Finite Group Databasebeta

← #11809005

Subgroups — #11809005

Order 1152.

3271 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C23×#625C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic, complemented
4C2×#63976C212yesmaximal, complemented
5C2×#63976C211yesmaximal, characteristic, complemented
6#10592919C211yesmaximal, characteristic, complemented
7#10591723C212yesmaximal, complemented
8#10591713C211yesmaximal, characteristic, complemented
9#10591706C211yesmaximal, characteristic, complemented
10#10591389C212yesmaximal, complemented
11#10591381C212yesmaximal, complemented
12#84052—31nomaximal
13#82604—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C24×C3×D3C2211yescharacteristic, complemented
16C24×C3×D3C2211yescharacteristic, complemented
17C22×C32×D4C2211yescharacteristic
18C23×C3⋊Dic3C2211yescharacteristic, complemented
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic, complemented
21C22×C3×#67C2212yescomplemented
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×#625—28no—
28C22×#625—24no—
29C22×#625C2212yes—
30C22×#625C2212yescomplemented
31C22×#625C2212yescomplemented
32C2×#3757C2211yescharacteristic, complemented
33C2×#3757C2212yescomplemented
34C2×C3×#217C2211yescharacteristic, complemented
35C3×#937—24no—
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37#63976—24no—
38#63976—28no—
39C2×(C2×D3)⋊Dic3C2212yescomplemented
40C2×(C2×D3)⋊Dic3C2212yescomplemented
41C2×(C2×D3)⋊Dic3C2212yescomplemented
42C2×(C2×D3)⋊Dic3C2212yescomplemented
43#63658C2212yescomplemented
44#63579C2212yescomplemented
45C23×C3×D4—31no—
46C23×#67—31no—
47C23×#67—31no—
48C22×D3×D4D311yescharacteristic, complemented
49C2×C3×#120—31no—
50C2×#953—31no—
51C2×#953—32no—
52C2×#937—31no—
53C2×#937—32no—
54C2×#937D311yescharacteristic, complemented
55#5247—31no—
56#5223—32no—
57#5223—32no—
58#5223—32no—
59#5220—31no—
60#5220—31no—
61#5220—31no—
62#5220—61no—
63#5213—32no—
64#4960—32no—
65#4958—31no—
66#4956—32no—
67#4955—31no—
68C24×C32C2311yescharacteristic
69C24×C32C2311yescharacteristic
70C23×C3×D3—22no—
71C23×C3×D3—22no—
72C23×C3×D3—22no—
73C23×C3×D3—22no—
74C23×C3×D3—24no—
75C23×C3×D3—22no—
76C23×C3×D3—24no—
77C23×C3×D3—22no—
78C23×C3×D3—22no—
79C23×C3×D3—22no—
80C23×C3×D3—24no—
81C23×C3×D3—42no—
82C23×C3×D3—42no—
83C23×C3×D3—42no—
84C23×C3×D3D414yescomplemented
85C23×C3×D3C2311yescharacteristic
86C23×C3×D3C2312yes—
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C2×C32×D4—22no—
90C2×C32×D4—22no—
91C2×C32×D4D414yescomplemented
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3—22no—
94C22×C3⋊Dic3—24no—
95C22×C3⋊Dic3C2312yes—
96C22×C3⋊Dic3C2312yes—
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—24no—
102C2×C3×#67—24no—
103C2×C3×#67—22no—
104C2×C3×#67—42no—
105C2×C3×#67D414yescomplemented
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×#625—232no—
116C2×#625—24no—
117C2×#625—24no—
118C2×#625—24no—
119C2×#625—24no—
120C2×#625—24no—
121C2×#625—24no—
122C2×#625—24no—
123C2×#625—42no—
124C2×#625D418yescomplemented
125#3757—22no—
126#3757—24no—
127C3×#217—22no—
128C3×(C2×D3)⋊C4—24no—
129(C2×D3)⋊Dic3—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—
136C25×C3—31no—
137C24×D3C2×D311yescharacteristic
138C24×D3C2×D311yescharacteristic, complemented
139C24×D3C2×D311yescharacteristic, complemented
140C22×C3×D4—21no—
141C22×C3×D4—31no—
142C22×C3×D4—31no—
143C22×C3×D4—32no—
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—
151C22×#67—32no—
152C22×#67—32no—
153C22×#67—32no—
154C22×#67—32no—
155C22×#67—32no—
156C22×#67—32no—
157C22×#67—68no—
158C22×#67—68no—
159C22×#67—64no—
160C22×#67—64no—
161C22×#67C2×D311yescharacteristic
162C22×#67C2×D311yescharacteristic, complemented
163C22×#67C2×D312yescomplemented
164C23×Dic3—31no—
165C23×Dic3—31no—
166C23×Dic3—61no—
167C2×D3×D4—24no—
168C2×D3×D4—24no—
169C2×D3×D4—24no—
170C22×D12C2×D311yescharacteristic, complemented
171C22×C4×D3C2×D311yescharacteristic, complemented
172C3×#120—64no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—32no—
175#953—68no—
176#953—64no—
177C2×#217—31no—
178C2×#217—32no—
179C2×#217—32no—
180C2×#217—31no—
181C2×#217—32no—
182C2×#217—32no—
183C2×#217—32no—
184C2×#217—32no—
185C2×#217—61no—
186C2×#217—62no—
187C2×#217C2×D311yescharacteristic, complemented
188#937—24no—
189#937—68no—
190#937—64no—
191C2×(C2×D3)⋊C4—32no—
192C2×(C2×D3)⋊C4—32no—
193C2×(C2×D3)⋊C4—32no—
194C2×(C2×D3)⋊C4—32no—
195C2×(C2×D3)⋊C4C2×D312yescomplemented
196C3⋊#95—32no—
197C3⋊#95—32no—
198C3⋊#95—32no—
199C3⋊#95—32no—
200C3⋊#95—62no—
201C23×C32—22no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32—22no—
207C23×C32C2×D412yes—
208C23×C32C2×D412yes—
209C23×C32C2×D412yes—
210C23×C32C2×D412yescomplemented
211C23×C32C2411yescharacteristic
212C22×C3×D3—21no—
213C22×C3×D3—21no—
214C22×C3×D3—22no—
215C22×C3×D3—28no—
216C22×C3×D3—28no—
217C22×C3×D3—28no—
218C22×C3×D3—22no—
219C22×C3×D3—22no—
220C22×C3×D3—22no—
221C22×C3×D3—22no—
222C22×C3×D3—22no—
223C22×C3×D3—22no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—22no—
229C22×C3×D3—22no—
230C22×C3×D3—22no—
231C22×C3×D3—22no—
232C22×C3×D3—28no—
233C22×C3×D3—44no—
234C22×C3×D3—48no—
235C22×C3×D3—48no—
236C22×C3×D3—48no—
237C22×C3×D3—48no—
238C22×C3×D3—48no—
239C22×C3×D3—48no—
240C22×C3×D3—44no—
241C22×C3×D3—44no—
242C22×C3×D3—44no—
243C22×C3×D3—44no—
244C22×C3×D3C2×D414yes—
245C22×C3×D3C2×D412yes—
246C22×C3×D3C2×D412yes—
247C22×C3×D3C2×D414yescomplemented
248C22×C3×D3C2×D412yescomplemented
249C32×D4—28no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D412yescomplemented
253C2×C3⋊Dic3—28no—
254C2×C3⋊Dic3—22no—
255C2×C3⋊Dic3—22no—
256C2×C3⋊Dic3—22no—
257C2×C3⋊Dic3—22no—
258C2×C3⋊Dic3—22no—
259C2×C3⋊Dic3C2×D414yescomplemented
260C3×#67—28no—
261C3×#67—28no—
262C3×#67—48no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—22no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3C2×D412yescomplemented
269C3×D12—28no—
270C3×C4×D3—28no—
271#625—216no—
272#625—216no—
273#625—48no—
274C23×D4—31no—
275C23×D4—91no—
276C2×#120—31no—
277C2×#120—92no—
278C2×#120—91no—
279#392—92no—
280#392—92no—
281#386—92no—
282#386—91no—
283#386—91no—
284#379—91no—
285C24×C3—21no—
286C24×C3—21no—
287C24×C3—31no—
288C24×C3—31no—
289C24×C3—31no—
290C24×C3—32no—
291C24×C3—34no—
292C24×C3—64no—
293C24×C3—64no—
294C24×C3—62no—
295C24×C3—62no—
296C24×C3—64no—
297C24×C3—62no—
298C24×C3—62no—
299C24×C3—62no—
300C24×C3—62no—
301C24×C3—62no—
302C24×C3—62no—
303C24×C3—122no—
304C24×C3—122no—
305C24×C3—122no—
306C24×C3C22×D311yescharacteristic
307C24×C3C22×D311yescharacteristic
308C24×C3C22×D311yescharacteristic
309C24×C3C22×D311yescharacteristic
310C23×D3—22no—
311C23×D3—22no—
312C23×D3—22no—
313C23×D3—22no—
314C23×D3—24no—
315C23×D3—24no—
316C23×D3—22no—
317C23×D3—22no—
318C23×D3—22no—
319C23×D3—22no—
320C23×D3—24no—
321C23×D3—42no—
322C23×D3—42no—
323C23×D3—42no—
324C23×D3#6714yescomplemented
325C23×D3C22×D312yes—
326C23×D3C22×D311yescharacteristic
327C23×D3C22×D311yescharacteristic
328C23×D3C22×D311yescharacteristic
329C2×C3×D4—22no—
330C2×C3×D4—22no—
331C2×C3×D4—22no—
332C2×C3×D4—22no—
333C2×C3×D4—24no—
334C2×C3×D4—34no—
335C2×C3×D4—42no—
336C2×C3×D4—42no—
337C2×C3×D4—62no—
338C2×C3×D4—62no—
339C2×C3×D4—62no—
340C2×C3×D4—632no—
341C2×C3×D4—62no—
342C2×C3×D4—62no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—64no—
346C2×C3×D4—64no—
347C2×C3×D4—62no—
348C2×C3×D4—122no—
349C2×C3×D4#6714yescomplemented
350C2×C3×D4#6714yescomplemented
351C22×C3×C4—21no—
352C22×C3×C4—31no—
353C22×C3×C4—32no—
354C22×C3×C4—62no—
355C22×C3×C4—62no—
356C22×C3×C4—62no—
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—22no—
360C2×#67—22no—
361C2×#67—22no—
362C2×#67—22no—
363C2×#67—24no—
364C2×#67—24no—
365C2×#67—22no—
366C2×#67—38no—
367C2×#67—38no—
368C2×#67—42no—
369C2×#67—64no—
370C2×#67—64no—
371C2×#67—64no—
372C2×#67—64no—
373C2×#67—64no—
374C2×#67—64no—
375C2×#67—632no—
376C2×#67—632no—
377C2×#67—64no—
378C2×#67—64no—
379C2×#67—64no—
380C2×#67—64no—
381C2×#67—64no—
382C2×#67—64no—
383C2×#67—64no—
384C2×#67—64no—
385C2×#67—122no—
386C2×#67—122no—
387C2×#67#6714yescomplemented
388C22×Dic3—32no—
389C22×Dic3—32no—
390C22×Dic3—32no—
391C22×Dic3—32no—
392C22×Dic3—62no—
393C22×Dic3—62no—
394C22×Dic3—64no—
395C22×Dic3—64no—
396C22×Dic3—62no—
397C22×Dic3—62no—
398C22×Dic3—124no—
399C22×Dic3—122no—
400C22×Dic3C22×D312yes—
401C22×Dic3C22×D311yescharacteristic
402D3×D4—232no—
403C2×D12—22no—
404C2×D12—22no—
405C2×D12—22no—
406C2×C4×D3—22no—
407C2×C4×D3—22no—
408C2×C4×D3—22no—
409C3×C22⋊C4—62no—
410C3×C22⋊C4—64no—
411#217—22no—
412#217—64no—
413#217—64no—
414#217—64no—
415#217—64no—
416#217—62no—
417#217—62no—
418#217—64no—
419#217—124no—
420#217—122no—
421#217—122no—
422(C2×D3)⋊C4—24no—
423(C2×D3)⋊C4—64no—
424(C2×D3)⋊C4—64no—
425(C2×D3)⋊C4—64no—
426(C2×D3)⋊C4—122no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32—24no—
430C22×C32—24no—
431C22×C32—22no—
432C22×C32—24no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—42no—
436C22×C32#12014yescomplemented
437C22×C32C22×D412yes—
438C22×C32C22×D411yescharacteristic
439C22×C32C22×D411yescharacteristic
440C22×C32C22×D411yescharacteristic
441C22×C32H(5,𝔽2)12yes—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—24no—
445C2×C3×D3—24no—
446C2×C3×D3—22no—
447C2×C3×D3—24no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—24no—
452C2×C3×D3—24no—
453C2×C3×D3—24no—
454C2×C3×D3—416no—
455C2×C3×D3—416no—
456C2×C3×D3—416no—
457C2×C3×D3—42no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—42no—
461C2×C3×D3—42no—
462C2×C3×D3—42no—
463C2×C3×D3—42no—
464C2×C3×D3—42no—
465C2×C3×D3—42no—
466C2×C3×D3#12014yescomplemented
467C32×C4—22no—
468C3⋊Dic3—24no—
469C3⋊Dic3—42no—
470C3×Dic3—22no—
471C3×Dic3—42no—
472C25—31no—
473C25—31no—
474C25—31no—
475C22×D4—31no—
476C22×D4—31no—
477C22×D4—32no—
478C22×D4—31no—
479C22×D4—64no—
480C22×D4—64no—
481C22×D4—64no—
482C22×D4—92no—
483C22×D4—92no—
484C22×D4—92no—
485C22×D4—188no—
486C22×D4—184no—
487C22×D4D3211yescharacteristic
488C23×C4—31no—
489C23×C4—91no—
490#120—64no—
491#120—184no—
492#120—188no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—32no—
495C2×C22⋊C4—92no—
496C2×C22⋊C4—92no—
497C2×C22⋊C4—92no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—92no—
500C2×C22⋊C4—92no—
501#95—92no—
502#95—92no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—34no—
521C23×C3—32no—
522C23×C3—32no—
523C23×C3—34no—
524C23×C3—32no—
525C23×C3—42no—
526C23×C3—42no—
527C23×C3—42no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—42no—
531C23×C3—68no—
532C23×C3—68no—
533C23×C3—68no—
534C23×C3—61no—
535C23×C3—62no—
536C23×C3—61no—
537C23×C3—68no—
538C23×C3—62no—
539C23×C3—62no—
540C23×C3—62no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—62no—
544C23×C3—62no—
545C23×C3—62no—
546C23×C3—62no—
547C23×C3—62no—
548C23×C3—62no—
549C23×C3—62no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—124no—
553C23×C3—128no—
554C23×C3—128no—
555C23×C3—128no—
556C23×C3—128no—
557C23×C3—128no—
558C23×C3—124no—
559C23×C3—124no—
560C23×C3—128no—
561C23×C3—124no—
562C23×C3—124no—
563C23×C3D3×D412yes—
564C23×C3D3×D412yes—
565C23×C3C2×#6712yes—
566C23×C3C2×#6712yes—
567C23×C3C2×#6712yes—
568C23×C3C2×#6712yes—
569C23×C3C2×#6712yescomplemented
570C23×C3C2×#6712yescomplemented
571C23×C3C23×D311yescharacteristic
572C23×C3C23×D311yescharacteristic
573C22×D3—22no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—28no—
577C22×D3—28no—
578C22×D3—28no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—28no—
594C22×D3—44no—
595C22×D3—48no—
596C22×D3—48no—
597C22×D3—48no—
598C22×D3—48no—
599C22×D3—48no—
600C22×D3—48no—
601C22×D3—44no—
602C22×D3—44no—
603C22×D3—44no—
604C22×D3—44no—
605C22×D3D3×D414yes—
606C22×D3D3×D414yescomplemented
607C22×D3C2×#6712yes—
608C22×D3C2×#6712yes—
609C22×D3C2×#6712yescomplemented
610C3×D4—28no—
611C3×D4—28no—
612C3×D4—48no—
613C3×D4—68no—
614C3×D4—68no—
615C3×D4—68no—
616C3×D4—128no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—22no—
622C2×C3×C4—32no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—68no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—62no—
629C2×C3×C4—62no—
630C2×C3×C4—62no—
631C2×C3×C4C2×#6712yescomplemented
632C2×C3×C4C2×#6712yescomplemented
633#67—28no—
634#67—28no—
635#67—48no—
636#67—616no—
637#67—616no—
638#67—616no—
639#67—616no—
640#67—128no—
641#67—128no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—34no—
648C2×Dic3—34no—
649C2×Dic3—64no—
650C2×Dic3—68no—
651C2×Dic3—68no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—122no—
663C2×Dic3—122no—
664C2×Dic3—128no—
665C2×Dic3—122no—
666C2×Dic3—122no—
667C2×Dic3—122no—
668C2×Dic3C2×#6712yescomplemented
669D12—28no—
670C4×D3—28no—
671C2×C32—24no—
672C2×C32—42no—
673C2×C32C2×#12011yescharacteristic
674C2×C32C2×#12011yescharacteristic
675C2×C32#53411yescharacteristic
676C2×C32D4212yes—
677C2×C32D4212yes—
678C3×D3—24no—
679C3×D3—42no—
680C3×D3—42no—
681C3×D3—44no—
682C24—31no—
683C24—32no—
684C24—31no—
685C24—31no—
686C24—34no—
687C24—62no—
688C24—62no—
689C24—64no—
690C24—64no—
691C24—64no—
692C24—62no—
693C24—62no—
694C24—62no—
695C24—62no—
696C24—62no—
697C24—62no—
698C24—122no—
699C24—122no—
700C24—122no—
701C24C2×D3211yescharacteristic
702C24C2×D3211yescharacteristic
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—34no—
706C2×D4—62no—
707C2×D4—62no—
708C2×D4—62no—
709C2×D4—632no—
710C2×D4—62no—
711C2×D4—62no—
712C2×D4—62no—
713C2×D4—62no—
714C2×D4—64no—
715C2×D4—64no—
716C2×D4—62no—
717C2×D4—98no—
718C2×D4—122no—
719C2×D4—184no—
720C2×D4—184no—
721C2×D4—184no—
722C2×D4—184no—
723C2×D4—184no—
724C2×D4—1832no—
725C2×D4—184no—
726C2×D4—184no—
727C2×D4—362no—
728C2×D4#62514yescomplemented
729C22×C4—31no—
730C22×C4—32no—
731C22×C4—62no—
732C22×C4—62no—
733C22×C4—62no—
734C22×C4—92no—
735C22×C4—92no—
736C22×C4—184no—
737C22×C4—182no—
738C22×C4C2×D3211yescharacteristic
739C22⋊C4—62no—
740C22⋊C4—64no—
741C22⋊C4—184no—
742C22⋊C4—184no—
743C22⋊C4—184no—
744C22⋊C4—184no—
745C22⋊C4—182no—
746C22⋊C4—362no—
747C22×C3—22no—
748C22×C3—24no—
749C22×C3—24no—
750C22×C3—24no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—24no—
755C22×C3—22no—
756C22×C3—24no—
757C22×C3—24no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—24no—
765C22×C3—34no—
766C22×C3—42no—
767C22×C3—44no—
768C22×C3—42no—
769C22×C3—44no—
770C22×C3—42no—
771C22×C3—44no—
772C22×C3—41no—
773C22×C3—42no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—42no—
778C22×C3—62no—
779C22×C3—64no—
780C22×C3—62no—
781C22×C3—64no—
782C22×C3—64no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—64no—
786C22×C3—64no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—64no—
790C22×C3—81no—
791C22×C3—81no—
792C22×C3—82no—
793C22×C3—1216no—
794C22×C3—1216no—
795C22×C3—1216no—
796C22×C3—122no—
797C22×C3—122no—
798C22×C3—122no—
799C22×C3—122no—
800C22×C3—122no—
801C22×C3—122no—
802C22×C3—121no—
803C22×C3—121no—
804C22×C3—122no—
805C22×C3#93714yescomplemented
806C22×C3#95314yescomplemented
807C22×C3C2×D3×D412yes—
808C22×C3C2×D3×D412yes—
809C22×C3C2×D3×D411yescharacteristic
810C22×C3C2×D3×D411yescharacteristic
811C22×C3#100412yes—
812C22×C3#100412yes—
813C22×C3C22×#6711yescharacteristic
814C22×C3C22×#6711yescharacteristic
815C22×C3C22×#6711yescharacteristic
816C22×C3C22×#6711yescharacteristic
817C2×D3—24no—
818C2×D3—24no—
819C2×D3—22no—
820C2×D3—22no—
821C2×D3—22no—
822C2×D3—24no—
823C2×D3—24no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—24no—
828C2×D3—24no—
829C2×D3—416no—
830C2×D3—416no—
831C2×D3—416no—
832C2×D3—42no—
833C2×D3—41no—
834C2×D3—42no—
835C2×D3—42no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—41no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3#93714yescomplemented
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—42no—
845C3×C4—62no—
846C3×C4—122no—
847Dic3—22no—
848Dic3—42no—
849Dic3—64no—
850Dic3—64no—
851Dic3—124no—
852Dic3—122no—
853Dic3—122no—
854Dic3—242no—
855C32#240311yescharacteristic, complemented, Sylow
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—21no—
861C23—21no—
862C23—34no—
863C23—32no—
864C23—34no—
865C23—32no—
866C23—32no—
867C23—68no—
868C23—68no—
869C23—68no—
870C23—62no—
871C23—61no—
872C23—61no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—61no—
882C23—61no—
883C23—62no—
884C23—61no—
885C23—61no—
886C23—62no—
887C23—68no—
888C23—124no—
889C23—128no—
890C23—128no—
891C23—128no—
892C23—128no—
893C23—128no—
894C23—124no—
895C23—124no—
896C23—128no—
897C23—124no—
898C23—124no—
899C23C2×#62512yes—
900C23C2×#62512yescomplemented
901C23D3×#6712yes—
902C23D3×#6712yes—
903C23C22×D3211yescharacteristic
904D4—28no—
905D4—68no—
906D4—68no—
907D4—68no—
908D4—128no—
909D4—1816no—
910D4—1816no—
911D4—368no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—32no—
915C2×C4—68no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—94no—
922C2×C4—188no—
923C2×C4—182no—
924C2×C4—182no—
925C2×C4—182no—
926C2×C4—182no—
927C2×C4—182no—
928C2×C4C2×#62512yescomplemented
929C2×C3—24no—
930C2×C3—24no—
931C2×C3—22no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—22no—
936C2×C3—44no—
937C2×C3—42no—
938C2×C3—42no—
939C2×C3—64no—
940C2×C3—82no—
941C2×C3—124no—
942C2×C3—122no—
943C2×C3—122no—
944C2×C3D3×#12011yescharacteristic
945C2×C3#558911yescharacteristic
946C2×C3#559012yes—
947C2×C3C2×#93711yescharacteristic
948C2×C3C2×#93711yescharacteristic
949C2×C3D4×#6712yes—
950C2×C3D4×#6712yes—
951C2×C3D4×#6712yes—
952C2×C3#580411yescharacteristic
953C2×C3C2×#95311yescharacteristic
954D3—24no—
955D3—42no—
956D3—42no—
957D3—44no—
958C22—24no—
959C22—22no—
960C22—22no—
961C22—24no—
962C22—24no—
963C22—22no—
964C22—34no—
965C22—41no—
966C22—41no—
967C22—42no—
968C22—64no—
969C22—62no—
970C22—62no—
971C22—64no—
972C22—64no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—64no—
977C22—62no—
978C22—64no—
979C22—64no—
980C22—1216no—
981C22—1216no—
982C22—1216no—
983C22—122no—
984C22—122no—
985C22—122no—
986C22—122no—
987C22—121no—
988C22—122no—
989C22—121no—
990C22—122no—
991C22—122no—
992C22#6397614yescomplemented
993C22D32×D412yes—
994C22#6431312yes—
995C22C22×#62511yescharacteristic
996C22C2×D3×#6711yescharacteristic
997C22C2×D3×#6711yescharacteristic
998C4—22no—
999C4—62no—
1000C4—122no—
1001C4—184no—
1002C4—362no—
1003C3—21no—
1004C3#8260411yescharacteristic, complemented
1005C3#8405211yescharacteristic, complemented
1006C2—24no—
1007C2—42no—
1008C2—64no—
1009C2—124no—
1010C2—122no—
1011C2—122no—
1012C2D4×#62512yes—
1013C2#1059523011yescharacteristic
1014C2D3×#93711yescharacteristic
1015C2#1059528712yes—
1016C2C2×#6397611yescharacteristic
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×#625C2semidirect
3. C2×C3×#937C2semidirect
4. C2×#63976C2semidirect
5. C2×#63976C2semidirect
6. #10592919C2semidirect
7. #10591723C2semidirect
8. #10591713C2semidirect
9. #10591706C2semidirect
10. #10591389C2semidirect
11. #10591381C2semidirect
15. C24×C3×D3C22semidirect
16. C24×C3×D3C22semidirect
18. C23×C3⋊Dic3C22semidirect
20. C22×C3×#67C22semidirect
21. C22×C3×#67C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
30. C22×#625C22semidirect
31. C22×#625C22semidirect
32. C2×#3757C22semidirect
33. C2×#3757C22semidirect
34. C2×C3×#217C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×(C2×D3)⋊Dic3C22semidirect
40. C2×(C2×D3)⋊Dic3C22semidirect
41. C2×(C2×D3)⋊Dic3C22semidirect
42. C2×(C2×D3)⋊Dic3C22semidirect
43. #63658C22semidirect
44. #63579C22semidirect
48. C22×D3×D4D3semidirect
54. C2×#937D3semidirect
84. C23×C3×D3D4semidirect
91. C2×C32×D4D4semidirect
105. C2×C3×#67D4semidirect
124. C2×#625D4semidirect
138. C24×D3C2×D3semidirect
139. C24×D3C2×D3semidirect
162. C22×#67C2×D3semidirect
163. C22×#67C2×D3semidirect
170. C22×D12C2×D3semidirect
171. C22×C4×D3C2×D3semidirect
187. C2×#217C2×D3semidirect
195. C2×(C2×D3)⋊C4C2×D3semidirect
210. C23×C32C2×D4semidirect
247. C22×C3×D3C2×D4semidirect
248. C22×C3×D3C2×D4semidirect
252. C2×C32×C4C2×D4semidirect
259. C2×C3⋊Dic3C2×D4semidirect
268. C2×C3×Dic3C2×D4semidirect
324. C23×D3#67semidirect
349. C2×C3×D4#67semidirect
350. C2×C3×D4#67semidirect
387. C2×#67#67semidirect
436. C22×C32#120semidirect
466. C2×C3×D3#120semidirect
569. C23×C3C2×#67semidirect
570. C23×C3C2×#67semidirect
606. C22×D3D3×D4semidirect
609. C22×D3C2×#67semidirect
631. C2×C3×C4C2×#67semidirect
632. C2×C3×C4C2×#67semidirect
668. C2×Dic3C2×#67semidirect
728. C2×D4#625semidirect
805. C22×C3#937semidirect
806. C22×C3#953semidirect
841. C2×D3#937semidirect
855. C32#2403semidirect
900. C23C2×#625semidirect
928. C2×C4C2×#625semidirect
992. C22#63976semidirect
1004. C3#82604semidirect
1005. 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×#6252
C2×C3×#9372
C2×#639762
#105929192
#105917232
#105917132
#105917062
#105913892
#105913812
#840523
#826043