Finite Group Databasebeta

← #10972954

Subgroups — #10972954

Order 768.

2470 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#544C211yesmaximal, characteristic, complemented
2C2×D3×#117C211yesmaximal, characteristic
3#83269C212yesmaximal, complemented
4#83262C212yesmaximal, complemented
5#83256C212yesmaximal, complemented
6#83233C212yesmaximal, complemented
7#83072C212yesmaximal, complemented
8#83065C212yesmaximal, complemented
9#83058C212yesmaximal, complemented
10#83028C212yesmaximal, complemented
11#82816C214yesmaximal
12#82762C214yesmaximal, complemented
13#82267C211yesmaximal, characteristic
14#82233C211yesmaximal, characteristic, complemented
15#82232C211yesmaximal, characteristic, complemented
16C2×#4987C211yesmaximal, characteristic
17#82157C211yesmaximal, characteristic, complemented
18#35253—31nomaximal, Sylow
19C23×C4×D3C2211yescharacteristic
20C3×#544—28no—
21C2×C3×C4⋊Q8C2212yescomplemented
22C2×C3×C4⋊Q8C2212yescomplemented
23C2×C3×#125C2212yescomplemented
24C2×C3×#125C2212yescomplemented
25C2×C3×C22⋊Q8C2214yes—
26C2×C3×#117C2211yescharacteristic
27C2×C3×#117C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C2×#946C2214yes—
30C22×(C2×D3)⋊C4C2212yes—
31C2×#926C2211yescharacteristic
32C2×#926C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34D3×#117—28no—
35C2×#892C2211yescharacteristic
36C2×#892C2211yescharacteristic
37C2×D3×C4⋊C4C2211yescharacteristic
38C2×D3×C4⋊C4C2211yescharacteristic
39C2×D3×C22⋊C4C2212yes—
40C2×#877C2212yes—
41C2×#872C2212yes—
42C2×C42×D3C2212yes—
43#5231C2214yes—
44#5230C2214yescomplemented
45#5229C2214yescomplemented
46#5210C2214yes—
47C2×C3⋊#95C2212yes—
48#4994C2214yes—
49#4994C2214yes—
50#4993C2214yes—
51#4989C2214yes—
52#4989C2214yes—
53#4987C2212yes—
54#4987C2212yes—
55#4987C2212yes—
56#4987C2212yes—
57#4987C2211yescharacteristic
58#4987C2211yescharacteristic
59#4987C2214yes—
60#4987C2211yescharacteristic
61#4987C2211yescharacteristic
62#4985C2214yescomplemented
63#4984C2212yescomplemented
64#4984C2212yescomplemented
65#4982C2214yescomplemented
66#4982C2214yescomplemented
67#4978C2214yescomplemented
68#4978C2214yescomplemented
69#4977C2212yescomplemented
70#4975C2212yescomplemented
71#4972C2212yescomplemented
72#4972C2212yescomplemented
73#4972C2212yescomplemented
74#4972C2214yescomplemented
75#4972C2212yescomplemented
76#4955C2212yes—
77#4950C2214yes—
78#4943C2212yes—
79#4942C2214yes—
80C4×(C2×D3)⋊C4C2212yes—
81C4×(C2×D3)⋊C4C2212yes—
82#4936C2212yescomplemented
83#4935C2212yescomplemented
84#4928C2212yescomplemented
85#4928C2212yescomplemented
86C2×#544D311yescharacteristic, complemented
87C22×#117—31no—
88#2857—32no—
89#2851—32no—
90#2629—32no—
91#2628—32no—
92#2442—32no—
93#2441—32no—
94#2440—32no—
95#2439—32no—
96#2438—34no—
97#2437—34no—
98#2317—31no—
99#2317—31no—
100#2316—31no—
101#2280—31no—
102C2×#380—31no—
103C24×D3C2311yescharacteristic
104C22×C3×Q8C2314yes—
105C23×C3×C4C2312yes—
106C23×C3×C4C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2312yes—
109C22×C4×D3—24no—
110C22×C4×D3—24no—
111C22×C4×D3Q818yescomplemented
112C22×C4×D3C2312yes—
113C22×C4×D3C2312yes—
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2311yescharacteristic
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C3×C4⋊Q8—28no—
119C3×C4⋊Q8—28no—
120C3×#125—28no—
121C3×#125—28no—
122C3×C22⋊Q8—216no—
123C3×#117—24no—
124C3×#117D418yes—
125C2×C3×C4⋊C4—24no—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2314yes—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C4⋊C4C2314yes—
132C2×C3×C4⋊C4C2314yes—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4C2312yes—
136C2×C3×C22⋊C4C2312yes—
137C2×C3×C42C2312yes—
138C2×C3×C42C2312yes—
139C2×#217C2312yes—
140C2×#217C2312yes—
141#946—48no—
142C2×(C2×D3)⋊C4—44no—
143C2×(C2×D3)⋊C4C2312yes—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2314yes—
151#926—24no—
152#926—24no—
153C2×C4⋊Dic3—24no—
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2311yescharacteristic
160C2×C4⋊Dic3C2314yes—
161C2×C4⋊Dic3C2314yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2312yes—
164C2×Dic3⋊C4C2314yes—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×C4×Dic3C2312yes—
169C2×C4×Dic3C2312yes—
170C2×C4×Dic3C2312yes—
171C2×C4×Dic3C2312yes—
172#892—24no—
173#892—24no—
174D3×C4⋊C4—24no—
175D3×C4⋊C4—24no—
176D3×C22⋊C4—28no—
177#877—28no—
178#872—28no—
179C42×D3—28no—
180C3⋊#95C2314yes—
181C3⋊#95C2314yes—
182C3⋊#95C2314yes—
183C3⋊#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C24×C4—31no—
193#544—28no—
194C2×C4⋊Q8C2×D312yescomplemented
195C2×C4⋊Q8C2×D312yescomplemented
196C2×#125C2×D312yescomplemented
197C2×#125C2×D312yescomplemented
198C2×C22⋊Q8—34no—
199C2×C22⋊Q8C2×D314yes—
200C2×#117—31no—
201C2×#117—31no—
202C2×#117—31no—
203C2×#117—31no—
204C2×#117—32no—
205C2×#117—32no—
206C2×#117—68no—
207C2×#117C2×D311yescharacteristic
208C2×#117C2×D311yescharacteristic
209C22×C4⋊C4—31no—
210C22×C4⋊C4—31no—
211C22×C4⋊C4—31no—
212C22×C4⋊C4C2×D311yescharacteristic
213C22×C22⋊C4—32no—
214C22×C22⋊C4—32no—
215C22×C42—32no—
216#400—34no—
217#399—34no—
218#398—34no—
219#398—34no—
220#396—34no—
221#396—34no—
222#395—34no—
223#393—34no—
224#391—34no—
225#389—32no—
226#389—32no—
227#389—32no—
228#389—32no—
229#389—32no—
230#389—32no—
231#389—34no—
232#389—32no—
233#389—32no—
234#387—34no—
235#387—34no—
236#385—34no—
237#385—34no—
238#385—34no—
239#385—34no—
240#384—32no—
241#384—32no—
242#382—32no—
243#382—32no—
244#381—32no—
245#380—31no—
246#380—32no—
247#380—31no—
248#380—34no—
249#380—31no—
250#380—32no—
251#380—31no—
252#380—32no—
253#380—32no—
254#380—34no—
255#379—32no—
256C4×C22⋊C4—32no—
257C4×C22⋊C4—32no—
258C2×#95—32no—
259C24×C3C2411yescharacteristic
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—22no—
263C23×D3—22no—
264C23×D3—41no—
265C23×D3—41no—
266C23×D3C2×Q814yes—
267C23×D3C2411yescharacteristic
268C23×D3C2411yescharacteristic
269C2×C3×Q8—28no—
270C2×C3×Q8—44no—
271C2×C3×Q8—44no—
272C22×C3×C4—24no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4C2×D414yes—
276C22×C3×C4C2×Q814yes—
277C22×C3×C4#4114yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2414yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2412yes—
283C22×C3×C4C2411yescharacteristic
284C22×C3×C4C2411yescharacteristic
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—24no—
288C22×Dic3—42no—
289C22×Dic3—42no—
290C22×Dic3C2×Q814yes—
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293C22×Dic3C2414yes—
294C22×Dic3C2412yes—
295C22×Dic3C2412yes—
296C22×Dic3C2411yescharacteristic
297C22×Dic3C2411yescharacteristic
298C2×C4×D3—232no—
299C2×C4×D3—22no—
300C2×C4×D3—22no—
301C2×C4×D3—22no—
302C2×C4×D3—22no—
303C2×C4×D3—22no—
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3—22no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—24no—
310C2×C4×D3—24no—
311C2×C4×D3—42no—
312C2×C4×D3—42no—
313C2×C4×D3C2×Q814yes—
314C2×C4×D3C2×Q814yes—
315C2×C4×D3C2×Q814yes—
316C2×C4×D3C2×Q814yes—
317C3×C4⋊C4—24no—
318C3×C4⋊C4—24no—
319C3×C4⋊C4—22no—
320C3×C4⋊C4—22no—
321C3×C4⋊C4—28no—
322C3×C4⋊C4—28no—
323C3×C4⋊C4—28no—
324C3×C4⋊C4C2×D414yes—
325C3×C4⋊C4C2×D414yes—
326C3×C22⋊C4—24no—
327C3×C22⋊C4C2×D418yes—
328C3×C42—24no—
329C3×C42C2×D418yes—
330#217—24no—
331#217—24no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340C4⋊Dic3—22no—
341C4⋊Dic3—22no—
342C4⋊Dic3—24no—
343C4⋊Dic3—24no—
344C4⋊Dic3—22no—
345C4⋊Dic3—22no—
346C4⋊Dic3—44no—
347C4⋊Dic3—44no—
348Dic3⋊C4—24no—
349Dic3⋊C4—24no—
350Dic3⋊C4—44no—
351Dic3⋊C4—44no—
352Dic3⋊C4—44no—
353Dic3⋊C4—44no—
354C4×Dic3—24no—
355C4×Dic3—24no—
356C4×Dic3—24no—
357C4×Dic3—24no—
358C25—31no—
359C22×Q8C22×D314yes—
360C23×C4—31no—
361C23×C4—38no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—32no—
367C23×C4—32no—
368C23×C4—32no—
369C23×C4—64no—
370C23×C4—64no—
371C23×C4C22×D312yes—
372C23×C4C22×D311yescharacteristic
373C4⋊Q8—28no—
374C4⋊Q8—28no—
375#125—28no—
376#125—28no—
377C22⋊Q8—216no—
378C22⋊Q8—128no—
379#117—24no—
380#117—64no—
381#117—64no—
382#117—64no—
383#117—64no—
384#117—68no—
385#117—68no—
386#117#6718yes—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4—34no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—64no—
403C2×C4⋊C4—64no—
404C2×C4⋊C4—64no—
405C2×C4⋊C4C22×D312yes—
406C2×C4⋊C4C22×D312yes—
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D311yescharacteristic
409C2×C4⋊C4C22×D314yes—
410C2×C4⋊C4C22×D314yes—
411C2×C4⋊C4C22×D314yes—
412C2×C4⋊C4C22×D311yescharacteristic
413C2×C4⋊C4C22×D311yescharacteristic
414C2×C22⋊C4—32no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—68no—
425C2×C22⋊C4—124no—
426C2×C22⋊C4C22×D312yes—
427C2×C22⋊C4C22×D312yes—
428C2×C42—32no—
429C2×C42—32no—
430C2×C42—32no—
431C2×C42—32no—
432C2×C42—68no—
433C2×C42C22×D312yes—
434C2×C42C22×D312yes—
435#95—34no—
436#95—34no—
437#95—32no—
438#95—32no—
439#95—32no—
440#95—32no—
441#95—34no—
442#95—34no—
443#95—34no—
444#95—34no—
445#95—34no—
446#95—34no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3C22×D412yes—
452C23×C3C22×Q812yes—
453C23×C3C2×#4112yes—
454C23×C3C2511yescharacteristic
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—28no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—28no—
467C22×D3—44no—
468C22×D3—44no—
469C22×D3—44no—
470C22×D3—44no—
471C22×D3—44no—
472C22×D3C22×Q812yes—
473C22×D3C22×Q812yes—
474C22×D3H(5,𝔽2)12yes—
475C22×D32−1+412yes—
476C3×Q8—88no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—24no—
484C2×C3×C4—22no—
485C2×C3×C4—24no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—24no—
489C2×C3×C4—22no—
490C2×C3×C4—84no—
491C2×C3×C4C22⋊Q8116yescomplemented
492C2×C3×C4C22×D414yes—
493C2×C3×C4C22×D414yes—
494C2×C3×C4C22×D412yes—
495C2×C3×C4C22×D412yes—
496C2×C3×C4C22×Q812yes—
497C2×C3×C4C22×Q812yes—
498C2×C3×C4C2×#4112yes—
499C2×C3×C4C2×#4112yes—
500C2×Dic3—28no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—24no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—24no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—24no—
519C2×Dic3—22no—
520C2×Dic3—84no—
521C2×Dic3C22×Q812yes—
522C2×Dic3C22×Q812yes—
523C4×D3—28no—
524C4×D3—28no—
525C4×D3—28no—
526C4×D3—28no—
527C4×D3—48no—
528C4×D3—48no—
529C24—31no—
530C24—31no—
531C24—34no—
532C24—62no—
533C24—62no—
534C24—62no—
535C24—62no—
536C24—121no—
537C24—121no—
538C24C23×D311yescharacteristic
539C2×Q8—28no—
540C2×Q8—44no—
541C2×Q8—44no—
542C22×C4—24no—
543C22×C4—34no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—34no—
547C22×C4—34no—
548C22×C4—34no—
549C22×C4—34no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—34no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—64no—
558C22×C4—64no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—632no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—64no—
571C22×C4—64no—
572C22×C4—64no—
573C22×C4—122no—
574C22×C4—122no—
575C22×C4—122no—
576C22×C4—122no—
577C22×C4D3×Q814yes—
578C22×C4#23914yes—
579C22×C4C2×#6714yes—
580C22×C4C23×D312yes—
581C22×C4C23×D312yes—
582C22×C4C23×D314yes—
583C22×C4C23×D312yes—
584C22×C4C23×D312yes—
585C22×C4C23×D311yescharacteristic
586C22×C4C23×D311yescharacteristic
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—28no—
592C4⋊C4—28no—
593C4⋊C4—28no—
594C4⋊C4—64no—
595C4⋊C4—64no—
596C4⋊C4—62no—
597C4⋊C4—62no—
598C4⋊C4—64no—
599C4⋊C4—64no—
600C4⋊C4—62no—
601C4⋊C4—62no—
602C4⋊C4—124no—
603C4⋊C4—124no—
604C4⋊C4—124no—
605C4⋊C4—124no—
606C4⋊C4—124no—
607C4⋊C4—124no—
608C4⋊C4C2×#6714yes—
609C4⋊C4C2×#6714yes—
610C22⋊C4—24no—
611C22⋊C4—68no—
612C22⋊C4—64no—
613C22⋊C4—64no—
614C22⋊C4—64no—
615C22⋊C4—64no—
616C22⋊C4—64no—
617C22⋊C4—64no—
618C22⋊C4—124no—
619C22⋊C4—122no—
620C22⋊C4—122no—
621C22⋊C4C2×#6718yes—
622C42—24no—
623C42—64no—
624C42—64no—
625C42—64no—
626C42—64no—
627C42C2×#6718yes—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3C2×C22⋊Q814yes—
635C22×C3C23×D411yescharacteristic
636C22×C3C23×Q811yescharacteristic
637C22×C3C22×#4111yescharacteristic
638C22×C3C2×H(5,𝔽2)11yescharacteristic
639C22×C3C2×2−1+411yescharacteristic
640C22×C3#58511yescharacteristic
641C22×C3#58511yescharacteristic
642C2×D3—22no—
643C2×D3—22no—
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—416no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3#54414yescomplemented
657C3×C4—24no—
658C3×C4—24no—
659C3×C4—44no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4C2×C22⋊Q814yes—
663C3×C4C2×C22⋊Q814yes—
664Dic3—22no—
665Dic3—22no—
666Dic3—42no—
667Dic3—42no—
668Dic3—42no—
669Dic3—44no—
670Dic3—42no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—32no—
676C23—32no—
677C23—32no—
678C23—32no—
679C23—68no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—68no—
691C23—124no—
692C23—124no—
693C23—124no—
694C23—124no—
695C23—124no—
696C23C2×D3×Q812yes—
697C23C2×#23912yes—
698C23C22×#6712yes—
699C23C24×D311yescharacteristic
700Q8—88no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—68no—
721C2×C4—68no—
722C2×C4—68no—
723C2×C4—68no—
724C2×C4—68no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—64no—
728C2×C4—64no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—64no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—84no—
741C2×C4—128no—
742C2×C4—128no—
743C2×C4—244no—
744C2×C4#946116yescomplemented
745C2×C4C2×D3×Q812yes—
746C2×C4C2×D3×Q812yes—
747C2×C4C2×#23912yes—
748C2×C4C2×#23912yes—
749C2×C4C22×#6714yes—
750C2×C4C22×#6714yes—
751C2×C4C22×#6712yes—
752C2×C4C22×#6712yes—
753C2×C3—24no—
754C2×C3C22×C22⋊Q811yescharacteristic
755C2×C3C2×#54411yescharacteristic
756C2×C3#345811yescharacteristic
757C2×C3#348811yescharacteristic
758C2×C3#348911yescharacteristic
759C2×C3#349411yescharacteristic
760C2×C3#349511yescharacteristic
761D3—24no—
762D3—42no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—34no—
770C22—62no—
771C22—62no—
772C22—62no—
773C22—62no—
774C22—62no—
775C22—62no—
776C22—62no—
777C22—62no—
778C22—62no—
779C22—1216no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22C2×#94614yes—
785C22C22×D3×Q811yescharacteristic
786C22C22×#23911yescharacteristic
787C22D3×H(5,𝔽2)11yescharacteristic
788C22#596611yescharacteristic
789C22D3×2−1+411yescharacteristic
790C22#596811yescharacteristic
791C22C23×#6711yescharacteristic
792C4—24no—
793C4—24no—
794C4—44no—
795C4—42no—
796C4—42no—
797C4—62no—
798C4—62no—
799C4—124no—
800C4—122no—
801C4—122no—
802C4—122no—
803C4—122no—
804C4C2×#94614yes—
805C4C2×#94614yes—
806C3#3525311yescharacteristic, complemented, Sylow
807C2—24no—
808C2—64no—
809C2—122no—
810C2#8658111yescharacteristic
811C2D3×#54411yescharacteristic
812C2#8659711yescharacteristic
813C2#8659811yescharacteristic
814C2C22×#94611yescharacteristic
815C2#8728511yescharacteristic
816C2#8729511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#544C2
prime radicalC24×D3C23
hypercenterC2×#544D3
hypocenterC3#35253
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×C3×#544C2semidirect
3. #83269C2semidirect
4. #83262C2semidirect
5. #83256C2semidirect
6. #83233C2semidirect
7. #83072C2semidirect
8. #83065C2semidirect
9. #83058C2semidirect
10. #83028C2semidirect
12. #82762C2semidirect
14. #82233C2semidirect
15. #82232C2semidirect
17. #82157C2semidirect
21. C2×C3×C4⋊Q8C22semidirect
22. C2×C3×C4⋊Q8C22semidirect
23. C2×C3×#125C22semidirect
24. C2×C3×#125C22semidirect
44. #5230C22semidirect
45. #5229C22semidirect
62. #4985C22semidirect
63. #4984C22semidirect
64. #4984C22semidirect
65. #4982C22semidirect
66. #4982C22semidirect
67. #4978C22semidirect
68. #4978C22semidirect
69. #4977C22semidirect
70. #4975C22semidirect
71. #4972C22semidirect
72. #4972C22semidirect
73. #4972C22semidirect
74. #4972C22semidirect
75. #4972C22semidirect
82. #4936C22semidirect
83. #4935C22semidirect
84. #4928C22semidirect
85. #4928C22semidirect
86. C2×#544D3semidirect
111. C22×C4×D3Q8semidirect
194. C2×C4⋊Q8C2×D3semidirect
195. C2×C4⋊Q8C2×D3semidirect
196. C2×#125C2×D3semidirect
197. C2×#125C2×D3semidirect
491. C2×C3×C4C22⋊Q8semidirect
656. C2×D3#544semidirect
744. C2×C4#946semidirect
806. C3#35253semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5442
C2×D3×#1172
#832692
#832622
#832562
#832332
#830722
#830652
#830582
#830282
#828162
#827622
#822672
#822332
#822322
C2×#49872
#821572
#352533