Finite Group Databasebeta

← #19148826

Subgroups — #19148826

Order 5504.

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#14583638C212yesmaximal, complemented
2#14583637C212yesmaximal, complemented
3#14583601C211yesmaximal, characteristic, complemented
4#14583599C211yesmaximal, characteristic, complemented
5#14583596C211yesmaximal, characteristic, complemented
6#14583595C211yesmaximal, characteristic, complemented
7#14583534C211yesmaximal, characteristic, complemented
8D4×C22⋊D43C211yesmaximal, characteristic, complemented
9D4×C22⋊D43C212yesmaximal, complemented
10D4×C22⋊D43C211yesmaximal, characteristic, complemented
11#14583531C212yesmaximal, complemented
12#14583503C211yesmaximal, characteristic, complemented
13#14583500C211yesmaximal, characteristic, complemented
14#14583484C212yesmaximal, complemented
15#14583481C212yesmaximal, complemented
16#14583466C211yesmaximal, characteristic, complemented
17#14583465C211yesmaximal, characteristic, complemented
18#14583459C212yesmaximal, complemented
19#14583458C212yesmaximal, complemented
20#14583408C211yesmaximal, characteristic, complemented
21C2×#13063296C211yesmaximal, characteristic, complemented
22#121×D43C211yesmaximal, characteristic, complemented
23D42×C43C211yesmaximal, characteristic, complemented
24C2×#10621898C2211yescharacteristic, complemented
25C22×C22⋊D43C2212yescomplemented
26C22×C22⋊D43C2212yescomplemented
27C22×C22⋊D43C2212yescomplemented
28C2×D4×D43C2212yescomplemented
29C2×D4×D43C2211yescharacteristic, complemented
30C2×D4×D43C2212yescomplemented
31C2×D4×D43C2211yescharacteristic, complemented
32C22×C4×D43C2211yescharacteristic, complemented
33#13063321C2212yescomplemented
34#13063321C2212yescomplemented
35#13063321C2211yescharacteristic, complemented
36#13063320C2212yescomplemented
37#13063318C2212yescomplemented
38#13063318C2212yescomplemented
39#13063318C2212yescomplemented
40#13063317C2211yescharacteristic, complemented
41#13063316C2211yescharacteristic, complemented
42#13063312C2212yescomplemented
43#13063311C2212yescomplemented
44#13063310C2211yescharacteristic, complemented
45#13063309C2212yescomplemented
46#13063308C2212yescomplemented
47#13063308C2212yescomplemented
48#13063307C2212yescomplemented
49#13063307C2211yescharacteristic, complemented
50#13063307C2212yescomplemented
51#13063306C2212yescomplemented
52#13063306C2212yescomplemented
53#13063306C2212yescomplemented
54#13063303C2211yescharacteristic, complemented
55#13063302C2211yescharacteristic, complemented
56#13063300C2211yescharacteristic, complemented
57#13063299C2211yescharacteristic, complemented
58#13063299C2211yescharacteristic, complemented
59#13063299C2212yescomplemented
60#13063298C2212yescomplemented
61#13063298C2212yescomplemented
62#13063298C2212yescomplemented
63#13063298C2211yescharacteristic, complemented
64#13063297C2212yescomplemented
65#13063297C2212yescomplemented
66#13063297C2212yescomplemented
67#13063297C2212yescomplemented
68#13063297C2212yescomplemented
69#13063297C2212yescomplemented
70#13063297C2212yescomplemented
71#13063297C2211yescharacteristic, complemented
72#13063296C2211yescharacteristic, complemented
73#13063296C2212yescomplemented
74#13063296C2211yescharacteristic, complemented
75#13063296C2211yescharacteristic, complemented
76#13063296C2211yescharacteristic, complemented
77#13063296C2212yescomplemented
78#13063296C2212yescomplemented
79#13063296C2211yescharacteristic, complemented
80#13063296C2212yescomplemented
81#13063296C2211yescharacteristic, complemented
82#13063296C2211yescharacteristic, complemented
83#13063295C2212yescomplemented
84#13063295C2211yescharacteristic, complemented
85#13063294C2212yescomplemented
86#13063294C2212yescomplemented
87#13063294C2212yescomplemented
88#13063294C2212yescomplemented
89#13063293C2212yescomplemented
90#13063293C2212yescomplemented
91#13063293C2211yescharacteristic, complemented
92#13063293C2212yescomplemented
93#13063293C2212yescomplemented
94#13063293C2212yescomplemented
95C4×D172C2211yescharacteristic, complemented
96C4×D172C2211yescharacteristic, complemented
97D4×Dic43C2211yescharacteristic, complemented
98D4×Dic43C2212yescomplemented
99D4×Dic43C2211yescharacteristic, complemented
100C4×C22⋊D43C2211yescharacteristic, complemented
101C4×C22⋊D43C2212yescomplemented
102C4×C22⋊D43C2211yescharacteristic, complemented
103(C22⋊D43)⋊C4C2212yescomplemented
104(C22⋊D43)⋊C4C2212yescomplemented
105#13063284C2211yescharacteristic, complemented
106#13063283C2211yescharacteristic, complemented
107#13063282C2211yescharacteristic, complemented
108C2×C4⋊Dic43C2211yescharacteristic, complemented
109C4⋊C4×D43C2211yescharacteristic, complemented
110C2×C22⋊Dic43C2212yescomplemented
111C22⋊C4×D43C2212yescomplemented
112C22×D4×C43C2211yescharacteristic, complemented
113C22×D4×C43C2212yescomplemented
114C22×D4×C43C2211yescharacteristic, complemented
115#127×C43C2211yescharacteristic, complemented
116#121×C43C2211yescharacteristic, complemented
117#121×C43C2211yescharacteristic, complemented
118#121×C43C2212yescomplemented
119#120×C43C2212yescomplemented
120#120×C43C2212yescomplemented
121C4×D4×C43C2211yescharacteristic, complemented
122C4×D4×C43C2211yescharacteristic, complemented
123C24×C43C2312yes—
124C24×C43C2312yes—
125C23×D43C2311yescharacteristic
126C23×D43C2312yes—
127C23×D43C2312yes—
128C2×D4×C43—44no—
129C2×D4×C43—42no—
130C2×D4×C43—42no—
131C2×D4×C43C2311yescharacteristic
132C2×D4×C43C2311yescharacteristic
133C2×D4×C43C2312yes—
134C2×D4×C43C2311yescharacteristic
135C2×D4×C43C2311yescharacteristic
136C2×D4×C43C2312yes—
137C2×D4×C43C2312yes—
138C2×D4×C43C2312yes—
139C2×D4×C43C2312yes—
140C2×D4×C43C2312yes—
141C22×C4×C43C2311yescharacteristic
142C22×C4×C43C2311yescharacteristic
143C22×C4×C43C2312yes—
144C2×C22⋊D43—44no—
145C2×C22⋊D43—44no—
146C2×C22⋊D43—44no—
147C2×C22⋊D43C2312yes—
148C2×C22⋊D43C2312yes—
149C2×C22⋊D43C2311yescharacteristic
150C2×C22⋊D43C2312yes—
151C2×C22⋊D43C2311yescharacteristic
152C2×C22⋊D43C2311yescharacteristic
153C2×C22⋊D43C2311yescharacteristic
154C2×C22⋊D43C2312yes—
155C2×C22⋊D43C2312yes—
156C2×C22⋊D43C2312yes—
157C2×C22⋊D43C2312yes—
158C2×C22⋊D43C2312yes—
159C2×C22⋊D43C2312yes—
160C2×C22⋊D43C2312yes—
161C2×C22⋊D43C2312yes—
162C2×C22⋊D43C2312yes—
163C2×C22⋊D43C2312yes—
164C22×Dic43C2311yescharacteristic
165C22×Dic43C2312yes—
166C22×Dic43C2312yes—
167C22×Dic43C2312yes—
168D4×D43—44no—
169D4×D43—44no—
170D4×D43—42no—
171D4×D43—42no—
172#10621898—42no—
173C2×D172C2311yescharacteristic
174C2×D172C2311yescharacteristic
175C2×D172C2311yescharacteristic
176C2×D172C2312yes—
177C2×C4×D43—42no—
178C2×C4×D43C2311yescharacteristic
179C2×C4×D43C2311yescharacteristic
180C2×C4×D43C2311yescharacteristic
181C2×C4×D43C2311yescharacteristic
182C2×C4×D43C2312yes—
183C2×C4×D43C2312yes—
184C2×C4×D43C2311yescharacteristic
185C2×Dic86C2311yescharacteristic
186C4⋊C4×C43C2311yescharacteristic
187C4⋊C4×C43C2311yescharacteristic
188C22⋊C4×C43C2311yescharacteristic
189C22⋊C4×C43C2312yes—
190C22⋊C4×C43C2311yescharacteristic
191C22⋊C4×C43C2312yes—
192C22⋊C4×C43C2312yes—
193C42×C43C2311yescharacteristic
194C22⋊Dic43C2312yes—
195C22⋊Dic43C2312yes—
196C22⋊Dic43C2312yes—
197C22⋊Dic43C2312yes—
198C22⋊Dic43C2312yes—
199C22⋊Dic43C2312yes—
200C22⋊Dic43C2311yescharacteristic
201C22⋊Dic43C2312yes—
202C22⋊Dic43C2311yescharacteristic
203C22⋊Dic43C2312yes—
204C22⋊Dic43C2312yes—
205C22⋊Dic43C2312yes—
206(C2×D43)⋊C4C2312yes—
207(C2×D43)⋊C4C2312yes—
208(C2×D43)⋊C4C2311yescharacteristic
209(C2×D43)⋊C4C2311yescharacteristic
210(C2×D43)⋊C4C2312yes—
211(C2×D43)⋊C4C2311yescharacteristic
212(C2×D43)⋊C4C2312yes—
213(C2×D43)⋊C4C2311yescharacteristic
214(C2×D43)⋊C4C2311yescharacteristic
215(C2×D43)⋊C4C2312yes—
216(C2×D43)⋊C4C2311yescharacteristic
217C4⋊Dic43C2311yescharacteristic
218C4⋊Dic43C2311yescharacteristic
219C4⋊Dic43C2311yescharacteristic
220C4⋊Dic43C2312yes—
221C4⋊Dic43C2312yes—
222C4⋊Dic43C2311yescharacteristic
223Dic43⋊C4C2312yes—
224Dic43⋊C4C2311yescharacteristic
225Dic43⋊C4C2311yescharacteristic
226Dic43⋊C4C2312yes—
227Dic43⋊C4C2312yes—
228Dic43⋊C4C2311yescharacteristic
229Dic43⋊C4C2311yescharacteristic
230Dic43⋊C4C2312yes—
231C4×Dic43C2311yescharacteristic
232C4×Dic43C2312yes—
233C4×Dic43C2312yes—
234C23×C43—24no—
235C23×C43—42no—
236C23×C43—42no—
237C23×C43—42no—
238C23×C43—42no—
239C23×C43—42no—
240C23×C43C2412yes—
241C23×C43C2412yes—
242C23×C43C2412yes—
243C23×C43C2411yescharacteristic
244C23×C43C2411yescharacteristic
245C22×D43—22no—
246C22×D43—22no—
247C22×D43—24no—
248C22×D43—41no—
249C22×D43—42no—
250C22×D43—42no—
251C22×D43—42no—
252C22×D43—42no—
253C22×D43—42no—
254C22×D43C2412yes—
255C22×D43C2411yescharacteristic
256C22×D43C2411yescharacteristic
257C22×D43C2411yescharacteristic
258D4×C43—24no—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—42no—
264D4×C43—42no—
265D4×C43—42no—
266D4×C43—42no—
267D4×C43—42no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—42no—
271C2×C4×C43C2411yescharacteristic
272C2×C4×C43C2412yes—
273C2×C4×C43C2411yescharacteristic
274C2×C4×C43C2411yescharacteristic
275C2×C4×C43C2411yescharacteristic
276C2×C4×C43C2411yescharacteristic
277C22⋊D43—24no—
278C22⋊D43—22no—
279C22⋊D43—24no—
280C22⋊D43—24no—
281C22⋊D43—22no—
282C22⋊D43—41no—
283C22⋊D43—41no—
284C22⋊D43—42no—
285C22⋊D43—42no—
286C22⋊D43—42no—
287C22⋊D43—42no—
288C22⋊D43—42no—
289C22⋊D43—42no—
290C22⋊D43—42no—
291C22⋊D43—42no—
292C22⋊D43—42no—
293C22⋊D43—42no—
294C2×Dic43—41no—
295C2×Dic43—42no—
296C2×Dic43—42no—
297C2×Dic43—42no—
298C2×Dic43C2411yescharacteristic
299C2×Dic43C2411yescharacteristic
300C2×Dic43C2412yes—
301C2×Dic43C2411yescharacteristic
302C2×Dic43C2412yes—
303C2×Dic43C2412yes—
304C2×Dic43C2411yescharacteristic
305C2×Dic43C2411yescharacteristic
306D172—22no—
307D172—22no—
308D172—41no—
309D172—42no—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—41no—
314C4×D43—41no—
315C4×D43—42no—
316C4×D43—42no—
317Dic86—41no—
318C22×C43—21no—
319C22×C43—21no—
320C22×C43—22no—
321C22×C43—22no—
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—21no—
329C22×C43—21no—
330C22×C43—21no—
331C22×C43—22no—
332C22×C43—84no—
333C22×C43—84no—
334C22×C43H(5,𝔽2)12yes—
335C22×C43C2511yescharacteristic
336C2×D43—21no—
337C2×D43—21no—
338C2×D43—22no—
339C2×D43—21no—
340C2×D43—21no—
341C2×D43—21no—
342C2×D43—21no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—21no—
346C2×D43—21no—
347C2×D43—44no—
348C2×D43—84no—
349C2×D43—84no—
350C2×D43H(5,𝔽2)12yes—
351C4×C43—21no—
352C4×C43—21no—
353C4×C43—21no—
354C4×C43—22no—
355C4×C43—21no—
356C4×C43H(5,𝔽2)12yes—
357Dic43—21no—
358Dic43—21no—
359Dic43—21no—
360Dic43—22no—
361Dic43—22no—
362Dic43—22no—
363Dic43—21no—
364Dic43—21no—
365#3537—431nomaximal, Sylow
366C2×C43—22no—
367C2×C43—42no—
368C2×C43—42no—
369C2×C43—42no—
370C2×C43—41no—
371C2×C43C2×H(5,𝔽2)11yescharacteristic
372C2×C43C2×H(5,𝔽2)11yescharacteristic
373C2×C43C2×H(5,𝔽2)11yescharacteristic
374D43—22no—
375D43—41no—
376D43—42no—
377D43—41no—
378#560—432no—
379#560—432no—
380#553—431no—
381#553—431no—
382#553—431no—
383#553—431no—
384D42—432no—
385D42—431no—
386D42—431no—
387D42—431no—
388D42—432no—
389D42D4311yescharacteristic, complemented
390#540—431no—
391#540—431no—
392#538—432no—
393#538—432no—
394#535—431no—
395#535—431no—
396#534—432no—
397#534—432no—
398#525—431no—
399C2×#121—431no—
400C2×#121—431no—
401C43#353711yescharacteristic, complemented, Sylow
402C2×#41—431no—
403C22×D4—432no—
404C22×D4—432no—
405C22×D4—432no—
406C22×D4—431no—
407C22×D4—432no—
408C22×D4—432no—
409C22×D4—431no—
410C22×D4C2×D4311yescharacteristic, complemented
411C22×D4C2×D4312yescomplemented
412C22×D4C2×D4311yescharacteristic, complemented
413C23×C4—431no—
414#127—432no—
415#127—432no—
416#127—431no—
417#127C2×D4311yescharacteristic, complemented
418#126—432no—
419#126—432no—
420#126—432no—
421#126—432no—
422#125—431no—
423#125—431no—
424#124—432no—
425#124—432no—
426#123—432no—
427#123—432no—
428#123—432no—
429#123—432no—
430#123—432no—
431#123—431no—
432#123—431no—
433#123—432no—
434#123—432no—
435#123—432no—
436C22⋊Q8—431no—
437C22⋊Q8—431no—
438#121—432no—
439#121—432no—
440#121—431no—
441#121—431no—
442#121—431no—
443#121—431no—
444#121—431no—
445#121—432no—
446#121—431no—
447#121—432no—
448#121—432no—
449#121—432no—
450#121—431no—
451#121—431no—
452#121—432no—
453#121—432no—
454#121—432no—
455#121—432no—
456#121—432no—
457#121—431no—
458#121—431no—
459#121—432no—
460#121—431no—
461#121—432no—
462#121—431no—
463#121—432no—
464#121—432no—
465#121C2×D4311yescharacteristic, complemented
466#121C2×D4311yescharacteristic, complemented
467#121C2×D4312yescomplemented
468#120—432no—
469#120—432no—
470#120—432no—
471#120—432no—
472#120—431no—
473#120—432no—
474#120—432no—
475#120—432no—
476#120—432no—
477#120—432no—
478#120—431no—
479#120—432no—
480#120C2×D4312yescomplemented
481#120C2×D4312yescomplemented
482C4×D4—432no—
483C4×D4—431no—
484C4×D4—431no—
485C4×D4—431no—
486C4×D4—431no—
487C4×D4—432no—
488C4×D4—432no—
489C4×D4—432no—
490C4×D4—431no—
491C4×D4—431no—
492C4×D4C2×D4311yescharacteristic, complemented
493C4×D4C2×D4311yescharacteristic, complemented
494#117—431no—
495#117—431no—
496#117—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C22⋊C4—432no—
500C2×C22⋊C4—432no—
501C24—431no—
502C24—432no—
503C24—432no—
504C24C22×D4312yes—
505C24C22×D4312yes—
506#41—1722no—
507C2×Q8—431no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—44no—
511C2×D4—432no—
512C2×D4—431no—
513C2×D4—432no—
514C2×D4—431no—
515C2×D4—432no—
516C2×D4—431no—
517C2×D4—431no—
518C2×D4—432no—
519C2×D4—432no—
520C2×D4—432no—
521C2×D4—432no—
522C2×D4—432no—
523C2×D4—432no—
524C2×D4—432no—
525C2×D4—432no—
526C2×D4—432no—
527C2×D4—432no—
528C2×D4—431no—
529C2×D4—431no—
530C2×D4—431no—
531C2×D4—432no—
532C2×D4—1722no—
533C2×D4—1722no—
534C2×D4—1724no—
535C2×D4—1724no—
536C2×D4—1724no—
537C2×D4—1724no—
538C2×D4—1724no—
539C2×D4C22×D4312yes—
540C2×D4C22×D4311yescharacteristic
541C2×D4C22×D4311yescharacteristic
542C2×D4C22×D4311yescharacteristic
543C2×D4C22×D4311yescharacteristic
544C2×D4C22×D4312yes—
545C2×D4C22×D4312yes—
546C2×D4C22×D4312yes—
547C2×D4C22×D4312yes—
548C2×D4C22×D4312yes—
549C22×C4—431no—
550C22×C4—432no—
551C22×C4—432no—
552C22×C4—432no—
553C22×C4—431no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—432no—
558C22×C4—432no—
559C22×C4—431no—
560C22×C4—1722no—
561C22×C4C22×D4311yescharacteristic
562C22×C4C22×D4311yescharacteristic
563C22×C4C22×D4312yes—
564C4⋊C4—431no—
565C4⋊C4—431no—
566C4⋊C4—431no—
567C4⋊C4—432no—
568C4⋊C4—432no—
569C4⋊C4—431no—
570C4⋊C4—431no—
571C4⋊C4—431no—
572C4⋊C4—431no—
573C4⋊C4—431no—
574C4⋊C4—432no—
575C4⋊C4—432no—
576C4⋊C4—432no—
577C4⋊C4—432no—
578C4⋊C4C22×D4311yescharacteristic
579C4⋊C4C22×D4311yescharacteristic
580C22⋊C4—432no—
581C22⋊C4—432no—
582C22⋊C4—432no—
583C22⋊C4—432no—
584C22⋊C4—432no—
585C22⋊C4—432no—
586C22⋊C4—431no—
587C22⋊C4—432no—
588C22⋊C4—432no—
589C22⋊C4—432no—
590C22⋊C4—432no—
591C22⋊C4—431no—
592C22⋊C4—432no—
593C22⋊C4—432no—
594C22⋊C4—432no—
595C22⋊C4—431no—
596C22⋊C4—431no—
597C22⋊C4—431no—
598C22⋊C4—431no—
599C22⋊C4—432no—
600C22⋊C4—432no—
601C22⋊C4—431no—
602C22⋊C4—431no—
603C22⋊C4C22×D4312yes—
604C22⋊C4C22×D4311yescharacteristic
605C22⋊C4C22×D4312yes—
606C22⋊C4C22×D4312yes—
607C22⋊C4C22×D4311yescharacteristic
608C42—431no—
609C42—432no—
610C42—432no—
611C42C22×D4311yescharacteristic
612C23—24no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—431no—
619C23—432no—
620C23—431no—
621C23—431no—
622C23—864no—
623C23—862no—
624C23—862no—
625C23—1722no—
626C23—1722no—
627C23—1722no—
628C23—1722no—
629C23—1722no—
630C23—1721no—
631C23C23×D4312yes—
632C23C23×D4312yes—
633C23C23×D4311yescharacteristic
634C23C23×D4312yes—
635C23C23×D4311yescharacteristic
636Q8—1721no—
637D4—22no—
638D4—24no—
639D4—22no—
640D4—22no—
641D4—22no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647D4—862no—
648D4—864no—
649D4—862no—
650D4—864no—
651D4—864no—
652D4—862no—
653D4—862no—
654D4—1722no—
655D4—1721no—
656D4—1722no—
657D4—1722no—
658D4—1722no—
659D4—1722no—
660D4—1722no—
661D4—1722no—
662D4—1722no—
663D4—1722no—
664D4—1722no—
665D4—1722no—
666D4—1721no—
667D4—1721no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—431no—
672C2×C4—431no—
673C2×C4—432no—
674C2×C4—432no—
675C2×C4—431no—
676C2×C4—432no—
677C2×C4—431no—
678C2×C4—431no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1722no—
685C2×C4—1722no—
686C2×C4—1721no—
687C2×C4—1722no—
688C2×C4—1722no—
689C2×C4—1722no—
690C2×C4C23×D4311yescharacteristic
691C2×C4C23×D4312yes—
692C2×C4C23×D4311yescharacteristic
693C2×C4C23×D4311yescharacteristic
694C2×C4C23×D4311yescharacteristic
695C2×C4C23×D4311yescharacteristic
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—432no—
713C22—861no—
714C22—861no—
715C22—862no—
716C22—861no—
717C22—861no—
718C22—861no—
719C22—861no—
720C22—862no—
721C22—861no—
722C22—862no—
723C22—861no—
724C22—3444no—
725C22—3444no—
726C22—1724no—
727C22#1306337012yes—
728C22C24×D4311yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—21no—
733C4—22no—
734C4—862no—
735C4—861no—
736C4—862no—
737C4—861no—
738C4—861no—
739C4—861no—
740C4—862no—
741C4—861no—
742C4#1306337012yes—
743C2—22no—
744C2—41no—
745C2—42no—
746C2—42no—
747C2—42no—
748C2—862no—
749C2—1722no—
750C2—1721no—
751C2—1721no—
752C2H(5,𝔽2)×D4311yescharacteristic
753C2C2×#1306337011yescharacteristic
754C2C2×#1306337011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D43
commutator, socleC22×C43C25
FittingD42×C43C2
hypercenterD42D43
hypocenterC43#3537
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #14583638C2semidirect
2. #14583637C2semidirect
3. #14583601C2semidirect
4. #14583599C2semidirect
5. #14583596C2semidirect
6. #14583595C2semidirect
7. #14583534C2semidirect
8. D4×C22⋊D43C2semidirect
9. D4×C22⋊D43C2semidirect
10. D4×C22⋊D43C2semidirect
11. #14583531C2semidirect
12. #14583503C2semidirect
13. #14583500C2semidirect
14. #14583484C2semidirect
15. #14583481C2semidirect
16. #14583466C2semidirect
17. #14583465C2semidirect
18. #14583459C2semidirect
19. #14583458C2semidirect
20. #14583408C2semidirect
21. C2×#13063296C2semidirect
22. #121×D43C2semidirect
23. D42×C43C2semidirect
24. C2×#10621898C22semidirect
25. C22×C22⋊D43C22semidirect
26. C22×C22⋊D43C22semidirect
27. C22×C22⋊D43C22semidirect
28. C2×D4×D43C22semidirect
29. C2×D4×D43C22semidirect
30. C2×D4×D43C22semidirect
31. C2×D4×D43C22semidirect
32. C22×C4×D43C22semidirect
33. #13063321C22semidirect
34. #13063321C22semidirect
35. #13063321C22semidirect
36. #13063320C22semidirect
37. #13063318C22semidirect
38. #13063318C22semidirect
39. #13063318C22semidirect
40. #13063317C22semidirect
41. #13063316C22semidirect
42. #13063312C22semidirect
43. #13063311C22semidirect
44. #13063310C22semidirect
45. #13063309C22semidirect
46. #13063308C22semidirect
47. #13063308C22semidirect
48. #13063307C22semidirect
49. #13063307C22semidirect
50. #13063307C22semidirect
51. #13063306C22semidirect
52. #13063306C22semidirect
53. #13063306C22semidirect
54. #13063303C22semidirect
55. #13063302C22semidirect
56. #13063300C22semidirect
57. #13063299C22semidirect
58. #13063299C22semidirect
59. #13063299C22semidirect
60. #13063298C22semidirect
61. #13063298C22semidirect
62. #13063298C22semidirect
63. #13063298C22semidirect
64. #13063297C22semidirect
65. #13063297C22semidirect
66. #13063297C22semidirect
67. #13063297C22semidirect
68. #13063297C22semidirect
69. #13063297C22semidirect
70. #13063297C22semidirect
71. #13063297C22semidirect
72. #13063296C22semidirect
73. #13063296C22semidirect
74. #13063296C22semidirect
75. #13063296C22semidirect
76. #13063296C22semidirect
77. #13063296C22semidirect
78. #13063296C22semidirect
79. #13063296C22semidirect
80. #13063296C22semidirect
81. #13063296C22semidirect
82. #13063296C22semidirect
83. #13063295C22semidirect
84. #13063295C22semidirect
85. #13063294C22semidirect
86. #13063294C22semidirect
87. #13063294C22semidirect
88. #13063294C22semidirect
89. #13063293C22semidirect
90. #13063293C22semidirect
91. #13063293C22semidirect
92. #13063293C22semidirect
93. #13063293C22semidirect
94. #13063293C22semidirect
95. C4×D172C22semidirect
96. C4×D172C22semidirect
97. D4×Dic43C22semidirect
98. D4×Dic43C22semidirect
99. D4×Dic43C22semidirect
100. C4×C22⋊D43C22semidirect
101. C4×C22⋊D43C22semidirect
102. C4×C22⋊D43C22semidirect
103. (C22⋊D43)⋊C4C22semidirect
104. (C22⋊D43)⋊C4C22semidirect
105. #13063284C22semidirect
106. #13063283C22semidirect
107. #13063282C22semidirect
108. C2×C4⋊Dic43C22semidirect
109. C4⋊C4×D43C22semidirect
110. C2×C22⋊Dic43C22semidirect
111. C22⋊C4×D43C22semidirect
112. C22×D4×C43C22semidirect
113. C22×D4×C43C22semidirect
114. C22×D4×C43C22semidirect
115. #127×C43C22semidirect
116. #121×C43C22semidirect
117. #121×C43C22semidirect
118. #121×C43C22semidirect
119. #120×C43C22semidirect
120. #120×C43C22semidirect
121. C4×D4×C43C22semidirect
122. C4×D4×C43C22semidirect
389. D42D43semidirect
401. C43#3537semidirect
410. C22×D4C2×D43semidirect
411. C22×D4C2×D43semidirect
412. C22×D4C2×D43semidirect
417. #127C2×D43semidirect
465. #121C2×D43semidirect
466. #121C2×D43semidirect
467. #121C2×D43semidirect
480. #120C2×D43semidirect
481. #120C2×D43semidirect
492. C4×D4C2×D43semidirect
493. C4×D4C2×D43semidirect