Finite Group Databasebeta

← #11166139

Subgroups — #11166139

Order 768.

2816 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5612C211yesmaximal, characteristic, complemented
2C2×#5599C211yesmaximal, characteristic, complemented
3C3×#2619C211yesmaximal, characteristic, complemented
4#83187C211yesmaximal, characteristic, complemented
5#83175C211yesmaximal, characteristic, complemented
6#82705C211yesmaximal, characteristic, complemented
7#82705C211yesmaximal, characteristic, complemented
8#82273C211yesmaximal, characteristic, complemented
9#82270C211yesmaximal, characteristic, complemented
10#77160C212yesmaximal, complemented
11#77123C212yesmaximal, complemented
12#77119C212yesmaximal, complemented
13#76974C212yesmaximal, complemented
14#76773C212yesmaximal, complemented
15#76769C212yesmaximal, complemented
16#76764C212yesmaximal, complemented
17#76763C212yesmaximal, complemented
18#76436C211yesmaximal, characteristic, complemented
19#76435C211yesmaximal, characteristic, complemented
20#76321C211yesmaximal, characteristic, complemented
21#76318C211yesmaximal, characteristic, complemented
22#74232C211yesmaximal, characteristic, complemented
23#74231C211yesmaximal, characteristic, complemented
24#42951—31nomaximal, Sylow
25C22×#237C2211yescharacteristic, complemented
26C22×D3×D4C2211yescharacteristic
27C22×#235C2211yescharacteristic
28C2×C3×#127C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic, complemented
31C2×C3×#117C2211yescharacteristic, complemented
32C2×#940C2211yescharacteristic
33C2×#940C2212yescomplemented
34C2×#939C2212yes—
35C2×#939C2212yescomplemented
36C2×#939C2212yescomplemented
37C2×#938C2212yes—
38C2×#938C2211yescharacteristic
39C2×#938C2211yescharacteristic
40C2×#937C2212yes—
41C2×#937C2212yes—
42C2×#937C2212yes—
43C2×#936C2211yescharacteristic
44C2×C4×#67C2211yescharacteristic
45C2×C4×#67C2211yescharacteristic, complemented
46C22×C4⋊Dic3C2211yescharacteristic, complemented
47#5612—28no—
48#5599—28no—
49C2×#897C2211yescharacteristic
50C2×#895C2211yescharacteristic
51C2×#893C2211yescharacteristic
52C2×#887C2211yescharacteristic, complemented
53C2×#884C2212yescomplemented
54C2×#883C2212yes—
55C2×#883C2212yescomplemented
56C2×#882C2212yes—
57C2×#67⋊C4C2212yescomplemented
58C2×D3×C22⋊C4C2212yes—
59C2×C4×D12C2211yescharacteristic
60C3×#394C2212yescomplemented
61C3×#394C2212yescomplemented
62C3×#392C2212yescomplemented
63C3×#392C2212yescomplemented
64C3×#390C2211yescharacteristic
65C3×#390C2211yescharacteristic, complemented
66C3×#382C2211yescharacteristic, complemented
67#5223C2212yes—
68#5223C2212yes—
69#5223C2212yescomplemented
70#5223C2212yescomplemented
71#5221C2211yescharacteristic
72#5221C2211yescharacteristic, complemented
73#5220C2212yescomplemented
74#5220C2212yescomplemented
75#5220C2212yescomplemented
76#5220C2212yescomplemented
77#4994C2211yescharacteristic
78#4994C2211yescharacteristic, complemented
79#4991C2211yescharacteristic
80#4987C2211yescharacteristic
81#4987C2211yescharacteristic, complemented
82#4987C2212yescomplemented
83#4987C2212yescomplemented
84#4981C2211yescharacteristic, complemented
85#4972C2211yescharacteristic, complemented
86#4972C2211yescharacteristic, complemented
87#4961C2212yes—
88#4961C2211yescharacteristic
89#4961C2212yes—
90#4961C2212yescomplemented
91#4961C2212yescomplemented
92#4961C2211yescharacteristic, complemented
93#4961C2212yescomplemented
94#4960C2212yes—
95#4960C2211yescharacteristic
96#4960C2212yes—
97#4959C2212yescomplemented
98#4958C2212yes—
99#4958C2212yescomplemented
100#4958C2212yescomplemented
101#4956C2212yescomplemented
102#4955C2212yes—
103#4953C2211yescharacteristic, complemented
104#4952C2212yescomplemented
105#4951C2212yescomplemented
106#4950C2212yescomplemented
107#4949C2212yescomplemented
108#4948C2212yescomplemented
109#4948C2212yescomplemented
110#4945C2212yescomplemented
111#4939C2211yescharacteristic
112#4939C2211yescharacteristic
113C4×(C2×D3)⋊C4C2211yescharacteristic
114C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
115C4×C4⋊Dic3C2211yescharacteristic, complemented
116#4929C2211yescharacteristic, complemented
117#4929C2211yescharacteristic, complemented
118#4675C2212yes—
119#4675C2212yescomplemented
120#4672C2212yescomplemented
121#4669C2212yes—
122#4665C2212yescomplemented
123#4664C2212yescomplemented
124#4660C2212yescomplemented
125#4655C2212yescomplemented
126C2×#550—31no—
127C2×#546—31no—
128#2813—32no—
129#2688—32no—
130#2673—32no—
131#2669—32no—
132#2668—32no—
133#2630—32no—
134#2619D311yescharacteristic, complemented
135#2617—32no—
136#2534—32no—
137#2448—31no—
138#2445—31no—
139#2433—31no—
140#2431—31no—
141#2421—31no—
142#2420—31no—
143#2416—31no—
144#2416—31no—
145#2408—31no—
146#2407—31no—
147#2392—31no—
148#2311—31no—
149C24×D3C2312yes—
150C22×C3×D4C2311yescharacteristic
151C22×C3×D4C2311yescharacteristic
152C22×C3×D4C2312yes—
153C22×C3×D4C2312yes—
154C22×C3×D4C2312yes—
155C22×C3×D4C2312yes—
156C23×C3×C4C2311yescharacteristic
157C22×#67C2312yes—
158C22×#67C2311yescharacteristic
159C22×#67C2311yescharacteristic
160C22×#67C2312yes—
161C22×#67C2312yes—
162C22×#67C2312yes—
163C22×#67C2312yes—
164C22×#67C2312yes—
165C22×#67C2312yes—
166C23×Dic3C2312yes—
167C23×Dic3C2312yes—
168C2×#237—24no—
169C2×#237—42no—
170C2×#237—42no—
171C2×D3×D4—24no—
172C2×D3×D4—42no—
173C2×D3×D4—42no—
174C2×#235—42no—
175C2×#235—42no—
176C2×#235D418yescomplemented
177C22×D12C2311yescharacteristic
178C22×D12C2312yes—
179C22×D12C2311yescharacteristic
180C22×C4×D3C2311yescharacteristic
181C22×C4×D3C2311yescharacteristic
182C22×C4×D3C2312yes—
183C22×C4×D3C2312yes—
184C22×Dic6C2311yescharacteristic
185C3×#127—42no—
186C3×#121—24no—
187C3×#121—24no—
188C3×#117—42no—
189C2×C3×C4⋊C4C2311yescharacteristic
190C2×C3×C4⋊C4C2311yescharacteristic
191C2×C3×C4⋊C4C2311yescharacteristic
192C2×C3×C4⋊C4C2311yescharacteristic
193C2×C3×C22⋊C4C2312yes—
194C2×C3×C22⋊C4C2312yes—
195C2×C3×C22⋊C4C2312yes—
196C2×C3×C22⋊C4C2312yes—
197C2×C3×C22⋊C4C2312yes—
198C2×C3×C22⋊C4C2311yescharacteristic
199C2×C3×C22⋊C4C2312yes—
200C2×C3×C22⋊C4C2311yescharacteristic
201C2×C3×C42C2311yescharacteristic
202C2×C3×C42C2311yescharacteristic
203C2×#217C2312yes—
204C2×#217C2312yes—
205C2×#217C2312yes—
206C2×#217C2311yescharacteristic
207C2×#217C2311yescharacteristic
208C2×#217C2312yes—
209C2×#217C2312yes—
210C2×#217C2312yes—
211C2×#217C2312yes—
212C2×#217C2312yes—
213#940—28no—
214#940—24no—
215#939—28no—
216#939—44no—
217#939—44no—
218#938—28no—
219#938—42no—
220#938—42no—
221#937—28no—
222#937—44no—
223#937—44no—
224#936—24no—
225C4×#67—24no—
226C4×#67—24no—
227C2×(C2×D3)⋊C4C2312yes—
228C2×(C2×D3)⋊C4C2311yescharacteristic
229C2×(C2×D3)⋊C4C2312yes—
230C2×(C2×D3)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2311yescharacteristic
233C2×(C2×D3)⋊C4C2311yescharacteristic
234C2×(C2×D3)⋊C4C2311yescharacteristic
235C2×(C2×D3)⋊C4C2312yes—
236C2×(C2×D3)⋊C4C2311yescharacteristic
237C2×(C2×D3)⋊C4C2312yes—
238C2×(C2×D3)⋊C4C2312yes—
239C2×(C2×D3)⋊C4C2311yescharacteristic
240C2×(C2×D3)⋊C4C2312yes—
241C2×(C2×D3)⋊C4C2312yes—
242C2×(C2×D3)⋊C4C2311yescharacteristic
243C2×(C2×D3)⋊C4C2311yescharacteristic
244C2×C4⋊Dic3—42no—
245C2×C4⋊Dic3C2312yes—
246C2×C4⋊Dic3C2311yescharacteristic
247C2×C4⋊Dic3C2311yescharacteristic
248C2×C4⋊Dic3C2311yescharacteristic
249C2×C4⋊Dic3C2311yescharacteristic
250C2×C4⋊Dic3C2312yes—
251C2×C4⋊Dic3C2311yescharacteristic
252C2×Dic3⋊C4C2312yes—
253C2×Dic3⋊C4C2312yes—
254C2×Dic3⋊C4C2311yescharacteristic
255C2×Dic3⋊C4C2311yescharacteristic
256C2×Dic3⋊C4C2312yes—
257C2×C4×Dic3C2312yes—
258C2×C4×Dic3C2311yescharacteristic
259C2×C4×Dic3C2311yescharacteristic
260#897—24no—
261#895—24no—
262#893—24no—
263#887—24no—
264#884—28no—
265#883—28no—
266#883—44no—
267#882—44no—
268#67⋊C4—28no—
269D3×C22⋊C4—28no—
270C4×D12—42no—
271C3×#95C2312yes—
272C3×#95C2312yes—
273C3⋊#95C2311yescharacteristic
274C3⋊#95C2312yes—
275C3⋊#95C2312yes—
276C3⋊#95C2311yescharacteristic
277C3⋊#95C2312yes—
278C3⋊#95C2312yes—
279C3⋊#95C2311yescharacteristic
280C3⋊#95C2312yes—
281C3⋊#95C2312yes—
282C3⋊#95C2312yes—
283C3⋊#95C2312yes—
284C3⋊#95C2311yescharacteristic
285C3⋊#95C2311yescharacteristic
286C3⋊#95C2311yescharacteristic
287C22×#41—31no—
288C22×#41—31no—
289C23×D4—31no—
290#550—68no—
291#546—68no—
292C2×#127—32no—
293C2×#127—31no—
294C2×#127C2×D311yescharacteristic
295C2×#124—31no—
296C2×#123—32no—
297C2×#123—32no—
298C2×C22⋊Q8—31no—
299C2×#121—32no—
300C2×#121—32no—
301C2×#121—31no—
302C2×#121—31no—
303C2×#121—32no—
304C2×#121—32no—
305C2×#121—31no—
306C2×#121—32no—
307C2×#121C2×D311yescharacteristic
308C2×#121C2×D311yescharacteristic, complemented
309C2×#120—32no—
310C2×#120—32no—
311C2×#120—32no—
312C2×#120—32no—
313C2×C4×Q8—31no—
314C2×C4×D4—31no—
315C2×C4×D4—31no—
316C2×C4×D4—31no—
317C2×C4×D4—32no—
318C2×C4×D4—31no—
319C2×#117C2×D311yescharacteristic, complemented
320C22×C4⋊C4—31no—
321C22×C22⋊C4—32no—
322#400—32no—
323#399—32no—
324#398—31no—
325#397—32no—
326#397—31no—
327#397—32no—
328#397—32no—
329#396—31no—
330#396—31no—
331#396—32no—
332#396—32no—
333#394—31no—
334#394—32no—
335#394—32no—
336#394—32no—
337#394—32no—
338#394—31no—
339#394—31no—
340#394—32no—
341#394—32no—
342#394—32no—
343#394C2×D312yescomplemented
344#394C2×D312yescomplemented
345#392—32no—
346#392—32no—
347#392—32no—
348#392—32no—
349#392—32no—
350#392—31no—
351#392—32no—
352#392C2×D312yescomplemented
353#392C2×D312yescomplemented
354#391—31no—
355#391—31no—
356#390—31no—
357#390—31no—
358#390—31no—
359#390—31no—
360#390C2×D311yescharacteristic
361#390C2×D311yescharacteristic, complemented
362#389—31no—
363#389—31no—
364#388—32no—
365#388—32no—
366#388—32no—
367#387—32no—
368#386—32no—
369#386—32no—
370#386—32no—
371#386—32no—
372#386—32no—
373#386—32no—
374#386—32no—
375#386—32no—
376#386—32no—
377#385—32no—
378#382C2×D311yescharacteristic, complemented
379#381—32no—
380#380—32no—
381#380—32no—
382#380—31no—
383#380—31no—
384#379—32no—
385C4×C4⋊C4—31no—
386C4×C22⋊C4—31no—
387C4×C22⋊C4—31no—
388C24×C3C2412yes—
389C24×C3C2412yes—
390C24×C3C2411yescharacteristic
391C23×D3—24no—
392C23×D3—24no—
393C23×D3—42no—
394C23×D3—42no—
395C23×D3—42no—
396C23×D3—42no—
397C23×D3—42no—
398C23×D3C2411yescharacteristic
399C23×D3C2412yes—
400C23×D3C2411yescharacteristic
401C2×C3×D4—24no—
402C2×C3×D4—24no—
403C2×C3×D4—22no—
404C2×C3×D4—22no—
405C2×C3×D4—22no—
406C2×C3×D4—22no—
407C2×C3×D4—22no—
408C2×C3×D4—22no—
409C2×C3×D4—42no—
410C2×C3×D4—42no—
411C2×C3×D4—42no—
412C2×C3×D4—42no—
413C2×C3×D4—42no—
414C2×C3×D4—42no—
415C2×C3×D4—42no—
416C2×C3×D4—42no—
417C2×C3×D4—42no—
418C2×C3×D4—42no—
419C22×C3×C4—22no—
420C22×C3×C4—22no—
421C22×C3×C4C2×D414yes—
422C22×C3×C4C2411yescharacteristic
423C22×C3×C4C2411yescharacteristic
424C22×C3×C4C2411yescharacteristic
425C22×C3×C4C2412yes—
426C22×C3×C4C2412yes—
427C22×C3×C4C2411yescharacteristic
428C22×C3×C4C2411yescharacteristic
429C22×C3×C4C2411yescharacteristic
430C2×#67—22no—
431C2×#67—22no—
432C2×#67—24no—
433C2×#67—24no—
434C2×#67—22no—
435C2×#67—24no—
436C2×#67—24no—
437C2×#67—24no—
438C2×#67—24no—
439C2×#67—22no—
440C2×#67—42no—
441C2×#67—42no—
442C2×#67—42no—
443C2×#67—42no—
444C2×#67—42no—
445C2×#67—42no—
446C2×#67—42no—
447C2×#67—41no—
448C2×#67—41no—
449C2×#67—42no—
450C2×#67—42no—
451C2×#67—42no—
452C2×#67—42no—
453C2×#67—42no—
454C2×#67—42no—
455C2×#67—42no—
456C2×#67C2×D418yes—
457C22×Dic3—24no—
458C22×Dic3—42no—
459C22×Dic3—42no—
460C22×Dic3—42no—
461C22×Dic3—42no—
462C22×Dic3—42no—
463C22×Dic3C2411yescharacteristic
464C22×Dic3C2411yescharacteristic
465C22×Dic3C2411yescharacteristic
466C22×Dic3C2412yes—
467C22×Dic3C2412yes—
468C22×Dic3C2411yescharacteristic
469C22×Dic3C2411yescharacteristic
470C22×Dic3C2412yes—
471C22×Dic3C2411yescharacteristic
472#237—416no—
473D3×D4—416no—
474#235—416no—
475C2×D12—22no—
476C2×D12—22no—
477C2×D12—22no—
478C2×D12—24no—
479C2×D12—41no—
480C2×D12—41no—
481C2×D12—42no—
482C2×D12—42no—
483C2×D12C2×D414yes—
484C2×C4×D3—22no—
485C2×C4×D3—22no—
486C2×C4×D3—22no—
487C2×C4×D3—22no—
488C2×C4×D3—22no—
489C2×C4×D3—22no—
490C2×C4×D3—24no—
491C2×C4×D3—42no—
492C2×C4×D3—42no—
493C2×C4×D3—42no—
494C2×C4×D3—42no—
495C2×C4×D3C2×D418yes—
496C2×Dic6—22no—
497C2×Dic6—22no—
498C2×Dic6C2×D414yes—
499C3×C4⋊C4—22no—
500C3×C4⋊C4—22no—
501C3×C4⋊C4—41no—
502C3×C4⋊C4—41no—
503C3×C22⋊C4—24no—
504C3×C22⋊C4—24no—
505C3×C22⋊C4—42no—
506C3×C22⋊C4—42no—
507C3×C22⋊C4—42no—
508C3×C22⋊C4—42no—
509C3×C22⋊C4—41no—
510C3×C22⋊C4—41no—
511C3×C42—22no—
512C3×C42—22no—
513#217—22no—
514#217—22no—
515#217—24no—
516#217—24no—
517#217—24no—
518#217—42no—
519#217—42no—
520#217—42no—
521#217—42no—
522#217—42no—
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—24no—
530(C2×D3)⋊C4—22no—
531(C2×D3)⋊C4—41no—
532(C2×D3)⋊C4—41no—
533(C2×D3)⋊C4—42no—
534(C2×D3)⋊C4—42no—
535(C2×D3)⋊C4—41no—
536(C2×D3)⋊C4—41no—
537(C2×D3)⋊C4—42no—
538(C2×D3)⋊C4—42no—
539(C2×D3)⋊C4—42no—
540C4⋊Dic3—22no—
541C4⋊Dic3—22no—
542C4⋊Dic3—24no—
543C4⋊Dic3—22no—
544C4⋊Dic3—41no—
545C4⋊Dic3—42no—
546C4⋊Dic3—41no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—24no—
550Dic3⋊C4—24no—
551Dic3⋊C4—42no—
552C4×Dic3—22no—
553C4×Dic3—22no—
554C4×Dic3—24no—
555C25—32no—
556C2×#41—38no—
557C2×#41—64no—
558C2×#41—122no—
559C2×#41—122no—
560C2×#41—122no—
561C2×#41—122no—
562C22×Q8—31no—
563C22×D4—32no—
564C22×D4—31no—
565C22×D4—32no—
566C22×D4—31no—
567C22×D4—32no—
568C22×D4—32no—
569C22×D4—32no—
570C22×D4—32no—
571C22×D4—32no—
572C22×D4—31no—
573C22×D4—31no—
574C22×D4—32no—
575C22×D4—64no—
576C22×D4—122no—
577C22×D4—122no—
578C22×D4C22×D311yescharacteristic
579C22×D4C22×D311yescharacteristic
580C22×D4C22×D312yes—
581C22×D4C22×D312yes—
582C22×D4C22×D312yes—
583C22×D4C22×D312yes—
584C23×C4—32no—
585C23×C4—32no—
586C23×C4—32no—
587C23×C4—31no—
588C23×C4—31no—
589C23×C4—32no—
590C23×C4C22×D311yescharacteristic
591#127—42no—
592#127—68no—
593#127—64no—
594#124—64no—
595#123—68no—
596#123—124no—
597C22⋊Q8—64no—
598#121—24no—
599#121—24no—
600#121—68no—
601#121—64no—
602#121—68no—
603#121—68no—
604#121—124no—
605#121—124no—
606#121—122no—
607#121—122no—
608#120—68no—
609#120—124no—
610#120—124no—
611#120—124no—
612C4×Q8—64no—
613C4×D4—68no—
614C4×D4—64no—
615C4×D4—64no—
616C4×D4—64no—
617C4×D4—122no—
618#117—42no—
619C2×C4⋊C4—31no—
620C2×C4⋊C4—31no—
621C2×C4⋊C4—31no—
622C2×C4⋊C4—31no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—32no—
625C2×C4⋊C4—32no—
626C2×C4⋊C4—31no—
627C2×C4⋊C4—32no—
628C2×C4⋊C4—31no—
629C2×C4⋊C4—32no—
630C2×C4⋊C4—31no—
631C2×C4⋊C4—122no—
632C2×C4⋊C4C22×D311yescharacteristic
633C2×C4⋊C4C22×D311yescharacteristic
634C2×C4⋊C4C22×D311yescharacteristic
635C2×C4⋊C4C22×D311yescharacteristic
636C2×C22⋊C4—32no—
637C2×C22⋊C4—31no—
638C2×C22⋊C4—31no—
639C2×C22⋊C4—32no—
640C2×C22⋊C4—32no—
641C2×C22⋊C4—31no—
642C2×C22⋊C4—32no—
643C2×C22⋊C4—32no—
644C2×C22⋊C4—32no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—31no—
647C2×C22⋊C4—31no—
648C2×C22⋊C4—32no—
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—32no—
658C2×C22⋊C4—32no—
659C2×C22⋊C4—32no—
660C2×C22⋊C4—32no—
661C2×C22⋊C4—31no—
662C2×C22⋊C4—31no—
663C2×C22⋊C4—68no—
664C2×C22⋊C4C22×D312yes—
665C2×C22⋊C4C22×D312yes—
666C2×C22⋊C4C22×D311yescharacteristic
667C2×C22⋊C4C22×D311yescharacteristic
668C2×C22⋊C4C22×D312yes—
669C2×C22⋊C4C22×D312yes—
670C2×C22⋊C4C22×D312yes—
671C2×C22⋊C4C22×D312yes—
672C2×C42—31no—
673C2×C42—31no—
674C2×C42—32no—
675C2×C42C22×D311yescharacteristic
676C2×C42C22×D311yescharacteristic
677#95—31no—
678#95—31no—
679#95—31no—
680#95—31no—
681#95—31no—
682#95—31no—
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#95C22×D312yes—
692#95C22×D312yes—
693C23×C3—21no—
694C23×C3—21no—
695C23×C3—21no—
696C23×C3—21no—
697C23×C3—21no—
698C23×C3—21no—
699C23×C3—22no—
700C23×C3—22no—
701C23×C3—22no—
702C23×C3—22no—
703C23×C3—22no—
704C23×C3—22no—
705C23×C3—22no—
706C23×C3—22no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—22no—
711C23×C3—22no—
712C23×C3—22no—
713C23×C3C22×D412yes—
714C23×C3C2511yescharacteristic
715C22×D3—21no—
716C22×D3—21no—
717C22×D3—22no—
718C22×D3—22no—
719C22×D3—21no—
720C22×D3—21no—
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—22no—
724C22×D3—22no—
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—48no—
735C22×D3—48no—
736C22×D3—84no—
737C22×D3—84no—
738C22×D3—84no—
739C22×D3—84no—
740C22×D3—84no—
741C22×D3C22×D414yes—
742C22×D3H(5,𝔽2)12yes—
743C3×D4—44no—
744C3×D4—44no—
745C3×D4—84no—
746C3×D4—84no—
747C3×D4—84no—
748C3×D4—84no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—28no—
752C2×C3×C4—22no—
753C2×C3×C4—22no—
754C2×C3×C4—22no—
755C2×C3×C4—22no—
756C2×C3×C4—21no—
757C2×C3×C4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—21no—
767C2×C3×C4—21no—
768C2×C3×C4—22no—
769C2×C3×C4—22no—
770C2×C3×C4C22×D412yes—
771C2×C3×C4C22×D412yes—
772C2×C3×C4H(5,𝔽2)12yes—
773C2×C3×C4H(5,𝔽2)12yes—
774#67—48no—
775#67—48no—
776#67—44no—
777#67—48no—
778#67—44no—
779#67—48no—
780#67—84no—
781#67—84no—
782#67—84no—
783C2×Dic3—21no—
784C2×Dic3—22no—
785C2×Dic3—22no—
786C2×Dic3—21no—
787C2×Dic3—21no—
788C2×Dic3—21no—
789C2×Dic3—21no—
790C2×Dic3—21no—
791C2×Dic3—21no—
792C2×Dic3—22no—
793C2×Dic3—21no—
794C2×Dic3—22no—
795C2×Dic3—22no—
796C2×Dic3—22no—
797C2×Dic3—21no—
798C2×Dic3—21no—
799C2×Dic3—21no—
800C2×Dic3—22no—
801C2×Dic3—21no—
802C2×Dic3—22no—
803C2×Dic3—21no—
804C2×Dic3—21no—
805C2×Dic3—21no—
806C2×Dic3—21no—
807C2×Dic3—21no—
808C2×Dic3—48no—
809C2×Dic3—84no—
810C2×Dic3C22×D414yes—
811C2×Dic3H(5,𝔽2)12yes—
812D12—28no—
813D12—44no—
814D12—84no—
815C4×D3—48no—
816C4×D3—44no—
817C4×D3—44no—
818C4×D3—84no—
819Dic6—28no—
820C24—31no—
821C24—32no—
822C24—31no—
823C24—64no—
824C24—64no—
825C24—122no—
826C24—122no—
827C24—122no—
828C24—122no—
829C24—122no—
830C24C23×D312yes—
831C24C23×D312yes—
832C24C23×D311yescharacteristic
833#41—1216no—
834#41—1216no—
835C2×Q8—34no—
836C2×Q8—62no—
837C2×Q8—62no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—38no—
847C2×D4—34no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—62no—
859C2×D4—64no—
860C2×D4—64no—
861C2×D4—64no—
862C2×D4—62no—
863C2×D4—64no—
864C2×D4—64no—
865C2×D4—62no—
866C2×D4—62no—
867C2×D4—62no—
868C2×D4—64no—
869C2×D4—64no—
870C2×D4—62no—
871C2×D4—62no—
872C2×D4—121no—
873C2×D4—121no—
874C2×D4—122no—
875C2×D4—122no—
876C2×D4—122no—
877C2×D4—122no—
878C2×D4—122no—
879C2×D4—122no—
880C2×D4—122no—
881C2×D4—122no—
882C2×D4—121no—
883C2×D4—122no—
884C2×D4—121no—
885C2×D4—122no—
886C2×D4—122no—
887C2×D4—122no—
888C2×D4—122no—
889C2×D4—122no—
890C2×D4—122no—
891C2×D4—122no—
892C2×D4—1216no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—32no—
896C22×C4—31no—
897C22×C4—38no—
898C22×C4—31no—
899C22×C4—31no—
900C22×C4—32no—
901C22×C4—32no—
902C22×C4—31no—
903C22×C4—31no—
904C22×C4—31no—
905C22×C4—64no—
906C22×C4—64no—
907C22×C4—62no—
908C22×C4—62no—
909C22×C4—62no—
910C22×C4—62no—
911C22×C4—62no—
912C22×C4—62no—
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—122no—
922C22×C4D3×D414yes—
923C22×C4C23×D311yescharacteristic
924C22×C4C23×D311yescharacteristic
925C22×C4C23×D311yescharacteristic
926C22×C4C23×D312yes—
927C22×C4C23×D312yes—
928C22×C4C23×D311yescharacteristic
929C22×C4C23×D311yescharacteristic
930C22×C4C23×D311yescharacteristic
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—64no—
936C4⋊C4—64no—
937C4⋊C4—64no—
938C4⋊C4—62no—
939C4⋊C4—62no—
940C4⋊C4—62no—
941C4⋊C4—62no—
942C4⋊C4—62no—
943C4⋊C4—122no—
944C4⋊C4—121no—
945C4⋊C4—122no—
946C4⋊C4—121no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—64no—
956C22⋊C4—62no—
957C22⋊C4—64no—
958C22⋊C4—64no—
959C22⋊C4—62no—
960C22⋊C4—64no—
961C22⋊C4—64no—
962C22⋊C4—64no—
963C22⋊C4—64no—
964C22⋊C4—62no—
965C22⋊C4—62no—
966C22⋊C4—62no—
967C22⋊C4—62no—
968C22⋊C4—121no—
969C22⋊C4—121no—
970C22⋊C4—122no—
971C22⋊C4—122no—
972C22⋊C4—122no—
973C22⋊C4—122no—
974C22⋊C4—122no—
975C22⋊C4—121no—
976C22⋊C4—121no—
977C22⋊C4—122no—
978C22⋊C4—122no—
979C22⋊C4—122no—
980C22⋊C4—122no—
981C22⋊C4—122no—
982C42—22no—
983C42—22no—
984C42—64no—
985C42—62no—
986C42—62no—
987C22×C3—22no—
988C22×C3—22no—
989C22×C3—22no—
990C22×C3—41no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—42no—
995C22×C3—42no—
996C22×C3—42no—
997C22×C3—42no—
998C22×C3—42no—
999C22×C3—42no—
1000C22×C3—42no—
1001C22×C3—42no—
1002C22×C3—42no—
1003C22×C3—42no—
1004C22×C3—42no—
1005C22×C3—42no—
1006C22×C3—42no—
1007C22×C3—42no—
1008C22×C3C23×D411yescharacteristic
1009C22×C3C2×H(5,𝔽2)11yescharacteristic
1010C22×C3C2×H(5,𝔽2)11yescharacteristic
1011C22×C3C2×H(5,𝔽2)11yescharacteristic
1012C22×C3C2×H(5,𝔽2)11yescharacteristic
1013C22×C3#58511yescharacteristic
1014C22×C3#58511yescharacteristic
1015C2×D3—24no—
1016C2×D3—24no—
1017C2×D3—24no—
1018C2×D3—22no—
1019C2×D3—22no—
1020C2×D3—22no—
1021C2×D3—41no—
1022C2×D3—41no—
1023C2×D3—42no—
1024C2×D3—42no—
1025C2×D3—42no—
1026C2×D3—41no—
1027C2×D3—42no—
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—816no—
1037C3×C4—22no—
1038C3×C4—42no—
1039C3×C4—42no—
1040C3×C4—41no—
1041C3×C4—41no—
1042C3×C4—41no—
1043C3×C4—41no—
1044C3×C4#53414yes—
1045Dic3—24no—
1046Dic3—22no—
1047Dic3—41no—
1048Dic3—41no—
1049Dic3—41no—
1050Dic3—41no—
1051Dic3—41no—
1052Dic3—42no—
1053Dic3—42no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—34no—
1075C23—32no—
1076C23—61no—
1077C23—61no—
1078C23—62no—
1079C23—61no—
1080C23—62no—
1081C23—61no—
1082C23—62no—
1083C23—62no—
1084C23—62no—
1085C23—62no—
1086C23—61no—
1087C23—61no—
1088C23—61no—
1089C23—61no—
1090C23—61no—
1091C23—61no—
1092C23—61no—
1093C23—61no—
1094C23—61no—
1095C23—128no—
1096C23—128no—
1097C23—244no—
1098C23—244no—
1099C23—244no—
1100C23—244no—
1101C23—244no—
1102C23C2×D3×D412yes—
1103C23C24×D311yescharacteristic
1104Q8—68no—
1105D4—44no—
1106D4—44no—
1107D4—68no—
1108D4—84no—
1109D4—84no—
1110D4—84no—
1111D4—84no—
1112D4—124no—
1113D4—128no—
1114D4—124no—
1115D4—128no—
1116D4—128no—
1117D4—124no—
1118D4—128no—
1119D4—244no—
1120D4—244no—
1121D4—244no—
1122D4—244no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—28no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—34no—
1145C2×C4—32no—
1146C2×C4—61no—
1147C2×C4—62no—
1148C2×C4—62no—
1149C2×C4—61no—
1150C2×C4—61no—
1151C2×C4—61no—
1152C2×C4—61no—
1153C2×C4—61no—
1154C2×C4—61no—
1155C2×C4—61no—
1156C2×C4—61no—
1157C2×C4—61no—
1158C2×C4—61no—
1159C2×C4—62no—
1160C2×C4—62no—
1161C2×C4—62no—
1162C2×C4—62no—
1163C2×C4—61no—
1164C2×C4—61no—
1165C2×C4—62no—
1166C2×C4—61no—
1167C2×C4—62no—
1168C2×C4—61no—
1169C2×C4—61no—
1170C2×C4—61no—
1171C2×C4—128no—
1172C2×C4—128no—
1173C2×C4—124no—
1174C2×C4—124no—
1175C2×C4—244no—
1176C2×C4—244no—
1177C2×C4C2×D3×D412yes—
1178C2×C4C2×D3×D412yes—
1179C2×C4#100412yes—
1180C2×C4#100912yes—
1181C2×C3—42no—
1182C2×C3—82no—
1183C2×C3—82no—
1184C2×C3C2×#53411yescharacteristic
1185C2×C3#348811yescharacteristic
1186C2×C3#348811yescharacteristic
1187C2×C3#354211yescharacteristic
1188C2×C3#354311yescharacteristic
1189C2×C3#354611yescharacteristic
1190C2×C3#356211yescharacteristic
1191D3—44no—
1192D3—42no—
1193D3—81no—
1194C22—22no—
1195C22—22no—
1196C22—22no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—64no—
1216C22—62no—
1217C22—64no—
1218C22—62no—
1219C22—64no—
1220C22—62no—
1221C22—121no—
1222C22—122no—
1223C22—121no—
1224C22—122no—
1225C22—121no—
1226C22—121no—
1227C22—122no—
1228C22—122no—
1229C22—121no—
1230C22—121no—
1231C22—121no—
1232C22—121no—
1233C22—121no—
1234C22—121no—
1235C22—121no—
1236C22—2416no—
1237C22C22×D3×D411yescharacteristic
1238C22C2×#100411yescharacteristic
1239C22C2×#100911yescharacteristic
1240C22D3×H(5,𝔽2)11yescharacteristic
1241C22D3×H(5,𝔽2)11yescharacteristic
1242C22#596611yescharacteristic
1243C22#596611yescharacteristic
1244C4—22no—
1245C4—41no—
1246C4—41no—
1247C4—42no—
1248C4—42no—
1249C4—41no—
1250C4—41no—
1251C4—62no—
1252C4—64no—
1253C4—121no—
1254C4—121no—
1255C4—121no—
1256C4—121no—
1257C4—121no—
1258C4—122no—
1259C4—122no—
1260C4#560514yes—
1261C3#4295111yescharacteristic, complemented, Sylow
1262C2—42no—
1263C2—82no—
1264C2—82no—
1265C2—122no—
1266C2—124no—
1267C2—241no—
1268C2C2×#560511yescharacteristic
1269C2#8632411yescharacteristic
1270C2#8633111yescharacteristic
1271C2#8633111yescharacteristic
1272C2#8633511yescharacteristic
1273C2#8648011yescharacteristic
1274C2#8649311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2619C2
hypercenter#2619D3
hypocenterC3#42951
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2619

Complements

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

NH ≅ G/Ntype
1. C2×#5612C2semidirect
2. C2×#5599C2semidirect
3. C3×#2619C2semidirect
4. #83187C2semidirect
5. #83175C2semidirect
6. #82705C2semidirect
7. #82705C2semidirect
8. #82273C2semidirect
9. #82270C2semidirect
10. #77160C2semidirect
11. #77123C2semidirect
12. #77119C2semidirect
13. #76974C2semidirect
14. #76773C2semidirect
15. #76769C2semidirect
16. #76764C2semidirect
17. #76763C2semidirect
18. #76436C2semidirect
19. #76435C2semidirect
20. #76321C2semidirect
21. #76318C2semidirect
22. #74232C2semidirect
23. #74231C2semidirect
25. C22×#237C22semidirect
30. C2×C3×#121C22semidirect
31. C2×C3×#117C22semidirect
33. C2×#940C22semidirect
35. C2×#939C22semidirect
36. C2×#939C22semidirect
45. C2×C4×#67C22semidirect
46. C22×C4⋊Dic3C22semidirect
52. C2×#887C22semidirect
53. C2×#884C22semidirect
55. C2×#883C22semidirect
57. C2×#67⋊C4C22semidirect
60. C3×#394C22semidirect
61. C3×#394C22semidirect
62. C3×#392C22semidirect
63. C3×#392C22semidirect
65. C3×#390C22semidirect
66. C3×#382C22semidirect
69. #5223C22semidirect
70. #5223C22semidirect
72. #5221C22semidirect
73. #5220C22semidirect
74. #5220C22semidirect
75. #5220C22semidirect
76. #5220C22semidirect
78. #4994C22semidirect
81. #4987C22semidirect
82. #4987C22semidirect
83. #4987C22semidirect
84. #4981C22semidirect
85. #4972C22semidirect
86. #4972C22semidirect
90. #4961C22semidirect
91. #4961C22semidirect
92. #4961C22semidirect
93. #4961C22semidirect
97. #4959C22semidirect
99. #4958C22semidirect
100. #4958C22semidirect
101. #4956C22semidirect
103. #4953C22semidirect
104. #4952C22semidirect
105. #4951C22semidirect
106. #4950C22semidirect
107. #4949C22semidirect
108. #4948C22semidirect
109. #4948C22semidirect
110. #4945C22semidirect
114. C4×(C2×D3)⋊C4C22semidirect
115. C4×C4⋊Dic3C22semidirect
116. #4929C22semidirect
117. #4929C22semidirect
119. #4675C22semidirect
120. #4672C22semidirect
122. #4665C22semidirect
123. #4664C22semidirect
124. #4660C22semidirect
125. #4655C22semidirect
134. #2619D3semidirect
176. C2×#235D4semidirect
308. C2×#121C2×D3semidirect
319. C2×#117C2×D3semidirect
343. #394C2×D3semidirect
344. #394C2×D3semidirect
352. #392C2×D3semidirect
353. #392C2×D3semidirect
361. #390C2×D3semidirect
378. #382C2×D3semidirect
1261. C3#42951semidirect

Maximal subgroups

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

subgroupindex
C2×#56122
C2×#55992
C3×#26192
#831872
#831752
#827052
#822732
#822702
#771602
#771232
#771192
#769742
#767732
#767692
#767642
#767632
#764362
#764352
#763212
#763182
#742322
#742312
#429513