Finite Group Databasebeta

← #11017349

Subgroups — #11017349

Order 768.

2078 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5689C211yesmaximal, characteristic, complemented
2C2×#5582C211yesmaximal, characteristic
3C3×#2565C211yesmaximal, characteristic, complemented
4#83040C211yesmaximal, characteristic, complemented
5#82478C211yesmaximal, characteristic, complemented
6#77969C214yesmaximal, complemented
7#77968C214yesmaximal, complemented
8#76643C211yesmaximal, characteristic, complemented
9#76634C211yesmaximal, characteristic, complemented
10#76606C211yesmaximal, characteristic, complemented
11#76519C211yesmaximal, characteristic, complemented
12#75388C214yesmaximal, complemented
13#75170C214yesmaximal, complemented
14#74356C211yesmaximal, characteristic, complemented
15#74328C211yesmaximal, characteristic
16#74196C211yesmaximal, characteristic, complemented
17#74166C211yesmaximal, characteristic
18#73800C211yesmaximal, characteristic, complemented
19#73620C211yesmaximal, characteristic, complemented
20#37303—31nomaximal, Sylow
21C2×C3×#125C2211yescharacteristic
22C2×C3×C4×Q8C2211yescharacteristic
23C2×#947C2211yescharacteristic
24C2×#946C2211yescharacteristic
25#5689—28no—
26#5582—28no—
27C2×#897C2212yes—
28C2×#897C2214yes—
29C2×#896C2212yes—
30C2×#896C2212yes—
31C2×#895C2211yescharacteristic
32C2×#894C2212yes—
33C2×#894C2214yes—
34C2×#892C2211yescharacteristic
35C2×D3×C4⋊C4C2211yescharacteristic
36C2×#890C2211yescharacteristic
37C2×#889C2212yes—
38C2×#888C2211yescharacteristic
39C2×#888C2211yescharacteristic
40C2×#888C2212yes—
41C2×#888C2214yes—
42C2×#876C2212yes—
43C2×#875C2212yes—
44C2×C4×D12C2211yescharacteristic
45C2×#872C2211yescharacteristic
46C2×#869C2211yescharacteristic
47C3×#398C2214yes—
48C3×#391C2211yescharacteristic
49C3×#391C2211yescharacteristic
50C3×#387C2214yes—
51C3×#384C2211yescharacteristic
52C3×#382C2211yescharacteristic
53C3×C4×C4⋊C4C2211yescharacteristic
54#5229C2211yescharacteristic
55#5229C2211yescharacteristic
56#4994C2214yes—
57#4993C2214yes—
58#4990C2212yes—
59#4989C2214yes—
60#4988C2211yescharacteristic
61#4988C2211yescharacteristic
62#4979C2214yes—
63#4978C2212yes—
64#4977C2211yescharacteristic
65#4975C2211yescharacteristic
66#4975C2211yescharacteristic
67#4975C2211yescharacteristic
68#4975C2214yes—
69#4939C2211yescharacteristic
70#4939C2211yescharacteristic
71C4×(C2×D3)⋊C4C2211yescharacteristic
72C4×(C2×D3)⋊C4C2211yescharacteristic
73#4935C2211yescharacteristic
74#4935C2211yescharacteristic
75C4×C4⋊Dic3C2211yescharacteristic
76#4932C2211yescharacteristic
77C42×Dic3C2211yescharacteristic
78#4928C2214yes—
79#4677C2214yes—
80#4675C2214yes—
81#4674C2214yes—
82#4673C2214yes—
83#4672C2214yes—
84#4670C2214yes—
85#4670C2212yes—
86#4669C2214yes—
87#4669C2214yes—
88#4668C2214yes—
89#4657C2214yes—
90#4657C2214yes—
91#4656C2214yes—
92#4655C2212yes—
93#4654C2214yes—
94C2×#544—31no—
95C2×#542—31no—
96#2868—31no—
97#2861—31no—
98#2721—34no—
99#2680—34no—
100#2677—34no—
101#2674—34no—
102#2660—31no—
103#2640—31no—
104#2567—31no—
105#2566—31no—
106#2565D311yescharacteristic, complemented
107#2542—31no—
108#2502—31no—
109#2501—31no—
110#2500—31no—
111#2499—31no—
112#2298—31no—
113C22×C3×Q8C2311yescharacteristic
114C22×D12C2311yescharacteristic
115C22×D12C2312yes—
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2312yes—
118C22×C4×D3C2312yes—
119C22×Dic6C2312yes—
120C22×Dic6C2312yes—
121C22×Dic6C2312yes—
122C3×#125—24no—
123C3×C4×Q8—24no—
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2314yes—
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C4⋊C4C2312yes—
132C2×C3×C42C2312yes—
133C2×C3×C42C2311yescharacteristic
134C2×C3×C42C2311yescharacteristic
135C2×C3×C42C2311yescharacteristic
136#947—24no—
137#946—24no—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2312yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2311yescharacteristic
151C2×(C2×D3)⋊C4C2311yescharacteristic
152C2×C4⋊Dic3C2314yes—
153C2×C4⋊Dic3C2312yes—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2314yes—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2312yes—
164C2×Dic3⋊C4C2312yes—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2311yescharacteristic
169C2×Dic3⋊C4C2311yescharacteristic
170C2×C4×Dic3C2312yes—
171C2×C4×Dic3C2312yes—
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2311yescharacteristic
174C2×C4×Dic3C2311yescharacteristic
175C2×C4×Dic3C2311yescharacteristic
176#897—28no—
177#897—48no—
178#896—28no—
179#896—28no—
180#895—24no—
181#894—28no—
182#894—48no—
183#892—24no—
184D3×C4⋊C4—24no—
185#890—24no—
186#889—28no—
187#888—28no—
188#888—24no—
189#888—24no—
190#888—48no—
191#876—28no—
192#875—28no—
193C4×D12—24no—
194#872D418yes—
195#869—24no—
196C3×#95C2314yes—
197C3×#95C2312yes—
198C3×#95C2314yes—
199C3×#95C2314yes—
200C3⋊#95C2312yes—
201C3⋊#95C2314yes—
202C3⋊#95C2314yes—
203C3⋊#95C2312yes—
204C3⋊#95C2312yes—
205C3⋊#95C2312yes—
206C3⋊#95C2314yes—
207C3⋊#95C2312yes—
208#544—68no—
209#542—68no—
210C2×C4⋊Q8—31no—
211C2×C4⋊Q8—31no—
212C2×C4⋊Q8—32no—
213C2×C4⋊Q8—34no—
214C2×C4⋊Q8—31no—
215C2×#126—32no—
216C2×#125—31no—
217C2×#125—32no—
218C2×#125C2×D311yescharacteristic
219C2×#124—31no—
220C2×#124—32no—
221C2×#123—32no—
222C2×#123—34no—
223C2×C22⋊Q8—31no—
224C2×C22⋊Q8—32no—
225C2×C22⋊Q8—32no—
226C2×C22⋊Q8—32no—
227C2×C22⋊Q8—34no—
228C2×#121—31no—
229C2×C4×Q8C2×D311yescharacteristic
230C2×C4×D4—31no—
231C2×#117—31no—
232C2×#117—31no—
233C22×C4⋊C4—31no—
234#399—34no—
235#399—34no—
236#398—34no—
237#398—34no—
238#398C2×D314yes—
239#397—34no—
240#397—34no—
241#396—34no—
242#395—34no—
243#395—34no—
244#394—34no—
245#393—34no—
246#391—31no—
247#391—31no—
248#391C2×D311yescharacteristic
249#391C2×D311yescharacteristic
250#390—31no—
251#390—31no—
252#390—31no—
253#390—31no—
254#389—34no—
255#388—32no—
256#388—34no—
257#388—34no—
258#388—34no—
259#388—32no—
260#387—32no—
261#387—34no—
262#387—32no—
263#387C2×D314yes—
264#385—34no—
265#385—34no—
266#384—31no—
267#384—31no—
268#384—31no—
269#384—34no—
270#384—31no—
271#384—31no—
272#384C2×D311yescharacteristic
273#382—31no—
274#382C2×D311yescharacteristic
275C4×C4⋊C4—31no—
276C4×C4⋊C4C2×D311yescharacteristic
277C4×C22⋊C4—31no—
278C4×C22⋊C4—31no—
279#376—31no—
280C43—31no—
281C23×D3C2412yes—
282C23×D3C2411yescharacteristic
283C2×C3×Q8—22no—
284C2×C3×Q8—22no—
285C2×C3×Q8—22no—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C22×C3×C4C2412yes—
291C22×C3×C4C2411yescharacteristic
292C22×C3×C4C2411yescharacteristic
293C22×C3×C4C2412yes—
294C22×C3×C4C2411yescharacteristic
295C22×Dic3C2412yes—
296C22×Dic3C2412yes—
297C22×Dic3C2412yes—
298C22×Dic3C2412yes—
299C22×Dic3C2411yescharacteristic
300C22×Dic3C2411yescharacteristic
301C22×Dic3C2411yescharacteristic
302C22×Dic3C2412yes—
303C2×D12—22no—
304C2×D12—22no—
305C2×D12—22no—
306C2×D12—24no—
307C2×D12—44no—
308C2×C4×D3—22no—
309C2×C4×D3—22no—
310C2×C4×D3—24no—
311C2×C4×D3—24no—
312C2×C4×D3—44no—
313C2×C4×D3—44no—
314C2×C4×D3C2×D414yes—
315C2×Dic6—24no—
316C2×Dic6—24no—
317C2×Dic6—24no—
318C2×Dic6—44no—
319C2×Dic6—44no—
320C2×Dic6—44no—
321C3×C4⋊C4—22no—
322C3×C4⋊C4—22no—
323C3×C4⋊C4—24no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4—22no—
326C3×C4⋊C4—24no—
327C3×C4⋊C4—28no—
328C3×C4⋊C4—24no—
329C3×C42—24no—
330C3×C42—22no—
331C3×C42—22no—
332C3×C42C2×D414yes—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—28no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—24no—
342(C2×D3)⋊C4—28no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345(C2×D3)⋊C4C2×D414yes—
346(C2×D3)⋊C4C2×D414yes—
347C4⋊Dic3—22no—
348C4⋊Dic3—24no—
349C4⋊Dic3—22no—
350C4⋊Dic3—22no—
351C4⋊Dic3—28no—
352C4⋊Dic3—24no—
353C4⋊Dic3—24no—
354C4⋊Dic3—44no—
355Dic3⋊C4—24no—
356Dic3⋊C4—24no—
357Dic3⋊C4—24no—
358Dic3⋊C4—24no—
359Dic3⋊C4—24no—
360Dic3⋊C4—44no—
361Dic3⋊C4—44no—
362Dic3⋊C4—44no—
363Dic3⋊C4C2×D414yes—
364Dic3⋊C4C2×D414yes—
365C4×Dic3—24no—
366C4×Dic3—22no—
367C4×Dic3—22no—
368C4×Dic3—24no—
369C4×Dic3—24no—
370C4×Dic3C2×D414yes—
371C22×Q8—32no—
372C22×Q8—32no—
373C22×Q8—32no—
374C22×Q8C22×D311yescharacteristic
375C22×D4—31no—
376C22×D4—32no—
377C23×C4—31no—
378C23×C4—32no—
379C23×C4—32no—
380C4⋊Q8—64no—
381C4⋊Q8—64no—
382C4⋊Q8—68no—
383C4⋊Q8—64no—
384C4⋊Q8—128no—
385#126—68no—
386#125—24no—
387#125—64no—
388#125—68no—
389#124—68no—
390#124—64no—
391#123—68no—
392#123—128no—
393C22⋊Q8—68no—
394C22⋊Q8—68no—
395C22⋊Q8—68no—
396C22⋊Q8—64no—
397C22⋊Q8—128no—
398#121—64no—
399C4×Q8—24no—
400C4×D4—64no—
401#117—38no—
402#117—64no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—32no—
410C2×C4⋊C4—32no—
411C2×C4⋊C4—32no—
412C2×C4⋊C4—32no—
413C2×C4⋊C4—32no—
414C2×C4⋊C4—34no—
415C2×C4⋊C4—32no—
416C2×C4⋊C4—32no—
417C2×C4⋊C4—34no—
418C2×C4⋊C4—34no—
419C2×C4⋊C4—34no—
420C2×C4⋊C4—34no—
421C2×C4⋊C4—64no—
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C4⋊C4C22×D311yescharacteristic
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C4⋊C4C22×D312yes—
426C2×C4⋊C4C22×D312yes—
427C2×C4⋊C4C22×D312yes—
428C2×C4⋊C4C22×D312yes—
429C2×C4⋊C4C22×D314yes—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—32no—
433C2×C22⋊C4—32no—
434C2×C22⋊C4—32no—
435C2×C22⋊C4—32no—
436C2×C22⋊C4—34no—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—32no—
440C2×C22⋊C4—32no—
441C2×C22⋊C4—34no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4—34no—
444C2×C42—31no—
445C2×C42—32no—
446C2×C42—32no—
447C2×C42—31no—
448C2×C42—32no—
449C2×C42—31no—
450C2×C42C22×D312yes—
451C2×C42C22×D311yescharacteristic
452C2×C42C22×D311yescharacteristic
453C2×C42C22×D311yescharacteristic
454#95—32no—
455#95—32no—
456#95—32no—
457#95—32no—
458#95—32no—
459#95—34no—
460#95—34no—
461#95—34no—
462#95C22×D312yes—
463#95C22×D314yes—
464#95C22×D314yes—
465#95C22×D314yes—
466C23×C3C2511yescharacteristic
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—22no—
472C22×D3—24no—
473C22×D3—24no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3C22×D412yes—
477C3×Q8—44no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—24no—
487C2×C3×C4—24no—
488C2×C3×C4—22no—
489C2×C3×C4—24no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4C22×D412yes—
495C2×C3×C4C22×D412yes—
496C2×C3×C4C22×D412yes—
497C2×C3×C4H(5,𝔽2)14yes—
498C2×C3×C42−1+412yes—
499C2×C3×C42−1+412yes—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—24no—
511C2×Dic3—24no—
512C2×Dic3—24no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3C22×D412yes—
516C2×Dic3C22×D412yes—
517C2×Dic3C22×D412yes—
518C2×Dic32−1+414yes—
519D12—44no—
520D12—84no—
521C4×D3—28no—
522C4×D3—84no—
523C4×D3—84no—
524Dic6—84no—
525Dic6—84no—
526Dic6—84no—
527C24—31no—
528C24—32no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—64no—
533C2×Q8—64no—
534C2×Q8—64no—
535C2×Q8—124no—
536C2×Q8—124no—
537C2×Q8—124no—
538C2×D4—64no—
539C2×D4—62no—
540C2×D4—62no—
541C2×D4—62no—
542C2×D4—124no—
543C22×C4—32no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—34no—
548C22×C4—32no—
549C22×C4—32no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—64no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—64no—
556C22×C4—124no—
557C22×C4—124no—
558C22×C4C23×D312yes—
559C22×C4C23×D312yes—
560C22×C4C23×D312yes—
561C22×C4C23×D312yes—
562C22×C4C23×D312yes—
563C22×C4C23×D311yescharacteristic
564C22×C4C23×D311yescharacteristic
565C22×C4C23×D312yes—
566C22×C4C23×D311yescharacteristic
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—28no—
575C4⋊C4—34no—
576C4⋊C4—34no—
577C4⋊C4—64no—
578C4⋊C4—64no—
579C4⋊C4—64no—
580C4⋊C4—64no—
581C4⋊C4—64no—
582C4⋊C4—64no—
583C4⋊C4—64no—
584C4⋊C4—62no—
585C4⋊C4—62no—
586C4⋊C4—62no—
587C4⋊C4—64no—
588C4⋊C4—68no—
589C4⋊C4—124no—
590C4⋊C4—124no—
591C4⋊C4—124no—
592C4⋊C4—124no—
593C22⋊C4—34no—
594C22⋊C4—34no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—68no—
600C22⋊C4—64no—
601C22⋊C4—64no—
602C22⋊C4—64no—
603C22⋊C4—68no—
604C22⋊C4—64no—
605C22⋊C4—124no—
606C22⋊C4—124no—
607C42—24no—
608C42—22no—
609C42—22no—
610C42—34no—
611C42—64no—
612C42—64no—
613C42—62no—
614C42—62no—
615C42—64no—
616C42D3×D414yes—
617C22×C3C23×D411yescharacteristic
618C22×C3C2×H(5,𝔽2)12yes—
619C22×C3C2×2−1+411yescharacteristic
620C22×C3C2×2−1+411yescharacteristic
621C22×C3C2×2−1+412yes—
622C2×D3—22no—
623C2×D3—22no—
624C2×D3—22no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3—42no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—44no—
631C2×D3—44no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—24no—
635C3×C4—42no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4#53614yes—
641Dic3—22no—
642Dic3—22no—
643Dic3—22no—
644Dic3—24no—
645Dic3—42no—
646Dic3—42no—
647Dic3—42no—
648Dic3—42no—
649C23—32no—
650C23—61no—
651C23—62no—
652C23—61no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—64no—
657C23—62no—
658C23—64no—
659C23C24×D311yescharacteristic
660Q8—44no—
661Q8—244no—
662Q8—244no—
663Q8—244no—
664D4—124no—
665D4—244no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—32no—
683C2×C4—32no—
684C2×C4—32no—
685C2×C4—34no—
686C2×C4—62no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—61no—
691C2×C4—62no—
692C2×C4—68no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—64no—
699C2×C4—64no—
700C2×C4—64no—
701C2×C4—62no—
702C2×C4—244no—
703C2×C4—244no—
704C2×C4C2×D3×D412yes—
705C2×C4C2×D3×D412yes—
706C2×C4C2×D3×D412yes—
707C2×C4#100712yes—
708C2×C4#100914yes—
709C2×C4#101012yes—
710C2×C3C2×#53611yescharacteristic
711C2×C3#349811yescharacteristic
712C2×C3#349911yescharacteristic
713C2×C3#354412yes—
714C2×C3#355212yes—
715D3—42no—
716D3—82no—
717C22—62no—
718C22—62no—
719C22—62no—
720C22—122no—
721C22—122no—
722C22—124no—
723C22—122no—
724C22—122no—
725C22—122no—
726C22—124no—
727C22C22×D3×D411yescharacteristic
728C22C2×#100711yescharacteristic
729C22C2×#100912yes—
730C22C2×#101011yescharacteristic
731C22D3×2−1+412yes—
732C4—24no—
733C4—22no—
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—62no—
741C4—62no—
742C4—62no—
743C4—64no—
744C4—122no—
745C4—122no—
746C4—122no—
747C4—122no—
748C4#562814yes—
749C3#3730311yescharacteristic, complemented, Sylow
750C2—122no—
751C2—242no—
752C2C2×#562811yescharacteristic
753C2#8624211yescharacteristic
754C2#8634011yescharacteristic
755C2#8684712yes—
756C2#8703412yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2565C2
prime radicalC2×#895C22
hypercenter#2565D3
hypocenterC3#37303
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2565

Complements

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

NH ≅ G/Ntype
1. C2×#5689C2semidirect
3. C3×#2565C2semidirect
4. #83040C2semidirect
5. #82478C2semidirect
6. #77969C2semidirect
7. #77968C2semidirect
8. #76643C2semidirect
9. #76634C2semidirect
10. #76606C2semidirect
11. #76519C2semidirect
12. #75388C2semidirect
13. #75170C2semidirect
14. #74356C2semidirect
16. #74196C2semidirect
18. #73800C2semidirect
19. #73620C2semidirect
106. #2565D3semidirect
749. C3#37303semidirect

Maximal subgroups

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

subgroupindex
C2×#56892
C2×#55822
C3×#25652
#830402
#824782
#779692
#779682
#766432
#766342
#766062
#765192
#753882
#751702
#743562
#743282
#741962
#741662
#738002
#736202
#373033