Finite Group Databasebeta

← C2×#20253558 #27084425

Subgroups — C2×#20253558 #27084425

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×#15689652C211yesmaximal, characteristic
2C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
3#20253558C2116yesmaximal, direct product factor
4C2×#15689457C211yesmaximal, characteristic, complemented
5C2×#15689440C211yesmaximal, characteristic
6C2×#15689431C211yesmaximal, characteristic, complemented
7C2×#15689430C211yesmaximal, characteristic, complemented
8C2×#15689342C211yesmaximal, characteristic, complemented
9C2×#15689277C211yesmaximal, characteristic, complemented
10C2×#15689260C211yesmaximal, characteristic
11C2×#15689230C211yesmaximal, characteristic, complemented
12C2×#15689227C211yesmaximal, characteristic, complemented
13C2×#15689224C211yesmaximal, characteristic, complemented
14C2×#15689220C211yesmaximal, characteristic, complemented
15C2×#15689179C211yesmaximal, characteristic, complemented
16C2×C47×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20#15689652—24no—
21#15689652C2218yes—
22C2×#13094017—21no—
23C2×#13094016C2211yescharacteristic
24C2×#13094006—21no—
25C2×#13094000C2211yescharacteristic
26C2×#13093995C2211yescharacteristic
27C2×Q8×Dic47C2211yescharacteristic
28C2×Q8×Dic47C2211yescharacteristic
29C2×C4×Dic94—21no—
30C2×C4×Dic94C2211yescharacteristic
31C2×#13093989—21no—
32C2×#13093989C2211yescharacteristic
33C4×Q8×D47—24no—
34C4×Q8×D47C2218yescomplemented
35C2×D4×Dic47C2211yescharacteristic
36C2×(C22⋊D47)⋊C4—21no—
37C2×#13093980—21no—
38C2×C4⋊C4×D47—21no—
39C2×C4⋊C4×D47C2211yescharacteristic
40C2×C42×D47—21no—
41C2×C42×D47C2211yescharacteristic
42#15689457C2218yescomplemented
43#15689440C2218yes—
44#15689431C2218yescomplemented
45#15689430C2218yescomplemented
46#15689342C2218yescomplemented
47#15689277C2218yescomplemented
48#15689260C2218yes—
49#15689230C2218yescomplemented
50#15689227C2218yescomplemented
51#15689224C2218yescomplemented
52#15689220C2218yescomplemented
53#15689179C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×SD16×C47C2211yescharacteristic
71C2×#124×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C47×#464C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C2×Q8×D47—24no—
80C2×Q8×D47—22no—
81C2×Q8×D47—24no—
82C2×Q8×D47C2314yes—
83C22×C22⋊D47—21no—
84C23×Dic47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47D411yescharacteristic
88C22×C4×D47D411yescharacteristic
89C22×C4×D47C2311yescharacteristic
90C2×#10625337—24no—
91C2×#10625337C2314yes—
92C2×#10625335—24no—
93C2×#10625335C2314yes—
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2311yescharacteristic
96#13094017—28no—
97#13094016—22no—
98#13094016C2314yes—
99#13094006—28no—
100#13094000—22no—
101#13094000C2314yes—
102#13093995—22no—
103#13093995C2314yes—
104Q8×Dic47—22no—
105Q8×Dic47—22no—
106Q8×Dic47C2314yes—
107Q8×Dic47C2314yes—
108C4×Dic94—22no—
109C4×Dic94—28no—
110C4×Dic94C2314yes—
111#13093989—22no—
112#13093989—28no—
113#13093989C2314yes—
114D4×Dic47—22no—
115D4×Dic47C2314yes—
116(C22⋊D47)⋊C4—28no—
117#13093980—28no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C4⋊C4×D47—28no—
130C4⋊C4×D47—22no—
131C4⋊C4×D47C2314yes—
132C2×C22⋊Dic47—21no—
133C2×C22⋊Dic47—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×C4×Dic47—21no—
136C2×C4×Dic47—21no—
137C2×C4×Dic47—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47D411yescharacteristic
140C2×C4×Dic47D411yescharacteristic
141C2×C4×Dic47C2311yescharacteristic
142C42×D47—28no—
143C42×D47D414yes—
144C42×D47C2314yes—
145#13093958C2314yes—
146#13093957C2314yes—
147#13093956C2314yes—
148#13093955C2314yes—
149C4⋊(C47⋊C8)C2314yes—
150#13093949C2314yes—
151#13093949C2314yes—
152#13093948C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093945C2314yes—
156(C2×D47)⋊C8C2314yes—
157(C2×D47)⋊C8C2314yes—
158#13093934C2314yes—
159#13093934C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×Q8×C47C2311yescharacteristic
162C22×D4×C47C2311yescharacteristic
163C2×Q16×C47—24no—
164C2×Q16×C47C2314yes—
165C2×SD16×C47—24no—
166C2×SD16×C47C2314yes—
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169#124×C47—22no—
170#124×C47C2314yes—
171C4×Q8×C47—22no—
172C4×Q8×C47C2314yes—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C42×C47—21no—
178C2×C42×C47C2311yescharacteristic
179C4⋊C8×C47C2314yes—
180#103×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C23×D47C2×D411yescharacteristic
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47#4114yes—
190C2×Q8×C47C2412yes—
191C2×Q8×C47C2412yes—
192C2×D4×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47C2412yes—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2411yescharacteristic
202C2×C22⋊D47—24no—
203C2×C22⋊D47—44no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—24no—
209C22×Dic47—44no—
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213Q8×D47—216no—
214Q8×D47—28no—
215Q8×D47—28no—
216C2×C4×D47—28no—
217C2×C4×D47—24no—
218C2×C4×D47—24no—
219C2×C4×D47—22no—
220C2×C4×D47—22no—
221C2×C4×D47—24no—
222C2×C4×D47—42no—
223C2×C4×D47—44no—
224C2×C4×D47C2×D414yes—
225C2×C4×D47C2×D412yes—
226C2×C4×D47C2×D414yes—
227C2×C4×D47C2412yes—
228C2×Dic94—28no—
229C2×Dic94—21no—
230C2×Dic94—22no—
231C2×Dic94—24no—
232C2×Dic94#4114yes—
233C2×Dic94C2412yes—
234Q16×C47—28no—
235SD16×C47—28no—
236C2×C8×C47—22no—
237C2×C8×C47—22no—
238C2×C8×C47C2412yes—
239C2×C8×C47C2412yes—
240C4⋊C4×C47—24no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47C2412yes—
243C22⋊C4×C47—24no—
244C22⋊C4×C47—24no—
245C42×C47—24no—
246C42×C47C2×D412yes—
247C42×C47C2412yes—
248C22⋊Dic47—24no—
249C22⋊Dic47—24no—
250#10625337—28no—
251#10625335—28no—
252(C2×D47)⋊C4—24no—
253C4⋊Dic47—21no—
254C4⋊Dic47—21no—
255C4⋊Dic47—21no—
256C4⋊Dic47—24no—
257C4⋊Dic47—24no—
258C4⋊Dic47C2412yes—
259C4⋊Dic47C2412yes—
260C4⋊Dic47C2412yes—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267C4×Dic47—24no—
268C4×Dic47—24no—
269C4×Dic47—24no—
270C4×Dic47—24no—
271C4×Dic47C2×D412yes—
272C4×Dic47C2×D414yes—
273C4×Dic47C2×D414yes—
274C4×Dic47C2412yes—
275C2×C47⋊C8—22no—
276C2×C47⋊C8—22no—
277C2×C47⋊C8C2412yes—
278C2×C47⋊C8C2412yes—
279C23×C47—22no—
280C23×C47—42no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47C22×D411yescharacteristic
284C22×D47—22no—
285C22×D47—22no—
286C22×D47#13714yes—
287C22×D47C22×D412yes—
288Q8×C47—24no—
289Q8×C47—22no—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—42no—
293Q8×C47C2×#4114yes—
294D4×C47—22no—
295D4×C47—22no—
296D4×C47—42no—
297C2×C4×C47—24no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47C22×D412yes—
306C2×C4×C47C22×D412yes—
307C2×C4×C47C22×D411yescharacteristic
308C2×C4×C47C2×#4112yes—
309C2×C4×C47C2×#4112yes—
310C2×C4×C47C2511yescharacteristic
311C22⋊D47—48no—
312C2×Dic47—22no—
313C2×Dic47—24no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—48no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47C22×D412yes—
325C2×Dic47C22×D412yes—
326C2×Dic47C22×D412yes—
327C4×D47—216no—
328C4×D47—28no—
329C4×D47—24no—
330C4×D47—22no—
331C4×D47—22no—
332C4×D47—44no—
333C4×D47—48no—
334Dic94—216no—
335Dic94—24no—
336Dic94—22no—
337Dic94C2×#4114yes—
338C8×C47—22no—
339C8×C47—22no—
340C47⋊C8—22no—
341C47⋊C8—22no—
342C2×#3117—471nomaximal, Sylow
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—84no—
347C22×C47#52512yes—
348C22×C47C2×#13712yes—
349C22×C47#57512yes—
350C22×C47C23×D411yescharacteristic
351C2×D47—28no—
352C2×D47—22no—
353C2×D47—22no—
354C2×D47C2×#13714yes—
355C4×C47—24no—
356C4×C47—22no—
357C4×C47—22no—
358C4×C47—42no—
359C4×C47—42no—
360C4×C47#52512yes—
361C4×C47C22×#4111yescharacteristic
362C4×C47C22×#4111yescharacteristic
363Dic47—22no—
364Dic47—24no—
365Dic47—22no—
366Dic47—22no—
367Dic47—42no—
368Dic47—42no—
369Dic47—42no—
370C2×#529—471no—
371C22×C4×Q8—471no—
372#3117—4716no—
373C2×#484—471no—
374C2×#481—471no—
375C2×#479—471no—
376C2×#479—471no—
377C2×#464—471no—
378C2×#464D4711yescharacteristic, complemented
379C2×#451—471no—
380C2×#448—471no—
381C2×#441—471no—
382C2×#441—471no—
383C2×#440—471no—
384C2×#440—471no—
385C2×#432—471no—
386C2×C47—82no—
387C2×C47#311714yescomplemented
388C2×C47C2×#52511yescharacteristic
389C2×C47C22×#13711yescharacteristic
390C2×C47C2×#57511yescharacteristic
391D47—24no—
392C23×Q8—471no—
393C22×Q16—471no—
394C22×Q16C2×D4711yescharacteristic
395C22×SD16—471no—
396C22×SD16C2×D4711yescharacteristic
397#529—478no—
398#529—944no—
399C2×#126—941no—
400C2×#125—471no—
401C2×#124C2×D4711yescharacteristic
402C2×#123—941no—
403C2×C22⋊Q8—471no—
404C2×#121—471no—
405C2×C4×Q8—471no—
406C2×C4×Q8—471no—
407C2×C4×Q8—478no—
408C2×C4×Q8—471no—
409C2×C4×Q8—471no—
410C2×C4×Q8—941no—
411C2×C4×Q8—941no—
412C2×C4×Q8—944no—
413C2×C4×Q8C2×D4711yescharacteristic
414C2×C4×D4—471no—
415C2×C4×D4—941no—
416C2×#117—941no—
417C22×C4⋊C4—471no—
418C22×C4⋊C4—941no—
419C22×C42—471no—
420C22×C42—941no—
421#484—478no—
422#481—478no—
423#479—478no—
424#479—478no—
425#464—478no—
426#464C2×D4718yescomplemented
427#451—478no—
428#448—478no—
429#441—478no—
430#441—478no—
431#440—478no—
432#440—478no—
433#432—478no—
434C2×#107—471no—
435C2×#107—471no—
436C2×#106—471no—
437C2×#106—471no—
438C2×C4⋊C8—471no—
439C2×C4⋊C8C2×D4711yescharacteristic
440C2×#103—471no—
441C2×#103—471no—
442C2×#103—471no—
443C2×#103—471no—
444C2×#103—471no—
445C2×#103C2×D4711yescharacteristic
446C2×#102—471no—
447C2×#102C2×D4711yescharacteristic
448C2×C22⋊C8—471no—
449C2×C22⋊C8—471no—
450C2×#97—471no—
451C2×#97—471no—
452C47C2×#311711yescharacteristic, complemented, Sylow
453C22×Q8—474no—
454C22×Q8—471no—
455C22×Q8—941no—
456C22×Q8—942no—
457C22×Q8—944no—
458C22×Q8—944no—
459C22×Q8C22×D4711yescharacteristic
460C22×Q8C22×D4711yescharacteristic
461C22×D4—941no—
462C22×D4C22×D4711yescharacteristic
463C23×C4—471no—
464C23×C4—471no—
465C23×C4—471no—
466C23×C4—941no—
467C23×C4—941no—
468C23×C4—941no—
469C2×Q16—24no—
470C2×Q16—474no—
471C2×Q16—944no—
472C2×Q16C22×D4714yes—
473C2×SD16—24no—
474C2×SD16—474no—
475C2×SD16—944no—
476C2×SD16C22×D4714yes—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8C22×D4711yescharacteristic
480C22×C8C22×D4711yescharacteristic
481#126—948no—
482#125—474no—
483#125—942no—
484#124—22no—
485#124C22×D4714yes—
486#123—948no—
487C22⋊Q8—474no—
488C22⋊Q8—942no—
489#121—474no—
490#121—942no—
491C4×Q8—22no—
492C4×Q8—474no—
493C4×Q8—474no—
494C4×Q8—474no—
495C4×Q8—474no—
496C4×Q8—948no—
497C4×Q8—942no—
498C4×Q8—948no—
499C4×Q8—942no—
500C4×Q8—942no—
501C4×Q8—942no—
502C4×Q8C22×D4714yes—
503C4×D4—474no—
504C4×D4—942no—
505C4×D4—948no—
506#117—948no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—474no—
512C2×C4⋊C4—942no—
513C2×C4⋊C4—948no—
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⋊C4—941no—
521C2×C4⋊C4—941no—
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—471no—
531C2×C42—471no—
532C2×C42—474no—
533C2×C42—474no—
534C2×C42—948no—
535C2×C42—941no—
536C2×C42—941no—
537C2×C42—941no—
538C2×C42—941no—
539C2×C42C22×D4711yescharacteristic
540#107—474no—
541#107—474no—
542#106—474no—
543#106—474no—
544C4⋊C8—474no—
545C4⋊C8C22×D4714yes—
546#103—474no—
547#103—474no—
548#103—474no—
549#103—474no—
550#103—474no—
551#103C22×D4714yes—
552#102—474no—
553#102C22×D4714yes—
554C22⋊C8—474no—
555C22⋊C8—474no—
556#97—474no—
557#97—474no—
558C24—21no—
559C24—471no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—474no—
566C2×Q8—472no—
567C2×Q8—944no—
568C2×Q8—948no—
569C2×Q8—948no—
570C2×Q8—9416no—
571C2×Q8—948no—
572C2×Q8—941no—
573C2×Q8—942no—
574C2×Q8#1062535214yes—
575C2×Q8C23×D4712yes—
576C2×Q8C23×D4712yes—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—944no—
581C2×D4—1884no—
582C2×D4C23×D4712yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—471no—
587C22×C4—471no—
588C22×C4—471no—
589C22×C4—474no—
590C22×C4—472no—
591C22×C4—472no—
592C22×C4—474no—
593C22×C4—944no—
594C22×C4—944no—
595C22×C4—948no—
596C22×C4—944no—
597C22×C4—944no—
598C22×C4—941no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—1882no—
605C22×C4—1884no—
606C22×C4—1884no—
607C22×C4D4×D4711yescharacteristic
608C22×C4D4×D4711yescharacteristic
609C22×C4C23×D4711yescharacteristic
610Q16—28no—
611Q16—948no—
612SD16—28no—
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—472no—
625C4⋊C4—472no—
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⋊C4—941no—
637C4⋊C4—941no—
638C4⋊C4C23×D4712yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C42—24no—
645C42—474no—
646C42—472no—
647C42—474no—
648C42—472no—
649C42—944no—
650C42—944no—
651C42—944no—
652C42—944no—
653C42D4×D4712yes—
654C42C23×D4712yes—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—474no—
660C23—472no—
661C23—942no—
662C23—942no—
663C23C2×D4×D4711yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—474no—
670Q8—9416no—
671Q8—944no—
672Q8—942no—
673Q8C2×#1062535214yes—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—1888no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—472no—
687C2×C4—472no—
688C2×C4—472no—
689C2×C4—948no—
690C2×C4—9416no—
691C2×C4—942no—
692C2×C4—944no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—944no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—1884no—
703C2×C4—1888no—
704C2×C4—1888no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4—1882no—
708C2×C4C2×D4×D4712yes—
709C2×C4C2×D4×D4712yes—
710C2×C4C2×D4×D4711yescharacteristic
711C2×C4#41×D4712yes—
712C2×C4C2×#1062535212yes—
713C2×C4C24×D4711yescharacteristic
714C8—22no—
715C8—22no—
716C8—942no—
717C8—942no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—474no—
723C22—942no—
724C22—942no—
725C22—948no—
726C22#1568963312yes—
727C22#137×D4712yes—
728C22#1568992012yes—
729C22C22×D4×D4711yescharacteristic
730C4—22no—
731C4—22no—
732C4—24no—
733C4—42no—
734C4—42no—
735C4—942no—
736C4—942no—
737C4—942no—
738C4—944no—
739C4—1882no—
740C4—1882no—
741C4—1882no—
742C4#1568963312yes—
743C4C2×#41×D4711yescharacteristic
744C4C22×#1062535211yescharacteristic
745C2—82no—
746C2—944no—
747C2#2025355814yesdirect product factor
748C2C2×#1568963311yescharacteristic
749C2C2×#137×D4711yescharacteristic
750C2C2×#1568992011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#464C2
socleC23×C47C22×D4
prime radicalC2×#13093995C22
hypercenterC2×#464D47
hypocenterC47C2×#3117
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D47C2semidirect
3. #20253558C2direct (N × H)
4. C2×#15689457C2semidirect
6. C2×#15689431C2semidirect
7. C2×#15689430C2semidirect
8. C2×#15689342C2semidirect
9. C2×#15689277C2semidirect
11. C2×#15689230C2semidirect
12. C2×#15689227C2semidirect
13. C2×#15689224C2semidirect
14. C2×#15689220C2semidirect
15. C2×#15689179C2semidirect
16. C2×C47×#464C2semidirect
34. C4×Q8×D47C22semidirect
42. #15689457C22semidirect
44. #15689431C22semidirect
45. #15689430C22semidirect
46. #15689342C22semidirect
47. #15689277C22semidirect
49. #15689230C22semidirect
50. #15689227C22semidirect
51. #15689224C22semidirect
52. #15689220C22semidirect
53. #15689179C22semidirect
73. C47×#464C22semidirect
378. C2×#464D47semidirect
387. C2×C47#3117semidirect
426. #464C2×D47semidirect
452. C47C2×#3117semidirect
747. C2#20253558direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896522
C2×C4×Q8×D472
#202535582
C2×#156894572
C2×#156894402
C2×#156894312
C2×#156894302
C2×#156893422
C2×#156892772
C2×#156892602
C2×#156892302
C2×#156892272
C2×#156892242
C2×#156892202
C2×#156891792
C2×C47×#4642
C2×#311747