Finite Group Databasebeta

← #11028612

Subgroups — #11028612

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×#5618C211yesmaximal, characteristic, complemented
2C2×#5547C211yesmaximal, characteristic, complemented
3C3×#2416C211yesmaximal, characteristic, complemented
4#82723C211yesmaximal, characteristic, complemented
5#82709C211yesmaximal, characteristic, complemented
6#82706C212yesmaximal, complemented
7#82671C212yesmaximal, complemented
8#82667C211yesmaximal, characteristic, complemented
9#82374C211yesmaximal, characteristic, complemented
10C4⋊C4×#67C211yesmaximal, characteristic, complemented
11C2×#4987C211yesmaximal, characteristic, complemented
12#77440C212yesmaximal, complemented
13#77348C212yesmaximal, complemented
14#77024C212yesmaximal, complemented
15#76999C212yesmaximal, complemented
16#76439C211yesmaximal, characteristic, complemented
17#76430C211yesmaximal, characteristic, complemented
18#76251C211yesmaximal, characteristic, complemented
19#76230C211yesmaximal, characteristic, complemented
20#74893C212yesmaximal, complemented
21#74712C212yesmaximal, complemented
22#74003C211yesmaximal, characteristic, complemented
23#73941C211yesmaximal, characteristic, complemented
24#37836—31nomaximal, Sylow
25C22×#235C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2212yes—
29C2×C3×#121C2211yescharacteristic, complemented
30C2×C3×C4×D4C2211yescharacteristic
31C22×C3×C4⋊C4C2211yescharacteristic
32C2×#939C2211yescharacteristic
33C2×#939C2212yes—
34C2×#939C2212yes—
35C2×#938C2211yescharacteristic
36C2×#938C2211yescharacteristic
37C2×#938C2211yescharacteristic, complemented
38C2×#937C2211yescharacteristic
39C2×#937C2212yes—
40C2×D4×Dic3C2212yes—
41C2×D4×Dic3C2211yescharacteristic, complemented
42C2×C4×#67C2211yescharacteristic
43C2×C4×#67C2212yes—
44C2×C4×#67C2211yescharacteristic
45C22×(C2×D3)⋊C4C2212yes—
46C22×C4⋊Dic3C2211yescharacteristic
47#5618—28no—
48#5547—28no—
49C2×#896C2211yescharacteristic
50C2×#894C2211yescharacteristic
51C2×#892C2211yescharacteristic, complemented
52C2×D3×C4⋊C4C2211yescharacteristic, complemented
53C2×#890C2211yescharacteristic, complemented
54C2×#886C2212yescomplemented
55C2×#884C2211yescharacteristic
56C2×#884C2212yes—
57C2×#883C2211yescharacteristic
58C2×#882C2211yescharacteristic
59C2×#879C2212yescomplemented
60C2×#878C2211yescharacteristic
61C2×C4×D12C2211yescharacteristic
62C2×#872C2211yescharacteristic
63C3×#396C2212yescomplemented
64C3×#394C2212yescomplemented
65C3×#390C2211yescharacteristic, complemented
66C3×#389C2211yescharacteristic, complemented
67C3×#386C2212yes—
68C3×#380C2211yescharacteristic, complemented
69#5223C2212yes—
70#5223C2212yescomplemented
71#5222C2212yescomplemented
72#5220C2212yes—
73#5220C2212yes—
74#5212C2211yescharacteristic
75#5212C2211yescharacteristic, complemented
76#5212C2211yescharacteristic, complemented
77#5210C2212yes—
78C2×C3⋊#95C2212yes—
79#4994C2212yes—
80#4992C2212yescomplemented
81#4990C2212yes—
82#4989C2212yescomplemented
83#4987C2211yescharacteristic
84#4987C2211yescharacteristic
85#4987C2212yes—
86#4987C2212yes—
87#4987C2211yescharacteristic
88#4987C2211yescharacteristic
89#4987C2211yescharacteristic
90#4987C2211yescharacteristic
91#4987C2211yescharacteristic, complemented
92#4986C2212yescomplemented
93#4983C2212yescomplemented
94#4976C2212yescomplemented
95#4975C2211yescharacteristic, complemented
96Dic3×C4⋊C4C2211yescharacteristic, complemented
97#4961C2212yes—
98#4960C2212yes—
99#4959C2212yes—
100#4959C2212yes—
101#4958C2212yes—
102#4957C2212yes—
103#4957C2212yes—
104#4956C2212yes—
105#4956C2212yes—
106#4956C2212yescomplemented
107#4956C2212yescomplemented
108#4949C2212yescomplemented
109#4948C2212yescomplemented
110#4947C2212yescomplemented
111#4946C2212yes—
112#4946C2212yescomplemented
113#4944C2212yescomplemented
114#4944C2212yescomplemented
115#4942C2212yescomplemented
116#4928C2211yescharacteristic, complemented
117#4928C2211yescharacteristic, complemented
118#4676C2212yes—
119#4672C2212yes—
120#4669C2212yes—
121#4665C2212yes—
122#4660C2212yescomplemented
123#4657C2212yescomplemented
124#4655C2212yescomplemented
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#2562—31no—
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#2416D311yescharacteristic, complemented
145D4×C4⋊C4—31no—
146#2324—31no—
147#2311—31no—
148C2×#380—31no—
149C24×D3C2311yescharacteristic
150C22×C3×D4C2311yescharacteristic
151C22×C3×D4C2312yes—
152C22×C3×D4C2311yescharacteristic
153C22×C3×D4C2312yes—
154C23×C3×C4C2311yescharacteristic
155C23×C3×C4C2311yescharacteristic
156C23×C3×C4C2312yes—
157C22×#67C2311yescharacteristic
158C22×#67C2311yescharacteristic
159C22×#67C2311yescharacteristic
160C22×#67C2311yescharacteristic
161C22×#67C2312yes—
162C22×#67C2312yes—
163C22×#67C2312yes—
164C23×Dic3C2311yescharacteristic
165C23×Dic3C2312yes—
166C23×Dic3C2312yes—
167C2×#235—24no—
168C2×#235—24no—
169C2×#235—42no—
170C22×D12C2311yescharacteristic
171C22×D12C2311yescharacteristic
172C22×C4×D3—24no—
173C22×C4×D3—24no—
174C22×C4×D3—42no—
175C22×C4×D3C2311yescharacteristic
176C22×C4×D3C2311yescharacteristic
177C22×C4×D3C2311yescharacteristic
178C22×C4×D3C2311yescharacteristic
179C22×C4×D3C2311yescharacteristic
180C22×C4×D3C2312yes—
181C22×Dic6C2311yescharacteristic
182C3×#121—24no—
183C3×#121—42no—
184C3×#121—44no—
185C3×C4×D4—24no—
186C2×C3×C4⋊C4—42no—
187C2×C3×C4⋊C4C2311yescharacteristic
188C2×C3×C4⋊C4C2311yescharacteristic
189C2×C3×C4⋊C4C2311yescharacteristic
190C2×C3×C4⋊C4C2311yescharacteristic
191C2×C3×C4⋊C4C2312yes—
192C2×C3×C4⋊C4C2312yes—
193C2×C3×C22⋊C4C2311yescharacteristic
194C2×C3×C22⋊C4C2311yescharacteristic
195C2×C3×C22⋊C4C2312yes—
196C2×C3×C22⋊C4C2312yes—
197C2×C3×C22⋊C4C2312yes—
198C2×C3×C22⋊C4C2312yes—
199C2×C3×C22⋊C4C2312yes—
200C2×C3×C42C2311yescharacteristic
201C2×#217C2311yescharacteristic
202C2×#217C2312yes—
203C2×#217C2312yes—
204C2×#217C2312yes—
205C2×#217C2312yes—
206C2×#217C2312yes—
207C2×#217C2312yes—
208C2×#217C2312yes—
209C2×#217C2311yescharacteristic
210#939—24no—
211#939—28no—
212#939—44no—
213#938—24no—
214#938—24no—
215#938—42no—
216#937—24no—
217#937—44no—
218D4×Dic3—28no—
219D4×Dic3—24no—
220C4×#67—24no—
221C4×#67—44no—
222C4×#67D418yescomplemented
223C2×(C2×D3)⋊C4—44no—
224C2×(C2×D3)⋊C4C2312yes—
225C2×(C2×D3)⋊C4C2311yescharacteristic
226C2×(C2×D3)⋊C4C2312yes—
227C2×(C2×D3)⋊C4C2312yes—
228C2×(C2×D3)⋊C4C2311yescharacteristic
229C2×(C2×D3)⋊C4C2311yescharacteristic
230C2×(C2×D3)⋊C4C2311yescharacteristic
231C2×(C2×D3)⋊C4C2311yescharacteristic
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×(C2×D3)⋊C4C2312yes—
236C2×(C2×D3)⋊C4C2312yes—
237C2×(C2×D3)⋊C4C2311yescharacteristic
238C2×C4⋊Dic3—24no—
239C2×C4⋊Dic3C2311yescharacteristic
240C2×C4⋊Dic3C2312yes—
241C2×C4⋊Dic3C2311yescharacteristic
242C2×C4⋊Dic3C2311yescharacteristic
243C2×C4⋊Dic3C2311yescharacteristic
244C2×C4⋊Dic3C2311yescharacteristic
245C2×C4⋊Dic3C2312yes—
246C2×Dic3⋊C4C2311yescharacteristic
247C2×Dic3⋊C4C2311yescharacteristic
248C2×Dic3⋊C4C2312yes—
249C2×Dic3⋊C4C2311yescharacteristic
250C2×Dic3⋊C4C2312yes—
251C2×Dic3⋊C4C2312yes—
252C2×Dic3⋊C4C2312yes—
253C2×Dic3⋊C4C2312yes—
254C2×Dic3⋊C4C2312yes—
255C2×Dic3⋊C4C2311yescharacteristic
256C2×C4×Dic3C2312yes—
257C2×C4×Dic3C2312yes—
258C2×C4×Dic3C2311yescharacteristic
259#896—24no—
260#894—24no—
261#892—24no—
262D3×C4⋊C4—42no—
263#890—24no—
264#886—28no—
265#884—24no—
266#884—44no—
267#883—24no—
268#882—24no—
269#879—28no—
270#878—24no—
271C4×D12—24no—
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×#125—31no—
293#525—68no—
294C2×#123—31no—
295C2×#123—31no—
296C2×#123—32no—
297C2×C22⋊Q8—31no—
298C2×C22⋊Q8—31no—
299C2×#121—31no—
300C2×#121—31no—
301C2×#121—31no—
302C2×#121—32no—
303C2×#121—31no—
304C2×#121—32no—
305C2×#121—31no—
306C2×#121—32no—
307C2×#121C2×D311yescharacteristic
308C2×#121C2×D312yes—
309C2×#121C2×D311yescharacteristic, complemented
310C2×#120—31no—
311C2×#120—32no—
312C2×#120—31no—
313C2×C4×D4—31no—
314C2×C4×D4—31no—
315C2×C4×D4—32no—
316C2×C4×D4—31no—
317C2×C4×D4—32no—
318C2×C4×D4—31no—
319C2×C4×D4C2×D311yescharacteristic
320C2×#117—31no—
321C2×#117—31no—
322C22×C4⋊C4—31no—
323C22×C4⋊C4—31no—
324C22×C4⋊C4C2×D311yescharacteristic
325C22×C22⋊C4—32no—
326#400—32no—
327#400—32no—
328#399—32no—
329#398—32no—
330#398—32no—
331#397—32no—
332#396—32no—
333#396—32no—
334#396—32no—
335#396C2×D312yescomplemented
336#394—32no—
337#394—32no—
338#394—32no—
339#394—32no—
340#394—32no—
341#394C2×D312yescomplemented
342#393—32no—
343#392—32no—
344#392—32no—
345#392—32no—
346#391—32no—
347#390—32no—
348#390—32no—
349#390C2×D311yescharacteristic, complemented
350#389—32no—
351#389—31no—
352#389—31no—
353#389C2×D311yescharacteristic, complemented
354#388—32no—
355#388—32no—
356#388—32no—
357#388—32no—
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#386C2×D312yes—
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—31no—
381#380—31no—
382#380—32no—
383#380—32no—
384#380—31no—
385#380—32no—
386#380C2×D311yescharacteristic, complemented
387C4×C4⋊C4—31no—
388C2×#95—32no—
389C24×C3C2411yescharacteristic
390C24×C3C2412yes—
391C24×C3C2411yescharacteristic
392C23×D3—22no—
393C23×D3—22no—
394C23×D3—22no—
395C23×D3—22no—
396C23×D3—22no—
397C23×D3—41no—
398C23×D3—41no—
399C23×D3C2411yescharacteristic
400C23×D3C2411yescharacteristic
401C23×D3C2411yescharacteristic
402C2×C3×D4—24no—
403C2×C3×D4—22no—
404C2×C3×D4—24no—
405C2×C3×D4—22no—
406C2×C3×D4—22no—
407C2×C3×D4—24no—
408C2×C3×D4—22no—
409C2×C3×D4—22no—
410C2×C3×D4—22no—
411C2×C3×D4—42no—
412C2×C3×D4—42no—
413C2×C3×D4—42no—
414C22×C3×C4—22no—
415C22×C3×C4—22no—
416C22×C3×C4—24no—
417C22×C3×C4—22no—
418C22×C3×C4—22no—
419C22×C3×C4—22no—
420C22×C3×C4—42no—
421C22×C3×C4—42no—
422C22×C3×C4C2×D414yes—
423C22×C3×C4C2411yescharacteristic
424C22×C3×C4C2411yescharacteristic
425C22×C3×C4C2412yes—
426C22×C3×C4C2412yes—
427C22×C3×C4C2412yes—
428C22×C3×C4C2411yescharacteristic
429C22×C3×C4C2411yescharacteristic
430C22×C3×C4C2411yescharacteristic
431C2×#67—22no—
432C2×#67—22no—
433C2×#67—22no—
434C2×#67—22no—
435C2×#67—22no—
436C2×#67—24no—
437C2×#67—24no—
438C2×#67—24no—
439C2×#67—22no—
440C2×#67—22no—
441C2×#67—22no—
442C2×#67—41no—
443C2×#67—41no—
444C2×#67—41no—
445C2×#67—42no—
446C2×#67—42no—
447C2×#67—42no—
448C2×#67—42no—
449C2×#67—42no—
450C2×#67—42no—
451C2×#67C2×D414yes—
452C22×Dic3—22no—
453C22×Dic3—24no—
454C22×Dic3—22no—
455C22×Dic3—24no—
456C22×Dic3—41no—
457C22×Dic3—42no—
458C22×Dic3—42no—
459C22×Dic3—42no—
460C22×Dic3—42no—
461C22×Dic3C2412yes—
462C22×Dic3C2411yescharacteristic
463C22×Dic3C2412yes—
464C22×Dic3C2412yes—
465C22×Dic3C2412yes—
466C22×Dic3C2411yescharacteristic
467C22×Dic3C2411yescharacteristic
468C22×Dic3C2411yescharacteristic
469C22×Dic3C2411yescharacteristic
470#235—416no—
471C2×D12—22no—
472C2×D12—22no—
473C2×D12—22no—
474C2×D12—22no—
475C2×D12—41no—
476C2×D12—41no—
477C2×C4×D3—22no—
478C2×C4×D3—22no—
479C2×C4×D3—22no—
480C2×C4×D3—22no—
481C2×C4×D3—22no—
482C2×C4×D3—22no—
483C2×C4×D3—22no—
484C2×C4×D3—22no—
485C2×C4×D3—22no—
486C2×C4×D3—22no—
487C2×C4×D3—22no—
488C2×C4×D3—416no—
489C2×C4×D3—41no—
490C2×C4×D3—41no—
491C2×C4×D3—42no—
492C2×C4×D3—42no—
493C2×C4×D3—42no—
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—22no—
502C3×C4⋊C4—22no—
503C3×C4⋊C4—42no—
504C3×C4⋊C4—42no—
505C3×C22⋊C4—22no—
506C3×C22⋊C4—24no—
507C3×C22⋊C4—22no—
508C3×C22⋊C4—42no—
509C3×C22⋊C4—42no—
510C3×C22⋊C4—42no—
511C3×C22⋊C4—42no—
512C3×C42—22no—
513#217—24no—
514#217—24no—
515#217—24no—
516#217—22no—
517#217—24no—
518#217—42no—
519#217—42no—
520#217—42no—
521#217C2×D414yes—
522(C2×D3)⋊C4—22no—
523(C2×D3)⋊C4—24no—
524(C2×D3)⋊C4—24no—
525(C2×D3)⋊C4—24no—
526(C2×D3)⋊C4—22no—
527(C2×D3)⋊C4—22no—
528(C2×D3)⋊C4—22no—
529(C2×D3)⋊C4—22no—
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)⋊C4C2×D414yes—
536C4⋊Dic3—24no—
537C4⋊Dic3—22no—
538C4⋊Dic3—22no—
539C4⋊Dic3—22no—
540C4⋊Dic3—22no—
541C4⋊Dic3—22no—
542C4⋊Dic3—24no—
543Dic3⋊C4—22no—
544Dic3⋊C4—22no—
545Dic3⋊C4—22no—
546Dic3⋊C4—24no—
547Dic3⋊C4—42no—
548Dic3⋊C4—42no—
549Dic3⋊C4—42no—
550Dic3⋊C4—42no—
551Dic3⋊C4—42no—
552Dic3⋊C4C2×D414yes—
553C4×Dic3—24no—
554C4×Dic3—42no—
555C4×Dic3C2×D414yes—
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—32no—
568C22×D4—31no—
569C22×D4—31no—
570C22×D4C22×D312yes—
571C22×D4C22×D311yescharacteristic
572C22×D4C22×D311yescharacteristic
573C22×D4C22×D312yes—
574C23×C4—31no—
575C23×C4—31no—
576C23×C4—31no—
577C23×C4—32no—
578C23×C4—32no—
579C23×C4—31no—
580C23×C4—31no—
581C23×C4—31no—
582C23×C4—32no—
583C23×C4—64no—
584C23×C4—64no—
585C23×C4—122no—
586C23×C4C22×D311yescharacteristic
587C23×C4C22×D311yescharacteristic
588C23×C4C22×D312yes—
589#126—68no—
590#125—64no—
591#123—68no—
592#123—64no—
593#123—64no—
594C22⋊Q8—64no—
595C22⋊Q8—64no—
596#121—24no—
597#121—42no—
598#121—44no—
599#121—64no—
600#121—64no—
601#121—64no—
602#121—64no—
603#121—68no—
604#121—124no—
605#121—124no—
606#121—122no—
607#120—64no—
608#120—64no—
609#120—124no—
610C4×D4—24no—
611C4×D4—38no—
612C4×D4—64no—
613C4×D4—64no—
614C4×D4—64no—
615C4×D4—68no—
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—31no—
631C2×C4⋊C4—32no—
632C2×C4⋊C4—32no—
633C2×C4⋊C4—32no—
634C2×C4⋊C4—32no—
635C2×C4⋊C4—32no—
636C2×C4⋊C4—42no—
637C2×C4⋊C4—64no—
638C2×C4⋊C4—122no—
639C2×C4⋊C4C22×D311yescharacteristic
640C2×C4⋊C4C22×D311yescharacteristic
641C2×C4⋊C4C22×D311yescharacteristic
642C2×C4⋊C4C22×D311yescharacteristic
643C2×C4⋊C4C22×D312yes—
644C2×C4⋊C4C22×D312yes—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—31no—
647C2×C22⋊C4—32no—
648C2×C22⋊C4—31no—
649C2×C22⋊C4—32no—
650C2×C22⋊C4—32no—
651C2×C22⋊C4—32no—
652C2×C22⋊C4—32no—
653C2×C22⋊C4—32no—
654C2×C22⋊C4—31no—
655C2×C22⋊C4—31no—
656C2×C22⋊C4—32no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—31no—
659C2×C22⋊C4—31no—
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—124no—
669C2×C22⋊C4C22×D311yescharacteristic
670C2×C22⋊C4C22×D311yescharacteristic
671C2×C22⋊C4C22×D312yes—
672C2×C22⋊C4C22×D312yes—
673C2×C22⋊C4C22×D312yes—
674C2×C22⋊C4C22×D312yes—
675C2×C22⋊C4C22×D312yes—
676C2×C42—31no—
677C2×C42—32no—
678C2×C42—32no—
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#95—32no—
691#95—32no—
692#95—32no—
693#95C22×D312yes—
694#95C22×D312yes—
695C23×C3—21no—
696C23×C3—21no—
697C23×C3—21no—
698C23×C3—21no—
699C23×C3—22no—
700C23×C3—21no—
701C23×C3—22no—
702C23×C3—21no—
703C23×C3—21no—
704C23×C3—22no—
705C23×C3—21no—
706C23×C3—22no—
707C23×C3—22no—
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—22no—
711C23×C3—21no—
712C23×C3—22no—
713C23×C3C22×D412yes—
714C23×C3H(5,𝔽2)12yes—
715C23×C32−1+412yes—
716C23×C3C2511yescharacteristic
717C22×D3—28no—
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—21no—
728C22×D3—21no—
729C22×D3—21no—
730C22×D3—21no—
731C22×D3—21no—
732C22×D3—21no—
733C22×D3—21no—
734C22×D3—21no—
735C22×D3—21no—
736C22×D3—44no—
737C22×D3—44no—
738C22×D3—44no—
739C22×D3—44no—
740C22×D3—44no—
741C22×D3—44no—
742C22×D3C22×D412yes—
743C22×D3C2×#4112yes—
744C22×D3H(5,𝔽2)12yes—
745C3×D4—48no—
746C3×D4—44no—
747C3×D4—44no—
748C3×D4—84no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—28no—
752C2×C3×C4—22no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—21no—
756C2×C3×C4—21no—
757C2×C3×C4—22no—
758C2×C3×C4—21no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—22no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—22no—
767C2×C3×C4—21no—
768C2×C3×C4—22no—
769C2×C3×C4—21no—
770C2×C3×C4—44no—
771C2×C3×C4—84no—
772C2×C3×C4C22×D412yes—
773C2×C3×C4C22×D412yes—
774C2×C3×C4C2×#4112yes—
775C2×C3×C4H(5,𝔽2)12yes—
776#67—28no—
777#67—44no—
778#67—44no—
779#67—44no—
780#67—84no—
781#67—84no—
782#67—84no—
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—21no—
787C2×Dic3—21no—
788C2×Dic3—21no—
789C2×Dic3—21no—
790C2×Dic3—21no—
791C2×Dic3—22no—
792C2×Dic3—22no—
793C2×Dic3—21no—
794C2×Dic3—22no—
795C2×Dic3—21no—
796C2×Dic3—22no—
797C2×Dic3—22no—
798C2×Dic3—22no—
799C2×Dic3—22no—
800C2×Dic3—22no—
801C2×Dic3—22no—
802C2×Dic3—21no—
803C2×Dic3—22no—
804C2×Dic3—22no—
805C2×Dic3—22no—
806C2×Dic3—44no—
807C2×Dic3—84no—
808C2×Dic3—84no—
809C2×Dic3C22×D412yes—
810C2×Dic3C22×D412yes—
811C2×Dic3C22×D412yes—
812C2×Dic3C2×#4112yes—
813D12—44no—
814D12—44no—
815C4×D3—28no—
816C4×D3—28no—
817C4×D3—44no—
818C4×D3—44no—
819C4×D3—44no—
820C4×D3—84no—
821Dic6—44no—
822C24—31no—
823C24—31no—
824C24—31no—
825C24—62no—
826C24—62no—
827C24—62no—
828C24—62no—
829C24—62no—
830C24—121no—
831C24—121no—
832C24C23×D311yescharacteristic
833C24C23×D312yes—
834C24C23×D311yescharacteristic
835#41—1216no—
836C2×Q8—62no—
837C2×Q8—62no—
838C2×Q8—121no—
839C2×D4—22no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—22no—
843C2×D4—24no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—22no—
848C2×D4—34no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
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—62no—
862C2×D4—62no—
863C2×D4—62no—
864C2×D4—64no—
865C2×D4—64no—
866C2×D4—64no—
867C2×D4—121no—
868C2×D4—121no—
869C2×D4—121no—
870C2×D4—121no—
871C2×D4—121no—
872C2×D4—122no—
873C2×D4—122no—
874C2×D4—122no—
875C2×D4—122no—
876C2×D4—122no—
877C2×D4—122no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—24no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—31no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—31no—
888C22×C4—34no—
889C22×C4—34no—
890C22×C4—32no—
891C22×C4—31no—
892C22×C4—32no—
893C22×C4—32no—
894C22×C4—32no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—62no—
898C22×C4—62no—
899C22×C4—62no—
900C22×C4—64no—
901C22×C4—62no—
902C22×C4—62no—
903C22×C4—62no—
904C22×C4—62no—
905C22×C4—62no—
906C22×C4—64no—
907C22×C4—62no—
908C22×C4—62no—
909C22×C4—62no—
910C22×C4—62no—
911C22×C4—62no—
912C22×C4—121no—
913C22×C4—121no—
914C22×C4—1216no—
915C22×C4—122no—
916C22×C4—122no—
917C22×C4—122no—
918C22×C4—121no—
919C22×C4—122no—
920C22×C4—122no—
921C22×C4—122no—
922C22×C4—122no—
923C22×C4D3×D414yes—
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—22no—
936C4⋊C4—34no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—62no—
940C4⋊C4—62no—
941C4⋊C4—62no—
942C4⋊C4—62no—
943C4⋊C4—64no—
944C4⋊C4—64no—
945C4⋊C4—62no—
946C4⋊C4—62no—
947C4⋊C4—64no—
948C4⋊C4—62no—
949C4⋊C4—62no—
950C4⋊C4—122no—
951C4⋊C4—122no—
952C4⋊C4—122no—
953C4⋊C4—122no—
954C4⋊C4—122no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—24no—
958C22⋊C4—34no—
959C22⋊C4—34no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—62no—
965C22⋊C4—62no—
966C22⋊C4—62no—
967C22⋊C4—62no—
968C22⋊C4—64no—
969C22⋊C4—64no—
970C22⋊C4—64no—
971C22⋊C4—62no—
972C22⋊C4—62no—
973C22⋊C4—64no—
974C22⋊C4—64no—
975C22⋊C4—64no—
976C22⋊C4—64no—
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—22no—
986C42—34no—
987C42—64no—
988C42—122no—
989C22×C3—22no—
990C22×C3—22no—
991C22×C3—22no—
992C22×C3—22no—
993C22×C3—22no—
994C22×C3—22no—
995C22×C3—42no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—42no—
999C22×C3—42no—
1000C22×C3—41no—
1001C22×C3—42no—
1002C22×C3—41no—
1003C22×C3—42no—
1004C22×C3—41no—
1005C22×C3—42no—
1006C22×C3—41no—
1007C22×C3—42no—
1008C22×C3—41no—
1009C22×C3#53714yes—
1010C22×C3C23×D411yescharacteristic
1011C22×C3C22×#4111yescharacteristic
1012C22×C3C2×H(5,𝔽2)11yescharacteristic
1013C22×C3C2×H(5,𝔽2)11yescharacteristic
1014C22×C3C2×H(5,𝔽2)11yescharacteristic
1015C22×C3C2×2−1+411yescharacteristic
1016C22×C3#58511yescharacteristic
1017C2×D3—22no—
1018C2×D3—22no—
1019C2×D3—22no—
1020C2×D3—22no—
1021C2×D3—22no—
1022C2×D3—22no—
1023C2×D3—22no—
1024C2×D3—22no—
1025C2×D3—22no—
1026C2×D3—416no—
1027C2×D3—41no—
1028C2×D3—41no—
1029C2×D3—41no—
1030C2×D3—41no—
1031C2×D3—41no—
1032C2×D3—41no—
1033C2×D3—41no—
1034C2×D3—41no—
1035C2×D3—41no—
1036C2×D3—41no—
1037C2×D3—41no—
1038C2×D3—41no—
1039C3×C4—22no—
1040C3×C4—42no—
1041C3×C4—41no—
1042C3×C4—41no—
1043C3×C4—41no—
1044C3×C4—42no—
1045C3×C4—42no—
1046C3×C4#54614yes—
1047Dic3—22no—
1048Dic3—22no—
1049Dic3—22no—
1050Dic3—22no—
1051Dic3—41no—
1052Dic3—42no—
1053Dic3—42no—
1054Dic3—42no—
1055Dic3—42no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—22no—
1061C23—21no—
1062C23—21no—
1063C23—22no—
1064C23—22no—
1065C23—21no—
1066C23—22no—
1067C23—21no—
1068C23—21no—
1069C23—22no—
1070C23—22no—
1071C23—21no—
1072C23—21no—
1073C23—22no—
1074C23—32no—
1075C23—32no—
1076C23—32no—
1077C23—68no—
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—61no—
1092C23—61no—
1093C23—61no—
1094C23—61no—
1095C23—61no—
1096C23—124no—
1097C23—124no—
1098C23—124no—
1099C23—124no—
1100C23—124no—
1101C23—124no—
1102C23C2×D3×D412yes—
1103C23#100412yes—
1104C23#101012yes—
1105C23C24×D311yescharacteristic
1106Q8—124no—
1107D4—44no—
1108D4—48no—
1109D4—44no—
1110D4—68no—
1111D4—84no—
1112D4—124no—
1113D4—124no—
1114D4—124no—
1115D4—124no—
1116D4—124no—
1117D4—244no—
1118D4—244no—
1119D4—244no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—28no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—32no—
1142C2×C4—32no—
1143C2×C4—32no—
1144C2×C4—32no—
1145C2×C4—44no—
1146C2×C4—61no—
1147C2×C4—61no—
1148C2×C4—61no—
1149C2×C4—61no—
1150C2×C4—61no—
1151C2×C4—61no—
1152C2×C4—61no—
1153C2×C4—61no—
1154C2×C4—68no—
1155C2×C4—68no—
1156C2×C4—62no—
1157C2×C4—61no—
1158C2×C4—62no—
1159C2×C4—62no—
1160C2×C4—62no—
1161C2×C4—61no—
1162C2×C4—62no—
1163C2×C4—62no—
1164C2×C4—61no—
1165C2×C4—62no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—84no—
1172C2×C4—124no—
1173C2×C4—124no—
1174C2×C4—124no—
1175C2×C4—124no—
1176C2×C4—244no—
1177C2×C4—244no—
1178C2×C4—244no—
1179C2×C4C2×D3×D412yes—
1180C2×C4C2×D3×D412yes—
1181C2×C4#100412yes—
1182C2×C4D3×#4112yes—
1183C2×C3—24no—
1184C2×C3—81no—
1185C2×C3—82no—
1186C2×C3C2×#53711yescharacteristic
1187C2×C3C2×#54611yescharacteristic
1188C2×C3#348811yescharacteristic
1189C2×C3#349211yescharacteristic
1190C2×C3#349411yescharacteristic
1191C2×C3#353711yescharacteristic
1192C2×C3#354111yescharacteristic
1193D3—42no—
1194D3—42no—
1195D3—42no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—41no—
1203C22—42no—
1204C22—42no—
1205C22—41no—
1206C22—42no—
1207C22—41no—
1208C22—42no—
1209C22—41no—
1210C22—42no—
1211C22—41no—
1212C22—41no—
1213C22—42no—
1214C22—42no—
1215C22—41no—
1216C22—62no—
1217C22—62no—
1218C22—62no—
1219C22—62no—
1220C22—62no—
1221C22—62no—
1222C22—62no—
1223C22—62no—
1224C22—62no—
1225C22—1216no—
1226C22—121no—
1227C22—121no—
1228C22—121no—
1229C22—121no—
1230C22—121no—
1231C22—121no—
1232C22—121no—
1233C22—121no—
1234C22—121no—
1235C22—121no—
1236C22—121no—
1237C22—121no—
1238C22#560814yes—
1239C22C22×D3×D411yescharacteristic
1240C22C2×#100411yescharacteristic
1241C22C2×#100411yescharacteristic
1242C22C2×D3×#4111yescharacteristic
1243C22C2×#101011yescharacteristic
1244C22D3×H(5,𝔽2)11yescharacteristic
1245C22#596811yescharacteristic
1246C4—22no—
1247C4—42no—
1248C4—42no—
1249C4—41no—
1250C4—41no—
1251C4—42no—
1252C4—41no—
1253C4—62no—
1254C4—62no—
1255C4—62no—
1256C4—62no—
1257C4—122no—
1258C4—122no—
1259C4—122no—
1260C4—122no—
1261C4—121no—
1262C4#561014yes—
1263C3#3783611yescharacteristic, complemented, Sylow
1264C2—24no—
1265C2—81no—
1266C2—82no—
1267C2—122no—
1268C2—122no—
1269C2—122no—
1270C2C2×#560811yescharacteristic
1271C2C2×#561011yescharacteristic
1272C2#8637911yescharacteristic
1273C2#8662311yescharacteristic
1274C2#8667811yescharacteristic
1275C2#8672511yescharacteristic
1276C2#8690911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2416C2
hypercenter#2416D3
hypocenterC3#37836
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#5618C2semidirect
2. C2×#5547C2semidirect
3. C3×#2416C2semidirect
4. #82723C2semidirect
5. #82709C2semidirect
6. #82706C2semidirect
7. #82671C2semidirect
8. #82667C2semidirect
9. #82374C2semidirect
10. C4⋊C4×#67C2semidirect
11. C2×#4987C2semidirect
12. #77440C2semidirect
13. #77348C2semidirect
14. #77024C2semidirect
15. #76999C2semidirect
16. #76439C2semidirect
17. #76430C2semidirect
18. #76251C2semidirect
19. #76230C2semidirect
20. #74893C2semidirect
21. #74712C2semidirect
22. #74003C2semidirect
23. #73941C2semidirect
29. C2×C3×#121C22semidirect
37. C2×#938C22semidirect
41. C2×D4×Dic3C22semidirect
51. C2×#892C22semidirect
52. C2×D3×C4⋊C4C22semidirect
53. C2×#890C22semidirect
54. C2×#886C22semidirect
59. C2×#879C22semidirect
63. C3×#396C22semidirect
64. C3×#394C22semidirect
65. C3×#390C22semidirect
66. C3×#389C22semidirect
68. C3×#380C22semidirect
70. #5223C22semidirect
71. #5222C22semidirect
75. #5212C22semidirect
76. #5212C22semidirect
80. #4992C22semidirect
82. #4989C22semidirect
91. #4987C22semidirect
92. #4986C22semidirect
93. #4983C22semidirect
94. #4976C22semidirect
95. #4975C22semidirect
96. Dic3×C4⋊C4C22semidirect
106. #4956C22semidirect
107. #4956C22semidirect
108. #4949C22semidirect
109. #4948C22semidirect
110. #4947C22semidirect
112. #4946C22semidirect
113. #4944C22semidirect
114. #4944C22semidirect
115. #4942C22semidirect
116. #4928C22semidirect
117. #4928C22semidirect
122. #4660C22semidirect
123. #4657C22semidirect
124. #4655C22semidirect
125. #4646C22semidirect
144. #2416D3semidirect
222. C4×#67D4semidirect
309. C2×#121C2×D3semidirect
335. #396C2×D3semidirect
341. #394C2×D3semidirect
349. #390C2×D3semidirect
353. #389C2×D3semidirect
386. #380C2×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×#56182
C2×#55472
C3×#24162
#827232
#827092
#827062
#826712
#826672
#823742
C4⋊C4×#672
C2×#49872
#774402
#773482
#770242
#769992
#764392
#764302
#762512
#762302
#748932
#747122
#740032
#739412
#378363