Finite Group Databasebeta

← #11024279

Subgroups — #11024279

Order 768.

2868 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#121C211yesmaximal, characteristic
2C2×#5603C211yesmaximal, characteristic, complemented
3C3×#2324C211yesmaximal, characteristic, complemented
4#82408C211yesmaximal, characteristic, complemented
5D4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#82287C211yesmaximal, characteristic, complemented
7#82267C211yesmaximal, characteristic, complemented
8#76441C211yesmaximal, characteristic, complemented
9#76386C212yesmaximal, complemented
10#76315C211yesmaximal, characteristic, complemented
11#76315C212yesmaximal, complemented
12#76218C211yesmaximal, characteristic, complemented
13#75999C211yesmaximal, characteristic, complemented
14#75665C212yesmaximal, complemented
15#75540C212yesmaximal, complemented
16#74796C212yesmaximal, complemented
17#74686C212yesmaximal, complemented
18#74635C212yesmaximal, complemented
19#74413C212yesmaximal, complemented
20#74049C211yesmaximal, characteristic, complemented
21#74033C211yesmaximal, characteristic, complemented
22#73788C211yesmaximal, characteristic, complemented
23#73773C211yesmaximal, characteristic, complemented
24#37664—31nomaximal, Sylow
25C22×D3×D4C2211yescharacteristic
26C22×D3×D4C2212yes—
27C23×C4×D3C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic, complemented
30C2×C3×#117C2211yescharacteristic, complemented
31C2×#939C2212yes—
32C2×#938C2211yescharacteristic
33C2×#936C2212yescomplemented
34C2×#936C2211yescharacteristic, complemented
35C2×#935C2212yescomplemented
36C2×D4×Dic3C2211yescharacteristic, complemented
37C2×#930C2211yescharacteristic
38C22×(C2×D3)⋊C4C2212yes—
39C2×#926C2211yescharacteristic, complemented
40C2×#924C2211yescharacteristic, complemented
41D3×#121—28no—
42#5603—28no—
43C2×#897C2211yescharacteristic
44C2×#897C2212yes—
45C2×#897C2211yescharacteristic, complemented
46C2×#895C2211yescharacteristic
47C2×D3×C4⋊C4C2211yescharacteristic
48C2×#888C2211yescharacteristic, complemented
49C2×#887C2211yescharacteristic, complemented
50C2×#886C2212yescomplemented
51C2×#884C2212yes—
52C2×D3×C22⋊C4C2212yes—
53C2×#879C2212yescomplemented
54C2×#878C2212yescomplemented
55C2×#875C2212yescomplemented
56C2×#875C2211yescharacteristic, complemented
57C3×#390C2212yescomplemented
58C3×#390C2211yescharacteristic, complemented
59C3×#389C2211yescharacteristic, complemented
60C3×#388C2212yescomplemented
61C3×#386C2212yescomplemented
62C3×#385C2212yescomplemented
63C3×#380C2211yescharacteristic, complemented
64C3×C4×C4⋊C4C2211yescharacteristic, complemented
65#5213C2212yescomplemented
66#5213C2212yescomplemented
67#5212C2212yescomplemented
68#4994C2212yescomplemented
69#4994C2212yescomplemented
70#4994C2212yescomplemented
71#4988C2211yescharacteristic, complemented
72#4988C2212yescomplemented
73#4988C2211yescharacteristic, complemented
74#4987C2211yescharacteristic
75#4987C2211yescharacteristic
76#4987C2211yescharacteristic
77#4987C2211yescharacteristic, complemented
78#4987C2211yescharacteristic, complemented
79#4987C2211yescharacteristic, complemented
80#4984C2211yescharacteristic, complemented
81#4984C2211yescharacteristic, complemented
82#4981C2212yescomplemented
83#4961C2212yescomplemented
84#4961C2212yescomplemented
85#4961C2212yescomplemented
86#4961C2212yescomplemented
87#4961C2212yescomplemented
88#4961C2212yescomplemented
89#4961C2212yescomplemented
90#4961C2212yescomplemented
91#4958C2212yescomplemented
92#4955C2212yes—
93#4955C2212yes—
94#4955C2211yescharacteristic
95#4955C2212yes—
96#4955C2212yes—
97#4955C2211yescharacteristic
98#4953C2212yescomplemented
99#4953C2212yescomplemented
100#4950C2212yescomplemented
101#4950C2212yescomplemented
102#4943C2211yescharacteristic, complemented
103#4943C2211yescharacteristic, complemented
104#4940C2212yescomplemented
105#4939C2211yescharacteristic, complemented
106C4×(C2×D3)⋊C4C2212yes—
107C4×(C2×D3)⋊C4C2211yescharacteristic
108C4×(C2×D3)⋊C4C2211yescharacteristic
109C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
110C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
111#4935C2211yescharacteristic, complemented
112#4929C2211yescharacteristic, complemented
113#4928C2212yescomplemented
114#4677C2212yescomplemented
115#4674C2212yescomplemented
116#4673C2212yescomplemented
117#4672C2212yescomplemented
118#4672C2212yescomplemented
119#4670C2212yescomplemented
120#4668C2212yes—
121#4668C2212yes—
122#4668C2212yes—
123#4668C2212yescomplemented
124#4656C2212yescomplemented
125#4653C2212yescomplemented
126C2×#542—31no—
127C22×#121—31no—
128#2848—31no—
129#2701—32no—
130#2691—32no—
131#2686—32no—
132#2672—32no—
133#2624—31no—
134#2620—31no—
135#2491—31no—
136#2480—32no—
137#2440—31no—
138#2437—32no—
139#2435—31no—
140#2435—32no—
141#2427—31no—
142#2426—31no—
143#2422—31no—
144#2405—32no—
145#2360—31no—
146D4×C22⋊C4—31no—
147#2324D311yescharacteristic, complemented
148#2280—31no—
149C24×D3C2311yescharacteristic
150C24×D3C2312yes—
151C22×C3×D4C2311yescharacteristic
152C22×C3×D4C2312yes—
153C23×C3×C4C2311yescharacteristic
154C23×C3×C4C2312yes—
155C22×#67C2312yes—
156C22×#67C2312yes—
157C22×#67C2312yes—
158C23×Dic3C2311yescharacteristic
159C23×Dic3C2312yes—
160C2×D3×D4—24no—
161C2×D3×D4—28no—
162C2×D3×D4—24no—
163C2×D3×D4—42no—
164C2×D3×D4—44no—
165C2×D3×D4—44no—
166C22×D12C2311yescharacteristic
167C22×D12C2312yes—
168C22×C4×D3—24no—
169C22×C4×D3—24no—
170C22×C4×D3—42no—
171C22×C4×D3C2311yescharacteristic
172C22×C4×D3C2311yescharacteristic
173C22×C4×D3C2312yes—
174C22×C4×D3C2311yescharacteristic
175C22×C4×D3C2311yescharacteristic
176C22×Dic6C2311yescharacteristic
177C22×Dic6C2312yes—
178C3×#121D418yes—
179C3×C4×D4—42no—
180C3×#117—42no—
181C2×C3×C4⋊C4C2311yescharacteristic
182C2×C3×C4⋊C4C2311yescharacteristic
183C2×C3×C4⋊C4C2312yes—
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C4⋊C4C2311yescharacteristic
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C22⋊C4C2311yescharacteristic
188C2×C3×C22⋊C4C2311yescharacteristic
189C2×C3×C22⋊C4C2312yes—
190C2×C3×C22⋊C4C2312yes—
191C2×C3×C22⋊C4C2312yes—
192C2×C3×C22⋊C4C2312yes—
193C2×C3×C22⋊C4C2312yes—
194C2×C3×C42C2311yescharacteristic
195C2×C3×C42C2311yescharacteristic
196C2×C3×C42C2312yes—
197C2×#217C2311yescharacteristic
198C2×#217C2311yescharacteristic
199C2×#217C2312yes—
200C2×#217C2312yes—
201C2×#217C2312yes—
202C2×#217C2312yes—
203C2×#217C2312yes—
204#939—28no—
205#938—24no—
206#936—28no—
207#936—24no—
208#935—28no—
209D4×Dic3—24no—
210#930—24no—
211C2×(C2×D3)⋊C4—44no—
212C2×(C2×D3)⋊C4C2311yescharacteristic
213C2×(C2×D3)⋊C4C2312yes—
214C2×(C2×D3)⋊C4C2311yescharacteristic
215C2×(C2×D3)⋊C4C2312yes—
216C2×(C2×D3)⋊C4C2312yes—
217C2×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2311yescharacteristic
219C2×(C2×D3)⋊C4C2312yes—
220C2×(C2×D3)⋊C4C2311yescharacteristic
221C2×(C2×D3)⋊C4C2311yescharacteristic
222C2×(C2×D3)⋊C4C2311yescharacteristic
223C2×(C2×D3)⋊C4C2312yes—
224C2×(C2×D3)⋊C4C2312yes—
225C2×(C2×D3)⋊C4C2312yes—
226C2×(C2×D3)⋊C4C2311yescharacteristic
227C2×(C2×D3)⋊C4C2312yes—
228C2×(C2×D3)⋊C4C2312yes—
229C2×(C2×D3)⋊C4C2312yes—
230C2×(C2×D3)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2311yescharacteristic
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234#926—24no—
235C2×C4⋊Dic3C2312yes—
236C2×C4⋊Dic3C2311yescharacteristic
237C2×C4⋊Dic3C2311yescharacteristic
238C2×C4⋊Dic3C2311yescharacteristic
239C2×C4⋊Dic3C2311yescharacteristic
240C2×C4⋊Dic3C2312yes—
241C2×C4⋊Dic3C2312yes—
242C2×C4⋊Dic3C2312yes—
243C2×C4⋊Dic3C2312yes—
244C2×C4⋊Dic3C2312yes—
245#924—24no—
246C2×Dic3⋊C4C2312yes—
247C2×Dic3⋊C4C2312yes—
248C2×Dic3⋊C4C2312yes—
249C2×Dic3⋊C4C2312yes—
250C2×C4×Dic3C2312yes—
251C2×C4×Dic3C2311yescharacteristic
252C2×C4×Dic3C2311yescharacteristic
253#897—24no—
254#897—44no—
255#897—42no—
256#895—24no—
257D3×C4⋊C4—24no—
258#888—24no—
259#887—24no—
260#886—44no—
261#884—28no—
262D3×C22⋊C4—28no—
263#879—28no—
264#878—28no—
265#875—44no—
266#875—42no—
267C3×#95C2312yes—
268C3×#95C2312yes—
269C3×#95C2312yes—
270C3⋊#95C2311yescharacteristic
271C3⋊#95C2312yes—
272C3⋊#95C2312yes—
273C3⋊#95C2311yescharacteristic
274C3⋊#95C2312yes—
275C3⋊#95C2312yes—
276C3⋊#95C2312yes—
277C3⋊#95C2311yescharacteristic
278C3⋊#95C2311yescharacteristic
279C3⋊#95C2312yes—
280C3⋊#95C2311yescharacteristic
281C3⋊#95C2311yescharacteristic
282C3⋊#95C2311yescharacteristic
283C3⋊#95C2311yescharacteristic
284C23×D4—31no—
285C23×D4—32no—
286C24×C4—31no—
287#542—68no—
288C2×C4⋊Q8—31no—
289C2×#126—32no—
290C2×#124—31no—
291C2×#124—32no—
292C2×#124—31no—
293C2×#124—32no—
294C2×#123—32no—
295C2×#123—32no—
296C2×C22⋊Q8—31no—
297C2×C22⋊Q8—31no—
298C2×C22⋊Q8—31no—
299C2×C22⋊Q8—32no—
300C2×C22⋊Q8—32no—
301C2×#121—31no—
302C2×#121—32no—
303C2×#121—31no—
304C2×#121—31no—
305C2×#121—32no—
306C2×#121—68no—
307C2×#121C2×D311yescharacteristic
308C2×C4×Q8—31no—
309C2×C4×D4—31no—
310C2×C4×D4C2×D311yescharacteristic, complemented
311C2×#117—31no—
312C2×#117C2×D311yescharacteristic, complemented
313C22×C4⋊C4—31no—
314C22×C22⋊C4—32no—
315C22×C22⋊C4—32no—
316#399—32no—
317#398—32no—
318#397—32no—
319#397—32no—
320#397—32no—
321#396—32no—
322#396—32no—
323#396—32no—
324#395—32no—
325#394—32no—
326#394—32no—
327#394—32no—
328#394—32no—
329#394—32no—
330#394—32no—
331#394—32no—
332#394—32no—
333#394—32no—
334#394—32no—
335#393—32no—
336#391—31no—
337#390—31no—
338#390—31no—
339#390—32no—
340#390—31no—
341#390C2×D311yescharacteristic, complemented
342#390C2×D312yescomplemented
343#389—31no—
344#389—31no—
345#389—32no—
346#389C2×D311yescharacteristic, complemented
347#388—32no—
348#388—32no—
349#388C2×D312yescomplemented
350#387—32no—
351#386—32no—
352#386—32no—
353#386—32no—
354#386C2×D312yescomplemented
355#385—32no—
356#385—32no—
357#385—32no—
358#385—32no—
359#385—32no—
360#385—32no—
361#385C2×D312yescomplemented
362#384—31no—
363#381—31no—
364#381—31no—
365#380—32no—
366#380—31no—
367#380—31no—
368#380—31no—
369#380—31no—
370#380—31no—
371#380—31no—
372#380C2×D311yescharacteristic, complemented
373#379—32no—
374#379—32no—
375#379—31no—
376#379—32no—
377#379—32no—
378#379—31no—
379C4×C4⋊C4C2×D311yescharacteristic, complemented
380C4×C22⋊C4—31no—
381C4×C22⋊C4—32no—
382C4×C22⋊C4—31no—
383C4×C22⋊C4—31no—
384C4×C22⋊C4—31no—
385C24×C3C2411yescharacteristic
386C24×C3C2412yes—
387C23×D3—22no—
388C23×D3—22no—
389C23×D3—22no—
390C23×D3—24no—
391C23×D3—22no—
392C23×D3—22no—
393C23×D3—24no—
394C23×D3—24no—
395C23×D3—24no—
396C23×D3—41no—
397C23×D3—41no—
398C23×D3—42no—
399C23×D3—42no—
400C23×D3—42no—
401C23×D3C2412yes—
402C23×D3C2411yescharacteristic
403C23×D3C2411yescharacteristic
404C2×C3×D4—22no—
405C2×C3×D4—22no—
406C2×C3×D4—42no—
407C2×C3×D4—42no—
408C2×C3×D4C2×D414yes—
409C2×C3×D4C2×D418yes—
410C22×C3×C4—22no—
411C22×C3×C4—22no—
412C22×C3×C4—42no—
413C22×C3×C4—42no—
414C22×C3×C4—42no—
415C22×C3×C4C2×D414yes—
416C22×C3×C4C2411yescharacteristic
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2412yes—
419C22×C3×C4C2411yescharacteristic
420C22×C3×C4C2412yes—
421C22×C3×C4C2411yescharacteristic
422C22×C3×C4C2412yes—
423C22×C3×C4C2411yescharacteristic
424C22×C3×C4C2411yescharacteristic
425C2×#67—24no—
426C2×#67—24no—
427C2×#67—24no—
428C2×#67—24no—
429C2×#67—24no—
430C2×#67—42no—
431C2×#67—42no—
432C2×#67—42no—
433C2×#67—42no—
434C22×Dic3—22no—
435C22×Dic3—24no—
436C22×Dic3—22no—
437C22×Dic3—41no—
438C22×Dic3—42no—
439C22×Dic3—42no—
440C22×Dic3C2411yescharacteristic
441C22×Dic3C2411yescharacteristic
442C22×Dic3C2411yescharacteristic
443C22×Dic3C2412yes—
444C22×Dic3C2411yescharacteristic
445C22×Dic3C2412yes—
446C22×Dic3C2411yescharacteristic
447C22×Dic3C2412yes—
448C22×Dic3C2411yescharacteristic
449D3×D4—416no—
450D3×D4—432no—
451C2×D12—24no—
452C2×D12—24no—
453C2×D12—22no—
454C2×D12—22no—
455C2×D12—22no—
456C2×D12—42no—
457C2×C4×D3—22no—
458C2×C4×D3—22no—
459C2×C4×D3—22no—
460C2×C4×D3—24no—
461C2×C4×D3—22no—
462C2×C4×D3—24no—
463C2×C4×D3—22no—
464C2×C4×D3—22no—
465C2×C4×D3—22no—
466C2×C4×D3—22no—
467C2×C4×D3—22no—
468C2×C4×D3—416no—
469C2×C4×D3—41no—
470C2×C4×D3—41no—
471C2×C4×D3—42no—
472C2×C4×D3#4114yes—
473C2×Dic6—22no—
474C2×Dic6—22no—
475C2×Dic6—22no—
476C2×Dic6—24no—
477C2×Dic6—42no—
478C2×Dic6—42no—
479C3×C4⋊C4—22no—
480C3×C4⋊C4—22no—
481C3×C4⋊C4—42no—
482C3×C4⋊C4—41no—
483C3×C4⋊C4—41no—
484C3×C4⋊C4C2×D414yes—
485C3×C22⋊C4—42no—
486C3×C22⋊C4—42no—
487C3×C22⋊C4—42no—
488C3×C22⋊C4—41no—
489C3×C22⋊C4—41no—
490C3×C22⋊C4—42no—
491C3×C22⋊C4C2×D418yes—
492C3×C42—22no—
493C3×C42—22no—
494C3×C42—42no—
495#217—24no—
496#217—24no—
497#217—24no—
498#217—24no—
499#217—24no—
500#217—22no—
501#217—22no—
502(C2×D3)⋊C4—24no—
503(C2×D3)⋊C4—22no—
504(C2×D3)⋊C4—24no—
505(C2×D3)⋊C4—22no—
506(C2×D3)⋊C4—22no—
507(C2×D3)⋊C4—24no—
508(C2×D3)⋊C4—22no—
509(C2×D3)⋊C4—22no—
510(C2×D3)⋊C4—22no—
511(C2×D3)⋊C4—24no—
512(C2×D3)⋊C4—24no—
513(C2×D3)⋊C4—42no—
514(C2×D3)⋊C4—42no—
515(C2×D3)⋊C4—42no—
516(C2×D3)⋊C4—42no—
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—41no—
524C4⋊Dic3—22no—
525C4⋊Dic3—22no—
526C4⋊Dic3—22no—
527C4⋊Dic3—22no—
528C4⋊Dic3—24no—
529C4⋊Dic3—42no—
530C4⋊Dic3—42no—
531C4⋊Dic3—42no—
532C4⋊Dic3—42no—
533C4⋊Dic3—42no—
534Dic3⋊C4—24no—
535Dic3⋊C4—24no—
536Dic3⋊C4—24no—
537Dic3⋊C4—24no—
538C4×Dic3—24no—
539C4×Dic3—22no—
540C4×Dic3—22no—
541C25—31no—
542C25—32no—
543C22×Q8—31no—
544C22×Q8—32no—
545C22×D4—32no—
546C22×D4—32no—
547C22×D4—32no—
548C22×D4—31no—
549C22×D4—32no—
550C22×D4—64no—
551C22×D4—64no—
552C22×D4—68no—
553C22×D4—122no—
554C22×D4—124no—
555C22×D4—124no—
556C22×D4C22×D311yescharacteristic
557C22×D4C22×D312yes—
558C23×C4—31no—
559C23×C4—31no—
560C23×C4—32no—
561C23×C4—31no—
562C23×C4—31no—
563C23×C4—32no—
564C23×C4—31no—
565C23×C4—64no—
566C23×C4—64no—
567C23×C4—122no—
568C23×C4C22×D311yescharacteristic
569C23×C4C22×D312yes—
570C4⋊Q8—64no—
571#126—68no—
572#124—64no—
573#124—68no—
574#124—122no—
575#124—124no—
576#123—68no—
577#123—124no—
578C22⋊Q8—64no—
579C22⋊Q8—64no—
580C22⋊Q8—68no—
581C22⋊Q8—124no—
582C22⋊Q8—122no—
583#121—64no—
584#121—68no—
585#121—64no—
586#121—64no—
587#121—68no—
588#121D1218yes—
589C4×Q8—64no—
590C4×D4—42no—
591C4×D4—64no—
592#117—42no—
593#117—64no—
594C2×C4⋊C4—31no—
595C2×C4⋊C4—32no—
596C2×C4⋊C4—31no—
597C2×C4⋊C4—31no—
598C2×C4⋊C4—31no—
599C2×C4⋊C4—32no—
600C2×C4⋊C4—32no—
601C2×C4⋊C4—32no—
602C2×C4⋊C4—32no—
603C2×C4⋊C4—32no—
604C2×C4⋊C4—32no—
605C2×C4⋊C4—32no—
606C2×C4⋊C4—32no—
607C2×C4⋊C4—32no—
608C2×C4⋊C4—64no—
609C2×C4⋊C4C22×D311yescharacteristic
610C2×C4⋊C4C22×D311yescharacteristic
611C2×C4⋊C4C22×D311yescharacteristic
612C2×C4⋊C4C22×D311yescharacteristic
613C2×C4⋊C4C22×D312yes—
614C2×C4⋊C4C22×D311yescharacteristic
615C2×C22⋊C4—32no—
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—31no—
623C2×C22⋊C4—32no—
624C2×C22⋊C4—32no—
625C2×C22⋊C4—32no—
626C2×C22⋊C4—31no—
627C2×C22⋊C4—32no—
628C2×C22⋊C4—31no—
629C2×C22⋊C4—32no—
630C2×C22⋊C4—31no—
631C2×C22⋊C4—31no—
632C2×C22⋊C4—31no—
633C2×C22⋊C4—32no—
634C2×C22⋊C4—32no—
635C2×C22⋊C4—32no—
636C2×C22⋊C4—32no—
637C2×C22⋊C4—32no—
638C2×C22⋊C4—32no—
639C2×C22⋊C4—32no—
640C2×C22⋊C4—31no—
641C2×C22⋊C4—31no—
642C2×C22⋊C4—32no—
643C2×C22⋊C4—32no—
644C2×C22⋊C4—68no—
645C2×C22⋊C4—124no—
646C2×C22⋊C4C22×D311yescharacteristic
647C2×C22⋊C4C22×D311yescharacteristic
648C2×C22⋊C4C22×D312yes—
649C2×C22⋊C4C22×D312yes—
650C2×C22⋊C4C22×D312yes—
651C2×C22⋊C4C22×D312yes—
652C2×C22⋊C4C22×D312yes—
653C2×C42—31no—
654C2×C42—31no—
655C2×C42—32no—
656C2×C42C22×D311yescharacteristic
657C2×C42C22×D311yescharacteristic
658C2×C42C22×D312yes—
659#95—31no—
660#95—31no—
661#95—31no—
662#95—31no—
663#95—31no—
664#95—31no—
665#95—31no—
666#95—31no—
667#95—32no—
668#95—32no—
669#95—32no—
670#95—32no—
671#95—32no—
672#95—32no—
673#95C22×D312yes—
674#95C22×D312yes—
675#95C22×D312yes—
676C23×C3—21no—
677C23×C3—22no—
678C23×C3—21no—
679C23×C3—22no—
680C23×C3—22no—
681C23×C3—22no—
682C23×C3—21no—
683C23×C3—21no—
684C23×C3—21no—
685C23×C3—22no—
686C23×C3—21no—
687C23×C3—22no—
688C23×C3C22×D414yes—
689C23×C3C22×D412yes—
690C23×C3C2511yescharacteristic
691C22×D3—21no—
692C22×D3—21no—
693C22×D3—21no—
694C22×D3—21no—
695C22×D3—28no—
696C22×D3—21no—
697C22×D3—21no—
698C22×D3—21no—
699C22×D3—21no—
700C22×D3—21no—
701C22×D3—21no—
702C22×D3—22no—
703C22×D3—22no—
704C22×D3—22no—
705C22×D3—22no—
706C22×D3—22no—
707C22×D3—22no—
708C22×D3—22no—
709C22×D3—44no—
710C22×D3—44no—
711C22×D3—44no—
712C22×D3—44no—
713C22×D3—44no—
714C22×D3—48no—
715C22×D3—48no—
716C22×D3—48no—
717C22×D3—44no—
718C22×D3—48no—
719C22×D3—84no—
720C22×D3—84no—
721C22×D3—84no—
722C22×D3C2×#4112yes—
723C22×D3H(5,𝔽2)12yes—
724C22×D3H(5,𝔽2)12yes—
725C22×D32−1+412yes—
726C3×D4—28no—
727C3×D4—48no—
728C2×C3×C4—21no—
729C2×C3×C4—22no—
730C2×C3×C4—21no—
731C2×C3×C4—22no—
732C2×C3×C4—28no—
733C2×C3×C4—22no—
734C2×C3×C4—21no—
735C2×C3×C4—21no—
736C2×C3×C4—22no—
737C2×C3×C4—22no—
738C2×C3×C4—22no—
739C2×C3×C4—21no—
740C2×C3×C4—21no—
741C2×C3×C4—21no—
742C2×C3×C4—21no—
743C2×C3×C4—21no—
744C2×C3×C4—21no—
745C2×C3×C4—21no—
746C2×C3×C4—21no—
747C2×C3×C4—22no—
748C2×C3×C4—21no—
749C2×C3×C4—22no—
750C2×C3×C4—21no—
751C2×C3×C4—84no—
752C2×C3×C4C22×D414yes—
753C2×C3×C4C22×D412yes—
754C2×C3×C4C22×D412yes—
755C2×C3×C4C2×#4112yes—
756C2×C3×C4H(5,𝔽2)12yes—
757#67—48no—
758#67—48no—
759#67—48no—
760C2×Dic3—21no—
761C2×Dic3—21no—
762C2×Dic3—21no—
763C2×Dic3—21no—
764C2×Dic3—21no—
765C2×Dic3—22no—
766C2×Dic3—21no—
767C2×Dic3—22no—
768C2×Dic3—22no—
769C2×Dic3—21no—
770C2×Dic3—22no—
771C2×Dic3—21no—
772C2×Dic3—21no—
773C2×Dic3—21no—
774C2×Dic3—21no—
775C2×Dic3—22no—
776C2×Dic3—22no—
777C2×Dic3—22no—
778C2×Dic3—22no—
779C2×Dic3—22no—
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—21no—
783C2×Dic3—21no—
784C2×Dic3—21no—
785C2×Dic3—21no—
786C2×Dic3—44no—
787C2×Dic3—84no—
788C2×Dic3C2×#4112yes—
789D12—48no—
790D12—44no—
791C4×D3—28no—
792C4×D3—44no—
793C4×D3—44no—
794C4×D3—48no—
795C4×D3—44no—
796Dic6—44no—
797Dic6—84no—
798C24—31no—
799C24—31no—
800C24—32no—
801C24—62no—
802C24—62no—
803C24—62no—
804C24—62no—
805C24—64no—
806C24—64no—
807C24—64no—
808C24—62no—
809C24—64no—
810C24—121no—
811C24—121no—
812C24—122no—
813C24—122no—
814C24—122no—
815C24C23×D311yescharacteristic
816C24C23×D312yes—
817C2×Q8—62no—
818C2×Q8—64no—
819C2×Q8—62no—
820C2×Q8—62no—
821C2×Q8—122no—
822C2×Q8—122no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—42no—
826C2×D4—42no—
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—62no—
837C2×D4—122no—
838C2×D4—1216no—
839C2×D4—122no—
840C2×D4—122no—
841C2×D4—122no—
842C2×D4—122no—
843C2×D4—1232no—
844C2×D4C2×D1214yes—
845C2×D4C2×D1218yes—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—31no—
849C22×C4—34no—
850C22×C4—31no—
851C22×C4—31no—
852C22×C4—31no—
853C22×C4—32no—
854C22×C4—32no—
855C22×C4—31no—
856C22×C4—31no—
857C22×C4—32no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—62no—
862C22×C4—64no—
863C22×C4—62no—
864C22×C4—62no—
865C22×C4—62no—
866C22×C4—62no—
867C22×C4—62no—
868C22×C4—64no—
869C22×C4—62no—
870C22×C4—64no—
871C22×C4—62no—
872C22×C4—62no—
873C22×C4—62no—
874C22×C4—62no—
875C22×C4—121no—
876C22×C4—121no—
877C22×C4—122no—
878C22×C4—1216no—
879C22×C4—121no—
880C22×C4—122no—
881C22×C4—122no—
882C22×C4C2×D1214yes—
883C22×C4C23×D311yescharacteristic
884C22×C4C23×D311yescharacteristic
885C22×C4C23×D311yescharacteristic
886C22×C4C23×D312yes—
887C22×C4C23×D312yes—
888C22×C4C23×D311yescharacteristic
889C22×C4C23×D312yes—
890C22×C4C23×D311yescharacteristic
891C22×C4C23×D311yescharacteristic
892C4⋊C4—22no—
893C4⋊C4—22no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—42no—
897C4⋊C4—64no—
898C4⋊C4—64no—
899C4⋊C4—62no—
900C4⋊C4—62no—
901C4⋊C4—62no—
902C4⋊C4—62no—
903C4⋊C4—64no—
904C4⋊C4—64no—
905C4⋊C4—64no—
906C4⋊C4—122no—
907C4⋊C4—122no—
908C4⋊C4—122no—
909C4⋊C4—122no—
910C4⋊C4—122no—
911C4⋊C4C2×D1214yes—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—62no—
919C22⋊C4—64no—
920C22⋊C4—64no—
921C22⋊C4—62no—
922C22⋊C4—62no—
923C22⋊C4—64no—
924C22⋊C4—62no—
925C22⋊C4—62no—
926C22⋊C4—62no—
927C22⋊C4—64no—
928C22⋊C4—62no—
929C22⋊C4—62no—
930C22⋊C4—64no—
931C22⋊C4—64no—
932C22⋊C4—64no—
933C22⋊C4—64no—
934C22⋊C4—64no—
935C22⋊C4—64no—
936C22⋊C4—122no—
937C22⋊C4—122no—
938C22⋊C4—122no—
939C22⋊C4—122no—
940C22⋊C4—122no—
941C22⋊C4—122no—
942C22⋊C4—122no—
943C22⋊C4—121no—
944C22⋊C4—122no—
945C22⋊C4—122no—
946C22⋊C4—121no—
947C22⋊C4C2×D1218yes—
948C42—22no—
949C42—22no—
950C42—42no—
951C42—62no—
952C42—62no—
953C42—64no—
954C22×C3—22no—
955C22×C3—24no—
956C22×C3—24no—
957C22×C3—22no—
958C22×C3—22no—
959C22×C3—24no—
960C22×C3—41no—
961C22×C3—42no—
962C22×C3—41no—
963C22×C3—42no—
964C22×C3—41no—
965C22×C3—42no—
966C22×C3—42no—
967C22×C3—41no—
968C22×C3C23×D411yescharacteristic
969C22×C3C22×#4111yescharacteristic
970C22×C3C2×H(5,𝔽2)11yescharacteristic
971C22×C3C2×H(5,𝔽2)11yescharacteristic
972C22×C3C2×H(5,𝔽2)11yescharacteristic
973C22×C3C2×2−1+411yescharacteristic
974C22×C3#58511yescharacteristic
975C2×D3—22no—
976C2×D3—22no—
977C2×D3—22no—
978C2×D3—22no—
979C2×D3—22no—
980C2×D3—22no—
981C2×D3—22no—
982C2×D3—22no—
983C2×D3—22no—
984C2×D3—416no—
985C2×D3—41no—
986C2×D3—41no—
987C2×D3—41no—
988C2×D3—41no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—42no—
994C2×D3—42no—
995C2×D3—42no—
996C2×D3—816no—
997C2×D3#54214yescomplemented
998C3×C4—22no—
999C3×C4—24no—
1000C3×C4—42no—
1001C3×C4—41no—
1002C3×C4—41no—
1003C3×C4—41no—
1004C3×C4—42no—
1005C3×C4—41no—
1006C3×C4#54614yes—
1007Dic3—22no—
1008Dic3—42no—
1009Dic3—41no—
1010Dic3—41no—
1011Dic3—42no—
1012Dic3—42no—
1013Dic3—41no—
1014Dic3—41no—
1015Dic3—41no—
1016C23—21no—
1017C23—22no—
1018C23—21no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—22no—
1026C23—21no—
1027C23—22no—
1028C23—32no—
1029C23—32no—
1030C23—32no—
1031C23—32no—
1032C23—68no—
1033C23—61no—
1034C23—61no—
1035C23—61no—
1036C23—61no—
1037C23—61no—
1038C23—61no—
1039C23—61no—
1040C23—61no—
1041C23—61no—
1042C23—61no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—62no—
1047C23—62no—
1048C23—62no—
1049C23—62no—
1050C23—124no—
1051C23—124no—
1052C23—128no—
1053C23—128no—
1054C23—128no—
1055C23—124no—
1056C23—128no—
1057C23—124no—
1058C23—124no—
1059C23—124no—
1060C23—244no—
1061C23—244no—
1062C23—244no—
1063C23C22×D1214yes—
1064C23C22×D1212yes—
1065C23C24×D311yescharacteristic
1066Q8—124no—
1067Q8—244no—
1068D4—28no—
1069D4—48no—
1070D4—128no—
1071D4—128no—
1072D4—128no—
1073D4—128no—
1074D4—124no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—28no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—32no—
1099C2×C4—61no—
1100C2×C4—61no—
1101C2×C4—68no—
1102C2×C4—61no—
1103C2×C4—61no—
1104C2×C4—62no—
1105C2×C4—61no—
1106C2×C4—61no—
1107C2×C4—61no—
1108C2×C4—62no—
1109C2×C4—62no—
1110C2×C4—62no—
1111C2×C4—61no—
1112C2×C4—62no—
1113C2×C4—61no—
1114C2×C4—61no—
1115C2×C4—61no—
1116C2×C4—62no—
1117C2×C4—62no—
1118C2×C4—61no—
1119C2×C4—61no—
1120C2×C4—62no—
1121C2×C4—62no—
1122C2×C4—61no—
1123C2×C4—61no—
1124C2×C4—61no—
1125C2×C4—61no—
1126C2×C4—84no—
1127C2×C4—124no—
1128C2×C4—124no—
1129C2×C4—128no—
1130C2×C4—124no—
1131C2×C4—124no—
1132C2×C4—244no—
1133C2×C4C22×D1214yes—
1134C2×C4C22×D1212yes—
1135C2×C4C22×D1212yes—
1136C2×C4#100412yes—
1137C2×C4D3×#4112yes—
1138C2×C3—42no—
1139C2×C3—44no—
1140C2×C3C2×#54211yescharacteristic
1141C2×C3C2×#54611yescharacteristic
1142C2×C3#348411yescharacteristic
1143C2×C3#348911yescharacteristic
1144C2×C3#349411yescharacteristic
1145C2×C3#353611yescharacteristic
1146C2×C3#354211yescharacteristic
1147D3—24no—
1148D3—42no—
1149D3—82no—
1150C22—22no—
1151C22—24no—
1152C22—24no—
1153C22—22no—
1154C22—22no—
1155C22—24no—
1156C22—34no—
1157C22—41no—
1158C22—42no—
1159C22—42no—
1160C22—41no—
1161C22—41no—
1162C22—42no—
1163C22—41no—
1164C22—42no—
1165C22—62no—
1166C22—62no—
1167C22—62no—
1168C22—62no—
1169C22—62no—
1170C22—62no—
1171C22—62no—
1172C22—62no—
1173C22—62no—
1174C22—1216no—
1175C22—121no—
1176C22—121no—
1177C22—121no—
1178C22—121no—
1179C22—122no—
1180C22—122no—
1181C22—122no—
1182C22—122no—
1183C22—122no—
1184C22—122no—
1185C22—122no—
1186C22—2416no—
1187C22C23×D1211yescharacteristic
1188C22C2×#100411yescharacteristic
1189C22C2×D3×#4111yescharacteristic
1190C22D3×H(5,𝔽2)11yescharacteristic
1191C22D3×H(5,𝔽2)11yescharacteristic
1192C22#596611yescharacteristic
1193C22D3×2−1+411yescharacteristic
1194C4—22no—
1195C4—24no—
1196C4—41no—
1197C4—42no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—42no—
1202C4—62no—
1203C4—121no—
1204C4—122no—
1205C4—122no—
1206C4—121no—
1207C4—122no—
1208C4—121no—
1209C4—121no—
1210C4—121no—
1211C4#555414yes—
1212C3#3766411yescharacteristic, complemented, Sylow
1213C2—42no—
1214C2—44no—
1215C2—64no—
1216C2—122no—
1217C2—242no—
1218C2C2×#555411yescharacteristic
1219C2#8586711yescharacteristic
1220C2#8590111yescharacteristic
1221C2#8633511yescharacteristic
1222C2#8638411yescharacteristic
1223C2#8648511yescharacteristic
1224C2D3×#54211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2324C2
prime radicalC2×D3×#121C2
hypercenter#2324D3
hypocenterC3#37664
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×#5603C2semidirect
3. C3×#2324C2semidirect
4. #82408C2semidirect
5. D4×(C2×D3)⋊C4C2semidirect
6. #82287C2semidirect
7. #82267C2semidirect
8. #76441C2semidirect
9. #76386C2semidirect
10. #76315C2semidirect
11. #76315C2semidirect
12. #76218C2semidirect
13. #75999C2semidirect
14. #75665C2semidirect
15. #75540C2semidirect
16. #74796C2semidirect
17. #74686C2semidirect
18. #74635C2semidirect
19. #74413C2semidirect
20. #74049C2semidirect
21. #74033C2semidirect
22. #73788C2semidirect
23. #73773C2semidirect
29. C2×C3×C4×D4C22semidirect
30. C2×C3×#117C22semidirect
33. C2×#936C22semidirect
34. C2×#936C22semidirect
35. C2×#935C22semidirect
36. C2×D4×Dic3C22semidirect
39. C2×#926C22semidirect
40. C2×#924C22semidirect
45. C2×#897C22semidirect
48. C2×#888C22semidirect
49. C2×#887C22semidirect
50. C2×#886C22semidirect
53. C2×#879C22semidirect
54. C2×#878C22semidirect
55. C2×#875C22semidirect
56. C2×#875C22semidirect
57. C3×#390C22semidirect
58. C3×#390C22semidirect
59. C3×#389C22semidirect
60. C3×#388C22semidirect
61. C3×#386C22semidirect
62. C3×#385C22semidirect
63. C3×#380C22semidirect
64. C3×C4×C4⋊C4C22semidirect
65. #5213C22semidirect
66. #5213C22semidirect
67. #5212C22semidirect
68. #4994C22semidirect
69. #4994C22semidirect
70. #4994C22semidirect
71. #4988C22semidirect
72. #4988C22semidirect
73. #4988C22semidirect
77. #4987C22semidirect
78. #4987C22semidirect
79. #4987C22semidirect
80. #4984C22semidirect
81. #4984C22semidirect
82. #4981C22semidirect
83. #4961C22semidirect
84. #4961C22semidirect
85. #4961C22semidirect
86. #4961C22semidirect
87. #4961C22semidirect
88. #4961C22semidirect
89. #4961C22semidirect
90. #4961C22semidirect
91. #4958C22semidirect
98. #4953C22semidirect
99. #4953C22semidirect
100. #4950C22semidirect
101. #4950C22semidirect
102. #4943C22semidirect
103. #4943C22semidirect
104. #4940C22semidirect
105. #4939C22semidirect
109. C4×(C2×D3)⋊C4C22semidirect
110. C4×(C2×D3)⋊C4C22semidirect
111. #4935C22semidirect
112. #4929C22semidirect
113. #4928C22semidirect
114. #4677C22semidirect
115. #4674C22semidirect
116. #4673C22semidirect
117. #4672C22semidirect
118. #4672C22semidirect
119. #4670C22semidirect
123. #4668C22semidirect
124. #4656C22semidirect
125. #4653C22semidirect
147. #2324D3semidirect
310. C2×C4×D4C2×D3semidirect
312. C2×#117C2×D3semidirect
341. #390C2×D3semidirect
342. #390C2×D3semidirect
346. #389C2×D3semidirect
349. #388C2×D3semidirect
354. #386C2×D3semidirect
361. #385C2×D3semidirect
372. #380C2×D3semidirect
379. C4×C4⋊C4C2×D3semidirect
997. C2×D3#542semidirect
1212. C3#37664semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#1212
C2×#56032
C3×#23242
#824082
D4×(C2×D3)⋊C42
#822872
#822672
#764412
#763862
#763152
#762182
#759992
#756652
#755402
#747962
#746862
#746352
#744132
#740492
#740332
#737882
#737732
#376643