Finite Group Databasebeta

← #26376833

Subgroups — #26376833

Order 12032.

2698 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689635C211yesmaximal, characteristic
2#20246518C214yesmaximal, complemented
3#20246428C212yesmaximal, complemented
4#20246414C212yesmaximal, complemented
5#20246359C212yesmaximal, complemented
6#20246321C212yesmaximal, complemented
7#20246273C211yesmaximal, characteristic, complemented
8#20246228C211yesmaximal, characteristic, complemented
9#20246216C211yesmaximal, characteristic, complemented
10#20246041C214yesmaximal, complemented
11#20246019C212yesmaximal, complemented
12C4×#13094004C212yesmaximal, complemented
13#20245896C212yesmaximal, complemented
14#20245770C211yesmaximal, characteristic, complemented
15#20245748C212yesmaximal, complemented
16C4×C22⋊C4×D47C211yesmaximal, characteristic, complemented
17C47×#2347C211yesmaximal, characteristic, complemented
18C22×#10625350C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20#15689635C4116yescomplemented
21C2×#13094008C2212yes—
22C2×#13094004C2211yescharacteristic
23C2×#13094004C2211yescharacteristic
24C2×#13093999C2211yescharacteristic
25C2×#13093999C2211yescharacteristic
26C2×#13093994C2212yes—
27C2×C4×Dic94C2212yescomplemented
28C2×C4×D188C2212yes—
29C2×C4×D188C2212yes—
30C2×#13093986C2214yes—
31C2×#13093986C2212yescomplemented
32C2×#13093982C2212yes—
33C2×C22⋊C4×D47C2212yes—
34C2×C42×D47C2212yes—
35#15689028C2212yescomplemented
36#15689025C2214yes—
37#15689025C2212yescomplemented
38#15689023C2214yes—
39#15689022C2212yescomplemented
40#15689016C2214yes—
41#15689015C2214yescomplemented
42#15689013C2214yes—
43#15689013C2214yescomplemented
44#15689012C2214yes—
45#15689008C2214yescomplemented
46#15689006C2214yescomplemented
47#15689001C2214yes—
48#15689001C2214yes—
49#15688999C2214yes—
50#15688997C2214yes—
51#15688989C2212yescomplemented
52#15688985C2212yes—
53#15688985C2212yescomplemented
54#15688983C2211yescharacteristic
55#15688982C2212yescomplemented
56#15688980C2212yes—
57#15688978C2212yes—
58C4⋊C4×Dic47C2212yescomplemented
59C4⋊C4×Dic47C2214yescomplemented
60C4×C4⋊Dic47C2214yescomplemented
61C22⋊C4×Dic47C2212yes—
62C22⋊C4×Dic47C2212yes—
63C4×(C2×D47)⋊C4C2214yes—
64C4×(C2×D47)⋊C4C2212yes—
65C4×(C2×D47)⋊C4C2214yescomplemented
66C4×C22⋊Dic47C2211yescharacteristic
67#15688970C2212yes—
68#15688970C2211yescharacteristic
69#15688970C2211yescharacteristic
70#15688970C2214yescomplemented
71#15688970C2212yescomplemented
72#15688969C2212yescomplemented
73#95×D47C2211yescharacteristic
74#95×D47C2211yescharacteristic
75#95×D47C2212yescomplemented
76C2×#117×C47C2211yescharacteristic
77C47×#389C2212yescomplemented
78C47×#388C2214yes—
79C47×#383C2212yescomplemented
80C47×#380C2211yescharacteristic
81C4×C4⋊C4×C47C2212yescomplemented
82C4×C4⋊C4×C47C2212yescomplemented
83C4×C22⋊C4×C47C2211yescharacteristic
84C24×D47C2311yescharacteristic
85C2×#10625350—44no—
86C2×#10625350C2×C418yescomplemented
87C22×Dic94C2311yescharacteristic
88C22×D188C2312yes—
89C22×D188C2311yescharacteristic
90C22×D188C2312yes—
91C22×C22⋊D47C2312yes—
92C23×Dic47C2311yescharacteristic
93C22×C4×D47—44no—
94C22×C4×D47C2×C418yescomplemented
95C22×C4×D47C2311yescharacteristic
96C22×C4×D47C2311yescharacteristic
97C22×C4×D47C2312yes—
98C22×C4×D47C2314yes—
99C22×C4×D47C2311yescharacteristic
100C22×C4×D47C2312yes—
101C22×C4×D47C2311yescharacteristic
102C22×C4×D47C2312yes—
103#13094008C2×C4116yescomplemented
104#13094004C2×C418yescomplemented
105#13094004C2×C418yescomplemented
106#13093999C2×C418yes—
107#13093999C2×C418yescomplemented
108#13093994C2×C4116yescomplemented
109C4×Dic94—44no—
110C4×D188C2×C4116yescomplemented
111C4×D188C2×C4116yescomplemented
112#13093986—216no—
113#13093986—44no—
114#13093982—44no—
115C2×C4⋊Dic47C2312yes—
116C2×C4⋊Dic47C2314yes—
117C2×C4⋊Dic47C2312yes—
118C2×C4⋊Dic47C2312yes—
119C2×Dic47⋊C4C2314yes—
120C2×C22⋊Dic47C2312yes—
121C2×C22⋊Dic47C2312yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2312yes—
124C2×(C2×D47)⋊C4C2312yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2312yes—
130C2×(C2×D47)⋊C4C2312yes—
131C2×(C2×D47)⋊C4C2312yes—
132C2×(C2×D47)⋊C4C2312yes—
133C22⋊C4×D47—28no—
134C2×C4×Dic47C2314yes—
135C2×C4×Dic47C2312yes—
136C2×C4×Dic47C2312yes—
137C2×C4×Dic47C2314yes—
138C2×C4×Dic47C2312yes—
139C2×C4×Dic47C2314yes—
140C42×D47—44no—
141C47⋊#95C2311yescharacteristic
142C47⋊#95C2311yescharacteristic
143C47⋊#95C2312yes—
144C47⋊#95C2312yes—
145C47⋊#95C2314yes—
146C47⋊#95C2312yes—
147C47⋊#95C2314yes—
148C47⋊#95C2314yes—
149C47⋊#95C2314yes—
150C47⋊#95C2314yes—
151C23×C4×C47C2311yescharacteristic
152#117×C47C2×C418yescomplemented
153C2×C4⋊C4×C47C2314yes—
154C2×C4⋊C4×C47C2312yes—
155C2×C4⋊C4×C47C2311yescharacteristic
156C2×C4⋊C4×C47C2311yescharacteristic
157C2×C22⋊C4×C47C2312yes—
158C2×C22⋊C4×C47C2312yes—
159C2×C22⋊C4×C47C2312yes—
160C2×C42×C47C2312yes—
161C2×C42×C47C2314yes—
162C2×C42×C47C2312yes—
163#95×C47C2311yescharacteristic
164#95×C47C2311yescharacteristic
165#95×C47C2312yes—
166#95×C47C2314yes—
167#95×C47C2314yes—
168C24×C47C2411yescharacteristic
169C23×D47—24no—
170C23×D47—42no—
171C23×D47—41no—
172C23×D47—41no—
173C23×D47C22×C414yes—
174C23×D47C2411yescharacteristic
175C23×D47C2412yes—
176C23×D47C2411yescharacteristic
177C22×C4×C47—24no—
178C22×C4×C47C22×C414yes—
179C22×C4×C47C2414yes—
180C22×C4×C47C2412yes—
181C22×C4×C47C2412yes—
182C22×C4×C47C2411yescharacteristic
183C22×C4×C47C2412yes—
184C22×C4×C47C2412yes—
185C22×C4×C47C2411yescharacteristic
186C2×C22⋊D47—44no—
187C2×C22⋊D47C22×C418yes—
188C22×Dic47—42no—
189C22×Dic47C22×C414yes—
190C22×Dic47C2412yes—
191C22×Dic47C2414yes—
192C22×Dic47C2411yescharacteristic
193C22×Dic47C2411yescharacteristic
194C22×Dic47C2412yes—
195C22×Dic47C2412yes—
196#10625350—416no—
197C2×D188—28no—
198C2×D188—24no—
199C2×D188—42no—
200C2×D188—42no—
201C2×D188C22×C418yes—
202C2×D188C22×C414yes—
203C2×D188C22×C418yes—
204C2×C4×D47—24no—
205C2×C4×D47—24no—
206C2×C4×D47—24no—
207C2×C4×D47—28no—
208C2×C4×D47—416no—
209C2×C4×D47—42no—
210C2×C4×D47—42no—
211C2×C4×D47—42no—
212C2×C4×D47—42no—
213C2×C4×D47—42no—
214C2×C4×D47—42no—
215C2×C4×D47—44no—
216C2×C4×D47—44no—
217C2×C4×D47—44no—
218C2×C4×D47C22×C414yes—
219C2×C4×D47C22×C414yes—
220C2×C4×D47C22×C414yes—
221C2×C4×D47C22×C414yes—
222C2×C4×D47C22×C418yes—
223C2×C4×D47#4118yescomplemented
224C2×Dic94—24no—
225C2×Dic94C22×C414yes—
226C4⋊C4×C47—28no—
227C4⋊C4×C47—24no—
228C4⋊C4×C47C22×C414yes—
229C4⋊C4×C47C22×C414yes—
230C22⋊C4×C47—24no—
231C22⋊C4×C47—42no—
232C22⋊C4×C47C22×C418yes—
233C42×C47—24no—
234C42×C47—44no—
235C42×C47C22×C418yes—
236C22⋊Dic47—24no—
237C22⋊Dic47—42no—
238(C2×D47)⋊C4—28no—
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4—28no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—44no—
243(C2×D47)⋊C4—44no—
244(C2×D47)⋊C4—44no—
245(C2×D47)⋊C4C22×C418yes—
246(C2×D47)⋊C4C22×C418yes—
247(C2×D47)⋊C4C22×C418yes—
248(C2×D47)⋊C4C22×C418yes—
249C4⋊Dic47—24no—
250C4⋊Dic47—44no—
251C4⋊Dic47C22×C418yes—
252C4⋊Dic47C22×C418yes—
253Dic47⋊C4—44no—
254C4×Dic47—24no—
255C4×Dic47—28no—
256C4×Dic47—42no—
257C4×Dic47—42no—
258C4×Dic47—44no—
259C4×Dic47—44no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47C23×C412yes—
265C23×C47C2511yescharacteristic
266C22×D47—22no—
267C22×D47—21no—
268C22×D47—21no—
269C22×D47—22no—
270C22×D47—24no—
271C22×D47—22no—
272C22×D47—24no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—21no—
276C22×D47—21no—
277C22×D47—28no—
278C22×D47—44no—
279C22×D47—44no—
280C22×D47—48no—
281C22×D47—48no—
282C22×D47C23×C412yes—
283C22×D47C23×C414yes—
284C22×D47C23×C412yes—
285C22×D47C2×#4114yes—
286C2×C4×C47—24no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—28no—
293C2×C4×C47—22no—
294C2×C4×C47—24no—
295C2×C4×C47—22no—
296C2×C4×C47—24no—
297C2×C4×C47—22no—
298C2×C4×C47—24no—
299C2×C4×C47C23×C414yes—
300C2×C4×C47C23×C414yes—
301C2×C4×C47C23×C412yes—
302C2×C4×C47C23×C412yes—
303C2×C4×C47C2×#4114yes—
304C2×C4×C47H(5,𝔽2)14yes—
305C22⋊D47—48no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—24no—
310C2×Dic47—22no—
311C2×Dic47—24no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—24no—
315C2×Dic47—22no—
316C2×Dic47—24no—
317C2×Dic47—44no—
318C2×Dic47C23×C414yes—
319C2×Dic47C23×C412yes—
320C2×Dic47C23×C412yes—
321C2×Dic47C2×#4114yes—
322D188—216no—
323D188—28no—
324D188—48no—
325C4×D47—28no—
326C4×D47—28no—
327C4×D47—44no—
328C4×D47—44no—
329C4×D47—48no—
330C4×D47—48no—
331C4×D47—48no—
332C4×D47—88no—
333Dic94—28no—
334#34223—471nomaximal, Sylow
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47C24×C411yescharacteristic
341C22×C47C22×#4112yes—
342C22×C47C2×H(5,𝔽2)12yes—
343C22×C47#58511yescharacteristic
344C22×C47#58511yescharacteristic
345C2×D47—22no—
346C2×D47—22no—
347C2×D47—24no—
348C2×D47—24no—
349C2×D47—24no—
350C2×D47—22no—
351C2×D47—22no—
352C2×D47—24no—
353C2×D47—22no—
354C2×D47—24no—
355C2×D47—416no—
356C2×D47—44no—
357C2×D47—42no—
358C2×D47—44no—
359C2×D47—42no—
360C2×D47C4×#4114yes—
361C4×C47—24no—
362C4×C47—22no—
363C4×C47—24no—
364C4×C47—24no—
365C4×C47—44no—
366C4×C47—42no—
367C4×C47#51814yes—
368Dic47—24no—
369Dic47—22no—
370Dic47—22no—
371Dic47—24no—
372Dic47—42no—
373Dic47—44no—
374C2×#525—471no—
375#2374—474no—
376#2363—472no—
377#2362—472no—
378#2357—472no—
379#2353—472no—
380#2347D4711yescharacteristic, complemented
381#2346—471no—
382#2341—471no—
383#2339—471no—
384#2321—474no—
385#2318—472no—
386C4×C22⋊Q8—472no—
387C4×#121—472no—
388#2280—471no—
389#2275—472no—
390C2×C4×C22⋊C4—471no—
391C2×C47—42no—
392C2×C47C2×C4×#4111yescharacteristic
393C2×C47C2×#51811yescharacteristic
394C2×C47#342811yescharacteristic
395C2×C47#350512yes—
396C2×C47#350612yes—
397D47—24no—
398D47—44no—
399D47—42no—
400C22×#41—471no—
401C24×C4—471no—
402#525—4716no—
403C2×#123—472no—
404C2×C22⋊Q8—471no—
405C2×C22⋊Q8—471no—
406C2×#121—471no—
407C2×#121—471no—
408C2×#120—472no—
409C2×C4×Q8—472no—
410C2×C4×D4—474no—
411C2×C4×D4—472no—
412C2×C4×D4—472no—
413C2×C4×D4—472no—
414C2×#117—472no—
415C2×#117C2×D4711yescharacteristic
416C22×C22⋊C4—472no—
417C22×C42—472no—
418#391—472no—
419#390—474no—
420#390—474no—
421#390—472no—
422#389—472no—
423#389C2×D4712yescomplemented
424#388—474no—
425#388—474no—
426#388—474no—
427#388—474no—
428#388—474no—
429#388C2×D4714yes—
430#387—474no—
431#387—474no—
432#386—474no—
433#386—474no—
434#386—474no—
435#385—474no—
436#383C2×D4712yescomplemented
437#382—472no—
438#381—472no—
439#381—472no—
440#380—471no—
441#380—472no—
442#380—472no—
443#380C2×D4711yescharacteristic
444#379—472no—
445C4×C4⋊C4—472no—
446C4×C4⋊C4—474no—
447C4×C4⋊C4—474no—
448C4×C4⋊C4C2×D4712yescomplemented
449C4×C4⋊C4C2×D4712yescomplemented
450C4×C22⋊C4—471no—
451C4×C22⋊C4—472no—
452C4×C22⋊C4—472no—
453C4×C22⋊C4—474no—
454C4×C22⋊C4—472no—
455C4×C22⋊C4—474no—
456C4×C22⋊C4—472no—
457C4×C22⋊C4—471no—
458C4×C22⋊C4—471no—
459C4×C22⋊C4—472no—
460C4×C22⋊C4—474no—
461C4×C22⋊C4C2×D4711yescharacteristic
462#376—472no—
463C2×#95—471no—
464C2×#95—471no—
465C2×#95—472no—
466C47#3422311yescharacteristic, complemented, Sylow
467C25—471no—
468C2×#41—478no—
469C2×#41—1884no—
470C22×Q8—471no—
471C22×D4—472no—
472C22×D4—472no—
473C22×D4—471no—
474C22×D4—472no—
475C23×C4—471no—
476C23×C4—471no—
477C23×C4—471no—
478C23×C4—478no—
479C23×C4—472no—
480C23×C4—471no—
481C23×C4—471no—
482C23×C4—472no—
483C23×C4—472no—
484C23×C4—474no—
485C23×C4—1884no—
486C23×C4C22×D4711yescharacteristic
487#123—4716no—
488C22⋊Q8—478no—
489C22⋊Q8—478no—
490#121—478no—
491#121—478no—
492#120—4716no—
493C4×Q8—1884no—
494C4×D4—4716no—
495C4×D4—4716no—
496C4×D4—9416no—
497C4×D4—1884no—
498#117—1884no—
499#117C4×D4718yescomplemented
500C2×C4⋊C4—472no—
501C2×C4⋊C4—472no—
502C2×C4⋊C4—472no—
503C2×C4⋊C4—474no—
504C2×C4⋊C4—474no—
505C2×C4⋊C4C22×D4712yes—
506C2×C4⋊C4C22×D4714yes—
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C22⋊C4—472no—
510C2×C22⋊C4—472no—
511C2×C22⋊C4—472no—
512C2×C22⋊C4—472no—
513C2×C22⋊C4—472no—
514C2×C22⋊C4—472no—
515C2×C22⋊C4—472no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—472no—
519C2×C22⋊C4—474no—
520C2×C22⋊C4—474no—
521C2×C22⋊C4—474no—
522C2×C22⋊C4—948no—
523C2×C22⋊C4C22×D4712yes—
524C2×C22⋊C4C22×D4712yes—
525C2×C22⋊C4C22×D4712yes—
526C2×C42—474no—
527C2×C42—472no—
528C2×C42—474no—
529C2×C42—474no—
530C2×C42—472no—
531C2×C42—472no—
532C2×C42—1884no—
533C2×C42C22×D4712yes—
534C2×C42C22×D4714yes—
535C2×C42C22×D4712yes—
536#95—471no—
537#95—472no—
538#95—471no—
539#95—472no—
540#95—474no—
541#95—472no—
542#95—474no—
543#95—474no—
544#95—474no—
545#95—474no—
546#95C22×D4711yescharacteristic
547#95C22×D4711yescharacteristic
548#95C22×D4712yes—
549#95C22×D4714yes—
550#95C22×D4714yes—
551C24—471no—
552C24—471no—
553C24—472no—
554C24—474no—
555C24—944no—
556C24—1882no—
557C24—1881no—
558C24—1881no—
559C24C23×D4711yescharacteristic
560#41—18816no—
561C2×Q8—474no—
562C2×Q8—944no—
563C2×D4—478no—
564C2×D4—478no—
565C2×D4—474no—
566C2×D4—478no—
567C2×D4—948no—
568C2×D4—944no—
569C2×D4—1882no—
570C2×D4—1882no—
571C2×D4—1884no—
572C22×C4—24no—
573C22×C4—472no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—472no—
577C22×C4—474no—
578C22×C4—474no—
579C22×C4—474no—
580C22×C4—474no—
581C22×C4—474no—
582C22×C4—478no—
583C22×C4—478no—
584C22×C4—472no—
585C22×C4—474no—
586C22×C4—948no—
587C22×C4—944no—
588C22×C4—944no—
589C22×C4—944no—
590C22×C4—18816no—
591C22×C4—1884no—
592C22×C4—1884no—
593C22×C4—1882no—
594C22×C4—1882no—
595C22×C4—1882no—
596C22×C4—1882no—
597C22×C4—1882no—
598C22×C4—1882no—
599C22×C4—1884no—
600C22×C4—1882no—
601C22×C4C2×C4×D4714yes—
602C22×C4C23×D4714yes—
603C22×C4C23×D4712yes—
604C22×C4C23×D4711yescharacteristic
605C22×C4C23×D4712yes—
606C22×C4C23×D4712yes—
607C22×C4C23×D4712yes—
608C22×C4C23×D4711yescharacteristic
609C4⋊C4—28no—
610C4⋊C4—24no—
611C4⋊C4—478no—
612C4⋊C4—478no—
613C4⋊C4—944no—
614C4⋊C4—1884no—
615C4⋊C4—1884no—
616C4⋊C4C2×C4×D4714yes—
617C4⋊C4C2×C4×D4714yes—
618C22⋊C4—24no—
619C22⋊C4—42no—
620C22⋊C4—478no—
621C22⋊C4—478no—
622C22⋊C4—478no—
623C22⋊C4—478no—
624C22⋊C4—944no—
625C22⋊C4—948no—
626C22⋊C4—944no—
627C22⋊C4—944no—
628C22⋊C4—948no—
629C22⋊C4—1884no—
630C22⋊C4—1884no—
631C22⋊C4—1884no—
632C22⋊C4—1882no—
633C22⋊C4C2×C4×D4718yes—
634C42—24no—
635C42—44no—
636C42—948no—
637C42—944no—
638C42—1882no—
639C42—1882no—
640C42—1884no—
641C42—1884no—
642C42C2×C4×D4718yes—
643C23—22no—
644C23—22no—
645C23—21no—
646C23—21no—
647C23—472no—
648C23—474no—
649C23—472no—
650C23—474no—
651C23—948no—
652C23—942no—
653C23—941no—
654C23—941no—
655C23—942no—
656C23—944no—
657C23—942no—
658C23—944no—
659C23—942no—
660C23—941no—
661C23—942no—
662C23—941no—
663C23—1884no—
664C23—1884no—
665C23—1888no—
666C23—1888no—
667C23C22×C4×D4712yes—
668C23C24×D4711yescharacteristic
669Q8—948no—
670D4—9416no—
671D4—948no—
672D4—1888no—
673D4—1888no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—28no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—472no—
688C2×C4—472no—
689C2×C4—474no—
690C2×C4—474no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—944no—
695C2×C4—942no—
696C2×C4—948no—
697C2×C4—948no—
698C2×C4—944no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—944no—
702C2×C4—944no—
703C2×C4—942no—
704C2×C4—3768no—
705C2×C4—1888no—
706C2×C4—1884no—
707C2×C4—1884no—
708C2×C4—1888no—
709C2×C4—1888no—
710C2×C4—1884no—
711C2×C4C22×C4×D4712yes—
712C2×C4C22×C4×D4714yes—
713C2×C4C22×C4×D4714yes—
714C2×C4C22×C4×D4712yes—
715C2×C4#41×D4714yes—
716C2×C4#1309407014yes—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—42no—
721C22—42no—
722C22—474no—
723C22—942no—
724C22—942no—
725C22—944no—
726C22—944no—
727C22—944no—
728C22—942no—
729C22—942no—
730C22—944no—
731C22—942no—
732C22—944no—
733C22—18816no—
734C22—1884no—
735C22—1882no—
736C22—1882no—
737C22—1884no—
738C22C23×C4×D4711yescharacteristic
739C22C2×#41×D4712yes—
740C22C2×#1309407012yes—
741C22#1568995811yescharacteristic
742C22#1568996011yescharacteristic
743C4—24no—
744C4—22no—
745C4—24no—
746C4—24no—
747C4—44no—
748C4—42no—
749C4—942no—
750C4—942no—
751C4—944no—
752C4—944no—
753C4—1882no—
754C4—1884no—
755C4#1568959714yes—
756C2—42no—
757C2—944no—
758C2—1882no—
759C2—1884no—
760C2C4×#41×D4711yescharacteristic
761C2C2×#1568959711yescharacteristic
762C2#2025658811yescharacteristic
763C2#2025721712yes—
764C2#2025724112yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2347C2
socle, cosocleC23×C47C25
prime radicalC2×#15689635C2
hypercenter#2347D47
hypocenterC47#34223
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #20246518C2semidirect
3. #20246428C2semidirect
4. #20246414C2semidirect
5. #20246359C2semidirect
6. #20246321C2semidirect
7. #20246273C2semidirect
8. #20246228C2semidirect
9. #20246216C2semidirect
10. #20246041C2semidirect
11. #20246019C2semidirect
12. C4×#13094004C2semidirect
13. #20245896C2semidirect
14. #20245770C2semidirect
15. #20245748C2semidirect
16. C4×C22⋊C4×D47C2semidirect
17. C47×#2347C2semidirect
20. #15689635C4semidirect
27. C2×C4×Dic94C22semidirect
31. C2×#13093986C22semidirect
35. #15689028C22semidirect
37. #15689025C22semidirect
39. #15689022C22semidirect
41. #15689015C22semidirect
43. #15689013C22semidirect
45. #15689008C22semidirect
46. #15689006C22semidirect
51. #15688989C22semidirect
53. #15688985C22semidirect
55. #15688982C22semidirect
58. C4⋊C4×Dic47C22semidirect
59. C4⋊C4×Dic47C22semidirect
60. C4×C4⋊Dic47C22semidirect
65. C4×(C2×D47)⋊C4C22semidirect
70. #15688970C22semidirect
71. #15688970C22semidirect
72. #15688969C22semidirect
75. #95×D47C22semidirect
77. C47×#389C22semidirect
79. C47×#383C22semidirect
81. C4×C4⋊C4×C47C22semidirect
82. C4×C4⋊C4×C47C22semidirect
86. C2×#10625350C2×C4semidirect
94. C22×C4×D47C2×C4semidirect
103. #13094008C2×C4semidirect
104. #13094004C2×C4semidirect
105. #13094004C2×C4semidirect
107. #13093999C2×C4semidirect
108. #13093994C2×C4semidirect
110. C4×D188C2×C4semidirect
111. C4×D188C2×C4semidirect
152. #117×C47C2×C4semidirect
223. C2×C4×D47#41semidirect
380. #2347D47semidirect
423. #389C2×D47semidirect
436. #383C2×D47semidirect
448. C4×C4⋊C4C2×D47semidirect
449. C4×C4⋊C4C2×D47semidirect
466. C47#34223semidirect
499. #117C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896352
#202465182
#202464282
#202464142
#202463592
#202463212
#202462732
#202462282
#202462162
#202460412
#202460192
C4×#130940042
#202458962
#202457702
#202457482
C4×C22⋊C4×D472
C47×#23472
#3422347