Finite Group Databasebeta

← #10720099

Subgroups — #10720099

Order 768.

4046 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D3)⋊C4C211yesmaximal, characteristic
2C22×D3×C22⋊C4C211yesmaximal, characteristic
3C2×#4955C211yesmaximal, characteristic
4C2×#4950C211yesmaximal, characteristic, complemented
5C2×#4946C211yesmaximal, characteristic, complemented
6C2×#4668C212yesmaximal, complemented
7C3×C22⋊#95C211yesmaximal, characteristic, complemented
8#72127C211yesmaximal, characteristic, complemented
9#69428C212yesmaximal, complemented
10#69427C212yesmaximal, complemented
11(C2×D3)⋊#95C212yesmaximal, complemented
12#14127—31nomaximal, Sylow
13C25×D3C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C23×C4×D3C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×(C2×D3)⋊C4—24no—
23C22×(C2×D3)⋊C4—28no—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2212yes—
30C22×C4⋊Dic3C2212yescomplemented
31C22×Dic3⋊C4C2212yescomplemented
32C2×D3×C22⋊C4—24no—
33C2×D3×C22⋊C4—24no—
34C2×D3×C22⋊C4—24no—
35C2×C3×#95C2212yescomplemented
36C2×C3×#95C2212yescomplemented
37C2×C3⋊#95C2212yescomplemented
38C2×C3⋊#95C2212yescomplemented
39C2×C3⋊#95C2212yescomplemented
40C2×C3⋊#95C2212yescomplemented
41#4955C418yescomplemented
42#4950—24no—
43#4946—24no—
44#4668—28no—
45C23×C22⋊C4—31no—
46C23×C22⋊C4—31no—
47C2×#385—32no—
48C2×#385—31no—
49C2×#385—31no—
50C2×#379—31no—
51#1439—32no—
52#1439—32no—
53C22⋊#95—32no—
54C22⋊#95—31no—
55C22⋊#95D311yescharacteristic, complemented
56C25×C3C2311yescharacteristic
57C24×D3—22no—
58C24×D3—22no—
59C24×D3—22no—
60C24×D3—22no—
61C24×D3—24no—
62C24×D3—24no—
63C24×D3—42no—
64C24×D3—42no—
65C24×D3C2×C414yes—
66C24×D3D414yes—
67C24×D3Q814yes—
68C24×D3C2311yescharacteristic
69C24×D3C2311yescharacteristic
70C23×C3×C4—22no—
71C23×C3×C4—24no—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—42no—
75C23×C3×C4C2312yes—
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2312yes—
79C23×Dic3—22no—
80C23×Dic3—24no—
81C23×Dic3—22no—
82C23×Dic3—22no—
83C23×Dic3—42no—
84C23×Dic3C2312yes—
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2312yes—
88C22×C4×D3—22no—
89C22×C4×D3—22no—
90C22×C4×D3—22no—
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—24no—
95C22×C4×D3—24no—
96C22×C4×D3—42no—
97C22×C4×D3—42no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4C2×C414yescomplemented
103C2×C3×C22⋊C4D414yes—
104C2×#217—22no—
105C2×#217—22no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217C2×C414yescomplemented
109C2×#217D414yes—
110C2×(C2×D3)⋊C4—232no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—42no—
125C2×(C2×D3)⋊C4—42no—
126C2×(C2×D3)⋊C4C2×C418yescomplemented
127C2×(C2×D3)⋊C4C2×C418yescomplemented
128C2×(C2×D3)⋊C4D418yes—
129C2×C4⋊Dic3—24no—
130C2×C4⋊Dic3—24no—
131C2×C4⋊Dic3—42no—
132C2×Dic3⋊C4—24no—
133C2×Dic3⋊C4—24no—
134C2×Dic3⋊C4—42no—
135D3×C22⋊C4—232no—
136C3×#95—24no—
137C3×#95—42no—
138C3⋊#95—24no—
139C3⋊#95—24no—
140C3⋊#95—24no—
141C3⋊#95—42no—
142C26—31no—
143C24×C4—31no—
144C24×C4—31no—
145C24×C4—31no—
146C24×C4C2×D311yescharacteristic
147C22×C4⋊C4—32no—
148C22×C4⋊C4—32no—
149C22×C22⋊C4—31no—
150C22×C22⋊C4—31no—
151C22×C22⋊C4—32no—
152C22×C22⋊C4—32no—
153C22×C22⋊C4—32no—
154C22×C22⋊C4—31no—
155C22×C22⋊C4—31no—
156C22×C22⋊C4—32no—
157C22×C22⋊C4—64no—
158C22×C22⋊C4—64no—
159C22×C22⋊C4—68no—
160C22×C22⋊C4—64no—
161C22×C22⋊C4—64no—
162C22×C22⋊C4C2×D311yescharacteristic
163C22×C22⋊C4C2×D311yescharacteristic
164#385—68no—
165#385—64no—
166#385—64no—
167#379—38no—
168C2×#95—32no—
169C2×#95—32no—
170C2×#95—32no—
171C2×#95—32no—
172C2×#95C2×D312yescomplemented
173C2×#95C2×D312yescomplemented
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3C22×C412yes—
179C24×C3C2×D412yes—
180C24×C3C2×D412yes—
181C24×C3C2×D412yes—
182C24×C3C2×Q812yes—
183C24×C3#4112yes—
184C24×C3#4112yes—
185C24×C3C2411yescharacteristic
186C23×D3—21no—
187C23×D3—21no—
188C23×D3—21no—
189C23×D3—21no—
190C23×D3—22no—
191C23×D3—22no—
192C23×D3—28no—
193C23×D3—28no—
194C23×D3—28no—
195C23×D3—28no—
196C23×D3—28no—
197C23×D3—28no—
198C23×D3—21no—
199C23×D3—22no—
200C23×D3—21no—
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—22no—
204C23×D3—22no—
205C23×D3—22no—
206C23×D3—216no—
207C23×D3—28no—
208C23×D3—216no—
209C23×D3—28no—
210C23×D3—48no—
211C23×D3—44no—
212C23×D3—44no—
213C23×D3—48no—
214C23×D3—48no—
215C23×D3—48no—
216C23×D3—48no—
217C23×D3—48no—
218C23×D3—48no—
219C23×D3—48no—
220C23×D3—48no—
221C23×D3—48no—
222C23×D3C4⋊C4116yescomplemented
223C23×D3C22×C412yes—
224C23×D3C22×C412yes—
225C23×D3C2×D412yes—
226C23×D3C2×D412yes—
227C23×D3C2×D414yes—
228C23×D3C2×Q812yes—
229C23×D3C2×Q812yes—
230C23×D3#4114yes—
231C22×C3×C4—28no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—48no—
253C22×C3×C4—48no—
254C22×C3×C4—44no—
255C22×C3×C4—44no—
256C22×C3×C4C22×C414yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2×D412yes—
259C22×C3×C4C2×D414yes—
260C22×Dic3—28no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—48no—
282C22×Dic3—48no—
283C22×Dic3—44no—
284C22×Dic3—44no—
285C22×Dic3C22×C414yes—
286C22×Dic3C2×D412yes—
287C22×Dic3C2×D414yes—
288C22×Dic3C2×D412yes—
289C2×C4×D3—28no—
290C2×C4×D3—28no—
291C2×C4×D3—48no—
292C2×C4×D3—48no—
293C2×C4×D3—48no—
294C2×C4×D3—48no—
295C2×C4×D3—44no—
296C2×C4×D3—44no—
297C2×C4×D3—44no—
298C2×C4×D3—44no—
299C3×C22⋊C4—28no—
300C3×C22⋊C4—28no—
301#217—28no—
302#217—28no—
303(C2×D3)⋊C4—28no—
304(C2×D3)⋊C4—28no—
305(C2×D3)⋊C4—216no—
306(C2×D3)⋊C4—216no—
307(C2×D3)⋊C4—216no—
308(C2×D3)⋊C4—48no—
309C4⋊Dic3—48no—
310Dic3⋊C4—48no—
311C25—31no—
312C25—31no—
313C25—34no—
314C25—34no—
315C25—34no—
316C25—64no—
317C25—64no—
318C25—62no—
319C25—62no—
320C25—62no—
321C25—62no—
322C25—122no—
323C25—122no—
324C25C22×D311yescharacteristic
325C23×C4—22no—
326C23×C4—24no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—32no—
330C23×C4—32no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—42no—
334C23×C4—62no—
335C23×C4—62no—
336C23×C4—62no—
337C23×C4—62no—
338C23×C4—64no—
339C23×C4—64no—
340C23×C4—64no—
341C23×C4—62no—
342C23×C4—62no—
343C23×C4—62no—
344C23×C4—62no—
345C23×C4—62no—
346C23×C4—122no—
347C23×C4—122no—
348C23×C4—122no—
349C23×C4C22×D312yes—
350C23×C4C22×D311yescharacteristic
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D312yes—
353C2×C4⋊C4—64no—
354C2×C4⋊C4—64no—
355C2×C4⋊C4—64no—
356C2×C4⋊C4—64no—
357C2×C4⋊C4—122no—
358C2×C4⋊C4—122no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—34no—
364C2×C22⋊C4—34no—
365C2×C22⋊C4—38no—
366C2×C22⋊C4—38no—
367C2×C22⋊C4—38no—
368C2×C22⋊C4—632no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—62no—
371C2×C22⋊C4—64no—
372C2×C22⋊C4—64no—
373C2×C22⋊C4—64no—
374C2×C22⋊C4—62no—
375C2×C22⋊C4—62no—
376C2×C22⋊C4—64no—
377C2×C22⋊C4—64no—
378C2×C22⋊C4—64no—
379C2×C22⋊C4—632no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—62no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—62no—
385C2×C22⋊C4—62no—
386C2×C22⋊C4—64no—
387C2×C22⋊C4—122no—
388C2×C22⋊C4—122no—
389C2×C22⋊C4C4×D314yescomplemented
390C2×C22⋊C4D1214yes—
391#95—24no—
392#95—42no—
393#95—64no—
394#95—64no—
395#95—64no—
396#95—122no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3—22no—
400C23×C3—24no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—24no—
405C23×C3—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3C2×C4⋊C414yes—
414C23×C3C4×D414yes—
415C23×C3C4×D414yes—
416C23×C3#12014yes—
417C23×C3C22⋊Q814yes—
418C23×C3C22⋊Q814yes—
419C23×C3#12314yes—
420C23×C3C23×C411yescharacteristic
421C23×C3C22×D411yescharacteristic
422C23×C3C22×D411yescharacteristic
423C23×C3C22×D412yes—
424C23×C3C22×D411yescharacteristic
425C23×C3C22×Q811yescharacteristic
426C23×C3C2×#4111yescharacteristic
427C23×C3C2×#4111yescharacteristic
428C23×C3C2×#4112yes—
429C23×C3H(5,𝔽2)12yes—
430C23×C3H(5,𝔽2)12yes—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—24no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—24no—
441C22×D3—24no—
442C22×D3—24no—
443C22×D3—24no—
444C22×D3—24no—
445C22×D3—24no—
446C22×D3—24no—
447C22×D3—24no—
448C22×D3—24no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—24no—
452C22×D3—24no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—24no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—24no—
463C22×D3—232no—
464C22×D3—232no—
465C22×D3—416no—
466C22×D3—432no—
467C22×D3—432no—
468C22×D3—416no—
469C22×D3—416no—
470C22×D3—416no—
471C22×D3—432no—
472C22×D3—432no—
473C22×D3—416no—
474C22×D3—42no—
475C22×D3—42no—
476C22×D3—42no—
477C22×D3—42no—
478C22×D3—42no—
479C22×D3—42no—
480C22×D3—42no—
481C22×D3—42no—
482C22×D3C2×C4⋊C414yes—
483C22×D3C2×C4⋊C414yes—
484C22×D3C4×D418yes—
485C22×D3#12014yes—
486C22×D3C22⋊Q818yes—
487C22×D3#12314yes—
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—24no—
495C2×C3×C4—24no—
496C2×C3×C4—24no—
497C2×C3×C4—24no—
498C2×C3×C4—416no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—42no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—42no—
505C2×C3×C4—42no—
506C2×C3×C4—42no—
507C2×C3×C4—42no—
508C2×C3×C4—42no—
509C2×C3×C4—42no—
510C2×C3×C4—42no—
511C2×C3×C4—42no—
512C2×C3×C4—42no—
513C2×Dic3—24no—
514C2×Dic3—24no—
515C2×Dic3—24no—
516C2×Dic3—24no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—24no—
520C2×Dic3—24no—
521C2×Dic3—24no—
522C2×Dic3—24no—
523C2×Dic3—416no—
524C2×Dic3—41no—
525C2×Dic3—42no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—42no—
530C2×Dic3—42no—
531C2×Dic3—42no—
532C2×Dic3—42no—
533C2×Dic3—42no—
534C2×Dic3—42no—
535C2×Dic3—42no—
536C2×Dic3—42no—
537C2×Dic3—42no—
538C4×D3—416no—
539C4×D3—416no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—32no—
545C24—34no—
546C24—32no—
547C24—32no—
548C24—34no—
549C24—32no—
550C24—32no—
551C24—32no—
552C24—316no—
553C24—68no—
554C24—68no—
555C24—616no—
556C24—616no—
557C24—61no—
558C24—61no—
559C24—61no—
560C24—61no—
561C24—62no—
562C24—62no—
563C24—68no—
564C24—68no—
565C24—68no—
566C24—68no—
567C24—68no—
568C24—68no—
569C24—61no—
570C24—61no—
571C24—61no—
572C24—62no—
573C24—61no—
574C24—62no—
575C24—62no—
576C24—62no—
577C24—128no—
578C24—124no—
579C24—128no—
580C24—124no—
581C24—128no—
582C24—128no—
583C24—128no—
584C24—128no—
585C24—128no—
586C24—128no—
587C24—128no—
588C24—128no—
589C24C2×C4×D312yes—
590C24C2×D1212yes—
591C24#23512yes—
592C24D3×D412yes—
593C24D3×D412yes—
594C24#23712yes—
595C24D3×Q812yes—
596C24C23×D311yescharacteristic
597C22×C4—28no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—34no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—34no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—68no—
627C22×C4—68no—
628C22×C4—68no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—62no—
646C22×C4—62no—
647C22×C4—62no—
648C22×C4—62no—
649C22×C4—128no—
650C22×C4—128no—
651C22×C4—128no—
652C22×C4—128no—
653C22×C4—124no—
654C22×C4—124no—
655C22×C4—124no—
656C22×C4—124no—
657C22×C4—128no—
658C22×C4—128no—
659C22×C4—124no—
660C22×C4—124no—
661C22×C4C2×C4×D314yes—
662C22×C4C2×D1212yes—
663C22×C4C2×D1212yes—
664C22×C4D3×D414yes—
665C4⋊C4—128no—
666C4⋊C4—128no—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—616no—
670C22⋊C4—616no—
671C22⋊C4—68no—
672C22⋊C4—68no—
673C22⋊C4—616no—
674C22⋊C4—68no—
675C22⋊C4—68no—
676C22⋊C4—128no—
677C22×C3—24no—
678C22×C3—28no—
679C22×C3—28no—
680C22×C3—24no—
681C22×C3—24no—
682C22×C3—24no—
683C22×C3—28no—
684C22×C3—28no—
685C22×C3—24no—
686C22×C3—24no—
687C22×C3#38518yescomplemented
688C22×C3C22×C4⋊C411yescharacteristic
689C22×C3C2×C4×D411yescharacteristic
690C22×C3C2×C4×D411yescharacteristic
691C22×C3C2×C4×D412yes—
692C22×C3#51812yes—
693C22×C3C2×#12011yescharacteristic
694C22×C3C2×#12011yescharacteristic
695C22×C3C2×C22⋊Q811yescharacteristic
696C22×C3C2×C22⋊Q811yescharacteristic
697C22×C3C2×C22⋊Q812yes—
698C22×C3C2×#12311yescharacteristic
699C22×C3C2×#12311yescharacteristic
700C22×C3#53411yescharacteristic
701C22×C3#53411yescharacteristic
702C22×C3#54312yes—
703C22×C3D4212yes—
704C22×C3D4212yes—
705C22×C3#54612yes—
706C22×C3#54612yes—
707C22×C3#54612yes—
708C22×C3#54612yes—
709C22×C3#55112yes—
710C22×C3#55112yes—
711C2×D3—24no—
712C2×D3—28no—
713C2×D3—28no—
714C2×D3—24no—
715C2×D3—24no—
716C2×D3—24no—
717C2×D3—28no—
718C2×D3—28no—
719C2×D3—24no—
720C2×D3—24no—
721C2×D3—24no—
722C2×D3—24no—
723C2×D3—24no—
724C2×D3—464no—
725C2×D3—44no—
726C2×D3—44no—
727C2×D3—42no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—44no—
731C2×D3—44no—
732C2×D3—42no—
733C2×D3#38518yescomplemented
734C3×C4—44no—
735C3×C4—42no—
736C3×C4—42no—
737C3×C4—44no—
738Dic3—44no—
739Dic3—42no—
740Dic3—44no—
741Dic3—42no—
742C23—24no—
743C23—22no—
744C23—22no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—22no—
753C23—22no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—34no—
759C23—34no—
760C23—38no—
761C23—34no—
762C23—38no—
763C23—34no—
764C23—632no—
765C23—64no—
766C23—62no—
767C23—64no—
768C23—62no—
769C23—62no—
770C23—62no—
771C23—62no—
772C23—64no—
773C23—62no—
774C23—62no—
775C23—64no—
776C23—64no—
777C23—64no—
778C23—64no—
779C23—62no—
780C23—64no—
781C23—64no—
782C23—64no—
783C23—64no—
784C23—62no—
785C23—62no—
786C23—632no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—64no—
794C23—64no—
795C23—62no—
796C23—62no—
797C23—64no—
798C23—1216no—
799C23—1232no—
800C23—1216no—
801C23—1232no—
802C23—1216no—
803C23—1216no—
804C23—1232no—
805C23—1232no—
806C23—1216no—
807C23—122no—
808C23—122no—
809C23—122no—
810C23—122no—
811C23—122no—
812C23—122no—
813C23—122no—
814C23—122no—
815C23C4×D1214yes—
816C23#67⋊C414yes—
817C23#88214yes—
818C23#88314yes—
819C23D3×C4⋊C414yes—
820C23#89614yes—
821C23#89714yes—
822C23C22×C4×D311yescharacteristic
823C23C22×D1211yescharacteristic
824C23C2×#23511yescharacteristic
825C23C2×D3×D411yescharacteristic
826C23C2×D3×D411yescharacteristic
827C23C2×D3×D412yes—
828C23C2×#23711yescharacteristic
829C23#100412yes—
830C23C2×D3×Q811yescharacteristic
831C23D3×#4112yes—
832C23#100912yes—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—416no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—64no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—64no—
862C2×C4—64no—
863C2×C4—64no—
864C2×C4—64no—
865C2×C4—64no—
866C2×C4—64no—
867C2×C4—64no—
868C2×C4—1216no—
869C2×C4—1216no—
870C2×C4—1216no—
871C2×C4—121no—
872C2×C4—121no—
873C2×C4—122no—
874C2×C4—122no—
875C2×C4—122no—
876C2×C4—122no—
877C2×C4—122no—
878C2×C4—122no—
879C2×C4—122no—
880C2×C4—122no—
881C2×C4—122no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—122no—
885C2×C3—28no—
886C2×C3C2×#38511yescharacteristic
887C2×C3C2×#38511yescharacteristic
888C2×C3#231511yescharacteristic
889C2×C3#235812yes—
890C2×C3#235812yes—
891C2×C3#240311yescharacteristic
892C2×C3#240511yescharacteristic
893C2×C3#240511yescharacteristic
894C2×C3#243712yes—
895C2×C3#243712yes—
896C2×C3#248311yescharacteristic
897D3—28no—
898D3—44no—
899C22—24no—
900C22—24no—
901C22—28no—
902C22—24no—
903C22—28no—
904C22—24no—
905C22—24no—
906C22—28no—
907C22—28no—
908C22—24no—
909C22—38no—
910C22—64no—
911C22—68no—
912C22—64no—
913C22—68no—
914C22—64no—
915C22—64no—
916C22—64no—
917C22—68no—
918C22—68no—
919C22—64no—
920C22—64no—
921C22—64no—
922C22—64no—
923C22—1264no—
924C22—124no—
925C22—122no—
926C22—124no—
927C22—122no—
928C22—122no—
929C22—124no—
930C22—124no—
931C22—122no—
932C22#466818yescomplemented
933C22C2×C4×D1211yescharacteristic
934C22C2×#67⋊C411yescharacteristic
935C22C2×#88211yescharacteristic
936C22C2×#88311yescharacteristic
937C22#549012yes—
938C22C2×D3×C4⋊C411yescharacteristic
939C22C2×#89611yescharacteristic
940C22C2×#89711yescharacteristic
941C22#552712yes—
942C22C4×D3×D412yes—
943C22#554512yes—
944C22D4×D1212yes—
945C22#555412yes—
946C22D3×#12011yescharacteristic
947C22#558911yescharacteristic
948C22#559112yes—
949C22#560912yes—
950C22#561012yes—
951C22D3×C22⋊Q812yes—
952C22#563412yes—
953C22D3×#12311yescharacteristic
954C22#565311yescharacteristic
955C22#565812yes—
956C4—44no—
957C4—44no—
958C4—42no—
959C4—42no—
960C4—124no—
961C4—122no—
962C4—124no—
963C4—122no—
964C3#1412711yescharacteristic, complemented, Sylow
965C2—28no—
966C2—68no—
967C2—124no—
968C2C2×#466811yescharacteristic
969C2#7357712yes—
970C2#7385311yescharacteristic
971C2#7389612yes—
972C2#7413011yescharacteristic
973C2#7441312yes—
974C2D3×#38511yescharacteristic
975C2#7459111yescharacteristic
976C2#7468611yescharacteristic
977C2#7487912yes—
978C2#7488411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C22⋊#95C2
socle, cosocleC24×C3C24
prime radicalC25×D3C22
hypercenterC22⋊#95D3
hypocenterC3#14127
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#4950C2semidirect
5. C2×#4946C2semidirect
6. C2×#4668C2semidirect
7. C3×C22⋊#95C2semidirect
8. #72127C2semidirect
9. #69428C2semidirect
10. #69427C2semidirect
11. (C2×D3)⋊#95C2semidirect
30. C22×C4⋊Dic3C22semidirect
31. C22×Dic3⋊C4C22semidirect
35. C2×C3×#95C22semidirect
36. C2×C3×#95C22semidirect
37. C2×C3⋊#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
40. C2×C3⋊#95C22semidirect
41. #4955C4semidirect
55. C22⋊#95D3semidirect
102. C2×C3×C22⋊C4C2×C4semidirect
108. C2×#217C2×C4semidirect
126. C2×(C2×D3)⋊C4C2×C4semidirect
127. C2×(C2×D3)⋊C4C2×C4semidirect
172. C2×#95C2×D3semidirect
173. C2×#95C2×D3semidirect
222. C23×D3C4⋊C4semidirect
389. C2×C22⋊C4C4×D3semidirect
687. C22×C3#385semidirect
733. C2×D3#385semidirect
932. C22#4668semidirect
964. C3#14127semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D3)⋊C42
C22×D3×C22⋊C42
C2×#49552
C2×#49502
C2×#49462
C2×#46682
C3×C22⋊#952
#721272
#694282
#694272
(C2×D3)⋊#952
#141273