Finite Group Databasebeta

← #10727870

Subgroups — #10727870

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×C4×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#4994C212yesmaximal, complemented
3C2×#4991C212yesmaximal, complemented
4C2×#4939C212yesmaximal, complemented
5C2×#4939C211yesmaximal, characteristic, complemented
6C2×#4940C211yesmaximal, characteristic, complemented
7C2×#4671C211yesmaximal, characteristic
8#71537C212yesmaximal, complemented
9#69427C211yesmaximal, characteristic, complemented
10#69426C211yesmaximal, characteristic, complemented
11#69419C211yesmaximal, characteristic, complemented
12#14815—31nomaximal, Sylow
13C23×D12C2212yes—
14C23×D12C2211yescharacteristic
15C22×C3×C4⋊C4C2212yes—
16C22×C3×C42C2212yes—
17C22×C3×C42C2211yescharacteristic
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×C4⋊Dic3C2212yes—
28C22×C4⋊Dic3C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C3×C4×C4⋊C4—24no—
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37#4994—28no—
38#4991—28no—
39#4940—24no—
40#4939—24no—
41#4939—28no—
42#4671—24no—
43C2×#396—32no—
44C2×#394—32no—
45C2×#392—31no—
46C2×#390—32no—
47C2×#390—31no—
48C2×#388—31no—
49C2×C4×C4⋊C4D311yescharacteristic, complemented
50#1444—31no—
51#1439—31no—
52#1438—31no—
53#1437—32no—
54C24×D3C2311yescharacteristic
55C24×D3C2312yes—
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2312yes—
60C23×C3×C4C2311yescharacteristic
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2312yes—
64C23×Dic3C2311yescharacteristic
65C22×D12—24no—
66C22×D12—24no—
67C22×D12—24no—
68C22×D12—22no—
69C22×D12—24no—
70C22×D12—22no—
71C22×D12—24no—
72C22×D12—24no—
73C22×D12—22no—
74C22×D12—42no—
75C22×D12—42no—
76C22×D12—42no—
77C2×C3×C4⋊C4—24no—
78C2×C3×C4⋊C4—24no—
79C2×C3×C4⋊C4D418yescomplemented
80C2×C3×C42—22no—
81C2×C3×C42—22no—
82C2×C3×C42—24no—
83C2×C3×C42—24no—
84C2×C3×C42—42no—
85C2×C3×C42D414yescomplemented
86C2×(C2×D3)⋊C4—22no—
87C2×(C2×D3)⋊C4—22no—
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—24no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—24no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—24no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—22no—
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—24no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—42no—
109C2×(C2×D3)⋊C4—42no—
110C2×(C2×D3)⋊C4—42no—
111C2×(C2×D3)⋊C4D414yescomplemented
112C2×C4⋊Dic3—22no—
113C2×C4⋊Dic3—24no—
114C2×C4⋊Dic3—24no—
115C2×C4⋊Dic3—42no—
116C2×C4⋊Dic3—42no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—24no—
119C3×#95—22no—
120C3×#95D414yes—
121C3⋊#95—22no—
122C3⋊#95—22no—
123C3⋊#95—24no—
124C3⋊#95—24no—
125C23×D4—32no—
126C23×D4—31no—
127C22×C4⋊C4—31no—
128C22×C4⋊C4—32no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4C2×D312yes—
131C22×C22⋊C4—31no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—31no—
134C22×C22⋊C4—31no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4—32no—
139C22×C22⋊C4—32no—
140C22×C42C2×D312yes—
141C22×C42C2×D311yescharacteristic
142#396—68no—
143#394—68no—
144#392—64no—
145#390—68no—
146#390—64no—
147#388—64no—
148C4×C4⋊C4—24no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95—31no—
152C2×#95—31no—
153C2×#95C2×D311yescharacteristic
154C2×#95C2×D311yescharacteristic
155C24×C3C2411yescharacteristic
156C23×D3—21no—
157C23×D3—22no—
158C23×D3—22no—
159C23×D3—22no—
160C23×D3—22no—
161C23×D3—22no—
162C23×D3—21no—
163C23×D3—22no—
164C23×D3—22no—
165C23×D3—21no—
166C23×D3—21no—
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—21no—
177C23×D3—22no—
178C23×D3—21no—
179C23×D3—22no—
180C23×D3C2×D412yes—
181C23×D3#4114yes—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4C2×D414yes—
202C22×C3×C4C2×D412yes—
203C22×C3×C4C2×D414yes—
204C22×C3×C4C2×D412yes—
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D414yes—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D412yes—
209C22×C3×C4C2×D414yes—
210C22×C3×C4#4112yes—
211C22×C3×C4#4114yes—
212C22×C3×C4#4112yes—
213C22×Dic3—21no—
214C22×Dic3—22no—
215C22×Dic3—21no—
216C22×Dic3—22no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—21no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3C2×D412yes—
235C2×D12—28no—
236C2×D12—216no—
237C2×D12—48no—
238C2×D12—48no—
239C2×D12—48no—
240C2×D12—48no—
241C2×D12—48no—
242C2×D12—48no—
243C2×D12—44no—
244C2×D12—48no—
245C2×D12—44no—
246C2×D12—48no—
247C3×C4⋊C4—216no—
248C3×C42—28no—
249C3×C42—48no—
250(C2×D3)⋊C4—28no—
251(C2×D3)⋊C4—48no—
252(C2×D3)⋊C4—48no—
253(C2×D3)⋊C4—48no—
254(C2×D3)⋊C4—48no—
255(C2×D3)⋊C4—44no—
256(C2×D3)⋊C4—48no—
257(C2×D3)⋊C4—48no—
258(C2×D3)⋊C4—44no—
259C4⋊Dic3—48no—
260C4⋊Dic3—44no—
261Dic3⋊C4—44no—
262C25—31no—
263C25—32no—
264C22×D4—64no—
265C22×D4—64no—
266C22×D4—64no—
267C22×D4—62no—
268C22×D4—64no—
269C22×D4—64no—
270C22×D4—62no—
271C22×D4—62no—
272C22×D4—64no—
273C22×D4—122no—
274C22×D4—122no—
275C22×D4—122no—
276C23×C4—31no—
277C23×C4—32no—
278C23×C4—31no—
279C23×C4—31no—
280C23×C4C22×D312yes—
281C23×C4C22×D311yescharacteristic
282C23×C4C22×D312yes—
283C23×C4C22×D311yescharacteristic
284C23×C4C22×D311yescharacteristic
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—64no—
288C2×C4⋊C4—62no—
289C2×C4⋊C4—62no—
290C2×C4⋊C4—64no—
291C2×C4⋊C4—64no—
292C2×C4⋊C4—122no—
293C2×C4⋊C4—122no—
294C2×C4⋊C4D1218yescomplemented
295C2×C22⋊C4—34no—
296C2×C22⋊C4—62no—
297C2×C22⋊C4—62no—
298C2×C22⋊C4—64no—
299C2×C22⋊C4—64no—
300C2×C22⋊C4—64no—
301C2×C22⋊C4—62no—
302C2×C22⋊C4—62no—
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—62no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—62no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—122no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321C2×C42—22no—
322C2×C42—22no—
323C2×C42—24no—
324C2×C42—24no—
325C2×C42—42no—
326C2×C42D1214yescomplemented
327#95—22no—
328#95—62no—
329#95—62no—
330#95—64no—
331#95—64no—
332#95#6714yes—
333C23×C3C22×D411yescharacteristic
334C23×C3C22×D412yes—
335C23×C3C22×D411yescharacteristic
336C23×C3C22×D411yescharacteristic
337C23×C3C2×#4112yes—
338C23×C3C2×#4111yescharacteristic
339C23×C3C2×#4111yescharacteristic
340C23×C3C2×#4112yes—
341C23×C3H(5,𝔽2)11yescharacteristic
342C23×C3H(5,𝔽2)12yes—
343C23×C32−1+411yescharacteristic
344C22×D3—22no—
345C22×D3—24no—
346C22×D3—24no—
347C22×D3—24no—
348C22×D3—24no—
349C22×D3—24no—
350C22×D3—22no—
351C22×D3—24no—
352C22×D3—24no—
353C22×D3—22no—
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—42no—
357C22×D3—41no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—41no—
363C22×D3—42no—
364C22×D3—42no—
365C22×D3—42no—
366C22×D3—42no—
367C22×D3—41no—
368C22×D3—41no—
369C22×D3—42no—
370C22×D3—42no—
371C22×D3—42no—
372C22×D3—42no—
373C22×D3—42no—
374C22×D3—41no—
375C22×D3—41no—
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—41no—
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—41no—
401C22×D3—42no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—22no—
406C2×C3×C4—24no—
407C2×C3×C4—22no—
408C2×C3×C4—24no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—24no—
421C2×C3×C4—22no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4#12114yes—
430C2×C3×C4#12114yes—
431C2×C3×C4#12118yes—
432C2×C3×C4#12714yes—
433C2×Dic3—22no—
434C2×Dic3—24no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—41no—
440C2×Dic3—42no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—42no—
445C2×Dic3—41no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—41no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455D12—416no—
456D12—432no—
457C24—32no—
458C24—34no—
459C24—61no—
460C24—62no—
461C24—62no—
462C24—62no—
463C24—62no—
464C24—61no—
465C24—62no—
466C24—62no—
467C24—62no—
468C24—62no—
469C24—62no—
470C24—62no—
471C24—61no—
472C24—61no—
473C24—62no—
474C24—61no—
475C24—62no—
476C24—62no—
477C24—62no—
478C24—62no—
479C24—62no—
480C24—62no—
481C24—61no—
482C24—62no—
483C24C23×D311yescharacteristic
484C2×D4—68no—
485C2×D4—616no—
486C2×D4—128no—
487C2×D4—128no—
488C2×D4—128no—
489C2×D4—128no—
490C2×D4—128no—
491C2×D4—128no—
492C2×D4—124no—
493C2×D4—128no—
494C2×D4—124no—
495C2×D4—128no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—32no—
516C22×C4—61no—
517C22×C4—62no—
518C22×C4—61no—
519C22×C4—62no—
520C22×C4—61no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—61no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—61no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—61no—
531C22×C4—62no—
532C22×C4—61no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—61no—
537C22×C4C2×D1214yes—
538C22×C4C2×D1212yes—
539C22×C4C2×D1214yes—
540C22×C4C2×D1212yes—
541C22×C4C2×D1212yes—
542C22×C4C2×D1214yes—
543C22×C4#23512yes—
544C22×C4#23514yes—
545C22×C4D3×D412yes—
546C22×C4#23912yes—
547C22×C4C2×#6712yes—
548C22×C4C2×#6714yes—
549C4⋊C4—216no—
550C4⋊C4—128no—
551C4⋊C4—124no—
552C4⋊C4—124no—
553C22⋊C4—68no—
554C22⋊C4—128no—
555C22⋊C4—128no—
556C22⋊C4—128no—
557C22⋊C4—124no—
558C22⋊C4—128no—
559C22⋊C4—128no—
560C22⋊C4—124no—
561C22⋊C4—128no—
562C42—28no—
563C42—48no—
564C22×C3C2×#12111yescharacteristic
565C22×C3C2×#12111yescharacteristic
566C22×C3C2×#12112yes—
567C22×C3#52511yescharacteristic
568C22×C3#52512yes—
569C22×C3#52912yes—
570C22×C3C2×#12711yescharacteristic
571C22×C3#53211yescharacteristic
572C22×C3#53212yes—
573C22×C3#53511yescharacteristic
574C22×C3#53711yescharacteristic
575C22×C3#53812yes—
576C22×C3#54212yes—
577C22×C3D4211yescharacteristic
578C22×C3D4212yes—
579C22×C3#54612yes—
580C22×C3#54612yes—
581C22×C3#54711yescharacteristic
582C22×C3#54811yescharacteristic
583C22×C3#54812yes—
584C22×C3#55012yes—
585C22×C3#55112yes—
586C22×C3#55311yescharacteristic
587C2×D3—42no—
588C2×D3—44no—
589C2×D3—44no—
590C2×D3—42no—
591C2×D3—44no—
592C2×D3—44no—
593C2×D3—44no—
594C2×D3—44no—
595C2×D3—44no—
596C2×D3—44no—
597C2×D3—42no—
598C2×D3—44no—
599C2×D3—82no—
600C2×D3—81no—
601C2×D3—82no—
602C2×D3—81no—
603C2×D3—81no—
604C2×D3—82no—
605C2×D3—82no—
606C2×D3—82no—
607C2×D3—82no—
608C2×D3—82no—
609C2×D3—81no—
610C2×D3—82no—
611C2×D3—82no—
612C2×D3—82no—
613C3×C4—24no—
614C3×C4—24no—
615C3×C4—24no—
616C3×C4—28no—
617C3×C4—44no—
618Dic3—42no—
619Dic3—81no—
620Dic3—81no—
621Dic3—82no—
622C23—62no—
623C23—62no—
624C23—64no—
625C23—64no—
626C23—62no—
627C23—64no—
628C23—64no—
629C23—64no—
630C23—64no—
631C23—64no—
632C23—64no—
633C23—64no—
634C23—122no—
635C23—121no—
636C23—121no—
637C23—122no—
638C23—122no—
639C23—122no—
640C23—122no—
641C23—122no—
642C23—122no—
643C23—121no—
644C23—122no—
645C23—121no—
646C23—122no—
647C23—121no—
648C23—122no—
649C23—121no—
650C23—122no—
651C23—122no—
652C23—121no—
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—121no—
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
681C23C22×D1212yes—
682C23C2×#23511yescharacteristic
683C23C2×#23512yes—
684C23C2×D3×D411yescharacteristic
685C23#100411yescharacteristic
686C23C2×#23911yescharacteristic
687C23#100711yescharacteristic
688C23D3×#4112yes—
689C23#100912yes—
690C23C22×#6711yescharacteristic
691D4—1216no—
692D4—1232no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—62no—
721C2×C4—64no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—122no—
725C2×C4—121no—
726C2×C4—122no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—122no—
734C2×C4—121no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4#87414yes—
743C2×C4#89514yes—
744C2×C4#93014yes—
745C2×C4#93018yes—
746C2×C3#239211yescharacteristic
747C2×C3#241111yescharacteristic
748C2×C3#241611yescharacteristic
749C2×C3#242412yes—
750C2×C3#242612yes—
751C2×C3#246112yes—
752C2×C3#254011yescharacteristic
753C2×C3#254111yescharacteristic
754C2×C3#255412yes—
755C2×C3#266211yescharacteristic
756C2×C3#285611yescharacteristic
757D3—84no—
758D3—82no—
759C22—122no—
760C22—122no—
761C22—124no—
762C22—124no—
763C22—124no—
764C22—124no—
765C22—124no—
766C22—122no—
767C22—124no—
768C22—124no—
769C22—124no—
770C22—124no—
771C22—242no—
772C22—242no—
773C22—242no—
774C22—242no—
775C22—241no—
776C22—242no—
777C22—242no—
778C22—242no—
779C22—242no—
780C22—241no—
781C22—241no—
782C22—241no—
783C22—242no—
784C22—242no—
785C22C2×#87411yescharacteristic
786C22#547711yescharacteristic
787C22#547712yes—
788C22C2×#89511yescharacteristic
789C22#550711yescharacteristic
790C22#551011yescharacteristic
791C22#551411yescharacteristic
792C22#552411yescharacteristic
793C22#552511yescharacteristic
794C22#552712yes—
795C22#554712yes—
796C22D4×D1212yes—
797C22#555412yes—
798C22#556012yes—
799C22#557612yes—
800C22#557712yes—
801C22#558012yes—
802C22#558212yes—
803C22C2×#93011yescharacteristic
804C22C2×#93012yes—
805C22D4×#6711yescharacteristic
806C22#581711yescharacteristic
807C22#582912yes—
808C4—24no—
809C4—24no—
810C4—24no—
811C4—28no—
812C4—44no—
813C4—122no—
814C4—241no—
815C4—242no—
816C4—241no—
817C3#1481511yescharacteristic, complemented, Sylow
818C2—242no—
819C2—244no—
820C2#7377611yescharacteristic
821C2#7378212yes—
822C2#7379811yescharacteristic
823C2#7379911yescharacteristic
824C2#7380312yes—
825C2#7381611yescharacteristic
826C2#8208111yescharacteristic
827C2#8219311yescharacteristic
828C2#8227511yescharacteristic
829C2#8240712yes—
830C2#8249512yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×C4×C4⋊C4C2
prime radicalC2×#4671C2
hypercenterC2×C4×C4⋊C4D3
hypocenterC3#14815
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C4⋊C4C2semidirect
2. C2×#4994C2semidirect
3. C2×#4991C2semidirect
4. C2×#4939C2semidirect
5. C2×#4939C2semidirect
6. C2×#4940C2semidirect
8. #71537C2semidirect
9. #69427C2semidirect
10. #69426C2semidirect
11. #69419C2semidirect
49. C2×C4×C4⋊C4D3semidirect
79. C2×C3×C4⋊C4D4semidirect
85. C2×C3×C42D4semidirect
111. C2×(C2×D3)⋊C4D4semidirect
294. C2×C4⋊C4D12semidirect
326. C2×C42D12semidirect
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×C4×C4⋊C42
C2×#49942
C2×#49912
C2×#49392
C2×#49402
C2×#46712
#715372
#694272
#694262
#694192
#148153