—
39C2×#3722C2212yescomplemented
40C2×(C2×D3)⋊Dic3C2212yescomplemented
41C2×(C2×D3)⋊Dic3C2212yescomplemented
42C2×(C2×D3)⋊Dic3C2212yescomplemented
43#63579C2212yescomplemented
44#63579C2212yescomplemented
45C23×C3×D4—31no—
46C23×#67—31no—
47C23×#67D311yescharacteristic, complemented
48C22×D3×D4—31no—
49C2×C3×#120—31no—
50C2×#953—31no—
51C2×#953—31no—
52C2×#953—61no—
53C2×#953D311yescharacteristic, complemented
54C2×#937—32no—
55C2×#937—32no—
56#5247—31no—
57#5223—32no—
58#5223—32no—
59#5223—32no—
60#5220—31no—
61#5220—32no—
62#5213—31no—
63#5213—31no—
64#4960—32no—
65#4958—31no—
66#4956—32no—
67#4955—31no—
68C24×C32—22no—
69C24×C32—24no—
70C24×C32—22no—
71C24×C32—22no—
72C24×C32—42no—
73C24×C32C2312yes—
74C24×C32C2311yescharacteristic
75C23×C3⋊D3C2311yescharacteristic
76C23×C3×D3—22no—
77C23×C3×D3—22no—
78C23×C3×D3—24no—
79C23×C3×D3—42no—
80C23×C3×D3D414yescomplemented
81C23×C3×D3C2311yescharacteristic
82C23×C3×D3C2311yescharacteristic
83C23×C3×D3C2311yescharacteristic
84C22×D32—22no—
85C22×D32—22no—
86C22×D32—22no—
87C22×D32—24no—
88C22×D32—42no—
89C2×#638—22no—
90C2×#638—22no—
91C2×#638—24no—
92C2×#638—24no—
93C2×#638—42no—
94C2×#638D414yescomplemented
95C22×C3⋊Dic3C2312yes—
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C3×#67—232no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67—24no—
101C2×C3×#67—24no—
102C2×C3×#67—24no—
103C2×C3×#67—24no—
104C2×C3×#67—24no—
105C2×C3×#67—24no—
106C2×C3×#67—24no—
107C2×C3×#67—42no—
108C2×C3×#67D418yescomplemented
109C2×C3×#67D414yescomplemented
110C22×C3×Dic3—22no—
111C22×C3×Dic3—24no—
112C22×C3×Dic3C2312yes—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2312yes—
115D3×#67—232no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#625—22no—
120C2×#625—22no—
121C2×#625—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125#3757—22no—
126#3757—24no—
127C3×#217—22no—
128C3×#217—24no—
129#3722—24no—
130(C2×D3)⋊Dic3—24no—
131(C2×D3)⋊Dic3—24no—
132(C2×D3)⋊Dic3—42no—
133#2403—91noSylow
134C25×C3—21no—
135C25×C3—31no—
136C25×C3C2×D311yescharacteristic, complemented
137C25×C3C2×D311yescharacteristic, complemented
138C24×D3—31no—
139C24×D3—31no—
140C24×D3C2×D311yescharacteristic
141C22×C3×D4—31no—
142C22×C3×D4—32no—
143C22×C3×D4—32no—
144C22×C3×D4—32no—
145C22×C3×D4—68no—
146C22×C3×D4—64no—
147C23×C3×C4—31no—
148C22×#67—24no—
149C22×#67—28no—
150C22×#67—31no—
151C22×#67—31no—
152C22×#67—31no—
153C22×#67—31no—
154C22×#67—32no—
155C22×#67—32no—
156C22×#67—31no—
157C22×#67—61no—
158C22×#67—62no—
159C22×#67—64no—
160C22×#67—64no—
161C22×#67—64no—
162C22×#67C2×D311yescharacteristic
163C22×#67C2×D312yes—
164C22×#67C2×D312yescomplemented
165C22×#67C2×D312yescomplemented
166C23×Dic3—31no—
167C23×Dic3C2×D311yescharacteristic, complemented
168C2×D3×D4—64no—
169C2×D3×D4—64no—
170C2×D3×D4—64no—
171C22×D12—31no—
172C22×C4×D3—31no—
173C3×#120—64no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—32no—
176#953—24no—
177#953—64no—
178#953—64no—
179#953—68no—
180C2×#217—31no—
181C2×#217—32no—
182C2×#217—31no—
183C2×#217—32no—
184C2×#217—32no—
185C2×#217—32no—
186C2×#217—32no—
187C2×#217—61no—
188C2×#217—62no—
189C2×#217C2×D311yescharacteristic, complemented
190C2×#217C2×D312yescomplemented
191#937—68no—
192#937—68no—
193C2×(C2×D3)⋊C4—32no—
194C2×(C2×D3)⋊C4—32no—
195C2×(C2×D3)⋊C4—32no—
196C2×(C2×D3)⋊C4—32no—
197C2×(C2×D3)⋊C4—32no—
198C3⋊#95—32no—
199C3⋊#95—32no—
200C3⋊#95—32no—
201C3⋊#95—32no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32—22no—
206C23×C32—28no—
207C23×C32—22no—
208C23×C32—22no—
209C23×C32—22no—
210C23×C32—22no—
211C23×C32—48no—
212C23×C32—48no—
213C23×C32—44no—
214C23×C32—44no—
215C23×C32C2×D412yes—
216C23×C32C2×D412yes—
217C23×C32C2×D412yes—
218C23×C32C2×D414yescomplemented
219C23×C32C2411yescharacteristic
220C22×C3⋊D3—22no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—22no—
224C22×C3⋊D3C2×D412yescomplemented
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—22no—
228C22×C3×D3—28no—
229C22×C3×D3—22no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—22no—
235C22×C3×D3—22no—
236C22×C3×D3—22no—
237C22×C3×D3—28no—
238C22×C3×D3—44no—
239C22×C3×D3—48no—
240C22×C3×D3—48no—
241C22×C3×D3C2×D412yes—
242C22×C3×D3C2×D414yes—
243C22×C3×D3C2×D412yes—
244C22×C3×D3C2×D412yescomplemented
245C2×D32—28no—
246C2×D32—48no—
247C2×D32—48no—
248C2×D32—44no—
249C2×D32—44no—
250#638—28no—
251#638—48no—
252C2×C3⋊Dic3—22no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—22no—
256C2×C3⋊Dic3—22no—
257C2×C3⋊Dic3C2×D412yescomplemented
258C3×#67—216no—
259C3×#67—28no—
260C3×#67—216no—
261C3×#67—48no—
262C2×C3×Dic3—28no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—22no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3C2×D414yescomplemented
271C2×C3×Dic3C2×D412yescomplemented
272#626—28no—
273#625—28no—
274D3×Dic3—28no—
275C23×D4—31no—
276C23×D4—91no—
277C2×#120—31no—
278C2×#120—92no—
279C2×#120—91no—
280#392—92no—
281#392—92no—
282#386—91no—
283#386—92no—
284#386—91no—
285#379—91no—
286C24×C3—22no—
287C24×C3—24no—
288C24×C3—22no—
289C24×C3—24no—
290C24×C3—24no—
291C24×C3—22no—
292C24×C3—22no—
293C24×C3—22no—
294C24×C3—22no—
295C24×C3—22no—
296C24×C3—21no—
297C24×C3—31no—
298C24×C3—31no—
299C24×C3—31no—
300C24×C3—34no—
301C24×C3—42no—
302C24×C3—44no—
303C24×C3—42no—
304C24×C3—42no—
305C24×C3—42no—
306C24×C3—44no—
307C24×C3—64no—
308C24×C3—62no—
309C24×C3—62no—
310C24×C3—122no—
311C24×C3C22×D312yes—
312C24×C3C22×D312yes—
313C24×C3C22×D311yescharacteristic
314C24×C3C22×D311yescharacteristic
315C23×D3—22no—
316C23×D3—22no—
317C23×D3—24no—
318C23×D3—31no—
319C23×D3—31no—
320C23×D3—42no—
321C23×D3—61no—
322C23×D3—62no—
323C23×D3—62no—
324C23×D3—62no—
325C23×D3—62no—
326C23×D3—64no—
327C23×D3—62no—
328C23×D3—62no—
329C23×D3—64no—
330C23×D3—122no—
331C23×D3—122no—
332C23×D3#6714yescomplemented
333C23×D3C22×D311yescharacteristic
334C23×D3C22×D311yescharacteristic
335C23×D3C22×D311yescharacteristic
336C2×C3×D4—34no—
337C2×C3×D4—38no—
338C2×C3×D4—64no—
339C2×C3×D4—64no—
340C2×C3×D4—64no—
341C2×C3×D4—64no—
342C2×C3×D4—632no—
343C2×C3×D4—62no—
344C2×C3×D4—64no—
345C2×C3×D4—62no—
346C2×C3×D4—64no—
347C2×C3×D4—64no—
348C2×C3×D4—122no—
349C22×C3×C4—32no—
350C22×C3×C4—31no—
351C22×C3×C4—32no—
352C22×C3×C4—64no—
353C22×C3×C4—62no—
354C2×#67—232no—
355C2×#67—22no—
356C2×#67—22no—
357C2×#67—24no—
358C2×#67—24no—
359C2×#67—24no—
360C2×#67—24no—
361C2×#67—24no—
362C2×#67—24no—
363C2×#67—24no—
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—42no—
367C2×#67—64no—
368C2×#67—62no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—632no—
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—62no—
376C2×#67—62no—
377C2×#67—62no—
378C2×#67—62no—
379C2×#67—62no—
380C2×#67—62no—
381C2×#67—64no—
382C2×#67—64no—
383C2×#67—68no—
384C2×#67—64no—
385C2×#67—64no—
386C2×#67—62no—
387C2×#67—122no—
388C2×#67—122no—
389C2×#67—124no—
390C2×#67—122no—
391C2×#67—122no—
392C2×#67—124no—
393C2×#67#6718yescomplemented
394C2×#67#6714yescomplemented
395C22×Dic3—22no—
396C22×Dic3—24no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—32no—
400C22×Dic3—32no—
401C22×Dic3—61no—
402C22×Dic3—62no—
403C22×Dic3—62no—
404C22×Dic3—62no—
405C22×Dic3—62no—
406C22×Dic3C22×D312yes—
407C22×Dic3C22×D312yes—
408C22×Dic3C22×D311yescharacteristic
409D3×D4—632no—
410C2×D12—62no—
411C2×D12—62no—
412C2×D12—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—62no—
416C3×C22⋊C4—64no—
417C3×C22⋊C4—62no—
418#217—22no—
419#217—24no—
420#217—64no—
421#217—64no—
422#217—64no—
423#217—68no—
424#217—64no—
425#217—62no—
426#217—62no—
427#217—64no—
428#217—122no—
429(C2×D3)⋊C4—64no—
430(C2×D3)⋊C4—64no—
431(C2×D3)⋊C4—64no—
432(C2×D3)⋊C4—64no—
433(C2×D3)⋊C4—122no—
434C22×C32—24no—
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—24no—
438C22×C32—24no—
439C22×C32—24no—
440C22×C32—24no—
441C22×C32—416no—
442C22×C32—42no—
443C22×C32—42no—
444C22×C32—42no—
445C22×C32—42no—
446C22×C32#12014yescomplemented
447C22×C32C22×D411yescharacteristic
448C22×C32C22×D411yescharacteristic
449C22×C32C22×D412yes—
450C22×C32C22×D411yescharacteristic
451C22×C32H(5,𝔽2)12yes—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—24no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—42no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—24no—
460C2×C3×D3—24no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—24no—
466C2×C3×D3—416no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—42no—
470C2×C3×D3—42no—
471C2×C3×D3—42no—
472C2×C3×D3#12014yescomplemented
473D32—416no—
474C3⋊Dic3—22no—
475C3⋊Dic3—42no—
476C3×Dic3—22no—
477C3×Dic3—24no—
478C3×Dic3—42no—
479C25—31no—
480C25—91no—
481C25D3211yescharacteristic, complemented
482C22×D4—31no—
483C22×D4—32no—
484C22×D4—32no—
485C22×D4—32no—
486C22×D4—68no—
487C22×D4—64no—
488C22×D4—91no—
489C22×D4—91no—
490C22×D4—91no—
491C22×D4—92no—
492C22×D4—184no—
493C22×D4—184no—
494C22×D4—184no—
495C23×C4—31no—
496C23×C4—91no—
497#120—64no—
498#120—188no—
499#120—184no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—32no—
502C2×C22⋊C4—92no—
503C2×C22⋊C4—92no—
504C2×C22⋊C4—92no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—92no—
507C2×C22⋊C4—92no—
508#95—92no—
509#95—92no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—24no—
515C23×C3—28no—
516C23×C3—24no—
517C23×C3—28no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—21no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—24no—
534C23×C3—22no—
535C23×C3—34no—
536C23×C3—32no—
537C23×C3—32no—
538C23×C3—32no—
539C23×C3—42no—
540C23×C3—42no—
541C23×C3—42no—
542C23×C3—42no—
543C23×C3—42no—
544C23×C3—42no—
545C23×C3—48no—
546C23×C3—48no—
547C23×C3—48no—
548C23×C3—48no—
549C23×C3—48no—
550C23×C3—416no—
551C23×C3—44no—
552C23×C3—44no—
553C23×C3—48no—
554C23×C3—416no—
555C23×C3—48no—
556C23×C3—44no—
557C23×C3—44no—
558C23×C3—68no—
559C23×C3—61no—
560C23×C3—62no—
561C23×C3—61no—
562C23×C3—68no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—62no—
566C23×C3—62no—
567C23×C3—62no—
568C23×C3—62no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3—124no—
572C23×C3—128no—
573C23×C3—128no—
574C23×C3D3×D412yes—
575C23×C3D3×D412yes—
576C23×C3D3×D412yes—
577C23×C3D3×D412yes—
578C23×C3D3×D414yescomplemented
579C23×C3C2×#6712yes—
580C23×C3C2×#6712yes—
581C23×C3C2×#6714yescomplemented
582C23×C3C23×D311yescharacteristic
583C23×C3C23×D311yescharacteristic
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—22no—
587C22×D3—28no—
588C22×D3—22no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—28no—
597C22×D3—32no—
598C22×D3—32no—
599C22×D3—44no—
600C22×D3—48no—
601C22×D3—48no—
602C22×D3—62no—
603C22×D3—68no—
604C22×D3—68no—
605C22×D3—62no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—62no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—122no—
614C22×D3—121no—
615C22×D3—121no—
616C22×D3—122no—
617C22×D3—128no—
618C22×D3—128no—
619C22×D3—128no—
620C22×D3—124no—
621C22×D3—128no—
622C22×D3—124no—
623C22×D3—124no—
624C22×D3—124no—
625C22×D3C2×#6712yes—
626C22×D3C2×#6714yes—
627C22×D3C2×#6712yes—
628C22×D3C2×#6712yescomplemented
629C3×D4—616no—
630C3×D4—616no—
631C3×D4—68no—
632C3×D4—128no—
633C2×C3×C4—34no—
634C2×C3×C4—32no—
635C2×C3×C4—68no—
636C2×C3×C4—61no—
637C2×C3×C4—62no—
638C2×C3×C4—62no—
639C2×C3×C4—61no—
640C2×C3×C4—62no—
641C2×C3×C4—62no—
642C2×C3×C4—62no—
643#67—216no—
644#67—28no—
645#67—216no—
646#67—48no—
647#67—68no—
648#67—68no—
649#67—68no—
650#67—68no—
651#67—68no—
652#67—128no—
653#67—128no—
654#67—128no—
655#67—1216no—
656C2×Dic3—28no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—22no—
660C2×Dic3—22no—
661C2×Dic3—22no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—62no—
667C2×Dic3—68no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—64no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—62no—
678C2×Dic3—62no—
679C2×Dic3—121no—
680C2×Dic3—121no—
681C2×Dic3—122no—
682C2×Dic3—122no—
683C2×Dic3C2×#6714yescomplemented
684C2×Dic3C2×#6712yescomplemented
685D12—68no—
686C4×D3—68no—
687C2×C32—24no—
688C2×C32—44no—
689C2×C32C2×#12011yescharacteristic
690C2×C32C2×#12011yescharacteristic
691C2×C32#53411yescharacteristic
692C2×C32D4212yes—
693C2×C32D4212yes—
694C3⋊D3—42no—
695C3×D3—24no—
696C3×D3—42no—
697C3×D3—42no—
698C24—22no—
699C24—24no—
700C24—22no—
701C24—22no—
702C24—31no—
703C24—31no—
704C24—31no—
705C24—34no—
706C24—42no—
707C24—64no—
708C24—62no—
709C24—62no—
710C24—91no—
711C24—122no—
712C24—182no—
713C24—182no—
714C24—184no—
715C24—182no—
716C24—362no—
717C24C2×D3212yes—
718C24C2×D3211yescharacteristic
719C2×D4—34no—
720C2×D4—38no—
721C2×D4—64no—
722C2×D4—64no—
723C2×D4—64no—
724C2×D4—64no—
725C2×D4—632no—
726C2×D4—62no—
727C2×D4—64no—
728C2×D4—62no—
729C2×D4—64no—
730C2×D4—64no—
731C2×D4—94no—
732C2×D4—122no—
733C2×D4—182no—
734C2×D4—182no—
735C2×D4—182no—
736C2×D4—182no—
737C2×D4—1832no—
738C2×D4—182no—
739C2×D4—182no—
740C2×D4—182no—
741C2×D4—182no—
742C2×D4—184no—
743C2×D4—184no—
744C2×D4—362no—
745C22×C4—31no—
746C22×C4—32no—
747C22×C4—32no—
748C22×C4—64no—
749C22×C4—62no—
750C22×C4—91no—
751C22×C4—92no—
752C22×C4—182no—
753C22×C4—182no—
754C22×C4—182no—
755C22⋊C4—64no—
756C22⋊C4—62no—
757C22⋊C4—184no—
758C22⋊C4—184no—
759C22⋊C4—184no—
760C22⋊C4—184no—
761C22⋊C4—182no—
762C22⋊C4—362no—
763C22×C3—24no—
764C22×C3—24no—
765C22×C3—24no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—24no—
771C22×C3—28no—
772C22×C3—24no—
773C22×C3—24no—
774C22×C3—24no—
775C22×C3—24no—
776C22×C3—24no—
777C22×C3—24no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—22no—
781C22×C3—21no—
782C22×C3—22no—
783C22×C3—24no—
784C22×C3—34no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—44no—
788C22×C3—44no—
789C22×C3—44no—
790C22×C3—44no—
791C22×C3—416no—
792C22×C3—416no—
793C22×C3—44no—
794C22×C3—44no—
795C22×C3—44no—
796C22×C3—44no—
797C22×C3—432no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—62no—
807C22×C3—64no—
808C22×C3—62no—
809C22×C3—64no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—64no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—1216no—
816C22×C3—122no—
817C22×C3—122no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—122no—
821C22×C3#93714yescomplemented
822C22×C3#93714yescomplemented
823C22×C3C2×D3×D411yescharacteristic
824C22×C3C2×D3×D411yescharacteristic
825C22×C3C2×D3×D412yes—
826C22×C3C2×D3×D411yescharacteristic
827C22×C3C2×D3×D411yescharacteristic
828C22×C3#100412yes—
829C22×C3#100412yes—
830C22×C3C22×#6711yescharacteristic
831C22×C3C22×#6711yescharacteristic
832C22×C3C22×#6712yes—
833C2×D3—22no—
834C2×D3—24no—
835C2×D3—24no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—24no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—416no—
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—41no—
846C2×D3—41no—
847C2×D3—42no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—64no—
851C2×D3—64no—
852C2×D3—122no—
853C2×D3—124no—
854C2×D3—1216no—
855C2×D3—1216no—
856C2×D3—122no—
857C2×D3—122no—
858C2×D3—121no—
859C2×D3—121no—
860C2×D3—121no—
861C2×D3—121no—
862C2×D3—241no—
863C2×D3—241no—
864C2×D3—242no—
865C2×D3#95314yescomplemented
866C3×C4—62no—
867C3×C4—64no—
868C3×C4—122no—
869Dic3—22no—
870Dic3—24no—
871Dic3—42no—
872Dic3—62no—
873Dic3—62no—
874Dic3—122no—
875Dic3—124no—
876Dic3—122no—
877Dic3—122no—
878C32#240311yescharacteristic, complemented, Sylow
879C23—22no—
880C23—22no—
881C23—28no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—34no—
889C23—32no—
890C23—32no—
891C23—32no—
892C23—48no—
893C23—48no—
894C23—44no—
895C23—44no—
896C23—68no—
897C23—61no—
898C23—61no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—61no—
903C23—61no—
904C23—61no—
905C23—61no—
906C23—62no—
907C23—62no—
908C23—68no—
909C23—92no—
910C23—124no—
911C23—128no—
912C23—128no—
913C23—188no—
914C23—182no—
915C23—181no—
916C23—181no—
917C23—182no—
918C23—364no—
919C23—368no—
920C23—368no—
921C23—364no—
922C23D3×#6712yes—
923C23D3×#6712yes—
924C23D3×#6714yescomplemented
925C23#381112yes—
926C23C22×D3211yescharacteristic
927D4—616no—
928D4—616no—
929D4—68no—
930D4—128no—
931D4—188no—
932D4—188no—
933D4—188no—
934D4—368no—
935C2×C4—32no—
936C2×C4—34no—
937C2×C4—68no—
938C2×C4—62no—
939C2×C4—62no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—62no—
943C2×C4—62no—
944C2×C4—62no—
945C2×C4—92no—
946C2×C4—188no—
947C2×C4—181no—
948C2×C4—181no—
949C2×C4—182no—
950C2×C4—182no—
951C2×C4—182no—
952C2×C3—24no—
953C2×C3—24no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—22no—
958C2×C3—22no—
959C2×C3—44no—
960C2×C3—48no—
961C2×C3—44no—
962C2×C3—44no—
963C2×C3—64no—
964C2×C3—122no—
965C2×C3—122no—
966C2×C3D3×#12011yescharacteristic
967C2×C3#558911yescharacteristic
968C2×C3#559012yes—
969C2×C3C2×#93711yescharacteristic
970C2×C3C2×#93711yescharacteristic
971C2×C3D4×#6712yes—
972C2×C3D4×#6712yes—
973C2×C3D4×#6712yes—
974C2×C3#580411yescharacteristic
975C2×C3C2×#95311yescharacteristic
976D3—24no—
977D3—42no—
978D3—42no—
979D3—122no—
980D3—122no—
981D3—242no—
982C22—22no—
983C22—22no—
984C22—24no—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—24no—
989C22—34no—
990C22—416no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—62no—
996C22—62no—
997C22—64no—
998C22—64no—
999C22—62no—
1000C22—62no—
1001C22—62no—
1002C22—62no—
1003C22—64no—
1004C22—1216no—
1005C22—121no—
1006C22—121no—
1007C22—122no—
1008C22—122no—
1009C22—122no—
1010C22—182no—
1011C22—184no—
1012C22—3616no—
1013C22—361no—
1014C22—361no—
1015C22—362no—
1016C22#6398314yescomplemented
1017C22C2×D3×#6711yescharacteristic
1018C22C2×D3×#6711yescharacteristic
1019C22C2×D3×#6712yes—
1020C22C2×#381111yescharacteristic
1021C22#6433012yes—
1022C4—62no—
1023C4—64no—
1024C4—122no—
1025C4—182no—
1026C4—362no—
1027C3—21no—
1028C3#8260411yescharacteristic, complemented
1029C3#8405211yescharacteristic, complemented
1030C2—24no—
1031C2—44no—
1032C2—64no—
1033C2—122no—
1034C2—122no—
1035C2—362no—
1036C2C2×#6398311yescharacteristic
1037C2D3×#95311yescharacteristic
1038C2#1059552411yescharacteristic
1039C2#67212yes—
1040C2#1059552612yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC25×C32C22
hypercenterC25D32
hypocenterC32#2403
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C23×C3×#67C2semidirect
2. C22×D3×#67C2semidirect
3. C2×#64162C2semidirect
4. C2×C3×#953C2semidirect
5. C2×#63983C2semidirect
6. #10591724C2semidirect
7. #10591723C2semidirect
8. #10591721C2semidirect
9. #10591711C2semidirect
10. #10591710C2semidirect
11. #10591706C2semidirect
14. C25×C32C22semidirect
16. C23×D32C22semidirect
18. C22×#638C22semidirect
23. C22×C3×#67C22semidirect
24. C22×C3×#67C22semidirect
25. C23×C3×Dic3C22semidirect
29. C22×#626C22semidirect
30. C22×#625C22semidirect
31. C22×D3×Dic3C22semidirect
33. C2×#3757C22semidirect
34. C2×#3757C22semidirect
36. C2×C3×#217C22semidirect
37. C2×C3×#217C22semidirect
39. C2×#3722C22semidirect
40. C2×(C2×D3)⋊Dic3C22semidirect
41. C2×(C2×D3)⋊Dic3C22semidirect
42. C2×(C2×D3)⋊Dic3C22semidirect
43. #63579C22semidirect
44. #63579C22semidirect
47. C23×#67D3semidirect
53. C2×#953D3semidirect
80. C23×C3×D3D4semidirect
94. C2×#638D4semidirect
108. C2×C3×#67D4semidirect
109. C2×C3×#67D4semidirect
136. C25×C3C2×D3semidirect
137. C25×C3C2×D3semidirect
164. C22×#67C2×D3semidirect
165. C22×#67C2×D3semidirect
167. C23×Dic3C2×D3semidirect
189. C2×#217C2×D3semidirect
190. C2×#217C2×D3semidirect
218. C23×C32C2×D4semidirect
224. C22×C3⋊D3C2×D4semidirect
244. C22×C3×D3C2×D4semidirect
257. C2×C3⋊Dic3C2×D4semidirect
270. C2×C3×Dic3C2×D4semidirect
271. C2×C3×Dic3C2×D4semidirect
332. C23×D3#67semidirect
393. C2×#67#67semidirect
394. C2×#67#67semidirect
446. C22×C32#120semidirect
472. C2×C3×D3#120semidirect
481. C25D32semidirect
578. C23×C3D3×D4semidirect
581. C23×C3C2×#67semidirect
628. C22×D3C2×#67semidirect
683. C2×Dic3C2×#67semidirect
684. C2×Dic3C2×#67semidirect
821. C22×C3#937semidirect
822. C22×C3#937semidirect
865. C2×D3#953semidirect
878. C32#2403semidirect
924. C23D3×#67semidirect
1016. C22#63983semidirect
1028. C3#82604semidirect
1029. C3#84052semidirect

Maximal subgroups

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

subgroupindex
C23×C3×#672
C22×D3×#672
C2×#641622
C2×C3×#9532
C2×#639832
#105917242
#105917232
#105917212
#105917112
#105917102
#105917062
#840523
#826043