Finite Group Databasebeta

← #10718587

Subgroups — #10718587

Order 768.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic3C211yesmaximal, characteristic
2C2×C3×#390C211yesmaximal, characteristic
3C2×#5221C211yesmaximal, characteristic
4C2×#4946C212yesmaximal, complemented
5C2×#4928C211yesmaximal, characteristic, complemented
6C2×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71563C211yesmaximal, characteristic, complemented
9#71547C212yesmaximal, complemented
10#71547C212yesmaximal, complemented
11#71544C212yesmaximal, complemented
12#14018—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×Dic3C2212yes—
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C22⋊C4C2212yes—
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C42C2211yescharacteristic
19C22×#217C2212yes—
20C22×#217C2212yes—
21C22×#217C2212yes—
22C2×D4×Dic3—24no—
23C2×D4×Dic3—24no—
24C2×D4×Dic3—24no—
25C22×C4⋊Dic3C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2212yes—
29C22×Dic3⋊C4C2211yescharacteristic
30C22×C4×Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C3×#390—24no—
33#5221C418yescomplemented
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4946—28no—
42C4×Dic3⋊C4—24no—
43#4928—24no—
44C22×C4×D4—31no—
45C2×#390—31no—
46C2×#390D311yescharacteristic
47C2×#389—31no—
48C2×#385—32no—
49C2×C4×C4⋊C4—31no—
50#1439—32no—
51#1439—32no—
52C4⋊#95—31no—
53C4⋊#95—31no—
54C22⋊#95—32no—
55C25×C3C2312yes—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4C2×C414yes—
61C22×C3×D4D414yes—
62C22×C3×D4Q814yes—
63C23×C3×C4C2312yes—
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2311yescharacteristic
67C23×Dic3—24no—
68C23×Dic3—24no—
69C23×Dic3—24no—
70C23×Dic3—24no—
71C23×Dic3—24no—
72C23×Dic3—42no—
73C23×Dic3—42no—
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2312yes—
76C23×Dic3C2312yes—
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C22⋊C4—24no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—42no—
88C2×C3×C22⋊C4—42no—
89C2×C3×C42—22no—
90C2×C3×C42—22no—
91C2×C3×C42—22no—
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—42no—
98C2×#217—42no—
99C2×#217C2×C418yescomplemented
100C2×#217C2×C418yescomplemented
101D4×Dic3—232no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3—22no—
105C2×C4⋊Dic3—22no—
106C2×C4⋊Dic3C2×C414yescomplemented
107C2×C4⋊Dic3D414yes—
108C2×Dic3⋊C4—22no—
109C2×Dic3⋊C4—22no—
110C2×Dic3⋊C4—22no—
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—22no—
113C2×Dic3⋊C4—24no—
114C2×Dic3⋊C4—24no—
115C2×Dic3⋊C4—42no—
116C2×Dic3⋊C4D414yescomplemented
117C2×C4×Dic3—22no—
118C2×C4×Dic3—22no—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3C2×C414yescomplemented
122C2×C4×Dic3D414yes—
123C3⋊#95—24no—
124C3⋊#95—22no—
125C3⋊#95—22no—
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95—42no—
129C3⋊#95—42no—
130C23×D4C2×D311yescharacteristic
131C24×C4—32no—
132C2×C4×D4—64no—
133C2×C4×D4—64no—
134C2×C4×D4—64no—
135C22×C4⋊C4—31no—
136C22×C4⋊C4—31no—
137C22×C4⋊C4—31no—
138C22×C4⋊C4—31no—
139C22×C4⋊C4—32no—
140C22×C4⋊C4C2×D311yescharacteristic
141C22×C22⋊C4—32no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4C2×D312yes—
145C22×C22⋊C4C2×D312yes—
146C22×C42—31no—
147C22×C42—31no—
148C22×C42C2×D311yescharacteristic
149#390—24no—
150#390—38no—
151#389—64no—
152#385—68no—
153C4×C4⋊C4—64no—
154C2×#95—31no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95—31no—
159C2×#95—32no—
160C2×#95—32no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3C22×C414yes—
174C24×C3C2×D414yes—
175C24×C3C2×Q814yes—
176C24×C3C2411yescharacteristic
177C2×C3×D4—28no—
178C2×C3×D4—28no—
179C2×C3×D4—28no—
180C2×C3×D4—28no—
181C2×C3×D4—28no—
182C2×C3×D4—28no—
183C2×C3×D4C4⋊C4116yescomplemented
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4C22×C412yes—
204C22×C3×C4C2×D412yes—
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D412yes—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×Q812yes—
209C22×C3×C4#4112yes—
210C22×C3×C4#4112yes—
211C22×C3×C4#4112yes—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—216no—
221C22×Dic3—21no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—48no—
246C22×Dic3—48no—
247C22×Dic3—48no—
248C22×Dic3—48no—
249C22×Dic3—48no—
250C22×Dic3—48no—
251C22×Dic3C22×C412yes—
252C22×Dic3C22×C414yes—
253C22×Dic3C22×C412yes—
254C22×Dic3C2×D412yes—
255C22×Dic3C2×D414yes—
256C22×Dic3C2×D412yes—
257C22×Dic3C2×D412yes—
258C22×Dic3C2×D412yes—
259C22×Dic3#4112yes—
260C22×Dic3#4112yes—
261C3×C4⋊C4—44no—
262C3×C22⋊C4—48no—
263C3×C22⋊C4—48no—
264C3×C42—44no—
265#217—216no—
266#217—216no—
267#217—48no—
268C4⋊Dic3—28no—
269C4⋊Dic3—28no—
270Dic3⋊C4—28no—
271Dic3⋊C4—28no—
272Dic3⋊C4—48no—
273C4×Dic3—28no—
274C4×Dic3—28no—
275C25C22×D312yes—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4Dic614yes—
281C22×D4C4×D314yes—
282C22×D4#6714yes—
283C23×C4—31no—
284C23×C4—31no—
285C23×C4—32no—
286C23×C4—31no—
287C23×C4—31no—
288C23×C4—32no—
289C23×C4—64no—
290C23×C4—64no—
291C23×C4—64no—
292C23×C4—64no—
293C23×C4—64no—
294C23×C4—122no—
295C23×C4—122no—
296C23×C4C22×D312yes—
297C23×C4C22×D311yescharacteristic
298C23×C4C22×D311yescharacteristic
299C23×C4C22×D311yescharacteristic
300C4×D4—632no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—34no—
305C2×C4⋊C4—34no—
306C2×C4⋊C4—34no—
307C2×C4⋊C4—62no—
308C2×C4⋊C4—62no—
309C2×C4⋊C4—62no—
310C2×C4⋊C4—62no—
311C2×C4⋊C4—62no—
312C2×C4⋊C4—62no—
313C2×C4⋊C4—62no—
314C2×C4⋊C4—62no—
315C2×C4⋊C4—62no—
316C2×C4⋊C4—64no—
317C2×C4⋊C4—64no—
318C2×C4⋊C4—122no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—38no—
324C2×C22⋊C4—38no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—122no—
333C2×C22⋊C4—122no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42—34no—
338C2×C42—34no—
339C2×C42—62no—
340C2×C42—62no—
341C2×C42—62no—
342C2×C42—62no—
343#95—62no—
344#95—62no—
345#95—64no—
346#95—64no—
347#95—64no—
348#95—122no—
349#95—122no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3C2×C4⋊C418yes—
385C23×C3C23×C411yescharacteristic
386C23×C3C22×D411yescharacteristic
387C23×C3C22×D411yescharacteristic
388C23×C3C22×D411yescharacteristic
389C23×C3C22×D411yescharacteristic
390C23×C3C22×Q811yescharacteristic
391C23×C3C2×#4111yescharacteristic
392C23×C3C2×#4111yescharacteristic
393C23×C3C2×#4111yescharacteristic
394C23×C3C2×#4111yescharacteristic
395C23×C3C2×#4111yescharacteristic
396C23×C3H(5,𝔽2)11yescharacteristic
397C23×C3H(5,𝔽2)11yescharacteristic
398C23×C3H(5,𝔽2)11yescharacteristic
399C23×C32−1+411yescharacteristic
400C3×D4—232no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4C2×C4⋊C414yes—
423C2×C3×C4C4×D414yes—
424C2×C3×C4C4×D414yes—
425C2×C3×C4#12014yes—
426C2×C3×C4C22⋊Q814yes—
427C2×C3×C4C22⋊Q814yes—
428C2×C3×C4#12314yes—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—22no—
445C2×Dic3—24no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—24no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—24no—
452C2×Dic3—24no—
453C2×Dic3—432no—
454C2×Dic3—42no—
455C2×Dic3—41no—
456C2×Dic3—42no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462C2×Dic3—41no—
463C2×Dic3—42no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—41no—
469C2×Dic3—42no—
470C2×Dic3C4×D414yescomplemented
471C2×Dic3#12114yes—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24C2×Dic614yes—
485C24C2×C4×D314yes—
486C24C2×#6714yes—
487C24C23×D311yescharacteristic
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—28no—
492C2×D4—28no—
493C2×D4—28no—
494C2×D4Dic3⋊C4116yescomplemented
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—32no—
515C22×C4—32no—
516C22×C4—32no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—34no—
522C22×C4—32no—
523C22×C4—34no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—616no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—61no—
538C22×C4—62no—
539C22×C4—61no—
540C22×C4—62no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—61no—
547C22×C4—62no—
548C22×C4—61no—
549C22×C4—62no—
550C22×C4—61no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—62no—
557C22×C4—128no—
558C22×C4—128no—
559C22×C4—128no—
560C22×C4—128no—
561C22×C4—128no—
562C22×C4—128no—
563C22×C4C2×Dic612yes—
564C22×C4C2×C4×D312yes—
565C22×C4D3×D412yes—
566C22×C4D3×D412yes—
567C22×C4D3×D412yes—
568C22×C4#23712yes—
569C22×C4#23712yes—
570C22×C4#23712yes—
571C22×C4C2×#6712yes—
572C4⋊C4—44no—
573C4⋊C4—68no—
574C4⋊C4—68no—
575C4⋊C4—68no—
576C4⋊C4—68no—
577C4⋊C4—128no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—616no—
581C22⋊C4—616no—
582C22⋊C4—128no—
583C42—44no—
584C42—68no—
585C42—68no—
586C22×C3—28no—
587C22×C3—28no—
588C22×C3—28no—
589C22×C3—44no—
590C22×C3—44no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—44no—
599C22×C3—44no—
600C22×C3—44no—
601C22×C3C22×C4⋊C411yescharacteristic
602C22×C3C2×C4×D411yescharacteristic
603C22×C3C2×C4×D411yescharacteristic
604C22×C3C2×C4×D411yescharacteristic
605C22×C3C4×#4111yescharacteristic
606C22×C3#51811yescharacteristic
607C22×C3#52011yescharacteristic
608C22×C3C2×#12011yescharacteristic
609C22×C3C2×#12111yescharacteristic
610C22×C3C2×C22⋊Q811yescharacteristic
611C22×C3C2×C22⋊Q811yescharacteristic
612C22×C3C2×#12311yescharacteristic
613C22×C3#52511yescharacteristic
614C22×C3#52911yescharacteristic
615C22×C3#53211yescharacteristic
616C22×C3#53511yescharacteristic
617C22×C3#53711yescharacteristic
618C22×C3#54011yescharacteristic
619C22×C3#54211yescharacteristic
620C22×C3D4211yescharacteristic
621C22×C3D4211yescharacteristic
622C22×C3#54611yescharacteristic
623C22×C3#54611yescharacteristic
624C22×C3#54611yescharacteristic
625C22×C3#54711yescharacteristic
626C22×C3#54811yescharacteristic
627C22×C3D4×Q811yescharacteristic
628C22×C3#55011yescharacteristic
629C22×C3#55011yescharacteristic
630C22×C3#55411yescharacteristic
631C22×C3#55411yescharacteristic
632C22×C3#55411yescharacteristic
633C22×C3#55611yescharacteristic
634C22×C3#55911yescharacteristic
635C22×C3#55911yescharacteristic
636C3×C4—42no—
637C3×C4—42no—
638C3×C4—82no—
639C3×C4#38518yescomplemented
640Dic3—24no—
641Dic3—24no—
642Dic3—42no—
643Dic3—44no—
644Dic3—42no—
645Dic3—44no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23C2×Dic3⋊C418yes—
681C23C22×Dic611yescharacteristic
682C23C22×C4×D311yescharacteristic
683C23C2×D3×D411yescharacteristic
684C23C2×D3×D411yescharacteristic
685C23C2×D3×D411yescharacteristic
686C23C2×#23711yescharacteristic
687C23C2×#23711yescharacteristic
688C23C2×#23711yescharacteristic
689C23#100411yescharacteristic
690C23#100411yescharacteristic
691C23D3×#4111yescharacteristic
692C23D3×#4111yescharacteristic
693C23#100911yescharacteristic
694C23#101011yescharacteristic
695C23C22×#6711yescharacteristic
696D4—232no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—34no—
704C2×C4—34no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—64no—
734C2×C4—62no—
735C2×C4—64no—
736C2×C4—64no—
737C2×C4—62no—
738C2×C4—64no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—64no—
743C2×C4—64no—
744C2×C4—1232no—
745C2×C4—122no—
746C2×C4—121no—
747C2×C4—122no—
748C2×C4—121no—
749C2×C4—122no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—122no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—122no—
761C2×C4#87814yes—
762C2×C4#87814yes—
763C2×C4#67⋊C414yes—
764C2×C4#67⋊C414yes—
765C2×C4C2×Dic3⋊C414yes—
766C2×C4#93514yes—
767C2×C4#93714yes—
768C2×C3—48no—
769C2×C3C2×#38511yescharacteristic
770C2×C3C4×#12111yescharacteristic
771C2×C3#232411yescharacteristic
772C2×C3D4×C4⋊C411yescharacteristic
773C2×C3#234911yescharacteristic
774C2×C3#236611yescharacteristic
775C2×C3#236711yescharacteristic
776C2×C3#240711yescharacteristic
777C2×C3#240811yescharacteristic
778C2×C3#244511yescharacteristic
779C2×C3#244711yescharacteristic
780C2×C3#245211yescharacteristic
781C2×C3#245411yescharacteristic
782C2×C3#253811yescharacteristic
783C2×C3#258011yescharacteristic
784C22—28no—
785C22—28no—
786C22—28no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22C2×#87811yescharacteristic
800C22C2×#87811yescharacteristic
801C22C2×#67⋊C411yescharacteristic
802C22C2×#67⋊C411yescharacteristic
803C22C4×#23711yescharacteristic
804C22D4×Dic611yescharacteristic
805C22#553911yescharacteristic
806C22#553911yescharacteristic
807C22#554311yescharacteristic
808C22C4×D3×D411yescharacteristic
809C22#554511yescharacteristic
810C22#554611yescharacteristic
811C22#559811yescharacteristic
812C22#559911yescharacteristic
813C22D3×#12111yescharacteristic
814C22#560611yescharacteristic
815C22#560711yescharacteristic
816C22#560811yescharacteristic
817C22#560911yescharacteristic
818C22#561211yescharacteristic
819C22#567111yescharacteristic
820C22#568011yescharacteristic
821C22#568111yescharacteristic
822C22#568211yescharacteristic
823C22#571311yescharacteristic
824C22#571611yescharacteristic
825C22#571811yescharacteristic
826C22#571911yescharacteristic
827C22C22×Dic3⋊C411yescharacteristic
828C22C2×#93511yescharacteristic
829C22C2×#93711yescharacteristic
830C22D4×#6711yescharacteristic
831C22#580611yescharacteristic
832C22#582411yescharacteristic
833C22#582911yescharacteristic
834C4—42no—
835C4—42no—
836C4—64no—
837C4—64no—
838C4—82no—
839C4—122no—
840C4—124no—
841C4—122no—
842C4—124no—
843C4#494618yescomplemented
844C3#1401811yescharacteristic, complemented, Sylow
845C2—48no—
846C2#7629111yescharacteristic
847C2#7630611yescharacteristic
848C2#7630711yescharacteristic
849C2#7632211yescharacteristic
850C2#7632411yescharacteristic
851C2#7634611yescharacteristic
852C2#7636411yescharacteristic
853C2#7643011yescharacteristic
854C2C2×#494611yescharacteristic
855C2D4×Dic3⋊C411yescharacteristic
856C2#8233411yescharacteristic
857C2#8264011yescharacteristic
858C2#8270111yescharacteristic
859C2#8296211yescharacteristic
860C2#8317611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#390C2
socle, cosocleC24×C3C24
prime radicalC23×C3×D4C22
hypercenterC2×#390D3
hypocenterC3#14018
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×#4946C2semidirect
5. C2×#4928C2semidirect
6. C2×C4×Dic3⋊C4C2semidirect
7. #71563C2semidirect
8. #71563C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. #71544C2semidirect
33. #5221C4semidirect
99. C2×#217C2×C4semidirect
100. C2×#217C2×C4semidirect
106. C2×C4⋊Dic3C2×C4semidirect
116. C2×Dic3⋊C4D4semidirect
121. C2×C4×Dic3C2×C4semidirect
183. C2×C3×D4C4⋊C4semidirect
470. C2×Dic3C4×D4semidirect
494. C2×D4Dic3⋊C4semidirect
639. C3×C4#385semidirect
843. C4#4946semidirect
844. C3#14018semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic32
C2×C3×#3902
C2×#52212
C2×#49462
C2×#49282
C2×C4×Dic3⋊C42
#715632
#715472
#715442
#140183