Finite Group Databasebeta

← C2×#19145219 #25966403

Subgroups — C2×#19145219 #25966403

Order 11008.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583507C211yesmaximal, characteristic, complemented
2C2×#14583500C211yesmaximal, characteristic
3#19145219C2116yesmaximal, direct product factor
4C2×#14583299C211yesmaximal, characteristic, complemented
5C2×#14583270C211yesmaximal, characteristic, complemented
6C2×#14583266C211yesmaximal, characteristic, complemented
7C2×#14583262C211yesmaximal, characteristic, complemented
8C2×#14583148C211yesmaximal, characteristic, complemented
9C2×#14583144C211yesmaximal, characteristic, complemented
10C2×#14583129C211yesmaximal, characteristic, complemented
11C2×#14583125C211yesmaximal, characteristic, complemented
12C2×#14582999C211yesmaximal, characteristic, complemented
13C2×#14582997C211yesmaximal, characteristic, complemented
14C2×C4×#10621873C211yesmaximal, characteristic, complemented
15C2×#14582853C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
17C22×#10621873C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22#14583507—24no—
23#14583507C2218yescomplemented
24#14583500—24no—
25#14583500C2218yes—
26C2×#13063323C2211yescharacteristic
27C2×#13063321C2211yescharacteristic
28C2×#13063320—21no—
29C2×#13063319—21no—
30C2×#13063317—21no—
31C2×#13063316C2211yescharacteristic
32C2×#13063316C2211yescharacteristic
33C2×#13063315—21no—
34C2×#13063308—21no—
35C2×#13063307—21no—
36C2×#13063305C2211yescharacteristic
37C2×#13063301C2211yescharacteristic
38C2×#13063300C2211yescharacteristic
39C2×#13063299—21no—
40C2×#13063298—21no—
41C2×#13063296C2211yescharacteristic
42C2×C4×Dic86C2211yescharacteristic
43C2×C4×D172C2211yescharacteristic
44C2×#13063282C2211yescharacteristic
45#14583299C2218yescomplemented
46#14583270C2218yescomplemented
47#14583266C2218yescomplemented
48#14583262C2218yescomplemented
49#14583148C2218yescomplemented
50#14583144C2218yescomplemented
51#14583129C2218yescomplemented
52#14583125C2218yescomplemented
53#14582999C2218yescomplemented
54#14582997C2218yescomplemented
55C4×#10621873C2218yescomplemented
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65#14582853C2218yescomplemented
66C2×#13063236C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C4×SD16×C43C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×D172—21no—
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×#10621873—24no—
86C2×#10621873C2314yes—
87C2×#10621883—24no—
88C2×#10621883C2314yes—
89C2×#10621884—24no—
90C2×#10621884C2314yes—
91C2×#10621872—24no—
92C2×#10621872C2314yes—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95C2×C8×D43—24no—
96C2×C8×D43C2314yes—
97#13063323—22no—
98#13063323C2314yes—
99#13063321—22no—
100#13063321C2314yes—
101#13063320—28no—
102#13063319—28no—
103#13063317—28no—
104#13063316—22no—
105#13063316—22no—
106#13063316C2314yes—
107#13063316C2314yes—
108#13063315—28no—
109#13063308—28no—
110#13063307—28no—
111#13063305—22no—
112#13063305C2314yes—
113#13063301—22no—
114#13063301C2314yes—
115#13063300—22no—
116#13063300C2314yes—
117#13063299—28no—
118#13063298—28no—
119#13063296—22no—
120#13063296C2314yes—
121C4×Dic86—22no—
122C4×Dic86C2314yes—
123C4×D172—22no—
124C4×D172C2314yes—
125#13063282D414yes—
126#13063282C2314yes—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4D411yescharacteristic
139C2×Dic43⋊C4D411yescharacteristic
140C2×C22⋊Dic43—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4D411yescharacteristic
146C2×(C2×D43)⋊C4D411yescharacteristic
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yes—
150#13063258C2314yes—
151#13063257C2314yes—
152#13063250C2314yes—
153#13063249C2314yes—
154#13063248C2314yes—
155#13063247C2314yes—
156#13063246C2314yes—
157#13063245C2314yes—
158#13063236C2314yes—
159#13063235C2314yes—
160C8×Dic43C2314yes—
161C22×Q8×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C2×SD16×C43—24no—
165C2×SD16×C43C2314yes—
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C4×Q8×C43—22no—
169C4×Q8×C43C2314yes—
170C4×D4×C43—22no—
171C4×D4×C43C2314yes—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C42×C43—21no—
177C2×C42×C43C2311yescharacteristic
178#106×C43C2314yes—
179#103×C43C2314yes—
180#102×C43C2314yes—
181C4×C8×C43C2314yes—
182C24×C43—21no—
183C23×D43—21no—
184C23×D43C2×D411yescharacteristic
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43C2412yes—
189C2×D4×C43—21no—
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43C2412yes—
193C22×C4×C43—24no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—82no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—82no—
205C2×C22⋊D43—82no—
206C2×C22⋊D43—82no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C2×D172—21no—
214C2×D172—24no—
215C2×D172—22no—
216C2×D172—22no—
217C2×D172—82no—
218C2×D172C2412yes—
219C2×C4×D43—22no—
220C2×C4×D43—22no—
221C2×C4×D43—24no—
222C2×C4×D43—82no—
223C2×C4×D43C2×D412yes—
224C2×C4×D43C2412yes—
225C2×Dic86—22no—
226C2×Dic86—22no—
227C2×Dic86—21no—
228C2×Dic86C2412yes—
229SD16×C43—28no—
230C2×C8×C43—22no—
231C2×C8×C43#4114yes—
232C2×C8×C43C2412yes—
233C2×C8×C43C2412yes—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C22⋊C4×C43—24no—
240C42×C43—24no—
241C42×C43C2×D412yes—
242C42×C43C2412yes—
243C22⋊Dic43—24no—
244#10621884—28no—
245#10621883—28no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4C2×D414yes—
251(C2×D43)⋊C4C2×D414yes—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—24no—
255C4⋊Dic43—24no—
256C4⋊Dic43—24no—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4C2×D414yes—
266Dic43⋊C4C2×D414yes—
267C4×Dic43—24no—
268C4×Dic43C2×D412yes—
269C4×Dic43C2412yes—
270C2×C43⋊C8—22no—
271C2×C43⋊C8#4114yes—
272C2×C43⋊C8C2412yes—
273C2×C43⋊C8C2412yes—
274#10621873—28no—
275#10621872—28no—
276C8×D43—28no—
277C23×C43—22no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43C22×D411yescharacteristic
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—42no—
287C22×D43—42no—
288C22×D43—42no—
289C22×D43C22×D412yes—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—42no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—42no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—84no—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D412yes—
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4112yes—
309C2×C4×C43C2×#4112yes—
310C2×C4×C43C2511yescharacteristic
311C22⋊D43—84no—
312C22⋊D43—84no—
313C22⋊D43—84no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43C22×D412yes—
324C2×Dic43C22×D412yes—
325C2×Dic43C22×D412yes—
326D172—22no—
327D172—22no—
328D172—42no—
329D172—84no—
330C4×D43—24no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—84no—
334Dic86—22no—
335Dic86—22no—
336Dic86—42no—
337C8×C43—22no—
338C8×C43C2×#4114yes—
339C43⋊C8—22no—
340C43⋊C8C2×#4114yes—
341C2×#3174—431nomaximal, Sylow
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—84no—
346C22×C43#53212yes—
347C22×C43#57712yes—
348C22×C43#57712yes—
349C22×C43C23×D411yescharacteristic
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—44no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—84no—
358C4×C43—22no—
359C4×C43—22no—
360C4×C43—42no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43#53212yes—
364C4×C43C22×#4111yescharacteristic
365C4×C43C22×#4111yescharacteristic
366Dic43—22no—
367Dic43—22no—
368Dic43—22no—
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372C2×#541—431no—
373C2×#540—431no—
374#3174—4316no—
375C2×#499—431no—
376C2×#492—431no—
377C2×#491—431no—
378C2×#490—431no—
379C2×#468—431no—
380C2×#468—431no—
381C2×#465—431no—
382C2×#465—431no—
383C2×#440—431no—
384C2×#440—431no—
385C2×C4×SD16—431no—
386C2×C4×SD16D4311yescharacteristic, complemented
387C2×#405—431no—
388C2×C43—82no—
389C2×C43#317414yescomplemented
390C2×C43C2×#53211yescharacteristic
391C2×C43C2×#57711yescharacteristic
392C2×C43C2×#57711yescharacteristic
393D43—42no—
394D43—82no—
395C22×SD16—431no—
396C22×SD16—431no—
397C22×SD16—431no—
398C22×SD16C2×D4311yescharacteristic
399C22×M16—431no—
400C23×C8—431no—
401#541—438no—
402#541—864no—
403#540—438no—
404#540—864no—
405C2×C4⋊Q8—431no—
406C2×#127—431no—
407C2×#126—861no—
408C2×#126—861no—
409C2×#125—431no—
410C2×#125—431no—
411C2×#125—861no—
412C2×#125—861no—
413C2×#123—861no—
414C2×#123—861no—
415C2×C22⋊Q8—431no—
416C2×C22⋊Q8—431no—
417C2×#121—431no—
418C2×#121—431no—
419C2×#121—861no—
420C2×#121—861no—
421C2×C4×Q8—431no—
422C2×C4×Q8C2×D4311yescharacteristic
423C2×C4×D4—431no—
424C2×C4×D4C2×D4311yescharacteristic
425C2×#117—431no—
426#499—438no—
427#492—438no—
428#491—438no—
429#490—438no—
430#468—438no—
431#468—438no—
432#465—438no—
433#465—438no—
434#440—438no—
435#440—438no—
436C4×SD16—438no—
437C4×SD16C2×D4318yescomplemented
438C2×#107—431no—
439C2×#107—431no—
440C2×#106—431no—
441C2×#106C2×D4311yescharacteristic
442C2×#103—431no—
443C2×#103—431no—
444C2×#103—431no—
445C2×#103C2×D4311yescharacteristic
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102C2×D4311yescharacteristic
450#405—438no—
451C2×#97—431no—
452C2×#97—431no—
453C2×C4×C8—431no—
454C2×C4×C8C2×D4311yescharacteristic
455C43C2×#317411yescharacteristic, complemented, Sylow
456C22×Q8—431no—
457C22×Q8C22×D4311yescharacteristic
458C22×D4—431no—
459C22×D4—861no—
460C22×D4—861no—
461C22×D4—861no—
462C22×D4—861no—
463C22×D4C22×D4311yescharacteristic
464C23×C4—21no—
465C23×C4—431no—
466C23×C4—861no—
467C2×SD16—24no—
468C2×SD16—434no—
469C2×SD16—434no—
470C2×SD16—434no—
471C2×SD16—864no—
472C2×SD16—864no—
473C2×SD16—864no—
474C2×SD16C22×D4314yes—
475C2×M16—434no—
476C2×M16—864no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8—434no—
480C22×C8—864no—
481C22×C8C22×D4311yescharacteristic
482C22×C8C22×D4311yescharacteristic
483C4⋊Q8—434no—
484C4⋊Q8—862no—
485#127—434no—
486#127—862no—
487#126—868no—
488#126—868no—
489#125—434no—
490#125—434no—
491#125—868no—
492#125—862no—
493#125—862no—
494#125—868no—
495#123—868no—
496#123—868no—
497C22⋊Q8—434no—
498C22⋊Q8—434no—
499C22⋊Q8—862no—
500C22⋊Q8—862no—
501#121—434no—
502#121—434no—
503#121—868no—
504#121—868no—
505#121—862no—
506#121—862no—
507C4×Q8—22no—
508C4×Q8—434no—
509C4×Q8—862no—
510C4×Q8C22×D4314yes—
511C4×D4—22no—
512C4×D4—434no—
513C4×D4—862no—
514C4×D4C22×D4314yes—
515#117—434no—
516#117—434no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4C22×D4311yescharacteristic
532C2×C4⋊C4C22×D4311yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—431no—
535C2×C22⋊C4—431no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C42—21no—
542C2×C42—431no—
543C2×C42—861no—
544C2×C42C22×D4311yescharacteristic
545#107—434no—
546#107—434no—
547#106—434no—
548#106C22×D4314yes—
549#103—434no—
550#103—434no—
551#103—434no—
552#103C22×D4314yes—
553#102—434no—
554#102—434no—
555#102—434no—
556#102C22×D4314yes—
557#97—434no—
558#97—434no—
559C4×C8—434no—
560C4×C8C22×D4314yes—
561C24—21no—
562C24—431no—
563C24—861no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—432no—
568C2×Q8—861no—
569C2×Q8—862no—
570C2×Q8—862no—
571C2×Q8C23×D4312yes—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—432no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—864no—
579C2×D4—864no—
580C2×D4—861no—
581C2×D4—862no—
582C2×D4—862no—
583C2×D4—3442no—
584C2×D4—3442no—
585C2×D4—3442no—
586C2×D4—3442no—
587C2×D4C23×D4312yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—82no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—431no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—864no—
604C22×C4—3442no—
605C22×C4D4×D4311yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4C23×D4311yescharacteristic
608SD16—28no—
609SD16—868no—
610SD16—868no—
611SD16—868no—
612M16—868no—
613C2×C8—22no—
614C2×C8—434no—
615C2×C8—432no—
616C2×C8—432no—
617C2×C8—862no—
618C2×C8—868no—
619C2×C8#1062189814yes—
620C2×C8C23×D4312yes—
621C2×C8C23×D4312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—434no—
626C4⋊C4—434no—
627C4⋊C4—432no—
628C4⋊C4—432no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4—864no—
635C4⋊C4—864no—
636C4⋊C4—864no—
637C4⋊C4—861no—
638C4⋊C4—861no—
639C4⋊C4—864no—
640C4⋊C4C23×D4312yes—
641C4⋊C4C23×D4312yes—
642C22⋊C4—24no—
643C22⋊C4—434no—
644C22⋊C4—434no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C42—24no—
651C42—432no—
652C42—432no—
653C42—864no—
654C42D4×D4312yes—
655C42C23×D4312yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—432no—
661C23—862no—
662C23—862no—
663C23—862no—
664C23—862no—
665C23—1722no—
666C23—1722no—
667C23—1722no—
668C23C2×D4×D4311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—862no—
673Q8—862no—
674Q8—1722no—
675D4—22no—
676D4—22no—
677D4—42no—
678D4—862no—
679D4—862no—
680D4—3444no—
681D4—3444no—
682D4—3444no—
683D4—3444no—
684D4—1722no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—84no—
694C2×C4—432no—
695C2×C4—432no—
696C2×C4—432no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—864no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—3444no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4C2×D4×D4312yes—
711C2×C4C2×D4×D4312yes—
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4#41×D4312yes—
714C2×C4C2×#1062189812yes—
715C2×C4C24×D4311yescharacteristic
716C8—22no—
717C8—434no—
718C8—862no—
719C8C2×#1062189814yes—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—862no—
725C22—862no—
726C22—862no—
727C22—3444no—
728C22—1722no—
729C22—1722no—
730C22—1722no—
731C22—1724no—
732C22#1458344612yes—
733C22#1458370512yes—
734C22#1458370612yes—
735C22C22×D4×D4311yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—862no—
742C4—862no—
743C4—862no—
744C4—1722no—
745C4—1722no—
746C4—1722no—
747C4#1458344612yes—
748C4C2×#41×D4311yescharacteristic
749C4C22×#1062189811yescharacteristic
750C2—82no—
751C2—3442no—
752C2—1722no—
753C2#1914521914yesdirect product factor
754C2C2×#1458344611yescharacteristic
755C2C2×#1458370511yescharacteristic
756C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583500C2
hypercenterC2×C4×SD16D43
hypocenterC43C2×#3174
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14583507C2semidirect
3. #19145219C2direct (N × H)
4. C2×#14583299C2semidirect
5. C2×#14583270C2semidirect
6. C2×#14583266C2semidirect
7. C2×#14583262C2semidirect
8. C2×#14583148C2semidirect
9. C2×#14583144C2semidirect
10. C2×#14583129C2semidirect
11. C2×#14583125C2semidirect
12. C2×#14582999C2semidirect
13. C2×#14582997C2semidirect
14. C2×C4×#10621873C2semidirect
15. C2×#14582853C2semidirect
16. C2×C4×SD16×C43C2semidirect
23. #14583507C22semidirect
45. #14583299C22semidirect
46. #14583270C22semidirect
47. #14583266C22semidirect
48. #14583262C22semidirect
49. #14583148C22semidirect
50. #14583144C22semidirect
51. #14583129C22semidirect
52. #14583125C22semidirect
53. #14582999C22semidirect
54. #14582997C22semidirect
55. C4×#10621873C22semidirect
65. #14582853C22semidirect
72. C4×SD16×C43C22semidirect
386. C2×C4×SD16D43semidirect
389. C2×C43#3174semidirect
437. C4×SD16C2×D43semidirect
455. C43C2×#3174semidirect
753. C2#19145219direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835072
C2×#145835002
#191452192
C2×#145832992
C2×#145832702
C2×#145832662
C2×#145832622
C2×#145831482
C2×#145831442
C2×#145831292
C2×#145831252
C2×#145829992
C2×#145829972
C2×C4×#106218732
C2×#145828532
C2×C4×SD16×C432
C2×#317443