Finite Group Databasebeta

← C2×#19144750 #25964728

Subgroups — C2×#19144750 #25964728

Order 11008.

2150 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic, complemented
2C2×#41×Dic43C211yesmaximal, characteristic
3#19144750C2116yesmaximal, direct product factor
4C2×#14583241C211yesmaximal, characteristic, complemented
5C2×#14583237C211yesmaximal, characteristic, complemented
6C2×#14583192C211yesmaximal, characteristic, complemented
7C2×#14583187C211yesmaximal, characteristic, complemented
8C2×#14583107C211yesmaximal, characteristic, complemented
9C2×#14583102C211yesmaximal, characteristic, complemented
10C2×#14583061C211yesmaximal, characteristic
11C2×#14583006C211yesmaximal, characteristic, complemented
12C2×#14583003C211yesmaximal, characteristic, complemented
13C2×#14583000C211yesmaximal, characteristic, complemented
14C2×#14582996C211yesmaximal, characteristic, complemented
15C2×#14582953C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19#14583451—24no—
20#14583451C2218yescomplemented
21C2×#13063324C2211yescharacteristic
22C2×#13063323C2211yescharacteristic
23C2×#13063315—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063302—21no—
26#41×Dic43—24no—
27#41×Dic43C2218yes—
28C2×Q8×Dic43C2211yescharacteristic
29C2×Q8×Dic43C2211yescharacteristic
30C2×Q8×Dic43C2211yescharacteristic
31C2×#13063290—21no—
32C2×#13063290C2211yescharacteristic
33C2×D4×Dic43—21no—
34C2×D4×Dic43—21no—
35C2×D4×Dic43C2211yescharacteristic
36C2×D4×Dic43C2211yescharacteristic
37C2×#13063284—21no—
38C2×#13063284C2211yescharacteristic
39C2×#13063281—21no—
40C22×C4×Dic43—21no—
41C22×C4×Dic43C2211yescharacteristic
42#14583241C2218yescomplemented
43#14583237C2218yescomplemented
44#14583192C2218yescomplemented
45#14583187C2218yescomplemented
46#14583107C2218yescomplemented
47#14583102C2218yescomplemented
48#14583061C2218yes—
49#14583006C2218yescomplemented
50#14583003C2218yescomplemented
51#14583000C2218yescomplemented
52#14582996C2218yescomplemented
53#14582953C2218yescomplemented
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063249C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C22×SD16×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#452C2218yes—
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C23×Dic43—21no—
80C23×Dic43—21no—
81C23×Dic43D411yescharacteristic
82C23×Dic43D411yescharacteristic
83C2×#10621885—24no—
84C2×#10621885C2314yes—
85C2×#10621883—24no—
86C2×#10621883C2314yes—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89#13063324—22no—
90#13063324C2314yes—
91#13063323—22no—
92#13063323C2314yes—
93#13063315—28no—
94#13063304—22no—
95#13063304C2314yes—
96#13063302—28no—
97Q8×Dic43—22no—
98Q8×Dic43—22no—
99Q8×Dic43—22no—
100Q8×Dic43C2314yes—
101Q8×Dic43C2314yes—
102Q8×Dic43C2314yes—
103#13063290—28no—
104#13063290—22no—
105#13063290C2314yes—
106D4×Dic43—28no—
107D4×Dic43—28no—
108D4×Dic43—22no—
109D4×Dic43—22no—
110D4×Dic43C2314yes—
111D4×Dic43C2314yes—
112#13063284—22no—
113#13063284—28no—
114#13063284C2314yes—
115#13063281—28no—
116C2×C4⋊Dic43—21no—
117C2×C4⋊Dic43—21no—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×Dic43⋊C4—21no—
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×C22⋊Dic43—21no—
128C2×C22⋊Dic43—21no—
129C2×C22⋊Dic43—21no—
130C2×C22⋊Dic43—21no—
131C2×C4×Dic43—21no—
132C2×C4×Dic43—21no—
133C2×C4×Dic43—21no—
134C2×C4×Dic43—21no—
135C2×C4×Dic43—21no—
136C2×C4×Dic43—28no—
137C2×C4×Dic43D411yescharacteristic
138C2×C4×Dic43D411yescharacteristic
139C2×C4×Dic43D414yes—
140C2×C4×Dic43C2311yescharacteristic
141C2×C4×Dic43C2311yescharacteristic
142C2×C4×Dic43C2314yes—
143#13063259C2314yes—
144#13063258C2314yes—
145#13063257C2314yes—
146#13063256C2314yes—
147Dic43⋊C8C2314yes—
148Dic43⋊C8C2314yes—
149#13063250C2314yes—
150#13063250C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063249C2314yes—
154#13063246C2314yes—
155C22⋊(C43⋊C8)C2314yes—
156#13063235C2314yes—
157#13063235C2314yes—
158C2×#41×C43—24no—
159C2×#41×C43—24no—
160C2×#41×C43—22no—
161C2×#41×C43C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C22×Q8×C43C2311yescharacteristic
164C22×D4×C43—21no—
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43—21no—
167C23×C4×C43C2311yescharacteristic
168C2×Q16×C43—24no—
169C2×Q16×C43C2314yes—
170C2×SD16×C43—24no—
171C2×SD16×C43C2314yes—
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174C22⋊Q8×C43—22no—
175C22⋊Q8×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179#103×C43C2314yes—
180#102×C43C2314yes—
181C22⋊C8×C43C2314yes—
182C24×C43—21no—
183C24×C43C2×D411yescharacteristic
184#41×C43—216no—
185#41×C43—28no—
186#41×C43—28no—
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43#4114yes—
193C2×Q8×C43C2412yes—
194C2×Q8×C43C2412yes—
195C2×D4×C43—28no—
196C2×D4×C43—21no—
197C2×D4×C43—22no—
198C2×D4×C43—24no—
199C2×D4×C43#4114yes—
200C2×D4×C43C2412yes—
201C22×C4×C43—28no—
202C22×C4×C43—24no—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D412yes—
210C22×C4×C43C2412yes—
211C22×C4×C43C2411yescharacteristic
212C22×Dic43—24no—
213C22×Dic43—24no—
214C22×Dic43—24no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—42no—
220C22×Dic43—44no—
221C22×Dic43—44no—
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D414yes—
226C22×Dic43C2×D414yes—
227C22×Dic43C2×D411yescharacteristic
228C2×Dic86—22no—
229C2×Dic86—22no—
230C2×Dic86—21no—
231C2×Dic86—24no—
232C2×Dic86—44no—
233C2×Dic86C2412yes—
234Q16×C43—28no—
235SD16×C43—28no—
236C2×C8×C43—22no—
237C2×C8×C43—22no—
238C2×C8×C43C2412yes—
239C2×C8×C43C2412yes—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43C2412yes—
243C22⋊C4×C43—24no—
244C22⋊Dic43—24no—
245C22⋊Dic43—24no—
246C22⋊Dic43—24no—
247C22⋊Dic43—24no—
248#10621885—28no—
249#10621883—28no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—24no—
254C4⋊Dic43—24no—
255C4⋊Dic43—24no—
256C4⋊Dic43C2412yes—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264C4×Dic43—24no—
265C4×Dic43—24no—
266C4×Dic43—24no—
267C4×Dic43—24no—
268C4×Dic43—24no—
269C4×Dic43C2×D414yes—
270C4×Dic43C2×D414yes—
271C4×Dic43C2×D412yes—
272C4×Dic43C2×D412yes—
273C4×Dic43C2412yes—
274C4×Dic43C2412yes—
275C2×C43⋊C8—22no—
276C2×C43⋊C8—22no—
277C2×C43⋊C8C2412yes—
278C2×C43⋊C8C2412yes—
279C23×C43—22no—
280C23×C43—24no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—42no—
285C23×C43—42no—
286C23×C43C22×D412yes—
287C23×C43C22×D411yescharacteristic
288Q8×C43—24no—
289Q8×C43—22no—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—42no—
293Q8×C43C2×#4114yes—
294D4×C43—216no—
295D4×C43—24no—
296D4×C43—22no—
297D4×C43C2×#4114yes—
298C2×C4×C43—216no—
299C2×C4×C43—22no—
300C2×C4×C43—24no—
301C2×C4×C43—22no—
302C2×C4×C43—24no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C2×#4112yes—
312C2×C4×C43C2×#4112yes—
313C2×C4×C43C2511yescharacteristic
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—28no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—44no—
323C2×Dic43—48no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—48no—
329C2×Dic43#13714yes—
330C2×Dic43C22×D412yes—
331C2×Dic43C22×D412yes—
332C2×Dic43C22×D412yes—
333C2×Dic43C22×D412yes—
334Dic86—22no—
335Dic86—22no—
336Dic86—48no—
337Dic86—42no—
338C8×C43—22no—
339C8×C43—22no—
340C43⋊C8—22no—
341C43⋊C8—22no—
342C2×#3116—431nomaximal, Sylow
343C22×C43—24no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—44no—
348C22×C43—48no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43#52512yes—
352C22×C43C2×#13712yes—
353C22×C43#57512yes—
354C22×C43C23×D411yescharacteristic
355C4×C43—22no—
356C4×C43—24no—
357C4×C43—42no—
358C4×C43—42no—
359C4×C43#52512yes—
360C4×C43C22×#4111yescharacteristic
361C4×C43C22×#4111yescharacteristic
362Dic43—22no—
363Dic43—22no—
364Dic43—22no—
365Dic43—42no—
366Dic43—42no—
367Dic43—42no—
368Dic43—42no—
369Dic43C2×#13714yes—
370C2×#533—431no—
371C2×C4×#41—431no—
372#3116—4316no—
373C2×#485—431no—
374C2×#485—431no—
375C2×#477—431no—
376C2×#476—431no—
377C2×#462—431no—
378C2×#461—431no—
379C2×#452—431no—
380C2×#452D4311yescharacteristic
381C2×#441—431no—
382C2×#441—431no—
383C2×#440—431no—
384C2×#440—431no—
385C2×#432—431no—
386C2×C43—42no—
387C2×C43—44no—
388C2×C43#311614yescomplemented
389C2×C43C2×#52511yescharacteristic
390C2×C43C22×#13711yescharacteristic
391C2×C43C2×#57511yescharacteristic
392C22×#41C2×D4311yescharacteristic
393C22×Q16—431no—
394C22×Q16C2×D4311yescharacteristic
395C22×SD16—431no—
396C22×SD16C2×D4311yescharacteristic
397#533—438no—
398#533—864no—
399C2×C4⋊Q8—431no—
400C2×C4⋊Q8—431no—
401C2×#125—861no—
402C2×C22⋊Q8—431no—
403C2×C22⋊Q8—861no—
404C2×C22⋊Q8C2×D4311yescharacteristic
405C4×#41—438no—
406C4×#41—864no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×Q8—861no—
412C2×C4×D4—431no—
413C2×C4×D4—431no—
414C2×C4×D4—861no—
415C2×C4×D4—861no—
416C2×#117—431no—
417C2×#117—861no—
418C2×#117—861no—
419C22×C42—431no—
420C22×C42—861no—
421#485—438no—
422#485—438no—
423#477—438no—
424#476—438no—
425#462—438no—
426#461—438no—
427#452—438no—
428#452C2×D4318yes—
429#441—438no—
430#441—438no—
431#440—438no—
432#440—438no—
433#432—438no—
434C2×#107—431no—
435C2×#107—431no—
436C2×#106—431no—
437C2×#106—431no—
438C2×C4⋊C8—431no—
439C2×C4⋊C8—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103—431no—
445C2×#103C2×D4311yescharacteristic
446C2×#102—431no—
447C2×#102C2×D4311yescharacteristic
448C2×C22⋊C8—431no—
449C2×C22⋊C8C2×D4311yescharacteristic
450C2×#97—431no—
451C2×#97—431no—
452C43C2×#311611yescharacteristic, complemented, Sylow
453C2×#41—24no—
454C2×#41—24no—
455C2×#41—22no—
456C2×#41C22×D4314yes—
457C22×Q8—431no—
458C22×Q8—861no—
459C22×Q8C22×D4311yescharacteristic
460C22×Q8C22×D4311yescharacteristic
461C22×D4—21no—
462C22×D4C22×D4311yescharacteristic
463C23×C4—21no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4C22×D4311yescharacteristic
469C2×Q16—24no—
470C2×Q16—434no—
471C2×Q16—864no—
472C2×Q16C22×D4314yes—
473C2×SD16—24no—
474C2×SD16—434no—
475C2×SD16—864no—
476C2×SD16C22×D4314yes—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8C22×D4311yescharacteristic
480C22×C8C22×D4311yescharacteristic
481C4⋊Q8—434no—
482C4⋊Q8—434no—
483C4⋊Q8—862no—
484C4⋊Q8—862no—
485#125—868no—
486C22⋊Q8—22no—
487C22⋊Q8—434no—
488C22⋊Q8—868no—
489C22⋊Q8—862no—
490C22⋊Q8C22×D4314yes—
491C4×Q8—434no—
492C4×Q8—434no—
493C4×Q8—434no—
494C4×Q8—434no—
495C4×Q8—862no—
496C4×Q8—868no—
497C4×Q8—862no—
498C4×Q8—862no—
499C4×Q8—862no—
500C4×D4—434no—
501C4×D4—434no—
502C4×D4—862no—
503C4×D4—862no—
504C4×D4—868no—
505C4×D4—868no—
506#117—434no—
507#117—868no—
508#117—868no—
509#117—862no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4C22×D4311yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—431no—
529C2×C42—434no—
530C2×C42—431no—
531C2×C42—431no—
532C2×C42—431no—
533C2×C42—434no—
534C2×C42—868no—
535C2×C42—861no—
536C2×C42—861no—
537C2×C42—861no—
538C2×C42—861no—
539C2×C42—861no—
540#107—434no—
541#107—434no—
542#106—434no—
543#106—434no—
544C4⋊C8—434no—
545C4⋊C8—434no—
546#103—434no—
547#103—434no—
548#103—434no—
549#103—434no—
550#103—434no—
551#103C22×D4314yes—
552#102—434no—
553#102C22×D4314yes—
554C22⋊C8—434no—
555C22⋊C8C22×D4314yes—
556#97—434no—
557#97—434no—
558C24—21no—
559C24D4×D4311yescharacteristic
560#41—216no—
561#41—28no—
562#41—28no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—432no—
569C2×Q8—864no—
570C2×Q8—861no—
571C2×Q8—862no—
572C2×Q8—862no—
573C2×Q8—1724no—
574C2×Q8#1062190014yes—
575C2×Q8C23×D4312yes—
576C2×Q8C23×D4312yes—
577C2×D4—28no—
578C2×D4—24no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4#1062190014yes—
582C2×D4C23×D4312yes—
583C22×C4—28no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—431no—
591C22×C4—434no—
592C22×C4—431no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—434no—
596C22×C4—864no—
597C22×C4—864no—
598C22×C4—864no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—1724no—
604C22×C4—1722no—
605C22×C4—1724no—
606C22×C4D4×D4312yes—
607C22×C4D4×D4311yescharacteristic
608C22×C4C23×D4312yes—
609C22×C4C23×D4311yescharacteristic
610Q16—28no—
611Q16—868no—
612SD16—28no—
613SD16—868no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—432no—
617C2×C8—432no—
618C2×C8—862no—
619C2×C8—862no—
620C2×C8C23×D4312yes—
621C2×C8C23×D4312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—432no—
625C4⋊C4—432no—
626C4⋊C4—432no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4—861no—
637C4⋊C4—864no—
638C4⋊C4C23×D4312yes—
639C22⋊C4—24no—
640C22⋊C4—864no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C42—434no—
645C42—434no—
646C42—432no—
647C42—432no—
648C42—432no—
649C42—432no—
650C42—864no—
651C42—864no—
652C42—864no—
653C42—864no—
654C42—864no—
655C23—22no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23C2×D4×D4312yes—
663C23C2×D4×D4311yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—862no—
670Q8—862no—
671Q8—1728no—
672Q8—1722no—
673Q8C2×#1062190014yes—
674D4—216no—
675D4—24no—
676D4—22no—
677D4C2×#1062190014yes—
678C2×C4—216no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—434no—
690C2×C4—432no—
691C2×C4—432no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—868no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—1728no—
703C2×C4—1724no—
704C2×C4—1728no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4C2×D4×D4312yes—
710C2×C4C2×D4×D4311yescharacteristic
711C2×C4C2×#1062190012yes—
712C2×C4C2×#1062190012yes—
713C2×C4C24×D4311yescharacteristic
714C8—22no—
715C8—22no—
716C8—862no—
717C8—862no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—24no—
722C22—42no—
723C22—42no—
724C22—44no—
725C22—48no—
726C22#1458340512yes—
727C22#137×D4312yes—
728C22#1458369612yes—
729C22C22×D4×D4311yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—434no—
735C4—862no—
736C4—862no—
737C4—862no—
738C4—1722no—
739C4—1722no—
740C4—1722no—
741C4—1722no—
742C4#1458340512yes—
743C4C22×#1062190011yescharacteristic
744C4C22×#1062190011yescharacteristic
745C2—42no—
746C2—44no—
747C2#1914475014yesdirect product factor
748C2C2×#1458340511yescharacteristic
749C2C2×#137×D4311yescharacteristic
750C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
hypercenterC2×#452D43
hypocenterC43C2×#3116
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#14583451C2semidirect
3. #19144750C2direct (N × H)
4. C2×#14583241C2semidirect
5. C2×#14583237C2semidirect
6. C2×#14583192C2semidirect
7. C2×#14583187C2semidirect
8. C2×#14583107C2semidirect
9. C2×#14583102C2semidirect
11. C2×#14583006C2semidirect
12. C2×#14583003C2semidirect
13. C2×#14583000C2semidirect
14. C2×#14582996C2semidirect
15. C2×#14582953C2semidirect
20. #14583451C22semidirect
42. #14583241C22semidirect
43. #14583237C22semidirect
44. #14583192C22semidirect
45. #14583187C22semidirect
46. #14583107C22semidirect
47. #14583102C22semidirect
49. #14583006C22semidirect
50. #14583003C22semidirect
51. #14583000C22semidirect
52. #14582996C22semidirect
53. #14582953C22semidirect
388. C2×C43#3116semidirect
452. C43C2×#3116semidirect
747. C2#19144750direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834512
C2×#41×Dic432
#191447502
C2×#145832412
C2×#145832372
C2×#145831922
C2×#145831872
C2×#145831072
C2×#145831022
C2×#145830612
C2×#145830062
C2×#145830032
C2×#145830002
C2×#145829962
C2×#145829532
C2×C43×#4522
C2×#311643