Finite Group Databasebeta

← #10731740

Subgroups — #10731740

Order 768.

2038 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
1C22×#888C211yesmaximal, characteristic, complemented
2C2×#4987C211yesmaximal, characteristic
3C2×#4987C211yesmaximal, characteristic
4C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
5C2×#4673C212yesmaximal
6C3×C4⋊#95C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71535C211yesmaximal, characteristic, complemented
9#69428C212yesmaximal
10#69424C212yesmaximal, complemented
11#69413C212yesmaximal, complemented
12#15125—31nomaximal, Sylow
13C23×C4×D3C2211yescharacteristic
14C23×Dic6C2212yes—
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×(C2×D3)⋊C4C2212yes—
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2212yes—
25C22×C4×Dic3C2211yescharacteristic
26C2×#888—24no—
27C2×#888—24no—
28C2×#888—24no—
29C2×C3×#95C2212yes—
30C2×C3×#95C2212yes—
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4987—24no—
40#4987—24no—
41C4×(C2×D3)⋊C4—24no—
42#4673—28no—
43C22×C4⋊Q8—31no—
44C2×#393—32no—
45C2×#380—31no—
46C2×#380—31no—
47C2×C4×C22⋊C4—31no—
48#1446—32no—
49#1442—32no—
50#1439—32no—
51C4⋊#95—31no—
52C4⋊#95—31no—
53C4⋊#95D311yescharacteristic, complemented
54C24×D3C2311yescharacteristic
55C23×C3×C4C2312yes—
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×Dic3C2312yes—
61C23×Dic3C2312yes—
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C23×Dic3C2311yescharacteristic
65C22×C4×D3—22no—
66C22×C4×D3—22no—
67C22×C4×D3—22no—
68C22×C4×D3—22no—
69C22×C4×D3—22no—
70C22×C4×D3—22no—
71C22×C4×D3Q814yescomplemented
72C22×Dic6—24no—
73C22×Dic6—24no—
74C22×Dic6—24no—
75C22×Dic6—24no—
76C22×Dic6—24no—
77C22×Dic6—42no—
78C22×Dic6—42no—
79C2×C3×C4⋊C4—22no—
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4D414yes—
85C2×C3×C42—22no—
86C2×C3×C42—22no—
87C2×C3×C42—22no—
88C2×(C2×D3)⋊C4—22no—
89C2×(C2×D3)⋊C4—22no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—22no—
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)⋊C4D414yes—
99C2×(C2×D3)⋊C4Q814yescomplemented
100C2×C4⋊Dic3—22no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3—22no—
105C2×C4⋊Dic3D414yes—
106C2×Dic3⋊C4—24no—
107C2×Dic3⋊C4—24no—
108C2×Dic3⋊C4—24no—
109C2×C4×Dic3—22no—
110C2×C4×Dic3—22no—
111C2×C4×Dic3D414yes—
112#888—232no—
113C3×#95—24no—
114C3×#95—42no—
115C3⋊#95—24no—
116C3⋊#95—24no—
117C3⋊#95—24no—
118C3⋊#95—22no—
119C3⋊#95—22no—
120C3⋊#95—24no—
121C3⋊#95—24no—
122C3⋊#95—42no—
123C23×Q8—32no—
124C24×C4—31no—
125C2×C4⋊Q8—64no—
126C2×C4⋊Q8—64no—
127C2×C4⋊Q8—64no—
128C22×C4⋊C4—31no—
129C22×C4⋊C4—32no—
130C22×C4⋊C4—31no—
131C22×C4⋊C4C2×D311yescharacteristic
132C22×C4⋊C4C2×D311yescharacteristic
133C22×C22⋊C4—31no—
134C22×C22⋊C4—31no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C42—31no—
138C22×C42C2×D311yescharacteristic
139#393—68no—
140#380—64no—
141#380—64no—
142C4×C22⋊C4—64no—
143C2×#95—32no—
144C2×#95—32no—
145C2×#95—32no—
146C2×#95—31no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—31no—
150C2×#95—32no—
151C2×#95C2×D312yes—
152C2×#95C2×D312yes—
153C24×C3C2411yescharacteristic
154C23×D3—21no—
155C23×D3—21no—
156C23×D3—21no—
157C23×D3—21no—
158C23×D3—21no—
159C23×D3—21no—
160C23×D3—21no—
161C23×D3—21no—
162C23×D3—21no—
163C23×D3—21no—
164C23×D3—21no—
165C23×D3—21no—
166C23×D3C2×D412yes—
167C23×D3C2×Q812yes—
168C23×D3C2×Q812yes—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
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—22no—
193C22×C3×C4—22no—
194C22×C3×C4C2×D414yes—
195C22×C3×C4C2×D412yes—
196C22×C3×C4C2×D412yes—
197C22×C3×C4C2×D412yes—
198C22×C3×C4C2×D412yes—
199C22×C3×C4C2×Q812yes—
200C22×C3×C4C2×Q812yes—
201C22×C3×C4#4112yes—
202C22×C3×C4#4112yes—
203C22×C3×C4#4112yes—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3C2×D414yes—
232C22×Dic3C2×D412yes—
233C22×Dic3C2×D412yes—
234C22×Dic3C2×D412yes—
235C22×Dic3C2×Q812yes—
236C22×Dic3C2×Q812yes—
237C22×Dic3#4112yes—
238C22×Dic3#4112yes—
239C2×C4×D3—28no—
240C2×C4×D3—28no—
241C2×C4×D3—28no—
242C2×C4×D3—44no—
243C2×C4×D3—44no—
244C2×C4×D3—44no—
245C2×C4×D3—44no—
246C2×Dic6—216no—
247C2×Dic6—48no—
248C2×Dic6—48no—
249C2×Dic6—48no—
250C2×Dic6—48no—
251C2×Dic6—48no—
252C2×Dic6—48no—
253C3×C4⋊C4—28no—
254C3×C4⋊C4—44no—
255C3×C42—44no—
256(C2×D3)⋊C4—28no—
257(C2×D3)⋊C4—28no—
258(C2×D3)⋊C4—48no—
259(C2×D3)⋊C4—48no—
260C4⋊Dic3—28no—
261C4⋊Dic3—44no—
262Dic3⋊C4—216no—
263C4×Dic3—28no—
264C25—31no—
265C22×Q8—64no—
266C22×Q8—64no—
267C22×Q8—64no—
268C22×Q8—64no—
269C22×Q8—64no—
270C22×Q8—122no—
271C22×Q8—122no—
272C23×C4—31no—
273C23×C4—31no—
274C23×C4—32no—
275C23×C4—31no—
276C23×C4—34no—
277C23×C4—32no—
278C23×C4—62no—
279C23×C4—62no—
280C23×C4—62no—
281C23×C4—62no—
282C23×C4—62no—
283C23×C4—62no—
284C23×C4C22×D312yes—
285C23×C4C22×D312yes—
286C23×C4C22×D311yescharacteristic
287C23×C4C22×D311yescharacteristic
288C23×C4C22×D311yescharacteristic
289C4⋊Q8—632no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—34no—
296C2×C4⋊C4—64no—
297C2×C4⋊C4—64no—
298C2×C4⋊C4—64no—
299C2×C4⋊C4—62no—
300C2×C4⋊C4—62no—
301C2×C4⋊C4—62no—
302C2×C4⋊C4—62no—
303C2×C4⋊C4—62no—
304C2×C4⋊C4D1214yes—
305C2×C22⋊C4—34no—
306C2×C22⋊C4—34no—
307C2×C22⋊C4—62no—
308C2×C22⋊C4—62no—
309C2×C22⋊C4—62no—
310C2×C22⋊C4—62no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—122no—
316C2×C22⋊C4—122no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—34no—
321C2×C42—62no—
322C2×C42—62no—
323#95—24no—
324#95—42no—
325#95—64no—
326#95—62no—
327#95—62no—
328#95—64no—
329#95—64no—
330#95—64no—
331#95—64no—
332#95—122no—
333C23×C3C22×D411yescharacteristic
334C23×C3C22×D411yescharacteristic
335C23×C3C22×D411yescharacteristic
336C23×C3C22×D411yescharacteristic
337C23×C3C22×Q811yescharacteristic
338C23×C3C22×Q811yescharacteristic
339C23×C3C2×#4111yescharacteristic
340C23×C3C2×#4111yescharacteristic
341C23×C3C2×#4111yescharacteristic
342C23×C3C2×#4111yescharacteristic
343C23×C3C2×#4111yescharacteristic
344C23×C3H(5,𝔽2)11yescharacteristic
345C23×C3H(5,𝔽2)11yescharacteristic
346C23×C32−1+411yescharacteristic
347C23×C32−1+411yescharacteristic
348C22×D3—22no—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—22no—
356C22×D3—22no—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—22no—
360C22×D3—22no—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—41no—
367C22×D3—41no—
368C22×D3—41no—
369C22×D3—41no—
370C22×D3—41no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—41no—
374C22×D3—41no—
375C22×D3—41no—
376C22×D3—41no—
377C22×D3—41no—
378C22×D3—41no—
379C22×D3—41no—
380C22×D3—41no—
381C22×D3—41no—
382C22×D3C4⋊Q814yescomplemented
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—42no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—42no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4#12014yes—
412C2×C3×C4C22⋊Q814yes—
413C2×C3×C4C22⋊Q814yes—
414C2×C3×C4C22⋊Q814yes—
415C2×C3×C4#12414yes—
416C2×C3×C4#12414yes—
417C2×C3×C4#12414yes—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
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—24no—
435C2×Dic3—24no—
436C2×Dic3—41no—
437C2×Dic3—42no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3#12114yes—
452C2×Dic3C22⋊Q814yes—
453C4×D3—416no—
454Dic6—432no—
455C24—32no—
456C24—32no—
457C24—32no—
458C24—61no—
459C24—61no—
460C24—61no—
461C24—61no—
462C24—61no—
463C24—61no—
464C24—61no—
465C24—61no—
466C24—61no—
467C24—61no—
468C24—61no—
469C24—61no—
470C24C23×D311yescharacteristic
471C2×Q8—616no—
472C2×Q8—128no—
473C2×Q8—128no—
474C2×Q8—128no—
475C2×Q8—128no—
476C2×Q8—128no—
477C2×Q8—128no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—32no—
506C22×C4—32no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—34no—
510C22×C4—32no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—62no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—61no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—68no—
532C22×C4—68no—
533C22×C4—68no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—124no—
542C22×C4—124no—
543C22×C4—124no—
544C22×C4—124no—
545C22×C4C2×D1214yes—
546C22×C4C2×D1212yes—
547C22×C4#23512yes—
548C22×C4#23512yes—
549C22×C4D3×D412yes—
550C22×C4D3×D412yes—
551C22×C4D3×D412yes—
552C22×C4#23712yes—
553C22×C4D3×Q812yes—
554C22×C4D3×Q812yes—
555C4⋊C4—28no—
556C4⋊C4—44no—
557C4⋊C4—616no—
558C4⋊C4—68no—
559C4⋊C4—124no—
560C22⋊C4—68no—
561C22⋊C4—68no—
562C22⋊C4—128no—
563C22⋊C4—128no—
564C42—44no—
565C42—68no—
566C22×C3C2×#12011yescharacteristic
567C22×C3C2×#12111yescharacteristic
568C22×C3C2×C22⋊Q811yescharacteristic
569C22×C3C2×C22⋊Q811yescharacteristic
570C22×C3C2×C22⋊Q811yescharacteristic
571C22×C3C2×C22⋊Q811yescharacteristic
572C22×C3C2×#12411yescharacteristic
573C22×C3C2×#12411yescharacteristic
574C22×C3C2×#12411yescharacteristic
575C22×C3C2×C4⋊Q811yescharacteristic
576C22×C3#53211yescharacteristic
577C22×C3#53311yescharacteristic
578C22×C3#53311yescharacteristic
579C22×C3#53511yescharacteristic
580C22×C3#53611yescharacteristic
581C22×C3#54211yescharacteristic
582C22×C3#54211yescharacteristic
583C22×C3#54411yescharacteristic
584C22×C3#54411yescharacteristic
585C22×C3D4211yescharacteristic
586C22×C3D4211yescharacteristic
587C22×C3#54611yescharacteristic
588C22×C3#54611yescharacteristic
589C22×C3#54711yescharacteristic
590C22×C3#54711yescharacteristic
591C22×C3#54811yescharacteristic
592C22×C3#54811yescharacteristic
593C22×C3D4×Q811yescharacteristic
594C22×C3D4×Q811yescharacteristic
595C22×C3#55411yescharacteristic
596C22×C3#55411yescharacteristic
597C22×C3#55511yescharacteristic
598C22×C3#55511yescharacteristic
599C22×C3#55611yescharacteristic
600C22×C3#55611yescharacteristic
601C2×D3—24no—
602C2×D3—24no—
603C2×D3—24no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—42no—
609C2×D3—42no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—42no—
615C2×D3—42no—
616C3×C4—42no—
617C3×C4—44no—
618C3×C4—42no—
619C3×C4—82no—
620C3×C4#39318yescomplemented
621Dic3—24no—
622Dic3—24no—
623Dic3—42no—
624Dic3—44no—
625Dic3—82no—
626C23—34no—
627C23—62no—
628C23—62no—
629C23—62no—
630C23—62no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23—62no—
636C23—62no—
637C23—62no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—62no—
645C23—121no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—121no—
661C23C22×D1211yescharacteristic
662C23C2×#23511yescharacteristic
663C23C2×#23511yescharacteristic
664C23C2×D3×D411yescharacteristic
665C23C2×D3×D411yescharacteristic
666C23C2×D3×D411yescharacteristic
667C23C2×#23711yescharacteristic
668C23#100411yescharacteristic
669C23C2×D3×Q811yescharacteristic
670C23C2×D3×Q811yescharacteristic
671C23#100711yescharacteristic
672C23D3×#4111yescharacteristic
673C23D3×#4111yescharacteristic
674C23#100911yescharacteristic
675C23#101011yescharacteristic
676Q8—1232no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—34no—
687C2×C4—34no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
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—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—64no—
720C2×C4—64no—
721C2×C4—64no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—1216no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4#87514yes—
742C2×C4#88214yes—
743C2×C4#88514yes—
744C2×C4#88514yes—
745C2×C4#89614yes—
746C2×C4#89614yes—
747C2×C4#89714yes—
748C2×C3C2×#39311yescharacteristic
749C2×C3#240811yescharacteristic
750C2×C3#240911yescharacteristic
751C2×C3#243911yescharacteristic
752C2×C3#243911yescharacteristic
753C2×C3#244011yescharacteristic
754C2×C3#244011yescharacteristic
755C2×C3#249111yescharacteristic
756C2×C3#249111yescharacteristic
757C2×C3#249211yescharacteristic
758C2×C3#249211yescharacteristic
759C2×C3#254711yescharacteristic
760C2×C3#256311yescharacteristic
761C2×C3#262811yescharacteristic
762C2×C3#285711yescharacteristic
763D3—44no—
764C22—64no—
765C22—64no—
766C22—64no—
767C22—122no—
768C22—122no—
769C22—122no—
770C22—122no—
771C22—122no—
772C22—122no—
773C22—122no—
774C22—122no—
775C22—122no—
776C22—122no—
777C22—122no—
778C22—122no—
779C22C2×#87511yescharacteristic
780C22C2×#88211yescharacteristic
781C22C2×#88511yescharacteristic
782C22C2×#88511yescharacteristic
783C22#550711yescharacteristic
784C22C2×#89611yescharacteristic
785C22C2×#89611yescharacteristic
786C22C2×#89711yescharacteristic
787C22#551111yescharacteristic
788C22#553211yescharacteristic
789C22#553311yescharacteristic
790C22#554811yescharacteristic
791C22D4×D1211yescharacteristic
792C22#555411yescharacteristic
793C22#556111yescharacteristic
794C22Q8×D1211yescharacteristic
795C22#557611yescharacteristic
796C22#557811yescharacteristic
797C22#558211yescharacteristic
798C22D3×#12111yescharacteristic
799C22#560711yescharacteristic
800C22#561111yescharacteristic
801C22#561611yescharacteristic
802C22D3×C22⋊Q811yescharacteristic
803C22#562811yescharacteristic
804C22#563511yescharacteristic
805C22#564111yescharacteristic
806C22#567611yescharacteristic
807C22#567711yescharacteristic
808C22#568811yescharacteristic
809C22#568911yescharacteristic
810C22#571711yescharacteristic
811C22D3×C4⋊Q811yescharacteristic
812C22#572711yescharacteristic
813C22#572911yescharacteristic
814C4—44no—
815C4—42no—
816C4—42no—
817C4—64no—
818C4—64no—
819C4—82no—
820C4—124no—
821C4—122no—
822C4—242no—
823C4#467318yescomplemented
824C3#1512511yescharacteristic, complemented, Sylow
825C2—124no—
826C2C2×#467311yescharacteristic
827C2#7378811yescharacteristic
828C2#7378911yescharacteristic
829C2#7393711yescharacteristic
830C2#7394211yescharacteristic
831C2#7416211yescharacteristic
832C2#7432611yescharacteristic
833C2#7599711yescharacteristic
834C2#7599911yescharacteristic
835C2#7625011yescharacteristic
836C2#7628811yescharacteristic
837C2#7643611yescharacteristic
838C2#7645111yescharacteristic
839C2#7661911yescharacteristic
840C2#7663211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C4⋊#95C2
prime radicalC24×D3C23
hypercenterC4⋊#95D3
hypocenterC3#15125
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×#888C2semidirect
6. C3×C4⋊#95C2semidirect
7. #71563C2semidirect
8. #71535C2semidirect
10. #69424C2semidirect
11. #69413C2semidirect
53. C4⋊#95D3semidirect
71. C22×C4×D3Q8semidirect
99. C2×(C2×D3)⋊C4Q8semidirect
382. C22×D3C4⋊Q8semidirect
620. C3×C4#393semidirect
823. C4#4673semidirect
824. C3#15125semidirect

Maximal subgroups

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

subgroupindex
C22×#8882
C2×#49872
C2×C4×(C2×D3)⋊C42
C2×#46732
C3×C4⋊#952
#715632
#715352
#694282
#694242
#694132
#151253