Finite Group Databasebeta

← #10720180

Subgroups — #10720180

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#884C211yesmaximal, characteristic
2C22×#872C211yesmaximal, characteristic, complemented
3C2×#4957C212yesmaximal, complemented
4C2×#4666C211yesmaximal, characteristic, complemented
5C3×#1437C211yesmaximal, characteristic, complemented
6#71550C212yesmaximal, complemented
7#71545C211yesmaximal, characteristic, complemented
8#71537C211yesmaximal, characteristic, complemented
9#69426C212yesmaximal, complemented
10#69408C211yesmaximal, characteristic, complemented
11Dic3⋊#95C212yesmaximal, complemented
12#14136—31nomaximal, Sylow
13C23×#67C2211yescharacteristic
14C23×#67C2211yescharacteristic
15C23×D12C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
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)⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2212yes—
28C22×C4×Dic3C2212yes—
29C22×C4×Dic3C2211yescharacteristic
30C2×#884—24no—
31C2×#884—24no—
32C2×#884C418yescomplemented
33C2×#872—24no—
34C2×#872—28no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4957—28no—
42#4666—24no—
43C22×#121—31no—
44C22×#117—31no—
45C2×#390—32no—
46C2×C4×C22⋊C4—31no—
47#1438—32no—
48#1438—32no—
49#1437—31no—
50#1437—31no—
51#1437—31no—
52#1437D311yescharacteristic, complemented
53C4⋊#95—32no—
54C25×C3C2311yescharacteristic
55C24×D3C2311yescharacteristic
56C24×D3C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2312yes—
59C23×C3×C4C2312yes—
60C23×C3×C4C2311yescharacteristic
61C22×#67—22no—
62C22×#67—22no—
63C22×#67—24no—
64C22×#67—22no—
65C22×#67—22no—
66C22×#67—24no—
67C22×#67—42no—
68C22×#67—42no—
69C22×#67C2×C414yes—
70C22×#67C2×C414yes—
71C23×Dic3C2311yescharacteristic
72C23×Dic3C2312yes—
73C23×Dic3C2312yes—
74C23×Dic3C2311yescharacteristic
75C22×D12—22no—
76C22×D12—22no—
77C22×D12—42no—
78C22×D12—42no—
79C22×D12C2×C414yes—
80C22×C4×D3—24no—
81C22×C4×D3—24no—
82C22×C4×D3C2×C414yes—
83C22×C4×D3D414yes—
84C22×C4×D3D414yes—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—42no—
90C2×C3×C22⋊C4C2×C414yes—
91C2×C3×C42—24no—
92C2×C3×C42—22no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—42no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
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—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—42no—
109C2×(C2×D3)⋊C4—42no—
110C2×(C2×D3)⋊C4C2×C414yes—
111C2×Dic3⋊C4—24no—
112C2×Dic3⋊C4—24no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4C2×C414yes—
116C2×Dic3⋊C4D418yescomplemented
117C2×C4×Dic3—22no—
118C2×C4×Dic3—24no—
119C2×C4×Dic3—24no—
120C2×C4×Dic3—24no—
121C2×C4×Dic3—24no—
122#884—232no—
123#872—232no—
124C3×#95—22no—
125C3×#95—42no—
126C3⋊#95—22no—
127C3⋊#95—42no—
128C3⋊#95—42no—
129C3⋊#95—42no—
130C23×D4—31no—
131C23×D4—31no—
132C23×D4—31no—
133C24×C4—31no—
134C2×#121—38no—
135C2×#121—64no—
136C2×#121—64no—
137C2×#117—68no—
138C2×#117—64no—
139C22×C4⋊C4—32no—
140C22×C4⋊C4—31no—
141C22×C22⋊C4—31no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4C2×D312yes—
148C22×C22⋊C4C2×D311yescharacteristic
149C22×C42—31no—
150C22×C42—32no—
151C22×C42C2×D311yescharacteristic
152#390—68no—
153C4×C22⋊C4—64no—
154C2×#95—31no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95C2×D311yescharacteristic
159C2×#95C2×D312yes—
160C24×C3—22no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3C22×C412yes—
169C24×C3C2411yescharacteristic
170C23×D3—22no—
171C23×D3—22no—
172C23×D3—22no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—21no—
178C23×D3—21no—
179C23×D3—22no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3C22×C412yes—
185C23×D3C22×C412yes—
186C23×D3C2×D412yes—
187C23×D3C2×D412yes—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
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×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4C22×C412yes—
207C22×C3×C4C22×C412yes—
208C22×C3×C4C2×D414yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4#4114yes—
212C2×#67—28no—
213C2×#67—28no—
214C2×#67—216no—
215C2×#67—48no—
216C2×#67—44no—
217C2×#67—44no—
218C2×#67—48no—
219C2×#67—44no—
220C2×#67—48no—
221C2×#67—44no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—21no—
227C22×Dic3—21no—
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×Dic3C22×C412yes—
239C22×Dic3C22×C412yes—
240C22×Dic3C2×D414yes—
241C22×Dic3C2×D412yes—
242C22×Dic3C2×D412yes—
243C22×Dic3C2×D414yes—
244C22×Dic3#4114yes—
245C22×Dic3#4114yes—
246C2×D12—28no—
247C2×D12—48no—
248C2×D12—44no—
249C2×D12—44no—
250C2×D12—48no—
251C2×C4×D3—216no—
252C2×C4×D3—28no—
253C2×C4×D3—216no—
254C2×C4×D3—28no—
255C2×C4×D3C22⋊C4116yescomplemented
256C3×C22⋊C4—28no—
257C3×C22⋊C4—48no—
258C3×C42—28no—
259#217—48no—
260(C2×D3)⋊C4—216no—
261(C2×D3)⋊C4—216no—
262(C2×D3)⋊C4—28no—
263(C2×D3)⋊C4—48no—
264(C2×D3)⋊C4—48no—
265Dic3⋊C4—28no—
266Dic3⋊C4—216no—
267C4×Dic3—28no—
268C4×Dic3—48no—
269C25—31no—
270C25—31no—
271C25C22×D311yescharacteristic
272C22×D4—34no—
273C22×D4—34no—
274C22×D4—34no—
275C22×D4—62no—
276C22×D4—62no—
277C22×D4—62no—
278C22×D4—62no—
279C22×D4—64no—
280C22×D4—64no—
281C22×D4—62no—
282C22×D4—62no—
283C22×D4—122no—
284C22×D4—122no—
285C22×D4—122no—
286C22×D4—122no—
287C23×C4—31no—
288C23×C4—34no—
289C23×C4—34no—
290C23×C4—34no—
291C23×C4—32no—
292C23×C4—32no—
293C23×C4—31no—
294C23×C4—64no—
295C23×C4—64no—
296C23×C4C22×D311yescharacteristic
297C23×C4C22×D312yes—
298C23×C4C22×D312yes—
299C23×C4C22×D311yescharacteristic
300#121—632no—
301#117—632no—
302C2×C4⋊C4—34no—
303C2×C4⋊C4—38no—
304C2×C4⋊C4—64no—
305C2×C4⋊C4—64no—
306C2×C4⋊C4—62no—
307C2×C4⋊C4—62no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—34no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—64no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—62no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—122no—
329C2×C22⋊C4—122no—
330C2×C22⋊C4—122no—
331C2×C22⋊C4C4×D314yes—
332C2×C42—24no—
333C2×C42—22no—
334C2×C42—64no—
335C2×C42—62no—
336C2×C42—64no—
337C2×C42—64no—
338C2×C42—64no—
339#95—22no—
340#95—42no—
341#95—62no—
342#95—122no—
343#95—122no—
344#95—122no—
345C23×C3—22no—
346C23×C3—24no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—24no—
350C23×C3—41no—
351C23×C3—42no—
352C23×C3—41no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3C23×C411yescharacteristic
367C23×C3C22×D411yescharacteristic
368C23×C3C22×D411yescharacteristic
369C23×C3C22×D412yes—
370C23×C3C2×#4112yes—
371C23×C3C2×#4112yes—
372C23×C3C2×#4112yes—
373C23×C3H(5,𝔽2)12yes—
374C23×C3H(5,𝔽2)12yes—
375C22×D3—24no—
376C22×D3—22no—
377C22×D3—22no—
378C22×D3—24no—
379C22×D3—22no—
380C22×D3—24no—
381C22×D3—22no—
382C22×D3—24no—
383C22×D3—24no—
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—24no—
387C22×D3—22no—
388C22×D3—24no—
389C22×D3—22no—
390C22×D3—22no—
391C22×D3—24no—
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—
402C22×D3—41no—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3C2×C22⋊C414yes—
417C2×C3×C4—24no—
418C2×C3×C4—22no—
419C2×C3×C4—24no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
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—41no—
432C2×C3×C4—41no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4C2×C22⋊C414yes—
441#67—416no—
442#67—416no—
443C2×Dic3—22no—
444C2×Dic3—24no—
445C2×Dic3—24no—
446C2×Dic3—24no—
447C2×Dic3—24no—
448C2×Dic3—24no—
449C2×Dic3—24no—
450C2×Dic3—24no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462C2×Dic3C2×C22⋊C414yes—
463C2×Dic3C4×D418yes—
464C2×Dic3#12014yes—
465C2×Dic3#12118yes—
466C2×Dic3#12314yes—
467D12—416no—
468C4×D3—232no—
469C24—22no—
470C24—22no—
471C24—21no—
472C24—21no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—32no—
478C24—32no—
479C24—32no—
480C24—32no—
481C24—62no—
482C24—62no—
483C24—62no—
484C24—62no—
485C24—62no—
486C24—62no—
487C24—62no—
488C24—62no—
489C24—61no—
490C24—61no—
491C24—62no—
492C24—62no—
493C24—62no—
494C24—62no—
495C24C2×C4×D312yes—
496C24C23×D311yescharacteristic
497C2×D4—68no—
498C2×D4—68no—
499C2×D4—616no—
500C2×D4—68no—
501C2×D4—128no—
502C2×D4—124no—
503C2×D4—124no—
504C2×D4—128no—
505C2×D4—124no—
506C2×D4—124no—
507C2×D4—128no—
508C2×D4—128no—
509C2×D4—124no—
510C2×D4—124no—
511C2×D4—128no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—32no—
531C22×C4—32no—
532C22×C4—34no—
533C22×C4—32no—
534C22×C4—34no—
535C22×C4—316no—
536C22×C4—32no—
537C22×C4—34no—
538C22×C4—34no—
539C22×C4—68no—
540C22×C4—68no—
541C22×C4—616no—
542C22×C4—616no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4C2×C4×D312yes—
560C22×C4C2×C4×D312yes—
561C22×C4#23514yes—
562C22×C4D3×D414yes—
563C22×C4D3×D412yes—
564C22×C4D3×D412yes—
565C4⋊C4—616no—
566C4⋊C4—68no—
567C22⋊C4—28no—
568C22⋊C4—48no—
569C22⋊C4—616no—
570C22⋊C4—616no—
571C22⋊C4—68no—
572C22⋊C4—128no—
573C22⋊C4—128no—
574C22⋊C4—128no—
575C42—28no—
576C42—68no—
577C42—128no—
578C22×C3—42no—
579C22×C3—44no—
580C22×C3—44no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—82no—
584C22×C3—82no—
585C22×C3—82no—
586C22×C3—82no—
587C22×C3C22×C22⋊C411yescharacteristic
588C22×C3C2×C4×D412yes—
589C22×C3C4×#4111yescharacteristic
590C22×C3C4×#4111yescharacteristic
591C22×C3#51812yes—
592C22×C3C2×#12011yescharacteristic
593C22×C3C2×#12112yes—
594C22×C3C2×#12311yescharacteristic
595C22×C3#52512yes—
596C22×C3#53212yes—
597C22×C3#53511yescharacteristic
598C22×C3#53511yescharacteristic
599C22×C3#53512yes—
600C22×C3#54612yes—
601C22×C3#54612yes—
602C22×C3#55012yes—
603C22×C3#55012yes—
604C22×C3#55312yes—
605C22×C3#55312yes—
606C22×C3#55512yes—
607C22×C3#55512yes—
608C2×D3—24no—
609C2×D3—24no—
610C2×D3—24no—
611C2×D3—44no—
612C2×D3—44no—
613C2×D3—44no—
614C2×D3—44no—
615C2×D3—44no—
616C2×D3—44no—
617C2×D3—42no—
618C2×D3—44no—
619C2×D3—44no—
620C2×D3—42no—
621C2×D3—42no—
622C2×D3—82no—
623C2×D3—82no—
624C2×D3—82no—
625C2×D3—82no—
626C3×C4—24no—
627C3×C4—42no—
628C3×C4—44no—
629C3×C4—44no—
630Dic3—42no—
631Dic3—44no—
632Dic3—44no—
633Dic3#38618yes—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—34no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—41no—
644C23—42no—
645C23—41no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—62no—
657C23—62no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23—64no—
662C23—64no—
663C23—64no—
664C23—64no—
665C23—62no—
666C23—64no—
667C23—64no—
668C23—62no—
669C23—62no—
670C23—62no—
671C23—64no—
672C23—64no—
673C23—122no—
674C23—122no—
675C23—122no—
676C23—122no—
677C23—122no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—121no—
682C23—122no—
683C23—122no—
684C23—121no—
685C23—122no—
686C23—121no—
687C23—122no—
688C23—122no—
689C23—122no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23—121no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23C22×C4×D311yescharacteristic
698C23C2×#23512yes—
699C23C2×D3×D411yescharacteristic
700C23C2×D3×D412yes—
701C23C2×D3×D411yescharacteristic
702C23#100412yes—
703C23D3×#4112yes—
704C23D3×#4112yes—
705C23#100912yes—
706D4—1216no—
707D4—1216no—
708D4—1216no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—34no—
722C2×C4—34no—
723C2×C4—38no—
724C2×C4—34no—
725C2×C4—38no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—632no—
738C2×C4—64no—
739C2×C4—64no—
740C2×C4—64no—
741C2×C4—62no—
742C2×C4—64no—
743C2×C4—64no—
744C2×C4—64no—
745C2×C4—64no—
746C2×C4—121no—
747C2×C4—122no—
748C2×C4—121no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4D3×C22⋊C414yes—
758C2×C3—82no—
759C2×C3C2×#38611yescharacteristic
760C2×C3#229711yescharacteristic
761C2×C3#230911yescharacteristic
762C2×C3#236312yes—
763C2×C3#236312yes—
764C2×C3#241412yes—
765C2×C3#241412yes—
766C2×C3#243112yes—
767C2×C3#250012yes—
768D3—44no—
769D3—82no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—44no—
774C22—44no—
775C22—64no—
776C22—64no—
777C22—64no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—124no—
783C22—124no—
784C22—124no—
785C22—124no—
786C22—124no—
787C22—124no—
788C22—122no—
789C22—122no—
790C22—122no—
791C22—124no—
792C22—124no—
793C22—242no—
794C22—242no—
795C22—242no—
796C22—242no—
797C22C4×#23511yescharacteristic
798C22C2×D3×C22⋊C411yescharacteristic
799C22#549012yes—
800C22#552211yescharacteristic
801C22#553212yes—
802C22#554012yes—
803C22C4×D3×D412yes—
804C22#554512yes—
805C22#554712yes—
806C22#554812yes—
807C22#555312yes—
808C22D3×#12011yescharacteristic
809C22#559912yes—
810C22D3×#12112yes—
811C22#560712yes—
812C22D3×#12311yescharacteristic
813C22#565412yes—
814C22#567012yes—
815C22#567411yescharacteristic
816C22#570912yes—
817C22#571511yescharacteristic
818C4—24no—
819C4—38no—
820C4—44no—
821C4—42no—
822C4—44no—
823C4—122no—
824C4—124no—
825C4—124no—
826C3#1413611yescharacteristic, complemented, Sylow
827C2—82no—
828C2—124no—
829C2—242no—
830C2#7347012yes—
831C2#7356311yescharacteristic
832C2#7470012yes—
833C2D3×#38611yescharacteristic
834C2#7548012yes—
835C2#7549512yes—
836C2#7555112yes—
837C2#7631112yes—
838C2#7642811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC22×#884C2
hypercenter#1437D3
hypocenterC3#14136
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×#872C2semidirect
3. C2×#4957C2semidirect
4. C2×#4666C2semidirect
5. C3×#1437C2semidirect
6. #71550C2semidirect
7. #71545C2semidirect
8. #71537C2semidirect
9. #69426C2semidirect
10. #69408C2semidirect
11. Dic3⋊#95C2semidirect
32. C2×#884C4semidirect
52. #1437D3semidirect
116. C2×Dic3⋊C4D4semidirect
255. C2×C4×D3C22⋊C4semidirect
826. C3#14136semidirect

Maximal subgroups

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

subgroupindex
C22×#8842
C22×#8722
C2×#49572
C2×#46662
C3×#14372
#715502
#715452
#715372
#694262
#694082
Dic3⋊#952
#141363