Finite Group Databasebeta

← #27080793

Subgroups — #27080793

Order 12032.

1950 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256680C211yesmaximal, characteristic
2#20252374C214yesmaximal, complemented
3#20252367C214yesmaximal, complemented
4#20252351C214yesmaximal, complemented
5#20252348C214yesmaximal, complemented
6#20252327C211yesmaximal, characteristic, complemented
7#20252326C211yesmaximal, characteristic, complemented
8#20252104C211yesmaximal, characteristic, complemented
9#20252103C211yesmaximal, characteristic, complemented
10#20252092C211yesmaximal, characteristic, complemented
11#20252091C211yesmaximal, characteristic, complemented
12#20252087C211yesmaximal, characteristic, complemented
13#20252031C211yesmaximal, characteristic, complemented
14#20252028C211yesmaximal, characteristic, complemented
15#20252017C211yesmaximal, characteristic, complemented
16#20251810C211yesmaximal, characteristic, complemented
17#131×Dic47C211yesmaximal, characteristic, complemented
18C2×M16×Dic47C211yesmaximal, characteristic, complemented
19C47×#2930C211yesmaximal, characteristic, complemented
20C2×#13094032C2211yescharacteristic
21C2×#13094031C2211yescharacteristic
22C2×#13094030C2211yescharacteristic
23C22×#10625329C2211yescharacteristic
24#15689676C2211yescharacteristic
25#15689675C412yes—
26#15689669C2211yescharacteristic
27#15689668C412yes—
28#15689659C412yes—
29#15689654C412yes—
30#15689653C2214yes—
31#15689650C414yes—
32#15689634C2211yescharacteristic
33#15689629C414yes—
34#41×Dic47C2211yescharacteristic
35#15689591C2211yescharacteristic
36C4×#10625352C2214yes—
37C22×C4×Dic47C2211yescharacteristic
38#15689253C2214yescomplemented
39#15689252C2214yescomplemented
40#15689251C2214yescomplemented
41#15689250C2214yescomplemented
42#15689201C2214yes—
43#15689199C2214yes—
44#15689198C2214yes—
45#15689197C2214yes—
46#15689197C2214yescomplemented
47#15689195C2214yes—
48#15689194C2214yescomplemented
49#15689192C2214yes—
50#15689192C2214yescomplemented
51#15689191C2214yescomplemented
52#15689183C2214yescomplemented
53#15689181C2214yescomplemented
54#15689177C2214yes—
55#15689175C2214yescomplemented
56#15689173C2214yes—
57#15689173C2214yescomplemented
58#15689151C2211yescharacteristic
59#15689150C2211yescharacteristic
60#15689149C2211yescharacteristic
61#15689146C2211yescharacteristic
62#15689146C2211yescharacteristic
63#15689091C2211yescharacteristic
64#15689090C2211yescharacteristic
65#15689089C2211yescharacteristic
66#15689087C2211yescharacteristic
67#15689081C2211yescharacteristic
68#15689081C2212yescomplemented
69#15689080C2212yescomplemented
70#15689079C2211yescharacteristic
71#15689078C2211yescharacteristic
72#15689078C2212yescomplemented
73#15689077C2212yescomplemented
74#15689075C2212yescomplemented
75M16×Dic47C2211yescharacteristic
76M16×Dic47C2211yescharacteristic
77M16×Dic47C2212yes—
78M16×Dic47C2212yes—
79M16×Dic47C2212yes—
80M16×Dic47C2212yes—
81M16×Dic47C2212yescomplemented
82C2×#13093934C2211yescharacteristic
83C2×#13093934C2211yescharacteristic
84C2×C8×Dic47C2211yescharacteristic
85C2×C8×Dic47C2211yescharacteristic
86C2×C8×Dic47C2212yescomplemented
87C4×C8×D47C2212yescomplemented
88C2×#131×C47C2211yescharacteristic
89C22×M16×C47C2211yescharacteristic
90C47×#525C2211yescharacteristic
91C47×#436C2214yes—
92C47×#435C2214yes—
93C47×#424C2211yescharacteristic
94C47×#408C2211yescharacteristic
95C47×#407C2211yescharacteristic
96C47×#405C2211yescharacteristic
97C2×#10625350C2311yescharacteristic
98C2×#10625352C2×C414yes—
99C23×Dic47C2×C412yes—
100#13094032—24no—
101#13094031—24no—
102#13094030—24no—
103C2×#10625329—24no—
104C2×#10625329C2312yes—
105C2×#10625329C2312yes—
106C2×#10625329C2311yescharacteristic
107C2×#10625329C2311yescharacteristic
108C2×#10625329C2312yes—
109C2×#10625324C2312yes—
110C2×#10625324C2312yes—
111C22×C47⋊C8C2311yescharacteristic
112C22×C47⋊C8C2312yes—
113C22×C47⋊C8C2311yescharacteristic
114C2×C8×D47C2312yes—
115C2×C8×D47C2312yes—
116#13094023C2×C412yes—
117#13094022C2×C411yescharacteristic
118#13094020C2×C411yescharacteristic
119#13094019C2×C414yes—
120#13094017C2×C414yes—
121#13094015C2×C412yes—
122#13094014C2×C414yes—
123#13094013C2×C411yescharacteristic
124#13094011C2×C411yescharacteristic
125#13094010C2×C414yes—
126#13094008C2×C414yes—
127#13094007C2×C412yes—
128#13094005C2×C414yes—
129#13094003C2×C412yes—
130#13094001C2×C414yes—
131#13094001C2×C414yes—
132#13093998C2×C412yes—
133#13093996C2×C414yes—
134#13093996C2×C414yes—
135#13093993C2×C412yes—
136Q8×Dic47C2×C412yes—
137C4×Dic94C2314yes—
138#13093989C2×C414yes—
139#13093989C2×C412yes—
140D4×Dic47C2×C414yes—
141D4×Dic47C2×C414yes—
142D4×Dic47C2×C412yes—
143#13093986C2×C412yes—
144C4×C22⋊D47C2314yes—
145C4×C22⋊D47C2314yes—
146(C22⋊D47)⋊C4C2×C414yes—
147(C22⋊D47)⋊C4C2×C414yes—
148(C22⋊D47)⋊C4C2×C414yes—
149#13093983C2311yescharacteristic
150#13093983C2312yes—
151#13093982C2×C414yes—
152#13093981C2312yes—
153#13093980C2×C414yes—
154#13093980C2×C414yes—
155C2×C4×Dic47C2×C412yes—
156C2×C4×Dic47C2×C412yes—
157C2×C4×Dic47C2×C412yes—
158C2×C4×Dic47C2311yescharacteristic
159C2×C4×Dic47C2311yescharacteristic
160C2×C4×Dic47C2312yes—
161C2×C4×Dic47C2312yes—
162C2×C4×Dic47C2312yes—
163C42×D47C2312yes—
164C4⋊(C47⋊C8)C2314yes—
165Dic47⋊C8C2314yes—
166Dic47⋊C8C2314yes—
167Dic47⋊C8C2314yes—
168Dic47⋊C8C2314yes—
169C22⋊(C47⋊C8)C2314yes—
170C22⋊(C47⋊C8)C2314yes—
171(C2×D47)⋊C8C2314yes—
172(C2×D47)⋊C8C2314yes—
173#13093935C2312yes—
174#13093934C2312yes—
175#13093934C2312yes—
176#13093934C2312yes—
177#13093934C2312yes—
178#13093934C2312yes—
179#13093934C2312yes—
180#13093934C2312yes—
181#13093934C2312yes—
182C4×C47⋊C8C2312yes—
183C8×Dic47C2312yes—
184C8×Dic47C2312yes—
185C8×Dic47C2311yescharacteristic
186C8×Dic47C2312yes—
187C8×Dic47C2311yescharacteristic
188C8×Dic47C2311yescharacteristic
189C8×Dic47C2311yescharacteristic
190C8×Dic47C2312yes—
191C8×Dic47C2312yes—
192C8×Dic47C2312yes—
193C2×#41×C47C2311yescharacteristic
194C23×C4×C47C2311yescharacteristic
195#131×C47—24no—
196C2×M16×C47—24no—
197C2×M16×C47C2312yes—
198C2×M16×C47C2312yes—
199C2×M16×C47C2311yescharacteristic
200C2×M16×C47C2311yescharacteristic
201C2×M16×C47C2312yes—
202C22×C8×C47C2311yescharacteristic
203C22×C8×C47C2312yes—
204C22×C8×C47C2311yescharacteristic
205#123×C47C2×C412yes—
206C22⋊Q8×C47C2×C412yes—
207#121×C47C2×C412yes—
208#120×C47C2×C412yes—
209C4×D4×C47C2314yes—
210#117×C47C2311yescharacteristic
211C4⋊C8×C47C2314yes—
212C22⋊C8×C47C2314yes—
213C22⋊C8×C47C2314yes—
214#97×C47C2312yes—
215C4×C8×C47C2312yes—
216C24×C47C22×C411yescharacteristic
217#41×C47—22no—
218#41×C47—22no—
219C2×Q8×C47C22×C411yescharacteristic
220C2×D4×C47C22×C412yes—
221C2×D4×C47C22×C411yescharacteristic
222C2×D4×C47C22×C414yes—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47C22×C412yes—
226C22×C4×C47C22×C411yescharacteristic
227C22×C4×C47C2412yes—
228C22×C4×C47C2412yes—
229C22×C4×C47C2411yescharacteristic
230C2×C22⋊D47C22×C412yes—
231C2×C22⋊D47C22×C414yes—
232C2×C22⋊D47C22×C414yes—
233C22×Dic47—44no—
234C22×Dic47C22×C412yes—
235C22×Dic47C22×C412yes—
236C22×Dic47C22×C412yes—
237C22×Dic47C22×C414yes—
238C22×Dic47C22×C412yes—
239C22×Dic47C22×C412yes—
240C22×Dic47C22×C412yes—
241#10625352—48no—
242#10625350—22no—
243#10625350—22no—
244C2×D188C22×C411yescharacteristic
245C2×C4×D47C22×C414yes—
246C2×C4×D47C2412yes—
247C2×Dic94C22×C411yescharacteristic
248C2×Dic94C22×C414yes—
249M16×C47—22no—
250M16×C47—22no—
251M16×C47—24no—
252M16×C47—24no—
253M16×C47—24no—
254C2×C8×C47—22no—
255C2×C8×C47—24no—
256C2×C8×C47#4114yescomplemented
257C2×C8×C47C2412yes—
258C2×C8×C47C2412yes—
259C2×C8×C47C2412yes—
260C2×C8×C47C2411yescharacteristic
261C2×C8×C47C2411yescharacteristic
262C4⋊C4×C47C22×C412yes—
263C4⋊C4×C47C22×C414yes—
264C22⋊C4×C47C22×C412yes—
265C22⋊C4×C47C22×C414yes—
266C22⋊C4×C47C22×C414yes—
267C42×C47C2412yes—
268C22⋊Dic47C22×C414yes—
269C22⋊Dic47C22×C414yes—
270C22⋊Dic47C22×C412yes—
271C22⋊Dic47C22×C414yes—
272(C2×D47)⋊C4C22×C414yes—
273(C2×D47)⋊C4C22×C414yes—
274(C2×D47)⋊C4C22×C414yes—
275C4⋊Dic47C22×C414yes—
276C4⋊Dic47C22×C412yes—
277C4⋊Dic47C22×C414yes—
278Dic47⋊C4C22×C414yes—
279Dic47⋊C4C22×C414yes—
280Dic47⋊C4C22×C414yes—
281Dic47⋊C4C22×C414yes—
282Dic47⋊C4C22×C414yes—
283C4×Dic47C22×C414yes—
284C4×Dic47C22×C412yes—
285C4×Dic47C22×C412yes—
286C4×Dic47C22×C412yes—
287C4×Dic47C22×C412yes—
288C4×Dic47C22×C411yescharacteristic
289C4×Dic47C22×C412yes—
290C4×Dic47C22×C411yescharacteristic
291C4×Dic47C22×C414yes—
292C4×Dic47C2411yescharacteristic
293C4×Dic47C2411yescharacteristic
294C4×Dic47C2412yes—
295C4×Dic47C2412yes—
296#10625329—22no—
297#10625329—22no—
298#10625329—24no—
299#10625329—24no—
300#10625329—24no—
301C2×C47⋊C8—22no—
302C2×C47⋊C8—24no—
303C2×C47⋊C8#4114yescomplemented
304C2×C47⋊C8C2412yes—
305C2×C47⋊C8C2412yes—
306C2×C47⋊C8C2412yes—
307C2×C47⋊C8C2411yescharacteristic
308C2×C47⋊C8C2411yescharacteristic
309#10625324—24no—
310#10625324—24no—
311C8×D47—24no—
312C8×D47—24no—
313C23×C47—22no—
314C23×C47—42no—
315C23×C47C23×C412yes—
316C23×C47C23×C412yes—
317C23×C47C23×C411yescharacteristic
318C22×D47C23×C412yes—
319Q8×C47—22no—
320D4×C47—24no—
321D4×C47—22no—
322D4×C47—44no—
323C2×C4×C47—22no—
324C2×C4×C47—24no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47C23×C412yes—
330C2×C4×C47C23×C412yes—
331C2×C4×C47C23×C414yes—
332C2×C4×C47C23×C411yescharacteristic
333C2×C4×C47C2×#4112yes—
334C2×C4×C47C2×#4112yes—
335C2×C4×C47C2511yescharacteristic
336C22⋊D47—24no—
337C22⋊D47—44no—
338C22⋊D47—44no—
339C2×Dic47—24no—
340C2×Dic47—28no—
341C2×Dic47—24no—
342C2×Dic47—24no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47C23×C412yes—
347C2×Dic47C23×C412yes—
348C2×Dic47C23×C412yes—
349C2×Dic47C23×C412yes—
350C2×Dic47C23×C414yes—
351C2×Dic47C23×C412yes—
352D188—22no—
353C4×D47—22no—
354C4×D47—22no—
355C4×D47—28no—
356Dic94—22no—
357Dic94—44no—
358C8×C47—22no—
359C8×C47—22no—
360C8×C47—22no—
361C8×C47C2×#4112yes—
362C8×C47C2×#4112yes—
363C47⋊C8—22no—
364C47⋊C8—22no—
365C47⋊C8—22no—
366C47⋊C8C2×#4112yes—
367C47⋊C8C2×#4112yes—
368#60205—471nomaximal, Sylow
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—22no—
373C22×C47—22no—
374C22×C47—24no—
375C22×C47—44no—
376C22×C47C4×#4112yes—
377C22×C47C24×C411yescharacteristic
378C2×D47—22no—
379C2×D47—24no—
380C4×C47—22no—
381C4×C47—22no—
382C4×C47—24no—
383C4×C47C4×#4112yes—
384C4×C47C22×#4111yescharacteristic
385C4×C47C22×#4111yescharacteristic
386Dic47—22no—
387Dic47—22no—
388Dic47—24no—
389Dic47—22no—
390Dic47—22no—
391Dic47#56814yes—
392#3444—471no—
393#2967—474no—
394#2967—474no—
395#2965—474no—
396#2965—474no—
397#2961—471no—
398#2961—471no—
399#2932—471no—
400#2932—471no—
401#2930—471no—
402#2930—471no—
403#2930—471no—
404#2930D4711yescharacteristic, complemented
405#2922—471no—
406#2922—471no—
407#2920—471no—
408C4×#131—471no—
409C4×#131—471no—
410C2×C4×M16—471no—
411C2×C47—22no—
412C2×C47—42no—
413C2×C47—42no—
414C2×C47C2×C4×#4111yescharacteristic
415C2×C47C2×#56812yes—
416D47—42no—
417C2×#131—471no—
418C2×#131—471no—
419C2×#131—471no—
420C2×#131C2×D4711yescharacteristic
421C22×M16—471no—
422C22×M16C2×D4711yescharacteristic
423#533—472no—
424#533—471no—
425#532—471no—
426#532—472no—
427#529—474no—
428#529—472no—
429#529—472no—
430#529—474no—
431#525—471no—
432#525—474no—
433#525C2×D4711yescharacteristic
434C4×#41—471no—
435C4×#41—474no—
436C4×#41—471no—
437C22×C42—471no—
438#446—474no—
439#446—474no—
440#446—474no—
441#446—474no—
442#436—474no—
443#436—474no—
444#436—474no—
445#436C2×D4714yes—
446#435—474no—
447#435—474no—
448#435—474no—
449#435—474no—
450#435—474no—
451#435—474no—
452#435—474no—
453#435C2×D4714yes—
454#433—474no—
455#433—474no—
456#432—474no—
457#431—474no—
458#431—474no—
459#431—474no—
460#424—471no—
461#424—471no—
462#424—471no—
463#424C2×D4711yescharacteristic
464#423—471no—
465#423—471no—
466#408—471no—
467#408—471no—
468#408—471no—
469#408C2×D4711yescharacteristic
470#407—471no—
471#407C2×D4711yescharacteristic
472#405—471no—
473#405—472no—
474#405—471no—
475#405—472no—
476#405—471no—
477#405—472no—
478#405—472no—
479#405C2×D4711yescharacteristic
480C4×M16—472no—
481C4×M16—472no—
482C4×M16—472no—
483C4×M16—472no—
484C4×M16—471no—
485C4×M16—471no—
486C4×M16—472no—
487C4×M16—472no—
488C2×#97—471no—
489C2×#97—471no—
490C2×C4×C8—471no—
491C2×C4×C8—471no—
492C2×C4×C8—472no—
493C2×C4×C8—472no—
494C47#6020511yescharacteristic, complemented, Sylow
495C2×#41—474no—
496C2×#41—471no—
497C2×#41C22×D4711yescharacteristic
498C23×C4—472no—
499C23×C4C22×D4711yescharacteristic
500#131—24no—
501#131—944no—
502#131—944no—
503#131—944no—
504C2×M16—24no—
505C2×M16—472no—
506C2×M16—472no—
507C2×M16—471no—
508C2×M16—471no—
509C2×M16—472no—
510C2×M16—472no—
511C2×M16—472no—
512C2×M16—944no—
513C2×M16C22×D4712yes—
514C2×M16C22×D4712yes—
515C2×M16C22×D4711yescharacteristic
516C2×M16C22×D4711yescharacteristic
517C2×M16C22×D4712yes—
518C22×C8—471no—
519C22×C8—471no—
520C22×C8—472no—
521C22×C8—472no—
522C22×C8—472no—
523C22×C8C22×D4711yescharacteristic
524C22×C8C22×D4712yes—
525C22×C8C22×D4711yescharacteristic
526C4⋊Q8—471no—
527C4⋊Q8—472no—
528#127—471no—
529#126—474no—
530#126—474no—
531#125—474no—
532#125—472no—
533#124—471no—
534#124—471no—
535#124—474no—
536#123—474no—
537#123—472no—
538#123—474no—
539#123C4×D4712yes—
540C22⋊Q8—472no—
541C22⋊Q8—474no—
542C22⋊Q8—474no—
543C22⋊Q8C4×D4712yes—
544#121—474no—
545#121—474no—
546#121—472no—
547#121C4×D4712yes—
548#120—472no—
549#120C4×D4712yes—
550C4×Q8—472no—
551C4×Q8—474no—
552C4×Q8—472no—
553C4×Q8—474no—
554C4×D4—474no—
555C4×D4—474no—
556C4×D4—472no—
557C4×D4—474no—
558C4×D4—474no—
559C4×D4—472no—
560C4×D4—474no—
561C4×D4—474no—
562C4×D4—474no—
563C4×D4C22×D4714yes—
564#117—471no—
565#117—472no—
566#117—474no—
567#117—474no—
568#117—474no—
569#117—472no—
570#117C22×D4711yescharacteristic
571C2×C42—472no—
572C2×C42—472no—
573C2×C42—472no—
574C2×C42—472no—
575C2×C42—471no—
576C2×C42—472no—
577C2×C42—472no—
578C2×C42—471no—
579C2×C42—472no—
580C4⋊C8—474no—
581C4⋊C8—474no—
582C4⋊C8—474no—
583C4⋊C8—474no—
584C4⋊C8—474no—
585C4⋊C8C22×D4714yes—
586C22⋊C8—474no—
587C22⋊C8—474no—
588C22⋊C8—474no—
589C22⋊C8—474no—
590C22⋊C8C22×D4714yes—
591C22⋊C8C22×D4714yes—
592#97—472no—
593#97—472no—
594#97—472no—
595#97—472no—
596#97—472no—
597#97—472no—
598#97—472no—
599#97—472no—
600#97—472no—
601#97C22×D4712yes—
602C4×C8—471no—
603C4×C8—471no—
604C4×C8—471no—
605C4×C8—471no—
606C4×C8—472no—
607C4×C8—472no—
608C4×C8—472no—
609C4×C8—472no—
610C4×C8—472no—
611C4×C8—472no—
612C4×C8—472no—
613C4×C8C22×D4712yes—
614C24C2×C4×D4711yescharacteristic
615#41—22no—
616#41—22no—
617#41—942no—
618#41—942no—
619#41—1888no—
620C2×Q8—471no—
621C2×Q8—474no—
622C2×Q8C2×C4×D4711yescharacteristic
623C2×D4—472no—
624C2×D4—474no—
625C2×D4—474no—
626C2×D4—471no—
627C2×D4C2×C4×D4712yes—
628C2×D4C2×C4×D4711yescharacteristic
629C2×D4C2×C4×D4714yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—472no—
633C22×C4—472no—
634C22×C4—472no—
635C22×C4—474no—
636C22×C4—472no—
637C22×C4—472no—
638C22×C4—472no—
639C22×C4—474no—
640C22×C4—472no—
641C22×C4—1884no—
642C22×C4C2×C4×D4712yes—
643C22×C4C2×C4×D4711yescharacteristic
644C22×C4C23×D4712yes—
645C22×C4C23×D4712yes—
646C22×C4C23×D4711yescharacteristic
647M16—22no—
648M16—22no—
649M16—24no—
650M16—24no—
651M16—24no—
652M16—944no—
653M16—944no—
654M16—944no—
655M16—944no—
656M16—942no—
657M16—942no—
658M16—944no—
659C2×C8—22no—
660C2×C8—24no—
661C2×C8—474no—
662C2×C8—471no—
663C2×C8—471no—
664C2×C8—472no—
665C2×C8—472no—
666C2×C8—472no—
667C2×C8—944no—
668C2×C8—944no—
669C2×C8—942no—
670C2×C8—944no—
671C2×C8#1062535214yescomplemented
672C2×C8C23×D4712yes—
673C2×C8C23×D4712yes—
674C2×C8C23×D4712yes—
675C2×C8C23×D4711yescharacteristic
676C2×C8C23×D4711yescharacteristic
677C4⋊C4—474no—
678C4⋊C4—474no—
679C4⋊C4—474no—
680C4⋊C4—474no—
681C4⋊C4—474no—
682C4⋊C4—472no—
683C4⋊C4—474no—
684C4⋊C4—474no—
685C4⋊C4C2×C4×D4714yes—
686C4⋊C4C2×C4×D4712yes—
687C22⋊C4—474no—
688C22⋊C4—472no—
689C22⋊C4—474no—
690C22⋊C4—474no—
691C22⋊C4—474no—
692C22⋊C4—474no—
693C22⋊C4—474no—
694C22⋊C4C2×C4×D4714yes—
695C22⋊C4C2×C4×D4714yes—
696C22⋊C4C2×C4×D4712yes—
697C42—472no—
698C42—472no—
699C42—472no—
700C42—471no—
701C42—472no—
702C42—472no—
703C42—471no—
704C42—474no—
705C42—474no—
706C42—471no—
707C42—471no—
708C42—472no—
709C42—472no—
710C42C23×D4712yes—
711C23—22no—
712C23—42no—
713C23—472no—
714C23C22×C4×D4712yes—
715C23C22×C4×D4712yes—
716C23C22×C4×D4711yescharacteristic
717Q8—22no—
718Q8—942no—
719Q8—1884no—
720D4—24no—
721D4—22no—
722D4—44no—
723D4—944no—
724D4—942no—
725D4—1884no—
726D4—1884no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—472no—
734C2×C4—472no—
735C2×C4—472no—
736C2×C4—472no—
737C2×C4—474no—
738C2×C4—472no—
739C2×C4—948no—
740C2×C4—944no—
741C2×C4—944no—
742C2×C4—944no—
743C2×C4—948no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4C22×C4×D4712yes—
750C2×C4C22×C4×D4712yes—
751C2×C4C22×C4×D4714yes—
752C2×C4C22×C4×D4711yescharacteristic
753C2×C4#41×D4712yes—
754C2×C4C2×#1062535212yes—
755C2×C4C24×D4711yescharacteristic
756C8—22no—
757C8—22no—
758C8—22no—
759C8—472no—
760C8—472no—
761C8—942no—
762C8—942no—
763C8—942no—
764C8C2×#1062535212yes—
765C8C2×#1062535212yes—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—24no—
770C22—22no—
771C22—22no—
772C22—44no—
773C22—944no—
774C22—942no—
775C22C4×#1062535212yes—
776C22C23×C4×D4711yescharacteristic
777C4—24no—
778C4—22no—
779C4—22no—
780C4—474no—
781C4—942no—
782C4—942no—
783C4—942no—
784C4—944no—
785C4—942no—
786C4C4×#1062535212yes—
787C4C2×#41×D4711yescharacteristic
788C4C22×#1062535211yescharacteristic
789C2—22no—
790C2—42no—
791C2—42no—
792C2—1882no—
793C2C2×C4×#1062535211yescharacteristic
794C2#568×D4712yes—
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC47×#2930C2
prime radical#20256680C2
cosocleC2×C4×C47C25
hypercenter#2930D47
hypocenterC47#60205
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2930

Complements

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

NH ≅ G/Ntype
2. #20252374C2semidirect
3. #20252367C2semidirect
4. #20252351C2semidirect
5. #20252348C2semidirect
6. #20252327C2semidirect
7. #20252326C2semidirect
8. #20252104C2semidirect
9. #20252103C2semidirect
10. #20252092C2semidirect
11. #20252091C2semidirect
12. #20252087C2semidirect
13. #20252031C2semidirect
14. #20252028C2semidirect
15. #20252017C2semidirect
16. #20251810C2semidirect
17. #131×Dic47C2semidirect
18. C2×M16×Dic47C2semidirect
19. C47×#2930C2semidirect
38. #15689253C22semidirect
39. #15689252C22semidirect
40. #15689251C22semidirect
41. #15689250C22semidirect
46. #15689197C22semidirect
48. #15689194C22semidirect
50. #15689192C22semidirect
51. #15689191C22semidirect
52. #15689183C22semidirect
53. #15689181C22semidirect
55. #15689175C22semidirect
57. #15689173C22semidirect
68. #15689081C22semidirect
69. #15689080C22semidirect
72. #15689078C22semidirect
73. #15689077C22semidirect
74. #15689075C22semidirect
81. M16×Dic47C22semidirect
86. C2×C8×Dic47C22semidirect
87. C4×C8×D47C22semidirect
256. C2×C8×C47#41semidirect
303. C2×C47⋊C8#41semidirect
404. #2930D47semidirect
494. C47#60205semidirect
671. C2×C8#10625352semidirect

Maximal subgroups

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

subgroupindex
#202566802
#202523742
#202523672
#202523512
#202523482
#202523272
#202523262
#202521042
#202521032
#202520922
#202520912
#202520872
#202520312
#202520282
#202520172
#202518102
#131×Dic472
C2×M16×Dic472
C47×#29302
#6020547