Finite Group Databasebeta

← #11809004

Subgroups — #11809004

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
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C23×#626C211yesmaximal, characteristic, complemented
3C2×#64146C211yesmaximal, characteristic, complemented
4C2×#63981C211yesmaximal, characteristic, complemented
5C2×#63977C212yesmaximal, complemented
6C3×#5220C211yesmaximal, characteristic, complemented
7#10591724C212yesmaximal, complemented
8#10591710C211yesmaximal, characteristic, complemented
9#10591706C211yesmaximal, characteristic, complemented
10#10591391C212yesmaximal, complemented
11#10591382C212yesmaximal, complemented
12#84052—31nomaximal
13#74884—31nomaximal
14C24×C3⋊D3C2211yescharacteristic, complemented
15C24×C3×D3C2211yescharacteristic
16C24×C3×D3C2211yescharacteristic, complemented
17C22×C32×D4C2211yescharacteristic
18C22×#638C2212yescomplemented
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic, complemented
21C23×C3×Dic3C2211yescharacteristic, complemented
22C2×C3×D3×D4—24no—
23C2×C3×D3×D4—24no—
24C2×C3×D3×D4—24no—
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×#626—28no—
28C22×#626—24no—
29C22×#626C2212yes—
30C22×#626C2212yescomplemented
31C22×#626C2212yescomplemented
32C2×#3757C2211yescharacteristic, complemented
33#64146—24no—
34C2×#3752C2212yescomplemented
35C2×C3×#217C2212yescomplemented
36C2×C3×#217C2211yescharacteristic, complemented
37#63981—24no—
38#63977—28no—
39C2×#3722C2212yescomplemented
40C2×(C2×D3)⋊Dic3C2212yescomplemented
41C2×(C2×D3)⋊Dic3C2212yescomplemented
42C2×(C2×D3)⋊Dic3C2212yescomplemented
43C3×C3⋊#95C2212yescomplemented
44#63579C2212yescomplemented
45C23×C3×D4—31no—
46C23×#67—31no—
47C22×D3×D4D311yescharacteristic, complemented
48C23×D12—31no—
49C2×#953—32no—
50C2×#937—31no—
51C2×#937—31no—
52C2×#937—31no—
53C2×#937—61no—
54C2×#882—32no—
55C2×#882—31no—
56C3×#386—31no—
57#5247—31no—
58#5223—32no—
59#5223—32no—
60#5220—31no—
61#5220D311yescharacteristic, complemented
62#5213—31no—
63#5213—32no—
64#4960—32no—
65#4955—31no—
66#4671—32no—
67#4665—32no—
68C24×C32C2311yescharacteristic
69C24×C32C2311yescharacteristic
70C23×C3⋊D3—22no—
71C23×C3⋊D3—24no—
72C23×C3⋊D3—22no—
73C23×C3⋊D3—22no—
74C23×C3⋊D3—42no—
75C23×C3⋊D3C2312yes—
76C23×C3×D3—22no—
77C23×C3×D3—22no—
78C23×C3×D3—22no—
79C23×C3×D3—24no—
80C23×C3×D3—22no—
81C23×C3×D3—22no—
82C23×C3×D3—24no—
83C23×C3×D3—42no—
84C23×C3×D3—42no—
85C23×C3×D3D414yescomplemented
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C2×C32×D4—22no—
90C2×C32×D4—22no—
91C2×C32×D4D414yescomplemented
92C22×C32×C4C2311yescharacteristic
93C2×#638—24no—
94C2×#638—24no—
95C2×#638—42no—
96C22×C3⋊Dic3C2312yes—
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—22no—
102C2×C3×#67D414yescomplemented
103C22×C3×Dic3—22no—
104C22×C3×Dic3—24no—
105C22×C3×Dic3C2312yes—
106C22×C3×Dic3C2312yes—
107C22×C3×Dic3C2311yescharacteristic
108C3×D3×D4—232no—
109C2×C3×D12—22no—
110C2×C3×D12—22no—
111C2×C3×D12—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×#626—232no—
116C2×#626—24no—
117C2×#626—24no—
118C2×#626—24no—
119C2×#626—24no—
120C2×#626—24no—
121C2×#626—24no—
122C2×#626—24no—
123C2×#626—42no—
124C2×#626D418yescomplemented
125#3757—22no—
126#3752—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—31no—
135C25×C3—31no—
136C24×D3—31no—
137C24×D3—31no—
138C24×D3—61no—
139C24×D3C2×D311yescharacteristic
140C24×D3C2×D311yescharacteristic, complemented
141C22×C3×D4—21no—
142C22×C3×D4—31no—
143C22×C3×D4—31no—
144C22×C3×D4—31no—
145C22×C3×D4—64no—
146C22×C3×D4—64no—
147C22×C3×D4—64no—
148C22×C3×D4C2×D311yescharacteristic
149C22×C3×D4C2×D311yescharacteristic
150C23×C3×C4—31no—
151C23×C3×C4—31no—
152C22×#67—32no—
153C22×#67—32no—
154C22×#67—32no—
155C22×#67—32no—
156C22×#67—32no—
157C22×#67—62no—
158C22×#67—68no—
159C22×#67—64no—
160C22×#67C2×D311yescharacteristic
161C22×#67C2×D311yescharacteristic, complemented
162C23×Dic3C2×D311yescharacteristic, complemented
163C2×D3×D4—24no—
164C2×D3×D4—24no—
165C2×D3×D4—24no—
166C22×D12—32no—
167C22×D12—32no—
168C22×D12—32no—
169C22×D12—68no—
170C22×D12—64no—
171C22×D12C2×D311yescharacteristic, complemented
172C22×C4×D3C2×D311yescharacteristic, complemented
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—32no—
175#953—68no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—32no—
179C2×#217—32no—
180C2×#217—32no—
181C2×#217—61no—
182C2×#217C2×D312yescomplemented
183C2×#217C2×D311yescharacteristic, complemented
184#937—64no—
185#937—68no—
186#937—64no—
187#937—64no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—32no—
190C2×(C2×D3)⋊C4—32no—
191C2×(C2×D3)⋊C4—32no—
192C2×(C2×D3)⋊C4—32no—
193C2×(C2×D3)⋊C4—32no—
194C2×(C2×D3)⋊C4—32no—
195C2×(C2×D3)⋊C4—62no—
196#882—68no—
197#882—64no—
198C3×#95—32no—
199C3⋊#95—32no—
200C3⋊#95—32no—
201C3⋊#95C2×D312yescomplemented
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32—21no—
206C23×C32—21no—
207C23×C32—22no—
208C23×C32C2×D412yes—
209C23×C32C2×D412yes—
210C23×C32C2×D412yes—
211C23×C32C2×D412yescomplemented
212C23×C32C2411yescharacteristic
213C22×C3⋊D3—22no—
214C22×C3⋊D3—22no—
215C22×C3⋊D3—28no—
216C22×C3⋊D3—22no—
217C22×C3⋊D3—22no—
218C22×C3⋊D3—22no—
219C22×C3⋊D3—22no—
220C22×C3⋊D3—48no—
221C22×C3⋊D3—48no—
222C22×C3⋊D3—44no—
223C22×C3⋊D3—44no—
224C22×C3⋊D3C2×D414yescomplemented
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—22no—
228C22×C3×D3—28no—
229C22×C3×D3—28no—
230C22×C3×D3—22no—
231C22×C3×D3—22no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—22no—
237C22×C3×D3—22no—
238C22×C3×D3—28no—
239C22×C3×D3—44no—
240C22×C3×D3—48no—
241C22×C3×D3—48no—
242C22×C3×D3—48no—
243C22×C3×D3—48no—
244C22×C3×D3—44no—
245C22×C3×D3—44no—
246C22×C3×D3C2×D414yes—
247C22×C3×D3C2×D412yes—
248C22×C3×D3C2×D412yes—
249C22×C3×D3C2×D412yescomplemented
250C32×D4—28no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D412yescomplemented
254#638—48no—
255C2×C3⋊Dic3—22no—
256C2×C3⋊Dic3—22no—
257C2×C3⋊Dic3—22no—
258C3×#67—28no—
259C3×#67—28no—
260C2×C3×Dic3—28no—
261C2×C3×Dic3—22no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—22no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3C2×D414yescomplemented
269C2×C3×Dic3C2×D412yescomplemented
270C3×D12—28no—
271C3×C4×D3—28no—
272#626—216no—
273#626—216no—
274#626—48no—
275C23×D4—31no—
276C23×D4—91no—
277C2×#120—91no—
278C2×#120—92no—
279C2×#120—91no—
280#392—92no—
281#392—92no—
282#386—31no—
283#386—92no—
284#386—91no—
285#379—91no—
286C24×C3—21no—
287C24×C3—21no—
288C24×C3—31no—
289C24×C3—31no—
290C24×C3—31no—
291C24×C3—34no—
292C24×C3—64no—
293C24×C3—62no—
294C24×C3—62no—
295C24×C3—64no—
296C24×C3—62no—
297C24×C3—62no—
298C24×C3—62no—
299C24×C3—122no—
300C24×C3—122no—
301C24×C3C22×D311yescharacteristic
302C24×C3C22×D311yescharacteristic
303C24×C3C22×D311yescharacteristic
304C24×C3C22×D311yescharacteristic
305C23×D3—22no—
306C23×D3—22no—
307C23×D3—22no—
308C23×D3—24no—
309C23×D3—22no—
310C23×D3—22no—
311C23×D3—24no—
312C23×D3—32no—
313C23×D3—32no—
314C23×D3—42no—
315C23×D3—42no—
316C23×D3—62no—
317C23×D3—64no—
318C23×D3—64no—
319C23×D3—62no—
320C23×D3—62no—
321C23×D3—64no—
322C23×D3—62no—
323C23×D3—62no—
324C23×D3—62no—
325C23×D3—62no—
326C23×D3—124no—
327C23×D3—122no—
328C23×D3—122no—
329C23×D3—122no—
330C23×D3—122no—
331C23×D3—124no—
332C23×D3#6714yescomplemented
333C23×D3C22×D311yescharacteristic
334C23×D3C22×D311yescharacteristic
335C23×D3C22×D311yescharacteristic
336C2×C3×D4—22no—
337C2×C3×D4—22no—
338C2×C3×D4—22no—
339C2×C3×D4—22no—
340C2×C3×D4—24no—
341C2×C3×D4—34no—
342C2×C3×D4—42no—
343C2×C3×D4—42no—
344C2×C3×D4—62no—
345C2×C3×D4—62no—
346C2×C3×D4—62no—
347C2×C3×D4—632no—
348C2×C3×D4—62no—
349C2×C3×D4—62no—
350C2×C3×D4—62no—
351C2×C3×D4—62no—
352C2×C3×D4—62no—
353C2×C3×D4D1214yescomplemented
354C2×C3×D4#6714yescomplemented
355C22×C3×C4—21no—
356C22×C3×C4—31no—
357C22×C3×C4—32no—
358C22×C3×C4—32no—
359C22×C3×C4—62no—
360C22×C3×C4—62no—
361C22×C3×C4—64no—
362C22×C3×C4—62no—
363C22×C3×C4—62no—
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C2×#67—22no—
367C2×#67—22no—
368C2×#67—22no—
369C2×#67—22no—
370C2×#67—22no—
371C2×#67—38no—
372C2×#67—64no—
373C2×#67—64no—
374C2×#67—64no—
375C2×#67—64no—
376C2×#67—632no—
377C2×#67—64no—
378C2×#67—64no—
379C2×#67—64no—
380C2×#67—64no—
381C2×#67—68no—
382C2×#67—64no—
383C2×#67—64no—
384C2×#67—64no—
385C2×#67—124no—
386C2×#67—122no—
387C2×#67—122no—
388C2×#67—122no—
389C2×#67—124no—
390C2×#67#6714yescomplemented
391C22×Dic3—22no—
392C22×Dic3—24no—
393C22×Dic3—32no—
394C22×Dic3—32no—
395C22×Dic3—62no—
396C22×Dic3C22×D312yes—
397C22×Dic3C22×D312yes—
398C22×Dic3C22×D311yescharacteristic
399D3×D4—232no—
400C2×D12—22no—
401C2×D12—22no—
402C2×D12—22no—
403C2×D12—38no—
404C2×D12—64no—
405C2×D12—64no—
406C2×D12—632no—
407C2×D12—64no—
408C2×D12—64no—
409C2×D12—64no—
410C2×D12—64no—
411C2×D12—64no—
412C2×D12—122no—
413C2×C4×D3—22no—
414C2×C4×D3—22no—
415C2×C4×D3—22no—
416C3×C22⋊C4—64no—
417C3×C22⋊C4—62no—
418#217—22no—
419#217—24no—
420#217—64no—
421#217—64no—
422#217—62no—
423#217—62no—
424#217—64no—
425#217—122no—
426(C2×D3)⋊C4—64no—
427(C2×D3)⋊C4—68no—
428(C2×D3)⋊C4—64no—
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—22no—
435C22×C32—22no—
436C22×C32—24no—
437C22×C32—24no—
438C22×C32—22no—
439C22×C32—24no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32—42no—
443C22×C32#12014yescomplemented
444C22×C32C22×D411yescharacteristic
445C22×C32C22×D412yes—
446C22×C32C22×D411yescharacteristic
447C22×C32C22×D411yescharacteristic
448C22×C32H(5,𝔽2)12yes—
449C2×C3⋊D3—24no—
450C2×C3⋊D3—24no—
451C2×C3⋊D3—24no—
452C2×C3⋊D3—416no—
453C2×C3⋊D3—42no—
454C2×C3⋊D3—42no—
455C2×C3⋊D3—42no—
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—416no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—42no—
471C2×C3×D3—42no—
472C2×C3×D3—42no—
473C2×C3×D3#12014yescomplemented
474C32×C4—22no—
475C3⋊Dic3—42no—
476C3×Dic3—24no—
477C3×Dic3—22no—
478C3×Dic3—42no—
479C25—31no—
480C25—31no—
481C25—91no—
482C22×D4—31no—
483C22×D4—31no—
484C22×D4—31no—
485C22×D4—64no—
486C22×D4—64no—
487C22×D4—64no—
488C22×D4—92no—
489C22×D4—92no—
490C22×D4—92no—
491C22×D4—92no—
492C22×D4—188no—
493C22×D4—184no—
494C22×D4D3211yescharacteristic
495C23×C4—31no—
496C23×C4—31no—
497#120—184no—
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—32no—
509#95—92no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—34no—
528C23×C3—32no—
529C23×C3—32no—
530C23×C3—32no—
531C23×C3—42no—
532C23×C3—42no—
533C23×C3—42no—
534C23×C3—42no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—68no—
538C23×C3—68no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—62no—
542C23×C3—68no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—62no—
546C23×C3—62no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—62no—
550C23×C3—62no—
551C23×C3—124no—
552C23×C3—128no—
553C23×C3—128no—
554C23×C3—128no—
555C23×C3—124no—
556C23×C3—128no—
557C23×C3—124no—
558C23×C3C2×D1212yes—
559C23×C3C2×D1212yescomplemented
560C23×C3D3×D412yes—
561C23×C3D3×D412yes—
562C23×C3C2×#6712yes—
563C23×C3C2×#6712yes—
564C23×C3C2×#6712yes—
565C23×C3C2×#6712yescomplemented
566C23×C3C23×D311yescharacteristic
567C23×C3C23×D311yescharacteristic
568C22×D3—22no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—28no—
572C22×D3—28no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—28no—
582C22×D3—34no—
583C22×D3—34no—
584C22×D3—44no—
585C22×D3—48no—
586C22×D3—48no—
587C22×D3—48no—
588C22×D3—48no—
589C22×D3—44no—
590C22×D3—44no—
591C22×D3—64no—
592C22×D3—64no—
593C22×D3—68no—
594C22×D3—68no—
595C22×D3—64no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—62no—
606C22×D3—62no—
607C22×D3—62no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3—122no—
611C22×D3—122no—
612C22×D3—128no—
613C22×D3—128no—
614C22×D3—128no—
615C22×D3—128no—
616C22×D3—128no—
617C22×D3—1216no—
618C22×D3—124no—
619C22×D3—124no—
620C22×D3—128no—
621C22×D3—1216no—
622C22×D3—128no—
623C22×D3—124no—
624C22×D3—124no—
625C22×D3D3×D414yes—
626C22×D3C2×#6712yes—
627C22×D3C2×#6712yes—
628C22×D3C2×#6712yescomplemented
629C3×D4—28no—
630C3×D4—28no—
631C3×D4—48no—
632C3×D4—68no—
633C3×D4—68no—
634C3×D4—68no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—22no—
640C2×C3×C4—32no—
641C2×C3×C4—34no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—68no—
645C2×C3×C4—68no—
646C2×C3×C4—61no—
647C2×C3×C4—62no—
648C2×C3×C4—61no—
649C2×C3×C4—62no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4C2×D1212yescomplemented
654C2×C3×C4C2×#6712yescomplemented
655#67—28no—
656#67—28no—
657#67—616no—
658#67—616no—
659#67—128no—
660#67—128no—
661#67—128no—
662#67—1216no—
663C2×Dic3—28no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—22no—
669C2×Dic3—22no—
670C2×Dic3—22no—
671C2×Dic3—64no—
672C2×Dic3—62no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—62no—
678C2×Dic3—122no—
679C2×Dic3—122no—
680C2×Dic3D3×D414yescomplemented
681C2×Dic3C2×#6712yescomplemented
682D12—28no—
683D12—616no—
684D12—616no—
685D12—128no—
686C4×D3—28no—
687C2×C32—24no—
688C2×C32—42no—
689C2×C32C2×#12011yescharacteristic
690C2×C32C2×#12011yescharacteristic
691C2×C32#53411yescharacteristic
692C2×C32D4212yes—
693C2×C32D4212yes—
694C3⋊D3—44no—
695C3×D3—24no—
696C3×D3—42no—
697C3×D3—42no—
698C24—31no—
699C24—31no—
700C24—31no—
701C24—34no—
702C24—62no—
703C24—62no—
704C24—64no—
705C24—64no—
706C24—62no—
707C24—62no—
708C24—62no—
709C24—92no—
710C24—122no—
711C24—122no—
712C24—184no—
713C24—182no—
714C24—182no—
715C24—182no—
716C24—362no—
717C24C2×D3211yescharacteristic
718C24C2×D3211yescharacteristic
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—34no—
722C2×D4—62no—
723C2×D4—62no—
724C2×D4—62no—
725C2×D4—632no—
726C2×D4—62no—
727C2×D4—62no—
728C2×D4—62no—
729C2×D4—62no—
730C2×D4—62no—
731C2×D4—98no—
732C2×D4—184no—
733C2×D4—184no—
734C2×D4—184no—
735C2×D4—184no—
736C2×D4—184no—
737C2×D4—1832no—
738C2×D4—184no—
739C2×D4—184no—
740C2×D4—184no—
741C2×D4—184no—
742C2×D4—362no—
743C2×D4—362no—
744C2×D4#62614yescomplemented
745C22×C4—32no—
746C22×C4—31no—
747C22×C4—32no—
748C22×C4—62no—
749C22×C4—62no—
750C22×C4—64no—
751C22×C4—62no—
752C22×C4—62no—
753C22×C4—92no—
754C22×C4C2×D3211yescharacteristic
755C22⋊C4—64no—
756C22⋊C4—62no—
757C22⋊C4—184no—
758C22⋊C4—184no—
759C22⋊C4—184no—
760C22⋊C4—182no—
761C22⋊C4—184no—
762C22⋊C4—362no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—24no—
766C22×C3—24no—
767C22×C3—22no—
768C22×C3—24no—
769C22×C3—22no—
770C22×C3—24no—
771C22×C3—22no—
772C22×C3—24no—
773C22×C3—24no—
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—24no—
781C22×C3—34no—
782C22×C3—44no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—44no—
786C22×C3—44no—
787C22×C3—42no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—42no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—42no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—64no—
797C22×C3—64no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—64no—
803C22×C3—81no—
804C22×C3—81no—
805C22×C3—82no—
806C22×C3—1216no—
807C22×C3—1216no—
808C22×C3—121no—
809C22×C3—122no—
810C22×C3—122no—
811C22×C3—121no—
812C22×C3—122no—
813C22×C3#88214yescomplemented
814C22×C3#95314yescomplemented
815C22×C3C22×D1211yescharacteristic
816C22×C3C2×D3×D412yes—
817C22×C3C2×D3×D412yes—
818C22×C3C2×D3×D411yescharacteristic
819C22×C3C2×D3×D411yescharacteristic
820C22×C3#100412yes—
821C22×C3#100912yes—
822C22×C3C22×#6711yescharacteristic
823C22×C3C22×#6711yescharacteristic
824C22×C3C22×#6711yescharacteristic
825C2×D3—24no—
826C2×D3—24no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—24no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—416no—
835C2×D3—416no—
836C2×D3—41no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—41no—
841C2×D3—68no—
842C2×D3—64no—
843C2×D3—64no—
844C2×D3—64no—
845C2×D3—64no—
846C2×D3—64no—
847C2×D3—64no—
848C2×D3—124no—
849C2×D3—124no—
850C2×D3—1216no—
851C2×D3—1216no—
852C2×D3—124no—
853C2×D3—124no—
854C2×D3—124no—
855C2×D3—124no—
856C2×D3—1232no—
857C2×D3—122no—
858C2×D3—122no—
859C2×D3—122no—
860C2×D3—122no—
861C2×D3—122no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—122no—
865C2×D3#93714yescomplemented
866C3×C4—22no—
867C3×C4—22no—
868C3×C4—42no—
869C3×C4—62no—
870C3×C4—64no—
871C3×C4—122no—
872Dic3—22no—
873Dic3—24no—
874Dic3—42no—
875Dic3—124no—
876Dic3—122no—
877Dic3—122no—
878C32#240311yescharacteristic, complemented, Sylow
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—21no—
884C23—21no—
885C23—34no—
886C23—32no—
887C23—32no—
888C23—32no—
889C23—68no—
890C23—68no—
891C23—62no—
892C23—61no—
893C23—61no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—61no—
899C23—61no—
900C23—61no—
901C23—61no—
902C23—68no—
903C23—94no—
904C23—124no—
905C23—128no—
906C23—128no—
907C23—128no—
908C23—124no—
909C23—128no—
910C23—124no—
911C23—188no—
912C23—182no—
913C23—182no—
914C23—182no—
915C23—182no—
916C23—182no—
917C23—182no—
918C23—368no—
919C23—368no—
920C23—364no—
921C23—364no—
922C23C2×#62612yes—
923C23C2×#62612yescomplemented
924C23D3×#6712yes—
925C23D3×#6712yes—
926C23C22×D3211yescharacteristic
927D4—28no—
928D4—68no—
929D4—68no—
930D4—68no—
931D4—1816no—
932D4—1816no—
933D4—368no—
934D4—368no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—34no—
938C2×C4—32no—
939C2×C4—68no—
940C2×C4—68no—
941C2×C4—62no—
942C2×C4—61no—
943C2×C4—61no—
944C2×C4—62no—
945C2×C4—62no—
946C2×C4—62no—
947C2×C4—62no—
948C2×C4—182no—
949C2×C4—182no—
950C2×C4—182no—
951C2×C4C2×#62612yescomplemented
952C2×C3—24no—
953C2×C3—24no—
954C2×C3—22no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—22no—
959C2×C3—44no—
960C2×C3—42no—
961C2×C3—42no—
962C2×C3—64no—
963C2×C3—82no—
964C2×C3—122no—
965C2×C3—122no—
966C2×C3C2×#88211yescharacteristic
967C2×C3D4×D1212yes—
968C2×C3D3×#12011yescharacteristic
969C2×C3#560912yes—
970C2×C3#565311yescharacteristic
971C2×C3C2×#93711yescharacteristic
972C2×C3D4×#6712yes—
973C2×C3D4×#6712yes—
974C2×C3#580411yescharacteristic
975C2×C3C2×#95311yescharacteristic
976D3—24no—
977D3—42no—
978D3—42no—
979D3—128no—
980D3—124no—
981D3—124no—
982C22—24no—
983C22—22no—
984C22—22no—
985C22—24no—
986C22—24no—
987C22—22no—
988C22—34no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—64no—
993C22—62no—
994C22—62no—
995C22—64no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—64no—
1001C22—1216no—
1002C22—1216no—
1003C22—122no—
1004C22—122no—
1005C22—121no—
1006C22—121no—
1007C22—122no—
1008C22—184no—
1009C22—184no—
1010C22—184no—
1011C22—3616no—
1012C22—362no—
1013C22—362no—
1014C22—362no—
1015C22—362no—
1016C22#6397714yescomplemented
1017C22D32×D412yes—
1018C22#6431412yes—
1019C22C22×#62611yescharacteristic
1020C22C2×D3×#6711yescharacteristic
1021C22C2×D3×#6711yescharacteristic
1022C4—22no—
1023C4—62no—
1024C4—64no—
1025C4—122no—
1026C4—362no—
1027C3—21no—
1028C3#7488411yescharacteristic, complemented
1029C3#8405211yescharacteristic, complemented
1030C2—24no—
1031C2—42no—
1032C2—64no—
1033C2—122no—
1034C2—122no—
1035C2—364no—
1036C2D4×#62612yes—
1037C2#1059523411yescharacteristic
1038C2D3×#93711yescharacteristic
1039C2#1059529112yes—
1040C2C2×#6397711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2403
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C23×#626C2semidirect
3. C2×#64146C2semidirect
4. C2×#63981C2semidirect
5. C2×#63977C2semidirect
6. C3×#5220C2semidirect
7. #10591724C2semidirect
8. #10591710C2semidirect
9. #10591706C2semidirect
10. #10591391C2semidirect
11. #10591382C2semidirect
14. C24×C3⋊D3C22semidirect
16. C24×C3×D3C22semidirect
18. C22×#638C22semidirect
20. C22×C3×#67C22semidirect
21. C23×C3×Dic3C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
30. C22×#626C22semidirect
31. C22×#626C22semidirect
32. C2×#3757C22semidirect
34. C2×#3752C22semidirect
35. C2×C3×#217C22semidirect
36. C2×C3×#217C22semidirect
39. C2×#3722C22semidirect
40. C2×(C2×D3)⋊Dic3C22semidirect
41. C2×(C2×D3)⋊Dic3C22semidirect
42. C2×(C2×D3)⋊Dic3C22semidirect
43. C3×C3⋊#95C22semidirect
44. #63579C22semidirect
47. C22×D3×D4D3semidirect
61. #5220D3semidirect
85. C23×C3×D3D4semidirect
91. C2×C32×D4D4semidirect
102. C2×C3×#67D4semidirect
124. C2×#626D4semidirect
140. C24×D3C2×D3semidirect
161. C22×#67C2×D3semidirect
162. C23×Dic3C2×D3semidirect
171. C22×D12C2×D3semidirect
172. C22×C4×D3C2×D3semidirect
182. C2×#217C2×D3semidirect
183. C2×#217C2×D3semidirect
201. C3⋊#95C2×D3semidirect
211. C23×C32C2×D4semidirect
224. C22×C3⋊D3C2×D4semidirect
249. C22×C3×D3C2×D4semidirect
253. C2×C32×C4C2×D4semidirect
268. C2×C3×Dic3C2×D4semidirect
269. C2×C3×Dic3C2×D4semidirect
332. C23×D3#67semidirect
353. C2×C3×D4D12semidirect
354. C2×C3×D4#67semidirect
390. C2×#67#67semidirect
443. C22×C32#120semidirect
473. C2×C3×D3#120semidirect
559. C23×C3C2×D12semidirect
565. C23×C3C2×#67semidirect
628. C22×D3C2×#67semidirect
653. C2×C3×C4C2×D12semidirect
654. C2×C3×C4C2×#67semidirect
680. C2×Dic3D3×D4semidirect
681. C2×Dic3C2×#67semidirect
744. C2×D4#626semidirect
813. C22×C3#882semidirect
814. C22×C3#953semidirect
865. C2×D3#937semidirect
878. C32#2403semidirect
923. C23C2×#626semidirect
951. C2×C4C2×#626semidirect
1016. C22#63977semidirect
1028. C3#74884semidirect
1029. C3#84052semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C23×#6262
C2×#641462
C2×#639812
C2×#639772
C3×#52202
#105917242
#105917102
#105917062
#105913912
#105913822
#840523
#748843