Finite Group Databasebeta

← C2×#20253172 #27083775

Subgroups — C2×#20253172 #27083775

Order 12032.

2162 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689676C211yesmaximal, characteristic, complemented
2C2×#41×Dic47C211yesmaximal, characteristic
3#20253172C2116yesmaximal, direct product factor
4C2×#15689432C211yesmaximal, characteristic, complemented
5C2×#15689428C211yesmaximal, characteristic, complemented
6C2×#15689416C211yesmaximal, characteristic, complemented
7C2×#15689406C211yesmaximal, characteristic, complemented
8C2×#15689425C211yesmaximal, characteristic, complemented
9C2×#15689421C211yesmaximal, characteristic, complemented
10C2×#15689411C211yesmaximal, characteristic, complemented
11C2×#15689401C211yesmaximal, characteristic, complemented
12C2×#15689161C211yesmaximal, characteristic, complemented
13C2×#15689159C211yesmaximal, characteristic, complemented
14C22×Dic47⋊C8C211yesmaximal, characteristic, complemented
15C2×#15689119C211yesmaximal, characteristic
16C2×C47×#416C211yesmaximal, characteristic
17C23×C47⋊C8C2211yescharacteristic
18#15689676—24no—
19#15689676C2218yescomplemented
20C2×#13094023C2211yescharacteristic
21C2×#13094023C2211yescharacteristic
22C2×#13094015C2211yescharacteristic
23C2×#13094015C2211yescharacteristic
24C2×#13094001—21no—
25C2×#13094001—21no—
26#41×Dic47—24no—
27#41×Dic47C2218yes—
28C2×Q8×Dic47C2211yescharacteristic
29C2×Q8×Dic47C2211yescharacteristic
30C2×C4×Dic94—21no—
31C2×C4×Dic94—21no—
32C2×D4×Dic47—21no—
33C2×D4×Dic47—21no—
34C2×D4×Dic47C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×#13093983—21no—
37C2×#13093983C2211yescharacteristic
38C2×#13093983C2211yescharacteristic
39C22×C4×Dic47—21no—
40C22×C4×Dic47C2211yescharacteristic
41#15689432C2218yescomplemented
42#15689428C2218yescomplemented
43#15689425C2218yescomplemented
44#15689421C2218yescomplemented
45#15689416C2218yescomplemented
46#15689411C2218yescomplemented
47#15689406C2218yescomplemented
48#15689401C2218yescomplemented
49#15689161C2218yescomplemented
50#15689159C2218yescomplemented
51C2×#13093958C2211yescharacteristic
52C2×#13093958C2211yescharacteristic
53C2×#13093957C2211yescharacteristic
54C2×#13093957C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×Dic47⋊C8C2218yescomplemented
64#15689119C2218yes—
65C2×#13093948C2211yescharacteristic
66C2×#13093948C2211yescharacteristic
67C2×#13093945C2211yescharacteristic
68C2×#13093945C2211yescharacteristic
69C22×#41×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×#117×C47C2211yescharacteristic
72C47×#416C2218yes—
73C2×#103×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C23×Dic47—21no—
80C23×Dic47—21no—
81C23×Dic47D411yescharacteristic
82C23×Dic47D411yescharacteristic
83C22×C47⋊C8—24no—
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2314yes—
87#13094023—22no—
88#13094023—22no—
89#13094023C2314yes—
90#13094023C2314yes—
91#13094015—22no—
92#13094015—22no—
93#13094015C2314yes—
94#13094015C2314yes—
95#13094001—28no—
96#13094001—28no—
97Q8×Dic47—22no—
98Q8×Dic47—22no—
99Q8×Dic47C2314yes—
100Q8×Dic47C2314yes—
101C4×Dic94—28no—
102C4×Dic94—28no—
103D4×Dic47—28no—
104D4×Dic47—28no—
105D4×Dic47—22no—
106D4×Dic47—22no—
107D4×Dic47C2314yes—
108D4×Dic47C2314yes—
109#13093983—22no—
110#13093983—22no—
111#13093983—28no—
112#13093983C2314yes—
113#13093983C2314yes—
114C2×C4⋊Dic47—21no—
115C2×C4⋊Dic47—21no—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47C2311yescharacteristic
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×Dic47⋊C4—21no—
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×C22⋊Dic47—21no—
127C2×C22⋊Dic47—21no—
128C2×C22⋊Dic47—21no—
129C2×C22⋊Dic47—21no—
130C2×C4×Dic47—21no—
131C2×C4×Dic47—21no—
132C2×C4×Dic47—21no—
133C2×C4×Dic47—21no—
134C2×C4×Dic47—28no—
135C2×C4×Dic47D411yescharacteristic
136C2×C4×Dic47D411yescharacteristic
137C2×C4×Dic47D414yes—
138C2×C4×Dic47C2311yescharacteristic
139C2×C4×Dic47C2311yescharacteristic
140C2×C4×Dic47C2314yes—
141#13093958C2314yes—
142#13093958C2314yes—
143#13093957C2314yes—
144#13093957C2314yes—
145#13093956C2314yes—
146#13093956C2314yes—
147#13093955C2314yes—
148#13093955C2314yes—
149Dic47⋊C8C2314yes—
150Dic47⋊C8C2314yes—
151Dic47⋊C8C2314yes—
152Dic47⋊C8C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093945C2314yes—
156#13093945C2314yes—
157C2×#41×C47—22no—
158C2×#41×C47—24no—
159C2×#41×C47Q818yescomplemented
160C2×#41×C47C2314yes—
161C22×Q8×C47C2311yescharacteristic
162C22×D4×C47—21no—
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47—21no—
165C23×C4×C47C2311yescharacteristic
166C22×C8×C47—24no—
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2314yes—
170#117×C47—22no—
171#117×C47C2314yes—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C42×C47—21no—
176#103×C47C2314yes—
177#103×C47C2314yes—
178#102×C47C2314yes—
179#102×C47C2314yes—
180C24×C47—21no—
181C24×C47C2×D411yescharacteristic
182#41×C47—216no—
183#41×C47—28no—
184#41×C47C2×Q8116yescomplemented
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47C2×Q814yes—
188C2×Q8×C47C2412yes—
189C2×D4×C47—28no—
190C2×D4×C47—24no—
191C2×D4×C47—21no—
192C2×D4×C47—22no—
193C2×D4×C47C2×Q814yes—
194C2×D4×C47C2412yes—
195C22×C4×C47—21no—
196C22×C4×C47—28no—
197C22×C4×C47—24no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×Q814yes—
203C22×C4×C47#4114yes—
204C22×C4×C47C2411yescharacteristic
205C22×C4×C47C2412yes—
206C22×Dic47—24no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—24no—
212C22×Dic47—24no—
213C22×Dic47—42no—
214C22×Dic47—44no—
215C22×Dic47—44no—
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D414yes—
220C22×Dic47C2×D414yes—
221C22×Dic47C2×D411yescharacteristic
222C2×Dic94—24no—
223C2×Dic94—24no—
224C2×Dic94—44no—
225C2×Dic94—44no—
226C2×C8×C47—22no—
227C2×C8×C47—22no—
228C2×C8×C47—28no—
229C2×C8×C47C2412yes—
230C2×C8×C47C2412yes—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47C2412yes—
234C4⋊C4×C47C2412yes—
235C22⋊C4×C47—24no—
236C42×C47—24no—
237C22⋊Dic47—24no—
238C22⋊Dic47—24no—
239C22⋊Dic47—24no—
240C22⋊Dic47—24no—
241C4⋊Dic47—21no—
242C4⋊Dic47—21no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—24no—
246C4⋊Dic47—24no—
247C4⋊Dic47—24no—
248C4⋊Dic47—24no—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257C4×Dic47—24no—
258C4×Dic47—24no—
259C4×Dic47—24no—
260C4×Dic47—24no—
261C4×Dic47C2×D414yes—
262C4×Dic47C2×D414yes—
263C4×Dic47C2×D412yes—
264C4×Dic47C2×D412yes—
265C4×Dic47C2412yes—
266C4×Dic47C2412yes—
267C2×C47⋊C8—22no—
268C2×C47⋊C8—22no—
269C2×C47⋊C8—28no—
270C2×C47⋊C8C2412yes—
271C2×C47⋊C8C2412yes—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—24no—
275C23×C47—22no—
276C23×C47—42no—
277C23×C47—42no—
278C23×C47C22⋊Q814yes—
279C23×C47C22×D412yes—
280C23×C47C22×D411yescharacteristic
281Q8×C47—24no—
282Q8×C47—22no—
283Q8×C47C22×Q814yes—
284D4×C47—216no—
285D4×C47—24no—
286D4×C47—22no—
287D4×C47C22×Q814yes—
288C2×C4×C47—24no—
289C2×C4×C47—22no—
290C2×C4×C47—216no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47C22⋊Q814yes—
296C2×C4×C47C22⋊Q818yes—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D411yescharacteristic
299C2×C4×C47C22×Q812yes—
300C2×C4×C47C22×Q814yes—
301C2×C4×C47C2×#4112yes—
302C2×C4×C47C2×#4114yes—
303C2×C4×C47C2511yescharacteristic
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—28no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—44no—
313C2×Dic47—48no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—48no—
319C2×Dic47#13514yes—
320C2×Dic47C22×D412yes—
321C2×Dic47C22×D412yes—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324Dic94—48no—
325Dic94—48no—
326C8×C47—22no—
327C8×C47—22no—
328C47⋊C8—22no—
329C47⋊C8—22no—
330C2×#3076—471nomaximal, Sylow
331C22×C47—28no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—24no—
335C22×C47—48no—
336C22×C47—42no—
337C22×C47—42no—
338C22×C47C2×C22⋊Q814yes—
339C22×C47C2×C22⋊Q812yes—
340C22×C47C2×#13512yes—
341C22×C47#57512yes—
342C22×C47C23×D411yescharacteristic
343C4×C47—24no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47C2×C22⋊Q814yes—
347C4×C47C2×C22⋊Q812yes—
348C4×C47C23×Q811yescharacteristic
349C4×C47C22×#4111yescharacteristic
350Dic47—22no—
351Dic47—22no—
352Dic47—22no—
353Dic47—42no—
354Dic47—42no—
355Dic47—42no—
356Dic47—42no—
357Dic47C2×#13514yes—
358C2×#533—471no—
359C2×C4×#41—471no—
360#3076—4716no—
361C2×#479—471no—
362C2×#479—471no—
363C2×#477—471no—
364C2×#475—471no—
365C2×#478—471no—
366C2×#478—471no—
367C2×#476—471no—
368C2×#474—471no—
369C2×#427—471no—
370C2×#427—471no—
371C22×C4⋊C8—471no—
372C2×#416—471no—
373C2×#416D4711yescharacteristic
374C2×C47—24no—
375C2×C47—44no—
376C2×C47#307614yescomplemented
377C2×C47C22×C22⋊Q811yescharacteristic
378C2×C47C22×#13511yescharacteristic
379C2×C47C2×#57511yescharacteristic
380C22×#41C2×D4711yescharacteristic
381C23×C8—471no—
382C23×C8C2×D4711yescharacteristic
383#533—478no—
384#533—944no—
385C2×C4⋊Q8—471no—
386C2×C4⋊Q8—471no—
387C2×#125—471no—
388C2×#125—471no—
389C2×C22⋊Q8—941no—
390C2×C22⋊Q8—941no—
391C4×#41—478no—
392C4×#41—944no—
393C2×C4×Q8—471no—
394C2×C4×Q8—471no—
395C2×C4×Q8—941no—
396C2×C4×Q8—941no—
397C2×C4×D4—471no—
398C2×C4×D4—471no—
399C2×C4×D4—941no—
400C2×C4×D4—941no—
401C2×#117—471no—
402C2×#117—471no—
403C2×#117—941no—
404C2×#117C2×D4711yescharacteristic
405C22×C42—471no—
406C22×C42—941no—
407#479—478no—
408#479—478no—
409#478—478no—
410#478—478no—
411#477—478no—
412#476—478no—
413#475—478no—
414#474—478no—
415#427—478no—
416#427—478no—
417C2×#107—471no—
418C2×#107—471no—
419C2×#107—471no—
420C2×#107—471no—
421C2×#106—471no—
422C2×#106—471no—
423C2×#106—471no—
424C2×#106—471no—
425C2×C4⋊C8—471no—
426C2×C4⋊C8—471no—
427C2×C4⋊C8—471no—
428C2×C4⋊C8—471no—
429C2×C4⋊C8—478no—
430#416—478no—
431#416C2×D4718yes—
432C2×#103—471no—
433C2×#103—471no—
434C2×#103C2×D4711yescharacteristic
435C2×#103C2×D4711yescharacteristic
436C2×#102—471no—
437C2×#102—471no—
438C2×#102C2×D4711yescharacteristic
439C2×#102C2×D4711yescharacteristic
440C47C2×#307611yescharacteristic, complemented, Sylow
441C2×#41—22no—
442C2×#41—24no—
443C2×#41Dic9418yescomplemented
444C2×#41C22×D4714yes—
445C22×Q8—941no—
446C22×Q8—941no—
447C22×Q8C22×D4711yescharacteristic
448C22×D4—21no—
449C22×D4C22×D4711yescharacteristic
450C23×C4—21no—
451C23×C4—471no—
452C23×C4—471no—
453C23×C4—941no—
454C23×C4—941no—
455C23×C4C22×D4711yescharacteristic
456C22×C8—24no—
457C22×C8—471no—
458C22×C8—471no—
459C22×C8—474no—
460C22×C8—944no—
461C22×C8C22×D4711yescharacteristic
462C22×C8C22×D4711yescharacteristic
463C22×C8C22×D4714yes—
464C4⋊Q8—474no—
465C4⋊Q8—474no—
466C4⋊Q8—942no—
467C4⋊Q8—942no—
468#125—474no—
469#125—474no—
470#125—942no—
471#125—942no—
472C22⋊Q8—948no—
473C22⋊Q8—948no—
474C4×Q8—474no—
475C4×Q8—474no—
476C4×Q8—948no—
477C4×Q8—948no—
478C4×Q8—942no—
479C4×Q8—942no—
480C4×D4—474no—
481C4×D4—474no—
482C4×D4—942no—
483C4×D4—942no—
484C4×D4—948no—
485C4×D4—948no—
486#117—22no—
487#117—474no—
488#117—474no—
489#117—948no—
490#117—942no—
491#117—942no—
492#117C22×D4714yes—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—941no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C42—21no—
513C2×C42—474no—
514C2×C42—471no—
515C2×C42—471no—
516C2×C42—471no—
517C2×C42—471no—
518C2×C42—474no—
519C2×C42—948no—
520C2×C42—941no—
521C2×C42—941no—
522C2×C42—941no—
523C2×C42—941no—
524#107—474no—
525#107—474no—
526#107—474no—
527#107—474no—
528#106—474no—
529#106—474no—
530#106—474no—
531#106—474no—
532C4⋊C8—474no—
533C4⋊C8—474no—
534C4⋊C8—474no—
535C4⋊C8—474no—
536#103—474no—
537#103—474no—
538#103C22×D4714yes—
539#103C22×D4714yes—
540#102—474no—
541#102—474no—
542#102C22×D4714yes—
543#102C22×D4714yes—
544C24—21no—
545C24D4×D4711yescharacteristic
546#41—216no—
547#41—28no—
548#41C2×Dic94116yescomplemented
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—944no—
552C2×Q8—944no—
553C2×Q8—1884no—
554C2×Q8—1884no—
555C2×Q8C2×Dic9414yes—
556C2×Q8C23×D4712yes—
557C2×D4—28no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4C2×Dic9414yes—
562C2×D4C23×D4712yes—
563C22×C4—21no—
564C22×C4—28no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—471no—
571C22×C4—471no—
572C22×C4—474no—
573C22×C4—474no—
574C22×C4—944no—
575C22×C4—944no—
576C22×C4—944no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—1884no—
582C22×C4—1882no—
583C22×C4—1884no—
584C22×C4C2×Dic9414yes—
585C22×C4D4×D4712yes—
586C22×C4D4×D4711yescharacteristic
587C22×C4#1062535214yes—
588C22×C4C23×D4711yescharacteristic
589C22×C4C23×D4712yes—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—472no—
594C2×C8—472no—
595C2×C8—942no—
596C2×C8—942no—
597C2×C8—948no—
598C2×C8C23×D4712yes—
599C2×C8C23×D4712yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—472no—
603C4⋊C4—472no—
604C4⋊C4—472no—
605C4⋊C4—472no—
606C4⋊C4—944no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—941no—
615C4⋊C4—941no—
616C4⋊C4—941no—
617C4⋊C4—941no—
618C4⋊C4C23×D4712yes—
619C4⋊C4C23×D4712yes—
620C22⋊C4—24no—
621C22⋊C4—944no—
622C22⋊C4—944no—
623C22⋊C4—944no—
624C22⋊C4—944no—
625C42—24no—
626C42—474no—
627C42—474no—
628C42—472no—
629C42—472no—
630C42—472no—
631C42—472no—
632C42—944no—
633C42—944no—
634C42—944no—
635C42—944no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—42no—
641C23—42no—
642C23#1309400114yes—
643C23C2×D4×D4712yes—
644C23C2×D4×D4711yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—1888no—
648Q8—1888no—
649Q8C22×Dic9414yes—
650D4—216no—
651D4—24no—
652D4—22no—
653D4C22×Dic9414yes—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—216no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—474no—
662C2×C4—472no—
663C2×C4—472no—
664C2×C4—472no—
665C2×C4—472no—
666C2×C4—948no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—1888no—
675C2×C4—1884no—
676C2×C4—1888no—
677C2×C4—1882no—
678C2×C4—1882no—
679C2×C4—1882no—
680C2×C4—1882no—
681C2×C4#1309400114yes—
682C2×C4#1309400118yes—
683C2×C4C2×D4×D4712yes—
684C2×C4C2×D4×D4711yescharacteristic
685C2×C4C22×Dic9412yes—
686C2×C4C22×Dic9414yes—
687C2×C4C2×#1062535212yes—
688C2×C4C2×#1062535214yes—
689C2×C4C24×D4711yescharacteristic
690C8—22no—
691C8—22no—
692C8—942no—
693C8—942no—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—24no—
698C22—42no—
699C22—42no—
700C22—48no—
701C22C2×#1309400114yes—
702C22C2×#1309400112yes—
703C22#135×D4712yes—
704C22#1568992012yes—
705C22C22×D4×D4711yescharacteristic
706C4—24no—
707C4—42no—
708C4—42no—
709C4—474no—
710C4—942no—
711C4—942no—
712C4—942no—
713C4—1882no—
714C4—1882no—
715C4—1882no—
716C4—1882no—
717C4C2×#1309400114yes—
718C4C2×#1309400112yes—
719C4C23×Dic9411yescharacteristic
720C4C22×#1062535211yescharacteristic
721C2—24no—
722C2—44no—
723C2#2025317214yesdirect product factor
724C2C22×#1309400111yescharacteristic
725C2C2×#135×D4711yescharacteristic
726C2C2×#1568992011yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#416C2
socleC23×C47C22×D4
prime radicalC22×#41×C47C22
hypercenterC2×#416D47
hypocenterC47C2×#3076
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#15689676C2semidirect
3. #20253172C2direct (N × H)
4. C2×#15689432C2semidirect
5. C2×#15689428C2semidirect
6. C2×#15689416C2semidirect
7. C2×#15689406C2semidirect
8. C2×#15689425C2semidirect
9. C2×#15689421C2semidirect
10. C2×#15689411C2semidirect
11. C2×#15689401C2semidirect
12. C2×#15689161C2semidirect
13. C2×#15689159C2semidirect
14. C22×Dic47⋊C8C2semidirect
19. #15689676C22semidirect
41. #15689432C22semidirect
42. #15689428C22semidirect
43. #15689425C22semidirect
44. #15689421C22semidirect
45. #15689416C22semidirect
46. #15689411C22semidirect
47. #15689406C22semidirect
48. #15689401C22semidirect
49. #15689161C22semidirect
50. #15689159C22semidirect
63. C2×Dic47⋊C8C22semidirect
159. C2×#41×C47Q8semidirect
184. #41×C47C2×Q8semidirect
376. C2×C47#3076semidirect
440. C47C2×#3076semidirect
443. C2×#41Dic94semidirect
548. #41C2×Dic94semidirect
723. C2#20253172direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896762
C2×#41×Dic472
#202531722
C2×#156894322
C2×#156894282
C2×#156894162
C2×#156894062
C2×#156894252
C2×#156894212
C2×#156894112
C2×#156894012
C2×#156891612
C2×#156891592
C22×Dic47⋊C82
C2×#156891192
C2×C47×#4162
C2×#307647