Finite Group Databasebeta

← #11069554

Subgroups — #11069554

Order 768.

2370 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5619C212yesmaximal, complemented
2C3×#2537C211yesmaximal, characteristic, complemented
3#82705C212yesmaximal, complemented
4#82643C212yesmaximal, complemented
5#82641C212yesmaximal, complemented
6#82417C211yesmaximal, characteristic, complemented
7D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
8C4×#940C211yesmaximal, characteristic, complemented
9#82319C211yesmaximal, characteristic, complemented
10#77148C214yesmaximal, complemented
11#77020C214yesmaximal, complemented
12#74360C211yesmaximal, characteristic, complemented
13#74355C211yesmaximal, characteristic, complemented
14#74027C212yesmaximal, complemented
15#73955C212yesmaximal, complemented
16#73911C212yesmaximal, complemented
17#73891C212yesmaximal, complemented
18#39378—31nomaximal, Sylow
19C2×C3×#121C2212yes—
20C2×C3×#121C2212yes—
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C2×#940C2211yescharacteristic
24C2×#939C2214yes—
25C2×#938C2214yes—
26C2×#938C2212yes—
27C2×D4×Dic3C2212yes—
28C2×#930C2212yes—
29C2×C4×#67C2212yes—
30C2×C4×#67C2212yes—
31C2×#926C2212yes—
32C22×C4⋊Dic3C2212yes—
33#5619—216no—
34C2×#893C2212yes—
35C2×D3×C4⋊C4C2212yes—
36C2×#890C2212yes—
37C2×#886C2214yes—
38C2×#883C2214yes—
39C2×C4×D12C2211yescharacteristic
40C3×#394C2214yes—
41C3×#384C2211yescharacteristic
42C3×#380C2212yes—
43C3×#380C2212yes—
44#5222C2214yes—
45#5221C2211yescharacteristic
46#5221C2211yescharacteristic
47#5221C2211yescharacteristic
48#5220C2214yes—
49#5212C2212yes—
50#5212C2212yes—
51C4×#217C2212yes—
52#4989C2214yes—
53#4988C2211yescharacteristic
54#4987C2212yes—
55#4987C2212yes—
56#4984C2211yescharacteristic
57#4984C2212yes—
58#4984C2212yes—
59#4984C2211yescharacteristic
60#4984C2212yes—
61#4977C2212yes—
62#4975C2211yescharacteristic
63#4972C2212yes—
64#4972C2212yes—
65#4972C2212yes—
66#4961C2214yes—
67#4961C2214yes—
68#4957C2212yes—
69#4957C2212yes—
70#4956C2214yes—
71#4952C2214yes—
72#4951C2212yes—
73#4951C2212yes—
74#4950C2214yes—
75#4948C2214yes—
76#4948C2214yes—
77#4943C2214yes—
78#4935C2211yescharacteristic
79C4×C4⋊Dic3C2211yescharacteristic
80C42×Dic3C2211yescharacteristic
81#4674C2214yes—
82#4664C2214yes—
83#4661C2214yes—
84#4657C2214yes—
85C2×#540—32no—
86#2859—31no—
87#2701—34no—
88#2701—34no—
89#2629—32no—
90#2537—31no—
91#2537D311yescharacteristic, complemented
92#2486—32no—
93#2486—32no—
94#2420—32no—
95#2420—32no—
96#2416—32no—
97#2416—32no—
98D4×C4⋊C4—31no—
99D4×C4⋊C4—31no—
100C4×#127—31no—
101#2293—31no—
102C22×C3×D4C2311yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2314yes—
105C23×C3×C4C2312yes—
106C23×C3×C4C2312yes—
107C22×#67C2314yes—
108C22×#67C2312yes—
109C22×#67C2312yes—
110C23×Dic3C2314yes—
111C22×D12C2311yescharacteristic
112C22×C4×D3C2312yes—
113C22×C4×D3C2314yes—
114C3×#121—28no—
115C3×#121—44no—
116C3×C4×D4—24no—
117C3×C4×D4—24no—
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C22⋊C4C2314yes—
124C2×C3×C22⋊C4C2312yes—
125C2×C3×C22⋊C4C2312yes—
126C2×C3×C22⋊C4C2314yes—
127C2×C3×C42C2311yescharacteristic
128C2×#217C2312yes—
129C2×#217C2312yes—
130C2×#217C2314yes—
131C2×#217C2312yes—
132C2×#217C2314yes—
133C2×#217C2312yes—
134C2×#217C2312yes—
135C2×#217C2312yes—
136#940D418yescomplemented
137#939—216no—
138#938—216no—
139#938—44no—
140D4×Dic3—28no—
141#930—28no—
142C4×#67—44no—
143C4×#67—44no—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2312yes—
149#926—28no—
150C2×C4⋊Dic3—44no—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2312yes—
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2314yes—
160C2×C4⋊Dic3C2312yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2312yes—
165C2×C4×Dic3C2311yescharacteristic
166C2×C4×Dic3C2311yescharacteristic
167C2×C4×Dic3C2311yescharacteristic
168C2×C4×Dic3C2312yes—
169C2×C4×Dic3C2311yescharacteristic
170C2×C4×Dic3C2311yescharacteristic
171C2×C4×Dic3C2311yescharacteristic
172#893—28no—
173D3×C4⋊C4—44no—
174#890—28no—
175#886—216no—
176#883—216no—
177C4×D12—24no—
178C3×#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C3⋊#95C2314yes—
182C3⋊#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187#540—616no—
188C2×#127—31no—
189C2×#125—32no—
190C2×#123—34no—
191C2×#123—34no—
192C2×#121—34no—
193C2×#121—34no—
194C2×#121—32no—
195C2×#121—32no—
196C2×#121C2×D312yes—
197C2×#121C2×D312yes—
198C2×C4×D4—32no—
199C2×C4×D4—32no—
200C2×C4×D4—32no—
201C2×C4×D4—32no—
202C2×C4×D4—31no—
203C2×C4×D4C2×D311yescharacteristic
204C2×C4×D4C2×D311yescharacteristic
205C2×#117—32no—
206C22×C4⋊C4—32no—
207C22×C4⋊C4—32no—
208#398—34no—
209#398—34no—
210#397—34no—
211#397—34no—
212#396—34no—
213#396—34no—
214#394—34no—
215#394—34no—
216#394—34no—
217#394C2×D314yes—
218#390—31no—
219#390—31no—
220#390—31no—
221#390—31no—
222#390—32no—
223#390—32no—
224#389—32no—
225#389—32no—
226#389—32no—
227#389—32no—
228#389—32no—
229#389—32no—
230#389—31no—
231#389—31no—
232#388—32no—
233#388—32no—
234#386—34no—
235#386—34no—
236#385—34no—
237#385—34no—
238#384—31no—
239#384—31no—
240#384C2×D311yescharacteristic
241#382—32no—
242#381—34no—
243#381—34no—
244#380—32no—
245#380—32no—
246#380—32no—
247#380—32no—
248#380C2×D312yes—
249#380C2×D312yes—
250C4×C4⋊C4—31no—
251C4×C22⋊C4—32no—
252C43—31no—
253C24×C3C2412yes—
254C24×C3C2412yes—
255C23×D3C2412yes—
256C2×C3×D4—28no—
257C2×C3×D4—22no—
258C2×C3×D4—22no—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4—22no—
262C2×C3×D4—44no—
263C2×C3×D4—44no—
264C2×C3×D4C2×D414yes—
265C22×C3×C4—24no—
266C22×C3×C4—24no—
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—24no—
270C22×C3×C4—24no—
271C22×C3×C4C2412yes—
272C22×C3×C4C2414yes—
273C22×C3×C4C2412yes—
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—28no—
278C2×#67—42no—
279C2×#67—42no—
280C2×#67—42no—
281C2×#67—42no—
282C2×#67—44no—
283C2×#67—44no—
284C2×#67C2×D418yes—
285C2×#67C2×D418yes—
286C22×Dic3—28no—
287C22×Dic3—44no—
288C22×Dic3—44no—
289C22×Dic3C2411yescharacteristic
290C22×Dic3C2411yescharacteristic
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293C22×Dic3C2412yes—
294C22×Dic3C2414yes—
295C22×Dic3C2411yescharacteristic
296C22×Dic3C2411yescharacteristic
297C2×D12—22no—
298C2×D12—22no—
299C2×D12C2×D414yes—
300C2×C4×D3—24no—
301C2×C4×D3—24no—
302C2×C4×D3—24no—
303C2×C4×D3—28no—
304C2×C4×D3—44no—
305C2×C4×D3—44no—
306C3×C4⋊C4—24no—
307C3×C4⋊C4—22no—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—42no—
311C3×C22⋊C4—28no—
312C3×C22⋊C4—24no—
313C3×C22⋊C4—24no—
314C3×C22⋊C4—44no—
315C3×C42#4114yes—
316#217—28no—
317#217—24no—
318#217—24no—
319#217—42no—
320#217—42no—
321#217—44no—
322#217—42no—
323#217—42no—
324(C2×D3)⋊C4—28no—
325(C2×D3)⋊C4—28no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—42no—
328(C2×D3)⋊C4—42no—
329C4⋊Dic3—24no—
330C4⋊Dic3—22no—
331C4⋊Dic3—22no—
332C4⋊Dic3—22no—
333C4⋊Dic3—24no—
334C4⋊Dic3—24no—
335C4⋊Dic3—24no—
336C4⋊Dic3—28no—
337C4⋊Dic3—44no—
338C4⋊Dic3—42no—
339Dic3⋊C4—28no—
340Dic3⋊C4—44no—
341Dic3⋊C4—42no—
342Dic3⋊C4—42no—
343C4×Dic3—24no—
344C4×Dic3—22no—
345C4×Dic3—22no—
346C4×Dic3—22no—
347C4×Dic3—41no—
348C4×Dic3—41no—
349C4×Dic3C2×D414yes—
350C22×D4—32no—
351C22×D4—32no—
352C22×D4—34no—
353C22×D4—31no—
354C22×D4C22×D311yescharacteristic
355C22×D4C22×D311yescharacteristic
356C22×D4C22×D314yes—
357C23×C4—34no—
358C23×C4—32no—
359C23×C4—34no—
360C23×C4C22×D312yes—
361C23×C4C22×D312yes—
362#127—38no—
363#125—68no—
364#123—616no—
365#123—616no—
366#121—28no—
367#121—44no—
368#121—68no—
369#121—616no—
370#121—616no—
371#121—124no—
372C4×D4—24no—
373C4×D4—24no—
374C4×D4—68no—
375C4×D4—68no—
376C4×D4—64no—
377C4×D4—124no—
378C4×D4—124no—
379#117—68no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—34no—
389C2×C4⋊C4—34no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—124no—
395C2×C4⋊C4—124no—
396C2×C4⋊C4C22×D312yes—
397C2×C4⋊C4C22×D312yes—
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C4⋊C4C22×D312yes—
401C2×C22⋊C4—32no—
402C2×C22⋊C4—32no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4C22×D312yes—
415C2×C22⋊C4C22×D312yes—
416C2×C22⋊C4C22×D314yes—
417C2×C22⋊C4C22×D314yes—
418C2×C42—31no—
419C2×C42—32no—
420C2×C42—31no—
421C2×C42—31no—
422C2×C42—31no—
423C2×C42—31no—
424C2×C42—31no—
425C2×C42C22×D311yescharacteristic
426#95—32no—
427#95—32no—
428#95—32no—
429#95—34no—
430#95—34no—
431#95—34no—
432#95—34no—
433#95—34no—
434#95C22×D314yes—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3C22×D414yes—
449C23×C3C2511yescharacteristic
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3C22×D414yes—
457C3×D4—28no—
458C3×D4—44no—
459C3×D4—88no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—24no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—24no—
469C2×C3×C4—22no—
470C2×C3×C4—24no—
471C2×C3×C4—48no—
472C2×C3×C4—48no—
473C2×C3×C4C22×D412yes—
474C2×C3×C4C2×#4112yes—
475C2×C3×C4C2×#4112yes—
476C2×C3×C4C2×#4112yes—
477C2×C3×C4H(5,𝔽2)12yes—
478C2×C3×C4H(5,𝔽2)12yes—
479C2×C3×C42−1+412yes—
480#67—48no—
481#67—48no—
482#67—88no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—24no—
490C2×Dic3—22no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—24no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—24no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—88no—
506C2×Dic3C22×D412yes—
507C2×Dic3C22×D412yes—
508D12—28no—
509C4×D3—48no—
510C4×D3—88no—
511C24—32no—
512C24C23×D312yes—
513C24C23×D312yes—
514C2×D4—28no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—38no—
521C2×D4—38no—
522C2×D4—34no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—68no—
526C2×D4—62no—
527C2×D4—62no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—124no—
533C2×D4—124no—
534C2×D4D3×D414yes—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—32no—
546C22×C4—32no—
547C22×C4—32no—
548C22×C4—34no—
549C22×C4—68no—
550C22×C4—68no—
551C22×C4—64no—
552C22×C4—64no—
553C22×C4—64no—
554C22×C4—124no—
555C22×C4—124no—
556C22×C4—124no—
557C22×C4—124no—
558C22×C4C23×D312yes—
559C22×C4C23×D314yes—
560C22×C4C23×D312yes—
561C22×C4C23×D311yescharacteristic
562C22×C4C23×D311yescharacteristic
563C22×C4C23×D311yescharacteristic
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—24no—
568C4⋊C4—42no—
569C4⋊C4—64no—
570C4⋊C4—64no—
571C4⋊C4—68no—
572C4⋊C4—68no—
573C4⋊C4—64no—
574C4⋊C4—62no—
575C4⋊C4—62no—
576C4⋊C4—62no—
577C4⋊C4—64no—
578C4⋊C4—124no—
579C4⋊C4—124no—
580C4⋊C4—122no—
581C4⋊C4—122no—
582C4⋊C4—122no—
583C22⋊C4—28no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—44no—
587C22⋊C4—68no—
588C22⋊C4—68no—
589C22⋊C4—64no—
590C22⋊C4—64no—
591C22⋊C4—68no—
592C22⋊C4—64no—
593C22⋊C4—122no—
594C22⋊C4—122no—
595C22⋊C4—122no—
596C22⋊C4—122no—
597C22⋊C4—124no—
598C22⋊C4—122no—
599C22⋊C4—122no—
600C42—34no—
601C42—64no—
602C42—62no—
603C42—62no—
604C42—62no—
605C42—121no—
606C42—121no—
607C42#23714yes—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—24no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3C23×D411yescharacteristic
623C22×C3C22×#4111yescharacteristic
624C22×C3C2×H(5,𝔽2)11yescharacteristic
625C22×C3C2×H(5,𝔽2)11yescharacteristic
626C22×C3C2×2−1+411yescharacteristic
627C22×C3#58511yescharacteristic
628C22×C3#58511yescharacteristic
629C2×D3—24no—
630C2×D3—24no—
631C2×D3—24no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C3×C4—22no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—44no—
640C3×C4#54014yescomplemented
641C3×C4#54714yes—
642Dic3—22no—
643Dic3—22no—
644Dic3—42no—
645Dic3—42no—
646Dic3—42no—
647Dic3—44no—
648Dic3—41no—
649Dic3—41no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—34no—
664C23—62no—
665C23—62no—
666C23—62no—
667C23—62no—
668C23—62no—
669C23—62no—
670C23C2×D3×D414yes—
671C23C24×D311yescharacteristic
672D4—28no—
673D4—44no—
674D4—68no—
675D4—88no—
676D4—128no—
677D4—128no—
678D4—248no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—48no—
693C2×C4—48no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—62no—
702C2×C4—61no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—61no—
706C2×C4—62no—
707C2×C4—64no—
708C2×C4—62no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—62no—
713C2×C4—61no—
714C2×C4—62no—
715C2×C4—64no—
716C2×C4—128no—
717C2×C4—248no—
718C2×C4—248no—
719C2×C4C2×D3×D412yes—
720C2×C4C2×#23712yes—
721C2×C4C2×#23712yes—
722C2×C4C2×#23712yes—
723C2×C4#100412yes—
724C2×C4#100912yes—
725C2×C4#101012yes—
726C2×C3—44no—
727C2×C3—82no—
728C2×C3C2×#54011yescharacteristic
729C2×C3C2×#54711yescharacteristic
730C2×C3#349611yescharacteristic
731C2×C3#349611yescharacteristic
732C2×C3#351211yescharacteristic
733C2×C3#354711yescharacteristic
734C2×C3#354711yescharacteristic
735D3—44no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—64no—
751C22—64no—
752C22—64no—
753C22—122no—
754C22—122no—
755C22—122no—
756C22—122no—
757C22C22×D3×D411yescharacteristic
758C22C22×#23711yescharacteristic
759C22C2×#100411yescharacteristic
760C22C2×#100911yescharacteristic
761C22C2×#101011yescharacteristic
762C22#596611yescharacteristic
763C22#596811yescharacteristic
764C4—22no—
765C4—44no—
766C4—42no—
767C4—42no—
768C4—62no—
769C4—62no—
770C4—122no—
771C4—122no—
772C4—122no—
773C4—124no—
774C4—121no—
775C4—121no—
776C4#561114yes—
777C4#561914yescomplemented
778C3#3937811yescharacteristic, complemented, Sylow
779C2—44no—
780C2—82no—
781C2—124no—
782C2C2×#561911yescharacteristic
783C2C2×#561111yescharacteristic
784C2#8636911yescharacteristic
785C2#8662111yescharacteristic
786C2#8670211yescharacteristic
787C2#8670811yescharacteristic
788C2#8697711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2537C2
hypercenter#2537D3
hypocenterC3#39378
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#5619C2semidirect
2. C3×#2537C2semidirect
3. #82705C2semidirect
4. #82643C2semidirect
5. #82641C2semidirect
6. #82417C2semidirect
7. D4×C4⋊Dic3C2semidirect
8. C4×#940C2semidirect
9. #82319C2semidirect
10. #77148C2semidirect
11. #77020C2semidirect
12. #74360C2semidirect
13. #74355C2semidirect
14. #74027C2semidirect
15. #73955C2semidirect
16. #73911C2semidirect
17. #73891C2semidirect
91. #2537D3semidirect
136. #940D4semidirect
640. C3×C4#540semidirect
777. C4#5619semidirect
778. C3#39378semidirect

Maximal subgroups

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

subgroupindex
C2×#56192
C3×#25372
#827052
#826432
#826412
#824172
D4×C4⋊Dic32
C4×#9402
#823192
#771482
#770202
#743602
#743552
#740272
#739552
#739112
#738912
#393783