Finite Group Databasebeta

← C2×#20253545 #27084411

Subgroups — C2×#20253545 #27084411

Order 12032.

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×#15689675C211yesmaximal, characteristic, complemented
2C2×#15689591C211yesmaximal, characteristic
3#20253545C2116yesmaximal, direct product factor
4C2×#15689464C211yesmaximal, characteristic, complemented
5C2×#15689417C211yesmaximal, characteristic, complemented
6C2×#15689412C211yesmaximal, characteristic, complemented
7C2×#15689332C211yesmaximal, characteristic, complemented
8C2×#15689327C211yesmaximal, characteristic, complemented
9C2×#15689287C211yesmaximal, characteristic
10C2×#15689283C211yesmaximal, characteristic
11C2×#15689229C211yesmaximal, characteristic, complemented
12C2×#15689227C211yesmaximal, characteristic, complemented
13C2×#15689226C211yesmaximal, characteristic, complemented
14C2×#15689222C211yesmaximal, characteristic, complemented
15C2×#15689177C211yesmaximal, characteristic, complemented
16C2×C47×#485C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22#15689675—24no—
23#15689675C2218yescomplemented
24C2×#13094023C2211yescharacteristic
25C2×#13094022C2211yescharacteristic
26C2×#13094014—21no—
27C2×#13094003C2211yescharacteristic
28C2×#13094001—21no—
29#15689591—24no—
30#15689591C2218yes—
31C2×Q8×Dic47C2211yescharacteristic
32C2×#13093989—21no—
33C2×#13093989C2211yescharacteristic
34C2×#13093989C2211yescharacteristic
35C2×#13093989C2211yescharacteristic
36C2×#13093986C2211yescharacteristic
37C2×#13093986C2211yescharacteristic
38C2×(C22⋊D47)⋊C4—21no—
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093981—21no—
41C2×#13093980—21no—
42C22×C4×Dic47C2211yescharacteristic
43C2×C42×D47—21no—
44#15689464C2218yescomplemented
45#15689417C2218yescomplemented
46#15689412C2218yescomplemented
47#15689332C2218yescomplemented
48#15689327C2218yescomplemented
49#15689287C2218yes—
50#15689283C2218yes—
51#15689229C2218yescomplemented
52#15689227C2218yescomplemented
53#15689226C2218yescomplemented
54#15689222C2218yescomplemented
55#15689177C2218yescomplemented
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C2×C22⋊Q8×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#485C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—24no—
80C2×#10625350C2314yes—
81C22×Dic94—21no—
82C22×Dic94C2311yescharacteristic
83C22×Dic94C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C22×C22⋊D47—21no—
86C23×Dic47D411yescharacteristic
87C23×Dic47D411yescharacteristic
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C2×Dic188—24no—
92C2×Dic188C2314yes—
93C2×#10625337—24no—
94C2×#10625337C2314yes—
95C2×#10625325—24no—
96C2×#10625325C2314yes—
97C2×#10625336—24no—
98C2×#10625336C2314yes—
99C22×C47⋊C8C2311yescharacteristic
100C22×C47⋊C8C2311yescharacteristic
101#13094023—22no—
102#13094023C2314yes—
103#13094022—22no—
104#13094022C2314yes—
105#13094014—28no—
106#13094003—22no—
107#13094003C2314yes—
108#13094001—28no—
109Q8×Dic47—22no—
110Q8×Dic47C2314yes—
111#13093989—28no—
112#13093989—22no—
113#13093989—22no—
114#13093989—22no—
115#13093989C2314yes—
116#13093989C2314yes—
117#13093989C2314yes—
118#13093986—22no—
119#13093986—22no—
120#13093986C2314yes—
121#13093986C2314yes—
122(C22⋊D47)⋊C4—28no—
123(C22⋊D47)⋊C4—28no—
124#13093981—28no—
125#13093980—28no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47C2311yescharacteristic
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×C22⋊Dic47—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47D411yescharacteristic
143C2×C4×Dic47D411yescharacteristic
144C2×C4×Dic47D414yes—
145C2×C4×Dic47C2311yescharacteristic
146C2×C4×Dic47C2311yescharacteristic
147C2×C4×Dic47C2314yes—
148C42×D47—28no—
149#13093957C2314yes—
150#13093955C2314yes—
151Dic47⋊C8C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093947C2314yes—
155#13093947C2314yes—
156#13093947C2314yes—
157#13093946C2314yes—
158#13093944C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160#13093934C2314yes—
161#13093934C2314yes—
162C22×Q8×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22⋊Q8×C47—22no—
167C22⋊Q8×C47C2314yes—
168#117×C47—22no—
169#117×C47C2314yes—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C42×C47—21no—
177#107×C47C2314yes—
178#106×C47C2314yes—
179#103×C47C2314yes—
180#103×C47C2314yes—
181C22⋊C8×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—22no—
186C2×Q8×C47—22no—
187C2×Q8×C47C2412yes—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2411yescharacteristic
198C2×C22⋊D47—28no—
199C2×C22⋊D47—24no—
200C22×Dic47—21no—
201C22×Dic47—24no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—42no—
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D414yes—
209C22×Dic47C2×D414yes—
210C22×Dic47C2×D411yescharacteristic
211#10625350—216no—
212#10625350—28no—
213#10625350—28no—
214C2×D188—21no—
215C2×D188—22no—
216C2×D188#4114yes—
217C2×D188C2412yes—
218C2×C4×D47—28no—
219C2×C4×D47—24no—
220C2×C4×D47—24no—
221C2×C4×D47—24no—
222C2×C4×D47—44no—
223C2×C4×D47—44no—
224C2×Dic94—21no—
225C2×Dic94—22no—
226C2×Dic94—22no—
227C2×Dic94—22no—
228C2×Dic94—21no—
229C2×Dic94—24no—
230C2×Dic94—44no—
231C2×Dic94#4114yes—
232C2×Dic94C2412yes—
233C2×Dic94C2412yes—
234C2×C8×C47—22no—
235C2×C8×C47—22no—
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C4⋊C4×C47—24no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47C2412yes—
243C4⋊C4×C47C2412yes—
244C4⋊C4×C47C2412yes—
245C22⋊C4×C47—24no—
246C22⋊C4×C47—24no—
247C42×C47—24no—
248C22⋊Dic47—24no—
249#10625337—28no—
250#10625336—28no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253C4⋊Dic47—21no—
254C4⋊Dic47—24no—
255C4⋊Dic47C2412yes—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263C4×Dic47—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C4×Dic47C2×D414yes—
268C4×Dic47C2×D414yes—
269C4×Dic47C2×D412yes—
270C4×Dic47C2×D412yes—
271C4×Dic47C2412yes—
272C4×Dic47C2412yes—
273C2×C47⋊C8—22no—
274C2×C47⋊C8—22no—
275C2×C47⋊C8C2412yes—
276C2×C47⋊C8C2412yes—
277Dic188—28no—
278#10625325—28no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47C22×D412yes—
283C23×C47C22×D411yescharacteristic
284C22×D47—24no—
285C22×D47—22no—
286C22×D47—42no—
287C22×D47—42no—
288Q8×C47—22no—
289Q8×C47—22no—
290Q8×C47—42no—
291C2×C4×C47—22no—
292C2×C4×C47—24no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C2×#4112yes—
306C2×C4×C47C2×#4112yes—
307C2×C4×C47C2511yescharacteristic
308C22⋊D47—216no—
309C2×Dic47—24no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—28no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—44no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47#13714yes—
321C2×Dic47C22×D412yes—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325D188—24no—
326D188—22no—
327D188C2×#4114yes—
328C4×D47—216no—
329C4×D47—48no—
330C4×D47—48no—
331Dic94—24no—
332Dic94—22no—
333Dic94—22no—
334Dic94—22no—
335Dic94—48no—
336Dic94—42no—
337Dic94C2×#4114yes—
338C8×C47—22no—
339C8×C47—22no—
340C47⋊C8—22no—
341C47⋊C8—22no—
342C2×#3116—471nomaximal, Sylow
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—44no—
347C22×C47#52512yes—
348C22×C47C2×#13712yes—
349C22×C47#57512yes—
350C22×C47C23×D411yescharacteristic
351C2×D47—24no—
352C2×D47—48no—
353C2×D47—42no—
354C2×D47—42no—
355C4×C47—22no—
356C4×C47—42no—
357C4×C47—42no—
358C4×C47—42no—
359C4×C47—42no—
360C4×C47#52512yes—
361C4×C47C22×#4111yescharacteristic
362C4×C47C22×#4111yescharacteristic
363Dic47—24no—
364Dic47—22no—
365Dic47—22no—
366Dic47—22no—
367Dic47—42no—
368Dic47—42no—
369Dic47C2×#13714yes—
370C2×#533—471no—
371C2×C4×#41—471no—
372#3116—4716no—
373C2×#485—471no—
374C2×#485D4711yescharacteristic, complemented
375C2×#477—471no—
376C2×#476—471no—
377C2×#462—471no—
378C2×#461—471no—
379C2×#452—471no—
380C2×#452—471no—
381C2×#441—471no—
382C2×#441—471no—
383C2×#440—471no—
384C2×#440—471no—
385C2×#432—471no—
386C2×C47—42no—
387C2×C47#311614yescomplemented
388C2×C47C2×#52511yescharacteristic
389C2×C47C22×#13711yescharacteristic
390C2×C47C2×#57511yescharacteristic
391D47—44no—
392C22×#41—471no—
393C22×Q16—471no—
394C22×Q16—471no—
395C22×SD16—471no—
396C22×SD16—471no—
397#533—478no—
398#533—944no—
399C2×C4⋊Q8—471no—
400C2×C4⋊Q8—471no—
401C2×#125—941no—
402C2×C22⋊Q8—471no—
403C2×C22⋊Q8—941no—
404C2×C22⋊Q8C2×D4711yescharacteristic
405C4×#41—478no—
406C4×#41—944no—
407C2×C4×Q8—471no—
408C2×C4×Q8—471no—
409C2×C4×Q8—471no—
410C2×C4×Q8—471no—
411C2×C4×Q8—941no—
412C2×C4×D4—471no—
413C2×C4×D4—471no—
414C2×C4×D4—941no—
415C2×C4×D4—941no—
416C2×#117—941no—
417C2×#117—941no—
418C2×#117C2×D4711yescharacteristic
419C22×C42—471no—
420C22×C42—941no—
421#485—478no—
422#485C2×D4718yescomplemented
423#477—478no—
424#476—478no—
425#462—478no—
426#461—478no—
427#452—478no—
428#452—478no—
429#441—478no—
430#441—478no—
431#440—478no—
432#440—478no—
433#432—478no—
434C2×#107—471no—
435C2×#107C2×D4711yescharacteristic
436C2×#106—471no—
437C2×#106C2×D4711yescharacteristic
438C2×C4⋊C8—471no—
439C2×C4⋊C8—471no—
440C2×#103—471no—
441C2×#103—471no—
442C2×#103—471no—
443C2×#103—471no—
444C2×#103C2×D4711yescharacteristic
445C2×#103C2×D4711yescharacteristic
446C2×#102—471no—
447C2×#102—471no—
448C2×C22⋊C8—471no—
449C2×C22⋊C8C2×D4711yescharacteristic
450C2×#97—471no—
451C2×#97—471no—
452C47C2×#311611yescharacteristic, complemented, Sylow
453C2×#41—474no—
454C2×#41—944no—
455C2×#41—944no—
456C2×#41—942no—
457C22×Q8—471no—
458C22×Q8—471no—
459C22×Q8—941no—
460C22×Q8C22×D4711yescharacteristic
461C22×D4—471no—
462C22×D4—941no—
463C23×C4—471no—
464C23×C4—471no—
465C23×C4—941no—
466C23×C4—941no—
467C23×C4—941no—
468C23×C4C22×D4711yescharacteristic
469C2×Q16—474no—
470C2×Q16—474no—
471C2×Q16—944no—
472C2×Q16—944no—
473C2×SD16—474no—
474C2×SD16—474no—
475C2×SD16—944no—
476C2×SD16—944no—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8C22×D4711yescharacteristic
480C22×C8C22×D4711yescharacteristic
481C4⋊Q8—474no—
482C4⋊Q8—474no—
483C4⋊Q8—942no—
484C4⋊Q8—942no—
485#125—948no—
486C22⋊Q8—22no—
487C22⋊Q8—474no—
488C22⋊Q8—948no—
489C22⋊Q8—942no—
490C22⋊Q8C22×D4714yes—
491C4×Q8—474no—
492C4×Q8—474no—
493C4×Q8—474no—
494C4×Q8—474no—
495C4×Q8—942no—
496C4×Q8—942no—
497C4×Q8—942no—
498C4×Q8—948no—
499C4×Q8—942no—
500C4×D4—474no—
501C4×D4—474no—
502C4×D4—942no—
503C4×D4—942no—
504C4×D4—948no—
505C4×D4—948no—
506#117—22no—
507#117—948no—
508#117—948no—
509#117C22×D4714yes—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4C22×D4711yescharacteristic
521C2×C4⋊C4C22×D4711yescharacteristic
522C2×C4⋊C4C22×D4711yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—21no—
529C2×C42—471no—
530C2×C42—474no—
531C2×C42—471no—
532C2×C42—471no—
533C2×C42—471no—
534C2×C42—474no—
535C2×C42—948no—
536C2×C42—941no—
537C2×C42—941no—
538C2×C42—941no—
539C2×C42—941no—
540#107—474no—
541#107C22×D4714yes—
542#106—474no—
543#106C22×D4714yes—
544C4⋊C8—474no—
545C4⋊C8—474no—
546#103—474no—
547#103—474no—
548#103—474no—
549#103—474no—
550#103C22×D4714yes—
551#103C22×D4714yes—
552#102—474no—
553#102—474no—
554C22⋊C8—474no—
555C22⋊C8C22×D4714yes—
556#97—474no—
557#97—474no—
558C24—941no—
559C24D4×D4711yescharacteristic
560#41—948no—
561#41—948no—
562#41—9416no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—474no—
567C2×Q8—472no—
568C2×Q8—472no—
569C2×Q8—944no—
570C2×Q8—941no—
571C2×Q8—941no—
572C2×Q8—942no—
573C2×Q8—942no—
574C2×Q8—942no—
575C2×Q8—1884no—
576C2×Q8C23×D4712yes—
577C2×D4—474no—
578C2×D4—472no—
579C2×D4—948no—
580C2×D4—944no—
581C2×D4—941no—
582C2×D4—942no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—471no—
590C22×C4—474no—
591C22×C4—471no—
592C22×C4—471no—
593C22×C4—471no—
594C22×C4—474no—
595C22×C4—944no—
596C22×C4—944no—
597C22×C4—948no—
598C22×C4—944no—
599C22×C4—941no—
600C22×C4—944no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—1884no—
604C22×C4—1884no—
605C22×C4—1882no—
606C22×C4D4×D4712yes—
607C22×C4D4×D4711yescharacteristic
608C22×C4C23×D4712yes—
609C22×C4C23×D4711yescharacteristic
610Q16—948no—
611Q16—948no—
612SD16—948no—
613SD16—948no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—472no—
617C2×C8—472no—
618C2×C8—942no—
619C2×C8—942no—
620C2×C8C23×D4712yes—
621C2×C8C23×D4712yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—472no—
627C4⋊C4—944no—
628C4⋊C4—944no—
629C4⋊C4—944no—
630C4⋊C4—944no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—944no—
635C4⋊C4—941no—
636C4⋊C4C23×D4712yes—
637C4⋊C4C23×D4712yes—
638C4⋊C4C23×D4712yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C42—24no—
645C42—474no—
646C42—474no—
647C42—472no—
648C42—472no—
649C42—472no—
650C42—472no—
651C42—944no—
652C42—944no—
653C42—944no—
654C42—944no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—944no—
659C23—942no—
660C23—1882no—
661C23—1882no—
662C23C2×D4×D4712yes—
663C23C2×D4×D4711yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—42no—
667Q8—474no—
668Q8—944no—
669Q8—942no—
670Q8—942no—
671Q8—942no—
672Q8—1888no—
673Q8—1882no—
674D4—474no—
675D4—9416no—
676D4—944no—
677D4—942no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—474no—
691C2×C4—472no—
692C2×C4—472no—
693C2×C4—472no—
694C2×C4—472no—
695C2×C4—9416no—
696C2×C4—948no—
697C2×C4—944no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—1888no—
705C2×C4—1888no—
706C2×C4—1884no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4C2×D4×D4712yes—
710C2×C4C2×D4×D4711yescharacteristic
711C2×C4#41×D4712yes—
712C2×C4#41×D4712yes—
713C2×C4C24×D4711yescharacteristic
714C8—22no—
715C8—22no—
716C8—942no—
717C8—942no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—944no—
723C22—1882no—
724C22—1882no—
725C22—1888no—
726C22#1568963112yes—
727C22#137×D4712yes—
728C22#1568992012yes—
729C22C22×D4×D4711yescharacteristic
730C4—22no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—474no—
736C4—942no—
737C4—942no—
738C4—942no—
739C4—944no—
740C4—1882no—
741C4—1882no—
742C4#1568963112yes—
743C4C2×#41×D4711yescharacteristic
744C4C2×#41×D4711yescharacteristic
745C2—42no—
746C2—1884no—
747C2#2025354514yesdirect product factor
748C2C2×#1568963111yescharacteristic
749C2C2×#137×D4711yescharacteristic
750C2C2×#1568992011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#485C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
hypercenterC2×#485D47
hypocenterC47C2×#3116
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#15689675C2semidirect
3. #20253545C2direct (N × H)
4. C2×#15689464C2semidirect
5. C2×#15689417C2semidirect
6. C2×#15689412C2semidirect
7. C2×#15689332C2semidirect
8. C2×#15689327C2semidirect
11. C2×#15689229C2semidirect
12. C2×#15689227C2semidirect
13. C2×#15689226C2semidirect
14. C2×#15689222C2semidirect
15. C2×#15689177C2semidirect
16. C2×C47×#485C2semidirect
23. #15689675C22semidirect
44. #15689464C22semidirect
45. #15689417C22semidirect
46. #15689412C22semidirect
47. #15689332C22semidirect
48. #15689327C22semidirect
51. #15689229C22semidirect
52. #15689227C22semidirect
53. #15689226C22semidirect
54. #15689222C22semidirect
55. #15689177C22semidirect
71. C47×#485C22semidirect
374. C2×#485D47semidirect
387. C2×C47#3116semidirect
422. #485C2×D47semidirect
452. C47C2×#3116semidirect
747. C2#20253545direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896752
C2×#156895912
#202535452
C2×#156894642
C2×#156894172
C2×#156894122
C2×#156893322
C2×#156893272
C2×#156892872
C2×#156892832
C2×#156892292
C2×#156892272
C2×#156892262
C2×#156892222
C2×#156891772
C2×C47×#4852
C2×#311647