Finite Group Databasebeta

← #10720225

Subgroups — #10720225

Order 768.

1938 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4988C211yesmaximal, characteristic
2C2×#4988C211yesmaximal, characteristic
3C2×#4984C211yesmaximal, characteristic, complemented
4C2×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×#4939C211yesmaximal, characteristic
6C2×#4670C212yesmaximal, complemented
7C3×C4⋊#95C211yesmaximal, characteristic, complemented
8C4×C3⋊#95C211yesmaximal, characteristic, complemented
9#69429C212yesmaximal, complemented
10#69427C212yesmaximal, complemented
11#69408C212yesmaximal, complemented
12#14141—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C42C2211yescharacteristic
17C22×(C2×D3)⋊C4C2212yes—
18C22×(C2×D3)⋊C4C2212yes—
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×C4⋊Dic3C2212yes—
24C22×C4⋊Dic3C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C22×C4×Dic3C2212yes—
27C22×C4×Dic3C2211yescharacteristic
28C2×C3×#95C2212yes—
29C2×C3×#95C2212yes—
30C2×C3⋊#95C2211yescharacteristic
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2211yescharacteristic
36#4988—24no—
37#4988C418yescomplemented
38#4984—24no—
39Dic3×C4⋊C4—24no—
40#4939—24no—
41#4670—28no—
42C2×#390—31no—
43C2×#390—31no—
44C2×#390—31no—
45C2×#389—31no—
46C2×#388—32no—
47C2×C4×C4⋊C4—31no—
48#1440—32no—
49#1439—32no—
50#1437—32no—
51C4⋊#95D311yescharacteristic, complemented
52C4×#95—31no—
53C24×D3C2312yes—
54C23×C3×C4C2312yes—
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×Dic3C2311yescharacteristic
60C23×Dic3C2312yes—
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C22×D12—22no—
65C22×D12—22no—
66C22×D12—22no—
67C22×D12—22no—
68C22×D12—22no—
69C22×D12—22no—
70C22×D12C2×C414yes—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4C2×C414yes—
76C2×C3×C4⋊C4D414yes—
77C2×C3×C42—22no—
78C2×C3×C42—22no—
79C2×C3×C42—22no—
80C2×(C2×D3)⋊C4—24no—
81C2×(C2×D3)⋊C4—24no—
82C2×(C2×D3)⋊C4—24no—
83C2×(C2×D3)⋊C4—24no—
84C2×(C2×D3)⋊C4—24no—
85C2×(C2×D3)⋊C4—24no—
86C2×(C2×D3)⋊C4—24no—
87C2×(C2×D3)⋊C4—24no—
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—24no—
90C2×(C2×D3)⋊C4—42no—
91C2×(C2×D3)⋊C4—42no—
92C2×(C2×D3)⋊C4—42no—
93C2×(C2×D3)⋊C4—42no—
94C2×(C2×D3)⋊C4—42no—
95C2×(C2×D3)⋊C4—42no—
96C2×(C2×D3)⋊C4C2×C418yes—
97C2×(C2×D3)⋊C4C2×C418yes—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—24no—
101C2×C4⋊Dic3—24no—
102C2×C4⋊Dic3—42no—
103C2×C4⋊Dic3D414yes—
104C2×C4×Dic3—22no—
105C2×C4×Dic3—22no—
106C2×C4×Dic3—24no—
107C2×C4×Dic3—22no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—22no—
110C2×C4×Dic3—24no—
111C2×C4×Dic3—42no—
112C2×C4×Dic3C2×C414yes—
113C3×#95—24no—
114C3×#95—42no—
115C3⋊#95—24no—
116C3⋊#95—22no—
117C3⋊#95—24no—
118C3⋊#95—22no—
119C3⋊#95—22no—
120C3⋊#95D414yescomplemented
121C23×D4—31no—
122C22×C4⋊C4—31no—
123C22×C4⋊C4—32no—
124C22×C4⋊C4C2×D311yescharacteristic
125C22×C4⋊C4C2×D311yescharacteristic
126C22×C22⋊C4—32no—
127C22×C22⋊C4—32no—
128C22×C22⋊C4—32no—
129C22×C22⋊C4—32no—
130C22×C22⋊C4—32no—
131C22×C22⋊C4—32no—
132C22×C42—31no—
133C22×C42—31no—
134C22×C42—32no—
135C22×C42C2×D311yescharacteristic
136#390—38no—
137#390—64no—
138#390—64no—
139#389—64no—
140#388—68no—
141C4×C4⋊C4—64no—
142C2×#95—31no—
143C2×#95—31no—
144C2×#95—31no—
145C2×#95—31no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95C2×D312yes—
149C2×#95C2×D312yes—
150C24×C3C2411yescharacteristic
151C23×D3—22no—
152C23×D3—22no—
153C23×D3—22no—
154C23×D3—22no—
155C23×D3—22no—
156C23×D3—22no—
157C23×D3—22no—
158C23×D3—22no—
159C23×D3—22no—
160C23×D3—22no—
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—22no—
165C23×D3C22×C414yes—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4C22×C414yes—
191C22×C3×C4C22×C412yes—
192C22×C3×C4C2×D414yes—
193C22×C3×C4C2×D412yes—
194C22×C3×C4C2×D412yes—
195C22×C3×C4C2×D412yes—
196C22×C3×C4#4112yes—
197C22×C3×C4#4112yes—
198C22×C3×C4#4112yes—
199C22×C3×C4#4112yes—
200C22×C3×C4#4112yes—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—22no—
208C22×Dic3—21no—
209C22×Dic3—22no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—21no—
223C22×Dic3—22no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3C22×C412yes—
230C22×Dic3C22×C412yes—
231C22×Dic3C2×D414yes—
232C22×Dic3C2×D412yes—
233C22×Dic3C2×D412yes—
234C22×Dic3#4112yes—
235C22×Dic3#4112yes—
236C2×D12—28no—
237C2×D12—28no—
238C2×D12—28no—
239C2×D12—44no—
240C2×D12—44no—
241C2×D12—44no—
242C2×D12—44no—
243C3×C4⋊C4—28no—
244C3×C4⋊C4—28no—
245C3×C42—44no—
246(C2×D3)⋊C4—216no—
247(C2×D3)⋊C4—48no—
248(C2×D3)⋊C4—48no—
249(C2×D3)⋊C4—48no—
250(C2×D3)⋊C4—48no—
251(C2×D3)⋊C4—48no—
252C4⋊Dic3—28no—
253C4⋊Dic3—48no—
254C4×Dic3—28no—
255C4×Dic3—48no—
256C4×Dic3—44no—
257C25—32no—
258C22×D4—34no—
259C22×D4—62no—
260C22×D4—62no—
261C22×D4—62no—
262C22×D4—62no—
263C22×D4—62no—
264C22×D4—62no—
265C23×C4—31no—
266C23×C4—31no—
267C23×C4—32no—
268C23×C4—31no—
269C23×C4—31no—
270C23×C4C22×D312yes—
271C23×C4C22×D312yes—
272C23×C4C22×D311yescharacteristic
273C23×C4C22×D311yescharacteristic
274C23×C4C22×D311yescharacteristic
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—34no—
280C2×C4⋊C4—62no—
281C2×C4⋊C4—62no—
282C2×C4⋊C4—64no—
283C2×C4⋊C4—64no—
284C2×C4⋊C4—122no—
285C2×C4⋊C4C4×D314yes—
286C2×C4⋊C4D1214yes—
287C2×C22⋊C4—38no—
288C2×C22⋊C4—38no—
289C2×C22⋊C4—64no—
290C2×C22⋊C4—64no—
291C2×C22⋊C4—64no—
292C2×C22⋊C4—64no—
293C2×C22⋊C4—64no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—64no—
298C2×C22⋊C4—64no—
299C2×C22⋊C4—122no—
300C2×C22⋊C4—122no—
301C2×C22⋊C4—122no—
302C2×C22⋊C4—122no—
303C2×C22⋊C4—122no—
304C2×C22⋊C4—122no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—34no—
309C2×C42—62no—
310C2×C42—62no—
311C2×C42—64no—
312C2×C42—64no—
313C2×C42—62no—
314C2×C42—62no—
315C2×C42—62no—
316C2×C42—122no—
317#95—24no—
318#95—34no—
319#95—42no—
320#95—62no—
321#95—62no—
322#95—64no—
323#95—64no—
324#95—62no—
325C23×C3C23×C411yescharacteristic
326C23×C3C22×D411yescharacteristic
327C23×C3C22×D411yescharacteristic
328C23×C3C22×D411yescharacteristic
329C23×C3C2×#4111yescharacteristic
330C23×C3C2×#4111yescharacteristic
331C23×C3C2×#4111yescharacteristic
332C23×C3C2×#4111yescharacteristic
333C23×C3C2×#4111yescharacteristic
334C23×C3C2×#4111yescharacteristic
335C23×C3C2×#4111yescharacteristic
336C23×C3H(5,𝔽2)11yescharacteristic
337C23×C3H(5,𝔽2)11yescharacteristic
338C23×C3H(5,𝔽2)11yescharacteristic
339C23×C32−1+411yescharacteristic
340C22×D3—24no—
341C22×D3—24no—
342C22×D3—24no—
343C22×D3—24no—
344C22×D3—24no—
345C22×D3—24no—
346C22×D3—24no—
347C22×D3—42no—
348C22×D3—42no—
349C22×D3—42no—
350C22×D3—42no—
351C22×D3—42no—
352C22×D3—42no—
353C22×D3—42no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—42no—
357C22×D3—42no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—42no—
364C22×D3—42no—
365C22×D3—42no—
366C22×D3—42no—
367C22×D3—42no—
368C22×D3—42no—
369C22×D3—42no—
370C22×D3—42no—
371C22×D3—42no—
372C22×D3—42no—
373C22×D3—42no—
374C22×D3—42no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—24no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—42no—
394C2×C3×C4—41no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4#11714yes—
404C2×C3×C4C4×D414yes—
405C2×C3×C4C4×D414yes—
406C2×C3×C4#12114yes—
407C2×C3×C4#12314yes—
408C2×C3×C4#12414yes—
409C2×C3×C4#12614yes—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—24no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—24no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—24no—
427C2×Dic3—22no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—42no—
431C2×Dic3—41no—
432C2×Dic3—42no—
433C2×Dic3—41no—
434C2×Dic3—42no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—42no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3C4×D414yes—
445D12—416no—
446C24—34no—
447C24—62no—
448C24—62no—
449C24—62no—
450C24—62no—
451C24—62no—
452C24—62no—
453C24—62no—
454C24—62no—
455C24—62no—
456C24—62no—
457C24—62no—
458C24—62no—
459C24—62no—
460C24—62no—
461C24C23×D311yescharacteristic
462C2×D4—68no—
463C2×D4—68no—
464C2×D4—68no—
465C2×D4—124no—
466C2×D4—124no—
467C2×D4—124no—
468C2×D4—124no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—32no—
494C22×C4—32no—
495C22×C4—32no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—34no—
499C22×C4—32no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—62no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—62no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—62no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—62no—
527C22×C4—61no—
528C22×C4C2×C4×D314yes—
529C22×C4C2×C4×D312yes—
530C22×C4C2×D1214yes—
531C22×C4C2×D1212yes—
532C22×C4#23512yes—
533C22×C4D3×D412yes—
534C22×C4D3×D412yes—
535C22×C4#23712yes—
536C22×C4#23712yes—
537C22×C4#23912yes—
538C22×C4#23912yes—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—68no—
542C4⋊C4—128no—
543C22⋊C4—616no—
544C22⋊C4—128no—
545C22⋊C4—128no—
546C22⋊C4—128no—
547C22⋊C4—128no—
548C22⋊C4—128no—
549C42—44no—
550C42—68no—
551C42—128no—
552C42—124no—
553C22×C3C2×#11711yescharacteristic
554C22×C3C2×C4×D411yescharacteristic
555C22×C3C2×C4×D411yescharacteristic
556C22×C3C2×C4×D411yescharacteristic
557C22×C3C4×#4111yescharacteristic
558C22×C3#51811yescharacteristic
559C22×C3#52011yescharacteristic
560C22×C3C2×#12111yescharacteristic
561C22×C3C2×#12311yescharacteristic
562C22×C3C2×#12411yescharacteristic
563C22×C3C2×#12611yescharacteristic
564C22×C3#52911yescharacteristic
565C22×C3#52911yescharacteristic
566C22×C3#53211yescharacteristic
567C22×C3#53211yescharacteristic
568C22×C3#54011yescharacteristic
569C22×C3#54011yescharacteristic
570C22×C3#54211yescharacteristic
571C22×C3#54211yescharacteristic
572C22×C3D4211yescharacteristic
573C22×C3D4211yescharacteristic
574C22×C3#54611yescharacteristic
575C22×C3#54611yescharacteristic
576C22×C3#54711yescharacteristic
577C22×C3#54811yescharacteristic
578C22×C3#54811yescharacteristic
579C22×C3#55011yescharacteristic
580C22×C3#55011yescharacteristic
581C22×C3#55011yescharacteristic
582C22×C3#55311yescharacteristic
583C22×C3#55311yescharacteristic
584C22×C3#55511yescharacteristic
585C22×C3#55611yescharacteristic
586C22×C3#55911yescharacteristic
587C22×C3#55911yescharacteristic
588C2×D3—44no—
589C2×D3—44no—
590C2×D3—44no—
591C2×D3—44no—
592C2×D3—44no—
593C2×D3—44no—
594C2×D3—44no—
595C2×D3—82no—
596C2×D3—82no—
597C2×D3—82no—
598C2×D3—82no—
599C2×D3—82no—
600C2×D3—82no—
601C2×D3—82no—
602C2×D3—82no—
603C3×C4—44no—
604C3×C4—44no—
605C3×C4—42no—
606C3×C4—42no—
607C3×C4#38818yescomplemented
608Dic3—24no—
609Dic3—42no—
610Dic3—42no—
611Dic3—44no—
612Dic3—42no—
613C23—64no—
614C23—64no—
615C23—64no—
616C23—64no—
617C23—64no—
618C23—64no—
619C23—64no—
620C23—122no—
621C23—122no—
622C23—122no—
623C23—122no—
624C23—122no—
625C23—122no—
626C23—122no—
627C23—122no—
628C23—122no—
629C23—122no—
630C23—122no—
631C23—122no—
632C23—122no—
633C23—122no—
634C23—122no—
635C23—122no—
636C23—122no—
637C23—122no—
638C23—122no—
639C23—122no—
640C23—122no—
641C23—122no—
642C23—122no—
643C23—122no—
644C23—122no—
645C23—122no—
646C23—122no—
647C23—122no—
648C23C22×C4×D311yescharacteristic
649C23C22×D1211yescharacteristic
650C23C2×#23511yescharacteristic
651C23C2×D3×D411yescharacteristic
652C23C2×D3×D411yescharacteristic
653C23C2×#23711yescharacteristic
654C23C2×#23711yescharacteristic
655C23#100411yescharacteristic
656C23C2×#23911yescharacteristic
657C23C2×#23911yescharacteristic
658C23#100711yescharacteristic
659C23D3×#4111yescharacteristic
660C23D3×#4111yescharacteristic
661C23#100911yescharacteristic
662C23#100911yescharacteristic
663D4—1216no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—34no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—64no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—64no—
709C2×C4—62no—
710C2×C4—64no—
711C2×C4—121no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—122no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—122no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4C4×D1214yes—
728C2×C4#67⋊C414yes—
729C2×C4#88514yes—
730C2×C4#88614yes—
731C2×C4#89214yes—
732C2×C4#89514yes—
733C2×C4#89814yes—
734C2×C3C2×#38811yescharacteristic
735C2×C3#229311yescharacteristic
736C2×C3#231911yescharacteristic
737C2×C3#236111yescharacteristic
738C2×C3#236311yescharacteristic
739C2×C3#236611yescharacteristic
740C2×C3#236711yescharacteristic
741C2×C3#242611yescharacteristic
742C2×C3#242811yescharacteristic
743C2×C3#244511yescharacteristic
744C2×C3#244811yescharacteristic
745C2×C3#249011yescharacteristic
746C2×C3#249111yescharacteristic
747C2×C3#251211yescharacteristic
748C2×C3#251311yescharacteristic
749D3—84no—
750C22—124no—
751C22—124no—
752C22—124no—
753C22—124no—
754C22—124no—
755C22—124no—
756C22—124no—
757C22—242no—
758C22—242no—
759C22—242no—
760C22—242no—
761C22—242no—
762C22—242no—
763C22—242no—
764C22—242no—
765C22C2×C4×D1211yescharacteristic
766C22C2×#67⋊C411yescharacteristic
767C22C2×#88511yescharacteristic
768C22C2×#88611yescharacteristic
769C22C2×#89211yescharacteristic
770C22C2×#89511yescharacteristic
771C22#550711yescharacteristic
772C22C2×#89811yescharacteristic
773C22#551411yescharacteristic
774C22#553011yescharacteristic
775C22#553211yescharacteristic
776C22C4×D3×D411yescharacteristic
777C22#554511yescharacteristic
778C22D4×D1211yescharacteristic
779C22#555411yescharacteristic
780C22C4×#23911yescharacteristic
781C22#557411yescharacteristic
782C22#557611yescharacteristic
783C22#557711yescharacteristic
784C22#559611yescharacteristic
785C22#559911yescharacteristic
786C22#560911yescharacteristic
787C22#561911yescharacteristic
788C22#562411yescharacteristic
789C22#563011yescharacteristic
790C22#563311yescharacteristic
791C22#564311yescharacteristic
792C22#568111yescharacteristic
793C22#568111yescharacteristic
794C22#569111yescharacteristic
795C22#569711yescharacteristic
796C22#571811yescharacteristic
797C22#572511yescharacteristic
798C22#573211yescharacteristic
799C22#573311yescharacteristic
800C4—44no—
801C4—44no—
802C4—42no—
803C4—42no—
804C4—64no—
805C4—122no—
806C4—122no—
807C4—122no—
808C4—124no—
809C4#467018yescomplemented
810C3#1414111yescharacteristic, complemented, Sylow
811C2—244no—
812C2C2×#467011yescharacteristic
813C2#7364911yescharacteristic
814C2#7377411yescharacteristic
815C2#7391411yescharacteristic
816C2#7391511yescharacteristic
817C2#7417211yescharacteristic
818C2#7433311yescharacteristic
819C2#7596111yescharacteristic
820C2#7596911yescharacteristic
821C2#7621811yescharacteristic
822C2#7622011yescharacteristic
823C2#7630611yescharacteristic
824C2#7631711yescharacteristic
825C2#7649311yescharacteristic
826C2#7650711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C4⋊#95C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenterC4⋊#95D3
hypocenterC3#14141
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#4984C2semidirect
4. C2×Dic3×C4⋊C4C2semidirect
6. C2×#4670C2semidirect
7. C3×C4⋊#95C2semidirect
8. C4×C3⋊#95C2semidirect
9. #69429C2semidirect
10. #69427C2semidirect
11. #69408C2semidirect
37. #4988C4semidirect
51. C4⋊#95D3semidirect
120. C3⋊#95D4semidirect
607. C3×C4#388semidirect
809. C4#4670semidirect
810. C3#14141semidirect

Maximal subgroups

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

subgroupindex
C2×#49882
C2×#49842
C2×Dic3×C4⋊C42
C2×#49392
C2×#46702
C3×C4⋊#952
C4×C3⋊#952
#694292
#694272
#694082
#141413