Finite Group Databasebeta

← #11223209

Subgroups — #11223209

Order 768.

2890 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5582C211yesmaximal, characteristic, complemented
2C2×D4×D12C211yesmaximal, characteristic
3C3×#2367C211yesmaximal, characteristic, complemented
4#82960C211yesmaximal, characteristic, complemented
5#82960C211yesmaximal, characteristic, complemented
6#82495C211yesmaximal, characteristic, complemented
7#82362C211yesmaximal, characteristic, complemented
8#76620C211yesmaximal, characteristic, complemented
9#76533C211yesmaximal, characteristic, complemented
10#76431C211yesmaximal, characteristic, complemented
11#76428C211yesmaximal, characteristic, complemented
12#75923C212yesmaximal, complemented
13#75920C212yesmaximal, complemented
14#75917C212yesmaximal, complemented
15#75526C212yesmaximal, complemented
16#74632C212yesmaximal, complemented
17#74599C212yesmaximal, complemented
18#73788C211yesmaximal, characteristic, complemented
19#73780C211yesmaximal, characteristic, complemented
20#73777C211yesmaximal, characteristic, complemented
21#73649C211yesmaximal, characteristic, complemented
22#73603C212yesmaximal, complemented
23#73588C212yesmaximal, complemented
24#44874—31nomaximal, Sylow
25C22×D3×D4C2211yescharacteristic
26C22×D3×D4C2211yescharacteristic
27C23×D12C2212yes—
28C2×C3×#124C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic, complemented
30C2×C3×C4×D4C2211yescharacteristic
31C2×#947C2211yescharacteristic, complemented
32C2×#947C2211yescharacteristic, complemented
33C2×#946C2211yescharacteristic, complemented
34C2×#946C2211yescharacteristic, complemented
35C2×#930C2212yes—
36C2×#924C2212yescomplemented
37#5582—28no—
38D4×D12—28no—
39C2×#896C2212yescomplemented
40C2×#895C2211yescharacteristic
41C2×#895C2211yescharacteristic
42C2×#894C2212yescomplemented
43C2×#894C2212yescomplemented
44C2×#893C2211yescharacteristic, complemented
45C2×#892C2211yescharacteristic, complemented
46C2×#888C2211yescharacteristic, complemented
47C2×#882C2212yes—
48C2×#882C2212yes—
49C2×D3×C22⋊C4C2212yescomplemented
50C2×#876C2212yescomplemented
51C2×#875C2212yescomplemented
52C2×#875C2212yescomplemented
53C2×#874C2211yescharacteristic
54C2×C4×D12C2211yescharacteristic
55C2×C4×D12C2211yescharacteristic, complemented
56C2×#872C2211yescharacteristic, complemented
57C3×#391C2211yescharacteristic, complemented
58C3×#390C2211yescharacteristic
59C3×#388C2212yescomplemented
60C3×#388C2212yescomplemented
61C3×#385C2212yescomplemented
62C3×C4×C4⋊C4C2211yescharacteristic, complemented
63C3×C4×C4⋊C4C2211yescharacteristic, complemented
64C3×C4×C22⋊C4C2212yescomplemented
65#5221C2211yescharacteristic
66#5221C2211yescharacteristic
67#5210C2212yescomplemented
68#4994C2212yescomplemented
69#4993C2211yescharacteristic, complemented
70#4992C2211yescharacteristic, complemented
71#4991C2211yescharacteristic
72#4991C2212yescomplemented
73#4991C2212yescomplemented
74#4988C2211yescharacteristic, complemented
75#4987C2211yescharacteristic, complemented
76#4984C2211yescharacteristic, complemented
77#4982C2211yescharacteristic, complemented
78#4959C2212yescomplemented
79#4959C2212yescomplemented
80#4959C2212yescomplemented
81#4959C2212yescomplemented
82#4957C2212yescomplemented
83#4957C2212yescomplemented
84#4956C2212yescomplemented
85#4956C2212yescomplemented
86#4955C2212yescomplemented
87#4955C2212yescomplemented
88#4955C2212yescomplemented
89#4955C2212yescomplemented
90#4955C2212yescomplemented
91#4955C2212yescomplemented
92#4955C2212yescomplemented
93#4948C2212yescomplemented
94#4947C2212yescomplemented
95#4940C2212yescomplemented
96#4940C2212yescomplemented
97#4939C2211yescharacteristic, complemented
98#4939C2211yescharacteristic, complemented
99#4939C2211yescharacteristic, complemented
100#4939C2212yescomplemented
101#4939C2212yescomplemented
102C4×(C2×D3)⋊C4C2212yescomplemented
103C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
104C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
105C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
106C4×Dic3⋊C4C2211yescharacteristic, complemented
107#4928C2211yescharacteristic, complemented
108#4675C2211yescharacteristic, complemented
109#4675C2211yescharacteristic, complemented
110#4675C2212yescomplemented
111#4673C2212yescomplemented
112#4672C2211yescharacteristic
113#4672C2212yes—
114#4672C2212yescomplemented
115#4672C2212yescomplemented
116#4672C2212yescomplemented
117#4672C2212yescomplemented
118#4670C2212yescomplemented
119#4669C2212yescomplemented
120#4665C2212yescomplemented
121#4665C2212yescomplemented
122#4665C2212yescomplemented
123#4665C2212yescomplemented
124#4660C2211yescharacteristic, complemented
125#4647C2212yescomplemented
126C2×D42—31no—
127C2×#542—31no—
128#2697—32no—
129#2685—32no—
130#2684—32no—
131#2681—32no—
132#2559—32no—
133#2544—31no—
134#2491—31no—
135#2472—32no—
136#2452—31no—
137#2445—31no—
138#2435—32no—
139#2435—31no—
140#2435—31no—
141#2426—31no—
142#2415—31no—
143#2405—32no—
144#2395—31no—
145#2367D311yescharacteristic, complemented
146#2363—31no—
147D4×C22⋊C4—31no—
148#2309—31no—
149C24×D3C2312yes—
150C24×D3C2312yes—
151C22×C3×Q8C2311yescharacteristic
152C22×C3×D4C2311yescharacteristic
153C23×C3×C4C2312yes—
154C22×#67C2312yes—
155C22×#67C2312yes—
156C2×D3×D4—24no—
157C2×D3×D4—24no—
158C2×D3×D4—24no—
159C2×D3×D4—24no—
160C2×D3×D4—42no—
161C2×D3×D4—42no—
162C22×D12—28no—
163C22×D12—44no—
164C22×D12—44no—
165C22×D12C2311yescharacteristic
166C22×D12C2311yescharacteristic
167C22×D12C2312yes—
168C22×D12C2312yes—
169C22×D12C2311yescharacteristic
170C22×D12C2312yes—
171C22×D12C2312yes—
172C22×C4×D3C2311yescharacteristic
173C22×C4×D3C2311yescharacteristic
174C22×C4×D3C2312yes—
175C22×C4×D3C2312yes—
176C22×Dic6C2312yes—
177C3×#124—24no—
178C3×C4×Q8—24no—
179C3×C4×D4—24no—
180C2×C3×C4⋊C4C2311yescharacteristic
181C2×C3×C4⋊C4C2311yescharacteristic
182C2×C3×C4⋊C4C2312yes—
183C2×C3×C4⋊C4C2311yescharacteristic
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C22⋊C4C2312yes—
186C2×C3×C22⋊C4C2312yes—
187C2×C3×C22⋊C4C2312yes—
188C2×C3×C22⋊C4C2312yes—
189C2×C3×C22⋊C4C2312yes—
190C2×C3×C42C2311yescharacteristic
191C2×C3×C42C2311yescharacteristic
192C2×C3×C42C2311yescharacteristic
193C2×C3×C42C2312yes—
194C2×C3×C42C2312yes—
195C2×#217C2312yes—
196C2×#217C2312yes—
197C2×#217C2312yes—
198C2×#217C2312yes—
199#947—24no—
200#947—42no—
201#946—24no—
202#946—42no—
203#930—28no—
204C2×(C2×D3)⋊C4C2312yes—
205C2×(C2×D3)⋊C4C2312yes—
206C2×(C2×D3)⋊C4C2311yescharacteristic
207C2×(C2×D3)⋊C4C2312yes—
208C2×(C2×D3)⋊C4C2311yescharacteristic
209C2×(C2×D3)⋊C4C2312yes—
210C2×(C2×D3)⋊C4C2311yescharacteristic
211C2×(C2×D3)⋊C4C2312yes—
212C2×(C2×D3)⋊C4C2312yes—
213C2×(C2×D3)⋊C4C2311yescharacteristic
214C2×(C2×D3)⋊C4C2311yescharacteristic
215C2×(C2×D3)⋊C4C2311yescharacteristic
216C2×(C2×D3)⋊C4C2311yescharacteristic
217C2×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
228C2×(C2×D3)⋊C4C2311yescharacteristic
229C2×(C2×D3)⋊C4C2311yescharacteristic
230C2×(C2×D3)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234C2×C4⋊Dic3C2311yescharacteristic
235C2×C4⋊Dic3C2311yescharacteristic
236C2×C4⋊Dic3C2311yescharacteristic
237C2×C4⋊Dic3C2312yes—
238#924—44no—
239C2×Dic3⋊C4C2312yes—
240C2×Dic3⋊C4C2312yes—
241C2×Dic3⋊C4C2311yescharacteristic
242C2×Dic3⋊C4C2311yescharacteristic
243C2×Dic3⋊C4C2312yes—
244C2×Dic3⋊C4C2311yescharacteristic
245C2×Dic3⋊C4C2312yes—
246C2×Dic3⋊C4C2311yescharacteristic
247C2×C4×Dic3C2311yescharacteristic
248C2×C4×Dic3C2311yescharacteristic
249C2×C4×Dic3C2312yes—
250#896—28no—
251#895—24no—
252#895D418yes—
253#894—28no—
254#894—44no—
255#893—42no—
256#892—42no—
257#888—24no—
258#882—28no—
259#882—28no—
260D3×C22⋊C4—44no—
261#876—28no—
262#875—28no—
263#875—44no—
264#874—24no—
265C4×D12—24no—
266C4×D12—24no—
267#872—24no—
268C3×#95C2312yes—
269C3×#95C2311yescharacteristic
270C3×#95C2311yescharacteristic
271C3×#95C2312yes—
272C3×#95C2312yes—
273C3⋊#95C2312yes—
274C3⋊#95C2311yescharacteristic
275C3⋊#95C2311yescharacteristic
276C3⋊#95C2311yescharacteristic
277C3⋊#95C2311yescharacteristic
278C3⋊#95C2311yescharacteristic
279C3⋊#95C2312yes—
280C3⋊#95C2312yes—
281C3⋊#95C2311yescharacteristic
282C3⋊#95C2311yescharacteristic
283C3⋊#95C2311yescharacteristic
284C23×D4—31no—
285C23×D4—31no—
286C23×D4—32no—
287D42—68no—
288#542—68no—
289C2×C4⋊Q8—31no—
290C2×#127—31no—
291C2×#126—32no—
292C2×#124—31no—
293C2×#124—31no—
294C2×#124—32no—
295C2×#124—32no—
296C2×#124C2×D311yescharacteristic
297C2×#123—32no—
298C2×#123—32no—
299C2×C22⋊Q8—31no—
300C2×C22⋊Q8—31no—
301C2×C22⋊Q8—32no—
302C2×C22⋊Q8—32no—
303C2×#121—32no—
304C2×#121—31no—
305C2×#121—31no—
306C2×#120—32no—
307C2×#120—32no—
308C2×C4×Q8C2×D311yescharacteristic, complemented
309C2×C4×D4—31no—
310C2×C4×D4—31no—
311C2×C4×D4—31no—
312C2×C4×D4C2×D311yescharacteristic
313C2×#117—31no—
314C2×#117—31no—
315C22×C22⋊C4—32no—
316#400—31no—
317#399—31no—
318#398—31no—
319#397—31no—
320#397—31no—
321#397—31no—
322#397—32no—
323#396—32no—
324#396—32no—
325#394—31no—
326#394—32no—
327#394—32no—
328#394—32no—
329#394—32no—
330#394—32no—
331#394—32no—
332#394—31no—
333#394—32no—
334#394—32no—
335#394—32no—
336#394—32no—
337#394—32no—
338#393—32no—
339#393—32no—
340#391C2×D311yescharacteristic, complemented
341#390—31no—
342#390—31no—
343#390—31no—
344#390—32no—
345#390—32no—
346#390—31no—
347#390—32no—
348#390—31no—
349#390—32no—
350#390—31no—
351#390C2×D311yescharacteristic
352#389—31no—
353#389—31no—
354#389—32no—
355#388—32no—
356#388—32no—
357#388—32no—
358#388—32no—
359#388C2×D312yescomplemented
360#388C2×D312yescomplemented
361#386—32no—
362#386—32no—
363#386—32no—
364#386—32no—
365#386—32no—
366#386—32no—
367#385—32no—
368#385C2×D312yescomplemented
369#380—31no—
370#379—32no—
371#379—32no—
372#379—32no—
373#379—32no—
374#379—32no—
375#379—32no—
376#379—32no—
377C4×C4⋊C4—31no—
378C4×C4⋊C4C2×D311yescharacteristic, complemented
379C4×C4⋊C4C2×D311yescharacteristic, complemented
380C4×C22⋊C4—31no—
381C4×C22⋊C4—31no—
382C4×C22⋊C4—32no—
383C4×C22⋊C4—31no—
384C4×C22⋊C4C2×D312yescomplemented
385C24×C3C2412yes—
386C23×D3—24no—
387C23×D3—24no—
388C23×D3—24no—
389C23×D3—24no—
390C23×D3—24no—
391C23×D3—42no—
392C23×D3—42no—
393C23×D3—42no—
394C23×D3—42no—
395C23×D3—42no—
396C23×D3—42no—
397C23×D3—42no—
398C23×D3—42no—
399C23×D3—42no—
400C23×D3C2412yes—
401C23×D3C2411yescharacteristic
402C23×D3C2412yes—
403C23×D3C2411yescharacteristic
404C2×C3×Q8—22no—
405C2×C3×Q8—22no—
406C2×C3×Q8—22no—
407C2×C3×D4—22no—
408C2×C3×D4—22no—
409C2×C3×D4#4114yes—
410C22×C3×C4—24no—
411C22×C3×C4—24no—
412C22×C3×C4—42no—
413C22×C3×C4C2411yescharacteristic
414C22×C3×C4C2411yescharacteristic
415C22×C3×C4C2411yescharacteristic
416C22×C3×C4C2412yes—
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2411yescharacteristic
419C22×C3×C4C2412yes—
420C22×C3×C4C2412yes—
421C22×C3×C4C2411yescharacteristic
422C22×C3×C4C2411yescharacteristic
423C2×#67—24no—
424C2×#67—24no—
425C2×#67—24no—
426C2×#67—24no—
427C2×#67—42no—
428C2×#67—42no—
429C22×Dic3C2411yescharacteristic
430C22×Dic3C2411yescharacteristic
431C22×Dic3C2411yescharacteristic
432C22×Dic3C2411yescharacteristic
433C22×Dic3C2412yes—
434C22×Dic3C2411yescharacteristic
435C22×Dic3C2412yes—
436C22×Dic3C2411yescharacteristic
437D3×D4—416no—
438D3×D4—416no—
439C2×D12—22no—
440C2×D12—22no—
441C2×D12—22no—
442C2×D12—22no—
443C2×D12—22no—
444C2×D12—24no—
445C2×D12—24no—
446C2×D12—22no—
447C2×D12—24no—
448C2×D12—22no—
449C2×D12—24no—
450C2×D12—22no—
451C2×D12—24no—
452C2×D12—432no—
453C2×D12—42no—
454C2×D12—42no—
455C2×D12—42no—
456C2×D12—42no—
457C2×D12—42no—
458C2×D12—42no—
459C2×D12C2×D414yes—
460C2×D12C2×D418yes—
461C2×C4×D3—22no—
462C2×C4×D3—22no—
463C2×C4×D3—22no—
464C2×C4×D3—22no—
465C2×C4×D3—22no—
466C2×C4×D3—24no—
467C2×C4×D3—42no—
468C2×C4×D3—42no—
469C2×C4×D3—42no—
470C2×C4×D3—42no—
471C2×C4×D3—42no—
472C2×C4×D3C2×D414yes—
473C2×Dic6—24no—
474C2×Dic6—42no—
475C2×Dic6—42no—
476C3×C4⋊C4—24no—
477C3×C4⋊C4—22no—
478C3×C4⋊C4—22no—
479C3×C4⋊C4—41no—
480C3×C4⋊C4C2×D414yes—
481C3×C22⋊C4—24no—
482C3×C22⋊C4—24no—
483C3×C22⋊C4—24no—
484C3×C22⋊C4—42no—
485C3×C22⋊C4—42no—
486C3×C42—22no—
487C3×C42—22no—
488C3×C42—24no—
489C3×C42—22no—
490C3×C42—42no—
491#217—42no—
492#217—42no—
493#217—42no—
494#217—42no—
495(C2×D3)⋊C4—22no—
496(C2×D3)⋊C4—22no—
497(C2×D3)⋊C4—24no—
498(C2×D3)⋊C4—22no—
499(C2×D3)⋊C4—24no—
500(C2×D3)⋊C4—24no—
501(C2×D3)⋊C4—24no—
502(C2×D3)⋊C4—22no—
503(C2×D3)⋊C4—24no—
504(C2×D3)⋊C4—22no—
505(C2×D3)⋊C4—24no—
506(C2×D3)⋊C4—22no—
507(C2×D3)⋊C4—42no—
508(C2×D3)⋊C4—42no—
509(C2×D3)⋊C4—42no—
510(C2×D3)⋊C4—42no—
511(C2×D3)⋊C4—42no—
512(C2×D3)⋊C4—42no—
513(C2×D3)⋊C4—42no—
514(C2×D3)⋊C4—41no—
515(C2×D3)⋊C4—41no—
516(C2×D3)⋊C4—41no—
517(C2×D3)⋊C4—42no—
518(C2×D3)⋊C4—42no—
519(C2×D3)⋊C4—42no—
520(C2×D3)⋊C4—41no—
521(C2×D3)⋊C4—42no—
522(C2×D3)⋊C4—42no—
523(C2×D3)⋊C4—42no—
524(C2×D3)⋊C4C2×D418yes—
525C4⋊Dic3—22no—
526C4⋊Dic3—22no—
527C4⋊Dic3—22no—
528C4⋊Dic3—42no—
529Dic3⋊C4—24no—
530Dic3⋊C4—24no—
531Dic3⋊C4—22no—
532Dic3⋊C4—22no—
533Dic3⋊C4—22no—
534Dic3⋊C4—24no—
535Dic3⋊C4—41no—
536Dic3⋊C4—42no—
537C4×Dic3—22no—
538C4×Dic3—22no—
539C4×Dic3—42no—
540C25—32no—
541C25—32no—
542C22×Q8—32no—
543C22×Q8C22×D311yescharacteristic
544C22×D4—32no—
545C22×D4—32no—
546C22×D4—31no—
547C22×D4—32no—
548C22×D4—31no—
549C22×D4—31no—
550C22×D4—32no—
551C22×D4—32no—
552C22×D4—32no—
553C22×D4—68no—
554C22×D4—64no—
555C22×D4—64no—
556C22×D4—64no—
557C22×D4—64no—
558C22×D4—124no—
559C22×D4—124no—
560C22×D4—122no—
561C22×D4—122no—
562C22×D4C22×D311yescharacteristic
563C23×C4—31no—
564C23×C4—31no—
565C23×C4—32no—
566C23×C4—32no—
567C23×C4C22×D312yes—
568C4⋊Q8—64no—
569#127—64no—
570#126—68no—
571#124—24no—
572#124—68no—
573#124—64no—
574#124—124no—
575#124—122no—
576#123—68no—
577#123—124no—
578C22⋊Q8—68no—
579C22⋊Q8—64no—
580C22⋊Q8—124no—
581C22⋊Q8—122no—
582#121—38no—
583#121—68no—
584#121—64no—
585#120—68no—
586#120—68no—
587C4×Q8—24no—
588C4×D4—24no—
589C4×D4—64no—
590C4×D4—64no—
591C4×D4—122no—
592#117—64no—
593#117—122no—
594C2×C4⋊C4—31no—
595C2×C4⋊C4—31no—
596C2×C4⋊C4—31no—
597C2×C4⋊C4—31no—
598C2×C4⋊C4—31no—
599C2×C4⋊C4—32no—
600C2×C4⋊C4—31no—
601C2×C4⋊C4—32no—
602C2×C4⋊C4—32no—
603C2×C4⋊C4—32no—
604C2×C4⋊C4—32no—
605C2×C4⋊C4—31no—
606C2×C4⋊C4C22×D311yescharacteristic
607C2×C4⋊C4C22×D312yes—
608C2×C4⋊C4C22×D311yescharacteristic
609C2×C4⋊C4C22×D311yescharacteristic
610C2×C4⋊C4C22×D311yescharacteristic
611C2×C22⋊C4—32no—
612C2×C22⋊C4—31no—
613C2×C22⋊C4—32no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—31no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—32no—
619C2×C22⋊C4—32no—
620C2×C22⋊C4—32no—
621C2×C22⋊C4—32no—
622C2×C22⋊C4—32no—
623C2×C22⋊C4—31no—
624C2×C22⋊C4—32no—
625C2×C22⋊C4—32no—
626C2×C22⋊C4—32no—
627C2×C22⋊C4—32no—
628C2×C22⋊C4—32no—
629C2×C22⋊C4—32no—
630C2×C22⋊C4—32no—
631C2×C22⋊C4—32no—
632C2×C22⋊C4—32no—
633C2×C22⋊C4—32no—
634C2×C22⋊C4—32no—
635C2×C22⋊C4—32no—
636C2×C22⋊C4—32no—
637C2×C22⋊C4—32no—
638C2×C22⋊C4—31no—
639C2×C22⋊C4—31no—
640C2×C22⋊C4—31no—
641C2×C22⋊C4—31no—
642C2×C22⋊C4—32no—
643C2×C22⋊C4—32no—
644C2×C22⋊C4—32no—
645C2×C22⋊C4—124no—
646C2×C22⋊C4C22×D312yes—
647C2×C22⋊C4C22×D312yes—
648C2×C22⋊C4C22×D312yes—
649C2×C22⋊C4C22×D312yes—
650C2×C22⋊C4C22×D312yes—
651C2×C42—31no—
652C2×C42—31no—
653C2×C42—32no—
654C2×C42C22×D311yescharacteristic
655C2×C42C22×D311yescharacteristic
656C2×C42C22×D312yes—
657C2×C42C22×D311yescharacteristic
658C2×C42C22×D312yes—
659#95—31no—
660#95—32no—
661#95—31no—
662#95—31no—
663#95—31no—
664#95—31no—
665#95—31no—
666#95—31no—
667#95—31no—
668#95—32no—
669#95—32no—
670#95C22×D311yescharacteristic
671#95C22×D312yes—
672#95C22×D312yes—
673#95C22×D311yescharacteristic
674#95C22×D312yes—
675C23×C3—22no—
676C23×C3—22no—
677C23×C3—22no—
678C23×C3—22no—
679C23×C3—22no—
680C23×C3—22no—
681C23×C3C2×#4114yes—
682C23×C3C2511yescharacteristic
683C22×D3—21no—
684C22×D3—21no—
685C22×D3—21no—
686C22×D3—22no—
687C22×D3—21no—
688C22×D3—21no—
689C22×D3—22no—
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—21no—
693C22×D3—21no—
694C22×D3—21no—
695C22×D3—22no—
696C22×D3—21no—
697C22×D3—21no—
698C22×D3—21no—
699C22×D3—21no—
700C22×D3—22no—
701C22×D3—22no—
702C22×D3—22no—
703C22×D3—22no—
704C22×D3—22no—
705C22×D3—22no—
706C22×D3—22no—
707C22×D3—22no—
708C22×D3—48no—
709C22×D3—48no—
710C22×D3—48no—
711C22×D3—48no—
712C22×D3—48no—
713C22×D3—84no—
714C22×D3—84no—
715C22×D3—84no—
716C22×D3—84no—
717C22×D3—84no—
718C22×D3—84no—
719C22×D3—84no—
720C22×D3—84no—
721C22×D3—84no—
722C22×D3C22×D412yes—
723C22×D3C22×D414yes—
724C22×D3H(5,𝔽2)12yes—
725C3×Q8—44no—
726C3×D4—28no—
727C2×C3×C4—21no—
728C2×C3×C4—22no—
729C2×C3×C4—22no—
730C2×C3×C4—21no—
731C2×C3×C4—21no—
732C2×C3×C4—22no—
733C2×C3×C4—21no—
734C2×C3×C4—21no—
735C2×C3×C4—21no—
736C2×C3×C4—21no—
737C2×C3×C4—22no—
738C2×C3×C4—22no—
739C2×C3×C4—22no—
740C2×C3×C4—21no—
741C2×C3×C4—22no—
742C2×C3×C4—21no—
743C2×C3×C4—21no—
744C2×C3×C4—21no—
745C2×C3×C4—21no—
746C2×C3×C4—21no—
747C2×C3×C4—21no—
748C2×C3×C4—21no—
749C2×C3×C4—22no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—48no—
753C2×C3×C4C22×D414yes—
754C2×C3×C4C22×D412yes—
755C2×C3×C4C2×#4112yes—
756C2×C3×C4H(5,𝔽2)12yes—
757C2×C3×C4H(5,𝔽2)12yes—
758#67—48no—
759#67—48no—
760C2×Dic3—21no—
761C2×Dic3—21no—
762C2×Dic3—21no—
763C2×Dic3—21no—
764C2×Dic3—22no—
765C2×Dic3—21no—
766C2×Dic3—21no—
767C2×Dic3—21no—
768C2×Dic3—21no—
769C2×Dic3—22no—
770C2×Dic3—21no—
771C2×Dic3—22no—
772C2×Dic3—22no—
773C2×Dic3—21no—
774C2×Dic3—21no—
775C2×Dic3—21no—
776C2×Dic3—22no—
777C2×Dic3—21no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—22no—
782C2×Dic3—21no—
783C2×Dic3C22×D412yes—
784D12—28no—
785D12—28no—
786D12—48no—
787D12—48no—
788D12—48no—
789D12—44no—
790D12—84no—
791C4×D3—28no—
792C4×D3—44no—
793C4×D3—84no—
794C4×D3—84no—
795Dic6—84no—
796C24—31no—
797C24—31no—
798C24—32no—
799C24—32no—
800C24—64no—
801C24—64no—
802C24—64no—
803C24—64no—
804C24—64no—
805C24—122no—
806C24—122no—
807C24—122no—
808C24—122no—
809C24—122no—
810C24—122no—
811C24—122no—
812C24—122no—
813C24—122no—
814C24C23×D312yes—
815C2×Q8—22no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—64no—
819C2×Q8—122no—
820C2×Q8—122no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—34no—
824C2×D4—38no—
825C2×D4—62no—
826C2×D4—62no—
827C2×D4—64no—
828C2×D4—64no—
829C2×D4—64no—
830C2×D4—64no—
831C2×D4—64no—
832C2×D4—64no—
833C2×D4—64no—
834C2×D4—62no—
835C2×D4—62no—
836C2×D4—64no—
837C2×D4—62no—
838C2×D4—62no—
839C2×D4—62no—
840C2×D4—64no—
841C2×D4—62no—
842C2×D4—122no—
843C2×D4—122no—
844C2×D4—122no—
845C2×D4—122no—
846C2×D4—122no—
847C2×D4—122no—
848C2×D4—1232no—
849C2×D4—1216no—
850C2×D4—122no—
851C2×D4—122no—
852C2×D4—1216no—
853C2×D4#23514yes—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—31no—
857C22×C4—34no—
858C22×C4—31no—
859C22×C4—31no—
860C22×C4—31no—
861C22×C4—31no—
862C22×C4—32no—
863C22×C4—31no—
864C22×C4—32no—
865C22×C4—42no—
866C22×C4—64no—
867C22×C4—62no—
868C22×C4—62no—
869C22×C4—62no—
870C22×C4—62no—
871C22×C4—62no—
872C22×C4—122no—
873C22×C4—122no—
874C22×C4—122no—
875C22×C4—122no—
876C22×C4—122no—
877C22×C4C23×D311yescharacteristic
878C22×C4C23×D311yescharacteristic
879C22×C4C23×D311yescharacteristic
880C22×C4C23×D312yes—
881C22×C4C23×D311yescharacteristic
882C22×C4C23×D311yescharacteristic
883C22×C4C23×D312yes—
884C22×C4C23×D312yes—
885C22×C4C23×D311yescharacteristic
886C22×C4C23×D311yescharacteristic
887C4⋊C4—24no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—41no—
891C4⋊C4—62no—
892C4⋊C4—62no—
893C4⋊C4—62no—
894C4⋊C4—64no—
895C4⋊C4—62no—
896C4⋊C4—64no—
897C4⋊C4—62no—
898C4⋊C4—62no—
899C4⋊C4—64no—
900C4⋊C4—122no—
901C4⋊C4—122no—
902C4⋊C4—121no—
903C4⋊C4D3×D414yes—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—38no—
908C22⋊C4—42no—
909C22⋊C4—42no—
910C22⋊C4—62no—
911C22⋊C4—62no—
912C22⋊C4—64no—
913C22⋊C4—62no—
914C22⋊C4—62no—
915C22⋊C4—62no—
916C22⋊C4—64no—
917C22⋊C4—64no—
918C22⋊C4—64no—
919C22⋊C4—64no—
920C22⋊C4—62no—
921C22⋊C4—64no—
922C22⋊C4—122no—
923C22⋊C4—122no—
924C22⋊C4—122no—
925C22⋊C4—122no—
926C22⋊C4—122no—
927C22⋊C4—122no—
928C22⋊C4—122no—
929C22⋊C4—122no—
930C22⋊C4—122no—
931C22⋊C4—122no—
932C22⋊C4—122no—
933C22⋊C4—121no—
934C22⋊C4—121no—
935C22⋊C4—122no—
936C22⋊C4—122no—
937C22⋊C4—121no—
938C22⋊C4—121no—
939C22⋊C4—122no—
940C22⋊C4—122no—
941C22⋊C4—122no—
942C22⋊C4—122no—
943C42—22no—
944C42—22no—
945C42—22no—
946C42—24no—
947C42—42no—
948C42—62no—
949C42—62no—
950C42—122no—
951C22×C3—24no—
952C22×C3—24no—
953C22×C3—24no—
954C22×C3—42no—
955C22×C3—42no—
956C22×C3—42no—
957C22×C3—42no—
958C22×C3C23×D411yescharacteristic
959C22×C3C22×#4111yescharacteristic
960C22×C3C2×H(5,𝔽2)11yescharacteristic
961C22×C3C2×H(5,𝔽2)11yescharacteristic
962C22×C3C2×H(5,𝔽2)11yescharacteristic
963C22×C3#58511yescharacteristic
964C22×C3#58511yescharacteristic
965C2×D3—22no—
966C2×D3—24no—
967C2×D3—24no—
968C2×D3—22no—
969C2×D3—22no—
970C2×D3—24no—
971C2×D3—22no—
972C2×D3—22no—
973C2×D3—22no—
974C2×D3—41no—
975C2×D3—41no—
976C2×D3—42no—
977C2×D3—41no—
978C2×D3—42no—
979C2×D3—41no—
980C2×D3—41no—
981C2×D3—42no—
982C2×D3—41no—
983C2×D3—41no—
984C2×D3—42no—
985C2×D3—41no—
986C2×D3—42no—
987C2×D3—42no—
988C2×D3—42no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—816no—
994C2×D3—816no—
995C3×C4—24no—
996C3×C4—22no—
997C3×C4—42no—
998C3×C4—41no—
999C3×C4—41no—
1000C3×C4—41no—
1001C3×C4—41no—
1002C3×C4—41no—
1003C3×C4—42no—
1004C3×C4#54614yes—
1005Dic3—22no—
1006Dic3—41no—
1007Dic3—41no—
1008Dic3—42no—
1009Dic3—41no—
1010Dic3—41no—
1011Dic3—42no—
1012Dic3—41no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—34no—
1020C23—32no—
1021C23—32no—
1022C23—61no—
1023C23—61no—
1024C23—62no—
1025C23—61no—
1026C23—61no—
1027C23—61no—
1028C23—62no—
1029C23—62no—
1030C23—61no—
1031C23—61no—
1032C23—61no—
1033C23—61no—
1034C23—62no—
1035C23—62no—
1036C23—61no—
1037C23—62no—
1038C23—61no—
1039C23—61no—
1040C23—62no—
1041C23—62no—
1042C23—62no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—62no—
1047C23—128no—
1048C23—128no—
1049C23—128no—
1050C23—128no—
1051C23—128no—
1052C23—244no—
1053C23—244no—
1054C23—244no—
1055C23—244no—
1056C23—244no—
1057C23—244no—
1058C23—244no—
1059C23—244no—
1060C23—244no—
1061C23C2×#23514yes—
1062C23C24×D311yescharacteristic
1063Q8—44no—
1064Q8—244no—
1065D4—28no—
1066D4—68no—
1067D4—68no—
1068D4—128no—
1069D4—128no—
1070D4—128no—
1071D4—128no—
1072D4—128no—
1073D4—124no—
1074D4—244no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—32no—
1101C2×C4—48no—
1102C2×C4—61no—
1103C2×C4—61no—
1104C2×C4—68no—
1105C2×C4—61no—
1106C2×C4—61no—
1107C2×C4—61no—
1108C2×C4—61no—
1109C2×C4—62no—
1110C2×C4—61no—
1111C2×C4—61no—
1112C2×C4—62no—
1113C2×C4—62no—
1114C2×C4—61no—
1115C2×C4—62no—
1116C2×C4—61no—
1117C2×C4—61no—
1118C2×C4—61no—
1119C2×C4—61no—
1120C2×C4—61no—
1121C2×C4—62no—
1122C2×C4—61no—
1123C2×C4—62no—
1124C2×C4—61no—
1125C2×C4—61no—
1126C2×C4—124no—
1127C2×C4—244no—
1128C2×C4—244no—
1129C2×C4C2×#23512yes—
1130C2×C4C2×D3×D414yes—
1131C2×C4C2×D3×D412yes—
1132C2×C4#100912yes—
1133C2×C4#100912yes—
1134C2×C3—44no—
1135C2×C3C2×#54611yescharacteristic
1136C2×C3#348411yescharacteristic
1137C2×C3#350011yescharacteristic
1138C2×C3#351311yescharacteristic
1139C2×C3#351411yescharacteristic
1140C2×C3#354611yescharacteristic
1141C2×C3#355811yescharacteristic
1142D3—44no—
1143D3—42no—
1144D3—42no—
1145D3—82no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—62no—
1154C22—64no—
1155C22—62no—
1156C22—64no—
1157C22—62no—
1158C22—62no—
1159C22—62no—
1160C22—64no—
1161C22—62no—
1162C22—121no—
1163C22—122no—
1164C22—121no—
1165C22—121no—
1166C22—121no—
1167C22—122no—
1168C22—122no—
1169C22—121no—
1170C22—121no—
1171C22—121no—
1172C22—121no—
1173C22—122no—
1174C22—122no—
1175C22—122no—
1176C22—122no—
1177C22—122no—
1178C22—122no—
1179C22—122no—
1180C22—122no—
1181C22—2416no—
1182C22—2416no—
1183C22C22×#23511yescharacteristic
1184C22C22×D3×D411yescharacteristic
1185C22C2×#100911yescharacteristic
1186C22C2×#100911yescharacteristic
1187C22#596411yescharacteristic
1188C22D3×H(5,𝔽2)11yescharacteristic
1189C22#596811yescharacteristic
1190C4—22no—
1191C4—24no—
1192C4—42no—
1193C4—42no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—62no—
1200C4—121no—
1201C4—121no—
1202C4—122no—
1203C4—121no—
1204C4—121no—
1205C4—121no—
1206C4—122no—
1207C4#555014yes—
1208C3#4487411yescharacteristic, complemented, Sylow
1209C2—44no—
1210C2—122no—
1211C2—122no—
1212C2—124no—
1213C2—242no—
1214C2C2×#555011yescharacteristic
1215C2#8585211yescharacteristic
1216C2#8590511yescharacteristic
1217C2#8666211yescharacteristic
1218C2#8671511yescharacteristic
1219C2#8700911yescharacteristic
1220C2#8706911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2367C2
prime radicalC2×D4×D12C2
hypercenter#2367D3
hypocenterC3#44874
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
1. C2×#5582C2semidirect
3. C3×#2367C2semidirect
4. #82960C2semidirect
5. #82960C2semidirect
6. #82495C2semidirect
7. #82362C2semidirect
8. #76620C2semidirect
9. #76533C2semidirect
10. #76431C2semidirect
11. #76428C2semidirect
12. #75923C2semidirect
13. #75920C2semidirect
14. #75917C2semidirect
15. #75526C2semidirect
16. #74632C2semidirect
17. #74599C2semidirect
18. #73788C2semidirect
19. #73780C2semidirect
20. #73777C2semidirect
21. #73649C2semidirect
22. #73603C2semidirect
23. #73588C2semidirect
29. C2×C3×C4×Q8C22semidirect
31. C2×#947C22semidirect
32. C2×#947C22semidirect
33. C2×#946C22semidirect
34. C2×#946C22semidirect
36. C2×#924C22semidirect
39. C2×#896C22semidirect
42. C2×#894C22semidirect
43. C2×#894C22semidirect
44. C2×#893C22semidirect
45. C2×#892C22semidirect
46. C2×#888C22semidirect
49. C2×D3×C22⋊C4C22semidirect
50. C2×#876C22semidirect
51. C2×#875C22semidirect
52. C2×#875C22semidirect
55. C2×C4×D12C22semidirect
56. C2×#872C22semidirect
57. C3×#391C22semidirect
59. C3×#388C22semidirect
60. C3×#388C22semidirect
61. C3×#385C22semidirect
62. C3×C4×C4⋊C4C22semidirect
63. C3×C4×C4⋊C4C22semidirect
64. C3×C4×C22⋊C4C22semidirect
67. #5210C22semidirect
68. #4994C22semidirect
69. #4993C22semidirect
70. #4992C22semidirect
72. #4991C22semidirect
73. #4991C22semidirect
74. #4988C22semidirect
75. #4987C22semidirect
76. #4984C22semidirect
77. #4982C22semidirect
78. #4959C22semidirect
79. #4959C22semidirect
80. #4959C22semidirect
81. #4959C22semidirect
82. #4957C22semidirect
83. #4957C22semidirect
84. #4956C22semidirect
85. #4956C22semidirect
86. #4955C22semidirect
87. #4955C22semidirect
88. #4955C22semidirect
89. #4955C22semidirect
90. #4955C22semidirect
91. #4955C22semidirect
92. #4955C22semidirect
93. #4948C22semidirect
94. #4947C22semidirect
95. #4940C22semidirect
96. #4940C22semidirect
97. #4939C22semidirect
98. #4939C22semidirect
99. #4939C22semidirect
100. #4939C22semidirect
101. #4939C22semidirect
102. C4×(C2×D3)⋊C4C22semidirect
103. C4×(C2×D3)⋊C4C22semidirect
104. C4×(C2×D3)⋊C4C22semidirect
105. C4×(C2×D3)⋊C4C22semidirect
106. C4×Dic3⋊C4C22semidirect
107. #4928C22semidirect
108. #4675C22semidirect
109. #4675C22semidirect
110. #4675C22semidirect
111. #4673C22semidirect
114. #4672C22semidirect
115. #4672C22semidirect
116. #4672C22semidirect
117. #4672C22semidirect
118. #4670C22semidirect
119. #4669C22semidirect
120. #4665C22semidirect
121. #4665C22semidirect
122. #4665C22semidirect
123. #4665C22semidirect
124. #4660C22semidirect
125. #4647C22semidirect
145. #2367D3semidirect
308. C2×C4×Q8C2×D3semidirect
340. #391C2×D3semidirect
359. #388C2×D3semidirect
360. #388C2×D3semidirect
368. #385C2×D3semidirect
378. C4×C4⋊C4C2×D3semidirect
379. C4×C4⋊C4C2×D3semidirect
384. C4×C22⋊C4C2×D3semidirect
1208. C3#44874semidirect

Maximal subgroups

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

subgroupindex
C2×#55822
C2×D4×D122
C3×#23672
#829602
#824952
#823622
#766202
#765332
#764312
#764282
#759232
#759202
#759172
#755262
#746322
#745992
#737882
#737802
#737772
#736492
#736032
#735882
#448743