Finite Group Databasebeta

← #10718586

Subgroups — #10718586

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×#4984C211yesmaximal, characteristic, complemented
5C2×#4950C212yesmaximal, complemented
6C2×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71546C212yesmaximal, complemented
9#71546C212yesmaximal, complemented
10#71544C212yesmaximal, complemented
11#71535C211yesmaximal, characteristic, 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×C4⋊Dic3C2212yes—
28C22×C4⋊Dic3C2211yescharacteristic
29C22×C4⋊Dic3C2211yescharacteristic
30C22×C4×Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C3×#390C418yescomplemented
33#5221—24no—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4984—24no—
42#4950—28no—
43C4×C4⋊Dic3—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×C4C2311yescharacteristic
64C23×C3×C4C2312yes—
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×Dic3C2312yes—
75C23×Dic3C2312yes—
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4C2×C414yescomplemented
83C2×C3×C22⋊C4—24no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—42no—
86C2×C3×C22⋊C4—42no—
87C2×C3×C22⋊C4C2×C418yescomplemented
88C2×C3×C22⋊C4C2×C418yescomplemented
89C2×C3×C42—22no—
90C2×C3×C42—22no—
91C2×C3×C42C2×C414yescomplemented
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—24no—
99C2×#217—42no—
100C2×#217—42no—
101D4×Dic3—232no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3—22no—
105C2×C4⋊Dic3—22no—
106C2×C4⋊Dic3—22no—
107C2×C4⋊Dic3—22no—
108C2×C4⋊Dic3—22no—
109C2×C4⋊Dic3—22no—
110C2×C4⋊Dic3—22no—
111C2×C4⋊Dic3—22no—
112C2×C4⋊Dic3—24no—
113C2×C4⋊Dic3—24no—
114C2×C4⋊Dic3—42no—
115C2×C4⋊Dic3D414yes—
116C2×C4⋊Dic3D414yescomplemented
117C2×C4×Dic3—22no—
118C2×C4×Dic3—22no—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3—22no—
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—64no—
150#390Dic318yescomplemented
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—22no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4C22×C412yes—
201C22×C3×C4C22×C414yes—
202C22×C3×C4C22×C412yes—
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—216no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—22no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—22no—
233C22×Dic3—21no—
234C22×Dic3—22no—
235C22×Dic3—21no—
236C22×Dic3—22no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—48no—
249C22×Dic3—48no—
250C22×Dic3—48no—
251C22×Dic3—48no—
252C22×Dic3—48no—
253C22×Dic3—48no—
254C22×Dic3C2×D412yes—
255C22×Dic3C2×D414yes—
256C22×Dic3C2×D412yes—
257C22×Dic3C2×D412yes—
258C22×Dic3C2×D412yes—
259C22×Dic3#4112yes—
260C22×Dic3#4112yes—
261C3×C4⋊C4—28no—
262C3×C22⋊C4—216no—
263C3×C22⋊C4—48no—
264C3×C42—28no—
265#217—216no—
266#217—48no—
267#217—48no—
268C4⋊Dic3—28no—
269C4⋊Dic3—28no—
270C4⋊Dic3—28no—
271C4⋊Dic3—48no—
272C4⋊Dic3—44no—
273C4×Dic3—28no—
274C4×Dic3—44no—
275C25C22×D312yes—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4Dic614yes—
281C22×D4D1214yes—
282C22×D4C2×Dic314yes—
283C23×C4—31no—
284C23×C4—31no—
285C23×C4—31no—
286C23×C4—31no—
287C23×C4—32no—
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—34no—
304C2×C4⋊C4—34no—
305C2×C4⋊C4—62no—
306C2×C4⋊C4—62no—
307C2×C4⋊C4—62no—
308C2×C4⋊C4—62no—
309C2×C4⋊C4—62no—
310C2×C4⋊C4—62no—
311C2×C4⋊C4—62no—
312C2×C4⋊C4—64no—
313C2×C4⋊C4—64no—
314C2×C4⋊C4—62no—
315C2×C4⋊C4—62no—
316C2×C4⋊C4—62no—
317C2×C4⋊C4—122no—
318C2×C4⋊C4C2×Dic314yescomplemented
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—122no—
331C2×C22⋊C4—122no—
332C2×C22⋊C4C2×Dic318yescomplemented
333C2×C22⋊C4C2×Dic318yescomplemented
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—34no—
337C2×C42—62no—
338C2×C42—62no—
339C2×C42—62no—
340C2×C42—62no—
341C2×C42—62no—
342C2×C42C2×Dic314yescomplemented
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—22no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—22no—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4C2×C4⋊C414yes—
422C2×C3×C4C4×D414yes—
423C2×C3×C4C4×D414yes—
424C2×C3×C4C4×D414yescomplemented
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—24no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—24no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—24no—
446C2×Dic3—22no—
447C2×Dic3—432no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—42no—
451C2×Dic3—41no—
452C2×Dic3—42no—
453C2×Dic3—41no—
454C2×Dic3—42no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—42no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—42no—
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×D1214yes—
486C24C22×Dic314yes—
487C24C23×D311yescharacteristic
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—28no—
492C2×D4—28no—
493C2×D4—28no—
494C2×D4C4⋊Dic3116yescomplemented
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—32no—
512C22×C4—32no—
513C22×C4—32no—
514C22×C4—32no—
515C22×C4—34no—
516C22×C4—32no—
517C22×C4—32no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—616no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—62no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—62no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—62no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—62no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—128no—
555C22×C4—128no—
556C22×C4—128no—
557C22×C4—128no—
558C22×C4—128no—
559C22×C4—128no—
560C22×C4C2×Dic612yes—
561C22×C4C2×D1212yes—
562C22×C4D3×D412yes—
563C22×C4D3×D412yes—
564C22×C4D3×D412yes—
565C22×C4#23712yes—
566C22×C4#23712yes—
567C22×C4#23712yes—
568C22×C4C22×Dic312yes—
569C22×C4C22×Dic314yes—
570C22×C4C22×Dic312yes—
571C22×C4C22×Dic312yes—
572C4⋊C4—28no—
573C4⋊C4—68no—
574C4⋊C4—68no—
575C4⋊C4—68no—
576C4⋊C4—128no—
577C4⋊C4—124no—
578C22⋊C4—216no—
579C22⋊C4—48no—
580C22⋊C4—616no—
581C22⋊C4—128no—
582C22⋊C4—128no—
583C42—28no—
584C42—68no—
585C42—124no—
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—24no—
637C3×C4—42no—
638C3×C4—44no—
639C3×C4#38518yescomplemented
640Dic3—24no—
641Dic3—42no—
642Dic3—42no—
643Dic3—42no—
644Dic3—44no—
645Dic3—82no—
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×C4⋊Dic318yes—
681C23C22×Dic611yescharacteristic
682C23C22×D1211yescharacteristic
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
695C23C23×Dic311yescharacteristic
696D4—232no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—34no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—64no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—64no—
728C2×C4—62no—
729C2×C4—64no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—1232no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4#87814yes—
761C2×C4#87814yes—
762C2×C4#88214yes—
763C2×C4#88614yes—
764C2×C4C2×C4⋊Dic314yes—
765C2×C4D4×Dic314yes—
766C2×C4D4×Dic314yes—
767C2×C4D4×Dic314yescomplemented
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×#88211yescharacteristic
802C22C2×#88611yescharacteristic
803C22D4×Dic611yescharacteristic
804C22#553911yescharacteristic
805C22#553911yescharacteristic
806C22#554311yescharacteristic
807C22D4×D1211yescharacteristic
808C22#555411yescharacteristic
809C22#555411yescharacteristic
810C22#555511yescharacteristic
811C22#559611yescharacteristic
812C22#560011yescharacteristic
813C22#560311yescharacteristic
814C22D3×#12111yescharacteristic
815C22#560611yescharacteristic
816C22#560711yescharacteristic
817C22#560811yescharacteristic
818C22#561911yescharacteristic
819C22#567111yescharacteristic
820C22#567611yescharacteristic
821C22#567711yescharacteristic
822C22#568111yescharacteristic
823C22#571311yescharacteristic
824C22#571711yescharacteristic
825C22#571811yescharacteristic
826C22#571811yescharacteristic
827C22C22×C4⋊Dic311yescharacteristic
828C22C2×D4×Dic311yescharacteristic
829C22C2×D4×Dic311yescharacteristic
830C22C2×D4×Dic311yescharacteristic
831C22#579811yescharacteristic
832C22Dic3×#4111yescharacteristic
833C22#582711yescharacteristic
834C4—24no—
835C4—42no—
836C4—44no—
837C4—64no—
838C4—122no—
839C4—122no—
840C4—124no—
841C4—122no—
842C4—242no—
843C4#495018yescomplemented
844C3#1401811yescharacteristic, complemented, Sylow
845C2—48no—
846C2#7631711yescharacteristic
847C2#7631911yescharacteristic
848C2#7632311yescharacteristic
849C2#7632511yescharacteristic
850C2#7634611yescharacteristic
851C2#7636411yescharacteristic
852C2#7643511yescharacteristic
853C2#7643611yescharacteristic
854C2C2×#495011yescharacteristic
855C2D4×C4⋊Dic311yescharacteristic
856C2#8233311yescharacteristic
857C2Dic3×#12111yescharacteristic
858C2#8263311yescharacteristic
859C2#8295511yescharacteristic
860C2#8317311yescharacteristic
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×#4984C2semidirect
5. C2×#4950C2semidirect
6. C2×C4×C4⋊Dic3C2semidirect
7. #71563C2semidirect
8. #71546C2semidirect
9. #71546C2semidirect
10. #71544C2semidirect
11. #71535C2semidirect
32. C3×#390C4semidirect
82. C2×C3×C4⋊C4C2×C4semidirect
87. C2×C3×C22⋊C4C2×C4semidirect
88. C2×C3×C22⋊C4C2×C4semidirect
91. C2×C3×C42C2×C4semidirect
116. C2×C4⋊Dic3D4semidirect
150. #390Dic3semidirect
183. C2×C3×D4C4⋊C4semidirect
318. C2×C4⋊C4C2×Dic3semidirect
332. C2×C22⋊C4C2×Dic3semidirect
333. C2×C22⋊C4C2×Dic3semidirect
342. C2×C42C2×Dic3semidirect
424. C2×C3×C4C4×D4semidirect
494. C2×D4C4⋊Dic3semidirect
639. C3×C4#385semidirect
767. C2×C4D4×Dic3semidirect
843. C4#4950semidirect
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×#49842
C2×#49502
C2×C4×C4⋊Dic32
#715632
#715462
#715442
#715352
#140183