Finite Group Databasebeta

← #10727868

Subgroups — #10727868

Order 768.

2278 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#388C211yesmaximal, characteristic, complemented
2C2×#4994C212yesmaximal, complemented
3C2×#4960C211yesmaximal, characteristic
4C2×#4961C212yesmaximal, complemented
5C2×#4957C212yesmaximal, complemented
6C2×#4939C211yesmaximal, characteristic, complemented
7C2×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
8#71546C211yesmaximal, characteristic, complemented
9#69426C211yesmaximal, characteristic, complemented
10#69420C211yesmaximal, characteristic, complemented
11#69408C212yesmaximal, complemented
12#14815—31nomaximal, Sylow
13C23×#67C2212yes—
14C23×D12C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C22⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×#217C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×C4⋊Dic3C2212yes—
27C22×C4⋊Dic3C2211yescharacteristic
28C22×Dic3⋊C4C2212yes—
29C22×C4×Dic3C2212yes—
30C3×#388—24no—
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37#4994—28no—
38#4961—28no—
39#4960—24no—
40#4957—28no—
41#4939—24no—
42C4×C4⋊Dic3—24no—
43C2×#396—32no—
44C2×#394—32no—
45C2×#392—31no—
46C2×#390—31no—
47C2×#390—32no—
48C2×#388D311yescharacteristic, complemented
49C2×C4×C4⋊C4—31no—
50#1444—31no—
51#1439—31no—
52#1438—31no—
53#1437—32no—
54C25×C3C2311yescharacteristic
55C24×D3C2312yes—
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2311yescharacteristic
62C22×#67—24no—
63C22×#67—24no—
64C22×#67—24no—
65C22×#67—24no—
66C22×#67—24no—
67C22×#67—42no—
68C22×#67—42no—
69C23×Dic3C2312yes—
70C23×Dic3C2312yes—
71C23×Dic3C2312yes—
72C22×D12—24no—
73C22×D12—22no—
74C22×D12—22no—
75C22×D12—22no—
76C22×D12—42no—
77C2×C3×C4⋊C4—24no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C22⋊C4—22no—
80C2×C3×C22⋊C4—22no—
81C2×C3×C22⋊C4—22no—
82C2×C3×C22⋊C4—24no—
83C2×C3×C22⋊C4—22no—
84C2×C3×C22⋊C4—22no—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4D414yescomplemented
87C2×C3×C42—22no—
88C2×C3×C42—22no—
89C2×C3×C42D414yescomplemented
90C2×#217—24no—
91C2×#217—24no—
92C2×#217—42no—
93C2×(C2×D3)⋊C4—24no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—24no—
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—24no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—42no—
107C2×(C2×D3)⋊C4—42no—
108C2×C4⋊Dic3—24no—
109C2×C4⋊Dic3—24no—
110C2×C4⋊Dic3—22no—
111C2×C4⋊Dic3—42no—
112C2×C4⋊Dic3D418yescomplemented
113C2×Dic3⋊C4—24no—
114C2×Dic3⋊C4—24no—
115C2×Dic3⋊C4—42no—
116C2×C4×Dic3—24no—
117C2×C4×Dic3—24no—
118C2×C4×Dic3—42no—
119C3×#95—22no—
120C3×#95—22no—
121C3⋊#95—22no—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95D414yes—
125C23×D4—32no—
126C23×D4—31no—
127C22×C4⋊C4—32no—
128C22×C4⋊C4—32no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4C2×D311yescharacteristic
131C22×C22⋊C4—32no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4C2×D311yescharacteristic
138C22×C22⋊C4C2×D311yescharacteristic
139C22×C22⋊C4C2×D311yescharacteristic
140C22×C42—32no—
141C22×C42C2×D311yescharacteristic
142#396—68no—
143#394—68no—
144#392—64no—
145#390—68no—
146#390—64no—
147#388—24no—
148C4×C4⋊C4—64no—
149C2×#95—31no—
150C2×#95—32no—
151C2×#95—32no—
152C2×#95—31no—
153C2×#95C2×D311yescharacteristic
154C2×#95C2×D311yescharacteristic
155C24×C3—22no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3—21no—
159C24×C3—21no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3C2×D412yes—
166C24×C3C2411yescharacteristic
167C23×D3—22no—
168C23×D3—22no—
169C23×D3—22no—
170C23×D3—22no—
171C23×D3—22no—
172C23×D3—22no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—22no—
179C23×D3—22no—
180C23×D3—22no—
181C23×D3#4114yes—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D412yes—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D414yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4#4112yes—
213C22×C3×C4#4112yes—
214C2×#67—216no—
215C2×#67—48no—
216C2×#67—48no—
217C2×#67—48no—
218C2×#67—48no—
219C2×#67—48no—
220C2×#67—48no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3C2×D414yes—
239C22×Dic3C2×D414yes—
240C22×Dic3C2×D414yes—
241C22×Dic3#4114yes—
242C2×D12—28no—
243C2×D12—48no—
244C2×D12—48no—
245C2×D12—44no—
246C2×D12—44no—
247C3×C4⋊C4—44no—
248C3×C22⋊C4—28no—
249C3×C22⋊C4—44no—
250C3×C22⋊C4—44no—
251C3×C42—28no—
252#217—48no—
253(C2×D3)⋊C4—48no—
254(C2×D3)⋊C4—48no—
255(C2×D3)⋊C4—48no—
256(C2×D3)⋊C4—48no—
257(C2×D3)⋊C4—48no—
258C4⋊Dic3—216no—
259C4⋊Dic3—44no—
260Dic3⋊C4—48no—
261C4×Dic3—48no—
262C25—32no—
263C25C22×D311yescharacteristic
264C22×D4—64no—
265C22×D4—64no—
266C22×D4—64no—
267C22×D4—64no—
268C22×D4—64no—
269C22×D4—64no—
270C22×D4—62no—
271C22×D4—62no—
272C22×D4—62no—
273C22×D4—122no—
274C22×D4—122no—
275C22×D4—122no—
276C23×C4—32no—
277C23×C4—32no—
278C23×C4—32no—
279C23×C4C22×D311yescharacteristic
280C23×C4C22×D311yescharacteristic
281C23×C4C22×D311yescharacteristic
282C23×C4C22×D311yescharacteristic
283C23×C4C22×D311yescharacteristic
284C23×C4C22×D311yescharacteristic
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—38no—
288C2×C4⋊C4—64no—
289C2×C4⋊C4—64no—
290C2×C4⋊C4—64no—
291C2×C4⋊C4—64no—
292C2×C4⋊C4—62no—
293C2×C4⋊C4—122no—
294C2×C4⋊C4—122no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—64no—
303C2×C22⋊C4—64no—
304C2×C22⋊C4—64no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—122no—
318C2×C22⋊C4—122no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4D1214yescomplemented
321C2×C42—22no—
322C2×C42—22no—
323C2×C42—64no—
324C2×C42—64no—
325C2×C42—122no—
326C2×C42#6714yescomplemented
327#95—22no—
328#95—22no—
329#95—34no—
330#95—64no—
331#95—64no—
332#95—62no—
333C23×C3—22no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—41no—
339C23×C3—42no—
340C23×C3—41no—
341C23×C3—42no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—42no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—41no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—41no—
356C23×C3C22×D411yescharacteristic
357C23×C3C22×D411yescharacteristic
358C23×C3C22×D412yes—
359C23×C3C22×D411yescharacteristic
360C23×C3C2×#4111yescharacteristic
361C23×C3C2×#4111yescharacteristic
362C23×C3C2×#4112yes—
363C23×C3C2×#4112yes—
364C23×C3H(5,𝔽2)12yes—
365C23×C3H(5,𝔽2)11yescharacteristic
366C23×C32−1+411yescharacteristic
367C22×D3—24no—
368C22×D3—24no—
369C22×D3—24no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—24no—
373C22×D3—24no—
374C22×D3—42no—
375C22×D3—42no—
376C22×D3—42no—
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—42no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—42no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—42no—
428C2×C3×C4—41no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4#12114yes—
432C2×C3×C4#12114yes—
433C2×C3×C4#12714yes—
434#67—432no—
435C2×Dic3—24no—
436C2×Dic3—24no—
437C2×Dic3—24no—
438C2×Dic3—24no—
439C2×Dic3—24no—
440C2×Dic3—24no—
441C2×Dic3—24no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3#12118yes—
456D12—416no—
457C24—21no—
458C24—22no—
459C24—21no—
460C24—21no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—34no—
468C24—62no—
469C24—62no—
470C24—62no—
471C24—62no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—62no—
476C24—62no—
477C24—62no—
478C24—62no—
479C24—62no—
480C24—62no—
481C24—62no—
482C24C2×D1212yes—
483C24C23×D311yescharacteristic
484C2×D4—68no—
485C2×D4—616no—
486C2×D4—128no—
487C2×D4—128no—
488C2×D4—124no—
489C2×D4—128no—
490C2×D4—128no—
491C2×D4—128no—
492C2×D4—128no—
493C2×D4—128no—
494C2×D4—128no—
495C2×D4—124no—
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—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—34no—
520C22×C4—34no—
521C22×C4—34no—
522C22×C4—34no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4C2×D1212yes—
541C22×C4C2×D1212yes—
542C22×C4#23512yes—
543C22×C4D3×D412yes—
544C22×C4D3×D414yes—
545C22×C4#23712yes—
546C22×C4C2×#6712yes—
547C22×C4C2×#6712yes—
548C22×C4C2×#6712yes—
549C4⋊C4—44no—
550C4⋊C4—616no—
551C4⋊C4—128no—
552C4⋊C4—124no—
553C22⋊C4—28no—
554C22⋊C4—44no—
555C22⋊C4—44no—
556C22⋊C4—128no—
557C22⋊C4—128no—
558C22⋊C4—128no—
559C22⋊C4—128no—
560C22⋊C4—128no—
561C22⋊C4—128no—
562C42—28no—
563C42—128no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—44no—
567C22×C3—44no—
568C22×C3—42no—
569C22×C3—81no—
570C22×C3—81no—
571C22×C3—81no—
572C22×C3—82no—
573C22×C3—81no—
574C22×C3—82no—
575C22×C3C2×#12111yescharacteristic
576C22×C3C2×#12111yescharacteristic
577C22×C3C2×#12112yes—
578C22×C3#52512yes—
579C22×C3#52511yescharacteristic
580C22×C3#52912yes—
581C22×C3C2×#12711yescharacteristic
582C22×C3#53211yescharacteristic
583C22×C3#53212yes—
584C22×C3#53511yescharacteristic
585C22×C3#53711yescharacteristic
586C22×C3#53812yes—
587C22×C3#54212yes—
588C22×C3D4211yescharacteristic
589C22×C3D4212yes—
590C22×C3#54612yes—
591C22×C3#54612yes—
592C22×C3#54711yescharacteristic
593C22×C3#54812yes—
594C22×C3#54811yescharacteristic
595C22×C3#55012yes—
596C22×C3#55112yes—
597C22×C3#55311yescharacteristic
598C2×D3—44no—
599C2×D3—44no—
600C2×D3—44no—
601C2×D3—44no—
602C2×D3—44no—
603C2×D3—44no—
604C2×D3—44no—
605C2×D3—82no—
606C2×D3—82no—
607C2×D3—82no—
608C2×D3—82no—
609C2×D3—82no—
610C2×D3—82no—
611C2×D3—82no—
612C2×D3—82no—
613C3×C4—24no—
614C3×C4—24no—
615C3×C4—24no—
616C3×C4—42no—
617C3×C4—81no—
618C3×C4—81no—
619Dic3—28no—
620Dic3—44no—
621Dic3—82no—
622C23—24no—
623C23—22no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—64no—
646C23—64no—
647C23—64no—
648C23—64no—
649C23—64no—
650C23—64no—
651C23—64no—
652C23—122no—
653C23—122no—
654C23—122no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23—122no—
659C23—122no—
660C23—122no—
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—
680C23C22×D1211yescharacteristic
681C23C2×#23511yescharacteristic
682C23C2×D3×D411yescharacteristic
683C23C2×D3×D412yes—
684C23C2×#23711yescharacteristic
685C23D3×#4112yes—
686C23D3×#4112yes—
687C23#100912yes—
688C23#100911yescharacteristic
689C23#101011yescharacteristic
690C23C22×#6711yescharacteristic
691D4—1216no—
692D4—1232no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—38no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—64no—
724C2×C4—64no—
725C2×C4—64no—
726C2×C4—64no—
727C2×C4—64no—
728C2×C4—64no—
729C2×C4—64no—
730C2×C4—64no—
731C2×C4—64no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4#93014yes—
744C2×C4#93914yes—
745C2×C4#94014yes—
746C2×C3—82no—
747C2×C3#239211yescharacteristic
748C2×C3#241111yescharacteristic
749C2×C3#241611yescharacteristic
750C2×C3#242412yes—
751C2×C3#242612yes—
752C2×C3#246112yes—
753C2×C3#254011yescharacteristic
754C2×C3#254111yescharacteristic
755C2×C3#255412yes—
756C2×C3#266211yescharacteristic
757C2×C3#285611yescharacteristic
758D3—84no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—44no—
764C22—81no—
765C22—81no—
766C22—82no—
767C22—81no—
768C22—81no—
769C22—82no—
770C22—124no—
771C22—124no—
772C22—124no—
773C22—124no—
774C22—124no—
775C22—124no—
776C22—124no—
777C22—242no—
778C22—242no—
779C22—242no—
780C22—242no—
781C22—242no—
782C22—242no—
783C22—242no—
784C22—242no—
785C22#552412yes—
786C22#552812yes—
787C22D4×D1211yescharacteristic
788C22D4×D1212yes—
789C22#555211yescharacteristic
790C22#555312yes—
791C22#555511yescharacteristic
792C22#556511yescharacteristic
793C22#559612yes—
794C22D3×#12112yes—
795C22#565412yes—
796C22#565812yes—
797C22#567612yes—
798C22#567712yes—
799C22#570412yes—
800C22#571012yes—
801C22C2×#93011yescharacteristic
802C22C2×#93911yescharacteristic
803C22C2×#94011yescharacteristic
804C22#582811yescharacteristic
805C22#583011yescharacteristic
806C22#583211yescharacteristic
807C22#583311yescharacteristic
808C4—24no—
809C4—24no—
810C4—24no—
811C4—42no—
812C4—68no—
813C4—81no—
814C4—81no—
815C4—124no—
816C4—242no—
817C3#1481511yescharacteristic, complemented, Sylow
818C2—82no—
819C2—244no—
820C2#7549912yes—
821C2#7551312yes—
822C2#7559512yes—
823C2#7584612yes—
824C2#8227311yescharacteristic
825C2#8235211yescharacteristic
826C2#8237811yescharacteristic
827C2#8270011yescharacteristic
828C2#8289411yescharacteristic
829C2#8299811yescharacteristic
830C2#8311311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#388C2
prime radicalC2×#4960C2
hypercenterC2×#388D3
hypocenterC3#14815
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×C3×#388C2semidirect
2. C2×#4994C2semidirect
4. C2×#4961C2semidirect
5. C2×#4957C2semidirect
6. C2×#4939C2semidirect
7. C2×C4×C4⋊Dic3C2semidirect
8. #71546C2semidirect
9. #69426C2semidirect
10. #69420C2semidirect
11. #69408C2semidirect
48. C2×#388D3semidirect
86. C2×C3×C22⋊C4D4semidirect
89. C2×C3×C42D4semidirect
112. C2×C4⋊Dic3D4semidirect
320. C2×C22⋊C4D12semidirect
326. C2×C42#67semidirect
817. C3#14815semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3882
C2×#49942
C2×#49602
C2×#49612
C2×#49572
C2×#49392
C2×C4×C4⋊Dic32
#715462
#694262
#694202
#694082
#148153