Finite Group Databasebeta

← #26221978

Subgroups — #26221978

Order 12032.

1468 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625350C211yesmaximal, characteristic
2C2×#15689283C211yesmaximal, characteristic
3C2×#15689228C211yesmaximal, characteristic, complemented
4C2×#15689221C211yesmaximal, characteristic, complemented
5#20243732C211yesmaximal, characteristic, complemented
6#20243725C211yesmaximal, characteristic, complemented
7#20243701C211yesmaximal, characteristic, complemented
8#20243648C211yesmaximal, characteristic, complemented
9#20243641C211yesmaximal, characteristic, complemented
10#20243585C211yesmaximal, characteristic, complemented
11#20243326C211yesmaximal, characteristic
12#20243221C211yesmaximal, characteristic, complemented
13#20243216C211yesmaximal, characteristic, complemented
14#20243150C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C22×#10625337C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19C4×#10625350—24no—
20C4×#10625350—24no—
21C2×C4×Dic94C2211yescharacteristic
22C2×C4×Dic94C2211yescharacteristic
23C2×C4×D188C2211yescharacteristic
24C2×C4×D188C2211yescharacteristic
25C2×C4×C22⋊D47—21no—
26C2×C4×C22⋊D47—21no—
27C2×#13093983C2211yescharacteristic
28C2×#13093981—21no—
29C2×C42×D47—21no—
30#15689283C418yescomplemented
31#15689228—24no—
32#15689221—24no—
33C2×#13093957C2211yescharacteristic
34C2×#13093955C2211yescharacteristic
35C2×#13093948C2211yescharacteristic
36C2×#13093948C2211yescharacteristic
37C2×#13093947C2211yescharacteristic
38C2×#13093947C2211yescharacteristic
39C2×#13093947C2211yescharacteristic
40C2×#13093944C2211yescharacteristic
41C2×#13093944C2211yescharacteristic
42C2×#13093944C2211yescharacteristic
43C2×C22⋊(C47⋊C8)C2211yescharacteristic
44C2×C22⋊(C47⋊C8)C2211yescharacteristic
45C2×#13093935C2211yescharacteristic
46C2×#13093935C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688878C2211yescharacteristic
53C2×C22⋊Q8×C47C2211yescharacteristic
54C2×C4×Q8×C47C2211yescharacteristic
55C22×C42×C47C2211yescharacteristic
56C47×#391C2211yescharacteristic
57C47×#389C2211yescharacteristic
58C47×#387—21no—
59C47×#385—21no—
60C47×#380C2211yescharacteristic
61C4×C4⋊C4×C47—21no—
62C4×C4⋊C4×C47C2211yescharacteristic
63C4×C22⋊C4×C47—21no—
64C2×#10625350—22no—
65C2×#10625350—22no—
66C2×#10625350—22no—
67C2×#10625350—22no—
68C2×#10625350—22no—
69C2×#10625350C2×C414yes—
70C22×Dic94C2311yescharacteristic
71C22×D188C2311yescharacteristic
72C22×C22⋊D47—21no—
73C22×C4×D47—21no—
74C22×C4×D47—21no—
75C22×C4×D47—21no—
76C2×#10625337—22no—
77C2×#10625337—22no—
78C2×#10625337C2×C414yescomplemented
79C2×#10625336—22no—
80C2×#10625336—22no—
81C2×#10625336C2×C414yescomplemented
82C22×C47⋊C8C2311yescharacteristic
83C22×C47⋊C8C2311yescharacteristic
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86C4×Dic94—22no—
87C4×Dic94—22no—
88C4×Dic94—22no—
89C4×Dic94D414yes—
90C4×D188—22no—
91C4×D188—22no—
92C4×D188—22no—
93C4×D188D414yes—
94C4×C22⋊D47—28no—
95C4×C22⋊D47—28no—
96#13093983—22no—
97#13093983—22no—
98#13093981—28no—
99C2×C4⋊Dic47C2311yescharacteristic
100C2×C4⋊Dic47C2311yescharacteristic
101C2×Dic47⋊C4—21no—
102C2×Dic47⋊C4—21no—
103C2×C22⋊Dic47—21no—
104C2×(C2×D47)⋊C4—21no—
105C2×(C2×D47)⋊C4—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47—21no—
108C2×C4×Dic47—21no—
109C42×D47—28no—
110#13093957—22no—
111#13093955—22no—
112#13093948—22no—
113#13093948—22no—
114#13093947—22no—
115#13093947—22no—
116#13093947C2×C414yescomplemented
117#13093944—22no—
118#13093944—22no—
119#13093944C2×C414yescomplemented
120C22⋊(C47⋊C8)—22no—
121C22⋊(C47⋊C8)C2×C414yescomplemented
122#13093935—22no—
123#13093935—22no—
124C22×Q8×C47C2311yescharacteristic
125C23×C4×C47D411yescharacteristic
126C23×C4×C47D411yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C22⋊Q8×C47—22no—
129C22⋊Q8×C47C2×C414yescomplemented
130C4×Q8×C47—22no—
131C4×Q8×C47—22no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47—21no—
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C4⋊C4×C47C2311yescharacteristic
138C2×C22⋊C4×C47—21no—
139C2×C22⋊C4×C47—21no—
140C2×C42×C47—22no—
141C2×C42×C47—22no—
142C2×C42×C47—21no—
143C2×C42×C47—21no—
144C2×C42×C47D411yescharacteristic
145C2×C42×C47D411yescharacteristic
146C2×C42×C47C2311yescharacteristic
147C2×C42×C47C2311yescharacteristic
148#95×C47—21no—
149#95×C47—21no—
150#95×C47—21no—
151#95×C47—21no—
152#95×C47—21no—
153C24×C47C2×D411yescharacteristic
154C23×D47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47C22×C412yes—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—41no—
173C22×C4×C47—41no—
174C22×C4×C47—41no—
175C22×C4×C47C22×C412yes—
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47#4112yes—
182C22×C4×C47C2411yescharacteristic
183C2×C22⋊D47—24no—
184C2×C22⋊D47—24no—
185C2×C22⋊D47—24no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189#10625350—28no—
190#10625350—28no—
191#10625350—28no—
192#10625350—28no—
193C2×D188—21no—
194C2×D188—21no—
195C2×D188—21no—
196C2×D188C22×C412yes—
197C2×D188C2×D412yes—
198C2×D188#4112yes—
199C2×C4×D47—24no—
200C2×C4×D47—24no—
201C2×C4×D47—24no—
202C2×C4×D47—24no—
203C2×C4×D47—24no—
204C2×C4×D47—42no—
205C2×C4×D47—42no—
206C2×C4×D47—42no—
207C2×C4×D47—42no—
208C2×Dic94—21no—
209C2×Dic94—21no—
210C2×Dic94—21no—
211C2×Dic94C22×C412yes—
212C2×Dic94C2×D412yes—
213C2×Dic94#4112yes—
214C4⋊C4×C47—24no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—42no—
221C4⋊C4×C47—42no—
222C4⋊C4×C47C22×C412yes—
223C22⋊C4×C47—24no—
224C22⋊C4×C47—42no—
225C42×C47—22no—
226C42×C47—22no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—42no—
230C42×C47—42no—
231C42×C47C2×D412yes—
232C42×C47C2×D412yes—
233C22⋊Dic47—24no—
234#10625337—28no—
235#10625336—28no—
236(C2×D47)⋊C4—24no—
237(C2×D47)⋊C4—24no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47C2×D412yes—
241C4⋊Dic47C2×D412yes—
242Dic47⋊C4—24no—
243Dic47⋊C4—24no—
244C4×Dic47—24no—
245C4×Dic47—24no—
246C4×Dic47—24no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C2×C47⋊C8C22×C412yes—
258C2×C47⋊C8C22×C412yes—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47C4×D412yes—
266C23×C47C22×D411yescharacteristic
267C22×D47—22no—
268C22×D47—22no—
269C22×D47—22no—
270C22×D47—41no—
271C22×D47—41no—
272C22×D47—41no—
273C22×D47—41no—
274Q8×C47—22no—
275Q8×C47—22no—
276Q8×C47—41no—
277Q8×C47—41no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—44no—
296C2×C4×C47—44no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47C4×D412yes—
308C2×C4×C47#12012yes—
309C2×C4×C47#12012yes—
310C2×C4×C47#13712yes—
311C2×C4×C47C23×C411yescharacteristic
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C2×#4111yescharacteristic
315C2×C4×C47C2×#4111yescharacteristic
316C2×C4×C47C2×#4111yescharacteristic
317C22⋊D47—216no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327D188—22no—
328D188—22no—
329D188—22no—
330D188C4×D414yes—
331C4×D47—216no—
332C4×D47—48no—
333C4×D47—48no—
334Dic94—22no—
335Dic94—22no—
336Dic94—22no—
337Dic94C4×D414yes—
338C47⋊C8—22no—
339C47⋊C8—22no—
340C47⋊C8—41no—
341C47⋊C8—41no—
342#21457—471nomaximal, Sylow
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47C2×C4×D411yescharacteristic
351C22×C47C2×#12011yescharacteristic
352C22×C47#52511yescharacteristic
353C22×C47C2×#13711yescharacteristic
354C22×C47#57511yescharacteristic
355C22×C47#57511yescharacteristic
356C22×C47#57511yescharacteristic
357C2×D47—24no—
358C2×D47—42no—
359C2×D47—42no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—42no—
363C2×D47—42no—
364C4×C47—22no—
365C4×C47—22no—
366C4×C47—22no—
367C4×C47—22no—
368C4×C47—42no—
369C4×C47—41no—
370C4×C47—42no—
371C4×C47—81no—
372C4×C47—81no—
373C4×C47C2×C4×D411yescharacteristic
374C4×C47C2×C4×D411yescharacteristic
375C4×C47#52511yescharacteristic
376C4×C47#52511yescharacteristic
377Dic47—24no—
378Dic47—42no—
379Dic47—42no—
380C2×C4×#41—471no—
381C2×#452—471no—
382C2×#441—471no—
383C2×#440—471no—
384C4×C22⋊Q8D4711yescharacteristic, complemented
385#1878—471no—
386#1877—471no—
387#1873—471no—
388#1864—471no—
389#1863—471no—
390#1854—471no—
391#1788—471no—
392#1763—471no—
393#1762—471no—
394#1749—471no—
395C2×C47—42no—
396C2×C47C4×#12011yescharacteristic
397C2×C47#294311yescharacteristic
398C2×C47C4×#13711yescharacteristic
399C2×C47#300511yescharacteristic
400C2×C47#300711yescharacteristic
401C2×C47#311111yescharacteristic
402C2×C47#311611yescharacteristic
403D47—44no—
404C22×#41—471no—
405C22×Q16—471no—
406C22×SD16—471no—
407C2×C22⋊Q8C2×D4711yescharacteristic
408C4×#41—944no—
409C4×#41—944no—
410C2×C4×Q8—471no—
411C2×C4×Q8—471no—
412C2×C4×Q8C2×D4711yescharacteristic
413C2×C4×D4—471no—
414C2×C4×D4—471no—
415C2×C4×D4—941no—
416C2×C4×D4—941no—
417C2×#117—471no—
418C2×#117—941no—
419C22×C42—941no—
420C22×C42C2×D4711yescharacteristic
421#452—478no—
422#441—944no—
423#440—944no—
424C2×#107—471no—
425C2×#106—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103—471no—
430C2×#103—471no—
431C2×#102—471no—
432C2×#102—471no—
433C2×#102—471no—
434C2×C22⋊C8—471no—
435C2×C22⋊C8—471no—
436C2×#97—471no—
437C2×#97—471no—
438#391C2×D4711yescharacteristic
439#389C2×D4711yescharacteristic
440#387—21no—
441#385—21no—
442#380C2×D4711yescharacteristic
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2×D4711yescharacteristic
445C4×C22⋊C4—21no—
446#340—471no—
447#340—471no—
448#340—471no—
449#340—471no—
450#336—471no—
451#336—471no—
452C47#2145711yescharacteristic, complemented, Sylow
453C2×#41—474no—
454C2×#41—942no—
455C2×#41—942no—
456C2×#41—942no—
457C2×#41—942no—
458C2×#41—942no—
459C22×Q8—471no—
460C22×Q8C22×D4711yescharacteristic
461C22×D4—471no—
462C22×D4—941no—
463C23×C4—941no—
464C23×C4—941no—
465C23×C4—941no—
466C23×C4C22⋊D4711yescharacteristic
467C23×C4C22⋊D4711yescharacteristic
468C23×C4C22×D4711yescharacteristic
469C2×Q16—474no—
470C2×Q16—942no—
471C2×Q16—942no—
472C2×SD16—474no—
473C2×SD16—942no—
474C2×SD16—942no—
475C22×C8—471no—
476C22×C8—471no—
477C22×C8—471no—
478C22×C8—471no—
479C22⋊Q8—22no—
480C22⋊Q8C4×D4714yescomplemented
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—474no—
484C4×Q8—942no—
485C4×Q8—942no—
486C4×Q8—942no—
487C4×D4—474no—
488C4×D4—942no—
489C4×D4—942no—
490C4×D4—948no—
491C4×D4—948no—
492C4×D4—942no—
493#117—948no—
494#117—942no—
495#117—942no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4C22×D4711yescharacteristic
504C2×C4⋊C4C22×D4711yescharacteristic
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—948no—
516C2×C42—941no—
517C2×C42—941no—
518C2×C42—941no—
519C2×C42C22⋊D4711yescharacteristic
520C2×C42C22⋊D4711yescharacteristic
521C2×C42C22×D4711yescharacteristic
522C2×C42C22×D4711yescharacteristic
523#107—942no—
524#106—942no—
525#103—474no—
526#103—942no—
527#103—942no—
528#103—942no—
529#103—942no—
530#102—474no—
531#102—942no—
532#102—942no—
533C22⋊C8—474no—
534C22⋊C8—942no—
535#97—942no—
536#97—942no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542C24—941no—
543C24C2×C22⋊D4711yescharacteristic
544#41—948no—
545#41—948no—
546#41—948no—
547#41—948no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—472no—
554C2×Q8—472no—
555C2×Q8—472no—
556C2×Q8—941no—
557C2×Q8—941no—
558C2×Q8—941no—
559C2×Q8C2×C4×D4712yes—
560C2×D4—472no—
561C2×D4—472no—
562C2×D4—472no—
563C2×D4—944no—
564C2×D4—944no—
565C2×D4—944no—
566C2×D4—941no—
567C2×D4—941no—
568C2×D4—941no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—944no—
584C22×C4—944no—
585C22×C4—944no—
586C22×C4—941no—
587C22×C4—944no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—944no—
591C22×C4—1882no—
592C22×C4—1882no—
593C22×C4—1882no—
594C22×C4—1882no—
595C22×C4C2×C4×D4712yes—
596C22×C4#1062535012yes—
597C22×C4C2×C22⋊D4711yescharacteristic
598C22×C4C2×C22⋊D4711yescharacteristic
599C22×C4C2×C22⋊D4711yescharacteristic
600C22×C4C2×C22⋊D4711yescharacteristic
601C22×C4C2×C22⋊D4711yescharacteristic
602C22×C4C23×D4711yescharacteristic
603Q16—948no—
604SD16—948no—
605C2×C8—472no—
606C2×C8—472no—
607C2×C8—941no—
608C2×C8—941no—
609C2×C8—941no—
610C2×C8—941no—
611C2×C8—941no—
612C2×C8—941no—
613C2×C8—941no—
614C2×C8—941no—
615C2×C8—941no—
616C2×C8—941no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—472no—
626C4⋊C4—472no—
627C4⋊C4—944no—
628C4⋊C4—944no—
629C4⋊C4—941no—
630C4⋊C4—941no—
631C4⋊C4C2×C4×D4712yes—
632C22⋊C4—24no—
633C22⋊C4—42no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C42—944no—
644C42—944no—
645C42—944no—
646C42D4×D4712yes—
647C42D4×D4712yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—942no—
655C23—942no—
656C23—942no—
657C23—1881no—
658C23—1881no—
659C23—1881no—
660C23—1881no—
661C23C4×C22⋊D4712yes—
662C23C22×C22⋊D4711yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—41no—
666Q8—41no—
667Q8—474no—
668Q8—942no—
669Q8—942no—
670Q8—942no—
671D4—474no—
672D4—9416no—
673D4—942no—
674D4—942no—
675D4—942no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—9416no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—1888no—
712C2×C4—1888no—
713C2×C4—1881no—
714C2×C4—1881no—
715C2×C4—1881no—
716C2×C4—1881no—
717C2×C4C4×C22⋊D4712yes—
718C2×C4#1309399212yes—
719C2×C4#1309399212yes—
720C2×C4#1309405512yes—
721C2×C4C22×C4×D4711yescharacteristic
722C2×C4C2×D4×D4711yescharacteristic
723C2×C4C2×D4×D4711yescharacteristic
724C2×C4#41×D4711yescharacteristic
725C2×C4#41×D4711yescharacteristic
726C2×C4C2×#1062535011yescharacteristic
727C8—942no—
728C8—942no—
729C8—1881no—
730C8—1881no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—944no—
739C22—1882no—
740C22—1882no—
741C22—1882no—
742C22—1882no—
743C22—1882no—
744C22—1882no—
745C22C2×C4×C22⋊D4711yescharacteristic
746C22C2×#1309399211yescharacteristic
747C22#1568963011yescharacteristic
748C22C2×#1309405511yescharacteristic
749C22#1568992111yescharacteristic
750C22#1568992111yescharacteristic
751C22#1568992111yescharacteristic
752C4—22no—
753C4—22no—
754C4—22no—
755C4—22no—
756C4—42no—
757C4—42no—
758C4—41no—
759C4—81no—
760C4—81no—
761C4—944no—
762C4—1882no—
763C4—1882no—
764C4C4×D4×D4711yescharacteristic
765C4C4×D4×D4711yescharacteristic
766C4#1568963211yescharacteristic
767C4#1568963211yescharacteristic
768C2—42no—
769C2—1884no—
770C2C4×#1309399211yescharacteristic
771C2#2025218611yescharacteristic
772C2C4×#1309405511yescharacteristic
773C2#2025262811yescharacteristic
774C2#2025264611yescharacteristic
775C2#2025349111yescharacteristic
776C2#2025354411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×C22⋊Q8×C47C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC4×C22⋊Q8D47
hypocenterC47#21457
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#15689228C2semidirect
4. C2×#15689221C2semidirect
5. #20243732C2semidirect
6. #20243725C2semidirect
7. #20243701C2semidirect
8. #20243648C2semidirect
9. #20243641C2semidirect
10. #20243585C2semidirect
12. #20243221C2semidirect
13. #20243216C2semidirect
14. #20243150C2semidirect
15. C4×C22⋊Q8×C47C2semidirect
30. #15689283C4semidirect
78. C2×#10625337C2×C4semidirect
81. C2×#10625336C2×C4semidirect
116. #13093947C2×C4semidirect
119. #13093944C2×C4semidirect
121. C22⋊(C47⋊C8)C2×C4semidirect
129. C22⋊Q8×C47C2×C4semidirect
384. C4×C22⋊Q8D47semidirect
452. C47#21457semidirect
480. C22⋊Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253502
C2×#156892832
C2×#156892282
C2×#156892212
#202437322
#202437252
#202437012
#202436482
#202436412
#202435852
#202433262
#202432212
#202432162
#202431502
C4×C22⋊Q8×C472
#2145747