Finite Group Databasebeta

← #10720187

Subgroups — #10720187

Order 768.

3158 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic
2C23×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic, complemented
4C2×#5220C211yesmaximal, characteristic, complemented
5C2×#5213C211yesmaximal, characteristic, complemented
6C2×#4957C212yesmaximal, complemented
7C2×#4958C211yesmaximal, characteristic, complemented
8C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
9#71547C212yesmaximal, complemented
10#69428C212yesmaximal, complemented
11Dic3⋊#95C212yesmaximal, complemented
12#14137—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C23×#67C2211yescharacteristic
17C24×Dic3C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×#217C2212yes—
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C2×#939—24no—
25C2×#939—24no—
26C2×#939C418yescomplemented
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×Dic3⋊C4—24no—
31C22×Dic3⋊C4—28no—
32C22×Dic3⋊C4C2212yes—
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2212yes—
35C22×C4×Dic3C2212yes—
36C3×#386—24no—
37C2×C3×#95C2212yes—
38#5220—24no—
39#5213—24no—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43C2×C3⋊#95C2212yes—
44#4958—24no—
45#4957—28no—
46Dic3×C22⋊C4—24no—
47C22×#121—31no—
48C23×C4⋊C4—31no—
49C2×#390—32no—
50C2×#386—31no—
51C2×#386—31no—
52C2×#386—31no—
53C2×#386D311yescharacteristic, complemented
54C2×C4×C22⋊C4—31no—
55#1439—32no—
56#1439—32no—
57C4⋊#95—32no—
58C25×C3C2311yescharacteristic
59C25×C3C2311yescharacteristic
60C24×D3C2311yescharacteristic
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4—22no—
67C22×C3×D4C2×C414yes—
68C23×C3×C4—22no—
69C23×C3×C4—24no—
70C23×C3×C4—22no—
71C23×C3×C4—22no—
72C23×C3×C4—42no—
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2312yes—
75C23×C3×C4C2312yes—
76C22×#67—22no—
77C22×#67—22no—
78C22×#67—22no—
79C22×#67—22no—
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—24no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—24no—
86C22×#67C2×C414yes—
87C22×#67C2×C414yescomplemented
88C23×Dic3—24no—
89C23×Dic3—24no—
90C23×Dic3—22no—
91C23×Dic3—24no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—42no—
95C23×Dic3C2×C414yes—
96C23×Dic3D414yes—
97C23×Dic3D414yes—
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2312yes—
100C23×Dic3C2312yes—
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—42no—
108C2×C3×C22⋊C4D414yescomplemented
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—24no—
114C2×#217—24no—
115C2×#217—42no—
116C2×#217C2×C414yescomplemented
117C2×#217D414yescomplemented
118#939—232no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—24no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—24no—
125C2×(C2×D3)⋊C4—42no—
126C2×(C2×D3)⋊C4—42no—
127C2×(C2×D3)⋊C4C2×C414yescomplemented
128C2×Dic3⋊C4—232no—
129C2×Dic3⋊C4—24no—
130C2×Dic3⋊C4—24no—
131C2×Dic3⋊C4—24no—
132C2×Dic3⋊C4—24no—
133C2×Dic3⋊C4—24no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4C2×C414yescomplemented
137C2×Dic3⋊C4D418yescomplemented
138C2×C4×Dic3—24no—
139C2×C4×Dic3—24no—
140C2×C4×Dic3—24no—
141C3×#95—24no—
142C3⋊#95—24no—
143C3⋊#95—24no—
144C3⋊#95—24no—
145C3⋊#95—24no—
146C23×D4—31no—
147C23×D4—31no—
148C23×D4C2×D311yescharacteristic
149C24×C4—31no—
150C24×C4—31no—
151C24×C4C2×D311yescharacteristic
152C2×#121—38no—
153C2×#121—64no—
154C2×#121—64no—
155C22×C4⋊C4—32no—
156C22×C4⋊C4—31no—
157C22×C4⋊C4—32no—
158C22×C4⋊C4—68no—
159C22×C4⋊C4—64no—
160C22×C22⋊C4—31no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—32no—
164C22×C22⋊C4—32no—
165C22×C22⋊C4—32no—
166C22×C22⋊C4C2×D312yes—
167C22×C22⋊C4C2×D311yescharacteristic
168C22×C42—32no—
169#390—68no—
170#386—24no—
171#386—64no—
172#386—64no—
173#386—64no—
174C4×C22⋊C4—64no—
175C2×#95—32no—
176C2×#95—32no—
177C2×#95—32no—
178C2×#95—32no—
179C2×#95C2×D312yes—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—21no—
185C24×C3—22no—
186C24×C3—21no—
187C24×C3—21no—
188C24×C3—21no—
189C24×C3—22no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3—22no—
193C24×C3—22no—
194C24×C3C22×C412yes—
195C24×C3C22×C412yes—
196C24×C3C2×D412yes—
197C24×C3C2×D412yes—
198C24×C3C2×D412yes—
199C24×C3C2×D412yes—
200C24×C3#4112yes—
201C24×C3#4112yes—
202C24×C3C2411yescharacteristic
203C23×D3—22no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—22no—
211C23×D3—22no—
212C23×D3—22no—
213C23×D3C22×C412yes—
214C2×C3×D4—28no—
215C2×C3×D4—28no—
216C2×C3×D4—28no—
217C2×C3×D4—44no—
218C2×C3×D4—44no—
219C2×C3×D4—44no—
220C2×C3×D4—44no—
221C22×C3×C4—28no—
222C22×C3×C4—21no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—48no—
241C22×C3×C4—48no—
242C22×C3×C4—44no—
243C22×C3×C4—44no—
244C22×C3×C4C22×C412yes—
245C22×C3×C4C2×D414yes—
246C22×C3×C4C2×D414yes—
247C2×#67—28no—
248C2×#67—28no—
249C2×#67—28no—
250C2×#67—28no—
251C2×#67—216no—
252C2×#67—44no—
253C2×#67—44no—
254C2×#67—44no—
255C2×#67—44no—
256C2×#67—44no—
257C2×#67—48no—
258C2×#67—44no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—216no—
262C22×Dic3—28no—
263C22×Dic3—216no—
264C22×Dic3—28no—
265C22×Dic3—28no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—48no—
285C22×Dic3—48no—
286C22×Dic3—44no—
287C22×Dic3—44no—
288C22×Dic3C22⋊C4116yescomplemented
289C22×Dic3C22×C412yes—
290C22×Dic3C22×C412yes—
291C22×Dic3C22×C412yes—
292C22×Dic3C2×D414yes—
293C22×Dic3C2×D414yes—
294C22×Dic3C2×D412yes—
295C22×Dic3C2×D412yes—
296C22×Dic3C2×D412yes—
297C22×Dic3C2×D412yes—
298C22×Dic3C2×D414yes—
299C22×Dic3#4114yes—
300C3×C22⋊C4—28no—
301C3×C22⋊C4—48no—
302#217—28no—
303#217—28no—
304#217—48no—
305(C2×D3)⋊C4—28no—
306(C2×D3)⋊C4—48no—
307(C2×D3)⋊C4—48no—
308Dic3⋊C4—216no—
309Dic3⋊C4—28no—
310Dic3⋊C4—216no—
311C4×Dic3—48no—
312C25—31no—
313C25C22×D311yescharacteristic
314C25C22×D311yescharacteristic
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—34no—
322C22×D4—34no—
323C22×D4—62no—
324C22×D4—62no—
325C22×D4—64no—
326C22×D4—64no—
327C22×D4—62no—
328C22×D4—62no—
329C22×D4—62no—
330C22×D4—62no—
331C22×D4—62no—
332C22×D4—62no—
333C22×D4C4×D314yes—
334C23×C4—22no—
335C23×C4—24no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—31no—
339C23×C4—34no—
340C23×C4—34no—
341C23×C4—34no—
342C23×C4—31no—
343C23×C4—32no—
344C23×C4—32no—
345C23×C4—31no—
346C23×C4—42no—
347C23×C4—64no—
348C23×C4—64no—
349C23×C4—64no—
350C23×C4—62no—
351C23×C4—62no—
352C23×C4—62no—
353C23×C4—122no—
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D312yes—
356C23×C4C22×D312yes—
357#121—632no—
358C2×C4⋊C4—34no—
359C2×C4⋊C4—38no—
360C2×C4⋊C4—64no—
361C2×C4⋊C4—64no—
362C2×C4⋊C4—64no—
363C2×C4⋊C4—64no—
364C2×C4⋊C4—62no—
365C2×C4⋊C4—62no—
366C2×C4⋊C4—632no—
367C2×C4⋊C4—64no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—34no—
373C2×C22⋊C4—34no—
374C2×C22⋊C4—34no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—62no—
377C2×C22⋊C4—62no—
378C2×C22⋊C4—62no—
379C2×C22⋊C4—62no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—64no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—64no—
386C2×C22⋊C4—64no—
387C2×C22⋊C4—64no—
388C2×C22⋊C4—122no—
389C2×C22⋊C4—122no—
390C2×C22⋊C4—122no—
391C2×C22⋊C4#6714yescomplemented
392C2×C42—64no—
393C2×C42—64no—
394C2×C42—64no—
395#95—24no—
396#95—64no—
397#95—64no—
398#95—64no—
399#95—64no—
400C23×C3—24no—
401C23×C3—24no—
402C23×C3—22no—
403C23×C3—24no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—24no—
416C23×C3—22no—
417C23×C3—24no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—24no—
421C23×C3—41no—
422C23×C3—42no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—42no—
436C23×C3—42no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3C2×C22⋊C414yes—
440C23×C3C4×D414yes—
441C23×C3C4×D414yes—
442C23×C3#12114yes—
443C23×C3#12114yes—
444C23×C3#12414yes—
445C23×C3#12714yes—
446C23×C3C23×C411yescharacteristic
447C23×C3C22×D411yescharacteristic
448C23×C3C22×D411yescharacteristic
449C23×C3C22×D412yes—
450C23×C3C22×D411yescharacteristic
451C23×C3C22×D411yescharacteristic
452C23×C3C2×#4111yescharacteristic
453C23×C3C2×#4111yescharacteristic
454C23×C3C2×#4112yes—
455C23×C3H(5,𝔽2)12yes—
456C23×C32−1+412yes—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—24no—
461C22×D3—24no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—42no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—42no—
472C22×D3—42no—
473C22×D3—42no—
474C22×D3—42no—
475C22×D3—42no—
476C22×D3—42no—
477C22×D3—42no—
478C22×D3—42no—
479C22×D3—42no—
480C3×D4—416no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—24no—
485C2×C3×C4—24no—
486C2×C3×C4—24no—
487C2×C3×C4—24no—
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—416no—
491C2×C3×C4—42no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—42no—
496C2×C3×C4—41no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—42no—
500C2×C3×C4—42no—
501C2×C3×C4—42no—
502C2×C3×C4—42no—
503#67—416no—
504#67—416no—
505C2×Dic3—24no—
506C2×Dic3—22no—
507C2×Dic3—24no—
508C2×Dic3—22no—
509C2×Dic3—232no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—24no—
514C2×Dic3—24no—
515C2×Dic3—24no—
516C2×Dic3—24no—
517C2×Dic3—24no—
518C2×Dic3—24no—
519C2×Dic3—416no—
520C2×Dic3—42no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—42no—
525C2×Dic3—41no—
526C2×Dic3—42no—
527C2×Dic3—42no—
528C2×Dic3—42no—
529C2×Dic3—42no—
530C2×Dic3—42no—
531C2×Dic3—42no—
532C2×Dic3C2×C22⋊C414yes—
533C2×Dic3C2×C22⋊C414yes—
534C2×Dic3C4×D418yes—
535C2×Dic3#12014yes—
536C2×Dic3#12118yes—
537C2×Dic3#12314yes—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—21no—
543C24—22no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—21no—
552C24—32no—
553C24—61no—
554C24—61no—
555C24—62no—
556C24—61no—
557C24—61no—
558C24—61no—
559C24—62no—
560C24—62no—
561C24—62no—
562C24—61no—
563C24C2×C4×D312yes—
564C24C2×C4×D312yes—
565C24#23512yes—
566C24D3×D412yes—
567C24D3×D412yes—
568C24D3×D412yes—
569C24#23712yes—
570C24C2×#6712yes—
571C24C23×D311yescharacteristic
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—44no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—68no—
580C2×D4—616no—
581C2×D4—68no—
582C2×D4—68no—
583C2×D4—68no—
584C2×D4—124no—
585C2×D4—124no—
586C2×D4—128no—
587C2×D4—124no—
588C2×D4—124no—
589C2×D4—124no—
590C2×D4—124no—
591C22×C4—28no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—32no—
611C22×C4—32no—
612C22×C4—34no—
613C22×C4—32no—
614C22×C4—34no—
615C22×C4—316no—
616C22×C4—32no—
617C22×C4—32no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—34no—
621C22×C4—34no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—68no—
627C22×C4—68no—
628C22×C4—616no—
629C22×C4—616no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—68no—
633C22×C4—62no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—62no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—61no—
644C22×C4—62no—
645C22×C4—62no—
646C22×C4—62no—
647C22×C4—62no—
648C22×C4—62no—
649C22×C4—61no—
650C22×C4—62no—
651C22×C4—128no—
652C22×C4—128no—
653C22×C4—124no—
654C22×C4—124no—
655C22×C4C2×C4×D312yes—
656C22×C4D3×D414yes—
657C22×C4C2×#6714yes—
658C4⋊C4—616no—
659C4⋊C4—68no—
660C4⋊C4—616no—
661C22⋊C4—28no—
662C22⋊C4—48no—
663C22⋊C4—68no—
664C22⋊C4—68no—
665C22⋊C4—68no—
666C22⋊C4—128no—
667C22⋊C4—128no—
668C22⋊C4—128no—
669C42—128no—
670C22×C3—24no—
671C22×C3—28no—
672C22×C3—28no—
673C22×C3—28no—
674C22×C3—28no—
675C22×C3—24no—
676C22×C3—24no—
677C22×C3—24no—
678C22×C3—24no—
679C22×C3—24no—
680C22×C3—42no—
681C22×C3—44no—
682C22×C3—44no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—82no—
686C22×C3—82no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3#39018yescomplemented
692C22×C3C22×C22⋊C411yescharacteristic
693C22×C3C2×C4×D411yescharacteristic
694C22×C3C2×C4×D411yescharacteristic
695C22×C3C2×C4×D412yes—
696C22×C3#52012yes—
697C22×C3C2×#12011yescharacteristic
698C22×C3C2×#12111yescharacteristic
699C22×C3C2×#12111yescharacteristic
700C22×C3C2×#12112yes—
701C22×C3C2×#12311yescharacteristic
702C22×C3C2×#12411yescharacteristic
703C22×C3C2×#12711yescharacteristic
704C22×C3#53511yescharacteristic
705C22×C3#53611yescharacteristic
706C22×C3#53712yes—
707C22×C3D4212yes—
708C22×C3D4212yes—
709C22×C3#54712yes—
710C22×C3#54712yes—
711C22×C3#54812yes—
712C22×C3#54812yes—
713C22×C3#55312yes—
714C22×C3#55312yes—
715C2×D3—42no—
716C2×D3—44no—
717C2×D3—44no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3—82no—
721C2×D3—82no—
722C2×D3—81no—
723C2×D3—81no—
724C2×D3—81no—
725C2×D3—81no—
726C3×C4—44no—
727C3×C4—44no—
728C3×C4—42no—
729Dic3—24no—
730Dic3—44no—
731Dic3—44no—
732Dic3—42no—
733Dic3#38618yescomplemented
734C23—22no—
735C23—22no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—22no—
744C23—24no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—24no—
754C23—24no—
755C23—41no—
756C23—41no—
757C23—42no—
758C23—41no—
759C23—41no—
760C23—42no—
761C23—42no—
762C23—41no—
763C23—41no—
764C23—42no—
765C23—42no—
766C23—41no—
767C23—42no—
768C23—41no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—62no—
774C23—62no—
775C23—62no—
776C23—64no—
777C23—64no—
778C23—121no—
779C23—121no—
780C23—122no—
781C23—121no—
782C23—121no—
783C23—122no—
784C23—122no—
785C23—121no—
786C23—121no—
787C23—122no—
788C23—122no—
789C23—121no—
790C23—122no—
791C23—121no—
792C23—122no—
793C23—122no—
794C23—122no—
795C23—122no—
796C23D3×C22⋊C414yes—
797C23#67⋊C414yes—
798C23#88414yes—
799C23#88514yes—
800C23C4×#6714yes—
801C23#93914yes—
802C23#94014yes—
803C23C22×C4×D311yescharacteristic
804C23C2×#23511yescharacteristic
805C23C2×D3×D411yescharacteristic
806C23C2×D3×D411yescharacteristic
807C23C2×D3×D411yescharacteristic
808C23C2×D3×D412yes—
809C23C2×#23711yescharacteristic
810C23#100412yes—
811C23D3×#4112yes—
812C23#101012yes—
813C23C22×#6711yescharacteristic
814D4—416no—
815D4—1216no—
816D4—1216no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—34no—
827C2×C4—34no—
828C2×C4—38no—
829C2×C4—34no—
830C2×C4—38no—
831C2×C4—34no—
832C2×C4—416no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—632no—
846C2×C4—62no—
847C2×C4—64no—
848C2×C4—62no—
849C2×C4—64no—
850C2×C4—64no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—64no—
854C2×C4—62no—
855C2×C4—64no—
856C2×C4—64no—
857C2×C4—64no—
858C2×C4—64no—
859C2×C4—1216no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—122no—
863C2×C4—122no—
864C2×C4—121no—
865C2×C4—122no—
866C2×C4—121no—
867C2×C4—122no—
868C2×C4—122no—
869C2×C4—122no—
870C2×C4—122no—
871C2×C4—122no—
872C2×C3—28no—
873C2×C3—82no—
874C2×C3C2×#38611yescharacteristic
875C2×C3C2×#39011yescharacteristic
876C2×C3#231111yescharacteristic
877C2×C3#236112yes—
878C2×C3#236112yes—
879C2×C3#241612yes—
880C2×C3#241612yes—
881C2×C3#243311yescharacteristic
882C2×C3#243611yescharacteristic
883C2×C3#250111yescharacteristic
884C2×C3#250411yescharacteristic
885D3—82no—
886C22—24no—
887C22—24no—
888C22—28no—
889C22—24no—
890C22—24no—
891C22—28no—
892C22—28no—
893C22—24no—
894C22—28no—
895C22—24no—
896C22—42no—
897C22—44no—
898C22—42no—
899C22—42no—
900C22—44no—
901C22—81no—
902C22—81no—
903C22—82no—
904C22—81no—
905C22—82no—
906C22—81no—
907C22—122no—
908C22—124no—
909C22—122no—
910C22—122no—
911C22—124no—
912C22—241no—
913C22—241no—
914C22—242no—
915C22—241no—
916C22—242no—
917C22—241no—
918C22#495718yescomplemented
919C22C2×D3×C22⋊C411yescharacteristic
920C22C2×#67⋊C411yescharacteristic
921C22C2×#88411yescharacteristic
922C22C2×#88511yescharacteristic
923C22#554012yes—
924C22C4×D3×D412yes—
925C22#554612yes—
926C22#555212yes—
927C22D3×#12011yescharacteristic
928C22#559012yes—
929C22#559211yescharacteristic
930C22#559712yes—
931C22#559812yes—
932C22#560112yes—
933C22D3×#12112yes—
934C22#564811yescharacteristic
935C22D3×#12311yescharacteristic
936C22#565512yes—
937C22C2×C4×#6711yescharacteristic
938C22D4×#6712yes—
939C22C2×#93911yescharacteristic
940C22C2×#94011yescharacteristic
941C22#582412yes—
942C4—38no—
943C4—44no—
944C4—42no—
945C4—44no—
946C4—64no—
947C4—124no—
948C4—122no—
949C4—124no—
950C3#1413711yescharacteristic, complemented, Sylow
951C2—28no—
952C2—82no—
953C2—242no—
954C2#7466211yescharacteristic
955C2#7467612yes—
956C2#7469212yes—
957C2#7470111yescharacteristic
958C2#7474211yescharacteristic
959C2D3×#38611yescharacteristic
960C2C2×#495711yescharacteristic
961C2#8234012yes—
962C2#8258811yescharacteristic
963C2#8264212yes—
964C2#8285911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#386C2
socle, cosocleC24×C3C24
prime radicalC22×#939C2
hypercenterC2×#386D3
hypocenterC3#14137
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×Dic3⋊C4C2semidirect
3. C2×C3×#386C2semidirect
4. C2×#5220C2semidirect
5. C2×#5213C2semidirect
6. C2×#4957C2semidirect
7. C2×#4958C2semidirect
8. C2×Dic3×C22⋊C4C2semidirect
9. #71547C2semidirect
10. #69428C2semidirect
11. Dic3⋊#95C2semidirect
26. C2×#939C4semidirect
53. C2×#386D3semidirect
87. C22×#67C2×C4semidirect
108. C2×C3×C22⋊C4D4semidirect
116. C2×#217C2×C4semidirect
117. C2×#217D4semidirect
127. C2×(C2×D3)⋊C4C2×C4semidirect
136. C2×Dic3⋊C4C2×C4semidirect
137. C2×Dic3⋊C4D4semidirect
288. C22×Dic3C22⋊C4semidirect
391. C2×C22⋊C4#67semidirect
691. C22×C3#390semidirect
733. Dic3#386semidirect
918. C22#4957semidirect
950. C3#14137semidirect

Maximal subgroups

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

subgroupindex
C22×#9392
C23×Dic3⋊C42
C2×C3×#3862
C2×#52202
C2×#52132
C2×#49572
C2×#49582
C2×Dic3×C22⋊C42
#715472
#694282
Dic3⋊#952
#141373