Finite Group Databasebeta

← #10716972

Subgroups — #10716972

Order 768.

3502 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#893C211yesmaximal, characteristic, complemented
2C22×#67⋊C4C212yesmaximal, complemented
3C2×#4960C211yesmaximal, characteristic
4C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×#4666C212yesmaximal, complemented
6C3×#1439C211yesmaximal, characteristic, complemented
7#71568C211yesmaximal, characteristic, complemented
8#71550C212yesmaximal, complemented
9#69428C212yesmaximal, complemented
10#69426C211yesmaximal, characteristic, complemented
11Dic3×#95C211yesmaximal, characteristic, complemented
12C4×#392—31nomaximal, Sylow
13C23×#67C2212yes—
14C24×Dic3C2211yescharacteristic
15C23×D12C2211yescharacteristic
16C23×C4×D3C2212yes—
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×Dic3⋊C4C2212yes—
26C22×C4×Dic3C2211yescharacteristic
27C22×C4×Dic3C2212yes—
28C22×C4×Dic3C2211yescharacteristic
29C2×#893—28no—
30C2×#893—24no—
31C2×#67⋊C4—28no—
32C2×#67⋊C4—28no—
33C2×#67⋊C4—28no—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2211yescharacteristic
41#4960C418yescomplemented
42Dic3×C22⋊C4—24no—
43#4666—28no—
44C22×C4×D4—31no—
45C22×C4×D4—32no—
46C2×#392—31no—
47C2×C4×C22⋊C4—32no—
48C2×C4×C22⋊C4—31no—
49#1444—31no—
50#1439—32no—
51#1439D311yescharacteristic, complemented
52#1438—31no—
53#1438—32no—
54C4×#95—31no—
55C25×C3C2311yescharacteristic
56C24×D3C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2312yes—
59C23×C3×C4C2312yes—
60C23×C3×C4C2311yescharacteristic
61C22×#67—24no—
62C22×#67—24no—
63C22×#67—24no—
64C22×#67—24no—
65C22×#67—24no—
66C22×#67—24no—
67C22×#67C2×C418yescomplemented
68C23×Dic3—22no—
69C23×Dic3—24no—
70C23×Dic3—24no—
71C23×Dic3—22no—
72C23×Dic3D414yescomplemented
73C23×Dic3C2311yescharacteristic
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2311yescharacteristic
76C23×Dic3C2312yes—
77C23×Dic3C2311yescharacteristic
78C22×D12—24no—
79C22×D12—24no—
80C22×D12—22no—
81C22×D12—22no—
82C22×D12C2×C414yescomplemented
83C22×C4×D3—24no—
84C22×C4×D3—24no—
85C22×C4×D3—24no—
86C22×C4×D3—24no—
87C22×C4×D3—24no—
88C22×C4×D3—24no—
89C22×C4×D3D418yescomplemented
90C2×C3×C4⋊C4—24no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4C2×C414yescomplemented
98C2×#217—22no—
99C2×#217—22no—
100C2×#217—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—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4C2×C418yescomplemented
113C2×Dic3⋊C4—24no—
114C2×Dic3⋊C4—24no—
115C2×Dic3⋊C4—24no—
116C2×C4×Dic3—24no—
117C2×C4×Dic3—24no—
118C2×C4×Dic3—24no—
119C2×C4×Dic3—24no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3D418yescomplemented
122C2×C4×Dic3D414yescomplemented
123#893—232no—
124#67⋊C4—264no—
125C3×#95—24no—
126C3×#95—22no—
127C3⋊#95—22no—
128C3⋊#95—24no—
129C3⋊#95—22no—
130C3⋊#95—24no—
131C3⋊#95C2×C414yescomplemented
132C23×D4—32no—
133C23×D4—31no—
134C24×C4—31no—
135C24×C4—32no—
136C2×C4×D4—68no—
137C2×C4×D4—64no—
138C2×C4×D4—68no—
139C2×C4×D4—68no—
140C2×C4×D4—68no—
141C22×C4⋊C4—32no—
142C22×C4⋊C4C2×D311yescharacteristic
143C22×C22⋊C4—32no—
144C22×C22⋊C4—31no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4C2×D312yes—
149C22×C22⋊C4C2×D311yescharacteristic
150C22×C42—32no—
151C22×C42—31no—
152C22×C42—31no—
153#392—38no—
154C4×C22⋊C4—68no—
155C4×C22⋊C4—64no—
156C2×#95—31no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95—31no—
160C2×#95—31no—
161C2×#95C2×D311yescharacteristic
162C2×#95C2×D312yes—
163C24×C3—21no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3C22×C412yes—
172C24×C3C2×D412yes—
173C24×C3#4112yes—
174C24×C3C2411yescharacteristic
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—22no—
179C23×D3—22no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3C22×C414yes—
188C23×D3C2×D414yes—
189C23×D3#4114yes—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
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×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4C22×C412yes—
209C22×C3×C4C22×C412yes—
210C22×C3×C4C2×D414yes—
211C22×C3×C4C2×D414yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4#4112yes—
214C2×#67—216no—
215C2×#67—216no—
216C2×#67—216no—
217C2×#67—216no—
218C2×#67—216no—
219C2×#67—216no—
220C2×#67—216no—
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—22no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—216no—
238C22×Dic3—28no—
239C22×Dic3—44no—
240C22×Dic3—48no—
241C22×Dic3—44no—
242C22×Dic3C22×C414yes—
243C22×Dic3C2×D412yes—
244C22×Dic3C2×D412yes—
245C22×Dic3C2×D414yes—
246C22×Dic3C2×D412yes—
247C22×Dic3C2×D414yes—
248C22×Dic3C2×D412yes—
249C22×Dic3C2×D414yes—
250C22×Dic3#4112yes—
251C22×Dic3#4114yes—
252C22×Dic3#4112yes—
253C2×D12—28no—
254C2×D12—28no—
255C2×D12—216no—
256C2×D12—216no—
257C2×D12—28no—
258C2×C4×D3—216no—
259C2×C4×D3—216no—
260C2×C4×D3—216no—
261C2×C4×D3—48no—
262C2×C4×D3—48no—
263C2×C4×D3—48no—
264C2×C4×D3—48no—
265C3×C4⋊C4—28no—
266C3×C22⋊C4—216no—
267C3×C22⋊C4—28no—
268#217—28no—
269(C2×D3)⋊C4—216no—
270(C2×D3)⋊C4—216no—
271(C2×D3)⋊C4—216no—
272(C2×D3)⋊C4—216no—
273Dic3⋊C4—216no—
274C4×Dic3—216no—
275C4×Dic3—28no—
276C4×Dic3—44no—
277C25—32no—
278C25C22×D311yescharacteristic
279C22×D4—38no—
280C22×D4—34no—
281C22×D4—64no—
282C22×D4—64no—
283C22×D4—64no—
284C22×D4—64no—
285C22×D4—64no—
286C22×D4—64no—
287C22×D4—64no—
288C22×D4—64no—
289C22×D4—62no—
290C22×D4—62no—
291C23×C4—31no—
292C23×C4—32no—
293C23×C4—34no—
294C23×C4—31no—
295C23×C4—31no—
296C23×C4—31no—
297C23×C4—38no—
298C23×C4—64no—
299C23×C4—64no—
300C23×C4—64no—
301C23×C4—64no—
302C23×C4—64no—
303C23×C4—64no—
304C23×C4—64no—
305C23×C4—64no—
306C23×C4—62no—
307C23×C4—62no—
308C23×C4C22×D311yescharacteristic
309C23×C4C22×D312yes—
310C23×C4C22×D312yes—
311C23×C4C22×D311yescharacteristic
312C4×D4—664no—
313C4×D4—632no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—64no—
317C2×C4⋊C4—64no—
318C2×C4⋊C4—64no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—38no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—62no—
334C2×C22⋊C4—62no—
335C2×C22⋊C4—62no—
336C2×C22⋊C4—64no—
337C2×C22⋊C4—64no—
338C2×C22⋊C4—64no—
339C2×C22⋊C4C4×D314yescomplemented
340C2×C42—38no—
341C2×C42—34no—
342C2×C42—64no—
343C2×C42—64no—
344C2×C42—64no—
345C2×C42—64no—
346C2×C42—62no—
347#95—24no—
348#95—22no—
349#95—34no—
350#95—64no—
351#95—64no—
352#95—62no—
353#95—62no—
354C23×C3—22no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—22no—
358C23×C3—24no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—24no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—41no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—41no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3C4×D414yescomplemented
377C23×C3C23×C411yescharacteristic
378C23×C3C22×D412yes—
379C23×C3C22×D411yescharacteristic
380C23×C3C22×D411yescharacteristic
381C23×C3C22×D412yes—
382C23×C3C2×#4111yescharacteristic
383C23×C3C2×#4111yescharacteristic
384C23×C3C2×#4112yes—
385C23×C3C2×#4112yes—
386C23×C3C2×#4111yescharacteristic
387C23×C3C2×#4111yescharacteristic
388C22×D3—24no—
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—24no—
392C22×D3—24no—
393C22×D3—24no—
394C22×D3—24no—
395C22×D3—24no—
396C22×D3—24no—
397C22×D3—24no—
398C22×D3—24no—
399C22×D3—24no—
400C22×D3—24no—
401C22×D3—24no—
402C22×D3—24no—
403C22×D3—24no—
404C22×D3—24no—
405C22×D3—24no—
406C22×D3—42no—
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×D3—42no—
417C22×D3—42no—
418C22×D3—42no—
419C22×D3—42no—
420C22×D3—42no—
421C22×D3—42no—
422C22×D3C4×D418yescomplemented
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—22no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—24no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—41no—
441C2×C3×C4—42no—
442C2×C3×C4—41no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4C4×D414yescomplemented
447#67—264no—
448C2×Dic3—24no—
449C2×Dic3—24no—
450C2×Dic3—24no—
451C2×Dic3—24no—
452C2×Dic3—24no—
453C2×Dic3—24no—
454C2×Dic3—22no—
455C2×Dic3—24no—
456C2×Dic3—22no—
457C2×Dic3—24no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—41no—
462C2×Dic3—42no—
463C2×Dic3—41no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—42no—
469C2×Dic3—416no—
470C2×Dic3C4×D418yescomplemented
471C2×Dic3#12014yes—
472C2×Dic3#12018yes—
473C2×Dic3#12118yes—
474C2×Dic3#12114yes—
475C2×Dic3#12714yes—
476D12—232no—
477C4×D3—432no—
478C24—21no—
479C24—22no—
480C24—22no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—22no—
485C24—22no—
486C24—34no—
487C24—34no—
488C24—34no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—62no—
493C24—62no—
494C24—62no—
495C24—62no—
496C24—62no—
497C24—62no—
498C24—62no—
499C24—62no—
500C24—62no—
501C24C2×C4×D312yes—
502C24D3×D412yes—
503C24#23912yes—
504C24C23×D311yescharacteristic
505C2×D4—616no—
506C2×D4—68no—
507C2×D4—68no—
508C2×D4—616no—
509C2×D4—616no—
510C2×D4—616no—
511C2×D4—616no—
512C2×D4—616no—
513C2×D4—616no—
514C2×D4—616no—
515C2×D4—616no—
516C2×D4—68no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—32no—
536C22×C4—34no—
537C22×C4—32no—
538C22×C4—34no—
539C22×C4—32no—
540C22×C4—34no—
541C22×C4—34no—
542C22×C4—34no—
543C22×C4—32no—
544C22×C4—32no—
545C22×C4—32no—
546C22×C4—616no—
547C22×C4—616no—
548C22×C4—616no—
549C22×C4—616no—
550C22×C4—68no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—61no—
556C22×C4—62no—
557C22×C4—61no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—128no—
568C22×C4—128no—
569C22×C4—128no—
570C22×C4—128no—
571C22×C4—124no—
572C22×C4—124no—
573C22×C4—128no—
574C22×C4C2×C4×D312yes—
575C22×C4C2×C4×D312yes—
576C22×C4D3×D414yes—
577C22×C4D3×D414yes—
578C22×C4D3×D412yes—
579C22×C4#23712yes—
580C4⋊C4—28no—
581C4⋊C4—616no—
582C22⋊C4—216no—
583C22⋊C4—28no—
584C22⋊C4—616no—
585C22⋊C4—616no—
586C22⋊C4—616no—
587C22⋊C4—616no—
588C22⋊C4—68no—
589C42—68no—
590C42—616no—
591C42—124no—
592C22×C3—28no—
593C22×C3—24no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—44no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—44no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—44no—
603C22×C3C2×C4×D411yescharacteristic
604C22×C3C2×C4×D411yescharacteristic
605C22×C3C2×C4×D412yes—
606C22×C3C2×C4×D412yes—
607C22×C3C4×#4111yescharacteristic
608C22×C3C2×#12012yes—
609C22×C3C2×#12011yescharacteristic
610C22×C3C2×#12111yescharacteristic
611C22×C3C2×#12112yes—
612C22×C3#52512yes—
613C22×C3#52512yes—
614C22×C3#52511yescharacteristic
615C22×C3#52512yes—
616C22×C3#52512yes—
617C22×C3#52511yescharacteristic
618C22×C3#52512yes—
619C22×C3#52912yes—
620C22×C3#52911yescharacteristic
621C22×C3C2×#12711yescharacteristic
622C22×C3#53211yescharacteristic
623C22×C3#53212yes—
624C22×C3#53212yes—
625C22×C3#53211yescharacteristic
626C2×D3—28no—
627C2×D3—28no—
628C2×D3—28no—
629C2×D3—44no—
630C2×D3—44no—
631C2×D3—44no—
632C2×D3—44no—
633C2×D3—44no—
634C2×D3—44no—
635C2×D3—44no—
636C2×D3—44no—
637C2×D3—44no—
638C2×D3—44no—
639C2×D3—44no—
640C2×D3—44no—
641C3×C4—24no—
642C3×C4—42no—
643C3×C4—44no—
644C3×C4—44no—
645Dic3—28no—
646Dic3—42no—
647Dic3—42no—
648Dic3—42no—
649Dic3#39218yescomplemented
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—38no—
663C23—42no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—64no—
674C23—64no—
675C23—64no—
676C23—64no—
677C23—64no—
678C23—64no—
679C23—64no—
680C23—64no—
681C23—64no—
682C23—64no—
683C23—64no—
684C23—64no—
685C23—64no—
686C23—64no—
687C23—64no—
688C23—64no—
689C23—64no—
690C23—64no—
691C23—122no—
692C23—122no—
693C23—122no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23—122no—
698C23—122no—
699C23—122no—
700C23—122no—
701C23—122no—
702C23—122no—
703C23—122no—
704C23—122no—
705C23—122no—
706C23—122no—
707C23#89314yescomplemented
708C23C22×C4×D311yescharacteristic
709C23C2×D3×D411yescharacteristic
710C23C2×D3×D411yescharacteristic
711C23C2×D3×D412yes—
712C23C2×D3×D412yes—
713C23C2×#23711yescharacteristic
714C23C2×#23911yescharacteristic
715C23D3×#4112yes—
716C23D3×#4111yescharacteristic
717C23D3×#4112yes—
718C23D3×#4111yescharacteristic
719D4—632no—
720D4—664no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—34no—
734C2×C4—38no—
735C2×C4—34no—
736C2×C4—34no—
737C2×C4—38no—
738C2×C4—38no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—64no—
751C2×C4—64no—
752C2×C4—64no—
753C2×C4—64no—
754C2×C4—64no—
755C2×C4—64no—
756C2×C4—64no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—64no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—1232no—
764C2×C4—1216no—
765C2×C4—121no—
766C2×C4—122no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4—122no—
773C2×C4#67⋊C414yescomplemented
774C2×C3—44no—
775C2×C3C4×#12012yes—
776C2×C3C4×#12011yescharacteristic
777C2×C3C4×#12111yescharacteristic
778C2×C3C4×#12112yes—
779C2×C3C4×#12711yescharacteristic
780C2×C3C2×#39211yescharacteristic
781C2×C3#238812yes—
782C2×C3#238811yescharacteristic
783C2×C3#239211yescharacteristic
784C2×C3#239212yes—
785C2×C3#239711yescharacteristic
786D3—48no—
787C22—24no—
788C22—28no—
789C22—42no—
790C22—44no—
791C22—42no—
792C22—42no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—68no—
799C22—68no—
800C22—68no—
801C22—124no—
802C22—124no—
803C22—124no—
804C22—124no—
805C22—124no—
806C22—124no—
807C22—124no—
808C22—124no—
809C22—124no—
810C22—124no—
811C22—124no—
812C22—124no—
813C22C2×#67⋊C411yescharacteristic
814C22C2×#89311yescharacteristic
815C22#552211yescharacteristic
816C22C4×D3×D412yes—
817C22C4×D3×D412yes—
818C22D3×#12012yes—
819C22D3×#12011yescharacteristic
820C22#559612yes—
821C22#559611yescharacteristic
822C22D3×#12111yescharacteristic
823C22D3×#12112yes—
824C22#560612yes—
825C22#562411yescharacteristic
826C22#562711yescharacteristic
827C22#562712yes—
828C22#562712yes—
829C22#565612yes—
830C22#565612yes—
831C22#565611yescharacteristic
832C22#566811yescharacteristic
833C22#566812yes—
834C22#570612yes—
835C22D3×#12711yescharacteristic
836C4—24no—
837C4—38no—
838C4—42no—
839C4—44no—
840C4—44no—
841C4—68no—
842C4—122no—
843C4—122no—
844C4—122no—
845C3C4×#39211yescharacteristic, complemented, Sylow
846C2—44no—
847C2—128no—
848C2#7386511yescharacteristic
849C2#7437912yes—
850C2#7465911yescharacteristic
851C2#7545212yes—
852C2#7629311yescharacteristic
853C2D3×#39211yescharacteristic
854C2#7677711yescharacteristic
855C2#7688912yes—
856C2#7728112yes—
857C2#7745711yescharacteristic
858C2#7801911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1439C2
socle, cosocleC24×C3C24
prime radicalC2×#4960C2
hypercenter#1439D3
hypocenterC3C4×#392
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#893C2semidirect
2. C22×#67⋊C4C2semidirect
4. C2×Dic3×C22⋊C4C2semidirect
5. C2×#4666C2semidirect
6. C3×#1439C2semidirect
7. #71568C2semidirect
8. #71550C2semidirect
9. #69428C2semidirect
10. #69426C2semidirect
11. Dic3×#95C2semidirect
41. #4960C4semidirect
51. #1439D3semidirect
67. C22×#67C2×C4semidirect
72. C23×Dic3D4semidirect
82. C22×D12C2×C4semidirect
89. C22×C4×D3D4semidirect
97. C2×C3×C22⋊C4C2×C4semidirect
112. C2×(C2×D3)⋊C4C2×C4semidirect
121. C2×C4×Dic3D4semidirect
122. C2×C4×Dic3D4semidirect
131. C3⋊#95C2×C4semidirect
339. C2×C22⋊C4C4×D3semidirect
376. C23×C3C4×D4semidirect
422. C22×D3C4×D4semidirect
446. C2×C3×C4C4×D4semidirect
470. C2×Dic3C4×D4semidirect
649. Dic3#392semidirect
707. C23#893semidirect
773. C2×C4#67⋊C4semidirect
845. C3C4×#392semidirect

Maximal subgroups

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

subgroupindex
C22×#8932
C22×#67⋊C42
C2×#49602
C2×Dic3×C22⋊C42
C2×#46662
C3×#14392
#715682
#715502
#694282
#694262
Dic3×#952
C4×#3923