Finite Group Databasebeta

← #10731936

Subgroups — #10731936

Order 768.

1922 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#389C211yesmaximal, characteristic, complemented
2C2×#4993C212yesmaximal, complemented
3C2×#4988C211yesmaximal, characteristic
4C2×#4988C211yesmaximal, characteristic
5C2×#4972C211yesmaximal, characteristic, complemented
6C2×#4939C211yesmaximal, characteristic
7C2×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
8#71570C212yesmaximal, complemented
9#71563C211yesmaximal, characteristic, complemented
10#69428C212yesmaximal, complemented
11#69428C212yesmaximal, complemented
12#15148—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2212yes—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×(C2×D3)⋊C4C2212yes—
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×C4⋊Dic3C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2212yes—
27C22×Dic3⋊C4C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C3×#389—24no—
31C2×C3×#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37#4993—28no—
38#4988—24no—
39#4988—24no—
40#4972—24no—
41#4939—24no—
42C4×Dic3⋊C4—24no—
43C2×#399—32no—
44C2×#390—31no—
45C2×#390—31no—
46C2×#390—31no—
47C2×#389—31no—
48C2×#389D311yescharacteristic, complemented
49C2×C4×C4⋊C4—31no—
50#1439—32no—
51#1439—32no—
52#1439—32no—
53C4⋊#95—31no—
54C24×D3C2312yes—
55C23×C3×C4C2312yes—
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×Dic3C2311yescharacteristic
61C23×Dic3C2312yes—
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C23×Dic3C2311yescharacteristic
65C22×D12—22no—
66C22×D12—22no—
67C22×D12—22no—
68C22×D12—22no—
69C22×D12—22no—
70C22×D12—22no—
71C22×D12Q814yes—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—24no—
77C2×C3×C4⋊C4—24no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—42no—
80C2×C3×C4⋊C4D414yes—
81C2×C3×C42—22no—
82C2×C3×C42—22no—
83C2×C3×C42—22no—
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—24no—
91C2×(C2×D3)⋊C4—24no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—24no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—42no—
97C2×(C2×D3)⋊C4—42no—
98C2×(C2×D3)⋊C4—42no—
99C2×(C2×D3)⋊C4—42no—
100C2×(C2×D3)⋊C4—42no—
101C2×(C2×D3)⋊C4—42no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3D414yes—
105C2×Dic3⋊C4—22no—
106C2×Dic3⋊C4—22no—
107C2×Dic3⋊C4—22no—
108C2×Dic3⋊C4—22no—
109C2×Dic3⋊C4—22no—
110C2×Dic3⋊C4—24no—
111C2×Dic3⋊C4—24no—
112C2×Dic3⋊C4—42no—
113C2×Dic3⋊C4D414yescomplemented
114C2×C4×Dic3—22no—
115C2×C4×Dic3—22no—
116C2×C4×Dic3—22no—
117C2×C4×Dic3—22no—
118C2×C4×Dic3—22no—
119C2×C4×Dic3D414yes—
120C3×#95—24no—
121C3⋊#95—22no—
122C3⋊#95—22no—
123C3⋊#95—24no—
124C3⋊#95—24no—
125C3⋊#95—42no—
126C23×D4—31no—
127C22×C4⋊C4—31no—
128C22×C4⋊C4—31no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4—32no—
131C22×C4⋊C4C2×D311yescharacteristic
132C22×C4⋊C4C2×D312yes—
133C22×C4⋊C4C2×D311yescharacteristic
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4—32no—
139C22×C22⋊C4—32no—
140C22×C42—31no—
141C22×C42—31no—
142C22×C42C2×D311yescharacteristic
143#399—68no—
144#390—64no—
145#390—64no—
146#390—64no—
147#389—24no—
148#389—64no—
149C4×C4⋊C4—64no—
150C2×#95—32no—
151C2×#95—31no—
152C2×#95—31no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95C2×D312yes—
156C24×C3C2411yescharacteristic
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×D3—22no—
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—22no—
169C23×D3—22no—
170C23×D3—22no—
171C23×D3C2×Q814yes—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—22no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4C2×D412yes—
198C22×C3×C4C2×D412yes—
199C22×C3×C4C2×D412yes—
200C22×C3×C4C2×D414yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×Q812yes—
203C22×C3×C4#4112yes—
204C22×C3×C4#4112yes—
205C22×C3×C4#4112yes—
206C22×C3×C4#4112yes—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—22no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—21no—
228C22×Dic3—22no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3C2×D412yes—
236C22×Dic3C2×D414yes—
237C22×Dic3C2×D412yes—
238C22×Dic3C2×D412yes—
239C22×Dic3C2×D412yes—
240C22×Dic3#4112yes—
241C22×Dic3#4112yes—
242C2×D12—28no—
243C2×D12—28no—
244C2×D12—28no—
245C2×D12—44no—
246C2×D12—44no—
247C2×D12—44no—
248C2×D12—44no—
249C3×C4⋊C4—28no—
250C3×C4⋊C4—48no—
251C3×C4⋊C4—44no—
252C3×C42—44no—
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—
258(C2×D3)⋊C4—48no—
259C4⋊Dic3—28no—
260Dic3⋊C4—28no—
261Dic3⋊C4—28no—
262Dic3⋊C4—48no—
263C4×Dic3—28no—
264C4×Dic3—44no—
265C25—32no—
266C22×D4—34no—
267C22×D4—62no—
268C22×D4—62no—
269C22×D4—62no—
270C22×D4—62no—
271C22×D4—62no—
272C22×D4—62no—
273C23×C4—31no—
274C23×C4—31no—
275C23×C4—32no—
276C23×C4—31no—
277C23×C4—31no—
278C23×C4C22×D312yes—
279C23×C4C22×D311yescharacteristic
280C23×C4C22×D311yescharacteristic
281C23×C4C22×D312yes—
282C23×C4C22×D311yescharacteristic
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—34no—
291C2×C4⋊C4—34no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—62no—
294C2×C4⋊C4—62no—
295C2×C4⋊C4—62no—
296C2×C4⋊C4—62no—
297C2×C4⋊C4—62no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4—62no—
300C2×C4⋊C4—64no—
301C2×C4⋊C4—64no—
302C2×C4⋊C4—122no—
303C2×C4⋊C4#6714yes—
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—122no—
317C2×C22⋊C4—122no—
318C2×C22⋊C4—122no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321C2×C22⋊C4—122no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—22no—
325C2×C42—34no—
326C2×C42—62no—
327C2×C42—62no—
328C2×C42—62no—
329C2×C42—62no—
330C2×C42—62no—
331#95—24no—
332#95—62no—
333#95—62no—
334#95—64no—
335#95—64no—
336#95—122no—
337C23×C3C22×D411yescharacteristic
338C23×C3C22×D411yescharacteristic
339C23×C3C22×D411yescharacteristic
340C23×C3C22×D411yescharacteristic
341C23×C3C22×Q811yescharacteristic
342C23×C3C2×#4111yescharacteristic
343C23×C3C2×#4111yescharacteristic
344C23×C3C2×#4111yescharacteristic
345C23×C3C2×#4111yescharacteristic
346C23×C3C2×#4111yescharacteristic
347C23×C3C2×#4111yescharacteristic
348C23×C3H(5,𝔽2)11yescharacteristic
349C23×C3H(5,𝔽2)11yescharacteristic
350C23×C3H(5,𝔽2)11yescharacteristic
351C23×C32−1+411yescharacteristic
352C22×D3—24no—
353C22×D3—24no—
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—24no—
357C22×D3—24no—
358C22×D3—24no—
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—
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—
387C2×C3×C4—22no—
388C2×C3×C4—24no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—24no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—42no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—42no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—42no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4C22⋊Q814yes—
416C2×C3×C4C22⋊Q814yes—
417C2×C3×C4C22⋊Q814yes—
418C2×C3×C4#12314yes—
419C2×C3×C4#12314yes—
420C2×C3×C4#12314yes—
421C2×C3×C4#12714yes—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—24no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—24no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—24no—
439C2×Dic3—22no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—42no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—42no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—42no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—42no—
456C2×Dic3#12114yes—
457D12—416no—
458C24—34no—
459C24—62no—
460C24—62no—
461C24—62no—
462C24—62no—
463C24—62no—
464C24—62no—
465C24—62no—
466C24—62no—
467C24—62no—
468C24—62no—
469C24—62no—
470C24—62no—
471C24—62no—
472C24—62no—
473C24C23×D311yescharacteristic
474C2×D4—68no—
475C2×D4—68no—
476C2×D4—68no—
477C2×D4—124no—
478C2×D4—124no—
479C2×D4—124no—
480C2×D4—124no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—32no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—34no—
511C22×C4—32no—
512C22×C4—32no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—62no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—62no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4#23512yes—
542C22×C4#23512yes—
543C22×C4D3×D412yes—
544C22×C4D3×D412yes—
545C22×C4D3×D412yes—
546C22×C4D3×Q812yes—
547C22×C4#23912yes—
548C22×C4#23912yes—
549C22×C4C2×#6714yes—
550C22×C4C2×#6712yes—
551C4⋊C4—28no—
552C4⋊C4—48no—
553C4⋊C4—44no—
554C4⋊C4—68no—
555C4⋊C4—68no—
556C4⋊C4—68no—
557C4⋊C4—128no—
558C22⋊C4—128no—
559C22⋊C4—128no—
560C22⋊C4—128no—
561C22⋊C4—128no—
562C22⋊C4—128no—
563C22⋊C4—128no—
564C42—44no—
565C42—68no—
566C42—124no—
567C22×C3C2×#12111yescharacteristic
568C22×C3C2×C22⋊Q811yescharacteristic
569C22×C3C2×C22⋊Q811yescharacteristic
570C22×C3C2×C22⋊Q811yescharacteristic
571C22×C3C2×#12311yescharacteristic
572C22×C3C2×#12311yescharacteristic
573C22×C3C2×#12311yescharacteristic
574C22×C3#52511yescharacteristic
575C22×C3#52911yescharacteristic
576C22×C3#52911yescharacteristic
577C22×C3C2×#12711yescharacteristic
578C22×C3#53211yescharacteristic
579C22×C3#53211yescharacteristic
580C22×C3#53511yescharacteristic
581C22×C3#53711yescharacteristic
582C22×C3#54011yescharacteristic
583C22×C3#54011yescharacteristic
584C22×C3#54211yescharacteristic
585C22×C3#54211yescharacteristic
586C22×C3D4211yescharacteristic
587C22×C3D4211yescharacteristic
588C22×C3#54611yescharacteristic
589C22×C3#54611yescharacteristic
590C22×C3#54811yescharacteristic
591C22×C3#54811yescharacteristic
592C22×C3D4×Q811yescharacteristic
593C22×C3#55011yescharacteristic
594C22×C3#55011yescharacteristic
595C22×C3#55011yescharacteristic
596C22×C3#55411yescharacteristic
597C22×C3#55411yescharacteristic
598C22×C3#55411yescharacteristic
599C22×C3#55611yescharacteristic
600C22×C3#55911yescharacteristic
601C22×C3#55911yescharacteristic
602C2×D3—44no—
603C2×D3—44no—
604C2×D3—44no—
605C2×D3—44no—
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C2×D3—82no—
610C2×D3—82no—
611C2×D3—82no—
612C2×D3—82no—
613C2×D3—82no—
614C2×D3—82no—
615C2×D3—82no—
616C2×D3—82no—
617C3×C4—44no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—82no—
621C3×C4#39918yescomplemented
622Dic3—24no—
623Dic3—42no—
624Dic3—44no—
625Dic3—42no—
626Dic3—42no—
627C23—64no—
628C23—64no—
629C23—64no—
630C23—64no—
631C23—64no—
632C23—64no—
633C23—64no—
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—
648C23—122no—
649C23—122no—
650C23—122no—
651C23—122no—
652C23—122no—
653C23—122no—
654C23—122no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23—122no—
659C23—122no—
660C23—122no—
661C23—122no—
662C23C2×#23511yescharacteristic
663C23C2×#23511yescharacteristic
664C23C2×D3×D411yescharacteristic
665C23C2×D3×D411yescharacteristic
666C23C2×D3×D411yescharacteristic
667C23#100411yescharacteristic
668C23C2×D3×Q811yescharacteristic
669C23C2×#23911yescharacteristic
670C23C2×#23911yescharacteristic
671C23#100711yescharacteristic
672C23D3×#4111yescharacteristic
673C23D3×#4111yescharacteristic
674C23#100911yescharacteristic
675C23#100911yescharacteristic
676C23C22×#6711yescharacteristic
677D4—1216no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—34no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—64no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—64no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—64no—
725C2×C4—121no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—122no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—122no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4#89414yes—
742C2×C4#89414yes—
743C2×C4#89614yes—
744C2×C4#89614yes—
745C2×C4#92914yes—
746C2×C4#94014yes—
747C2×C4#94614yes—
748C2×C3C2×#39911yescharacteristic
749C2×C3#244511yescharacteristic
750C2×C3#244511yescharacteristic
751C2×C3#244811yescharacteristic
752C2×C3#244811yescharacteristic
753C2×C3#245211yescharacteristic
754C2×C3#245211yescharacteristic
755C2×C3#245411yescharacteristic
756C2×C3#245411yescharacteristic
757C2×C3#253811yescharacteristic
758C2×C3#254011yescharacteristic
759C2×C3#254111yescharacteristic
760C2×C3#258011yescharacteristic
761C2×C3#262411yescharacteristic
762C2×C3#285411yescharacteristic
763D3—84no—
764C22—124no—
765C22—124no—
766C22—124no—
767C22—124no—
768C22—124no—
769C22—124no—
770C22—124no—
771C22—242no—
772C22—242no—
773C22—242no—
774C22—242no—
775C22—242no—
776C22—242no—
777C22—242no—
778C22—242no—
779C22C2×#89411yescharacteristic
780C22C2×#89411yescharacteristic
781C22C2×#89611yescharacteristic
782C22C2×#89611yescharacteristic
783C22#554811yescharacteristic
784C22#555311yescharacteristic
785C22#555911yescharacteristic
786C22#556211yescharacteristic
787C22#556811yescharacteristic
788C22#558011yescharacteristic
789C22#558211yescharacteristic
790C22#558511yescharacteristic
791C22#559911yescharacteristic
792C22D3×#12111yescharacteristic
793C22#560711yescharacteristic
794C22#560911yescharacteristic
795C22#562711yescharacteristic
796C22#562911yescharacteristic
797C22#563011yescharacteristic
798C22#563311yescharacteristic
799C22#569011yescharacteristic
800C22#569011yescharacteristic
801C22#569111yescharacteristic
802C22#569711yescharacteristic
803C22#572511yescharacteristic
804C22#572711yescharacteristic
805C22#573011yescharacteristic
806C22#573311yescharacteristic
807C22C2×#92911yescharacteristic
808C22D4×#6711yescharacteristic
809C22C2×#94011yescharacteristic
810C22C2×#94611yescharacteristic
811C22#581711yescharacteristic
812C22#582911yescharacteristic
813C22#583411yescharacteristic
814C4—42no—
815C4—44no—
816C4—42no—
817C4—64no—
818C4—82no—
819C4—122no—
820C4—122no—
821C4—124no—
822C4—122no—
823C4#499318yescomplemented
824C3#1514811yescharacteristic, complemented, Sylow
825C2—244no—
826C2#7600411yescharacteristic
827C2#7600711yescharacteristic
828C2#7601011yescharacteristic
829C2#7601511yescharacteristic
830C2#7605911yescharacteristic
831C2#7607511yescharacteristic
832C2#7624911yescharacteristic
833C2#7628611yescharacteristic
834C2C2×#499311yescharacteristic
835C2#8235811yescharacteristic
836C2#8246911yescharacteristic
837C2#8266911yescharacteristic
838C2#8277911yescharacteristic
839C2#8303011yescharacteristic
840C2#8323611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#389C2
prime radicalC23×D12C22
hypercenterC2×#389D3
hypocenterC3#15148
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×C3×#389C2semidirect
2. C2×#4993C2semidirect
5. C2×#4972C2semidirect
7. C2×C4×Dic3⋊C4C2semidirect
8. #71570C2semidirect
9. #71563C2semidirect
10. #69428C2semidirect
11. #69428C2semidirect
48. C2×#389D3semidirect
113. C2×Dic3⋊C4D4semidirect
621. C3×C4#399semidirect
823. C4#4993semidirect
824. C3#15148semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3892
C2×#49932
C2×#49882
C2×#49722
C2×#49392
C2×C4×Dic3⋊C42
#715702
#715632
#694282
#151483