Finite Group Databasebeta

← C2×#20253472 #27084365

Subgroups — C2×#20253472 #27084365

Order 12032.

2170 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×#15689660C211yesmaximal, characteristic
2C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
3#20253472C2116yesmaximal, direct product factor
4C2×#15689452C211yesmaximal, characteristic, complemented
5C2×#15689438C211yesmaximal, characteristic
6C2×#15689429C211yesmaximal, characteristic, complemented
7C2×#15689428C211yesmaximal, characteristic, complemented
8C2×#15689348C211yesmaximal, characteristic, complemented
9C2×#15689347C211yesmaximal, characteristic, complemented
10C2×#15689277C211yesmaximal, characteristic, complemented
11C2×#15689263C211yesmaximal, characteristic
12C2×C4×#10625337C211yesmaximal, characteristic, complemented
13C2×C4×#10625325C211yesmaximal, characteristic, complemented
14C2×C4×#10625336C211yesmaximal, characteristic, complemented
15C2×#15689174C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C47C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21#15689660—24no—
22#15689660C2218yes—
23C2×#13094019—21no—
24C2×#13094015C2211yescharacteristic
25C2×#13094013C2211yescharacteristic
26C2×#13094009—21no—
27C2×#13094000C2211yescharacteristic
28C2×#13093999C2211yescharacteristic
29C2×Q8×Dic47C2211yescharacteristic
30C2×C4×Dic94—21no—
31C2×C4×Dic94C2211yescharacteristic
32C2×#13093989—21no—
33C2×#13093989C2211yescharacteristic
34C4×Q8×D47—24no—
35C4×Q8×D47C2218yescomplemented
36C2×C4×D188—21no—
37C2×C4×D188C2211yescharacteristic
38C2×#13093981—21no—
39C2×C4⋊C4×D47—21no—
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C42×D47—21no—
42C2×C42×D47C2211yescharacteristic
43#15689452C2218yescomplemented
44#15689438C2218yes—
45#15689429C2218yescomplemented
46#15689428C2218yescomplemented
47#15689348C2218yescomplemented
48#15689347C2218yescomplemented
49#15689277C2218yescomplemented
50#15689263C2218yes—
51C4×#10625337C2218yescomplemented
52C4×#10625325C2218yescomplemented
53C4×#10625336C2218yescomplemented
54#15689174C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C4×C47⋊C8C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic
72C4×Q16×C47C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C2×Q8×D47—24no—
80C2×Q8×D47—22no—
81C2×Q8×D47—24no—
82C2×Q8×D47C2314yes—
83C22×D188—21no—
84C22×D188C2311yescharacteristic
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47D411yescharacteristic
89C22×C4×D47D411yescharacteristic
90C22×C4×D47C2311yescharacteristic
91C2×#10625337—24no—
92C2×#10625337C2314yes—
93C2×#10625325—24no—
94C2×#10625325C2314yes—
95C2×#10625336—24no—
96C2×#10625336C2314yes—
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99#13094019—28no—
100#13094015—22no—
101#13094015C2314yes—
102#13094013—22no—
103#13094013C2314yes—
104#13094009—28no—
105#13094000—22no—
106#13094000C2314yes—
107#13093999—22no—
108#13093999C2314yes—
109Q8×Dic47—22no—
110Q8×Dic47C2314yes—
111C4×Dic94—22no—
112C4×Dic94—28no—
113C4×Dic94C2314yes—
114#13093989—22no—
115#13093989—28no—
116#13093989C2314yes—
117C4×D188—28no—
118C4×D188—22no—
119C4×D188C2314yes—
120#13093981—28no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C4⋊C4×D47—28no—
131C4⋊C4×D47—22no—
132C4⋊C4×D47C2314yes—
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—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×Dic47D411yescharacteristic
142C2×C4×Dic47D411yescharacteristic
143C2×C4×Dic47C2311yescharacteristic
144C42×D47—28no—
145C42×D47D414yes—
146C42×D47C2314yes—
147#13093957C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150Dic47⋊C8C2314yes—
151Dic47⋊C8C2314yes—
152#13093949C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093947C2314yes—
156#13093946C2314yes—
157#13093944C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160C4×C47⋊C8C2314yes—
161C22×Q8×C47C2311yescharacteristic
162C22×Q8×C47C2311yescharacteristic
163C2×Q16×C47—24no—
164C2×Q16×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C4×Q8×C47—22no—
168C4×Q8×C47—22no—
169C4×Q8×C47C2314yes—
170C4×Q8×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C42×C47—21no—
176C2×C42×C47—21no—
177C2×C42×C47C2311yescharacteristic
178#107×C47C2314yes—
179#103×C47C2314yes—
180#103×C47C2314yes—
181C4×C8×C47C2314yes—
182C23×D47—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—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47C2×D411yescharacteristic
203C22×Dic47C2×D411yescharacteristic
204C22×Dic47C2×D411yescharacteristic
205Q8×D47—216no—
206Q8×D47—28no—
207Q8×D47—28no—
208C2×D188—22no—
209C2×D188—22no—
210C2×D188—24no—
211C2×D188—21no—
212C2×D188—44no—
213C2×D188C2412yes—
214C2×C4×D47—28no—
215C2×C4×D47—24no—
216C2×C4×D47—24no—
217C2×C4×D47—24no—
218C2×C4×D47—22no—
219C2×C4×D47—22no—
220C2×C4×D47—24no—
221C2×C4×D47—24no—
222C2×C4×D47—44no—
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—
235C2×C8×C47—22no—
236C2×C8×C47—22no—
237C2×C8×C47C2412yes—
238C2×C8×C47C2412yes—
239C4⋊C4×C47—24no—
240C4⋊C4×C47—24no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47C2412yes—
244C4⋊C4×C47C2412yes—
245C42×C47—24no—
246C42×C47—24no—
247C42×C47C2×D412yes—
248C42×C47C2412yes—
249#10625337—28no—
250#10625336—28no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47—24no—
259C4⋊Dic47—24no—
260C4⋊Dic47C2412yes—
261C4⋊Dic47C2412yes—
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×Dic47C2×D412yes—
271C4×Dic47C2×D414yes—
272C4×Dic47C2×D414yes—
273C4×Dic47C2412yes—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—22no—
276C2×C47⋊C8C2412yes—
277C2×C47⋊C8C2412yes—
278#10625325—28no—
279C23×C47C22×D411yescharacteristic
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47—42no—
286C22×D47#13514yes—
287C22×D47C22×D412yes—
288Q8×C47—24no—
289Q8×C47—22no—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—42no—
293Q8×C47C2×#4114yes—
294C2×C4×C47—24no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47#13714yes—
304C2×C4×C47C22×D412yes—
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C22×D412yes—
307C2×C4×C47C2×#4112yes—
308C2×C4×C47C2×#4112yes—
309C2×C4×C47C2511yescharacteristic
310C2×Dic47—22no—
311C2×Dic47—24no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321C2×Dic47C22×D412yes—
322D188—22no—
323D188—22no—
324D188—48no—
325D188—42no—
326C4×D47—216no—
327C4×D47—28no—
328C4×D47—24no—
329C4×D47—28no—
330C4×D47—22no—
331C4×D47—22no—
332C4×D47—48no—
333C4×D47—48no—
334Dic94—216no—
335Dic94—24no—
336Dic94—22no—
337Dic94C2×#4114yes—
338C8×C47—22no—
339C8×C47—22no—
340C47⋊C8—22no—
341C47⋊C8—22no—
342C2×#3108—471nomaximal, Sylow
343C22×C47#52512yes—
344C22×C47C2×#13512yes—
345C22×C47C2×#13712yes—
346C22×C47C23×D411yescharacteristic
347C2×D47—28no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—42no—
351C2×D47—42no—
352C2×D47—42no—
353C2×D47—84no—
354C2×D47C2×#13514yes—
355C4×C47—24no—
356C4×C47—22no—
357C4×C47—42no—
358C4×C47—42no—
359C4×C47—42no—
360C4×C47#52512yes—
361C4×C47C2×#13714yes—
362C4×C47C22×#4111yescharacteristic
363C4×C47C22×#4111yescharacteristic
364Dic47—22no—
365Dic47—24no—
366Dic47—22no—
367Dic47—22no—
368Dic47—42no—
369Dic47—42no—
370C2×#529—471no—
371C22×C4×Q8—471no—
372#3108—4716no—
373C2×#483—471no—
374C2×#480—471no—
375C2×#479—471no—
376C2×#479—471no—
377C2×#464—471no—
378C2×#464—471no—
379C2×#451—471no—
380C2×#448—471no—
381C2×C4×Q16—471no—
382C2×C4×Q16D4711yescharacteristic, complemented
383C2×C4×SD16—471no—
384C2×C4×SD16—471no—
385C2×#431—471no—
386C2×C47#310814yescomplemented
387C2×C47C2×#52511yescharacteristic
388C2×C47C22×#13511yescharacteristic
389C2×C47C22×#13711yescharacteristic
390D47—24no—
391D47—82no—
392C23×Q8—471no—
393C22×Q16—471no—
394C22×Q16C2×D4711yescharacteristic
395C22×SD16—471no—
396C22×SD16—471no—
397#529—478no—
398#529—944no—
399C2×#126—941no—
400C2×#125—471no—
401C2×#124—471no—
402C2×#123—941no—
403C2×C22⋊Q8—471no—
404C2×#121—471no—
405C2×C4×Q8—471no—
406C2×C4×Q8—478no—
407C2×C4×Q8—471no—
408C2×C4×Q8—471no—
409C2×C4×Q8—941no—
410C2×C4×Q8—941no—
411C2×C4×Q8—944no—
412C2×C4×Q8C2×D4711yescharacteristic
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#483—478no—
422#480—478no—
423#479—478no—
424#479—478no—
425#464—478no—
426#464—478no—
427#451—478no—
428#448—478no—
429C4×Q16—478no—
430C4×Q16C2×D4718yescomplemented
431C4×SD16—478no—
432C4×SD16—478no—
433#431—478no—
434C2×#107—471no—
435C2×#107C2×D4711yescharacteristic
436C2×#106—471no—
437C2×#106—471no—
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⋊C8—471no—
450C2×C4×C8—471no—
451C2×C4×C8C2×D4711yescharacteristic
452C47C2×#310811yescharacteristic, 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—471no—
462C22×D4—941no—
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—474no—
474C2×SD16—474no—
475C2×SD16—944no—
476C2×SD16—944no—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8C22×D4711yescharacteristic
480C22×C8C22×D4711yescharacteristic
481#126—948no—
482#125—474no—
483#125—942no—
484#124—474no—
485#124—942no—
486#123—948no—
487C22⋊Q8—474no—
488C22⋊Q8—942no—
489#121—474no—
490#121—942no—
491C4×Q8—22no—
492C4×Q8—22no—
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×Q8C22×D4714yes—
502C4×Q8C22×D4714yes—
503C4×D4—474no—
504C4×D4—948no—
505C4×D4—942no—
506#117—948no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
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⋊C4C22×D4711yescharacteristic
522C2×C4⋊C4C22×D4711yescharacteristic
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—471no—
531C2×C42—471no—
532C2×C42—471no—
533C2×C42—474no—
534C2×C42—474no—
535C2×C42—948no—
536C2×C42—941no—
537C2×C42—941no—
538C2×C42—941no—
539C2×C42C22×D4711yescharacteristic
540#107—474no—
541#107C22×D4714yes—
542#106—474no—
543#106—474no—
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⋊C8—474no—
556C4×C8—474no—
557C4×C8C22×D4714yes—
558C24—471no—
559C24—941no—
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#1062535014yes—
575C2×Q8C23×D4712yes—
576C2×Q8C23×D4712yes—
577C2×D4—472no—
578C2×D4—944no—
579C2×D4—941no—
580C2×D4—942no—
581C2×D4—942no—
582C2×D4—1884no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—471no—
588C22×C4—471no—
589C22×C4—471no—
590C22×C4—474no—
591C22×C4—474no—
592C22×C4—472no—
593C22×C4—472no—
594C22×C4—944no—
595C22×C4—944no—
596C22×C4—948no—
597C22×C4—944no—
598C22×C4—941no—
599C22×C4—944no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—944no—
605C22×C4—1884no—
606C22×C4—1884no—
607C22×C4D4×D4711yescharacteristic
608C22×C4D4×D4711yescharacteristic
609C22×C4C23×D4711yescharacteristic
610Q16—28no—
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—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—472no—
627C4⋊C4—472no—
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⋊C4C23×D4712yes—
638C4⋊C4C23×D4712yes—
639C22⋊C4—944no—
640C22⋊C4—944no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C42—24no—
645C42—24no—
646C42—474no—
647C42—472no—
648C42—474no—
649C42—472no—
650C42—944no—
651C42—944no—
652C42—944no—
653C42D4×D4712yes—
654C42C23×D4712yes—
655C23—474no—
656C23—472no—
657C23—942no—
658C23—942no—
659C23—942no—
660C23—1882no—
661C23—1882no—
662C23—1882no—
663C23C2×D4×D4711yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—474no—
670Q8—9416no—
671Q8—944no—
672Q8—942no—
673Q8C2×#1062535014yes—
674D4—942no—
675D4—942no—
676D4—1888no—
677D4—1882no—
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—42no—
687C2×C4—472no—
688C2×C4—472no—
689C2×C4—472no—
690C2×C4—948no—
691C2×C4—9416no—
692C2×C4—942no—
693C2×C4—944no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—944no—
698C2×C4—948no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—1888no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4—1888no—
707C2×C4#1309405614yes—
708C2×C4C2×D4×D4712yes—
709C2×C4C2×D4×D4711yescharacteristic
710C2×C4C2×D4×D4712yes—
711C2×C4#41×D4712yes—
712C2×C4C2×#1062535012yes—
713C2×C4C24×D4711yescharacteristic
714C8—22no—
715C8—22no—
716C8—942no—
717C8—942no—
718C22—474no—
719C22—948no—
720C22—942no—
721C22—942no—
722C22—3764no—
723C22—1882no—
724C22—1882no—
725C22—1882no—
726C22#1568963212yes—
727C22#135×D4712yes—
728C22C2×#1309405612yes—
729C22C22×D4×D4711yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—942no—
736C4—942no—
737C4—942no—
738C4—944no—
739C4—1882no—
740C4—1882no—
741C4#1568963212yes—
742C4C2×#1309405614yes—
743C4C2×#41×D4711yescharacteristic
744C4C22×#1062535011yescharacteristic
745C2—944no—
746C2—3762no—
747C2#2025347214yesdirect product factor
748C2C2×#1568963211yescharacteristic
749C2C2×#135×D4711yescharacteristic
750C2C22×#1309405611yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×Q16×C47C2
socleC23×C47C22×D4
prime radicalC2×#13093999C22
hypercenterC2×C4×Q16D47
hypocenterC47C2×#3108
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D47C2semidirect
3. #20253472C2direct (N × H)
4. C2×#15689452C2semidirect
6. C2×#15689429C2semidirect
7. C2×#15689428C2semidirect
8. C2×#15689348C2semidirect
9. C2×#15689347C2semidirect
10. C2×#15689277C2semidirect
12. C2×C4×#10625337C2semidirect
13. C2×C4×#10625325C2semidirect
14. C2×C4×#10625336C2semidirect
15. C2×#15689174C2semidirect
16. C2×C4×Q16×C47C2semidirect
35. C4×Q8×D47C22semidirect
43. #15689452C22semidirect
45. #15689429C22semidirect
46. #15689428C22semidirect
47. #15689348C22semidirect
48. #15689347C22semidirect
49. #15689277C22semidirect
51. C4×#10625337C22semidirect
52. C4×#10625325C22semidirect
53. C4×#10625336C22semidirect
54. #15689174C22semidirect
72. C4×Q16×C47C22semidirect
382. C2×C4×Q16D47semidirect
386. C2×C47#3108semidirect
430. C4×Q16C2×D47semidirect
452. C47C2×#3108semidirect
747. C2#20253472direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896602
C2×C4×Q8×D472
#202534722
C2×#156894522
C2×#156894382
C2×#156894292
C2×#156894282
C2×#156893482
C2×#156893472
C2×#156892772
C2×#156892632
C2×C4×#106253372
C2×C4×#106253252
C2×C4×#106253362
C2×#156891742
C2×C4×Q16×C472
C2×#310847