Finite Group Databasebeta

← #10796325

Subgroups — #10796325

Order 768.

1938 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
2C2×#5547C211yesmaximal, characteristic
3C2×#4727C212yesmaximal, complemented
4C2×D3×C22⋊C8C211yesmaximal, characteristic, complemented
5C3×#1869C211yesmaximal, characteristic, complemented
6#71975C211yesmaximal, characteristic, complemented
7#71610C211yesmaximal, characteristic, complemented
8#69958C212yesmaximal, complemented
9#69952C211yesmaximal, characteristic, complemented
10#68669C212yesmaximal, complemented
11#68661C212yesmaximal, complemented
12#20897—31nomaximal, Sylow
13C22×#235C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C23×C3×C8C2211yescharacteristic
16C2×C3×C4×D4C2211yescharacteristic
17C2×#939C411yescharacteristic
18C2×#937C411yescharacteristic
19C2×C4×#67C2211yescharacteristic
20C2×C4×#67C2211yescharacteristic
21C23×C3⋊C8C2211yescharacteristic
22C22×ΓL(1,𝔽25)—24no—
23C22×ΓL(1,𝔽25)—28no—
24C22×ΓL(1,𝔽25)C2212yes—
25C22×ΓL(1,𝔽25)C2212yes—
26C22×D3×C8C2212yes—
27#5547—24no—
28#5547—24no—
29C2×#896C411yescharacteristic
30C2×#894C411yescharacteristic
31C2×#884C411yescharacteristic
32C2×#883C411yescharacteristic
33C2×#882C411yescharacteristic
34C2×#878C411yescharacteristic
35C2×C4×D12C2211yescharacteristic
36C2×#872C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2212yescomplemented
39C2×#830C2211yescharacteristic
40C2×#830C2212yescomplemented
41C2×(C2×D3)⋊C8C2212yes—
42C2×(C2×D3)⋊C8C2212yescomplemented
43C2×(C2×D3)⋊C8C2212yescomplemented
44#4727—28no—
45D3×C22⋊C8—24no—
46C3×#336C2212yescomplemented
47#4550C2212yescomplemented
48#4550C2212yescomplemented
49#4524C2212yescomplemented
50C23×M16—31no—
51C2×#525—31no—
52C2×#408—32no—
53C22×C22⋊C8—31no—
54#1870—32no—
55#1870—32no—
56#1869—31no—
57#1869—31no—
58#1869—31no—
59#1869D311yescharacteristic, complemented
60#1729—32no—
61C24×D3C2×C411yescharacteristic
62C22×C3×D4C2×C411yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C22×#67C2×C411yescharacteristic
66C22×#67C2×C411yescharacteristic
67C22×#67C2×C411yescharacteristic
68C22×#67C2×C411yescharacteristic
69C23×Dic3C2×C411yescharacteristic
70C2×#235—24no—
71C2×#235—22no—
72C2×#235—22no—
73C2×#235—24no—
74C22×D12C2×C411yescharacteristic
75C22×D12C2×C411yescharacteristic
76C22×C4×D3—24no—
77C22×C4×D3—24no—
78C22×C4×D3C2×C411yescharacteristic
79C22×C4×D3C2×C411yescharacteristic
80C22×C4×D3D414yes—
81C22×C4×D3D414yes—
82C22×C4×D3C2311yescharacteristic
83C22×C4×D3C2311yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C22×Dic6C2×C411yescharacteristic
86C22×C3×C8—22no—
87C22×C3×C8—24no—
88C22×C3×C8C2312yes—
89C22×C3×C8C2312yes—
90C3×C4×D4—22no—
91C3×C4×D4—22no—
92C2×C3×C4⋊C4C2×C411yescharacteristic
93C2×C3×C22⋊C4C2×C411yescharacteristic
94C2×C3×C22⋊C4C2×C411yescharacteristic
95C2×C3×C42C2311yescharacteristic
96C2×#217C2×C411yescharacteristic
97C2×#217C2×C411yescharacteristic
98#939—24no—
99#937—24no—
100C4×#67—22no—
101C4×#67—22no—
102C4×#67—22no—
103C4×#67—22no—
104C2×(C2×D3)⋊C4C2×C411yescharacteristic
105C2×(C2×D3)⋊C4C2×C411yescharacteristic
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×Dic3⋊C4C2×C411yescharacteristic
114C2×Dic3⋊C4C2×C411yescharacteristic
115C2×C4×Dic3C2311yescharacteristic
116C22×C3⋊C8—22no—
117C22×C3⋊C8—24no—
118C22×C3⋊C8C2312yes—
119C22×C3⋊C8C2312yes—
120C2×ΓL(1,𝔽25)—232no—
121C2×ΓL(1,𝔽25)—24no—
122C2×ΓL(1,𝔽25)—24no—
123C2×ΓL(1,𝔽25)—24no—
124C2×ΓL(1,𝔽25)—24no—
125C2×ΓL(1,𝔽25)—24no—
126C2×ΓL(1,𝔽25)D418yescomplemented
127C2×D3×C8—24no—
128C2×D3×C8—24no—
129C2×D3×C8—24no—
130#896—24no—
131#894—24no—
132#884—24no—
133#883—24no—
134#882—24no—
135#878—24no—
136C4×D12—22no—
137C4×D12—22no—
138#872—22no—
139#872—22no—
140C3×C22⋊C8—22no—
141C3×C22⋊C8—24no—
142#830—22no—
143#830—24no—
144(C2×D3)⋊C8—24no—
145(C2×D3)⋊C8—24no—
146(C2×D3)⋊C8—24no—
147C22×#41—31no—
148C24×C4—31no—
149C22×M16—32no—
150C22×M16—32no—
151C22×M16—68no—
152C22×M16—64no—
153C23×C8—31no—
154C23×C8—32no—
155C23×C8C2×D311yescharacteristic
156#525—64no—
157#525—64no—
158C2×#123—31no—
159C2×#123—31no—
160C2×C22⋊Q8—31no—
161C2×C22⋊Q8—31no—
162C2×#121—31no—
163C2×#121—31no—
164C2×#120—31no—
165C2×#120—31no—
166C2×C4×D4—31no—
167C2×C4×D4—31no—
168C2×C4×D4—31no—
169C2×C4×D4C2×D311yescharacteristic
170C2×#117—31no—
171#408—68no—
172C2×C22⋊C8—31no—
173C2×C22⋊C8—32no—
174C2×C22⋊C8—32no—
175C2×C22⋊C8—32no—
176C2×C22⋊C8—32no—
177C2×C22⋊C8—64no—
178C2×C22⋊C8C2×D311yescharacteristic
179C2×C22⋊C8C2×D312yescomplemented
180#336—32no—
181#336—32no—
182#336—32no—
183#336C2×D312yescomplemented
184C24×C3C22×C411yescharacteristic
185C24×C3C22×C411yescharacteristic
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—24no—
189C23×D3—42no—
190C23×D3C22⋊C414yes—
191C23×D3C22×C411yescharacteristic
192C23×D3C22×C411yescharacteristic
193C23×D3C22×C411yescharacteristic
194C2×C3×D4—22no—
195C2×C3×D4—22no—
196C2×C3×D4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4C22×C411yescharacteristic
204C22×C3×C4C22×C411yescharacteristic
205C22×C3×C4C22×C411yescharacteristic
206C22×C3×C4C22×C411yescharacteristic
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D412yes—
209C22×C3×C4C2411yescharacteristic
210C2×#67—22no—
211C2×#67—22no—
212C2×#67—22no—
213C2×#67—22no—
214C2×#67—22no—
215C2×#67—24no—
216C2×#67—22no—
217C2×#67—24no—
218C2×#67—42no—
219C22×Dic3—24no—
220C22×Dic3C22⋊C414yes—
221C22×Dic3C22×C411yescharacteristic
222C22×Dic3C22×C411yescharacteristic
223C22×Dic3C22×C411yescharacteristic
224C22×Dic3C22×C411yescharacteristic
225C22×Dic3C22×C411yescharacteristic
226#235—44no—
227#235—48no—
228#235—44no—
229C2×D12—22no—
230C2×D12—22no—
231C2×D12—24no—
232C2×D12—42no—
233C2×C4×D3—24no—
234C2×C4×D3—22no—
235C2×C4×D3—22no—
236C2×C4×D3—24no—
237C2×C4×D3—28no—
238C2×C4×D3—216no—
239C2×C4×D3—28no—
240C2×C4×D3—22no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—22no—
244C2×C4×D3C22⋊C414yes—
245C2×C4×D3C22⋊C414yes—
246C2×C4×D3C2×D412yes—
247C2×C4×D3C2×D412yes—
248C2×C4×D3C2×D414yes—
249C2×C4×D3C2×D412yes—
250C2×C4×D3C2×D412yes—
251C2×C4×D3#4114yes—
252C2×Dic6—22no—
253C2×Dic6—24no—
254C2×C3×C8—28no—
255C2×C3×C8—22no—
256C2×C3×C8—22no—
257C2×C3×C8—22no—
258C2×C3×C8—22no—
259C2×C3×C8—22no—
260C2×C3×C8C2×D414yes—
261C3×C4⋊C4—22no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—22no—
264C3×C42—21no—
265C3×C42—21no—
266#217—22no—
267#217—22no—
268(C2×D3)⋊C4—22no—
269(C2×D3)⋊C4—22no—
270(C2×D3)⋊C4—22no—
271(C2×D3)⋊C4—22no—
272(C2×D3)⋊C4—22no—
273(C2×D3)⋊C4—22no—
274C4⋊Dic3—22no—
275Dic3⋊C4—22no—
276Dic3⋊C4—22no—
277Dic3⋊C4—22no—
278Dic3⋊C4—22no—
279C4×Dic3—21no—
280C4×Dic3—21no—
281C2×C3⋊C8—28no—
282C2×C3⋊C8—22no—
283C2×C3⋊C8—22no—
284C2×C3⋊C8—22no—
285C2×C3⋊C8—22no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8C2×D414yes—
288ΓL(1,𝔽25)—216no—
289ΓL(1,𝔽25)—216no—
290D3×C8—48no—
291C25—31no—
292C2×#41—62no—
293C2×#41—62no—
294C2×#41—64no—
295C2×#41—64no—
296C22×Q8—31no—
297C22×D4—31no—
298C22×D4—31no—
299C22×D4—31no—
300C22×D4—31no—
301C22×D4—31no—
302C22×D4—31no—
303C22×D4C4×D311yescharacteristic
304C23×C4—31no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—34no—
309C23×C4—34no—
310C23×C4—31no—
311C23×C4—31no—
312C23×C4—64no—
313C23×C4—64no—
314C23×C4C22×D311yescharacteristic
315C23×C4C22×D311yescharacteristic
316C2×M16—38no—
317C2×M16—64no—
318C2×M16—64no—
319C2×M16—64no—
320C2×M16—64no—
321C2×M16—632no—
322C2×M16—64no—
323C22×C8—22no—
324C22×C8—24no—
325C22×C8—32no—
326C22×C8—32no—
327C22×C8—64no—
328C22×C8—64no—
329C22×C8—64no—
330C22×C8—64no—
331C22×C8—62no—
332C22×C8C22×D312yes—
333C22×C8C22×D312yes—
334#123—64no—
335#123—64no—
336C22⋊Q8—64no—
337C22⋊Q8—64no—
338#121—64no—
339#121—64no—
340#120—64no—
341#120—64no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—62no—
345C4×D4—62no—
346C4×D4—62no—
347C4×D4—62no—
348C4×D4—62no—
349C4×D4—62no—
350#117—62no—
351#117—62no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4C4×D311yescharacteristic
358C2×C22⋊C4—31no—
359C2×C22⋊C4—31no—
360C2×C22⋊C4—31no—
361C2×C22⋊C4—31no—
362C2×C22⋊C4—31no—
363C2×C22⋊C4—31no—
364C2×C22⋊C4—31no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4C4×D311yescharacteristic
367C2×C22⋊C4C4×D311yescharacteristic
368C2×C42—31no—
369C2×C42C22×D311yescharacteristic
370C22⋊C8—22no—
371C22⋊C8—24no—
372C22⋊C8—64no—
373C22⋊C8—64no—
374C22⋊C8—64no—
375C22⋊C8—62no—
376C22⋊C8—64no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—21no—
380C23×C3—22no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—22no—
384C23×C3C2×C22⋊C412yes—
385C23×C3#13112yes—
386C23×C3#13112yes—
387C23×C3C23×C411yescharacteristic
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—22no—
391C22×D3—22no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—22no—
395C22×D3—28no—
396C22×D3—28no—
397C22×D3—21no—
398C22×D3—22no—
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—22no—
402C22×D3—44no—
403C22×D3—48no—
404C22×D3—48no—
405C22×D3C2×C22⋊C412yes—
406C22×D3C2×C22⋊C412yes—
407C22×D3C4×D414yes—
408C3×D4—44no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—22no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—22no—
420C2×C3×C4—41no—
421C2×C3×C4—42no—
422C2×C3×C4—41no—
423C2×C3×C4C2×C22⋊C412yes—
424C2×C3×C4C22×D412yes—
425C2×C3×C4C22×D411yescharacteristic
426C2×C3×C4C22×D411yescharacteristic
427C2×C3×C4C2×#4112yes—
428#67—44no—
429#67—44no—
430#67—44no—
431#67—44no—
432C2×Dic3—22no—
433C2×Dic3—28no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—22no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—22no—
441C2×Dic3C2×C22⋊C412yes—
442C2×Dic3C2×C22⋊C412yes—
443C2×Dic3C4×D414yes—
444D12—44no—
445D12—44no—
446C4×D3—28no—
447C4×D3—22no—
448C4×D3—24no—
449C4×D3—22no—
450C4×D3—28no—
451C4×D3—41no—
452C4×D3—42no—
453C4×D3—41no—
454C4×D3#12014yes—
455C4×D3#12118yes—
456C4×D3#12314yes—
457Dic6—44no—
458C3×C8—24no—
459C3×C8—42no—
460C3⋊C8—24no—
461C3⋊C8—42no—
462C24—31no—
463C24—31no—
464C24—34no—
465C24—31no—
466C24—64no—
467C24—62no—
468C24—62no—
469C24—122no—
470C24C2×C4×D311yescharacteristic
471C24C2×C4×D311yescharacteristic
472#41—124no—
473#41—124no—
474#41—128no—
475C2×Q8—62no—
476C2×Q8—64no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—62no—
481C2×D4—62no—
482C2×D4—64no—
483C2×D4—62no—
484C2×D4—64no—
485C2×D4—62no—
486C2×D4—62no—
487C2×D4—64no—
488C2×D4—62no—
489C2×D4—62no—
490C2×D4—62no—
491C2×D4—122no—
492C2×D4—122no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—31no—
500C22×C4—32no—
501C22×C4—32no—
502C22×C4—34no—
503C22×C4—34no—
504C22×C4—34no—
505C22×C4—31no—
506C22×C4—34no—
507C22×C4—34no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—31no—
511C22×C4—31no—
512C22×C4—31no—
513C22×C4—68no—
514C22×C4—64no—
515C22×C4—68no—
516C22×C4—616no—
517C22×C4—64no—
518C22×C4—64no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—62no—
525C22×C4C2×C4×D311yescharacteristic
526C22×C4C2×C4×D311yescharacteristic
527C22×C4C2×C4×D311yescharacteristic
528C22×C4C2×C4×D311yescharacteristic
529C22×C4D3×D412yes—
530C22×C4D3×D412yes—
531C22×C4C23×D311yescharacteristic
532M16—616no—
533M16—616no—
534C2×C8—28no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—34no—
541C2×C8—68no—
542C2×C8—62no—
543C2×C8—62no—
544C2×C8—62no—
545C2×C8—62no—
546C2×C8—62no—
547C2×C8—128no—
548C2×C8D3×D414yes—
549C4⋊C4—22no—
550C4⋊C4—62no—
551C4⋊C4—62no—
552C4⋊C4—62no—
553C4⋊C4—62no—
554C4⋊C4—62no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—62no—
558C22⋊C4—62no—
559C22⋊C4—62no—
560C22⋊C4—62no—
561C22⋊C4—62no—
562C22⋊C4—62no—
563C22⋊C4—62no—
564C22⋊C4—62no—
565C42—21no—
566C42—21no—
567C42—61no—
568C42—61no—
569C22×C3—22no—
570C22×C3—24no—
571C22×C3—24no—
572C22×C3—22no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—41no—
578C22×C3#40814yescomplemented
579C22×C3C22×C22⋊C411yescharacteristic
580C22×C3C2×C4×D412yes—
581C22×C3C2×#13111yescharacteristic
582C22×C3C2×#13111yescharacteristic
583C22×C3#56812yes—
584C2×D3—22no—
585C2×D3—22no—
586C2×D3—24no—
587C2×D3—24no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—416no—
592C2×D3—42no—
593C2×D3—42no—
594C2×D3—41no—
595C2×D3—41no—
596C2×D3—42no—
597C2×D3—42no—
598C2×D3—41no—
599C2×D3#38614yes—
600C3×C4—22no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4C2×#12011yescharacteristic
605C3×C4C2×#12112yes—
606C3×C4C2×#12311yescharacteristic
607Dic3—22no—
608Dic3—41no—
609Dic3—41no—
610Dic3—41no—
611Dic3#38614yes—
612C23—22no—
613C23—22no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—22no—
619C23—32no—
620C23—34no—
621C23—32no—
622C23—68no—
623C23—61no—
624C23—61no—
625C23—62no—
626C23—61no—
627C23—61no—
628C23—62no—
629C23—68no—
630C23—62no—
631C23—61no—
632C23—61no—
633C23—61no—
634C23—62no—
635C23—62no—
636C23—124no—
637C23—128no—
638C23—128no—
639C23D3×C22⋊C412yes—
640C23#90112yes—
641C23#90712yes—
642C23C22×C4×D311yescharacteristic
643Q8—124no—
644D4—44no—
645D4—124no—
646D4—124no—
647D4—124no—
648D4—124no—
649D4—124no—
650D4—124no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—32no—
663C2×C4—34no—
664C2×C4—34no—
665C2×C4—34no—
666C2×C4—38no—
667C2×C4—32no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—68no—
672C2×C4—68no—
673C2×C4—68no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—64no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—122no—
688C2×C4D3×C22⋊C412yes—
689C2×C4C2×D3×D411yescharacteristic
690C2×C4C2×D3×D412yes—
691C2×C4C2×D3×D411yescharacteristic
692C2×C4D3×#4112yes—
693C8—24no—
694C8—42no—
695C8—64no—
696C8—122no—
697C2×C3—24no—
698C2×C3—81no—
699C2×C3C2×#38611yescharacteristic
700C2×C3C2×#40811yescharacteristic
701C2×C3#287911yescharacteristic
702C2×C3#293312yes—
703C2×C3#293312yes—
704D3—24no—
705D3—42no—
706D3—81no—
707C22—24no—
708C22—22no—
709C22—22no—
710C22—24no—
711C22—34no—
712C22—41no—
713C22—42no—
714C22—41no—
715C22—41no—
716C22—42no—
717C22—62no—
718C22—64no—
719C22—62no—
720C22—64no—
721C22—62no—
722C22—62no—
723C22—62no—
724C22—1216no—
725C22—122no—
726C22—122no—
727C22—121no—
728C22—122no—
729C22—121no—
730C22—121no—
731C22—122no—
732C22#472714yescomplemented
733C22C2×D3×C22⋊C411yescharacteristic
734C22C4×D3×D412yes—
735C22C2×#90111yescharacteristic
736C22C2×#90711yescharacteristic
737C22#575012yes—
738C4—22no—
739C4—34no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—62no—
744C4—121no—
745C4—121no—
746C4—121no—
747C4D3×#12011yescharacteristic
748C4D3×#12112yes—
749C4D3×#12311yescharacteristic
750C3#2089711yescharacteristic, complemented, Sylow
751C2—24no—
752C2—64no—
753C2—81no—
754C2—122no—
755C2—241no—
756C2D3×#38611yescharacteristic
757C2C2×#472711yescharacteristic
758C2#7866211yescharacteristic
759C2#7942312yes—
760C2#7948112yes—
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1869C2
prime radicalC2×#5547C2
cosocleC22×C3×C4C24
hypercenter#1869D3
hypocenterC3#20897
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C23×ΓL(1,𝔽25)C2semidirect
3. C2×#4727C2semidirect
4. C2×D3×C22⋊C8C2semidirect
5. C3×#1869C2semidirect
6. #71975C2semidirect
7. #71610C2semidirect
8. #69958C2semidirect
9. #69952C2semidirect
10. #68669C2semidirect
11. #68661C2semidirect
38. C2×C3×C22⋊C8C22semidirect
40. C2×#830C22semidirect
42. C2×(C2×D3)⋊C8C22semidirect
43. C2×(C2×D3)⋊C8C22semidirect
46. C3×#336C22semidirect
47. #4550C22semidirect
48. #4550C22semidirect
49. #4524C22semidirect
59. #1869D3semidirect
126. C2×ΓL(1,𝔽25)D4semidirect
179. C2×C22⋊C8C2×D3semidirect
183. #336C2×D3semidirect
578. C22×C3#408semidirect
732. C22#4727semidirect
750. C3#20897semidirect

Maximal subgroups

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

subgroupindex
C23×ΓL(1,𝔽25)2
C2×#55472
C2×#47272
C2×D3×C22⋊C82
C3×#18692
#719752
#716102
#699582
#699522
#686692
#686612
#208973