Finite Group Databasebeta

← #10804099

Subgroups — #10804099

Order 768.

1802 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D4C211yesmaximal, characteristic
2C2×#5126C211yesmaximal, characteristic, complemented
3C2×#4726C211yesmaximal, characteristic, complemented
4C3×#1870C211yesmaximal, characteristic, complemented
5#71996C211yesmaximal, characteristic, complemented
6#71611C211yesmaximal, characteristic, complemented
7#69958C212yesmaximal, complemented
8#69955C212yesmaximal, complemented
9#69953C211yesmaximal, characteristic, complemented
10#68669C212yesmaximal, complemented
11#68664C212yesmaximal, complemented
12#21742—31nomaximal, Sylow
13C22×D3×D4C411yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C22×C3×M16C2211yescharacteristic, complemented
17C2×C3×C4×D4C2211yescharacteristic
18C2×D4×Dic3C411yescharacteristic
19C2×C4×#67C2211yescharacteristic
20C2×C4×#67C2211yescharacteristic
21C22×#208C2211yescharacteristic, complemented
22C22×ΓL(1,𝔽25)C2212yescomplemented
23C4×D3×D4—24no—
24C4×D3×D4—24no—
25C2×#893C411yescharacteristic
26C2×D3×C4⋊C4C411yescharacteristic
27C2×#67⋊C4C411yescharacteristic
28C2×#67⋊C4C411yescharacteristic
29C2×D3×C22⋊C4C411yescharacteristic
30C2×D3×C22⋊C4C411yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C2×C42×D3C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic, complemented
34C2×C3×C22⋊C8C2212yescomplemented
35C2×#830C2211yescharacteristic, complemented
36C2×#830C2212yescomplemented
37#5126—24no—
38C2×(C2×D3)⋊C8C2212yes—
39C2×(C2×D3)⋊C8C2212yes—
40C2×(C2×D3)⋊C8C2212yescomplemented
41C2×(C2×D3)⋊C8C2212yescomplemented
42C2×(C2×D3)⋊C8C2212yescomplemented
43#4726—24no—
44C3×#336C2212yescomplemented
45#4550C2212yescomplemented
46#4550C2212yescomplemented
47#4524C2212yescomplemented
48C22×C4×D4—31no—
49C2×#407—31no—
50C2×#407—31no—
51#1870—31no—
52#1870—32no—
53#1870—32no—
54#1870—31no—
55#1870—31no—
56#1870D311yescharacteristic, complemented
57#1817—32no—
58#1779—32no—
59C24×D3C2×C411yescharacteristic
60C24×D3C2×C411yescharacteristic
61C22×C3×D4C2×C411yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C22×#67C2×C411yescharacteristic
65C22×#67C2×C411yescharacteristic
66C23×Dic3C2×C411yescharacteristic
67C23×Dic3C2×C411yescharacteristic
68C2×D3×D4—24no—
69C2×D3×D4—24no—
70C2×D3×D4—24no—
71C22×D12C2×C411yescharacteristic
72C22×C4×D3—22no—
73C22×C4×D3—22no—
74C22×C4×D3—42no—
75C22×C4×D3—42no—
76C22×C4×D3—42no—
77C22×C4×D3—42no—
78C22×C4×D3C2×C411yescharacteristic
79C22×C4×D3C2×C411yescharacteristic
80C22×C4×D3C2×C411yescharacteristic
81C22×C4×D3C2×C411yescharacteristic
82C22×C4×D3C2×C411yescharacteristic
83C22×C4×D3C2×C411yescharacteristic
84C22×C4×D3D414yes—
85C22×C4×D3D414yes—
86C22×C4×D3C2311yescharacteristic
87C22×C4×D3C2311yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C2×C3×M16—22no—
90C2×C3×M16—42no—
91C22×C3×C8C2312yes—
92C22×C3×C8C2312yes—
93C3×C4×D4—22no—
94C3×C4×D4—22no—
95C2×C3×C4⋊C4C2×C411yescharacteristic
96C2×C3×C22⋊C4C2×C411yescharacteristic
97C2×C3×C22⋊C4C2×C411yescharacteristic
98C2×C3×C42C2311yescharacteristic
99C2×#217C2×C411yescharacteristic
100C2×#217C2×C411yescharacteristic
101D4×Dic3—24no—
102C4×#67—22no—
103C4×#67—22no—
104C4×#67—22no—
105C4×#67—22no—
106C2×(C2×D3)⋊C4C2×C411yescharacteristic
107C2×(C2×D3)⋊C4C2×C411yescharacteristic
108C2×(C2×D3)⋊C4C2×C411yescharacteristic
109C2×(C2×D3)⋊C4C2×C411yescharacteristic
110C2×C4⋊Dic3C2×C411yescharacteristic
111C2×Dic3⋊C4C2×C411yescharacteristic
112C2×Dic3⋊C4C2×C411yescharacteristic
113C2×C4×Dic3C2×C411yescharacteristic
114C2×C4×Dic3C2×C411yescharacteristic
115C2×C4×Dic3C2311yescharacteristic
116C2×#208—22no—
117C2×#208—42no—
118C22×C3⋊C8C2312yes—
119C22×C3⋊C8C2312yes—
120C2×ΓL(1,𝔽25)—24no—
121C2×ΓL(1,𝔽25)—42no—
122C2×ΓL(1,𝔽25)—42no—
123#893—24no—
124D3×C4⋊C4—24no—
125#67⋊C4—24no—
126#67⋊C4—24no—
127D3×C22⋊C4—24no—
128D3×C22⋊C4—24no—
129C4×D12—22no—
130C4×D12—22no—
131C42×D3—22no—
132C42×D3—22no—
133C3×C22⋊C8—22no—
134C3×C22⋊C8—42no—
135#830—22no—
136#830—42no—
137(C2×D3)⋊C8—24no—
138(C2×D3)⋊C8—24no—
139(C2×D3)⋊C8—24no—
140(C2×D3)⋊C8—42no—
141(C2×D3)⋊C8—42no—
142C23×D4—31no—
143C24×C4—31no—
144C24×C4—31no—
145C22×M16—31no—
146C22×M16—32no—
147C22×M16C2×D311yescharacteristic, complemented
148C2×C4×D4—31no—
149C2×C4×D4—31no—
150C2×C4×D4—31no—
151C2×C4×D4—31no—
152C2×C4×D4—31no—
153C2×C4×D4—31no—
154C2×C4×D4—31no—
155C2×C4×D4—64no—
156C2×C4×D4—64no—
157C2×C4×D4C2×D311yescharacteristic
158C22×C4⋊C4—31no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—31no—
161C22×C42—31no—
162#407—64no—
163#407—64no—
164C2×C22⋊C8—31no—
165C2×C22⋊C8—32no—
166C2×C22⋊C8—32no—
167C2×C22⋊C8—32no—
168C2×C22⋊C8—32no—
169C2×C22⋊C8—32no—
170C2×C22⋊C8—32no—
171C2×C22⋊C8C2×D311yescharacteristic, complemented
172C2×C22⋊C8C2×D312yescomplemented
173#336—32no—
174#336—32no—
175#336—32no—
176#336C2×D312yescomplemented
177C24×C3C22×C411yescharacteristic
178C24×C3C22×C411yescharacteristic
179C23×D3—22no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—42no—
184C23×D3—42no—
185C23×D3—42no—
186C23×D3—42no—
187C23×D3C22⋊C414yes—
188C23×D3M1614yescomplemented
189C23×D3C22×C411yescharacteristic
190C23×D3C22×C411yescharacteristic
191C23×D3C22×C411yescharacteristic
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4C22×C411yescharacteristic
202C22×C3×C4C22×C411yescharacteristic
203C22×C3×C4C22×C411yescharacteristic
204C22×C3×C4C22×C411yescharacteristic
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D412yes—
207C22×C3×C4C2411yescharacteristic
208C2×#67—22no—
209C2×#67—22no—
210C2×#67—22no—
211C2×#67—22no—
212C2×#67—22no—
213C2×#67—22no—
214C22×Dic3—22no—
215C22×Dic3—42no—
216C22×Dic3—42no—
217C22×Dic3C22⋊C414yes—
218C22×Dic3C22×C411yescharacteristic
219C22×Dic3C22×C411yescharacteristic
220C22×Dic3C22×C411yescharacteristic
221C22×Dic3C22×C411yescharacteristic
222C22×Dic3C22×C411yescharacteristic
223D3×D4—232no—
224C2×D12—22no—
225C2×D12—22no—
226C2×D12—22no—
227C2×C4×D3—22no—
228C2×C4×D3—22no—
229C2×C4×D3—22no—
230C2×C4×D3—22no—
231C2×C4×D3—22no—
232C2×C4×D3—22no—
233C2×C4×D3—22no—
234C2×C4×D3—22no—
235C2×C4×D3—21no—
236C2×C4×D3—21no—
237C2×C4×D3—22no—
238C2×C4×D3—22no—
239C2×C4×D3—22no—
240C2×C4×D3—48no—
241C2×C4×D3—44no—
242C2×C4×D3—44no—
243C2×C4×D3—44no—
244C2×C4×D3—44no—
245C2×C4×D3—48no—
246C2×C4×D3—42no—
247C2×C4×D3—42no—
248C2×C4×D3—42no—
249C2×C4×D3—42no—
250C2×C4×D3—42no—
251C2×C4×D3C22⋊C414yes—
252C2×C4×D3C22⋊C414yes—
253C2×C4×D3M1614yescomplemented
254C2×C4×D3C2×D412yes—
255C2×C4×D3C2×D412yes—
256C2×C4×D3C2×D412yes—
257C2×C4×D3C2×D412yes—
258C3×M16—44no—
259C2×C3×C8—22no—
260C2×C3×C8—22no—
261C2×C3×C8—22no—
262C2×C3×C8—22no—
263C2×C3×C8—22no—
264C2×C3×C8—22no—
265C3×C4⋊C4—22no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—22no—
268C3×C42—21no—
269C3×C42—21no—
270#217—22no—
271#217—22no—
272(C2×D3)⋊C4—22no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276C4⋊Dic3—22no—
277Dic3⋊C4—22no—
278Dic3⋊C4—22no—
279C4×Dic3—21no—
280C4×Dic3—21no—
281C4×Dic3—22no—
282C4×Dic3—22no—
283#208—44no—
284C2×C3⋊C8—22no—
285C2×C3⋊C8—22no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8—22no—
288C2×C3⋊C8—22no—
289C2×C3⋊C8—22no—
290ΓL(1,𝔽25)—48no—
291C25—31no—
292C25—31no—
293C22×D4—31no—
294C22×D4—31no—
295C22×D4—31no—
296C22×D4—64no—
297C22×D4—64no—
298C22×D4—64no—
299C22×D4C4×D311yescharacteristic
300C23×C4—31no—
301C23×C4—31no—
302C23×C4—31no—
303C23×C4—31no—
304C23×C4—31no—
305C23×C4—31no—
306C23×C4—34no—
307C23×C4—34no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—31no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4—62no—
314C23×C4—62no—
315C23×C4—122no—
316C23×C4—122no—
317C23×C4—122no—
318C23×C4—122no—
319C23×C4C22×D311yescharacteristic
320C23×C4C22×D311yescharacteristic
321C2×M16—22no—
322C2×M16—42no—
323C2×M16—64no—
324C2×M16—62no—
325C2×M16—122no—
326C2×M16—122no—
327C2×M16—122no—
328C22×C8—32no—
329C22×C8—32no—
330C22×C8C22×D312yes—
331C22×C8C22×D312yes—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—62no—
335C4×D4—62no—
336C4×D4—64no—
337C4×D4—64no—
338C4×D4—64no—
339C4×D4—62no—
340C4×D4—62no—
341C4×D4—64no—
342C4×D4—62no—
343C4×D4—62no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—64no—
348C2×C4⋊C4C4×D311yescharacteristic
349C2×C22⋊C4—31no—
350C2×C22⋊C4—31no—
351C2×C22⋊C4—31no—
352C2×C22⋊C4—31no—
353C2×C22⋊C4—31no—
354C2×C22⋊C4—31no—
355C2×C22⋊C4—64no—
356C2×C22⋊C4—64no—
357C2×C22⋊C4C4×D311yescharacteristic
358C2×C22⋊C4C4×D311yescharacteristic
359C2×C42—31no—
360C2×C42—31no—
361C2×C42—31no—
362C2×C42—62no—
363C2×C42—62no—
364C2×C42C22×D311yescharacteristic
365C22⋊C8—22no—
366C22⋊C8—42no—
367C22⋊C8—64no—
368C22⋊C8—64no—
369C22⋊C8—64no—
370C22⋊C8—62no—
371C22⋊C8—122no—
372C22⋊C8—122no—
373C22⋊C8—122no—
374C23×C3—21no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3C2×C22⋊C412yes—
383C23×C3C2×M1612yes—
384C23×C3C23×C411yescharacteristic
385C22×D3—22no—
386C22×D3—22no—
387C22×D3—21no—
388C22×D3—22no—
389C22×D3—22no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—22no—
394C22×D3—22no—
395C22×D3—28no—
396C22×D3—28no—
397C22×D3—44no—
398C22×D3—44no—
399C22×D3—48no—
400C22×D3—44no—
401C22×D3—44no—
402C22×D3—48no—
403C22×D3—48no—
404C22×D3—48no—
405C22×D3C2×C22⋊C412yes—
406C22×D3C2×C22⋊C412yes—
407C22×D3C2×M1612yes—
408C22×D3C2×M1612yes—
409C22×D3C2×M1612yes—
410C3×D4—28no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—42no—
424C2×C3×C4C2×C22⋊C412yes—
425C2×C3×C4C2×M1612yes—
426C2×C3×C4C22×D411yescharacteristic
427C2×C3×C4C22×D411yescharacteristic
428C2×C3×C4H(5,𝔽2)12yes—
429C2×C3×C4H(5,𝔽2)12yes—
430#67—28no—
431#67—28no—
432C2×Dic3—21no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—44no—
441C2×Dic3—44no—
442C2×Dic3C2×C22⋊C412yes—
443C2×Dic3C2×C22⋊C412yes—
444C2×Dic3C2×M1612yes—
445D12—28no—
446C4×D3—28no—
447C4×D3—24no—
448C4×D3—22no—
449C4×D3—22no—
450C4×D3—24no—
451C4×D3—22no—
452C4×D3—22no—
453C4×D3—44no—
454C4×D3—44no—
455C4×D3—44no—
456C4×D3—44no—
457C4×D3—44no—
458C4×D3—41no—
459C4×D3—41no—
460C4×D3—42no—
461C3×C8—42no—
462C3×C8—42no—
463C3⋊C8—42no—
464C3⋊C8—42no—
465C24—31no—
466C24—31no—
467C24—31no—
468C24—34no—
469C24—34no—
470C24—62no—
471C24—62no—
472C24—62no—
473C24—62no—
474C24—122no—
475C24—122no—
476C24—122no—
477C24—122no—
478C24C2×C4×D311yescharacteristic
479C24C2×C4×D311yescharacteristic
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—62no—
484C2×D4—62no—
485C2×D4—62no—
486C2×D4—62no—
487C2×D4—632no—
488C2×D4—62no—
489C2×D4—62no—
490C2×D4—62no—
491C2×D4—62no—
492C2×D4—62no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—31no—
500C22×C4—31no—
501C22×C4—31no—
502C22×C4—34no—
503C22×C4—34no—
504C22×C4—32no—
505C22×C4—32no—
506C22×C4—32no—
507C22×C4—32no—
508C22×C4—34no—
509C22×C4—34no—
510C22×C4—31no—
511C22×C4—31no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—124no—
527C22×C4—124no—
528C22×C4—128no—
529C22×C4—122no—
530C22×C4—122no—
531C22×C4—122no—
532C22×C4—122no—
533C22×C4—122no—
534C22×C4—124no—
535C22×C4—124no—
536C22×C4—128no—
537C22×C4—122no—
538C22×C4—122no—
539C22×C4C2×C4×D311yescharacteristic
540C22×C4C2×C4×D311yescharacteristic
541C22×C4C2×C4×D311yescharacteristic
542C22×C4C2×C4×D311yescharacteristic
543C22×C4D3×D412yes—
544C22×C4D3×D412yes—
545C22×C4C23×D311yescharacteristic
546M16—44no—
547M16—128no—
548M16—124no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—62no—
556C2×C8—62no—
557C2×C8—62no—
558C2×C8—62no—
559C2×C8—62no—
560C2×C8—62no—
561C4⋊C4—22no—
562C4⋊C4—62no—
563C4⋊C4—62no—
564C4⋊C4—62no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—62no—
568C22⋊C4—62no—
569C22⋊C4—62no—
570C22⋊C4—62no—
571C22⋊C4—62no—
572C22⋊C4—62no—
573C42—21no—
574C42—21no—
575C42—62no—
576C42—62no—
577C42—61no—
578C42—61no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—24no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—42no—
589C22×C3C22×C22⋊C411yescharacteristic
590C22×C3#51812yes—
591C22×C3C22×M1611yescharacteristic
592C22×C3C22×M1611yescharacteristic
593C22×C3#56812yes—
594C2×D3—22no—
595C2×D3—22no—
596C2×D3—24no—
597C2×D3—24no—
598C2×D3—22no—
599C2×D3—22no—
600C2×D3—22no—
601C2×D3—22no—
602C2×D3—24no—
603C2×D3—416no—
604C2×D3—416no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—42no—
608C2×D3—42no—
609C2×D3—42no—
610C2×D3#40714yes—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4#53411yescharacteristic
616C3×C4#53411yescharacteristic
617C3×C4#53412yes—
618Dic3—22no—
619Dic3—22no—
620Dic3—22no—
621Dic3—41no—
622Dic3—41no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—32no—
632C23—32no—
633C23—32no—
634C23—32no—
635C23—32no—
636C23—68no—
637C23—68no—
638C23—62no—
639C23—62no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—62no—
645C23—62no—
646C23—62no—
647C23—62no—
648C23—124no—
649C23—124no—
650C23—128no—
651C23—124no—
652C23—124no—
653C23—128no—
654C23—128no—
655C23—128no—
656C23D3×C22⋊C412yes—
657C23D3×M1612yes—
658C23C22×C4×D311yescharacteristic
659D4—28no—
660D4—68no—
661D4—68no—
662D4—68no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—32no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—68no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—64no—
689C2×C4—64no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—124no—
695C2×C4—124no—
696C2×C4—124no—
697C2×C4—124no—
698C2×C4—124no—
699C2×C4—124no—
700C2×C4—124no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—122no—
704C2×C4D3×C22⋊C412yes—
705C2×C4D3×M1612yes—
706C2×C4C2×D3×D411yescharacteristic
707C2×C4C2×D3×D411yescharacteristic
708C2×C4#100412yes—
709C2×C4#100912yes—
710C8—42no—
711C8—42no—
712C8—122no—
713C8—122no—
714C2×C3—42no—
715C2×C3—42no—
716C2×C3#230811yescharacteristic
717C2×C3C2×#40711yescharacteristic
718C2×C3#287911yescharacteristic
719C2×C3#297312yes—
720C2×C3#297512yes—
721D3—24no—
722D3—42no—
723D3—42no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—34no—
730C22—41no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—62no—
736C22—62no—
737C22—64no—
738C22—64no—
739C22—62no—
740C22—62no—
741C22—62no—
742C22—62no—
743C22—64no—
744C22—1216no—
745C22—1216no—
746C22—121no—
747C22—121no—
748C22—122no—
749C22—122no—
750C22—122no—
751C22C2×D3×C22⋊C411yescharacteristic
752C22#554512yes—
753C22C2×D3×M1611yescharacteristic
754C22C2×D3×M1611yescharacteristic
755C22#575012yes—
756C4—22no—
757C4—22no—
758C4—41no—
759C4—41no—
760C4—62no—
761C4—62no—
762C4—62no—
763C4—121no—
764C4—121no—
765C4#558911yescharacteristic
766C4#560512yes—
767C4#565311yescharacteristic
768C3#2174211yescharacteristic, complemented, Sylow
769C2—42no—
770C2—42no—
771C2—64no—
772C2—122no—
773C2—122no—
774C2#7487411yescharacteristic
775C2D3×#40711yescharacteristic
776C2#7866211yescharacteristic
777C2#7948512yes—
778C2#7954312yes—
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1870C2
prime radicalC22×D3×D4C4
cosocleC22×C3×C4C24
hypercenter#1870D3
hypocenterC3#21742
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#5126C2semidirect
3. C2×#4726C2semidirect
4. C3×#1870C2semidirect
5. #71996C2semidirect
6. #71611C2semidirect
7. #69958C2semidirect
8. #69955C2semidirect
9. #69953C2semidirect
10. #68669C2semidirect
11. #68664C2semidirect
16. C22×C3×M16C22semidirect
21. C22×#208C22semidirect
22. C22×ΓL(1,𝔽25)C22semidirect
33. C2×C3×C22⋊C8C22semidirect
34. C2×C3×C22⋊C8C22semidirect
35. C2×#830C22semidirect
36. C2×#830C22semidirect
40. C2×(C2×D3)⋊C8C22semidirect
41. C2×(C2×D3)⋊C8C22semidirect
42. C2×(C2×D3)⋊C8C22semidirect
44. C3×#336C22semidirect
45. #4550C22semidirect
46. #4550C22semidirect
47. #4524C22semidirect
56. #1870D3semidirect
147. C22×M16C2×D3semidirect
171. C2×C22⋊C8C2×D3semidirect
172. C2×C22⋊C8C2×D3semidirect
176. #336C2×D3semidirect
188. C23×D3M16semidirect
253. C2×C4×D3M16semidirect
768. C3#21742semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×D42
C2×#51262
C2×#47262
C3×#18702
#719962
#716112
#699582
#699552
#699532
#686692
#686642
#217423