Finite Group Databasebeta

← C2×#19147351 #25976349

Subgroups — C2×#19147351 #25976349

Order 11008.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583634C211yesmaximal, characteristic, complemented
2C2×#14583605C211yesmaximal, characteristic, complemented
3#19147351C2116yesmaximal, direct product factor
4C2×#14583265C211yesmaximal, characteristic, complemented
5C2×#14583260C211yesmaximal, characteristic, complemented
6C2×#14583255C211yesmaximal, characteristic, complemented
7C2×#14583198C211yesmaximal, characteristic, complemented
8C2×#14583178C211yesmaximal, characteristic, complemented
9C2×#14583117C211yesmaximal, characteristic, complemented
10C2×#14583117C211yesmaximal, characteristic, complemented
11C2×#14583095C211yesmaximal, characteristic
12C2×#14583028C211yesmaximal, characteristic, complemented
13C2×#14583010C211yesmaximal, characteristic, complemented
14C2×#14582997C211yesmaximal, characteristic, complemented
15C2×#14582981C211yesmaximal, characteristic, complemented
16C2×C43×#479C211yesmaximal, characteristic, complemented
17C22×#10621884C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C22×D344C2211yescharacteristic
20#14583634—24no—
21#14583634C2218yescomplemented
22#14583605—24no—
23#14583605C2218yescomplemented
24C2×#13063324C2211yescharacteristic
25C2×#13063322C2211yescharacteristic
26C2×#13063316C2211yescharacteristic
27C2×#13063314C2211yescharacteristic
28C2×#13063314C2211yescharacteristic
29C2×#13063313—21no—
30C2×#13063310—21no—
31C2×#13063310—21no—
32C2×#13063305—21no—
33C2×#13063303—21no—
34C2×#13063303—21no—
35C2×C4×Dic86C2211yescharacteristic
36C2×C4×D172—21no—
37C2×C4×D172C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×#13063287C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×#13063287C2211yescharacteristic
42C2×C4⋊C4×D43—21no—
43#14583265C2218yescomplemented
44#14583260C2218yescomplemented
45#14583255C2218yescomplemented
46#14583198C2218yescomplemented
47#14583178C2218yescomplemented
48#14583117C2218yescomplemented
49#14583117C2218yescomplemented
50#14583095C2218yes—
51#14583028C2218yescomplemented
52#14583010C2218yescomplemented
53#14582997C2218yescomplemented
54#14582981C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57C2×Dic43⋊C8C2211yescharacteristic
58C2×#13063249C2211yescharacteristic
59C2×#13063247C2211yescharacteristic
60C2×#13063247C2211yescharacteristic
61C2×#13063245C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063236C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#479C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86D411yescharacteristic
79C22×D172—21no—
80C22×D172—21no—
81C22×D172C2311yescharacteristic
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C2×#10621884—24no—
90C2×#10621884C2314yes—
91C2×D344—24no—
92C2×D344—24no—
93C2×D344C2314yes—
94C2×D344C2314yes—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97#13063324—22no—
98#13063324C2314yes—
99#13063322—22no—
100#13063322C2314yes—
101#13063316—22no—
102#13063316C2314yes—
103#13063314—22no—
104#13063314—22no—
105#13063314C2314yes—
106#13063314C2314yes—
107#13063313—28no—
108#13063310—28no—
109#13063310—28no—
110#13063305—28no—
111#13063303—28no—
112#13063303—28no—
113C4×Dic86D414yes—
114C4×Dic86C2314yes—
115C4×D172—22no—
116C4×D172—28no—
117C4×D172C2314yes—
118#13063287—22no—
119#13063287—22no—
120#13063287—22no—
121#13063287—22no—
122#13063287C2314yes—
123#13063287C2314yes—
124#13063287C2314yes—
125#13063287C2314yes—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43D411yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4D411yescharacteristic
132C2×Dic43⋊C4D411yescharacteristic
133C4⋊C4×D43—28no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×C4×Dic43C2311yescharacteristic
144C2×C4×Dic43C2311yescharacteristic
145#13063258C2314yes—
146Dic43⋊C8C2314yes—
147Dic43⋊C8C2314yes—
148#13063249C2314yes—
149#13063247C2314yes—
150#13063247C2314yes—
151#13063245C2314yes—
152#13063245C2314yes—
153#13063245C2314yes—
154#13063245C2314yes—
155#13063245C2314yes—
156#13063236C2314yes—
157#13063235C2314yes—
158C8×Dic43C2314yes—
159C22×Q8×C43C2311yescharacteristic
160C22×C8×C43C2311yescharacteristic
161C22×C8×C43C2311yescharacteristic
162#125×C43—22no—
163#125×C43C2314yes—
164C4×Q8×C43—22no—
165C4×Q8×C43C2314yes—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C42×C43—21no—
173C2×C42×C43C2311yescharacteristic
174#107×C43C2314yes—
175#106×C43C2314yes—
176C4⋊C8×C43C2314yes—
177#103×C43C2314yes—
178#103×C43C2314yes—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—22no—
184C2×Q8×C43—22no—
185C2×Q8×C43C2412yes—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2411yescharacteristic
193C22×Dic43—21no—
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C2×D172—21no—
199C2×D172—22no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—24no—
203C2×D172—24no—
204C2×D172—22no—
205C2×D172—22no—
206C2×D172—22no—
207C2×D172—22no—
208C2×D172—44no—
209C2×D172—82no—
210C2×D172#4114yes—
211C2×D172C2412yes—
212C2×D172C2412yes—
213C2×D172C2412yes—
214C2×C4×D43—24no—
215C2×C4×D43—24no—
216C2×C4×D43—24no—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—44no—
220C2×C4×D43—82no—
221C2×C4×D43—82no—
222C2×C4×D43—82no—
223C2×C4×D43—82no—
224C2×Dic86—24no—
225C2×Dic86—42no—
226C2×Dic86—82no—
227C2×Dic86C2×D414yes—
228C2×C8×C43—22no—
229C2×C8×C43—22no—
230C2×C8×C43C2412yes—
231C2×C8×C43C2412yes—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43C2412yes—
239C4⋊C4×C43C2412yes—
240C4⋊C4×C43C2412yes—
241C42×C43—24no—
242C42×C43C2×D412yes—
243C42×C43C2412yes—
244#10621884—28no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254C4⋊Dic43—21no—
255C4⋊Dic43—24no—
256C4⋊Dic43C2×D414yes—
257C4⋊Dic43C2412yes—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4C2×D414yes—
261Dic43⋊C4C2×D414yes—
262C4×Dic43C2×D412yes—
263C4×Dic43C2×D412yes—
264C4×Dic43C2412yes—
265C4×Dic43C2412yes—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8C2412yes—
269C2×C43⋊C8C2412yes—
270D344—28no—
271D344—28no—
272C23×C43C22×D411yescharacteristic
273C22×D43—24no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—42no—
278C22×D43—42no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43—42no—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—42no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43C22×D412yes—
299C2×C4×C43C22×D412yes—
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C2×#4112yes—
302C2×C4×C432−1+412yes—
303C2×C4×C43C2511yescharacteristic
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—42no—
310C2×Dic43C22×D412yes—
311C2×Dic43C22×D412yes—
312C2×Dic43C22×D412yes—
313C2×Dic43C22×D412yes—
314D172—24no—
315D172—22no—
316D172—22no—
317D172—22no—
318D172—22no—
319D172—22no—
320D172—48no—
321D172—42no—
322D172—42no—
323D172—84no—
324D172C2×#4114yes—
325C4×D43—48no—
326C4×D43—84no—
327C4×D43—84no—
328C4×D43—84no—
329C4×D43—84no—
330Dic86—44no—
331Dic86—84no—
332C8×C43—22no—
333C8×C43—22no—
334C43⋊C8—22no—
335C43⋊C8—22no—
336C2×#3370—431nomaximal, Sylow
337C22×C43#54812yes—
338C22×C43#57512yes—
339C22×C43#57612yes—
340C22×C43C23×D411yescharacteristic
341C2×D43—24no—
342C2×D43—48no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—84no—
352C2×D43—84no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—42no—
358C4×C43—42no—
359C4×C43#54812yes—
360C4×C43C22×#4111yescharacteristic
361C4×C43C2×2−1+411yescharacteristic
362Dic43—22no—
363Dic43—22no—
364Dic43—22no—
365Dic43—22no—
366Dic43—42no—
367C2×#559—431no—
368C2×#554—431no—
369#3370—4316no—
370C2×#490—431no—
371C2×#489—431no—
372C2×#488—431no—
373C2×#479D4311yescharacteristic, complemented
374C2×#478—431no—
375C2×#474—431no—
376C2×#463—431no—
377C2×#463—431no—
378C2×#459—431no—
379C2×#446—431no—
380C2×#442—431no—
381C2×#440—431no—
382C2×C4×D8—431no—
383C2×C43#337014yescomplemented
384C2×C43C2×#54811yescharacteristic
385C2×C43C2×#57511yescharacteristic
386C2×C43C2×#57611yescharacteristic
387D43—44no—
388D43—82no—
389D43—82no—
390C22×SD16—431no—
391C22×D8—431no—
392C22×D8—431no—
393#559—438no—
394#559—864no—
395#554—438no—
396#554—864no—
397C2×C4⋊Q8—431no—
398C2×#127—431no—
399C2×#125—431no—
400C2×#125C2×D4311yescharacteristic
401C2×#124—431no—
402C2×#124—431no—
403C2×#124—861no—
404C2×#123—861no—
405C2×#123—861no—
406C2×C22⋊Q8—861no—
407C2×C22⋊Q8—861no—
408C2×C22⋊Q8—861no—
409C2×C4×Q8—431no—
410C2×C4×Q8C2×D4311yescharacteristic
411C2×C4×D4—431no—
412C2×C4×D4—431no—
413C2×C4×D4—431no—
414C2×C4×D4—431no—
415C2×C4×D4—431no—
416C2×C4×D4—861no—
417C22×C4⋊C4—861no—
418#490—438no—
419#489—438no—
420#488—438no—
421#479C2×D4318yescomplemented
422#478—438no—
423#474—438no—
424#463—438no—
425#463—438no—
426#459—438no—
427#446—438no—
428#442—438no—
429#440—438no—
430C4×D8—438no—
431C2×#107—431no—
432C2×#107C2×D4311yescharacteristic
433C2×#106C2×D4311yescharacteristic
434C2×C4⋊C8—431no—
435C2×C4⋊C8—431no—
436C2×C4⋊C8C2×D4311yescharacteristic
437C2×#103—431no—
438C2×#103C2×D4311yescharacteristic
439C2×#103C2×D4311yescharacteristic
440C2×#102—431no—
441C2×#102—431no—
442C2×#102—431no—
443C2×#102—431no—
444C2×#102—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#97—431no—
448C2×#97—431no—
449C2×C4×C8—431no—
450C43C2×#337011yescharacteristic, complemented, Sylow
451C22×Q8—431no—
452C22×Q8—861no—
453C22×Q8C22×D4311yescharacteristic
454C22×D4—431no—
455C22×D4—431no—
456C22×D4—431no—
457C22×D4—861no—
458C22×D4—861no—
459C23×C4—861no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C2×SD16—434no—
465C2×SD16—864no—
466C2×D8—434no—
467C2×D8—434no—
468C2×D8—864no—
469C2×D8—864no—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474C4⋊Q8—434no—
475C4⋊Q8—862no—
476#127—434no—
477#127—862no—
478#125—22no—
479#125—434no—
480#125—862no—
481#125C22×D4314yes—
482#124—434no—
483#124—434no—
484#124—868no—
485#124—862no—
486#124—862no—
487#123—868no—
488#123—868no—
489C22⋊Q8—868no—
490C22⋊Q8—868no—
491C22⋊Q8—868no—
492C4×Q8—22no—
493C4×Q8—434no—
494C4×Q8—434no—
495C4×Q8C22×D4314yes—
496C4×D4—434no—
497C4×D4—434no—
498C4×D4—434no—
499C4×D4—434no—
500C4×D4—434no—
501C4×D4—868no—
502C4×D4—862no—
503C4×D4—862no—
504C4×D4—862no—
505C4×D4—862no—
506C4×D4—862no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—868no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C42—21no—
531C2×C42—431no—
532C2×C42—431no—
533C2×C42C22×D4311yescharacteristic
534#107—434no—
535#107C22×D4314yes—
536#106C22×D4314yes—
537C4⋊C8—434no—
538C4⋊C8—434no—
539C4⋊C8C22×D4314yes—
540#103—434no—
541#103C22×D4314yes—
542#103C22×D4314yes—
543#102—434no—
544#102—434no—
545#102—434no—
546#102—434no—
547#102—434no—
548#102—434no—
549#102—434no—
550#97—434no—
551#97—434no—
552C4×C8—434no—
553C24—861no—
554C24—861no—
555C24—861no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—434no—
560C2×Q8—864no—
561C2×Q8—3442no—
562C2×Q8—1722no—
563C2×Q8C23×D4312yes—
564C2×D4—434no—
565C2×D4—432no—
566C2×D4—432no—
567C2×D4—432no—
568C2×D4—861no—
569C2×D4—864no—
570C2×D4—864no—
571C2×D4—861no—
572C2×D4—861no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—3442no—
579C2×D4—1724no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—431no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—864no—
589C22×C4—864no—
590C22×C4—864no—
591C22×C4—864no—
592C22×C4—861no—
593C22×C4—864no—
594C22×C4—3442no—
595C22×C4—3442no—
596C22×C4—3442no—
597C22×C4—3442no—
598C22×C4—1724no—
599C22×C4D4×D4311yescharacteristic
600C22×C4D4×D4311yescharacteristic
601C22×C4C23×D4311yescharacteristic
602SD16—868no—
603D8—868no—
604D8—868no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—432no—
608C2×C8—432no—
609C2×C8—862no—
610C2×C8—862no—
611C2×C8C23×D4312yes—
612C2×C8C23×D4312yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—434no—
620C4⋊C4—434no—
621C4⋊C4—434no—
622C4⋊C4—432no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—861no—
627C4⋊C4C23×D4312yes—
628C4⋊C4C23×D4312yes—
629C4⋊C4C23×D4312yes—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—864no—
639C42—24no—
640C42—432no—
641C42—432no—
642C42—432no—
643C42—432no—
644C42D4×D4312yes—
645C42C23×D4312yes—
646C23—864no—
647C23—862no—
648C23—862no—
649C23—862no—
650C23—1722no—
651C23—1722no—
652C23—1722no—
653C23—1722no—
654C23—1722no—
655C23—1722no—
656C23—1722no—
657C23—1722no—
658C23C2×D4×D4311yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—3444no—
663Q8—1724no—
664D4—434no—
665D4—864no—
666D4—862no—
667D4—862no—
668D4—862no—
669D4—862no—
670D4—862no—
671D4—3444no—
672D4—1728no—
673D4—1722no—
674D4—1722no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—432no—
686C2×C4—432no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—3444no—
695C2×C4—3444no—
696C2×C4—3444no—
697C2×C4—3444no—
698C2×C4—1728no—
699C2×C4—1722no—
700C2×C4C2×D4×D4312yes—
701C2×C4C2×D4×D4312yes—
702C2×C4C2×D4×D4311yescharacteristic
703C2×C4#41×D4312yes—
704C2×C4#1306337312yes—
705C2×C4C24×D4311yescharacteristic
706C8—22no—
707C8—22no—
708C8—862no—
709C8—862no—
710C22—864no—
711C22—3444no—
712C22—3444no—
713C22—1722no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22—1722no—
718C22—1722no—
719C22—1722no—
720C22—1722no—
721C22—1728no—
722C22#1458355912yes—
723C22#1458369812yes—
724C22#1458370112yes—
725C22C22×D4×D4311yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—862no—
733C4—862no—
734C4—862no—
735C4—862no—
736C4—1722no—
737C4#1458355912yes—
738C4C2×#41×D4311yescharacteristic
739C4C2×#1306337311yescharacteristic
740C2—3442no—
741C2—3442no—
742C2—1724no—
743C2#1914735114yesdirect product factor
744C2C2×#1458355911yescharacteristic
745C2C2×#1458369811yescharacteristic
746C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC2×#14583095C2
hypercenterC2×#479D43
hypocenterC43C2×#3370
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#14583634C2semidirect
2. C2×#14583605C2semidirect
3. #19147351C2direct (N × H)
4. C2×#14583265C2semidirect
5. C2×#14583260C2semidirect
6. C2×#14583255C2semidirect
7. C2×#14583198C2semidirect
8. C2×#14583178C2semidirect
9. C2×#14583117C2semidirect
10. C2×#14583117C2semidirect
12. C2×#14583028C2semidirect
13. C2×#14583010C2semidirect
14. C2×#14582997C2semidirect
15. C2×#14582981C2semidirect
16. C2×C43×#479C2semidirect
21. #14583634C22semidirect
23. #14583605C22semidirect
43. #14583265C22semidirect
44. #14583260C22semidirect
45. #14583255C22semidirect
46. #14583198C22semidirect
47. #14583178C22semidirect
48. #14583117C22semidirect
49. #14583117C22semidirect
51. #14583028C22semidirect
52. #14583010C22semidirect
53. #14582997C22semidirect
54. #14582981C22semidirect
71. C43×#479C22semidirect
373. C2×#479D43semidirect
383. C2×C43#3370semidirect
421. #479C2×D43semidirect
450. C43C2×#3370semidirect
743. C2#19147351direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836342
C2×#145836052
#191473512
C2×#145832652
C2×#145832602
C2×#145832552
C2×#145831982
C2×#145831782
C2×#145831172
C2×#145830952
C2×#145830282
C2×#145830102
C2×#145829972
C2×#145829812
C2×C43×#4792
C2×#337043