Finite Group Databasebeta

← #10727623

Subgroups — #10727623

Order 768.

2678 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D12C211yesmaximal, characteristic, complemented
2C2×#4940C211yesmaximal, characteristic, complemented
3C2×#4677C211yesmaximal, characteristic, complemented
4C2×#4671C211yesmaximal, characteristic
5C2×#4665C212yesmaximal, complemented
6C2×#4668C212yesmaximal, complemented
7C3×#1434C211yesmaximal, characteristic, complemented
8#69427C212yesmaximal, complemented
9#69426C211yesmaximal, characteristic, complemented
10#69426C212yesmaximal, complemented
11#69422C211yesmaximal, characteristic, complemented
12#14796—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C23×D12C2212yes—
15C23×C4×D3C2212yes—
16C22×C3×C42C2211yescharacteristic
17C22×(C2×D3)⋊C4C2211yescharacteristic
18C22×(C2×D3)⋊C4C2212yes—
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×C4⋊Dic3C2212yes—
26C22×C4⋊Dic3C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C2×C4×D12—24no—
29C2×C4×D12—24no—
30C2×C4×D12—24no—
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2212yes—
34C2×C3×#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39#4940—24no—
40#4677—24no—
41#4671—24no—
42#4668—28no—
43#4665—28no—
44C22×C4×D4—31no—
45C2×#399—31no—
46C2×#392—31no—
47C2×#388—31no—
48C2×#386—32no—
49C2×#385—32no—
50#1445—31no—
51#1439—32no—
52#1438—32no—
53#1438—31no—
54#1434D311yescharacteristic, complemented
55C24×D3C2311yescharacteristic
56C24×D3C2312yes—
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2312yes—
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2311yescharacteristic
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C23×Dic3C2312yes—
65C23×Dic3C2311yescharacteristic
66C22×D12—24no—
67C22×D12—24no—
68C22×D12—22no—
69C22×D12—22no—
70C22×D12—24no—
71C22×D12—24no—
72C22×D12—24no—
73C22×D12—24no—
74C22×D12—24no—
75C22×D12—42no—
76C22×D12—42no—
77C22×D12D414yes—
78C22×C4×D3—24no—
79C22×C4×D3—24no—
80C22×C4×D3—24no—
81C22×C4×D3—24no—
82C22×C4×D3—24no—
83C22×C4×D3—42no—
84C22×C4×D3—42no—
85C2×C3×C42—22no—
86C2×C3×C42—22no—
87C2×C3×C42D414yescomplemented
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—22no—
90C2×(C2×D3)⋊C4—24no—
91C2×(C2×D3)⋊C4—24no—
92C2×(C2×D3)⋊C4—22no—
93C2×(C2×D3)⋊C4—24no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—22no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—42no—
109C2×(C2×D3)⋊C4—42no—
110C2×(C2×D3)⋊C4—42no—
111C2×C4⋊Dic3—22no—
112C2×C4⋊Dic3—22no—
113C2×C4⋊Dic3—24no—
114C2×C4⋊Dic3—24no—
115C2×C4⋊Dic3—42no—
116C2×C4⋊Dic3D414yescomplemented
117C2×Dic3⋊C4—24no—
118C2×Dic3⋊C4—22no—
119C4×D12—232no—
120C3×#95—22no—
121C3×#95—22no—
122C3×#95—42no—
123C3×#95D418yescomplemented
124C3⋊#95—24no—
125C3⋊#95—24no—
126C3⋊#95—22no—
127C3⋊#95—22no—
128C23×D4—31no—
129C23×D4—32no—
130C24×C4—32no—
131C2×C4×D4—64no—
132C2×C4×D4—64no—
133C2×C4×D4—64no—
134C22×C4⋊C4—31no—
135C22×C4⋊C4—31no—
136C22×C4⋊C4—32no—
137C22×C22⋊C4—31no—
138C22×C22⋊C4—32no—
139C22×C22⋊C4—32no—
140C22×C22⋊C4—31no—
141C22×C22⋊C4—31no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C42C2×D311yescharacteristic
146#399—64no—
147#392—64no—
148#388—64no—
149#386—68no—
150#385—68no—
151C2×#95—32no—
152C2×#95—31no—
153C2×#95—31no—
154C2×#95—32no—
155C2×#95C2×D311yescharacteristic
156C2×#95C2×D311yescharacteristic
157C2×#95C2×D312yes—
158C2×#95C2×D312yes—
159C24×C3C2411yescharacteristic
160C23×D3—22no—
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—22no—
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—22no—
169C23×D3—22no—
170C23×D3—22no—
171C23×D3—22no—
172C23×D3—21no—
173C23×D3—21no—
174C23×D3—22no—
175C23×D3—21no—
176C23×D3—21no—
177C23×D3—22no—
178C23×D3—22no—
179C23×D3—22no—
180C23×D3—21no—
181C23×D3—21no—
182C23×D3C2×D414yes—
183C23×D3#4112yes—
184C23×D3#4114yes—
185C23×D3#4114yes—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4C2×D414yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D414yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×D414yes—
214C22×C3×C4C2×D412yes—
215C22×C3×C4C2×D412yes—
216C22×C3×C4C2×D412yes—
217C22×Dic3—21no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—21no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3C2×D414yes—
238C22×Dic3#4112yes—
239C2×D12—216no—
240C2×D12—28no—
241C2×D12—28no—
242C2×D12—216no—
243C2×D12—28no—
244C2×D12—216no—
245C2×D12—48no—
246C2×D12—48no—
247C2×D12—48no—
248C2×D12—48no—
249C2×D12—48no—
250C2×D12—48no—
251C2×C4×D3—216no—
252C2×C4×D3—48no—
253C2×C4×D3—48no—
254C2×C4×D3—48no—
255C2×C4×D3—48no—
256C2×C4×D3—48no—
257C2×C4×D3—48no—
258C3×C42—28no—
259(C2×D3)⋊C4—216no—
260(C2×D3)⋊C4—216no—
261(C2×D3)⋊C4—28no—
262(C2×D3)⋊C4—48no—
263(C2×D3)⋊C4—48no—
264(C2×D3)⋊C4—48no—
265(C2×D3)⋊C4—44no—
266(C2×D3)⋊C4—44no—
267C4⋊Dic3—28no—
268C4⋊Dic3—48no—
269Dic3⋊C4—44no—
270C25—32no—
271C25—31no—
272C22×D4—34no—
273C22×D4—64no—
274C22×D4—64no—
275C22×D4—64no—
276C22×D4—64no—
277C22×D4—64no—
278C22×D4—64no—
279C22×D4—62no—
280C22×D4—64no—
281C22×D4—62no—
282C22×D4—122no—
283C22×D4—122no—
284C23×C4—31no—
285C23×C4—32no—
286C23×C4—31no—
287C23×C4—31no—
288C23×C4—64no—
289C23×C4—64no—
290C23×C4—64no—
291C23×C4—64no—
292C23×C4—64no—
293C23×C4—122no—
294C23×C4—122no—
295C23×C4C22×D312yes—
296C23×C4C22×D311yescharacteristic
297C23×C4C22×D312yes—
298C23×C4C22×D311yescharacteristic
299C23×C4C22×D311yescharacteristic
300C4×D4—632no—
301C2×C4⋊C4—34no—
302C2×C4⋊C4—62no—
303C2×C4⋊C4—62no—
304C2×C4⋊C4—64no—
305C2×C4⋊C4—64no—
306C2×C4⋊C4—64no—
307C2×C4⋊C4—62no—
308C2×C4⋊C4—122no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—62no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—62no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—62no—
318C2×C22⋊C4—64no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—64no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—62no—
326C2×C22⋊C4—62no—
327C2×C22⋊C4—62no—
328C2×C22⋊C4—62no—
329C2×C22⋊C4—122no—
330C2×C22⋊C4—122no—
331C2×C22⋊C4—122no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42D1214yescomplemented
335#95—22no—
336#95—22no—
337#95—42no—
338#95—64no—
339#95—64no—
340#95—62no—
341#95—62no—
342#95D1218yescomplemented
343C23×C3C22×D411yescharacteristic
344C23×C3C22×D412yes—
345C23×C3C22×D411yescharacteristic
346C23×C3C22×D411yescharacteristic
347C23×C3C2×#4112yes—
348C23×C3C2×#4112yes—
349C23×C3C2×#4111yescharacteristic
350C23×C3C2×#4111yescharacteristic
351C23×C3H(5,𝔽2)11yescharacteristic
352C23×C3H(5,𝔽2)12yes—
353C23×C32−1+411yescharacteristic
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—24no—
357C22×D3—24no—
358C22×D3—24no—
359C22×D3—24no—
360C22×D3—24no—
361C22×D3—24no—
362C22×D3—24no—
363C22×D3—24no—
364C22×D3—24no—
365C22×D3—24no—
366C22×D3—24no—
367C22×D3—24no—
368C22×D3—24no—
369C22×D3—24no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—22no—
373C22×D3—24no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3—24no—
377C22×D3—42no—
378C22×D3—42no—
379C22×D3—42no—
380C22×D3—42no—
381C22×D3—42no—
382C22×D3—42no—
383C22×D3—42no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—42no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—41no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—41no—
397C22×D3—41no—
398C22×D3—42no—
399C22×D3—41no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—42no—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3—42no—
406C22×D3—42no—
407C22×D3—41no—
408C22×D3—42no—
409C22×D3—41no—
410C22×D3—42no—
411C22×D3#12318yes—
412C2×C3×C4—22no—
413C2×C3×C4—24no—
414C2×C3×C4—24no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4#12014yes—
442C2×C3×C4#12714yes—
443C2×Dic3—24no—
444C2×Dic3—22no—
445C2×Dic3—24no—
446C2×Dic3—24no—
447C2×Dic3—24no—
448C2×Dic3—41no—
449C2×Dic3—42no—
450C2×Dic3—41no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464C2×Dic3—42no—
465D12—232no—
466D12—432no—
467C4×D3—432no—
468C24—34no—
469C24—34no—
470C24—34no—
471C24—32no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—62no—
476C24—62no—
477C24—62no—
478C24—62no—
479C24—62no—
480C24—62no—
481C24—62no—
482C24—62no—
483C24—62no—
484C24—61no—
485C24—62no—
486C24—61no—
487C24—61no—
488C24—61no—
489C24—61no—
490C24—61no—
491C24—62no—
492C24—62no—
493C24—62no—
494C24C23×D311yescharacteristic
495C2×D4—616no—
496C2×D4—616no—
497C2×D4—68no—
498C2×D4—68no—
499C2×D4—616no—
500C2×D4—68no—
501C2×D4—128no—
502C2×D4—128no—
503C2×D4—128no—
504C2×D4—128no—
505C2×D4—128no—
506C2×D4—128no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—34no—
531C22×C4—32no—
532C22×C4—616no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—61no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—61no—
544C22×C4—62no—
545C22×C4—61no—
546C22×C4—62no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—128no—
554C22×C4—128no—
555C22×C4—128no—
556C22×C4—128no—
557C22×C4—128no—
558C22×C4—128no—
559C22×C4C2×D1214yes—
560C22×C4C2×D1212yes—
561C22×C4C2×D1214yes—
562C22×C4C2×D1214yes—
563C22×C4C2×D1212yes—
564C22×C4C2×D1212yes—
565C22×C4D3×D412yes—
566C22×C4D3×D412yes—
567C4⋊C4—68no—
568C4⋊C4—128no—
569C4⋊C4—124no—
570C22⋊C4—616no—
571C22⋊C4—616no—
572C22⋊C4—68no—
573C22⋊C4—128no—
574C22⋊C4—128no—
575C22⋊C4—128no—
576C22⋊C4—124no—
577C22⋊C4—124no—
578C42—28no—
579C22×C3C2×#12011yescharacteristic
580C22×C3C2×#12312yes—
581C22×C3#52512yes—
582C22×C3#52511yescharacteristic
583C22×C3#52511yescharacteristic
584C22×C3#52511yescharacteristic
585C22×C3#52512yes—
586C22×C3#52512yes—
587C22×C3C2×#12711yescharacteristic
588C22×C3#53511yescharacteristic
589C22×C3#53711yescharacteristic
590C22×C3#53812yes—
591C22×C3#53912yes—
592C22×C3D4212yes—
593C22×C3D4212yes—
594C22×C3#54612yes—
595C22×C3#54611yescharacteristic
596C22×C3#54711yescharacteristic
597C22×C3#54811yescharacteristic
598C22×C3#54812yes—
599C22×C3#55011yescharacteristic
600C22×C3#55112yes—
601C22×C3#55312yes—
602C2×D3—28no—
603C2×D3—28no—
604C2×D3—28no—
605C2×D3—44no—
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C2×D3—44no—
610C2×D3—44no—
611C2×D3—44no—
612C2×D3—44no—
613C2×D3—44no—
614C2×D3—44no—
615C2×D3—44no—
616C2×D3—44no—
617C2×D3—42no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—44no—
621C2×D3—44no—
622C2×D3—81no—
623C2×D3—81no—
624C2×D3—81no—
625C2×D3—82no—
626C2×D3—82no—
627C2×D3—81no—
628C3×C4—24no—
629C3×C4—24no—
630C3×C4—42no—
631C3×C4—44no—
632C3×C4—44no—
633Dic3—42no—
634Dic3—44no—
635Dic3—81no—
636Dic3—81no—
637C23—38no—
638C23—64no—
639C23—64no—
640C23—64no—
641C23—64no—
642C23—64no—
643C23—64no—
644C23—64no—
645C23—64no—
646C23—64no—
647C23—64no—
648C23—64no—
649C23—64no—
650C23—64no—
651C23—64no—
652C23—64no—
653C23—64no—
654C23—64no—
655C23—64no—
656C23—62no—
657C23—64no—
658C23—62no—
659C23—64no—
660C23—62no—
661C23—122no—
662C23—122no—
663C23—122no—
664C23—122no—
665C23—122no—
666C23—122no—
667C23—122no—
668C23—122no—
669C23—122no—
670C23—122no—
671C23—122no—
672C23—122no—
673C23—122no—
674C23—122no—
675C23—122no—
676C23—122no—
677C23—122no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—122no—
688C23—121no—
689C23—122no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23—121no—
694C23—121no—
695C23C22×D1211yescharacteristic
696C23C22×D1212yes—
697C23C2×D3×D411yescharacteristic
698C23C2×D3×D411yescharacteristic
699C23#100411yescharacteristic
700C23#100711yescharacteristic
701C23D3×#4111yescharacteristic
702C23D3×#4112yes—
703C23D3×#4112yes—
704C23D3×#4111yescharacteristic
705C23#100912yes—
706D4—632no—
707D4—1232no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—64no—
738C2×C4—62no—
739C2×C4—64no—
740C2×C4—64no—
741C2×C4—64no—
742C2×C4—1232no—
743C2×C4—121no—
744C2×C4—122no—
745C2×C4—121no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4#87414yes—
761C2×C4#88214yes—
762C2×C3#239711yescharacteristic
763C2×C3#240711yescharacteristic
764C2×C3#241812yes—
765C2×C3#243311yescharacteristic
766C2×C3#244312yes—
767C2×C3#245612yes—
768C2×C3#246312yes—
769C2×C3#254011yescharacteristic
770C2×C3#259811yescharacteristic
771C2×C3#263611yescharacteristic
772C2×C3#284911yescharacteristic
773D3—48no—
774D3—82no—
775C22—68no—
776C22—68no—
777C22—68no—
778C22—124no—
779C22—124no—
780C22—124no—
781C22—124no—
782C22—124no—
783C22—124no—
784C22—124no—
785C22—124no—
786C22—124no—
787C22—124no—
788C22—124no—
789C22—124no—
790C22—122no—
791C22—124no—
792C22—122no—
793C22—124no—
794C22—122no—
795C22—241no—
796C22—242no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22—242no—
801C22C2×#87411yescharacteristic
802C22C2×#88211yescharacteristic
803C22#551011yescharacteristic
804C22#552411yescharacteristic
805C22#552411yescharacteristic
806C22#552412yes—
807C22#552412yes—
808C22#552411yescharacteristic
809C22#552511yescharacteristic
810C22D4×D1212yes—
811C22D4×D1212yes—
812C22#555412yes—
813C22#557612yes—
814C22#559911yescharacteristic
815C22#561211yescharacteristic
816C22#563111yescharacteristic
817C22#563311yescharacteristic
818C22D3×#12312yes—
819C22#565612yes—
820C22#567812yes—
821C22#569212yes—
822C22#570512yes—
823C22#570912yes—
824C4—24no—
825C4—24no—
826C4—42no—
827C4—44no—
828C4—44no—
829C4—124no—
830C4—122no—
831C4—241no—
832C4—241no—
833C3#1479611yescharacteristic, complemented, Sylow
834C2—128no—
835C2—242no—
836C2#7341811yescharacteristic
837C2#7358711yescharacteristic
838C2#7379811yescharacteristic
839C2#7401511yescharacteristic
840C2#7414611yescharacteristic
841C2#7424511yescharacteristic
842C2#7430711yescharacteristic
843C2#7531912yes—
844C2#7532712yes—
845C2#7550312yes—
846C2#7584412yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1434C2
prime radicalC2×#4671C2
hypercenter#1434D3
hypocenterC3#14796
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C22×C4×D12C2semidirect
2. C2×#4940C2semidirect
3. C2×#4677C2semidirect
5. C2×#4665C2semidirect
6. C2×#4668C2semidirect
7. C3×#1434C2semidirect
8. #69427C2semidirect
9. #69426C2semidirect
10. #69426C2semidirect
11. #69422C2semidirect
54. #1434D3semidirect
87. C2×C3×C42D4semidirect
116. C2×C4⋊Dic3D4semidirect
123. C3×#95D4semidirect
334. C2×C42D12semidirect
342. #95D12semidirect
833. C3#14796semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D122
C2×#49402
C2×#46772
C2×#46712
C2×#46652
C2×#46682
C3×#14342
#694272
#694262
#694222
#147963