Finite Group Databasebeta

← C2×#19145730 #25968654

Subgroups — C2×#19145730 #25968654

Order 11008.

2058 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583455C211yesmaximal, characteristic, complemented
2C2×#14583446C211yesmaximal, characteristic
3#19145730C2116yesmaximal, direct product factor
4C2×#14583303C211yesmaximal, characteristic, complemented
5C2×#14583296C211yesmaximal, characteristic, complemented
6C2×#14583244C211yesmaximal, characteristic, complemented
7C2×#14583244C211yesmaximal, characteristic, complemented
8C2×#14583226C211yesmaximal, characteristic, complemented
9C2×#14583225C211yesmaximal, characteristic, complemented
10C2×#14583222C211yesmaximal, characteristic, complemented
11C2×#14583221C211yesmaximal, characteristic, complemented
12C2×#14583200C211yesmaximal, characteristic, complemented
13C2×#14583199C211yesmaximal, characteristic, complemented
14C2×#14583196C211yesmaximal, characteristic, complemented
15C2×#14582951C211yesmaximal, characteristic, complemented
16C2×C43×#478C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18#14583455—24no—
19#14583455C2218yescomplemented
20#14583446—24no—
21#14583446C2218yes—
22C2×#13063324C2211yescharacteristic
23C2×#13063324C2211yescharacteristic
24C2×#13063324C2211yescharacteristic
25C2×#13063321C2211yescharacteristic
26C2×#13063317C2211yescharacteristic
27C2×#13063311—21no—
28C2×#13063303—21no—
29C2×#13063303—21no—
30C2×#13063300C2211yescharacteristic
31C2×#13063298—21no—
32C2×#13063296C2211yescharacteristic
33C2×#13063290—21no—
34C2×#13063290—21no—
35C2×C4×D172C2211yescharacteristic
36C2×C4×C22⋊D43—21no—
37C2×#13063283C2211yescharacteristic
38C2×#13063283C2211yescharacteristic
39C2×C42×D43C2211yescharacteristic
40#14583303C2218yescomplemented
41#14583296C2218yescomplemented
42#14583244C2218yescomplemented
43#14583244C2218yescomplemented
44#14583226C2218yescomplemented
45#14583225C2218yescomplemented
46#14583222C2218yescomplemented
47#14583221C2218yescomplemented
48#14583200C2218yescomplemented
49#14583199C2218yescomplemented
50#14583196C2218yescomplemented
51#14582951C2218yescomplemented
52C2×#13063259C2211yescharacteristic
53C2×#13063258C2211yescharacteristic
54C2×#13063258C2211yescharacteristic
55C2×#13063257C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×#13063247C2211yescharacteristic
60C2×#13063247C2211yescharacteristic
61C2×#13063246C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C43×#478C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C22×Dic86—21no—
80C22×Dic86—21no—
81C22×Dic86—21no—
82C22×D172—21no—
83C22×D172C2311yescharacteristic
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43D411yescharacteristic
89C22×C4×D43D411yescharacteristic
90C22×C4×D43C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93#13063324—22no—
94#13063324—22no—
95#13063324—22no—
96#13063324C2314yes—
97#13063324C2314yes—
98#13063324C2314yes—
99#13063321—22no—
100#13063321C2314yes—
101#13063317—22no—
102#13063317C2314yes—
103#13063311—28no—
104#13063303—28no—
105#13063303—28no—
106#13063300—22no—
107#13063300C2314yes—
108#13063298—28no—
109#13063296—22no—
110#13063296C2314yes—
111#13063290—28no—
112#13063290—28no—
113C4×D172—22no—
114C4×D172C2314yes—
115C4×C22⋊D43—28no—
116#13063283—22no—
117#13063283—22no—
118#13063283C2314yes—
119#13063283C2314yes—
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×C22⋊Dic43—21no—
129C2×(C2×D43)⋊C4—21no—
130C2×(C2×D43)⋊C4—21no—
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C2×C4×Dic43—21no—
134C2×C4×Dic43—21no—
135C2×C4×Dic43D411yescharacteristic
136C2×C4×Dic43D411yescharacteristic
137C2×C4×Dic43C2311yescharacteristic
138C42×D43D414yes—
139C42×D43C2314yes—
140#13063259C2314yes—
141#13063258C2314yes—
142#13063258C2314yes—
143#13063257C2314yes—
144#13063256C2314yes—
145#13063256C2314yes—
146C4⋊(C43⋊C8)C2314yes—
147#13063247C2314yes—
148#13063247C2314yes—
149#13063246C2314yes—
150#13063246C2314yes—
151#13063245C2314yes—
152#13063245C2314yes—
153(C2×D43)⋊C8C2314yes—
154(C2×D43)⋊C8C2314yes—
155C8×Dic43C2314yes—
156C8×Dic43C2314yes—
157C22×D4×C43C2311yescharacteristic
158C23×C4×C43—21no—
159C22×C8×C43C2311yescharacteristic
160C22×C8×C43C2311yescharacteristic
161#125×C43—22no—
162#125×C43C2314yes—
163C4×D4×C43—22no—
164C4×D4×C43C2314yes—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43C2311yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C22⋊C4×C43—21no—
171C2×C42×C43C2311yescharacteristic
172#107×C43C2314yes—
173#106×C43C2314yes—
174C4⋊C8×C43C2314yes—
175#102×C43C2314yes—
176#102×C43C2314yes—
177C24×C43—21no—
178C23×D43—21no—
179C23×D43C2×D411yescharacteristic
180C2×D4×C43—21no—
181C2×D4×C43—22no—
182C2×D4×C43—22no—
183C2×D4×C43C2412yes—
184C22×C4×C43—24no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—44no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2411yescharacteristic
192C2×C22⋊D43—24no—
193C2×C22⋊D43—24no—
194C2×C22⋊D43—24no—
195C2×C22⋊D43—44no—
196C2×C22⋊D43—44no—
197C2×C22⋊D43—44no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204#10621898—432no—
205C2×D172—21no—
206C2×D172—24no—
207C2×D172—22no—
208C2×D172—22no—
209C2×D172—44no—
210C2×D172C2412yes—
211C2×C4×D43—22no—
212C2×C4×D43—22no—
213C2×C4×D43—24no—
214C2×C4×D43—24no—
215C2×C4×D43—24no—
216C2×C4×D43—44no—
217C2×C4×D43C2×D412yes—
218C2×C4×D43C2×D414yes—
219C2×C4×D43C2×D414yes—
220C2×C4×D43C2412yes—
221C2×Dic86—24no—
222C2×Dic86—24no—
223C2×Dic86—24no—
224C2×Dic86—44no—
225C2×Dic86—44no—
226C2×Dic86—44no—
227C2×C8×C43—22no—
228C2×C8×C43—22no—
229C2×C8×C43C2412yes—
230C2×C8×C43C2412yes—
231C4⋊C4×C43—24no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C22⋊C4×C43—24no—
240C42×C43C2×D412yes—
241C42×C43C2412yes—
242C22⋊Dic43—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43C2412yes—
251C4⋊Dic43C2412yes—
252C4⋊Dic43C2412yes—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258C4×Dic43—24no—
259C4×Dic43—24no—
260C4×Dic43C2×D412yes—
261C4×Dic43C2×D414yes—
262C4×Dic43C2×D414yes—
263C4×Dic43C2412yes—
264C2×C43⋊C8—22no—
265C2×C43⋊C8—22no—
266C2×C43⋊C8C2412yes—
267C2×C43⋊C8C2412yes—
268C23×C43—22no—
269C23×C43—42no—
270C23×C43—42no—
271C23×C43—42no—
272C23×C43C22×D411yescharacteristic
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—42no—
278C22×D43—42no—
279C22×D43—42no—
280C22×D43C22×D412yes—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—42no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—48no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43C22×D412yes—
294C2×C4×C43C22×D412yes—
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C432−1+412yes—
297C2×C4×C432−1+412yes—
298C2×C4×C43C2511yescharacteristic
299C22⋊D43—48no—
300C22⋊D43—48no—
301C22⋊D43—48no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43#13514yes—
310C2×Dic43AGL(1,ℤ/8)14yes—
311C2×Dic43C22×D412yes—
312C2×Dic43C22×D412yes—
313C2×Dic43C22×D412yes—
314D172—22no—
315D172—22no—
316D172—48no—
317D172—42no—
318C4×D43—24no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—28no—
322C4×D43—28no—
323C4×D43—48no—
324Dic86—48no—
325Dic86—48no—
326Dic86—48no—
327C8×C43—22no—
328C8×C43—22no—
329C43⋊C8—22no—
330C43⋊C8—22no—
331C2×#3228—431nomaximal, Sylow
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—84no—
336C22×C43#53612yes—
337C22×C43C2×#13512yes—
338C22×C43C2×AGL(1,ℤ/8)12yes—
339C22×C43C23×D411yescharacteristic
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—44no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—84no—
348C4×C43—22no—
349C4×C43—22no—
350C4×C43—42no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43#53612yes—
354C4×C43C2×2−1+411yescharacteristic
355C4×C43C2×2−1+411yescharacteristic
356Dic43—22no—
357Dic43—42no—
358Dic43—42no—
359Dic43—42no—
360Dic43C2×#13514yes—
361Dic43C2×AGL(1,ℤ/8)14yes—
362C2×#533—431no—
363C2×#532—431no—
364#3228—4316no—
365C2×#500—431no—
366C2×#498—431no—
367C2×#486—431no—
368C2×#486—431no—
369C2×#482—431no—
370C2×#482—431no—
371C2×#482—431no—
372C2×#482—431no—
373C2×#478—431no—
374C2×#478—431no—
375C2×#478—431no—
376C2×#478D4311yescharacteristic, complemented
377C2×#431—431no—
378C2×C43—82no—
379C2×C43#322814yescomplemented
380C2×C43C2×#53611yescharacteristic
381C2×C43C22×#13511yescharacteristic
382C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
383D43—42no—
384D43—82no—
385C22×#41—861no—
386#533—438no—
387#533—864no—
388#532—438no—
389#532—864no—
390C2×C4⋊Q8—431no—
391C2×C4⋊Q8—431no—
392C2×C4⋊Q8—431no—
393C2×#127—431no—
394C2×#125—431no—
395C2×#125C2×D4311yescharacteristic
396C2×#124—861no—
397C2×C22⋊Q8—861no—
398C2×C22⋊Q8—861no—
399C2×#121—431no—
400C2×#121—431no—
401C2×#121—861no—
402C2×C4×Q8—861no—
403C2×C4×Q8—861no—
404C2×C4×D4—431no—
405C2×C4×D4—861no—
406C2×C4×D4C2×D4311yescharacteristic
407C2×#117—431no—
408C2×#117—431no—
409C22×C42—431no—
410#500—438no—
411#498—438no—
412#486—438no—
413#486—438no—
414#482—438no—
415#482—438no—
416#482—438no—
417#482—438no—
418#478—438no—
419#478—438no—
420#478—438no—
421#478C2×D4318yescomplemented
422#431—438no—
423C2×#107—431no—
424C2×#107—431no—
425C2×#107—431no—
426C2×#107C2×D4311yescharacteristic
427C2×#106—431no—
428C2×#106—431no—
429C2×#106—431no—
430C2×#106C2×D4311yescharacteristic
431C2×C4⋊C8—431no—
432C2×C4⋊C8C2×D4311yescharacteristic
433C2×#102—431no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102C2×D4311yescharacteristic
440C2×#102C2×D4311yescharacteristic
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C4×C8—431no—
444C2×C4×C8—431no—
445C43C2×#322811yescharacteristic, complemented, Sylow
446C2×#41—868no—
447C2×#41—1728no—
448C22×Q8—861no—
449C22×Q8—861no—
450C22×Q8—861no—
451C22×D4—431no—
452C22×D4—861no—
453C22×D4—861no—
454C22×D4—861no—
455C22×D4—861no—
456C22×D4C22×D4311yescharacteristic
457C23×C4—21no—
458C23×C4—431no—
459C23×C4—431no—
460C23×C4—431no—
461C23×C4—861no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8C22×D4311yescharacteristic
465C22×C8C22×D4311yescharacteristic
466C4⋊Q8—434no—
467C4⋊Q8—434no—
468C4⋊Q8—434no—
469C4⋊Q8—862no—
470C4⋊Q8—862no—
471C4⋊Q8—862no—
472#127—434no—
473#127—862no—
474#125—22no—
475#125—434no—
476#125—862no—
477#125C22×D4314yes—
478#124—868no—
479C22⋊Q8—868no—
480C22⋊Q8—868no—
481#121—434no—
482#121—434no—
483#121—868no—
484#121—862no—
485#121—862no—
486C4×Q8—868no—
487C4×Q8—868no—
488C4×D4—22no—
489C4×D4—434no—
490C4×D4—868no—
491C4×D4—862no—
492C4×D4C22×D4314yes—
493#117—434no—
494#117—434no—
495#117—862no—
496#117—862no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C4⋊C4C22×D4311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C42—431no—
517C2×C42—431no—
518C2×C42—431no—
519C2×C42—434no—
520C2×C42—434no—
521C2×C42—861no—
522C2×C42—861no—
523C2×C42C22×D4311yescharacteristic
524#107—434no—
525#107—434no—
526#107—434no—
527#107C22×D4314yes—
528#106—434no—
529#106—434no—
530#106—434no—
531#106C22×D4314yes—
532C4⋊C8—434no—
533C4⋊C8C22×D4314yes—
534#102—434no—
535#102—434no—
536#102—434no—
537#102—434no—
538#102—434no—
539#102—434no—
540#102C22×D4314yes—
541#102C22×D4314yes—
542C22⋊C8—434no—
543C22⋊C8—434no—
544C4×C8—434no—
545C4×C8—434no—
546C24—21no—
547C24—431no—
548C24—861no—
549#41—17232no—
550C2×Q8—864no—
551C2×Q8—864no—
552C2×Q8—864no—
553C2×Q8—1724no—
554C2×Q8—1724no—
555C2×Q8—1724no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—432no—
560C2×D4—864no—
561C2×D4—864no—
562C2×D4—864no—
563C2×D4—864no—
564C2×D4—861no—
565C2×D4—862no—
566C2×D4—862no—
567C2×D4—1724no—
568C2×D4—1724no—
569C2×D4—1724no—
570C2×D4—1724no—
571C2×D4C23×D4312yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—44no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—432no—
581C22×C4—434no—
582C22×C4—434no—
583C22×C4—432no—
584C22×C4—864no—
585C22×C4—864no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—864no—
592C22×C4—1724no—
593C22×C4D4×D4311yescharacteristic
594C22×C4D4×D4311yescharacteristic
595C22×C4C23×D4311yescharacteristic
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—432no—
599C2×C8—432no—
600C2×C8—862no—
601C2×C8—862no—
602C2×C8C23×D4312yes—
603C2×C8C23×D4312yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—432no—
610C4⋊C4—432no—
611C4⋊C4—432no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4C23×D4312yes—
621C4⋊C4C23×D4312yes—
622C4⋊C4C23×D4312yes—
623C22⋊C4—24no—
624C22⋊C4—864no—
625C22⋊C4—864no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C42—434no—
630C42—434no—
631C42—432no—
632C42—432no—
633C42—864no—
634C42—864no—
635C42D4×D4312yes—
636C42C23×D4312yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—432no—
642C23—862no—
643C23—862no—
644C23—862no—
645C23—862no—
646C23—1722no—
647C23—1722no—
648C23—1722no—
649C23C2×D4×D4311yescharacteristic
650Q8—1728no—
651Q8—1728no—
652Q8—1728no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—862no—
657D4—862no—
658D4—1728no—
659D4—1728no—
660D4—1728no—
661D4—1728no—
662D4—1722no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—48no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—434no—
673C2×C4—434no—
674C2×C4—432no—
675C2×C4—432no—
676C2×C4—432no—
677C2×C4—868no—
678C2×C4—868no—
679C2×C4—862no—
680C2×C4—864no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—1728no—
687C2×C4—1722no—
688C2×C4—1722no—
689C2×C4—1722no—
690C2×C4C2×D4×D4312yes—
691C2×C4C2×D4×D4312yes—
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4#1306337212yes—
694C2×C4#1306337312yes—
695C2×C4C24×D4311yescharacteristic
696C8—22no—
697C8—22no—
698C8—862no—
699C8—862no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—3444no—
708C22—1722no—
709C22—1722no—
710C22—1722no—
711C22—1724no—
712C22#1458347212yes—
713C22#135×D4312yes—
714C22AGL(1,ℤ/8)×D4312yes—
715C22C22×D4×D4311yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—434no—
722C4—434no—
723C4—862no—
724C4—1722no—
725C4—1722no—
726C4—1722no—
727C4#1458347212yes—
728C4C2×#1306337211yescharacteristic
729C4C2×#1306337311yescharacteristic
730C2—82no—
731C2—3442no—
732C2—1722no—
733C2#1914573014yesdirect product factor
734C2C2×#1458347211yescharacteristic
735C2C2×#135×D4311yescharacteristic
736C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
prime radicalC2×#14583446C2
hypercenterC2×#478D43
hypocenterC43C2×#3228
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#14583455C2semidirect
3. #19145730C2direct (N × H)
4. C2×#14583303C2semidirect
5. C2×#14583296C2semidirect
6. C2×#14583244C2semidirect
7. C2×#14583244C2semidirect
8. C2×#14583226C2semidirect
9. C2×#14583225C2semidirect
10. C2×#14583222C2semidirect
11. C2×#14583221C2semidirect
12. C2×#14583200C2semidirect
13. C2×#14583199C2semidirect
14. C2×#14583196C2semidirect
15. C2×#14582951C2semidirect
16. C2×C43×#478C2semidirect
19. #14583455C22semidirect
40. #14583303C22semidirect
41. #14583296C22semidirect
42. #14583244C22semidirect
43. #14583244C22semidirect
44. #14583226C22semidirect
45. #14583225C22semidirect
46. #14583222C22semidirect
47. #14583221C22semidirect
48. #14583200C22semidirect
49. #14583199C22semidirect
50. #14583196C22semidirect
51. #14582951C22semidirect
71. C43×#478C22semidirect
376. C2×#478D43semidirect
379. C2×C43#3228semidirect
421. #478C2×D43semidirect
445. C43C2×#3228semidirect
733. C2#19145730direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834552
C2×#145834462
#191457302
C2×#145833032
C2×#145832962
C2×#145832442
C2×#145832262
C2×#145832252
C2×#145832222
C2×#145832212
C2×#145832002
C2×#145831992
C2×#145831962
C2×#145829512
C2×C43×#4782
C2×#322843