Finite Group Databasebeta

← #27124828

Subgroups — #27124828

Order 12032.

11346 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689959C212yesmaximal, complemented
2#20257180C214yesmaximal, complemented
3#20257177C214yesmaximal, complemented
4#20257170C214yesmaximal, complemented
5#20257163C214yesmaximal, complemented
6#20257157C214yesmaximal, complemented
7#20257151C214yesmaximal, complemented
8#20257149C218yesmaximal, complemented
9#20256871C2116yesmaximal, complemented
10#20256721C211yesmaximal, characteristic, complemented
11#20256715C214yesmaximal, complemented
12C2×#15689669C212yesmaximal, complemented
13#532×D47C214yesmaximal, complemented
14C2×#15689591C211yesmaximal, characteristic, complemented
15C47×#3449C211yesmaximal, characteristic, complemented
16#15689959—232no—
17C2×#13094072C2214yescomplemented
18C2×#13094071C2214yescomplemented
19C2×#13094071C2214yescomplemented
20C2×#13094070C2214yescomplemented
21C2×#13094070C2214yescomplemented
22C2×#13094069C2218yescomplemented
23C2×#13094069C2214yescomplemented
24C22×#10625350C2211yescharacteristic
25C22×#10625350C2218yescomplemented
26C22×#10625350C2212yescomplemented
27C2×#41×D47C2218yescomplemented
28C2×#41×D47C2218yescomplemented
29#15689791C22116yescomplemented
30#15689786C22116yescomplemented
31#15689783C22116yescomplemented
32#15689779C22116yescomplemented
33#15689775C22116yescomplemented
34#15689771C22132yescomplemented
35#15689770C22116yescomplemented
36#15689765C22132yescomplemented
37#15689764C22116yescomplemented
38#15689760C22132yescomplemented
39#15689757C22116yescomplemented
40#15689755C22132yescomplemented
41#15689704C2214yescomplemented
42#15689700C22116yescomplemented
43#15689699C2214yescomplemented
44#15689698C2218yescomplemented
45#15689693C2218yescomplemented
46#15689692C2214yescomplemented
47#15689691C2218yescomplemented
48#15689686C2218yescomplemented
49#15689685C2214yescomplemented
50#15689681C22116yescomplemented
51#15689674C2214yescomplemented
52#15689673C2214yescomplemented
53#15689672C2218yescomplemented
54#15689671C2214yescomplemented
55#15689670C22116yescomplemented
56#15689669C2218yescomplemented
57#15689669C2218yescomplemented
58#15689669C2214yescomplemented
59#15689669C2214yescomplemented
60#15689669C2214yescomplemented
61#15689669C2214yescomplemented
62#15689668C22116yescomplemented
63C2×#13094022C2212yescomplemented
64C4⋊Q8×D47C2214yescomplemented
65C2×#13094020C2212yescomplemented
66#127×D47C2214yescomplemented
67C2×#13094013C2212yescomplemented
68C2×#13094011C2212yescomplemented
69#124×D47C2218yescomplemented
70#15689635C2218yescomplemented
71#15689632C22132yescomplemented
72C2×#13093996C2218yescomplemented
73#121×D47C22116yescomplemented
74#15689591C2218yescomplemented
75#15689591C2214yescomplemented
76#15689591C2214yescomplemented
77C2×#13093989C2212yescomplemented
78C2×#13093986C2212yescomplemented
79C2×C4×C22⋊D47C2218yescomplemented
80C2×(C22⋊D47)⋊C4C2214yescomplemented
81C4×D4×D47C22116yescomplemented
82C2×#13093981C2212yescomplemented
83C22×C4×Dic47C2211yescharacteristic, complemented
84C2×C42×D47C2212yescomplemented
85C22×#41×C47C2212yescomplemented
86C47×#537C2214yescomplemented
87C47×#536C2214yescomplemented
88C47×#535C2214yescomplemented
89C47×#534C2214yescomplemented
90C47×#532C2214yescomplemented
91C47×#525C2218yescomplemented
92C2×#117×C47C2211yescharacteristic, complemented
93#13094072—232no—
94#13094071—232no—
95#13094071—232no—
96#13094070—232no—
97#13094070—232no—
98#13094069—264no—
99#13094069—232no—
100C2×#10625354C2318yes—
101C2×#10625354C2318yes—
102C2×#10625350—216no—
103C2×#10625350—264no—
104C2×#10625350D4116yescomplemented
105C2×#10625350C23116yes—
106C2×#10625350C2318yes—
107C2×#10625350C2318yes—
108C2×#10625350C23116yes—
109C2×#10625350C2314yes—
110C2×#10625350C2314yes—
111C2×#10625350C2314yes—
112C2×#10625350C2314yes—
113C2×#10625350C2314yes—
114C2×#10625350C2314yes—
115C2×#10625352C23116yes—
116C2×#10625352C2318yes—
117C2×#10625352C23116yes—
118C2×#10625352C2318yes—
119#41×D47—264no—
120#41×D47—264no—
121C22×Dic94C2318yes—
122C22×Dic94C2312yes—
123C22×Dic94C2311yescharacteristic
124C2×Q8×D47C2318yes—
125C2×Q8×D47C2318yes—
126C22×D188C2318yes—
127C22×D188C2312yes—
128C22×D188C2311yescharacteristic
129C22×C22⋊D47C23116yes—
130C22×C22⋊D47C2314yes—
131C22×C22⋊D47C2318yes—
132C22×C22⋊D47C2312yes—
133C2×D4×D47C23116yes—
134C2×D4×D47C2318yes—
135C2×D4×D47C23116yes—
136C2×D4×D47C2318yes—
137C2×D4×D47C23116yes—
138C23×Dic47C2312yes—
139C22×C4×D47C23116yes—
140C22×C4×D47C2314yes—
141C22×C4×D47C2314yes—
142C22×C4×D47C2312yes—
143#13094024C2314yes—
144#13094023C23116yes—
145#13094022C2318yes—
146#13094022C2314yes—
147#13094022C2314yes—
148#13094021C2314yes—
149#13094020C23116yes—
150#13094020C2318yes—
151#13094020C2314yes—
152#13094020C2314yes—
153#13094013C2318yes—
154#13094013C2314yes—
155#13094013C2314yes—
156#13094012C2318yes—
157#13094011C2318yes—
158#13094011C2314yes—
159#13094011C2314yes—
160#13094010C23132yes—
161#13094009C23132yes—
162#13094008C23116yes—
163#13094006C23132yes—
164#13094004C23116yes—
165#13094002C23132yes—
166#13094001C23132yes—
167#13093999C23116yes—
168#13093999C23116yes—
169#13093998C23116yes—
170#13093997C23132yes—
171#13093997C23132yes—
172#13093996C23116yes—
173#13093996C23132yes—
174#13093996C23116yes—
175#13093996C23116yes—
176#13093996C23116yes—
177#13093995C23116yes—
178#13093994C23116yes—
179#13093994C23132yes—
180#13093992C23132yes—
181#13093989C2318yes—
182#13093989C2318yes—
183C4×D188C23116yes—
184D4×Dic47C23116yes—
185#13093986C2318yes—
186#13093986C2318yes—
187#13093986C23116yes—
188C4×C22⋊D47C23116yes—
189C4×C22⋊D47C23116yes—
190C4×C22⋊D47C23116yes—
191C4×C22⋊D47C23116yes—
192(C22⋊D47)⋊C4C23116yes—
193(C22⋊D47)⋊C4C23132yes—
194(C22⋊D47)⋊C4C23116yes—
195#13093981C2318yes—
196#13093981C2318yes—
197C2×Dic47⋊C4C2318yes—
198C2×Dic47⋊C4C2314yes—
199C4⋊C4×D47C23116yes—
200C2×C22⋊Dic47C2318yes—
201C2×(C2×D47)⋊C4C2318yes—
202C2×(C2×D47)⋊C4C2314yes—
203C22⋊C4×D47C23132yes—
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2314yes—
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2314yes—
208C2×C4×Dic47C2312yes—
209C2×C4×Dic47C2312yes—
210C2×C4×Dic47C2312yes—
211C42×D47C2318yes—
212C42×D47C2314yes—
213C42×D47C2314yes—
214C2×#41×C47—216no—
215C2×#41×C47C2314yes—
216C2×#41×C47C2314yes—
217C2×#41×C47C2314yes—
218C2×#41×C47C2314yes—
219C22×Q8×C47C2312yes—
220C22×D4×C47C2314yes—
221C22×D4×C47C2312yes—
222C23×C4×C47C2314yes—
223C23×C4×C47C2311yescharacteristic
224C4⋊Q8×C47C2314yes—
225#127×C47C2314yes—
226#124×C47C2318yes—
227#123×C47C23116yes—
228C22⋊Q8×C47C23116yes—
229#121×C47C23116yes—
230#121×C47C23116yes—
231#120×C47C23116yes—
232C4×D4×C47C23116yes—
233#117×C47C2314yes—
234#117×C47C2314yes—
235C2×C4⋊C4×C47C2312yes—
236C2×C22⋊C4×C47C2312yes—
237C2×C42×C47C2312yes—
238C24×C47C2414yes—
239C24×C47C2411yescharacteristic
240C23×D47C24116yes—
241C23×D47C2414yes—
242C23×D47C2412yes—
243#41×C47—216no—
244#41×C47—216no—
245#41×C47—216no—
246#41×C47—216no—
247C2×Q8×C47—28no—
248C2×Q8×C47C2414yes—
249C2×Q8×C47C2414yes—
250C2×D4×C47—216no—
251C2×D4×C47—28no—
252C2×D4×C47C2418yes—
253C2×D4×C47C2418yes—
254C2×D4×C47C2414yes—
255C2×D4×C47C2414yes—
256C2×D4×C47C24116yes—
257C22×C4×C47—216no—
258C22×C4×C47C2×D418yescomplemented
259C22×C4×C47C2418yes—
260C22×C4×C47C2418yes—
261C22×C4×C47C2414yes—
262C22×C4×C47C2414yes—
263C22×C4×C47C2411yescharacteristic
264C22×C4×C47C2411yescharacteristic
265C22×C4×C47C2412yes—
266C22×C4×C47C2412yes—
267C2×C22⋊D47—216no—
268C2×C22⋊D47—264no—
269C2×C22⋊D47—416no—
270C2×C22⋊D47C2×D4116yescomplemented
271C2×C22⋊D47C24116yes—
272C2×C22⋊D47C24116yes—
273C2×C22⋊D47C2418yes—
274C2×C22⋊D47C2418yes—
275C2×C22⋊D47C24116yes—
276C2×C22⋊D47C24116yes—
277C2×C22⋊D47C2418yes—
278C22×Dic47—44no—
279C22×Dic47C2412yes—
280C22×Dic47C2414yes—
281C22×Dic47C2414yes—
282C22×Dic47C24116yes—
283C22×Dic47C2414yes—
284C22×Dic47C2412yes—
285C22×Dic47C2412yes—
286#10625354—232no—
287#10625354—232no—
288Q8×D47—232no—
289Q8×D47—232no—
290#10625352—264no—
291#10625352—264no—
292#10625352—232no—
293#10625352—232no—
294D4×D47—264no—
295D4×D47—264no—
296D4×D47—232no—
297D4×D47—232no—
298D4×D47—432no—
299#10625350—216no—
300#10625350—216no—
301#10625350—216no—
302#10625350—216no—
303#10625350—264no—
304#10625350—232no—
305#10625350—264no—
306#10625350—232no—
307#10625350C2×D4132yescomplemented
308#10625350C2×D4132yescomplemented
309C2×D188—28no—
310C2×D188—232no—
311C2×D188C2×D418yescomplemented
312C2×D188C24116yes—
313C2×D188C2414yes—
314C2×D188C2414yes—
315C2×D188C24116yes—
316C2×D188C2414yes—
317C2×C4×D47—216no—
318C2×C4×D47—264no—
319C2×C4×D47—48no—
320C2×C4×D47C2×D4116yescomplemented
321C2×C4×D47C2418yes—
322C2×C4×D47C24116yes—
323C2×C4×D47C24116yes—
324C2×C4×D47C2418yes—
325C2×C4×D47C2418yes—
326C2×C4×D47C2418yes—
327C2×C4×D47C2414yes—
328C2×C4×D47C2414yes—
329C2×Dic94—28no—
330C2×Dic94—232no—
331C2×Dic94C2×D418yescomplemented
332C2×Dic94C24116yes—
333C2×Dic94C2414yes—
334C2×Dic94C2414yes—
335C2×Dic94C2414yes—
336C4⋊C4×C47C2418yes—
337C4⋊C4×C47C24116yes—
338C22⋊C4×C47C2418yes—
339C22⋊C4×C47C24132yes—
340C42×C47C2414yes—
341C42×C47C2414yes—
342C22⋊Dic47C24116yes—
343C22⋊Dic47C24116yes—
344(C2×D47)⋊C4C24116yes—
345(C2×D47)⋊C4C24132yes—
346(C2×D47)⋊C4C24116yes—
347(C2×D47)⋊C4C24116yes—
348C4⋊Dic47C24116yes—
349Dic47⋊C4C24116yes—
350Dic47⋊C4C24116yes—
351Dic47⋊C4C24116yes—
352C4×Dic47C2412yes—
353C4×Dic47C2411yescharacteristic
354C4×Dic47C2411yescharacteristic
355C4×Dic47C2418yes—
356C4×Dic47C2418yes—
357C4×Dic47C2412yes—
358C4×Dic47C2412yes—
359C4×Dic47C2414yes—
360C4×Dic47C2414yes—
361C23×C47—28no—
362C23×C47—42no—
363C23×C47—48no—
364C23×C47C22×D414yes—
365C23×C47C2518yes—
366C23×C47C2512yes—
367C23×C47C2511yescharacteristic
368C22×D47—28no—
369C22×D47—232no—
370C22×D47—44no—
371C22×D47—432no—
372C22×D47—48no—
373C22×D47C22×D418yes—
374C22×D47C2518yes—
375C22×D47C2514yes—
376Q8×C47—28no—
377Q8×C47—28no—
378D4×C47—216no—
379D4×C47—216no—
380D4×C47—28no—
381D4×C47—28no—
382D4×C47—416no—
383C2×C4×C47—28no—
384C2×C4×C47—216no—
385C2×C4×C47—216no—
386C2×C4×C47—44no—
387C2×C4×C47C22×D418yes—
388C2×C4×C47C22×D414yes—
389C2×C4×C47C22×D418yes—
390C2×C4×C47C22×D414yes—
391C2×C4×C47C2518yes—
392C2×C4×C47C2518yes—
393C2×C4×C47C2511yescharacteristic
394C2×C4×C47C2512yes—
395C2×C4×C47C2511yescharacteristic
396C22⋊D47—216no—
397C22⋊D47—216no—
398C22⋊D47—232no—
399C22⋊D47—232no—
400C22⋊D47—232no—
401C22⋊D47—416no—
402C22⋊D47C22×D4132yes—
403C2×Dic47—28no—
404C2×Dic47—232no—
405C2×Dic47—24no—
406C2×Dic47—28no—
407C2×Dic47—44no—
408C2×Dic47—42no—
409C2×Dic47C22×D418yes—
410C2×Dic47C2512yes—
411C2×Dic47C2514yes—
412C2×Dic47C2518yes—
413C2×Dic47C2514yes—
414C2×Dic47C2512yes—
415D188—232no—
416D188—28no—
417D188—28no—
418D188—416no—
419D188C22×D4116yes—
420C4×D47—232no—
421C4×D47—216no—
422C4×D47—216no—
423C4×D47—232no—
424C4×D47—216no—
425C4×D47—48no—
426C4×D47C22×D4116yes—
427C4×D47C22×D4116yes—
428Dic94—28no—
429Dic94—28no—
430Dic94—232no—
431Dic94C22×D4116yes—
432#62812—471nomaximal, Sylow
433C22×C47—22no—
434C22×C47—24no—
435C22×C47—28no—
436C22×C47—216no—
437C22×C47—44no—
438C22×C47—88no—
439C22×C47C23×D414yes—
440C22×C47C23×D412yes—
441C22×C47C2611yescharacteristic
442C2×D47—28no—
443C2×D47—28no—
444C2×D47—216no—
445C2×D47—48no—
446C2×D47—832no—
447C2×D47—88no—
448C2×D47C23×D418yes—
449C4×C47—28no—
450C4×C47—28no—
451C4×C47C23×D412yes—
452C4×C47C23×D414yes—
453C4×C47C23×D412yes—
454Dic47—28no—
455Dic47—22no—
456Dic47—24no—
457Dic47C23×D418yes—
458Dic47#58514yescomplemented
459C2×#585—472no—
460#3500—474no—
461#3500—474no—
462#3499—474no—
463#3498—474no—
464#3497—474no—
465#3496—474no—
466#3496—478no—
467D4×#41—4716no—
468#3449—474no—
469#3449—471no—
470#3449D4711yescharacteristic, complemented
471C2×#532—472no—
472C2×#532—474no—
473C2×C4×#41—471no—
474C2×C47—22no—
475C2×C47—24no—
476C2×C47—48no—
477C2×C47C24×D411yescharacteristic
478C2×C47C2×#58512yes—
479D47—28no—
480D47—48no—
481#585—9432no—
482C2×2−1+4—474no—
483C2×2−1+4—474no—
484C2×2−1+4—474no—
485C2×H(5,𝔽2)—474no—
486C2×H(5,𝔽2)—474no—
487C2×H(5,𝔽2)—478no—
488C2×H(5,𝔽2)—474no—
489C22×#41—478no—
490C22×#41—478no—
491C22×#41—471no—
492C22×#41—472no—
493C22×#41—478no—
494C22×#41C2×D4712yescomplemented
495#550—4716no—
496D4×Q8—4716no—
497#548—4716no—
498#548—4716no—
499#547—4732no—
500#547—4716no—
501#546—4732no—
502#546—4716no—
503#546—4716no—
504#546—4732no—
505D42—4716no—
506D42—4732no—
507#537—4716no—
508#537—474no—
509#537C2×D4714yescomplemented
510#536—478no—
511#536—478no—
512#536—474no—
513#536C2×D4714yescomplemented
514#535—478no—
515#535—478no—
516#535—474no—
517#535C2×D4714yescomplemented
518#534—4716no—
519#534—474no—
520#534C2×D4714yescomplemented
521#532—474no—
522#532—474no—
523#532—478no—
524#532—478no—
525#532—474no—
526#532—474no—
527#532—474no—
528#532—474no—
529#532—478no—
530#532—4716no—
531#532—4716no—
532#532—474no—
533#532C2×D4714yescomplemented
534C2×C4⋊Q8—472no—
535C2×C4⋊Q8—474no—
536C2×#127—472no—
537C2×#127—474no—
538C2×#124—472no—
539C2×#124—472no—
540C2×#124—478no—
541#525—4732no—
542#525—478no—
543#525C2×D4718yescomplemented
544C2×#121—478no—
545C2×#121—4716no—
546C4×#41—478no—
547C4×#41—474no—
548C4×#41—474no—
549C2×C4×Q8—472no—
550C2×C4×D4—478no—
551C2×C4×D4—4716no—
552C2×C4×D4—472no—
553C2×C4×D4—474no—
554C2×#117—472no—
555C2×#117C2×D4711yescharacteristic, complemented
556C22×C42—471no—
557C22×C42—472no—
558C47#6281211yescharacteristic, complemented, Sylow
5592−1+4—9432no—
5602−1+4—9432no—
5612−1+4—9432no—
562H(5,𝔽2)—9464no—
563H(5,𝔽2)—9432no—
564H(5,𝔽2)—9432no—
565H(5,𝔽2)—9432no—
566C2×#41—216no—
567C2×#41—478no—
568C2×#41—478no—
569C2×#41—478no—
570C2×#41—4716no—
571C2×#41—4716no—
572C2×#41—478no—
573C2×#41—4716no—
574C2×#41—474no—
575C2×#41—474no—
576C2×#41—4716no—
577C2×#41—474no—
578C2×#41—474no—
579C2×#41—474no—
580C2×#41—474no—
581C2×#41—478no—
582C2×#41—4716no—
583C2×#41—478no—
584C2×#41—9464no—
585C2×#41—9464no—
586C2×#41—9464no—
587C2×#41—9416no—
588C2×#41C22×D4714yes—
589C2×#41C22×D4714yes—
590C2×#41C22×D4714yes—
591C2×#41C22×D4714yes—
592C22×Q8—478no—
593C22×Q8—478no—
594C22×Q8—471no—
595C22×Q8—472no—
596C22×Q8—478no—
597C22×Q8C22×D4712yes—
598C22×D4—472no—
599C22×D4—474no—
600C22×D4—4716no—
601C22×D4—478no—
602C22×D4—4716no—
603C22×D4—478no—
604C22×D4—4716no—
605C22×D4—478no—
606C22×D4—4716no—
607C22×D4—471no—
608C22×D4—472no—
609C22×D4—478no—
610C22×D4C22×D4714yes—
611C22×D4C22×D4712yes—
612C23×C4—472no—
613C23×C4—472no—
614C23×C4—4716no—
615C23×C4—474no—
616C23×C4—474no—
617C23×C4C22×D4714yes—
618C23×C4C22×D4711yescharacteristic
619C4⋊Q8—474no—
620C4⋊Q8—474no—
621C4⋊Q8—478no—
622C4⋊Q8—4716no—
623C4⋊Q8—474no—
624C4⋊Q8C22×D4714yes—
625#127—474no—
626#127—474no—
627#127—4716no—
628#127—478no—
629#127—474no—
630#127C22×D4714yes—
631#124—474no—
632#124—474no—
633#124—478no—
634#124—474no—
635#124—474no—
636#124—478no—
637#124—4732no—
638#124—478no—
639#124C22×D4718yes—
640#123—4732no—
641#123—4732no—
642#123—4716no—
643#123C22×D47116yes—
644C22⋊Q8—4732no—
645C22⋊Q8—4716no—
646C22⋊Q8—4732no—
647C22⋊Q8C22×D47116yes—
648#121—4716no—
649#121—4716no—
650#121—4716no—
651#121—4716no—
652#121—4716no—
653#121—4732no—
654#121—4716no—
655#121—4716no—
656#121—4716no—
657#121—4732no—
658#121—4732no—
659#121C22×D47116yes—
660#121C22×D47116yes—
661#120—4732no—
662#120—4732no—
663#120—4716no—
664#120C22×D47116yes—
665C4×Q8—478no—
666C4×Q8—478no—
667C4×D4—4716no—
668C4×D4—4716no—
669C4×D4—4716no—
670C4×D4—4716no—
671C4×D4—4716no—
672C4×D4—478no—
673C4×D4—478no—
674C4×D4—4716no—
675C4×D4—4716no—
676C4×D4—4716no—
677C4×D4—4732no—
678C4×D4—4716no—
679C4×D4C22×D47116yes—
680#117—478no—
681#117—478no—
682#117C22×D4714yes—
683#117C22×D4714yes—
684C2×C4⋊C4—474no—
685C2×C4⋊C4—478no—
686C2×C4⋊C4—4716no—
687C2×C4⋊C4C22×D4712yes—
688C2×C22⋊C4—478no—
689C2×C22⋊C4—474no—
690C2×C22⋊C4—478no—
691C2×C22⋊C4—4732no—
692C2×C22⋊C4C22×D4712yes—
693C2×C42—471no—
694C2×C42—474no—
695C2×C42—474no—
696C2×C42—472no—
697C2×C42—472no—
698C2×C42—472no—
699C2×C42—471no—
700C2×C42—478no—
701C2×C42—474no—
702C2×C42—474no—
703C2×C42C22×D4712yes—
704C24—472no—
705C24—4716no—
706C24—474no—
707C24C23×D4714yes—
708C24C23×D4711yescharacteristic
709#41—216no—
710#41—216no—
711#41—216no—
712#41—216no—
713#41—4732no—
714#41—4732no—
715#41—9464no—
716#41—9464no—
717#41—9432no—
718#41—9432no—
719#41—9464no—
720#41—9432no—
721#41—9432no—
722#41—9464no—
723#41—9432no—
724#41—9432no—
725#41—9416no—
726#41—9416no—
727#41—9416no—
728#41—9416no—
729C2×Q8—28no—
730C2×Q8—478no—
731C2×Q8—474no—
732C2×Q8—4716no—
733C2×Q8—474no—
734C2×Q8—474no—
735C2×Q8—9432no—
736C2×Q8—9432no—
737C2×Q8—9432no—
738C2×Q8—948no—
739C2×Q8C23×D4714yes—
740C2×Q8C23×D4714yes—
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—4716no—
744C2×D4—478no—
745C2×D4—4716no—
746C2×D4—4716no—
747C2×D4—478no—
748C2×D4—478no—
749C2×D4—4716no—
750C2×D4—4716no—
751C2×D4—478no—
752C2×D4—474no—
753C2×D4—4716no—
754C2×D4—474no—
755C2×D4—474no—
756C2×D4—4716no—
757C2×D4—9432no—
758C2×D4—9432no—
759C2×D4—9464no—
760C2×D4—9432no—
761C2×D4—9464no—
762C2×D4—9464no—
763C2×D4—9416no—
764C2×D4—948no—
765C2×D4—18832no—
766C2×D4—18816no—
767C2×D4C23×D4718yes—
768C2×D4C23×D4718yes—
769C2×D4C23×D4714yes—
770C2×D4C23×D4714yes—
771C2×D4C23×D47116yes—
772C22×C4—216no—
773C22×C4—472no—
774C22×C4—4716no—
775C22×C4—474no—
776C22×C4—474no—
777C22×C4—472no—
778C22×C4—474no—
779C22×C4—474no—
780C22×C4—4716no—
781C22×C4—474no—
782C22×C4—472no—
783C22×C4—478no—
784C22×C4—4716no—
785C22×C4—4716no—
786C22×C4—478no—
787C22×C4—478no—
788C22×C4—478no—
789C22×C4—9464no—
790C22×C4—9416no—
791C22×C4—1888no—
792C22×C4—1884no—
793C22×C4D4×D4718yescomplemented
794C22×C4C23×D4714yes—
795C22×C4C23×D4718yes—
796C22×C4C23×D4718yes—
797C22×C4C23×D4714yes—
798C22×C4C23×D4711yescharacteristic
799C22×C4C23×D4712yes—
800C22×C4C23×D4711yescharacteristic
801C22×C4C23×D4712yes—
802C4⋊C4—4716no—
803C4⋊C4—4716no—
804C4⋊C4—4716no—
805C4⋊C4—4716no—
806C4⋊C4C23×D47116yes—
807C4⋊C4C23×D4718yes—
808C22⋊C4—4716no—
809C22⋊C4—4716no—
810C22⋊C4—4716no—
811C22⋊C4—4716no—
812C22⋊C4—4716no—
813C22⋊C4—4732no—
814C22⋊C4C23×D47132yes—
815C22⋊C4C23×D4718yes—
816C42—471no—
817C42—471no—
818C42—472no—
819C42—478no—
820C42—474no—
821C42—478no—
822C42—474no—
823C42—472no—
824C42—472no—
825C42C23×D4714yes—
826C42C23×D4714yes—
827C23—28no—
828C23—42no—
829C23—48no—
830C23—474no—
831C23—478no—
832C23—478no—
833C23—9432no—
834C23—948no—
835C23—1888no—
836C23—18832no—
837C23—1884no—
838C23C2×D4×D4714yes—
839C23C24×D4718yes—
840C23C24×D4712yes—
841C23C24×D4711yescharacteristic
842Q8—28no—
843Q8—28no—
844Q8—4716no—
845Q8—9432no—
846Q8—948no—
847Q8—948no—
848D4—216no—
849D4—216no—
850D4—28no—
851D4—28no—
852D4—416no—
853D4—4732no—
854D4—4716no—
855D4—9432no—
856D4—9432no—
857D4—9432no—
858D4—9432no—
859D4—9416no—
860D4—9416no—
861D4—948no—
862D4—948no—
863D4—18816no—
864D4—18816no—
865C2×C4—28no—
866C2×C4—216no—
867C2×C4—216no—
868C2×C4—44no—
869C2×C4—478no—
870C2×C4—472no—
871C2×C4—474no—
872C2×C4—4716no—
873C2×C4—4716no—
874C2×C4—472no—
875C2×C4—474no—
876C2×C4—478no—
877C2×C4—9432no—
878C2×C4—9416no—
879C2×C4—9432no—
880C2×C4—9432no—
881C2×C4—944no—
882C2×C4—948no—
883C2×C4—948no—
884C2×C4—9416no—
885C2×C4—9416no—
886C2×C4—1888no—
887C2×C4—1884no—
888C2×C4—1882no—
889C2×C4C2×D4×D4718yes—
890C2×C4C2×D4×D4714yes—
891C2×C4C2×D4×D4718yes—
892C2×C4C2×D4×D4714yes—
893C2×C4C24×D4718yes—
894C2×C4C24×D4718yes—
895C2×C4C24×D4711yescharacteristic
896C2×C4C24×D4712yes—
897C2×C4C24×D4711yescharacteristic
898C22—22no—
899C22—24no—
900C22—28no—
901C22—216no—
902C22—44no—
903C22—88no—
904C22—478no—
905C22—948no—
906C22—948no—
907C22—9416no—
908C22—3768no—
909C22—37632no—
910C22—1888no—
911C22C22×D4×D4714yes—
912C22C22×D4×D4712yes—
913C22C25×D4711yescharacteristic
914C4—28no—
915C4—28no—
916C4—478no—
917C4—474no—
918C4—948no—
919C4—942no—
920C4—944no—
921C4C22×D4×D4712yes—
922C4C22×D4×D4714yes—
923C4C22×D4×D4712yes—
924C2—24no—
925C2—22no—
926C2—48no—
927C2—948no—
928C2—1888no—
929C2C23×D4×D4711yescharacteristic
930C2#585×D4712yes—
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC47×#3449C2
hypercenter#3449D47
hypocenterC47#62812
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#15689959C2semidirect
2. #20257180C2semidirect
3. #20257177C2semidirect
4. #20257170C2semidirect
5. #20257163C2semidirect
6. #20257157C2semidirect
7. #20257151C2semidirect
8. #20257149C2semidirect
9. #20256871C2semidirect
10. #20256721C2semidirect
11. #20256715C2semidirect
12. C2×#15689669C2semidirect
13. #532×D47C2semidirect
14. C2×#15689591C2semidirect
15. C47×#3449C2semidirect
17. C2×#13094072C22semidirect
18. C2×#13094071C22semidirect
19. C2×#13094071C22semidirect
20. C2×#13094070C22semidirect
21. C2×#13094070C22semidirect
22. C2×#13094069C22semidirect
23. C2×#13094069C22semidirect
25. C22×#10625350C22semidirect
26. C22×#10625350C22semidirect
27. C2×#41×D47C22semidirect
28. C2×#41×D47C22semidirect
29. #15689791C22semidirect
30. #15689786C22semidirect
31. #15689783C22semidirect
32. #15689779C22semidirect
33. #15689775C22semidirect
34. #15689771C22semidirect
35. #15689770C22semidirect
36. #15689765C22semidirect
37. #15689764C22semidirect
38. #15689760C22semidirect
39. #15689757C22semidirect
40. #15689755C22semidirect
41. #15689704C22semidirect
42. #15689700C22semidirect
43. #15689699C22semidirect
44. #15689698C22semidirect
45. #15689693C22semidirect
46. #15689692C22semidirect
47. #15689691C22semidirect
48. #15689686C22semidirect
49. #15689685C22semidirect
50. #15689681C22semidirect
51. #15689674C22semidirect
52. #15689673C22semidirect
53. #15689672C22semidirect
54. #15689671C22semidirect
55. #15689670C22semidirect
56. #15689669C22semidirect
57. #15689669C22semidirect
58. #15689669C22semidirect
59. #15689669C22semidirect
60. #15689669C22semidirect
61. #15689669C22semidirect
62. #15689668C22semidirect
63. C2×#13094022C22semidirect
64. C4⋊Q8×D47C22semidirect
65. C2×#13094020C22semidirect
66. #127×D47C22semidirect
67. C2×#13094013C22semidirect
68. C2×#13094011C22semidirect
69. #124×D47C22semidirect
70. #15689635C22semidirect
71. #15689632C22semidirect
72. C2×#13093996C22semidirect
73. #121×D47C22semidirect
74. #15689591C22semidirect
75. #15689591C22semidirect
76. #15689591C22semidirect
77. C2×#13093989C22semidirect
78. C2×#13093986C22semidirect
79. C2×C4×C22⋊D47C22semidirect
80. C2×(C22⋊D47)⋊C4C22semidirect
81. C4×D4×D47C22semidirect
82. C2×#13093981C22semidirect
83. C22×C4×Dic47C22semidirect
84. C2×C42×D47C22semidirect
85. C22×#41×C47C22semidirect
86. C47×#537C22semidirect
87. C47×#536C22semidirect
88. C47×#535C22semidirect
89. C47×#534C22semidirect
90. C47×#532C22semidirect
91. C47×#525C22semidirect
92. C2×#117×C47C22semidirect
104. C2×#10625350D4semidirect
258. C22×C4×C47C2×D4semidirect
270. C2×C22⋊D47C2×D4semidirect
307. #10625350C2×D4semidirect
308. #10625350C2×D4semidirect
311. C2×D188C2×D4semidirect
320. C2×C4×D47C2×D4semidirect
331. C2×Dic94C2×D4semidirect
458. Dic47#585semidirect
470. #3449D47semidirect
494. C22×#41C2×D47semidirect
509. #537C2×D47semidirect
513. #536C2×D47semidirect
517. #535C2×D47semidirect
520. #534C2×D47semidirect
533. #532C2×D47semidirect
543. #525C2×D47semidirect
555. C2×#117C2×D47semidirect
558. C47#62812semidirect
793. C22×C4D4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156899592
#202571802
#202571772
#202571702
#202571632
#202571572
#202571512
#202571492
#202568712
#202567212
#202567152
C2×#156896692
#532×D472
C2×#156895912
C47×#34492
#6281247