Finite Group Databasebeta

← #11652965

Subgroups — #11652965

Order 768.

3292 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5631C212yesmaximal, complemented
2C2×#5577C211yesmaximal, characteristic, complemented
3C2×#5553C211yesmaximal, characteristic, complemented
4C3×#2538C211yesmaximal, characteristic, complemented
5#82812C212yesmaximal, complemented
6C4×#944C211yesmaximal, characteristic, complemented
7C4×#940C211yesmaximal, characteristic, complemented
8#77432C214yesmaximal, complemented
9#77284C214yesmaximal, complemented
10#76348C212yesmaximal, complemented
11#76316C212yesmaximal, complemented
12#76202C212yesmaximal, complemented
13#76004C212yesmaximal, complemented
14#74369C211yesmaximal, characteristic, complemented
15#74319C211yesmaximal, characteristic, complemented
16#74015C212yesmaximal, complemented
17#73935C212yesmaximal, complemented
18#59815—31nomaximal, Sylow
19C22×#239C2212yes—
20C22×#235C2212yes—
21C2×C3×C22⋊Q8C2212yes—
22C2×C3×C4×Q8C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C2×#944C2211yescharacteristic
25C2×#940C2212yes—
26C2×#940C2211yescharacteristic
27C2×#930C2212yes—
28C2×C4×#67C2212yes—
29C2×C4×#67C2212yes—
30#5631—216no—
31#5577—28no—
32#5553—28no—
33C2×#897C2212yes—
34C2×#895C2212yes—
35C2×#895C2214yes—
36C2×#894C2214yes—
37C2×#893C2212yes—
38C2×#893C2212yes—
39C2×#893C2212yes—
40C2×#893C2212yes—
41C2×D3×C4⋊C4C2214yes—
42C2×#884C2214yes—
43C2×#884C2214yes—
44C2×#884C2214yes—
45C2×#883C2214yes—
46C2×#874C2212yes—
47C2×#874C2211yescharacteristic
48C2×C4×D12C2212yes—
49C2×C4×D12C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#396C2214yes—
52C3×#390C2212yes—
53C3×#389C2212yes—
54C3×#384C2211yescharacteristic
55C3×#380C2212yes—
56#5229C2211yescharacteristic
57#5221C2211yescharacteristic
58#4994C2214yes—
59#4991C2214yes—
60#4989C2214yes—
61#4988C2212yes—
62#4988C2212yes—
63#4988C2212yes—
64#4988C2212yes—
65#4988C2211yescharacteristic
66#4987C2212yes—
67#4984C2212yes—
68#4976C2212yes—
69#4976C2212yes—
70#4975C2211yescharacteristic
71#4975C2211yescharacteristic
72#4973C2211yescharacteristic
73#4961C2214yes—
74#4960C2214yes—
75#4960C2214yes—
76#4959C2214yes—
77#4957C2212yes—
78#4957C2212yes—
79#4956C2214yes—
80C4×Dic3⋊C4C2212yes—
81C4×Dic3⋊C4C2212yes—
82C42×Dic3C2211yescharacteristic
83#4672C2214yes—
84#4668C2214yes—
85#4667C2214yes—
86#4665C2214yes—
87C2×#550—31no—
88C2×#550—31no—
89C2×#547—32no—
90#2682—34no—
91#2541—32no—
92#2538—31no—
93#2538D311yescharacteristic, complemented
94#2537—32no—
95#2445—32no—
96#2445—32no—
97#2416—34no—
98#2407—32no—
99#2407—32no—
100D4×C4⋊C4—32no—
101C4×C4⋊Q8—31no—
102C4×#127—31no—
103C4×#127—31no—
104C22×C3×Q8C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4C2312yes—
107C22×#67C2312yes—
108C22×#67C2314yes—
109C22×#67C2314yes—
110C22×#67C2312yes—
111C2×#239—28no—
112C2×#239—28no—
113C2×#239—44no—
114C2×#235—28no—
115C2×#235—28no—
116C2×#235—44no—
117C22×D12C2311yescharacteristic
118C22×D12C2314yes—
119C22×D12C2312yes—
120C22×D12C2312yes—
121C22×D12C2314yes—
122C22×D12C2312yes—
123C22×C4×D3C2314yes—
124C22×C4×D3C2312yes—
125C22×C4×D3C2314yes—
126C22×C4×D3C2314yes—
127C22×Dic6C2311yescharacteristic
128C3×C22⋊Q8—28no—
129C3×C4×Q8—24no—
130C3×C4×D4—24no—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2312yes—
134C2×C3×C4⋊C4C2312yes—
135C2×C3×C4⋊C4C2312yes—
136C2×C3×C4⋊C4C2314yes—
137C2×C3×C4⋊C4C2312yes—
138C2×C3×C22⋊C4C2314yes—
139C2×C3×C22⋊C4C2312yes—
140C2×C3×C22⋊C4C2314yes—
141C2×C3×C42C2312yes—
142C2×C3×C42C2311yescharacteristic
143C2×#217C2312yes—
144C2×#217C2312yes—
145#944D418yescomplemented
146#940—28no—
147#940—24no—
148#930—28no—
149C4×#67—28no—
150C4×#67—44no—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2312yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2312yes—
158C2×(C2×D3)⋊C4C2312yes—
159C2×(C2×D3)⋊C4C2314yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×C4⋊Dic3C2314yes—
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2311yescharacteristic
164C2×Dic3⋊C4C2312yes—
165C2×Dic3⋊C4C2312yes—
166C2×Dic3⋊C4C2312yes—
167C2×Dic3⋊C4C2312yes—
168C2×Dic3⋊C4C2312yes—
169C2×Dic3⋊C4C2312yes—
170C2×Dic3⋊C4C2312yes—
171C2×C4×Dic3C2311yescharacteristic
172C2×C4×Dic3C2311yescharacteristic
173C2×C4×Dic3C2311yescharacteristic
174C2×C4×Dic3C2312yes—
175C2×C4×Dic3C2311yescharacteristic
176C2×C4×Dic3C2311yescharacteristic
177C2×C4×Dic3C2311yescharacteristic
178#897—28no—
179#895—28no—
180#895—216no—
181#894—216no—
182#893—28no—
183#893—28no—
184#893—28no—
185#893—44no—
186D3×C4⋊C4—216no—
187#884—216no—
188#884—216no—
189#884—48no—
190#883—216no—
191#874—28no—
192#874D418yescomplemented
193C4×D12—28no—
194C4×D12—24no—
195C4×Dic6—24no—
196C3×#95C2314yes—
197C3⋊#95C2312yes—
198C3⋊#95C2314yes—
199C3⋊#95C2312yes—
200C3⋊#95C2312yes—
201C3⋊#95C2312yes—
202C22×#41—32no—
203C22×#41—32no—
204#550—68no—
205#550—68no—
206#547—616no—
207C2×C4⋊Q8—31no—
208C2×#127—31no—
209C2×#127—32no—
210C2×#127—31no—
211C2×#127—32no—
212C2×#123—34no—
213C2×#123—34no—
214C2×C22⋊Q8—32no—
215C2×C22⋊Q8C2×D312yes—
216C2×#121—32no—
217C2×#121—32no—
218C2×#121—34no—
219C2×#121—34no—
220C2×#121—34no—
221C2×#121—34no—
222C2×C4×Q8—31no—
223C2×C4×Q8C2×D311yescharacteristic
224C2×C4×D4—32no—
225C2×C4×D4—32no—
226C2×C4×D4—32no—
227C2×C4×D4—32no—
228C2×C4×D4—32no—
229C2×C4×D4—32no—
230C2×C4×D4—31no—
231C2×C4×D4—32no—
232C2×C4×D4C2×D311yescharacteristic
233C22×C4⋊C4—34no—
234#396—34no—
235#396C2×D314yes—
236#394—34no—
237#394—34no—
238#394—34no—
239#394—34no—
240#392—34no—
241#392—34no—
242#391—31no—
243#391—31no—
244#390—31no—
245#390—32no—
246#390—32no—
247#390—31no—
248#390—32no—
249#390—32no—
250#390—32no—
251#390—32no—
252#390C2×D312yes—
253#389—32no—
254#389—32no—
255#389—32no—
256#389C2×D312yes—
257#386—34no—
258#386—34no—
259#385—34no—
260#385—34no—
261#384—31no—
262#384—31no—
263#384C2×D311yescharacteristic
264#380—32no—
265#380—34no—
266#380C2×D312yes—
267C4×C4⋊C4—32no—
268C4×C4⋊C4—32no—
269C43—31no—
270C24×C3C2412yes—
271C23×D3C2412yes—
272C23×D3C2414yes—
273C2×C3×Q8—22no—
274C2×C3×Q8—22no—
275C2×C3×Q8C2×D414yes—
276C2×C3×D4—22no—
277C2×C3×D4—22no—
278C2×C3×D4—22no—
279C22×C3×C4—24no—
280C22×C3×C4—24no—
281C22×C3×C4—24no—
282C22×C3×C4C2412yes—
283C22×C3×C4C2414yes—
284C22×C3×C4C2412yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2411yescharacteristic
287C22×C3×C4C2411yescharacteristic
288C22×C3×C4C2411yescharacteristic
289C2×#67—28no—
290C2×#67—28no—
291C2×#67—28no—
292C2×#67—24no—
293C2×#67—24no—
294C2×#67—24no—
295C2×#67—24no—
296C2×#67—42no—
297C2×#67—44no—
298C2×#67—42no—
299C2×#67—44no—
300C2×#67—44no—
301C22×Dic3C2411yescharacteristic
302C22×Dic3C2412yes—
303C22×Dic3C2412yes—
304C22×Dic3C2412yes—
305C22×Dic3C2411yescharacteristic
306C22×Dic3C2411yescharacteristic
307C22×Dic3C2411yescharacteristic
308#239—432no—
309#235—432no—
310C2×D12—24no—
311C2×D12—24no—
312C2×D12—24no—
313C2×D12—24no—
314C2×D12—28no—
315C2×D12—22no—
316C2×D12—28no—
317C2×D12—22no—
318C2×D12—22no—
319C2×D12—28no—
320C2×D12—42no—
321C2×D12—42no—
322C2×D12—44no—
323C2×D12—44no—
324C2×D12—44no—
325C2×D12C2×D418yes—
326C2×D12C2×D418yes—
327C2×D12C2×D418yes—
328C2×C4×D3—28no—
329C2×C4×D3—28no—
330C2×C4×D3—24no—
331C2×C4×D3—28no—
332C2×C4×D3—24no—
333C2×C4×D3—24no—
334C2×C4×D3—28no—
335C2×C4×D3—28no—
336C2×C4×D3—28no—
337C2×C4×D3—28no—
338C2×C4×D3—44no—
339C2×C4×D3—44no—
340C2×Dic6—22no—
341C2×Dic6—22no—
342C2×Dic6C2×D414yes—
343C3×C4⋊C4—28no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—24no—
346C3×C4⋊C4—24no—
347C3×C4⋊C4—22no—
348C3×C4⋊C4—24no—
349C3×C4⋊C4—42no—
350C3×C22⋊C4—28no—
351C3×C22⋊C4—24no—
352C3×C22⋊C4—44no—
353C3×C42—24no—
354C3×C42C2×D414yes—
355#217—24no—
356#217—42no—
357(C2×D3)⋊C4—28no—
358(C2×D3)⋊C4—28no—
359(C2×D3)⋊C4—24no—
360(C2×D3)⋊C4—28no—
361(C2×D3)⋊C4—28no—
362(C2×D3)⋊C4—24no—
363(C2×D3)⋊C4—28no—
364(C2×D3)⋊C4—44no—
365(C2×D3)⋊C4—44no—
366(C2×D3)⋊C4—42no—
367C4⋊Dic3—22no—
368C4⋊Dic3—22no—
369C4⋊Dic3—28no—
370Dic3⋊C4—24no—
371Dic3⋊C4—24no—
372Dic3⋊C4—24no—
373Dic3⋊C4—42no—
374Dic3⋊C4—42no—
375Dic3⋊C4C2×D418yes—
376Dic3⋊C4C2×D418yes—
377C4×Dic3—24no—
378C4×Dic3—22no—
379C4×Dic3—22no—
380C4×Dic3—22no—
381C4×Dic3—41no—
382C4×Dic3C2×D414yes—
383C4×Dic3#4114yescomplemented
384C2×#41—68no—
385C2×#41—68no—
386C2×#41—68no—
387C2×#41—68no—
388C2×#41—124no—
389C2×#41—124no—
390C22×Q8—31no—
391C22×Q8C22×D311yescharacteristic
392C22×D4—32no—
393C22×D4—34no—
394C22×D4—32no—
395C22×D4—34no—
396C22×D4—32no—
397C22×D4—32no—
398C22×D4—32no—
399C22×D4—31no—
400C22×D4—34no—
401C22×D4—34no—
402C22×D4C22×D311yescharacteristic
403C23×C4—34no—
404C23×C4—32no—
405C23×C4—34no—
406C23×C4—34no—
407C23×C4C22×D312yes—
408C4⋊Q8—38no—
409#127—38no—
410#127—68no—
411#127—64no—
412#127—68no—
413#123—616no—
414#123—616no—
415C22⋊Q8—28no—
416C22⋊Q8—68no—
417#121—616no—
418#121—616no—
419#121—68no—
420#121—616no—
421#121—68no—
422#121—128no—
423C4×Q8—24no—
424C4×Q8—64no—
425C4×D4—24no—
426C4×D4—68no—
427C4×D4—68no—
428C4×D4—68no—
429C4×D4—68no—
430C4×D4—68no—
431C4×D4—64no—
432C4×D4—124no—
433C4×D4—124no—
434C2×C4⋊C4—32no—
435C2×C4⋊C4—32no—
436C2×C4⋊C4—32no—
437C2×C4⋊C4—34no—
438C2×C4⋊C4—31no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—32no—
441C2×C4⋊C4—32no—
442C2×C4⋊C4—32no—
443C2×C4⋊C4—32no—
444C2×C4⋊C4—616no—
445C2×C4⋊C4C22×D314yes—
446C2×C4⋊C4C22×D311yescharacteristic
447C2×C4⋊C4C22×D312yes—
448C2×C4⋊C4C22×D312yes—
449C2×C4⋊C4C22×D311yescharacteristic
450C2×C4⋊C4C22×D312yes—
451C2×C4⋊C4C22×D312yes—
452C2×C22⋊C4—32no—
453C2×C22⋊C4—34no—
454C2×C22⋊C4—34no—
455C2×C22⋊C4—32no—
456C2×C22⋊C4—34no—
457C2×C22⋊C4—32no—
458C2×C22⋊C4—34no—
459C2×C22⋊C4—34no—
460C2×C22⋊C4—32no—
461C2×C22⋊C4—34no—
462C2×C22⋊C4—32no—
463C2×C22⋊C4—34no—
464C2×C22⋊C4C22×D312yes—
465C2×C22⋊C4C22×D314yes—
466C2×C22⋊C4C22×D314yes—
467C2×C42—31no—
468C2×C42—31no—
469C2×C42—31no—
470C2×C42—31no—
471C2×C42—32no—
472C2×C42—31no—
473C2×C42—31no—
474C2×C42C22×D312yes—
475C2×C42C22×D311yescharacteristic
476#95—32no—
477#95—32no—
478#95—32no—
479#95—32no—
480#95—34no—
481#95C22×D314yes—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3C2511yescharacteristic
490C22×D3—24no—
491C22×D3—24no—
492C22×D3—24no—
493C22×D3—24no—
494C22×D3—24no—
495C22×D3—24no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3C22×D418yes—
504C3×Q8—28no—
505C3×D4—44no—
506C2×C3×C4—22no—
507C2×C3×C4—21no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—24no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—24no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—24no—
518C2×C3×C4—22no—
519C2×C3×C4—48no—
520C2×C3×C4C22×D412yes—
521C2×C3×C4C22×D414yes—
522C2×C3×C4C22×D412yes—
523C2×C3×C4C22×D412yes—
524C2×C3×C4C22×D412yes—
525C2×C3×C4C2×#4112yes—
526C2×C3×C4H(5,𝔽2)12yes—
527C2×C3×C42−1+412yes—
528#67—416no—
529#67—48no—
530#67—48no—
531#67—88no—
532C2×Dic3—22no—
533C2×Dic3—21no—
534C2×Dic3—22no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—21no—
546C2×Dic3—22no—
547C2×Dic3C22×D412yes—
548C2×Dic3C22×D414yes—
549C2×Dic3C22×D412yes—
550C2×Dic3C2×#4112yes—
551C2×Dic3C2×#4112yes—
552C2×Dic3H(5,𝔽2)12yes—
553D12—216no—
554D12—216no—
555D12—48no—
556D12—416no—
557D12—44no—
558D12—88no—
559C4×D3—416no—
560C4×D3—416no—
561C4×D3—48no—
562C4×D3—416no—
563Dic6—28no—
564C24—34no—
565C24—32no—
566C24C23×D312yes—
567#41—1232no—
568#41—1232no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—34no—
572C2×Q8—62no—
573C2×Q8—62no—
574C2×Q8D3×D414yes—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—38no—
579C2×D4—38no—
580C2×D4—38no—
581C2×D4—68no—
582C2×D4—68no—
583C2×D4—64no—
584C2×D4—68no—
585C2×D4—64no—
586C2×D4—64no—
587C2×D4—64no—
588C2×D4—68no—
589C2×D4—68no—
590C2×D4—64no—
591C2×D4—62no—
592C2×D4—68no—
593C2×D4—64no—
594C2×D4—62no—
595C2×D4—64no—
596C2×D4—62no—
597C2×D4—64no—
598C2×D4—122no—
599C2×D4—124no—
600C2×D4—122no—
601C2×D4—124no—
602C2×D4—124no—
603C2×D4—122no—
604C2×D4—124no—
605C2×D4—122no—
606C2×D4—124no—
607C2×D4—124no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—32no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—32no—
617C22×C4—32no—
618C22×C4—68no—
619C22×C4—68no—
620C22×C4—68no—
621C22×C4—68no—
622C22×C4—68no—
623C22×C4—68no—
624C22×C4—68no—
625C22×C4—64no—
626C22×C4—64no—
627C22×C4—64no—
628C22×C4—124no—
629C22×C4—124no—
630C22×C4C23×D312yes—
631C22×C4C23×D314yes—
632C22×C4C23×D312yes—
633C22×C4C23×D312yes—
634C22×C4C23×D311yescharacteristic
635C22×C4C23×D311yescharacteristic
636C22×C4C23×D311yescharacteristic
637C4⋊C4—28no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—24no—
643C4⋊C4—38no—
644C4⋊C4—38no—
645C4⋊C4—42no—
646C4⋊C4—64no—
647C4⋊C4—68no—
648C4⋊C4—64no—
649C4⋊C4—62no—
650C4⋊C4—64no—
651C4⋊C4—62no—
652C4⋊C4—122no—
653C4⋊C4—122no—
654C22⋊C4—24no—
655C22⋊C4—28no—
656C22⋊C4—44no—
657C22⋊C4—68no—
658C22⋊C4—64no—
659C22⋊C4—68no—
660C22⋊C4—68no—
661C22⋊C4—68no—
662C22⋊C4—68no—
663C22⋊C4—64no—
664C22⋊C4—64no—
665C22⋊C4—122no—
666C22⋊C4—124no—
667C22⋊C4—124no—
668C22⋊C4—122no—
669C42—24no—
670C42—34no—
671C42—34no—
672C42—62no—
673C42—64no—
674C42—62no—
675C42—62no—
676C42—121no—
677C42D3×D414yes—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3C23×D411yescharacteristic
686C22×C3C23×D411yescharacteristic
687C22×C3C22×#4111yescharacteristic
688C22×C3C2×H(5,𝔽2)11yescharacteristic
689C22×C3C2×H(5,𝔽2)11yescharacteristic
690C22×C3C2×2−1+411yescharacteristic
691C22×C3#58511yescharacteristic
692C2×D3—28no—
693C2×D3—28no—
694C2×D3—28no—
695C2×D3—44no—
696C2×D3—44no—
697C2×D3—44no—
698C2×D3—44no—
699C2×D3—42no—
700C2×D3—42no—
701C2×D3—42no—
702C2×D3—42no—
703C2×D3—42no—
704C2×D3—42no—
705C2×D3—42no—
706C3×C4—24no—
707C3×C4—22no—
708C3×C4—42no—
709C3×C4—44no—
710C3×C4—42no—
711C3×C4D4214yes—
712C3×C4#54714yescomplemented
713Dic3—24no—
714Dic3—22no—
715Dic3—22no—
716Dic3—42no—
717Dic3—42no—
718Dic3—41no—
719Dic3#55014yescomplemented
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—38no—
728C23—64no—
729C23—64no—
730C23—64no—
731C23—64no—
732C23—64no—
733C23—64no—
734C23—62no—
735C23—62no—
736C23—62no—
737C23—62no—
738C23—62no—
739C23—62no—
740C23—62no—
741C23C24×D311yescharacteristic
742Q8—28no—
743Q8—68no—
744D4—44no—
745D4—616no—
746D4—616no—
747D4—128no—
748D4—1216no—
749D4—128no—
750D4—1216no—
751D4—128no—
752D4—124no—
753D4—248no—
754D4—248no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—34no—
773C2×C4—32no—
774C2×C4—48no—
775C2×C4—62no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—62no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—62no—
787C2×C4—61no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—1216no—
791C2×C4—1216no—
792C2×C4—1216no—
793C2×C4—128no—
794C2×C4C2×D3×D412yes—
795C2×C4C2×D3×D414yes—
796C2×C4C2×D3×D412yes—
797C2×C4C2×D3×D412yes—
798C2×C4C2×D3×D412yes—
799C2×C4#100712yes—
800C2×C4D3×#4112yes—
801C2×C4#100912yes—
802C2×C3—82no—
803C2×C3C2×D4211yescharacteristic
804C2×C3C2×#54711yescharacteristic
805C2×C3C2×#55011yescharacteristic
806C2×C3#349611yescharacteristic
807C2×C3#349711yescharacteristic
808C2×C3#350611yescharacteristic
809C2×C3#354811yescharacteristic
810D3—48no—
811D3—82no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—68no—
820C22—68no—
821C22—68no—
822C22—124no—
823C22—124no—
824C22—124no—
825C22—124no—
826C22—122no—
827C22—122no—
828C22—122no—
829C22—122no—
830C22—122no—
831C22—122no—
832C22—122no—
833C22C22×D3×D411yescharacteristic
834C22C22×D3×D411yescharacteristic
835C22C2×#100711yescharacteristic
836C22C2×D3×#4111yescharacteristic
837C22C2×#100911yescharacteristic
838C22D3×H(5,𝔽2)11yescharacteristic
839C22#596811yescharacteristic
840C4—22no—
841C4—24no—
842C4—34no—
843C4—42no—
844C4—42no—
845C4—44no—
846C4—64no—
847C4—62no—
848C4—62no—
849C4—122no—
850C4—121no—
851C4—122no—
852C4#560914yes—
853C4#563114yescomplemented
854C3#5981511yescharacteristic, complemented, Sylow
855C2—82no—
856C2—128no—
857C2—242no—
858C2C2×#560911yescharacteristic
859C2C2×#563111yescharacteristic
860C2#8638211yescharacteristic
861C2#8676011yescharacteristic
862C2D3×#55011yescharacteristic
863C2#8693911yescharacteristic
864C2#8700511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2538C2
hypercenter#2538D3
hypocenterC3#59815
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#5631C2semidirect
2. C2×#5577C2semidirect
3. C2×#5553C2semidirect
4. C3×#2538C2semidirect
5. #82812C2semidirect
6. C4×#944C2semidirect
7. C4×#940C2semidirect
8. #77432C2semidirect
9. #77284C2semidirect
10. #76348C2semidirect
11. #76316C2semidirect
12. #76202C2semidirect
13. #76004C2semidirect
14. #74369C2semidirect
15. #74319C2semidirect
16. #74015C2semidirect
17. #73935C2semidirect
93. #2538D3semidirect
145. #944D4semidirect
192. #874D4semidirect
383. C4×Dic3#41semidirect
712. C3×C4#547semidirect
719. Dic3#550semidirect
853. C4#5631semidirect
854. C3#59815semidirect

Maximal subgroups

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

subgroupindex
C2×#56312
C2×#55772
C2×#55532
C3×#25382
#828122
C4×#9442
C4×#9402
#774322
#772842
#763482
#763162
#762022
#760042
#743692
#743192
#740152
#739352
#598153