Finite Group Databasebeta

← C2×#20253455 #27084347

Subgroups — C2×#20253455 #27084347

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×#15689677C211yesmaximal, characteristic, complemented
2C2×C4×#10625352C211yesmaximal, characteristic
3#20253455C2116yesmaximal, direct product factor
4C2×#15689467C211yesmaximal, characteristic, complemented
5C2×#15689463C211yesmaximal, characteristic, complemented
6C2×#15689407C211yesmaximal, characteristic, complemented
7C2×#15689401C211yesmaximal, characteristic, complemented
8C2×#15689332C211yesmaximal, characteristic, complemented
9C2×#15689326C211yesmaximal, characteristic, complemented
10C2×#15689286C211yesmaximal, characteristic
11C2×#15689282C211yesmaximal, characteristic
12C2×C4×Dic188C211yesmaximal, characteristic, complemented
13C2×C4×#10625337C211yesmaximal, characteristic, complemented
14C2×C4×#10625335C211yesmaximal, characteristic, complemented
15C2×#15689174C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21#15689677—24no—
22#15689677C2218yescomplemented
23C2×#13094023C2211yescharacteristic
24C2×#13094022C2211yescharacteristic
25C2×#13094014—21no—
26C2×#13094004C2211yescharacteristic
27C2×#13094002—21no—
28C2×#13094000C2211yescharacteristic
29C4×#10625352—24no—
30C4×#10625352C2218yes—
31C2×C4×Dic94—21no—
32C2×C4×Dic94C2211yescharacteristic
33C2×C4×Dic94C2211yescharacteristic
34C2×#13093989C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×C4×C22⋊D47—21no—
37C2×(C22⋊D47)⋊C4—21no—
38C2×#13093982C2211yescharacteristic
39C2×#13093981—21no—
40C2×#13093980—21no—
41C22×C4×Dic47—21no—
42C2×C42×D47C2211yescharacteristic
43#15689467C2218yescomplemented
44#15689463C2218yescomplemented
45#15689407C2218yescomplemented
46#15689401C2218yescomplemented
47#15689332C2218yescomplemented
48#15689326C2218yescomplemented
49#15689286C2218yes—
50#15689282C2218yes—
51C4×Dic188C2218yescomplemented
52C4×#10625337C2218yescomplemented
53C4×#10625335C2218yescomplemented
54#15689174C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C4×C47⋊C8C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C4×SD16×C47C2218yescomplemented
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C2×#10625352—24no—
78C2×#10625352—22no—
79C2×#10625352—24no—
80C2×#10625352C2314yes—
81C22×Dic94—21no—
82C22×Dic94C2311yescharacteristic
83C22×Dic94C2311yescharacteristic
84C22×C22⋊D47—21no—
85C23×Dic47—21no—
86C23×Dic47—21no—
87C22×C4×D47D411yescharacteristic
88C22×C4×D47D411yescharacteristic
89C22×C4×D47C2311yescharacteristic
90C2×Dic188—24no—
91C2×Dic188C2314yes—
92C2×#10625337—24no—
93C2×#10625337C2314yes—
94C2×#10625335—24no—
95C2×#10625335C2314yes—
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98#13094023—22no—
99#13094023C2314yes—
100#13094022—22no—
101#13094022C2314yes—
102#13094014—28no—
103#13094004—22no—
104#13094004C2314yes—
105#13094002—28no—
106#13094000—22no—
107#13094000C2314yes—
108C4×Dic94—22no—
109C4×Dic94—22no—
110C4×Dic94—28no—
111C4×Dic94C2314yes—
112C4×Dic94C2314yes—
113#13093989—22no—
114#13093989C2314yes—
115D4×Dic47—22no—
116D4×Dic47C2314yes—
117C4×C22⋊D47—28no—
118(C22⋊D47)⋊C4—28no—
119#13093982—22no—
120#13093982C2314yes—
121#13093981—28no—
122#13093980—28no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×C22⋊Dic47—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×C4×Dic47—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—28no—
142C2×C4×Dic47D411yescharacteristic
143C2×C4×Dic47D411yescharacteristic
144C2×C4×Dic47C2311yescharacteristic
145C42×D47D414yes—
146C42×D47C2314yes—
147#13093958C2314yes—
148#13093957C2314yes—
149#13093955C2314yes—
150Dic47⋊C8C2314yes—
151Dic47⋊C8C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093948C2314yes—
155#13093947C2314yes—
156#13093947C2314yes—
157#13093945C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160C4×C47⋊C8C2314yes—
161C22×Q8×C47C2311yescharacteristic
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47—21no—
164C2×SD16×C47—24no—
165C2×SD16×C47C2314yes—
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C4×Q8×C47—22no—
169C4×Q8×C47C2314yes—
170C4×D4×C47—22no—
171C4×D4×C47C2314yes—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C42×C47—21no—
177C2×C42×C47C2311yescharacteristic
178#106×C47C2314yes—
179#103×C47C2314yes—
180#102×C47C2314yes—
181C4×C8×C47C2314yes—
182C24×C47—21no—
183C23×D47C2×D411yescharacteristic
184C2×Q8×C47—21no—
185C2×Q8×C47—22no—
186C2×Q8×C47—22no—
187C2×Q8×C47C2412yes—
188C2×D4×C47—21no—
189C2×D4×C47—22no—
190C2×D4×C47#4114yes—
191C2×D4×C47C2412yes—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—24no—
196C22×C4×C47—44no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2411yescharacteristic
200C2×C22⋊D47—28no—
201C2×C22⋊D47—24no—
202C22×Dic47—28no—
203C22×Dic47—21no—
204C22×Dic47—24no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—24no—
209C22×Dic47—44no—
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213#10625352—216no—
214#10625352—28no—
215#10625352—28no—
216C2×C4×D47—24no—
217C2×C4×D47—22no—
218C2×C4×D47—22no—
219C2×C4×D47—24no—
220C2×C4×D47C2×D412yes—
221C2×C4×D47C2×D414yes—
222C2×C4×D47C2×D414yes—
223C2×C4×D47C2412yes—
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—
234SD16×C47—28no—
235C2×C8×C47—22no—
236C2×C8×C47—22no—
237C2×C8×C47C2412yes—
238C2×C8×C47C2412yes—
239C4⋊C4×C47—24no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47C2412yes—
243C4⋊C4×C47C2412yes—
244C22⋊C4×C47—24no—
245C42×C47—24no—
246C42×C47C2×D412yes—
247C42×C47C2412yes—
248C22⋊Dic47—24no—
249#10625337—28no—
250#10625335—28no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254C4⋊Dic47—21no—
255C4⋊Dic47—21no—
256C4⋊Dic47—24no—
257C4⋊Dic47C2412yes—
258C4⋊Dic47C2412yes—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266C4×Dic47—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—
278Dic188—28no—
279C23×C47—24no—
280C23×C47—22no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47C22×D411yescharacteristic
284C22×D47—22no—
285C22×D47—22no—
286C22×D47—22no—
287C22×D47C22×D412yes—
288Q8×C47—22no—
289Q8×C47—22no—
290Q8×C47—42no—
291D4×C47—24no—
292D4×C47—22no—
293D4×C47C2×#4114yes—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—48no—
302C2×C4×C47#13714yes—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C22×D412yes—
306C2×C4×C47C2×#4112yes—
307C2×C4×C47C2×#4112yes—
308C2×C4×C47C2511yescharacteristic
309C22⋊D47—216no—
310C2×Dic47—216no—
311C2×Dic47—24no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—48no—
322C2×Dic47#13514yes—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325C2×Dic47C22×D412yes—
326C4×D47—24no—
327C4×D47—28no—
328C4×D47—22no—
329C4×D47—22no—
330C4×D47—28no—
331Dic94—24no—
332Dic94—22no—
333Dic94—22no—
334Dic94—22no—
335Dic94—42no—
336Dic94—48no—
337Dic94C2×#4114yes—
338C8×C47—22no—
339C8×C47—22no—
340C47⋊C8—22no—
341C47⋊C8—22no—
342C2×#3107—471nomaximal, Sylow
343C22×C47—24no—
344C22×C47—48no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47#52512yes—
348C22×C47C2×#13512yes—
349C22×C47C2×#13712yes—
350C22×C47C23×D411yescharacteristic
351C2×D47—22no—
352C2×D47—22no—
353C2×D47—22no—
354C2×D47—44no—
355C4×C47—22no—
356C4×C47—42no—
357C4×C47—42no—
358C4×C47—42no—
359C4×C47#52512yes—
360C4×C47C2×#13714yes—
361C4×C47C22×#4111yescharacteristic
362C4×C47C22×#4111yescharacteristic
363Dic47—24no—
364Dic47—22no—
365Dic47—22no—
366Dic47—42no—
367Dic47—42no—
368Dic47—42no—
369Dic47C2×#13514yes—
370C2×#533—471no—
371C2×C4×#41—471no—
372#3107—4716no—
373C2×#485—471no—
374C2×#485—471no—
375C2×#475—471no—
376C2×#474—471no—
377C2×#462—471no—
378C2×#461—471no—
379C2×#452—471no—
380C2×#452—471no—
381C2×C4×Q16—471no—
382C2×C4×Q16—471no—
383C2×C4×SD16—471no—
384C2×C4×SD16D4711yescharacteristic, complemented
385C2×#431—471no—
386C2×C47—44no—
387C2×C47#310714yescomplemented
388C2×C47C2×#52511yescharacteristic
389C2×C47C22×#13511yescharacteristic
390C2×C47C22×#13711yescharacteristic
391D47—42no—
392C22×#41—471no—
393C22×Q16—471no—
394C22×Q16—471no—
395C22×SD16—471no—
396C22×SD16C2×D4711yescharacteristic
397#533—478no—
398#533—944no—
399C2×C4⋊Q8—471no—
400C2×C4⋊Q8—471no—
401C2×#125—941no—
402C2×C22⋊Q8—471no—
403C2×C22⋊Q8—471no—
404C2×C22⋊Q8—941no—
405C4×#41—478no—
406C4×#41—944no—
407C2×C4×Q8—471no—
408C2×C4×Q8—471no—
409C2×C4×Q8—471no—
410C2×C4×Q8—941no—
411C2×C4×Q8C2×D4711yescharacteristic
412C2×C4×D4—471no—
413C2×C4×D4—941no—
414C2×C4×D4—941no—
415C2×C4×D4C2×D4711yescharacteristic
416C2×#117—471no—
417C2×#117—941no—
418C2×#117—941no—
419C22×C42—471no—
420C22×C42—941no—
421#485—478no—
422#485—478no—
423#475—478no—
424#474—478no—
425#462—478no—
426#461—478no—
427#452—478no—
428#452—478no—
429C4×Q16—478no—
430C4×Q16—478no—
431C4×SD16—478no—
432C4×SD16C2×D4718yescomplemented
433#431—478no—
434C2×#107—471no—
435C2×#107—471no—
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×#103—471no—
445C2×#103C2×D4711yescharacteristic
446C2×#102—471no—
447C2×#102C2×D4711yescharacteristic
448C2×C22⋊C8—471no—
449C2×C22⋊C8—471no—
450C2×C4×C8—471no—
451C2×C4×C8C2×D4711yescharacteristic
452C47C2×#310711yescharacteristic, complemented, Sylow
453C2×#41—474no—
454C2×#41—942no—
455C2×#41—944no—
456C2×#41—944no—
457C22×Q8—471no—
458C22×Q8—471no—
459C22×Q8—941no—
460C22×Q8C22×D4711yescharacteristic
461C22×D4—941no—
462C22×D4C22×D4711yescharacteristic
463C23×C4—21no—
464C23×C4—471no—
465C23×C4—471no—
466C23×C4—471no—
467C23×C4—941no—
468C23×C4—941no—
469C2×Q16—474no—
470C2×Q16—474no—
471C2×Q16—944no—
472C2×Q16—944no—
473C2×SD16—24no—
474C2×SD16—474no—
475C2×SD16—944no—
476C2×SD16C22×D4714yes—
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—474no—
487C22⋊Q8—474no—
488C22⋊Q8—942no—
489C22⋊Q8—948no—
490C22⋊Q8—942no—
491C4×Q8—22no—
492C4×Q8—474no—
493C4×Q8—474no—
494C4×Q8—474no—
495C4×Q8—948no—
496C4×Q8—942no—
497C4×Q8—942no—
498C4×Q8—942no—
499C4×Q8C22×D4714yes—
500C4×D4—22no—
501C4×D4—474no—
502C4×D4—942no—
503C4×D4—948no—
504C4×D4—948no—
505C4×D4C22×D4714yes—
506#117—474no—
507#117—948no—
508#117—948no—
509#117—942no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—471no—
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⋊C4—941no—
521C2×C4⋊C4C22×D4711yescharacteristic
522C2×C4⋊C4C22×D4711yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—941no—
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#106C22×D4714yes—
544C4⋊C8—474no—
545C4⋊C8—474no—
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—
556C4×C8—474no—
557C4×C8C22×D4714yes—
558C24—21no—
559C24—471no—
560#41—948no—
561#41—9416no—
562#41—948no—
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—21no—
578C2×D4—22no—
579C2×D4—944no—
580C2×D4—948no—
581C2×D4#1062535014yes—
582C2×D4C23×D4712yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—471no—
589C22×C4—471no—
590C22×C4—471no—
591C22×C4—474no—
592C22×C4—472no—
593C22×C4—474no—
594C22×C4—472no—
595C22×C4—944no—
596C22×C4—944no—
597C22×C4—944no—
598C22×C4—948no—
599C22×C4—941no—
600C22×C4—944no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—1884no—
607C22×C4D4×D4711yescharacteristic
608C22×C4D4×D4711yescharacteristic
609C22×C4C23×D4711yescharacteristic
610Q16—948no—
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—21no—
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⋊C4C23×D4712yes—
638C4⋊C4C23×D4712yes—
639C22⋊C4—24no—
640C22⋊C4—944no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C42—24no—
645C42—474no—
646C42—474no—
647C42—472no—
648C42—472no—
649C42—944no—
650C42—944no—
651C42—944no—
652C42—944no—
653C42D4×D4712yes—
654C42C23×D4712yes—
655C23—24no—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—472no—
660C23—942no—
661C23—942no—
662C23—942no—
663C23C2×D4×D4711yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—42no—
667Q8—474no—
668Q8—944no—
669Q8—942no—
670Q8—942no—
671Q8—942no—
672Q8—1888no—
673Q8—1882no—
674D4—24no—
675D4—22no—
676D4—9416no—
677D4C2×#1062535014yes—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—48no—
686C2×C4—474no—
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—944no—
697C2×C4—948no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—1888no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4#1309405314yes—
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—24no—
719C22—48no—
720C22—42no—
721C22—42no—
722C22—942no—
723C22—942no—
724C22—942no—
725C22—1884no—
726C22#1568963212yes—
727C22#135×D4712yes—
728C22C2×#1309405312yes—
729C22C22×D4×D4711yescharacteristic
730C4—22no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—474no—
735C4—942no—
736C4—942no—
737C4—944no—
738C4—1882no—
739C4—1882no—
740C4—1882no—
741C4#1568963212yes—
742C4C2×#1309405314yes—
743C4C2×#41×D4711yescharacteristic
744C4C22×#1062535011yescharacteristic
745C2—44no—
746C2—1882no—
747C2#2025345514yesdirect product factor
748C2C2×#1568963211yescharacteristic
749C2C2×#135×D4711yescharacteristic
750C2C22×#1309405311yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×SD16×C47C2
socleC23×C47C22×D4
prime radicalC22×#10625352C22
hypercenterC2×C4×SD16D47
hypocenterC47C2×#3107
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#15689677C2semidirect
3. #20253455C2direct (N × H)
4. C2×#15689467C2semidirect
5. C2×#15689463C2semidirect
6. C2×#15689407C2semidirect
7. C2×#15689401C2semidirect
8. C2×#15689332C2semidirect
9. C2×#15689326C2semidirect
12. C2×C4×Dic188C2semidirect
13. C2×C4×#10625337C2semidirect
14. C2×C4×#10625335C2semidirect
15. C2×#15689174C2semidirect
16. C2×C4×SD16×C47C2semidirect
22. #15689677C22semidirect
43. #15689467C22semidirect
44. #15689463C22semidirect
45. #15689407C22semidirect
46. #15689401C22semidirect
47. #15689332C22semidirect
48. #15689326C22semidirect
51. C4×Dic188C22semidirect
52. C4×#10625337C22semidirect
53. C4×#10625335C22semidirect
54. #15689174C22semidirect
72. C4×SD16×C47C22semidirect
384. C2×C4×SD16D47semidirect
387. C2×C47#3107semidirect
432. C4×SD16C2×D47semidirect
452. C47C2×#3107semidirect
747. C2#20253455direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896772
C2×C4×#106253522
#202534552
C2×#156894672
C2×#156894632
C2×#156894072
C2×#156894012
C2×#156893322
C2×#156893262
C2×#156892862
C2×#156892822
C2×C4×Dic1882
C2×C4×#106253372
C2×C4×#106253352
C2×#156891742
C2×C4×SD16×C472
C2×#310747