Finite Group Databasebeta

← #20257619

Subgroups — #20257619

Order 6016.

1270 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689862C212yesmaximal, complemented
2#15689861C212yesmaximal, complemented
3#15689825C211yesmaximal, characteristic, complemented
4#15689823C211yesmaximal, characteristic, complemented
5#15689820C211yesmaximal, characteristic, complemented
6#15689819C211yesmaximal, characteristic, complemented
7#15689758C211yesmaximal, characteristic, complemented
8D4×C22⋊D47C211yesmaximal, characteristic, complemented
9D4×C22⋊D47C212yesmaximal, complemented
10D4×C22⋊D47C211yesmaximal, characteristic, complemented
11#15689755C212yesmaximal, complemented
12#15689727C211yesmaximal, characteristic, complemented
13#15689724C211yesmaximal, characteristic, complemented
14#15689708C212yesmaximal, complemented
15#15689705C212yesmaximal, complemented
16#15689690C211yesmaximal, characteristic, complemented
17#15689689C211yesmaximal, characteristic, complemented
18#15689683C212yesmaximal, complemented
19#15689682C212yesmaximal, complemented
20#15689632C211yesmaximal, characteristic, complemented
21C2×#13093995C211yesmaximal, characteristic, complemented
22#121×D47C211yesmaximal, characteristic, complemented
23D42×C47C211yesmaximal, characteristic, complemented
24C2×#10625350C2211yescharacteristic, complemented
25C22×C22⋊D47C2212yescomplemented
26C22×C22⋊D47C2212yescomplemented
27C22×C22⋊D47C2212yescomplemented
28C2×D4×D47C2212yescomplemented
29C2×D4×D47C2212yescomplemented
30C2×D4×D47C2211yescharacteristic, complemented
31C2×D4×D47C2211yescharacteristic, complemented
32C22×C4×D47C2211yescharacteristic, complemented
33#13094020C2212yescomplemented
34#13094020C2211yescharacteristic, complemented
35#13094020C2212yescomplemented
36#13094019C2212yescomplemented
37#13094017C2212yescomplemented
38#13094017C2212yescomplemented
39#13094017C2212yescomplemented
40#13094016C2211yescharacteristic, complemented
41#13094015C2211yescharacteristic, complemented
42#13094011C2212yescomplemented
43#13094010C2212yescomplemented
44#13094009C2211yescharacteristic, complemented
45#13094008C2212yescomplemented
46#13094007C2212yescomplemented
47#13094007C2212yescomplemented
48#13094006C2212yescomplemented
49#13094006C2211yescharacteristic, complemented
50#13094006C2212yescomplemented
51#13094005C2212yescomplemented
52#13094005C2212yescomplemented
53#13094005C2212yescomplemented
54#13094002C2211yescharacteristic, complemented
55#13094001C2211yescharacteristic, complemented
56#13093999C2211yescharacteristic, complemented
57#13093998C2211yescharacteristic, complemented
58#13093998C2211yescharacteristic, complemented
59#13093998C2212yescomplemented
60#13093997C2212yescomplemented
61#13093997C2212yescomplemented
62#13093997C2212yescomplemented
63#13093997C2211yescharacteristic, complemented
64#13093996C2212yescomplemented
65#13093996C2212yescomplemented
66#13093996C2212yescomplemented
67#13093996C2212yescomplemented
68#13093996C2212yescomplemented
69#13093996C2212yescomplemented
70#13093996C2212yescomplemented
71#13093996C2211yescharacteristic, complemented
72#13093995C2212yescomplemented
73#13093995C2211yescharacteristic, complemented
74#13093995C2211yescharacteristic, complemented
75#13093995C2211yescharacteristic, complemented
76#13093995C2211yescharacteristic, complemented
77#13093995C2212yescomplemented
78#13093995C2212yescomplemented
79#13093995C2211yescharacteristic, complemented
80#13093995C2212yescomplemented
81#13093995C2211yescharacteristic, complemented
82#13093995C2211yescharacteristic, complemented
83#13093994C2211yescharacteristic, complemented
84#13093994C2212yescomplemented
85#13093993C2212yescomplemented
86#13093993C2212yescomplemented
87#13093993C2212yescomplemented
88#13093993C2212yescomplemented
89#13093992C2212yescomplemented
90#13093992C2211yescharacteristic, complemented
91#13093992C2212yescomplemented
92#13093992C2212yescomplemented
93#13093992C2212yescomplemented
94#13093992C2212yescomplemented
95C4×D188C2211yescharacteristic, complemented
96C4×D188C2211yescharacteristic, complemented
97D4×Dic47C2211yescharacteristic, complemented
98D4×Dic47C2212yescomplemented
99D4×Dic47C2211yescharacteristic, complemented
100C4×C22⋊D47C2211yescharacteristic, complemented
101C4×C22⋊D47C2212yescomplemented
102C4×C22⋊D47C2211yescharacteristic, complemented
103(C22⋊D47)⋊C4C2212yescomplemented
104(C22⋊D47)⋊C4C2212yescomplemented
105#13093983C2211yescharacteristic, complemented
106#13093982C2211yescharacteristic, complemented
107#13093981C2211yescharacteristic, complemented
108C2×C4⋊Dic47C2211yescharacteristic, complemented
109C4⋊C4×D47C2211yescharacteristic, complemented
110C2×C22⋊Dic47C2212yescomplemented
111C22⋊C4×D47C2212yescomplemented
112C22×D4×C47C2211yescharacteristic, complemented
113C22×D4×C47C2212yescomplemented
114C22×D4×C47C2211yescharacteristic, complemented
115#127×C47C2211yescharacteristic, complemented
116#121×C47C2211yescharacteristic, complemented
117#121×C47C2211yescharacteristic, complemented
118#121×C47C2212yescomplemented
119#120×C47C2212yescomplemented
120#120×C47C2212yescomplemented
121C4×D4×C47C2211yescharacteristic, complemented
122C4×D4×C47C2211yescharacteristic, complemented
123C24×C47C2312yes—
124C24×C47C2312yes—
125C23×D47C2311yescharacteristic
126C23×D47C2312yes—
127C23×D47C2312yes—
128C2×D4×C47—42no—
129C2×D4×C47—42no—
130C2×D4×C47—44no—
131C2×D4×C47C2311yescharacteristic
132C2×D4×C47C2311yescharacteristic
133C2×D4×C47C2312yes—
134C2×D4×C47C2311yescharacteristic
135C2×D4×C47C2311yescharacteristic
136C2×D4×C47C2312yes—
137C2×D4×C47C2312yes—
138C2×D4×C47C2312yes—
139C2×D4×C47C2312yes—
140C2×D4×C47C2312yes—
141C22×C4×C47C2311yescharacteristic
142C22×C4×C47C2311yescharacteristic
143C22×C4×C47C2312yes—
144C2×C22⋊D47—44no—
145C2×C22⋊D47—44no—
146C2×C22⋊D47—44no—
147C2×C22⋊D47C2312yes—
148C2×C22⋊D47C2312yes—
149C2×C22⋊D47C2311yescharacteristic
150C2×C22⋊D47C2312yes—
151C2×C22⋊D47C2311yescharacteristic
152C2×C22⋊D47C2311yescharacteristic
153C2×C22⋊D47C2311yescharacteristic
154C2×C22⋊D47C2312yes—
155C2×C22⋊D47C2312yes—
156C2×C22⋊D47C2312yes—
157C2×C22⋊D47C2312yes—
158C2×C22⋊D47C2312yes—
159C2×C22⋊D47C2312yes—
160C2×C22⋊D47C2312yes—
161C2×C22⋊D47C2312yes—
162C2×C22⋊D47C2312yes—
163C2×C22⋊D47C2312yes—
164C22×Dic47C2311yescharacteristic
165C22×Dic47C2312yes—
166C22×Dic47C2312yes—
167C22×Dic47C2312yes—
168D4×D47—42no—
169D4×D47—42no—
170D4×D47—44no—
171D4×D47—44no—
172#10625350—42no—
173C2×D188C2311yescharacteristic
174C2×D188C2311yescharacteristic
175C2×D188C2311yescharacteristic
176C2×D188C2312yes—
177C2×C4×D47—42no—
178C2×C4×D47C2311yescharacteristic
179C2×C4×D47C2311yescharacteristic
180C2×C4×D47C2311yescharacteristic
181C2×C4×D47C2311yescharacteristic
182C2×C4×D47C2312yes—
183C2×C4×D47C2312yes—
184C2×C4×D47C2311yescharacteristic
185C2×Dic94C2311yescharacteristic
186C4⋊C4×C47C2311yescharacteristic
187C4⋊C4×C47C2311yescharacteristic
188C22⋊C4×C47C2311yescharacteristic
189C22⋊C4×C47C2312yes—
190C22⋊C4×C47C2311yescharacteristic
191C22⋊C4×C47C2312yes—
192C22⋊C4×C47C2312yes—
193C42×C47C2311yescharacteristic
194C22⋊Dic47C2312yes—
195C22⋊Dic47C2312yes—
196C22⋊Dic47C2312yes—
197C22⋊Dic47C2312yes—
198C22⋊Dic47C2312yes—
199C22⋊Dic47C2312yes—
200C22⋊Dic47C2311yescharacteristic
201C22⋊Dic47C2312yes—
202C22⋊Dic47C2311yescharacteristic
203C22⋊Dic47C2312yes—
204C22⋊Dic47C2312yes—
205C22⋊Dic47C2312yes—
206(C2×D47)⋊C4C2312yes—
207(C2×D47)⋊C4C2312yes—
208(C2×D47)⋊C4C2311yescharacteristic
209(C2×D47)⋊C4C2311yescharacteristic
210(C2×D47)⋊C4C2312yes—
211(C2×D47)⋊C4C2311yescharacteristic
212(C2×D47)⋊C4C2312yes—
213(C2×D47)⋊C4C2311yescharacteristic
214(C2×D47)⋊C4C2311yescharacteristic
215(C2×D47)⋊C4C2312yes—
216(C2×D47)⋊C4C2311yescharacteristic
217C4⋊Dic47C2311yescharacteristic
218C4⋊Dic47C2311yescharacteristic
219C4⋊Dic47C2311yescharacteristic
220C4⋊Dic47C2312yes—
221C4⋊Dic47C2312yes—
222C4⋊Dic47C2311yescharacteristic
223Dic47⋊C4C2312yes—
224Dic47⋊C4C2311yescharacteristic
225Dic47⋊C4C2311yescharacteristic
226Dic47⋊C4C2312yes—
227Dic47⋊C4C2312yes—
228Dic47⋊C4C2311yescharacteristic
229Dic47⋊C4C2311yescharacteristic
230Dic47⋊C4C2312yes—
231C4×Dic47C2311yescharacteristic
232C4×Dic47C2312yes—
233C4×Dic47C2312yes—
234C23×C47—24no—
235C23×C47—42no—
236C23×C47—42no—
237C23×C47—42no—
238C23×C47—42no—
239C23×C47—42no—
240C23×C47C2412yes—
241C23×C47C2412yes—
242C23×C47C2411yescharacteristic
243C23×C47C2412yes—
244C23×C47C2411yescharacteristic
245C22×D47—22no—
246C22×D47—22no—
247C22×D47—24no—
248C22×D47—41no—
249C22×D47—42no—
250C22×D47—42no—
251C22×D47—42no—
252C22×D47—42no—
253C22×D47—42no—
254C22×D47C2411yescharacteristic
255C22×D47C2412yes—
256C22×D47C2411yescharacteristic
257C22×D47C2411yescharacteristic
258D4×C47—24no—
259D4×C47—22no—
260D4×C47—22no—
261D4×C47—22no—
262D4×C47—22no—
263D4×C47—42no—
264D4×C47—42no—
265D4×C47—42no—
266D4×C47—42no—
267D4×C47—42no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—42no—
271C2×C4×C47C2411yescharacteristic
272C2×C4×C47C2412yes—
273C2×C4×C47C2411yescharacteristic
274C2×C4×C47C2411yescharacteristic
275C2×C4×C47C2411yescharacteristic
276C2×C4×C47C2411yescharacteristic
277C22⋊D47—24no—
278C22⋊D47—22no—
279C22⋊D47—24no—
280C22⋊D47—24no—
281C22⋊D47—22no—
282C22⋊D47—41no—
283C22⋊D47—41no—
284C22⋊D47—42no—
285C22⋊D47—42no—
286C22⋊D47—42no—
287C22⋊D47—42no—
288C22⋊D47—42no—
289C22⋊D47—42no—
290C22⋊D47—42no—
291C22⋊D47—42no—
292C22⋊D47—42no—
293C22⋊D47—42no—
294C2×Dic47—41no—
295C2×Dic47—42no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47C2411yescharacteristic
299C2×Dic47C2411yescharacteristic
300C2×Dic47C2412yes—
301C2×Dic47C2411yescharacteristic
302C2×Dic47C2412yes—
303C2×Dic47C2412yes—
304C2×Dic47C2411yescharacteristic
305C2×Dic47C2411yescharacteristic
306D188—22no—
307D188—22no—
308D188—41no—
309D188—42no—
310C4×D47—22no—
311C4×D47—22no—
312C4×D47—22no—
313C4×D47—41no—
314C4×D47—41no—
315C4×D47—42no—
316C4×D47—42no—
317Dic94—41no—
318C22×C47—21no—
319C22×C47—21no—
320C22×C47—22no—
321C22×C47—22no—
322C22×C47—21no—
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—21no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—21no—
331C22×C47—22no—
332C22×C47—84no—
333C22×C47—84no—
334C22×C47H(5,𝔽2)12yes—
335C22×C47C2511yescharacteristic
336C2×D47—21no—
337C2×D47—21no—
338C2×D47—21no—
339C2×D47—21no—
340C2×D47—22no—
341C2×D47—21no—
342C2×D47—22no—
343C2×D47—21no—
344C2×D47—22no—
345C2×D47—21no—
346C2×D47—21no—
347C2×D47—44no—
348C2×D47—84no—
349C2×D47—84no—
350C2×D47H(5,𝔽2)12yes—
351C4×C47—21no—
352C4×C47—21no—
353C4×C47—21no—
354C4×C47—22no—
355C4×C47—21no—
356C4×C47H(5,𝔽2)12yes—
357Dic47—21no—
358Dic47—21no—
359Dic47—21no—
360Dic47—22no—
361Dic47—22no—
362Dic47—22no—
363Dic47—21no—
364Dic47—21no—
365#3537—471nomaximal, Sylow
366C2×C47—22no—
367C2×C47—42no—
368C2×C47—42no—
369C2×C47—41no—
370C2×C47—42no—
371C2×C47C2×H(5,𝔽2)11yescharacteristic
372C2×C47C2×H(5,𝔽2)11yescharacteristic
373C2×C47C2×H(5,𝔽2)11yescharacteristic
374D47—22no—
375D47—41no—
376D47—41no—
377D47—42no—
378#560—472no—
379#560—472no—
380#553—471no—
381#553—471no—
382#553—471no—
383#553—471no—
384D42—472no—
385D42—471no—
386D42—471no—
387D42—471no—
388D42—472no—
389D42D4711yescharacteristic, complemented
390#540—471no—
391#540—471no—
392#538—472no—
393#538—472no—
394#535—471no—
395#535—471no—
396#534—472no—
397#534—472no—
398#525—471no—
399C2×#121—471no—
400C2×#121—471no—
401C47#353711yescharacteristic, complemented, Sylow
402C2×#41—471no—
403C22×D4—472no—
404C22×D4—472no—
405C22×D4—472no—
406C22×D4—471no—
407C22×D4—472no—
408C22×D4—472no—
409C22×D4—471no—
410C22×D4C2×D4711yescharacteristic, complemented
411C22×D4C2×D4712yescomplemented
412C22×D4C2×D4711yescharacteristic, complemented
413C23×C4—471no—
414#127—472no—
415#127—472no—
416#127—471no—
417#127C2×D4711yescharacteristic, complemented
418#126—472no—
419#126—472no—
420#126—472no—
421#126—472no—
422#125—471no—
423#125—471no—
424#124—472no—
425#124—472no—
426#123—472no—
427#123—472no—
428#123—472no—
429#123—472no—
430#123—472no—
431#123—471no—
432#123—471no—
433#123—472no—
434#123—472no—
435#123—472no—
436C22⋊Q8—471no—
437C22⋊Q8—471no—
438#121—472no—
439#121—472no—
440#121—471no—
441#121—471no—
442#121—471no—
443#121—471no—
444#121—471no—
445#121—472no—
446#121—471no—
447#121—472no—
448#121—472no—
449#121—472no—
450#121—471no—
451#121—471no—
452#121—472no—
453#121—472no—
454#121—472no—
455#121—472no—
456#121—472no—
457#121—471no—
458#121—471no—
459#121—472no—
460#121—471no—
461#121—472no—
462#121—471no—
463#121—472no—
464#121—472no—
465#121C2×D4711yescharacteristic, complemented
466#121C2×D4711yescharacteristic, complemented
467#121C2×D4712yescomplemented
468#120—472no—
469#120—472no—
470#120—472no—
471#120—472no—
472#120—471no—
473#120—472no—
474#120—472no—
475#120—472no—
476#120—472no—
477#120—472no—
478#120—471no—
479#120—472no—
480#120C2×D4712yescomplemented
481#120C2×D4712yescomplemented
482C4×D4—472no—
483C4×D4—471no—
484C4×D4—471no—
485C4×D4—471no—
486C4×D4—471no—
487C4×D4—472no—
488C4×D4—472no—
489C4×D4—472no—
490C4×D4—471no—
491C4×D4—471no—
492C4×D4C2×D4711yescharacteristic, complemented
493C4×D4C2×D4711yescharacteristic, complemented
494#117—471no—
495#117—471no—
496#117—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C22⋊C4—472no—
500C2×C22⋊C4—472no—
501C24—471no—
502C24—472no—
503C24—472no—
504C24C22×D4712yes—
505C24C22×D4712yes—
506#41—1882no—
507C2×Q8—471no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—44no—
511C2×D4—472no—
512C2×D4—471no—
513C2×D4—472no—
514C2×D4—472no—
515C2×D4—471no—
516C2×D4—471no—
517C2×D4—471no—
518C2×D4—472no—
519C2×D4—472no—
520C2×D4—472no—
521C2×D4—472no—
522C2×D4—472no—
523C2×D4—472no—
524C2×D4—472no—
525C2×D4—472no—
526C2×D4—472no—
527C2×D4—472no—
528C2×D4—471no—
529C2×D4—471no—
530C2×D4—471no—
531C2×D4—472no—
532C2×D4—1882no—
533C2×D4—1882no—
534C2×D4—1884no—
535C2×D4—1884no—
536C2×D4—1884no—
537C2×D4—1884no—
538C2×D4—1884no—
539C2×D4C22×D4712yes—
540C2×D4C22×D4711yescharacteristic
541C2×D4C22×D4711yescharacteristic
542C2×D4C22×D4711yescharacteristic
543C2×D4C22×D4711yescharacteristic
544C2×D4C22×D4712yes—
545C2×D4C22×D4712yes—
546C2×D4C22×D4712yes—
547C2×D4C22×D4712yes—
548C2×D4C22×D4712yes—
549C22×C4—471no—
550C22×C4—472no—
551C22×C4—472no—
552C22×C4—472no—
553C22×C4—471no—
554C22×C4—471no—
555C22×C4—471no—
556C22×C4—471no—
557C22×C4—472no—
558C22×C4—472no—
559C22×C4—471no—
560C22×C4—1882no—
561C22×C4C22×D4711yescharacteristic
562C22×C4C22×D4711yescharacteristic
563C22×C4C22×D4712yes—
564C4⋊C4—472no—
565C4⋊C4—471no—
566C4⋊C4—471no—
567C4⋊C4—471no—
568C4⋊C4—471no—
569C4⋊C4—472no—
570C4⋊C4—472no—
571C4⋊C4—472no—
572C4⋊C4—471no—
573C4⋊C4—471no—
574C4⋊C4—471no—
575C4⋊C4—472no—
576C4⋊C4—471no—
577C4⋊C4—472no—
578C4⋊C4C22×D4711yescharacteristic
579C4⋊C4C22×D4711yescharacteristic
580C22⋊C4—472no—
581C22⋊C4—472no—
582C22⋊C4—472no—
583C22⋊C4—472no—
584C22⋊C4—472no—
585C22⋊C4—472no—
586C22⋊C4—471no—
587C22⋊C4—472no—
588C22⋊C4—472no—
589C22⋊C4—472no—
590C22⋊C4—472no—
591C22⋊C4—471no—
592C22⋊C4—472no—
593C22⋊C4—472no—
594C22⋊C4—472no—
595C22⋊C4—471no—
596C22⋊C4—471no—
597C22⋊C4—471no—
598C22⋊C4—471no—
599C22⋊C4—472no—
600C22⋊C4—472no—
601C22⋊C4—471no—
602C22⋊C4—471no—
603C22⋊C4C22×D4712yes—
604C22⋊C4C22×D4711yescharacteristic
605C22⋊C4C22×D4712yes—
606C22⋊C4C22×D4712yes—
607C22⋊C4C22×D4711yescharacteristic
608C42—471no—
609C42—472no—
610C42—472no—
611C42C22×D4711yescharacteristic
612C23—24no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—471no—
619C23—472no—
620C23—471no—
621C23—471no—
622C23—944no—
623C23—942no—
624C23—942no—
625C23—1882no—
626C23—1882no—
627C23—1882no—
628C23—1882no—
629C23—1882no—
630C23—1881no—
631C23C23×D4712yes—
632C23C23×D4712yes—
633C23C23×D4711yescharacteristic
634C23C23×D4712yes—
635C23C23×D4711yescharacteristic
636Q8—1881no—
637D4—22no—
638D4—24no—
639D4—22no—
640D4—22no—
641D4—22no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647D4—942no—
648D4—944no—
649D4—942no—
650D4—944no—
651D4—944no—
652D4—942no—
653D4—942no—
654D4—1882no—
655D4—1881no—
656D4—1882no—
657D4—1882no—
658D4—1882no—
659D4—1882no—
660D4—1882no—
661D4—1882no—
662D4—1882no—
663D4—1882no—
664D4—1882no—
665D4—1882no—
666D4—1881no—
667D4—1881no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—471no—
672C2×C4—471no—
673C2×C4—472no—
674C2×C4—472no—
675C2×C4—471no—
676C2×C4—472no—
677C2×C4—471no—
678C2×C4—471no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—1881no—
683C2×C4—1881no—
684C2×C4—1882no—
685C2×C4—1882no—
686C2×C4—1881no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4—1882no—
690C2×C4C23×D4711yescharacteristic
691C2×C4C23×D4712yes—
692C2×C4C23×D4711yescharacteristic
693C2×C4C23×D4711yescharacteristic
694C2×C4C23×D4711yescharacteristic
695C2×C4C23×D4711yescharacteristic
696C22—21no—
697C22—21no—
698C22—22no—
699C22—22no—
700C22—21no—
701C22—22no—
702C22—21no—
703C22—22no—
704C22—22no—
705C22—21no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—84no—
711C22—84no—
712C22—472no—
713C22—941no—
714C22—941no—
715C22—942no—
716C22—941no—
717C22—941no—
718C22—941no—
719C22—941no—
720C22—942no—
721C22—941no—
722C22—942no—
723C22—941no—
724C22—3764no—
725C22—3764no—
726C22—1884no—
727C22#1309406912yes—
728C22C24×D4711yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—21no—
733C4—22no—
734C4—942no—
735C4—941no—
736C4—942no—
737C4—941no—
738C4—941no—
739C4—941no—
740C4—942no—
741C4—941no—
742C4#1309406912yes—
743C2—22no—
744C2—41no—
745C2—42no—
746C2—42no—
747C2—42no—
748C2—942no—
749C2—1882no—
750C2—1881no—
751C2—1881no—
752C2H(5,𝔽2)×D4711yescharacteristic
753C2C2×#1309406911yescharacteristic
754C2C2×#1309406911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingD42×C47C2
hypercenterD42D47
hypocenterC47#3537
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #15689862C2semidirect
2. #15689861C2semidirect
3. #15689825C2semidirect
4. #15689823C2semidirect
5. #15689820C2semidirect
6. #15689819C2semidirect
7. #15689758C2semidirect
8. D4×C22⋊D47C2semidirect
9. D4×C22⋊D47C2semidirect
10. D4×C22⋊D47C2semidirect
11. #15689755C2semidirect
12. #15689727C2semidirect
13. #15689724C2semidirect
14. #15689708C2semidirect
15. #15689705C2semidirect
16. #15689690C2semidirect
17. #15689689C2semidirect
18. #15689683C2semidirect
19. #15689682C2semidirect
20. #15689632C2semidirect
21. C2×#13093995C2semidirect
22. #121×D47C2semidirect
23. D42×C47C2semidirect
24. C2×#10625350C22semidirect
25. C22×C22⋊D47C22semidirect
26. C22×C22⋊D47C22semidirect
27. C22×C22⋊D47C22semidirect
28. C2×D4×D47C22semidirect
29. C2×D4×D47C22semidirect
30. C2×D4×D47C22semidirect
31. C2×D4×D47C22semidirect
32. C22×C4×D47C22semidirect
33. #13094020C22semidirect
34. #13094020C22semidirect
35. #13094020C22semidirect
36. #13094019C22semidirect
37. #13094017C22semidirect
38. #13094017C22semidirect
39. #13094017C22semidirect
40. #13094016C22semidirect
41. #13094015C22semidirect
42. #13094011C22semidirect
43. #13094010C22semidirect
44. #13094009C22semidirect
45. #13094008C22semidirect
46. #13094007C22semidirect
47. #13094007C22semidirect
48. #13094006C22semidirect
49. #13094006C22semidirect
50. #13094006C22semidirect
51. #13094005C22semidirect
52. #13094005C22semidirect
53. #13094005C22semidirect
54. #13094002C22semidirect
55. #13094001C22semidirect
56. #13093999C22semidirect
57. #13093998C22semidirect
58. #13093998C22semidirect
59. #13093998C22semidirect
60. #13093997C22semidirect
61. #13093997C22semidirect
62. #13093997C22semidirect
63. #13093997C22semidirect
64. #13093996C22semidirect
65. #13093996C22semidirect
66. #13093996C22semidirect
67. #13093996C22semidirect
68. #13093996C22semidirect
69. #13093996C22semidirect
70. #13093996C22semidirect
71. #13093996C22semidirect
72. #13093995C22semidirect
73. #13093995C22semidirect
74. #13093995C22semidirect
75. #13093995C22semidirect
76. #13093995C22semidirect
77. #13093995C22semidirect
78. #13093995C22semidirect
79. #13093995C22semidirect
80. #13093995C22semidirect
81. #13093995C22semidirect
82. #13093995C22semidirect
83. #13093994C22semidirect
84. #13093994C22semidirect
85. #13093993C22semidirect
86. #13093993C22semidirect
87. #13093993C22semidirect
88. #13093993C22semidirect
89. #13093992C22semidirect
90. #13093992C22semidirect
91. #13093992C22semidirect
92. #13093992C22semidirect
93. #13093992C22semidirect
94. #13093992C22semidirect
95. C4×D188C22semidirect
96. C4×D188C22semidirect
97. D4×Dic47C22semidirect
98. D4×Dic47C22semidirect
99. D4×Dic47C22semidirect
100. C4×C22⋊D47C22semidirect
101. C4×C22⋊D47C22semidirect
102. C4×C22⋊D47C22semidirect
103. (C22⋊D47)⋊C4C22semidirect
104. (C22⋊D47)⋊C4C22semidirect
105. #13093983C22semidirect
106. #13093982C22semidirect
107. #13093981C22semidirect
108. C2×C4⋊Dic47C22semidirect
109. C4⋊C4×D47C22semidirect
110. C2×C22⋊Dic47C22semidirect
111. C22⋊C4×D47C22semidirect
112. C22×D4×C47C22semidirect
113. C22×D4×C47C22semidirect
114. C22×D4×C47C22semidirect
115. #127×C47C22semidirect
116. #121×C47C22semidirect
117. #121×C47C22semidirect
118. #121×C47C22semidirect
119. #120×C47C22semidirect
120. #120×C47C22semidirect
121. C4×D4×C47C22semidirect
122. C4×D4×C47C22semidirect
389. D42D47semidirect
401. C47#3537semidirect
410. C22×D4C2×D47semidirect
411. C22×D4C2×D47semidirect
412. C22×D4C2×D47semidirect
417. #127C2×D47semidirect
465. #121C2×D47semidirect
466. #121C2×D47semidirect
467. #121C2×D47semidirect
480. #120C2×D47semidirect
481. #120C2×D47semidirect
492. C4×D4C2×D47semidirect
493. C4×D4C2×D47semidirect