Finite Group Databasebeta

← #11028611

Subgroups — #11028611

Order 768.

2710 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5695C211yesmaximal, characteristic, complemented
2C2×#5547C211yesmaximal, characteristic, complemented
3C3×#2562C211yesmaximal, characteristic, complemented
4#83065C211yesmaximal, characteristic, complemented
5#82417C211yesmaximal, characteristic, complemented
6#78344C212yesmaximal, complemented
7#78238C212yesmaximal, complemented
8#77131C212yesmaximal, complemented
9#77113C212yesmaximal, complemented
10#75882C212yesmaximal, complemented
11#75846C212yesmaximal, complemented
12#75686C212yesmaximal, complemented
13#75681C212yesmaximal, complemented
14#74048C211yesmaximal, characteristic, complemented
15#74030C211yesmaximal, characteristic, complemented
16#74025C211yesmaximal, characteristic, complemented
17#74003C211yesmaximal, characteristic, complemented
18D3×#380C211yesmaximal, characteristic, complemented
19#73912C211yesmaximal, characteristic, complemented
20#73887C211yesmaximal, characteristic, complemented
21#73887C211yesmaximal, characteristic, complemented
22C4⋊C4×D12C211yesmaximal, characteristic, complemented
23#73763C211yesmaximal, characteristic, complemented
24#37836—31nomaximal, Sylow
25C22×#235C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C2×C3×#125C2211yescharacteristic, complemented
28C2×C3×C4×D4C2211yescharacteristic
29C2×#939C2211yescharacteristic
30C2×#938C2212yes—
31C2×#937C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×#930C2211yescharacteristic, complemented
34C2×C4×#67C2211yescharacteristic
35C2×C4×#67C2211yescharacteristic
36#5695—28no—
37#5547—28no—
38C2×#898C2212yescomplemented
39C2×#896C2211yescharacteristic
40C2×#895C2211yescharacteristic
41C2×#895C2211yescharacteristic
42C2×#895C2212yes—
43C2×#895C2211yescharacteristic, complemented
44C2×#894C2211yescharacteristic
45C2×#894C2212yescomplemented
46C2×#893C2212yes—
47C2×#892C2211yescharacteristic, complemented
48C2×D3×C4⋊C4C2211yescharacteristic
49C2×D3×C4⋊C4C2211yescharacteristic
50C2×D3×C4⋊C4C2211yescharacteristic, complemented
51C2×#884C2211yescharacteristic
52C2×#884C2212yes—
53C2×#884C2212yes—
54C2×#883C2211yescharacteristic
55C2×#882C2211yescharacteristic
56C2×#882C2212yes—
57C2×D3×C22⋊C4C2212yes—
58C2×#878C2211yescharacteristic
59C2×C4×D12C2212yes—
60C2×C4×D12C2211yescharacteristic
61C2×C4×D12C2211yescharacteristic, complemented
62C2×#872C2211yescharacteristic
63C3×#400C2212yescomplemented
64C3×#394C2212yes—
65C3×#388C2212yes—
66C3×#388C2212yescomplemented
67C3×#380C2211yescharacteristic
68C3×#380C2211yescharacteristic
69C3×#380C2211yescharacteristic, complemented
70C3×#380C2211yescharacteristic, complemented
71C3×C4×C4⋊C4C2211yescharacteristic, complemented
72#5212C2211yescharacteristic
73#5212C2211yescharacteristic, complemented
74#4994C2212yes—
75#4994C2212yes—
76#4988C2211yescharacteristic, complemented
77#4987C2211yescharacteristic
78#4987C2211yescharacteristic
79#4987C2211yescharacteristic
80#4987C2211yescharacteristic
81#4987C2212yescomplemented
82#4987C2211yescharacteristic, complemented
83#4984C2211yescharacteristic, complemented
84#4982C2212yescomplemented
85#4982C2212yescomplemented
86#4972C2211yescharacteristic, complemented
87#4972C2211yescharacteristic, complemented
88#4961C2212yes—
89#4961C2212yes—
90#4961C2212yescomplemented
91#4960C2212yes—
92#4960C2212yescomplemented
93#4959C2212yes—
94#4959C2212yescomplemented
95#4958C2212yes—
96#4957C2212yes—
97#4956C2212yes—
98#4956C2212yescomplemented
99#4949C2212yescomplemented
100#4945C2212yes—
101#4942C2212yes—
102#4940C2212yescomplemented
103#4939C2212yes—
104#4935C2211yescharacteristic, complemented
105#4928C2212yescomplemented
106#4676C2212yescomplemented
107#4676C2212yescomplemented
108#4675C2212yescomplemented
109#4673C2212yescomplemented
110#4671C2212yes—
111#4668C2212yes—
112#4668C2212yes—
113#4668C2212yescomplemented
114#4668C2212yescomplemented
115#4667C2212yes—
116#4665C2212yes—
117#4665C2212yes—
118#4665C2212yes—
119#4665C2212yes—
120#4665C2212yes—
121#4665C2212yescomplemented
122D3×#95C2212yes—
123#4658C2212yescomplemented
124#4654C2212yescomplemented
125#4646C2212yescomplemented
126C2×#553—31no—
127C2×#525—31no—
128#2847—31no—
129#2705—32no—
130#2702—32no—
131#2693—32no—
132#2671—32no—
133#2629—31no—
134#2615—31no—
135#2562D311yescharacteristic, complemented
136#2543—32no—
137#2537—31no—
138#2487—31no—
139#2485—31no—
140#2450—32no—
141#2424—32no—
142#2424—32no—
143#2416—31no—
144#2416—31no—
145D4×C4⋊C4—31no—
146#2324—31no—
147#2311—31no—
148C2×#380—31no—
149C24×D3C2311yescharacteristic
150C22×C3×D4C2311yescharacteristic
151C23×C3×C4C2311yescharacteristic
152C23×C3×C4C2311yescharacteristic
153C22×#67C2311yescharacteristic
154C22×#67C2311yescharacteristic
155C22×#67C2311yescharacteristic
156C22×#67C2311yescharacteristic
157C22×#67C2312yes—
158C22×#67C2312yes—
159C23×Dic3C2311yescharacteristic
160C2×#235—24no—
161C2×#235—24no—
162C2×#235—42no—
163C22×D12C2312yes—
164C22×D12C2311yescharacteristic
165C22×D12C2311yescharacteristic
166C22×D12C2311yescharacteristic
167C22×D12C2312yes—
168C22×D12C2312yes—
169C22×C4×D3—24no—
170C22×C4×D3—24no—
171C22×C4×D3—42no—
172C22×C4×D3C2311yescharacteristic
173C22×C4×D3C2311yescharacteristic
174C22×C4×D3C2311yescharacteristic
175C22×C4×D3C2311yescharacteristic
176C22×C4×D3C2311yescharacteristic
177C22×C4×D3C2312yes—
178C22×C4×D3C2312yes—
179C22×C4×D3C2312yes—
180C22×C4×D3C2312yes—
181C22×Dic6C2311yescharacteristic
182C3×#125—24no—
183C3×C4×D4—24no—
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C4⋊C4C2311yescharacteristic
186C2×C3×C4⋊C4C2312yes—
187C2×C3×C4⋊C4C2312yes—
188C2×C3×C4⋊C4C2311yescharacteristic
189C2×C3×C4⋊C4C2311yescharacteristic
190C2×C3×C4⋊C4C2311yescharacteristic
191C2×C3×C22⋊C4C2312yes—
192C2×C3×C22⋊C4C2311yescharacteristic
193C2×C3×C22⋊C4C2311yescharacteristic
194C2×C3×C22⋊C4C2312yes—
195C2×C3×C22⋊C4C2312yes—
196C2×C3×C22⋊C4C2312yes—
197C2×C3×C42C2312yes—
198C2×C3×C42C2311yescharacteristic
199C2×#217C2312yes—
200C2×#217C2311yescharacteristic
201C2×#217C2311yescharacteristic
202C2×#217C2312yes—
203#939—24no—
204#938—44no—
205#937—24no—
206#930—42no—
207#930—42no—
208C4×#67—24no—
209C4×#67—24no—
210C2×(C2×D3)⋊C4C2311yescharacteristic
211C2×(C2×D3)⋊C4C2311yescharacteristic
212C2×(C2×D3)⋊C4C2312yes—
213C2×(C2×D3)⋊C4C2312yes—
214C2×(C2×D3)⋊C4C2312yes—
215C2×(C2×D3)⋊C4C2312yes—
216C2×(C2×D3)⋊C4C2311yescharacteristic
217C2×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2311yescharacteristic
219C2×(C2×D3)⋊C4C2312yes—
220C2×(C2×D3)⋊C4C2312yes—
221C2×(C2×D3)⋊C4C2312yes—
222C2×(C2×D3)⋊C4C2312yes—
223C2×(C2×D3)⋊C4C2312yes—
224C2×(C2×D3)⋊C4C2312yes—
225C2×(C2×D3)⋊C4C2312yes—
226C2×(C2×D3)⋊C4C2312yes—
227C2×(C2×D3)⋊C4C2312yes—
228C2×(C2×D3)⋊C4C2311yescharacteristic
229C2×(C2×D3)⋊C4C2311yescharacteristic
230C2×C4⋊Dic3C2311yescharacteristic
231C2×C4⋊Dic3C2311yescharacteristic
232C2×C4⋊Dic3C2311yescharacteristic
233C2×C4⋊Dic3C2312yes—
234C2×C4⋊Dic3C2312yes—
235C2×C4⋊Dic3C2312yes—
236C2×C4⋊Dic3C2311yescharacteristic
237C2×Dic3⋊C4C2311yescharacteristic
238C2×Dic3⋊C4C2311yescharacteristic
239C2×Dic3⋊C4C2312yes—
240C2×Dic3⋊C4C2311yescharacteristic
241C2×Dic3⋊C4C2311yescharacteristic
242C2×Dic3⋊C4C2312yes—
243C2×Dic3⋊C4C2312yes—
244C2×Dic3⋊C4C2312yes—
245C2×Dic3⋊C4C2312yes—
246C2×C4×Dic3C2312yes—
247C2×C4×Dic3C2311yescharacteristic
248#898—28no—
249#896—24no—
250#895—28no—
251#895—24no—
252#895—24no—
253#895—24no—
254#894—28no—
255#894—24no—
256#893—28no—
257#892—24no—
258D3×C4⋊C4—24no—
259D3×C4⋊C4—42no—
260D3×C4⋊C4—42no—
261#884—24no—
262#884—44no—
263#884—44no—
264#883—24no—
265#882—24no—
266#882—44no—
267D3×C22⋊C4—44no—
268#878—24no—
269C4×D12—24no—
270C4×D12—44no—
271C4×D12D418yescomplemented
272#872—24no—
273C3×#95C2312yes—
274C3×#95C2312yes—
275C3×#95C2312yes—
276C3×#95C2312yes—
277C3×#95C2312yes—
278C3⋊#95C2312yes—
279C3⋊#95C2312yes—
280C3⋊#95C2312yes—
281C3⋊#95C2312yes—
282C3⋊#95C2312yes—
283C3⋊#95C2312yes—
284C3⋊#95C2312yes—
285C3⋊#95C2312yes—
286C3⋊#95C2312yes—
287C3⋊#95C2312yes—
288C22×#41—31no—
289C24×C4—31no—
290#553—68no—
291C2×#126—32no—
292C2×#125C2×D311yescharacteristic, complemented
293#525—68no—
294C2×#123—31no—
295C2×#123—32no—
296C2×#123—31no—
297C2×C22⋊Q8—31no—
298C2×C22⋊Q8—31no—
299C2×#121—31no—
300C2×#121—32no—
301C2×#121—31no—
302C2×#121—31no—
303C2×#121—31no—
304C2×#121—31no—
305C2×#121—31no—
306C2×#121—32no—
307C2×#121—31no—
308C2×#121—32no—
309C2×#121—32no—
310C2×#120—31no—
311C2×#120—31no—
312C2×#120—32no—
313C2×C4×D4—31no—
314C2×C4×D4—31no—
315C2×C4×D4—32no—
316C2×C4×D4—31no—
317C2×C4×D4—31no—
318C2×C4×D4—32no—
319C2×C4×D4C2×D311yescharacteristic
320C2×#117—31no—
321C2×#117—31no—
322C22×C4⋊C4—31no—
323C22×C4⋊C4—31no—
324C22×C4⋊C4—31no—
325C22×C22⋊C4—32no—
326#400—32no—
327#400C2×D312yescomplemented
328#399—32no—
329#398—32no—
330#398—32no—
331#397—32no—
332#396—32no—
333#396—32no—
334#396—32no—
335#396—32no—
336#394—32no—
337#394—32no—
338#394—32no—
339#394—32no—
340#394—32no—
341#394C2×D312yes—
342#393—32no—
343#392—32no—
344#392—32no—
345#392—32no—
346#391—32no—
347#390—31no—
348#390—32no—
349#390—32no—
350#389—31no—
351#389—31no—
352#389—31no—
353#389—32no—
354#388—32no—
355#388—32no—
356#388C2×D312yes—
357#388C2×D312yescomplemented
358#387—32no—
359#386—32no—
360#386—32no—
361#386—32no—
362#386—32no—
363#386—32no—
364#386—32no—
365#386—32no—
366#386—32no—
367#386—32no—
368#385—32no—
369#385—32no—
370#385—32no—
371#385—32no—
372#384—31no—
373#380—31no—
374#380—31no—
375#380—31no—
376#380—31no—
377#380—31no—
378#380—31no—
379#380—31no—
380#380—32no—
381#380—32no—
382#380—32no—
383#380C2×D311yescharacteristic
384#380C2×D311yescharacteristic
385#380C2×D311yescharacteristic, complemented
386#380C2×D311yescharacteristic, complemented
387C4×C4⋊C4C2×D311yescharacteristic, complemented
388C2×#95—32no—
389C24×C3C2411yescharacteristic
390C24×C3C2411yescharacteristic
391C23×D3—22no—
392C23×D3—22no—
393C23×D3—22no—
394C23×D3—22no—
395C23×D3—22no—
396C23×D3—41no—
397C23×D3—41no—
398C23×D3C2412yes—
399C23×D3C2411yescharacteristic
400C23×D3C2411yescharacteristic
401C23×D3C2411yescharacteristic
402C2×C3×D4—22no—
403C2×C3×D4—22no—
404C2×C3×D4—41no—
405C22×C3×C4—22no—
406C22×C3×C4—22no—
407C22×C3×C4—22no—
408C22×C3×C4—22no—
409C22×C3×C4—22no—
410C22×C3×C4—22no—
411C22×C3×C4C2412yes—
412C22×C3×C4C2411yescharacteristic
413C22×C3×C4C2411yescharacteristic
414C22×C3×C4C2412yes—
415C22×C3×C4C2412yes—
416C22×C3×C4C2412yes—
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2411yescharacteristic
419C22×C3×C4C2411yescharacteristic
420C2×#67—22no—
421C2×#67—22no—
422C2×#67—22no—
423C2×#67—22no—
424C2×#67—22no—
425C2×#67—22no—
426C2×#67—22no—
427C2×#67—24no—
428C2×#67—22no—
429C2×#67—22no—
430C2×#67—41no—
431C2×#67—41no—
432C2×#67—41no—
433C2×#67—42no—
434C2×#67—42no—
435C2×#67—42no—
436C2×#67—42no—
437C2×#67—42no—
438C22×Dic3—22no—
439C22×Dic3—22no—
440C22×Dic3—41no—
441C22×Dic3C2411yescharacteristic
442C22×Dic3C2412yes—
443C22×Dic3C2412yes—
444C22×Dic3C2412yes—
445C22×Dic3C2411yescharacteristic
446C22×Dic3C2411yescharacteristic
447C22×Dic3C2411yescharacteristic
448C22×Dic3C2411yescharacteristic
449#235—416no—
450C2×D12—22no—
451C2×D12—22no—
452C2×D12—22no—
453C2×D12—24no—
454C2×D12—22no—
455C2×D12—24no—
456C2×D12—24no—
457C2×D12—22no—
458C2×D12—22no—
459C2×D12—22no—
460C2×D12—24no—
461C2×D12—24no—
462C2×D12—41no—
463C2×D12—42no—
464C2×D12—42no—
465C2×D12—42no—
466C2×D12—42no—
467C2×D12C2×D414yes—
468C2×C4×D3—22no—
469C2×C4×D3—22no—
470C2×C4×D3—22no—
471C2×C4×D3—22no—
472C2×C4×D3—22no—
473C2×C4×D3—22no—
474C2×C4×D3—22no—
475C2×C4×D3—22no—
476C2×C4×D3—22no—
477C2×C4×D3—22no—
478C2×C4×D3—24no—
479C2×C4×D3—24no—
480C2×C4×D3—24no—
481C2×C4×D3—416no—
482C2×C4×D3—41no—
483C2×C4×D3—41no—
484C2×C4×D3—42no—
485C2×C4×D3—42no—
486C2×C4×D3—42no—
487C2×C4×D3—42no—
488C2×C4×D3—42no—
489C2×C4×D3—42no—
490C2×C4×D3—42no—
491C2×C4×D3—42no—
492C2×C4×D3—42no—
493C2×C4×D3C2×D414yes—
494C2×C4×D3C2×D414yes—
495C2×C4×D3#4114yes—
496C2×Dic6—22no—
497C2×Dic6—22no—
498C2×Dic6—41no—
499C3×C4⋊C4—22no—
500C3×C4⋊C4—22no—
501C3×C4⋊C4—24no—
502C3×C4⋊C4—22no—
503C3×C4⋊C4—24no—
504C3×C4⋊C4—22no—
505C3×C4⋊C4—22no—
506C3×C22⋊C4—24no—
507C3×C22⋊C4—22no—
508C3×C22⋊C4—22no—
509C3×C22⋊C4—42no—
510C3×C22⋊C4—42no—
511C3×C22⋊C4—42no—
512C3×C42—42no—
513C3×C42C2×D414yes—
514#217—24no—
515#217—22no—
516#217—22no—
517#217—42no—
518(C2×D3)⋊C4—22no—
519(C2×D3)⋊C4—22no—
520(C2×D3)⋊C4—24no—
521(C2×D3)⋊C4—24no—
522(C2×D3)⋊C4—22no—
523(C2×D3)⋊C4—22no—
524(C2×D3)⋊C4—24no—
525(C2×D3)⋊C4—24no—
526(C2×D3)⋊C4—24no—
527(C2×D3)⋊C4—24no—
528(C2×D3)⋊C4—42no—
529(C2×D3)⋊C4—42no—
530(C2×D3)⋊C4—42no—
531(C2×D3)⋊C4—42no—
532(C2×D3)⋊C4—42no—
533(C2×D3)⋊C4—42no—
534(C2×D3)⋊C4—42no—
535(C2×D3)⋊C4—42no—
536(C2×D3)⋊C4C2×D414yes—
537(C2×D3)⋊C4C2×D414yes—
538C4⋊Dic3—22no—
539C4⋊Dic3—22no—
540C4⋊Dic3—22no—
541C4⋊Dic3—42no—
542C4⋊Dic3—42no—
543C4⋊Dic3—42no—
544C4⋊Dic3C2×D414yes—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—24no—
550Dic3⋊C4—42no—
551Dic3⋊C4—42no—
552Dic3⋊C4—42no—
553Dic3⋊C4—42no—
554C4×Dic3—22no—
555C4×Dic3—24no—
556C25—31no—
557C2×#41—64no—
558C2×#41—64no—
559C2×#41—122no—
560C22×Q8—31no—
561C22×D4—31no—
562C22×D4—31no—
563C22×D4—31no—
564C22×D4—31no—
565C22×D4—32no—
566C22×D4—32no—
567C22×D4—31no—
568C22×D4—32no—
569C22×D4—31no—
570C22×D4—31no—
571C22×D4—32no—
572C22×D4—32no—
573C22×D4C22×D311yescharacteristic
574C23×C4—31no—
575C23×C4—31no—
576C23×C4—31no—
577C23×C4—31no—
578C23×C4—31no—
579C23×C4—31no—
580C23×C4—32no—
581C23×C4—32no—
582C23×C4—32no—
583C23×C4—32no—
584C23×C4—64no—
585C23×C4—64no—
586C23×C4—122no—
587C23×C4C22×D311yescharacteristic
588C23×C4C22×D311yescharacteristic
589#126—68no—
590#125—24no—
591#123—64no—
592#123—64no—
593#123—68no—
594C22⋊Q8—64no—
595C22⋊Q8—64no—
596#121—64no—
597#121—64no—
598#121—64no—
599#121—64no—
600#121—64no—
601#121—68no—
602#121—124no—
603#121—124no—
604#121—124no—
605#121—122no—
606#121—122no—
607#120—64no—
608#120—64no—
609#120—124no—
610C4×D4—24no—
611C4×D4—38no—
612C4×D4—68no—
613C4×D4—64no—
614C4×D4—64no—
615C4×D4—64no—
616C4×D4—124no—
617#117—64no—
618#117—64no—
619C2×C4⋊C4—31no—
620C2×C4⋊C4—31no—
621C2×C4⋊C4—31no—
622C2×C4⋊C4—31no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—31no—
625C2×C4⋊C4—31no—
626C2×C4⋊C4—31no—
627C2×C4⋊C4—31no—
628C2×C4⋊C4—32no—
629C2×C4⋊C4—32no—
630C2×C4⋊C4—32no—
631C2×C4⋊C4—32no—
632C2×C4⋊C4—32no—
633C2×C4⋊C4—32no—
634C2×C4⋊C4—32no—
635C2×C4⋊C4—64no—
636C2×C4⋊C4—122no—
637C2×C4⋊C4—122no—
638C2×C4⋊C4C22×D311yescharacteristic
639C2×C4⋊C4C22×D311yescharacteristic
640C2×C4⋊C4C22×D311yescharacteristic
641C2×C4⋊C4C22×D312yes—
642C2×C4⋊C4C22×D311yescharacteristic
643C2×C4⋊C4C22×D312yes—
644C2×C4⋊C4C22×D311yescharacteristic
645C2×C22⋊C4—31no—
646C2×C22⋊C4—31no—
647C2×C22⋊C4—32no—
648C2×C22⋊C4—31no—
649C2×C22⋊C4—31no—
650C2×C22⋊C4—31no—
651C2×C22⋊C4—31no—
652C2×C22⋊C4—32no—
653C2×C22⋊C4—31no—
654C2×C22⋊C4—32no—
655C2×C22⋊C4—31no—
656C2×C22⋊C4—32no—
657C2×C22⋊C4—32no—
658C2×C22⋊C4—32no—
659C2×C22⋊C4—32no—
660C2×C22⋊C4—32no—
661C2×C22⋊C4—32no—
662C2×C22⋊C4—32no—
663C2×C22⋊C4—32no—
664C2×C22⋊C4—32no—
665C2×C22⋊C4—32no—
666C2×C22⋊C4—32no—
667C2×C22⋊C4—32no—
668C2×C22⋊C4—32no—
669C2×C22⋊C4—124no—
670C2×C22⋊C4C22×D312yes—
671C2×C22⋊C4C22×D311yescharacteristic
672C2×C22⋊C4C22×D311yescharacteristic
673C2×C22⋊C4C22×D312yes—
674C2×C22⋊C4C22×D312yes—
675C2×C22⋊C4C22×D312yes—
676C2×C42—31no—
677C2×C42—32no—
678C2×C42C22×D312yes—
679C2×C42C22×D311yescharacteristic
680#95—32no—
681#95—32no—
682#95—32no—
683#95—32no—
684#95—32no—
685#95—32no—
686#95—32no—
687#95—32no—
688#95—32no—
689#95—32no—
690#95C22×D312yes—
691#95C22×D312yes—
692#95C22×D312yes—
693#95C22×D312yes—
694#95C22×D312yes—
695C23×C3—21no—
696C23×C3—21no—
697C23×C3—21no—
698C23×C3—21no—
699C23×C3—21no—
700C23×C3—21no—
701C23×C3—21no—
702C23×C3—21no—
703C23×C3—21no—
704C23×C3—21no—
705C23×C3—21no—
706C23×C3—21no—
707C23×C3—21no—
708C23×C3H(5,𝔽2)12yes—
709C23×C3C2511yescharacteristic
710C22×D3—21no—
711C22×D3—21no—
712C22×D3—21no—
713C22×D3—21no—
714C22×D3—28no—
715C22×D3—21no—
716C22×D3—21no—
717C22×D3—21no—
718C22×D3—21no—
719C22×D3—21no—
720C22×D3—21no—
721C22×D3—21no—
722C22×D3—21no—
723C22×D3—21no—
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—22no—
728C22×D3—22no—
729C22×D3—22no—
730C22×D3—22no—
731C22×D3—22no—
732C22×D3—22no—
733C22×D3—22no—
734C22×D3—44no—
735C22×D3—44no—
736C22×D3—44no—
737C22×D3—44no—
738C22×D3—44no—
739C22×D3—44no—
740C22×D3C22×D412yes—
741C22×D3C22×D412yes—
742C22×D3C2×#4112yes—
743C22×D3H(5,𝔽2)12yes—
744C22×D32−1+412yes—
745C3×D4—44no—
746C2×C3×C4—21no—
747C2×C3×C4—21no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
750C2×C3×C4—22no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—22no—
754C2×C3×C4—22no—
755C2×C3×C4—21no—
756C2×C3×C4—21no—
757C2×C3×C4—22no—
758C2×C3×C4—22no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—22no—
765C2×C3×C4—22no—
766C2×C3×C4—22no—
767C2×C3×C4—22no—
768C2×C3×C4—44no—
769C2×C3×C4—44no—
770C2×C3×C4C22×D412yes—
771C2×C3×C4C22×D412yes—
772C2×C3×C4C22×D412yes—
773C2×C3×C4C2×#4112yes—
774C2×C3×C4H(5,𝔽2)12yes—
775#67—44no—
776#67—44no—
777#67—44no—
778#67—44no—
779#67—84no—
780#67—84no—
781C2×Dic3—21no—
782C2×Dic3—21no—
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—21no—
787C2×Dic3—21no—
788C2×Dic3—21no—
789C2×Dic3—22no—
790C2×Dic3—21no—
791C2×Dic3—21no—
792C2×Dic3—22no—
793C2×Dic3—22no—
794C2×Dic3—22no—
795C2×Dic3—22no—
796C2×Dic3—22no—
797C2×Dic3—22no—
798C2×Dic3—22no—
799C2×Dic3—21no—
800C2×Dic3—21no—
801C2×Dic3—22no—
802C2×Dic3—44no—
803C2×Dic3C22×D412yes—
804C2×Dic3C22×D412yes—
805C2×Dic3C2×#4112yes—
806D12—28no—
807D12—44no—
808D12—48no—
809D12—44no—
810D12—84no—
811D12—84no—
812C4×D3—28no—
813C4×D3—28no—
814C4×D3—28no—
815C4×D3—44no—
816C4×D3—44no—
817C4×D3—84no—
818C4×D3—84no—
819C4×D3—84no—
820C4×D3—84no—
821Dic6—44no—
822C24—31no—
823C24—31no—
824C24—31no—
825C24—32no—
826C24—62no—
827C24—62no—
828C24—62no—
829C24—62no—
830C24—62no—
831C24—121no—
832C24—121no—
833C24C23×D311yescharacteristic
834C24C23×D311yescharacteristic
835#41—1216no—
836C2×Q8—62no—
837C2×Q8—62no—
838C2×Q8—121no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—34no—
842C2×D4—41no—
843C2×D4—62no—
844C2×D4—62no—
845C2×D4—64no—
846C2×D4—62no—
847C2×D4—64no—
848C2×D4—62no—
849C2×D4—64no—
850C2×D4—64no—
851C2×D4—64no—
852C2×D4—62no—
853C2×D4—62no—
854C2×D4—62no—
855C2×D4—62no—
856C2×D4—62no—
857C2×D4—62no—
858C2×D4—62no—
859C2×D4—62no—
860C2×D4—62no—
861C2×D4—64no—
862C2×D4—62no—
863C2×D4—62no—
864C2×D4—62no—
865C2×D4—121no—
866C2×D4—122no—
867C2×D4—122no—
868C2×D4—122no—
869C2×D4—122no—
870C2×D4—121no—
871C2×D4—121no—
872C2×D4—121no—
873C2×D4—122no—
874C2×D4—122no—
875C2×D4—122no—
876C2×D4—122no—
877C2×D4—122no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—31no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—34no—
888C22×C4—34no—
889C22×C4—34no—
890C22×C4—31no—
891C22×C4—32no—
892C22×C4—32no—
893C22×C4—32no—
894C22×C4—31no—
895C22×C4—62no—
896C22×C4—62no—
897C22×C4—62no—
898C22×C4—62no—
899C22×C4—64no—
900C22×C4—64no—
901C22×C4—62no—
902C22×C4—62no—
903C22×C4—62no—
904C22×C4—62no—
905C22×C4—62no—
906C22×C4—62no—
907C22×C4—62no—
908C22×C4—62no—
909C22×C4—64no—
910C22×C4—121no—
911C22×C4—121no—
912C22×C4—122no—
913C22×C4—122no—
914C22×C4—122no—
915C22×C4—122no—
916C22×C4—122no—
917C22×C4—122no—
918C22×C4—122no—
919C22×C4—122no—
920C22×C4—122no—
921C22×C4—1216no—
922C22×C4—121no—
923C22×C4C23×D312yes—
924C22×C4C23×D311yescharacteristic
925C22×C4C23×D311yescharacteristic
926C22×C4C23×D312yes—
927C22×C4C23×D312yes—
928C22×C4C23×D312yes—
929C22×C4C23×D311yescharacteristic
930C22×C4C23×D311yescharacteristic
931C22×C4C23×D311yescharacteristic
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—34no—
940C4⋊C4—64no—
941C4⋊C4—62no—
942C4⋊C4—62no—
943C4⋊C4—62no—
944C4⋊C4—62no—
945C4⋊C4—62no—
946C4⋊C4—62no—
947C4⋊C4—62no—
948C4⋊C4—122no—
949C4⋊C4—122no—
950C4⋊C4—122no—
951C4⋊C4—122no—
952C4⋊C4—122no—
953C4⋊C4—122no—
954C4⋊C4—122no—
955C22⋊C4—24no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—34no—
959C22⋊C4—34no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—64no—
964C22⋊C4—64no—
965C22⋊C4—64no—
966C22⋊C4—64no—
967C22⋊C4—62no—
968C22⋊C4—62no—
969C22⋊C4—64no—
970C22⋊C4—62no—
971C22⋊C4—62no—
972C22⋊C4—64no—
973C22⋊C4—62no—
974C22⋊C4—62no—
975C22⋊C4—64no—
976C22⋊C4—122no—
977C22⋊C4—122no—
978C22⋊C4—122no—
979C22⋊C4—122no—
980C22⋊C4—122no—
981C22⋊C4—122no—
982C22⋊C4—122no—
983C22⋊C4—122no—
984C22⋊C4—122no—
985C42—42no—
986C42—64no—
987C42—62no—
988C42D3×D414yes—
989C22×C3—22no—
990C22×C3—22no—
991C22×C3—22no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—41no—
1001C22×C3—41no—
1002C22×C3—41no—
1003C22×C3C23×D411yescharacteristic
1004C22×C3C22×#4111yescharacteristic
1005C22×C3C2×H(5,𝔽2)11yescharacteristic
1006C22×C3C2×H(5,𝔽2)11yescharacteristic
1007C22×C3C2×H(5,𝔽2)11yescharacteristic
1008C22×C3C2×2−1+411yescharacteristic
1009C22×C3#58511yescharacteristic
1010C2×D3—22no—
1011C2×D3—22no—
1012C2×D3—22no—
1013C2×D3—22no—
1014C2×D3—22no—
1015C2×D3—22no—
1016C2×D3—22no—
1017C2×D3—22no—
1018C2×D3—22no—
1019C2×D3—22no—
1020C2×D3—22no—
1021C2×D3—22no—
1022C2×D3—416no—
1023C2×D3—41no—
1024C2×D3—41no—
1025C2×D3—41no—
1026C2×D3—41no—
1027C2×D3—41no—
1028C2×D3—41no—
1029C2×D3—41no—
1030C2×D3—41no—
1031C2×D3—42no—
1032C2×D3—42no—
1033C2×D3—42no—
1034C2×D3—42no—
1035C2×D3—42no—
1036C2×D3—42no—
1037C2×D3—42no—
1038C2×D3#53714yes—
1039C3×C4—22no—
1040C3×C4—22no—
1041C3×C4—42no—
1042C3×C4—41no—
1043C3×C4—41no—
1044C3×C4—42no—
1045C3×C4—42no—
1046C3×C4—42no—
1047C3×C4#54614yes—
1048Dic3—22no—
1049Dic3—22no—
1050Dic3—22no—
1051Dic3—41no—
1052Dic3—42no—
1053Dic3—41no—
1054Dic3—42no—
1055Dic3—42no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—32no—
1070C23—32no—
1071C23—32no—
1072C23—32no—
1073C23—32no—
1074C23—68no—
1075C23—61no—
1076C23—61no—
1077C23—61no—
1078C23—61no—
1079C23—61no—
1080C23—61no—
1081C23—61no—
1082C23—61no—
1083C23—61no—
1084C23—61no—
1085C23—61no—
1086C23—61no—
1087C23—61no—
1088C23—61no—
1089C23—61no—
1090C23—61no—
1091C23—62no—
1092C23—62no—
1093C23—62no—
1094C23—62no—
1095C23—62no—
1096C23—62no—
1097C23—62no—
1098C23—124no—
1099C23—124no—
1100C23—124no—
1101C23—124no—
1102C23—124no—
1103C23—124no—
1104C23#100912yes—
1105C23C24×D311yescharacteristic
1106Q8—124no—
1107D4—44no—
1108D4—68no—
1109D4—128no—
1110D4—124no—
1111D4—124no—
1112D4—124no—
1113D4—124no—
1114D4—124no—
1115D4—124no—
1116D4—244no—
1117D4—244no—
1118D4—244no—
1119D4—244no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—32no—
1143C2×C4—32no—
1144C2×C4—32no—
1145C2×C4—44no—
1146C2×C4—44no—
1147C2×C4—61no—
1148C2×C4—61no—
1149C2×C4—61no—
1150C2×C4—61no—
1151C2×C4—61no—
1152C2×C4—61no—
1153C2×C4—68no—
1154C2×C4—68no—
1155C2×C4—68no—
1156C2×C4—61no—
1157C2×C4—61no—
1158C2×C4—62no—
1159C2×C4—62no—
1160C2×C4—62no—
1161C2×C4—61no—
1162C2×C4—62no—
1163C2×C4—62no—
1164C2×C4—62no—
1165C2×C4—61no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—61no—
1169C2×C4—62no—
1170C2×C4—61no—
1171C2×C4—124no—
1172C2×C4—124no—
1173C2×C4—124no—
1174C2×C4—244no—
1175C2×C4—244no—
1176C2×C4—244no—
1177C2×C4—244no—
1178C2×C4C2×D3×D412yes—
1179C2×C4C2×D3×D412yes—
1180C2×C4C2×D3×D412yes—
1181C2×C4D3×#4112yes—
1182C2×C4#100912yes—
1183C2×C3—42no—
1184C2×C3—81no—
1185C2×C3C2×#53711yescharacteristic
1186C2×C3C2×#54611yescharacteristic
1187C2×C3#348811yescharacteristic
1188C2×C3#349211yescharacteristic
1189C2×C3#349411yescharacteristic
1190C2×C3#353711yescharacteristic
1191C2×C3#354111yescharacteristic
1192D3—24no—
1193D3—42no—
1194D3—42no—
1195D3—82no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—34no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—62no—
1212C22—62no—
1213C22—62no—
1214C22—62no—
1215C22—62no—
1216C22—62no—
1217C22—62no—
1218C22—62no—
1219C22—62no—
1220C22—62no—
1221C22—62no—
1222C22—62no—
1223C22—1216no—
1224C22—121no—
1225C22—121no—
1226C22—121no—
1227C22—121no—
1228C22—121no—
1229C22—121no—
1230C22—121no—
1231C22—121no—
1232C22—122no—
1233C22—122no—
1234C22—122no—
1235C22—122no—
1236C22—122no—
1237C22—122no—
1238C22—122no—
1239C22C22×D3×D411yescharacteristic
1240C22C2×D3×#4111yescharacteristic
1241C22C2×#100911yescharacteristic
1242C22C2×#100911yescharacteristic
1243C22#596411yescharacteristic
1244C22D3×H(5,𝔽2)11yescharacteristic
1245C22D3×2−1+411yescharacteristic
1246C4—22no—
1247C4—22no—
1248C4—42no—
1249C4—41no—
1250C4—41no—
1251C4—42no—
1252C4—42no—
1253C4—42no—
1254C4—62no—
1255C4—62no—
1256C4—62no—
1257C4—122no—
1258C4—121no—
1259C4—121no—
1260C4—122no—
1261C4—122no—
1262C4#567614yes—
1263C3#3783611yescharacteristic, complemented, Sylow
1264C2—42no—
1265C2—64no—
1266C2—81no—
1267C2—122no—
1268C2—122no—
1269C2—242no—
1270C2#8604111yescharacteristic
1271C2C2×#567611yescharacteristic
1272C2D3×#53711yescharacteristic
1273C2#8684511yescharacteristic
1274C2#8686011yescharacteristic
1275C2#8687811yescharacteristic
1276C2#8691611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2562C2
hypercenter#2562D3
hypocenterC3#37836
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2562

Complements

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

NH ≅ G/Ntype
1. C2×#5695C2semidirect
2. C2×#5547C2semidirect
3. C3×#2562C2semidirect
4. #83065C2semidirect
5. #82417C2semidirect
6. #78344C2semidirect
7. #78238C2semidirect
8. #77131C2semidirect
9. #77113C2semidirect
10. #75882C2semidirect
11. #75846C2semidirect
12. #75686C2semidirect
13. #75681C2semidirect
14. #74048C2semidirect
15. #74030C2semidirect
16. #74025C2semidirect
17. #74003C2semidirect
18. D3×#380C2semidirect
19. #73912C2semidirect
20. #73887C2semidirect
21. #73887C2semidirect
22. C4⋊C4×D12C2semidirect
23. #73763C2semidirect
27. C2×C3×#125C22semidirect
33. C2×#930C22semidirect
38. C2×#898C22semidirect
43. C2×#895C22semidirect
45. C2×#894C22semidirect
47. C2×#892C22semidirect
50. C2×D3×C4⋊C4C22semidirect
61. C2×C4×D12C22semidirect
63. C3×#400C22semidirect
66. C3×#388C22semidirect
69. C3×#380C22semidirect
70. C3×#380C22semidirect
71. C3×C4×C4⋊C4C22semidirect
73. #5212C22semidirect
76. #4988C22semidirect
81. #4987C22semidirect
82. #4987C22semidirect
83. #4984C22semidirect
84. #4982C22semidirect
85. #4982C22semidirect
86. #4972C22semidirect
87. #4972C22semidirect
90. #4961C22semidirect
92. #4960C22semidirect
94. #4959C22semidirect
98. #4956C22semidirect
99. #4949C22semidirect
102. #4940C22semidirect
104. #4935C22semidirect
105. #4928C22semidirect
106. #4676C22semidirect
107. #4676C22semidirect
108. #4675C22semidirect
109. #4673C22semidirect
113. #4668C22semidirect
114. #4668C22semidirect
121. #4665C22semidirect
123. #4658C22semidirect
124. #4654C22semidirect
125. #4646C22semidirect
135. #2562D3semidirect
271. C4×D12D4semidirect
292. C2×#125C2×D3semidirect
327. #400C2×D3semidirect
357. #388C2×D3semidirect
385. #380C2×D3semidirect
386. #380C2×D3semidirect
387. C4×C4⋊C4C2×D3semidirect
1263. C3#37836semidirect

Maximal subgroups

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

subgroupindex
C2×#56952
C2×#55472
C3×#25622
#830652
#824172
#783442
#782382
#771312
#771132
#758822
#758462
#756862
#756812
#740482
#740302
#740252
#740032
D3×#3802
#739122
#738872
C4⋊C4×D122
#737632
#378363