Finite Group Databasebeta

← C2×#20253405 #27084292

Subgroups — C2×#20253405 #27084292

Order 12032.

2202 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689652C211yesmaximal, characteristic, complemented
2C2×C4×#10625354C211yesmaximal, characteristic, complemented
3#20253405C2116yesmaximal, direct product factor
4C2×#15689462C211yesmaximal, characteristic, complemented
5C2×#15689445C211yesmaximal, characteristic, complemented
6C2×#15689430C211yesmaximal, characteristic, complemented
7C2×#15689424C211yesmaximal, characteristic, complemented
8C2×#15689335C211yesmaximal, characteristic, complemented
9C2×#15689284C211yesmaximal, characteristic, complemented
10C2×#15689267C211yesmaximal, characteristic
11C2×Q16×Dic47C211yesmaximal, characteristic, complemented
12C2×SD16×Dic47C211yesmaximal, characteristic, complemented
13C2×#15689208C211yesmaximal, characteristic, complemented
14C2×#15689203C211yesmaximal, characteristic, complemented
15C2×#15689175C211yesmaximal, characteristic, complemented
16C2×C47×#464C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20#15689652—24no—
21#15689652C2218yescomplemented
22C2×#13094017—21no—
23C2×#13094016C2211yescharacteristic
24C2×#13094006—21no—
25C2×#13094000C2211yescharacteristic
26C2×#13093995C2211yescharacteristic
27C4×#10625354—24no—
28C4×#10625354C2218yescomplemented
29C2×Q8×Dic47C2211yescharacteristic
30C2×Q8×Dic47C2211yescharacteristic
31C2×C4×D188—21no—
32C2×C4×D188C2211yescharacteristic
33C2×D4×Dic47C2211yescharacteristic
34C2×#13093986—21no—
35C2×#13093986C2211yescharacteristic
36C2×(C22⋊D47)⋊C4—21no—
37C2×#13093982—21no—
38C2×#13093982C2211yescharacteristic
39C2×#13093980—21no—
40C2×C42×D47—21no—
41C2×C42×D47C2211yescharacteristic
42#15689462C2218yescomplemented
43#15689445C2218yescomplemented
44#15689430C2218yescomplemented
45#15689424C2218yescomplemented
46#15689335C2218yescomplemented
47#15689284C2218yescomplemented
48#15689267C2218yes—
49Q16×Dic47C2218yescomplemented
50SD16×Dic47C2218yescomplemented
51#15689208C2218yescomplemented
52#15689203C2218yescomplemented
53#15689175C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×#13093948C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
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
77C2×#10625354—24no—
78C2×#10625354—24no—
79C2×#10625354—22no—
80C2×#10625354C2314yes—
81C22×D188—21no—
82C22×D188C2311yescharacteristic
83C22×C22⋊D47—21no—
84C23×Dic47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47D411yescharacteristic
89C22×C4×D47D411yescharacteristic
90C22×C4×D47C2311yescharacteristic
91C2×#10625336—24no—
92C2×#10625336C2314yes—
93C2×#10625334—24no—
94C2×#10625334C2314yes—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97#13094017—28no—
98#13094016—22no—
99#13094016C2314yes—
100#13094006—28no—
101#13094000—22no—
102#13094000C2314yes—
103#13093995—22no—
104#13093995C2314yes—
105Q8×Dic47—22no—
106Q8×Dic47—22no—
107Q8×Dic47C2314yes—
108Q8×Dic47C2314yes—
109C4×D188—28no—
110C4×D188—22no—
111C4×D188C2314yes—
112D4×Dic47—22no—
113D4×Dic47C2314yes—
114#13093986—28no—
115#13093986—22no—
116#13093986C2314yes—
117(C22⋊D47)⋊C4—28no—
118#13093982—22no—
119#13093982—28no—
120#13093982C2314yes—
121#13093980—28no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×C22⋊Dic47—21no—
131C2×C22⋊Dic47—21no—
132C2×(C2×D47)⋊C4—21no—
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—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#13093948C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093946C2314yes—
154#13093946C2314yes—
155#13093945C2314yes—
156(C2×D47)⋊C8C2314yes—
157(C2×D47)⋊C8C2314yes—
158C8×Dic47C2314yes—
159C8×Dic47C2314yes—
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×D47—21no—
184C23×D47C2×D411yescharacteristic
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47#4114yes—
191C2×Q8×C47C2412yes—
192C2×Q8×C47C2412yes—
193C2×D4×C47—21no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47C2412yes—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2411yescharacteristic
203C2×C22⋊D47—24no—
204C2×C22⋊D47—44no—
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#10625354—216no—
214#10625354—28no—
215#10625354—28no—
216C2×D188—28no—
217C2×D188—24no—
218C2×D188—21no—
219C2×D188—22no—
220C2×D188#4114yes—
221C2×D188C2412yes—
222C2×C4×D47—28no—
223C2×C4×D47—22no—
224C2×C4×D47—22no—
225C2×C4×D47—24no—
226C2×C4×D47—24no—
227C2×C4×D47—24no—
228C2×C4×D47—24no—
229C2×C4×D47—42no—
230C2×C4×D47—44no—
231C2×C4×D47—44no—
232C2×C4×D47C2×D412yes—
233C2×C4×D47C2×D414yes—
234C2×C4×D47C2×D414yes—
235C2×C4×D47C2412yes—
236Q16×C47—28no—
237SD16×C47—28no—
238C2×C8×C47—22no—
239C2×C8×C47—22no—
240C2×C8×C47C2412yes—
241C2×C8×C47C2412yes—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47C2412yes—
245C22⋊C4×C47—24no—
246C22⋊C4×C47—24no—
247C42×C47—24no—
248C42×C47C2×D412yes—
249C42×C47C2412yes—
250C22⋊Dic47—24no—
251C22⋊Dic47—24no—
252#10625336—28no—
253#10625334—28no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47—21no—
261C4⋊Dic47—24no—
262C4⋊Dic47—24no—
263C4⋊Dic47C2412yes—
264C4⋊Dic47C2412yes—
265C4⋊Dic47C2412yes—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269C4×Dic47—24no—
270C4×Dic47—24no—
271C4×Dic47—24no—
272C4×Dic47C2×D414yes—
273C4×Dic47C2×D412yes—
274C4×Dic47C2×D414yes—
275C4×Dic47C2412yes—
276C2×C47⋊C8—22no—
277C2×C47⋊C8—22no—
278C2×C47⋊C8C2412yes—
279C2×C47⋊C8C2412yes—
280C23×C47—22no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D411yescharacteristic
285C22×D47—22no—
286C22×D47—24no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47C22×D412yes—
293Q8×C47—24no—
294Q8×C47—22no—
295Q8×C47—22no—
296Q8×C47—22no—
297Q8×C47—42no—
298Q8×C47C2×#4114yes—
299D4×C47—22no—
300D4×C47—22no—
301D4×C47—42no—
302C2×C4×C47—24no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D412yes—
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C2×#4112yes—
314C2×C4×C47C2×#4112yes—
315C2×C4×C47C2511yescharacteristic
316C22⋊D47—48no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—48no—
326C2×Dic47#13514yes—
327C2×Dic47C22×D412yes—
328C2×Dic47C22×D412yes—
329C2×Dic47C22×D412yes—
330D188—216no—
331D188—24no—
332D188—22no—
333D188C2×#4114yes—
334C4×D47—216no—
335C4×D47—24no—
336C4×D47—22no—
337C4×D47—22no—
338C4×D47—28no—
339C4×D47—44no—
340C4×D47—48no—
341C4×D47—48no—
342C8×C47—22no—
343C8×C47—22no—
344C47⋊C8—22no—
345C47⋊C8—22no—
346C2×#3102—471nomaximal, Sylow
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—84no—
351C22×C47#52512yes—
352C22×C47C2×#13512yes—
353C22×C47#57512yes—
354C22×C47C23×D411yescharacteristic
355C2×D47—22no—
356C2×D47—24no—
357C2×D47—22no—
358C2×D47—22no—
359C2×D47—44no—
360C2×D47—48no—
361C2×D47—42no—
362C2×D47—42no—
363C4×C47—24no—
364C4×C47—22no—
365C4×C47—22no—
366C4×C47—42no—
367C4×C47—42no—
368C4×C47#52512yes—
369C4×C47C22×#4111yescharacteristic
370C4×C47C22×#4111yescharacteristic
371Dic47—22no—
372Dic47—22no—
373Dic47—42no—
374Dic47—42no—
375Dic47—42no—
376Dic47C2×#13514yes—
377C2×#529—471no—
378C2×C4×#41—471no—
379#3102—4716no—
380C2×#485—471no—
381C2×#482—471no—
382C2×#479—471no—
383C2×#478—471no—
384C2×#464D4711yescharacteristic, complemented
385C2×#463—471no—
386C2×#452—471no—
387C2×#449—471no—
388C2×C4×Q16—471no—
389C2×C4×SD16—471no—
390C2×C4×SD16—471no—
391C2×C4×D8—471no—
392C2×#431—471no—
393C2×C47—82no—
394C2×C47#310214yescomplemented
395C2×C47C2×#52511yescharacteristic
396C2×C47C22×#13511yescharacteristic
397C2×C47C2×#57511yescharacteristic
398D47—42no—
399D47—44no—
400C22×#41—471no—
401C22×Q16C2×D4711yescharacteristic
402C22×SD16—471no—
403C22×SD16C2×D4711yescharacteristic
404C22×D8—471no—
405#529—478no—
406#529—944no—
407C2×#126—941no—
408C2×#125—471no—
409C2×#124C2×D4711yescharacteristic
410C2×#123—941no—
411C2×C22⋊Q8—471no—
412C2×#121—471no—
413C4×#41—478no—
414C4×#41—944no—
415C2×C4×Q8—471no—
416C2×C4×Q8—471no—
417C2×C4×Q8C2×D4711yescharacteristic
418C2×C4×D4—471no—
419C2×C4×D4—471no—
420C2×C4×D4—471no—
421C2×C4×D4—941no—
422C2×C4×D4—941no—
423C2×C4×D4—941no—
424C2×#117—471no—
425C2×#117—941no—
426C2×#117—941no—
427C22×C42—471no—
428C22×C42—941no—
429#485—478no—
430#482—478no—
431#479—478no—
432#478—478no—
433#464C2×D4718yescomplemented
434#463—478no—
435#452—478no—
436#449—478no—
437C4×Q16—478no—
438C4×SD16—478no—
439C4×SD16—478no—
440C4×D8—478no—
441#431—478no—
442C2×#107—471no—
443C2×#107—471no—
444C2×#106—471no—
445C2×#106—471no—
446C2×C4⋊C8—471no—
447C2×C4⋊C8C2×D4711yescharacteristic
448C2×#103—471no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#103C2×D4711yescharacteristic
452C2×#102—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×#102C2×D4711yescharacteristic
456C2×C22⋊C8—471no—
457C2×C22⋊C8—471no—
458C2×C4×C8—471no—
459C2×C4×C8—471no—
460C47C2×#310211yescharacteristic, complemented, Sylow
461C2×#41—474no—
462C2×#41—942no—
463C2×#41—944no—
464C2×#41—944no—
465C22×Q8C22×D4711yescharacteristic
466C22×Q8C22×D4711yescharacteristic
467C22×D4—471no—
468C22×D4—941no—
469C22×D4—941no—
470C22×D4C22×D4711yescharacteristic
471C23×C4—471no—
472C23×C4—471no—
473C23×C4—471no—
474C23×C4—941no—
475C23×C4—941no—
476C23×C4—941no—
477C23×C4—941no—
478C2×Q16—24no—
479C2×Q16C22×D4714yes—
480C2×SD16—24no—
481C2×SD16—474no—
482C2×SD16—944no—
483C2×SD16C22×D4714yes—
484C2×D8—474no—
485C2×D8—944no—
486C22×C8—471no—
487C22×C8—471no—
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490#126—948no—
491#125—474no—
492#125—942no—
493#124—22no—
494#124C22×D4714yes—
495#123—948no—
496C22⋊Q8—474no—
497C22⋊Q8—942no—
498#121—474no—
499#121—942no—
500C4×Q8—22no—
501C4×Q8—474no—
502C4×Q8—474no—
503C4×Q8—942no—
504C4×Q8—942no—
505C4×Q8C22×D4714yes—
506C4×D4—474no—
507C4×D4—474no—
508C4×D4—474no—
509C4×D4—948no—
510C4×D4—942no—
511C4×D4—942no—
512C4×D4—948no—
513C4×D4—948no—
514C4×D4—942no—
515#117—474no—
516#117—948no—
517#117—948no—
518#117—942no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C42—21no—
538C2×C42—471no—
539C2×C42—471no—
540C2×C42—471no—
541C2×C42—474no—
542C2×C42—474no—
543C2×C42—948no—
544C2×C42—941no—
545C2×C42—941no—
546C2×C42—941no—
547C2×C42C22×D4711yescharacteristic
548#107—474no—
549#107—474no—
550#106—474no—
551#106—474no—
552C4⋊C8—474no—
553C4⋊C8C22×D4714yes—
554#103—474no—
555#103—474no—
556#103—474no—
557#103C22×D4714yes—
558#102—474no—
559#102—474no—
560#102—474no—
561#102C22×D4714yes—
562C22⋊C8—474no—
563C22⋊C8—474no—
564C4×C8—474no—
565C4×C8—474no—
566C24—21no—
567C24—471no—
568C24—941no—
569#41—948no—
570#41—9416no—
571#41—948no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8#1062535214yes—
578C2×Q8C23×D4712yes—
579C2×Q8C23×D4712yes—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—474no—
584C2×D4—472no—
585C2×D4—944no—
586C2×D4—948no—
587C2×D4—944no—
588C2×D4—941no—
589C2×D4—942no—
590C2×D4—1884no—
591C2×D4C23×D4712yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—471no—
596C22×C4—471no—
597C22×C4—471no—
598C22×C4—472no—
599C22×C4—474no—
600C22×C4—472no—
601C22×C4—474no—
602C22×C4—944no—
603C22×C4—944no—
604C22×C4—944no—
605C22×C4—948no—
606C22×C4—944no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—944no—
613C22×C4—1882no—
614C22×C4—1884no—
615C22×C4—1884no—
616C22×C4—1884no—
617C22×C4D4×D4711yescharacteristic
618C22×C4D4×D4711yescharacteristic
619C22×C4C23×D4711yescharacteristic
620Q16—28no—
621SD16—28no—
622SD16—948no—
623D8—948no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—472no—
627C2×C8—472no—
628C2×C8—942no—
629C2×C8—942no—
630C2×C8C23×D4712yes—
631C2×C8C23×D4712yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—472no—
635C4⋊C4—472no—
636C4⋊C4—472no—
637C4⋊C4—944no—
638C4⋊C4—944no—
639C4⋊C4—944no—
640C4⋊C4—944no—
641C4⋊C4—944no—
642C4⋊C4—941no—
643C4⋊C4—941no—
644C4⋊C4—941no—
645C4⋊C4C23×D4712yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C22⋊C4—944no—
651C22⋊C4—944no—
652C22⋊C4—944no—
653C22⋊C4—944no—
654C42—24no—
655C42—474no—
656C42—474no—
657C42—472no—
658C42—472no—
659C42—944no—
660C42—944no—
661C42—944no—
662C42D4×D4712yes—
663C42C23×D4712yes—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—472no—
669C23—944no—
670C23—942no—
671C23—942no—
672C23—942no—
673C23—942no—
674C23—1882no—
675C23—1882no—
676C23C2×D4×D4711yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—42no—
682Q8C2×#1062535214yes—
683D4—22no—
684D4—22no—
685D4—42no—
686D4—474no—
687D4—9416no—
688D4—944no—
689D4—942no—
690D4—1888no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—474no—
700C2×C4—472no—
701C2×C4—472no—
702C2×C4—472no—
703C2×C4—948no—
704C2×C4—9416no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—944no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—1884no—
714C2×C4—1888no—
715C2×C4—1888no—
716C2×C4—1888no—
717C2×C4—1882no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4C2×D4×D4712yes—
721C2×C4C2×D4×D4712yes—
722C2×C4C2×D4×D4711yescharacteristic
723C2×C4#41×D4712yes—
724C2×C4C2×#1062535212yes—
725C2×C4C24×D4711yescharacteristic
726C8—22no—
727C8—22no—
728C8—942no—
729C8—942no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—942no—
735C22—942no—
736C22—944no—
737C22—942no—
738C22—1882no—
739C22—1882no—
740C22—1884no—
741C22—1888no—
742C22#1568963312yes—
743C22#135×D4712yes—
744C22#1568992212yes—
745C22C22×D4×D4711yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—474no—
752C4—942no—
753C4—942no—
754C4—1882no—
755C4—1882no—
756C4—1882no—
757C4#1568963312yes—
758C4C2×#41×D4711yescharacteristic
759C4C22×#1062535211yescharacteristic
760C2—82no—
761C2—1882no—
762C2—1884no—
763C2#2025340514yesdirect product factor
764C2C2×#1568963311yescharacteristic
765C2C2×#135×D4711yescharacteristic
766C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#464C2
socleC23×C47C22×D4
prime radicalC2×#15689267C2
hypercenterC2×#464D47
hypocenterC47C2×#3102
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
1. C2×#15689652C2semidirect
2. C2×C4×#10625354C2semidirect
3. #20253405C2direct (N × H)
4. C2×#15689462C2semidirect
5. C2×#15689445C2semidirect
6. C2×#15689430C2semidirect
7. C2×#15689424C2semidirect
8. C2×#15689335C2semidirect
9. C2×#15689284C2semidirect
11. C2×Q16×Dic47C2semidirect
12. C2×SD16×Dic47C2semidirect
13. C2×#15689208C2semidirect
14. C2×#15689203C2semidirect
15. C2×#15689175C2semidirect
16. C2×C47×#464C2semidirect
21. #15689652C22semidirect
28. C4×#10625354C22semidirect
42. #15689462C22semidirect
43. #15689445C22semidirect
44. #15689430C22semidirect
45. #15689424C22semidirect
46. #15689335C22semidirect
47. #15689284C22semidirect
49. Q16×Dic47C22semidirect
50. SD16×Dic47C22semidirect
51. #15689208C22semidirect
52. #15689203C22semidirect
53. #15689175C22semidirect
73. C47×#464C22semidirect
384. C2×#464D47semidirect
394. C2×C47#3102semidirect
433. #464C2×D47semidirect
460. C47C2×#3102semidirect
763. C2#20253405direct (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×#106253542
#202534052
C2×#156894622
C2×#156894452
C2×#156894302
C2×#156894242
C2×#156893352
C2×#156892842
C2×#156892672
C2×Q16×Dic472
C2×SD16×Dic472
C2×#156892082
C2×#156892032
C2×#156891752
C2×C47×#4642
C2×#310247