Finite Group Databasebeta

← D47×#3231 #27088340

Subgroups — D47×#3231 #27088340

Order 12032.

1778 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D47C211yesmaximal, characteristic
2#533×D47C211yesmaximal, characteristic
3#20254550C211yesmaximal, characteristic, complemented
4#20254549C211yesmaximal, characteristic, complemented
5#20254548C211yesmaximal, characteristic, complemented
6#20254547C211yesmaximal, characteristic, complemented
7#20254546C214yesmaximal, complemented
8#20254545C214yesmaximal, complemented
9#20254544C211yesmaximal, characteristic, complemented
10#20254543C211yesmaximal, characteristic, complemented
11#20254542C211yesmaximal, characteristic, complemented
12#500×D47C211yesmaximal, characteristic, complemented
13#498×D47C211yesmaximal, characteristic, complemented
14#487×D47C211yesmaximal, characteristic, complemented
15#487×D47C211yesmaximal, characteristic, complemented
16#485×D47C214yesmaximal
17#479×D47C214yesmaximal, complemented
18#431×D47C211yesmaximal, characteristic
19C47×#3231C211yesmaximal, characteristic, complemented
20#15689680C2211yescharacteristic
21#15689680C2211yescharacteristic
22#15689679—21no—
23#15689679C2212yes—
24#15689678C2211yescharacteristic
25#15689678C2211yescharacteristic
26#15689678C2211yescharacteristic
27#15689678C2211yescharacteristic
28#15689677—21no—
29#15689677—21no—
30#15689677—21no—
31#15689677C2212yes—
32#15689676—21no—
33#15689676C2212yes—
34#15689675—21no—
35#15689675—21no—
36#15689675—21no—
37#15689675C2212yes—
38C4⋊Q8×D47C2211yescharacteristic
39C4⋊Q8×D47C2211yescharacteristic
40C4⋊Q8×D47C2211yescharacteristic
41C4⋊Q8×D47C2211yescharacteristic
42#125×D47—21no—
43#125×D47C2212yes—
44C22⋊Q8×D47—21no—
45C22⋊Q8×D47—21no—
46C22⋊Q8×D47—21no—
47C22⋊Q8×D47C2212yes—
48C4×Q8×D47—21no—
49C4×Q8×D47—21no—
50C4×Q8×D47—21no—
51C4×Q8×D47C2212yes—
52#117×D47—21no—
53#117×D47C2212yes—
54C2×C42×D47C2211yescharacteristic
55#15689528C2211yescharacteristic, complemented
56#15689527C2214yescomplemented
57#15689526C2211yescharacteristic, complemented
58#15689526C2211yescharacteristic, complemented
59#15689521C2211yescharacteristic, complemented
60#15689520C2214yescomplemented
61#15689519C2211yescharacteristic, complemented
62#15689519C2211yescharacteristic, complemented
63#15689475C2211yescharacteristic, complemented
64#15689475C2211yescharacteristic, complemented
65#15689474C2211yescharacteristic, complemented
66#15689474C2211yescharacteristic, complemented
67#15689473C2211yescharacteristic, complemented
68#15689473C2211yescharacteristic, complemented
69#15689472C2214yescomplemented
70#15689472C2214yescomplemented
71#15689467C2214yes—
72#15689466C2214yes—
73#15689465C2214yes—
74#15689464C2214yes—
75#15689463C2214yes—
76#15689462C2214yes—
77#15689461C2214yes—
78#15689433C2214yescomplemented
79#15689432C2214yescomplemented
80#15689431C2214yescomplemented
81#15689430C2214yescomplemented
82#15689429C2214yescomplemented
83#15689428C2214yescomplemented
84#15689427C2214yescomplemented
85#15689176C2211yescharacteristic
86#15689175C2212yes—
87#15689174C2211yescharacteristic
88#15689174C2211yescharacteristic
89#15689173C2212yes—
90#107×D47C2214yes—
91#106×D47C2214yes—
92C4⋊C8×D47C2212yes—
93#103×D47C2214yes—
94#103×D47C2214yes—
95C22⋊C8×D47C2212yes—
96C4×C8×D47C2211yescharacteristic
97C4×C8×D47C2211yescharacteristic
98C47×#533C2211yescharacteristic
99C47×#533C2211yescharacteristic
100C47×#500C2211yescharacteristic, complemented
101C47×#498C2211yescharacteristic, complemented
102C47×#487C2211yescharacteristic, complemented
103C47×#487C2211yescharacteristic, complemented
104C47×#485C2214yes—
105C47×#479C2214yescomplemented
106C47×#431C2211yescharacteristic
107C2×Q8×D47—21no—
108C2×Q8×D47—21no—
109C2×Q8×D47—21no—
110C2×Q8×D47C2312yes—
111C22×C4×D47D411yescharacteristic
112C22×C4×D47D411yescharacteristic
113C22×C4×D47C2311yescharacteristic
114C2×C8×D47C2312yes—
115C2×C8×D47C2312yes—
116#13094024C2311yescharacteristic
117#13094024C2311yescharacteristic
118#13094024C2311yescharacteristic
119#13094024C2311yescharacteristic
120#13094023—21no—
121#13094023—21no—
122#13094023—21no—
123#13094023—21no—
124#13094023—21no—
125#13094023C2312yes—
126#13094023C2312yes—
127#13094023C2312yes—
128#13094022—21no—
129#13094022—21no—
130#13094022—21no—
131#13094022C2312yes—
132#13094016—21no—
133#13094016C2312yes—
134#13094015—21no—
135#13094015—21no—
136#13094015C2312yes—
137#13094015C2312yes—
138#13094014—22no—
139#13094014—22no—
140#13094014—22no—
141#13094014—22no—
142#13094004—21no—
143#13094004—21no—
144#13094004—21no—
145#13094004C2312yes—
146#13094003—21no—
147#13094003—21no—
148#13094003—21no—
149#13094003C2312yes—
150#13094002—22no—
151#13094002—22no—
152#13094002—22no—
153#13094002—22no—
154#13094001—22no—
155#13094001—22no—
156#13094001—22no—
157#13094001—22no—
158#13094000—21no—
159#13094000—21no—
160#13094000—21no—
161#13094000C2312yes—
162Q8×Dic47—21no—
163Q8×Dic47—21no—
164Q8×Dic47—21no—
165Q8×Dic47C2312yes—
166C4×Dic94—21no—
167C4×Dic94—21no—
168C4×Dic94—21no—
169C4×Dic94—22no—
170C4×Dic94—22no—
171C4×Dic94—22no—
172C4×Dic94—22no—
173C4×Dic94C2312yes—
174#13093989—21no—
175#13093989—21no—
176#13093989—21no—
177#13093989—22no—
178#13093989—22no—
179#13093989—22no—
180#13093989—22no—
181#13093989C2312yes—
182#13093983—21no—
183#13093983C2312yes—
184#13093982—21no—
185#13093982—21no—
186#13093982C2312yes—
187#13093982C2312yes—
188#13093981—22no—
189#13093981—22no—
190#13093980—22no—
191#13093980—22no—
192C4⋊C4×D47—21no—
193C4⋊C4×D47—21no—
194C4⋊C4×D47—22no—
195C4⋊C4×D47—22no—
196C4⋊C4×D47—21no—
197C4⋊C4×D47—21no—
198C4⋊C4×D47—21no—
199C4⋊C4×D47—22no—
200C4⋊C4×D47—22no—
201C4⋊C4×D47C2312yes—
202C4⋊C4×D47C2312yes—
203C4⋊C4×D47C2312yes—
204C22⋊C4×D47—22no—
205C22⋊C4×D47—22no—
206C2×C4×Dic47D411yescharacteristic
207C2×C4×Dic47D411yescharacteristic
208C2×C4×Dic47C2311yescharacteristic
209C42×D47—22no—
210C42×D47—22no—
211C42×D47D411yescharacteristic
212C42×D47D411yescharacteristic
213C42×D47D411yescharacteristic
214C42×D47D411yescharacteristic
215C42×D47C2311yescharacteristic
216C42×D47C2311yescharacteristic
217C42×D47C2311yescharacteristic
218C42×D47C2311yescharacteristic
219#13093958C2314yes—
220#13093957C2314yes—
221#13093957C2314yes—
222#13093956C2314yes—
223#13093955C2314yes—
224#13093955C2314yes—
225C4⋊(C47⋊C8)C2312yes—
226Dic47⋊C8C2312yes—
227Dic47⋊C8C2312yes—
228#13093949C2314yes—
229#13093949C2314yes—
230#13093948C2314yes—
231#13093948C2314yes—
232#13093947C2314yes—
233#13093947C2314yes—
234C22⋊(C47⋊C8)C2312yes—
235(C2×D47)⋊C8C2312yes—
236(C2×D47)⋊C8C2312yes—
237C4×C47⋊C8C2311yescharacteristic
238C4×C47⋊C8C2311yescharacteristic
239C8×Dic47C2312yes—
240C8×Dic47C2312yes—
241C4⋊Q8×C47C2311yescharacteristic
242C4⋊Q8×C47C2311yescharacteristic
243C4⋊Q8×C47C2311yescharacteristic
244C4⋊Q8×C47C2311yescharacteristic
245#125×C47—21no—
246#125×C47C2312yes—
247C22⋊Q8×C47—21no—
248C22⋊Q8×C47—21no—
249C22⋊Q8×C47—21no—
250C22⋊Q8×C47C2312yes—
251C4×Q8×C47—21no—
252C4×Q8×C47—21no—
253C4×Q8×C47—21no—
254C4×Q8×C47C2312yes—
255#117×C47—21no—
256#117×C47C2312yes—
257C2×C42×C47C2311yescharacteristic
258#107×C47C2314yes—
259#106×C47C2314yes—
260C4⋊C8×C47C2312yes—
261#103×C47C2314yes—
262#103×C47C2314yes—
263C22⋊C8×C47C2312yes—
264C4×C8×C47C2311yescharacteristic
265C4×C8×C47C2311yescharacteristic
266C23×D47C2×D411yescharacteristic
267C2×Q8×C47—21no—
268C2×Q8×C47—21no—
269C2×Q8×C47—21no—
270C2×Q8×C47C2412yes—
271C22×C4×C47C2×D411yescharacteristic
272C22×C4×C47C2×D411yescharacteristic
273C22×C4×C47C2411yescharacteristic
274C22×Dic47C2×D411yescharacteristic
275C22×Dic47C2×D411yescharacteristic
276C22×Dic47C2×D411yescharacteristic
277Q8×D47—28no—
278Q8×D47—44no—
279Q8×D47—44no—
280Q8×D47—44no—
281C2×C4×D47—24no—
282C2×C4×D47—24no—
283C2×C4×D47—24no—
284C2×C4×D47—22no—
285C2×C4×D47—22no—
286C2×C4×D47—22no—
287C2×C4×D47—22no—
288C2×C4×D47C2×D411yescharacteristic
289C2×C4×D47C2×D411yescharacteristic
290C2×C4×D47C2×D411yescharacteristic
291C2×C4×D47C2×D411yescharacteristic
292C2×C4×D47C2×D411yescharacteristic
293C2×C4×D47C2×D411yescharacteristic
294C2×C4×D47C2×D411yescharacteristic
295C2×C4×D47C2×D411yescharacteristic
296C2×C4×D47C2×D411yescharacteristic
297C2×C4×D47C2×D411yescharacteristic
298C2×C4×D47C2411yescharacteristic
299C2×C4×D47C2411yescharacteristic
300C2×Dic94—21no—
301C2×Dic94—21no—
302C2×Dic94—21no—
303C2×Dic94—22no—
304C2×Dic94—22no—
305C2×Dic94—22no—
306C2×Dic94—22no—
307C2×Dic94C2412yes—
308C2×C8×C47C2412yes—
309C2×C8×C47C2412yes—
310C4⋊C4×C47—21no—
311C4⋊C4×C47—21no—
312C4⋊C4×C47—22no—
313C4⋊C4×C47—22no—
314C4⋊C4×C47—21no—
315C4⋊C4×C47—21no—
316C4⋊C4×C47—21no—
317C4⋊C4×C47—22no—
318C4⋊C4×C47—22no—
319C4⋊C4×C47C2412yes—
320C4⋊C4×C47C2412yes—
321C4⋊C4×C47C2412yes—
322C22⋊C4×C47—22no—
323C22⋊C4×C47—22no—
324C42×C47—22no—
325C42×C47—22no—
326C42×C47C2×D411yescharacteristic
327C42×C47C2×D411yescharacteristic
328C42×C47C2411yescharacteristic
329C42×C47C2411yescharacteristic
330C22⋊Dic47—22no—
331C22⋊Dic47—22no—
332(C2×D47)⋊C4—22no—
333(C2×D47)⋊C4—22no—
334(C2×D47)⋊C4—22no—
335(C2×D47)⋊C4—22no—
336C4⋊Dic47—21no—
337C4⋊Dic47—21no—
338C4⋊Dic47—21no—
339C4⋊Dic47—21no—
340C4⋊Dic47—21no—
341C4⋊Dic47—22no—
342C4⋊Dic47—22no—
343C4⋊Dic47—22no—
344C4⋊Dic47—22no—
345C4⋊Dic47C2412yes—
346C4⋊Dic47C2412yes—
347C4⋊Dic47C2412yes—
348Dic47⋊C4—22no—
349Dic47⋊C4—22no—
350Dic47⋊C4—22no—
351Dic47⋊C4—22no—
352Dic47⋊C4—22no—
353Dic47⋊C4—22no—
354Dic47⋊C4—22no—
355Dic47⋊C4—22no—
356Dic47⋊C4—22no—
357Dic47⋊C4—22no—
358Dic47⋊C4—22no—
359Dic47⋊C4—22no—
360Dic47⋊C4—22no—
361Dic47⋊C4—22no—
362Dic47⋊C4—22no—
363Dic47⋊C4—22no—
364C4×Dic47—22no—
365C4×Dic47—22no—
366C4×Dic47—22no—
367C4×Dic47—22no—
368C4×Dic47—22no—
369C4×Dic47—22no—
370C4×Dic47C2×D411yescharacteristic
371C4×Dic47C2×D411yescharacteristic
372C4×Dic47C2×D411yescharacteristic
373C4×Dic47C2×D411yescharacteristic
374C4×Dic47C2×D411yescharacteristic
375C4×Dic47C2×D411yescharacteristic
376C4×Dic47C2×D411yescharacteristic
377C4×Dic47C2×D411yescharacteristic
378C4×Dic47C2×D411yescharacteristic
379C4×Dic47C2×D411yescharacteristic
380C4×Dic47C2411yescharacteristic
381C4×Dic47C2411yescharacteristic
382C2×C47⋊C8C2412yes—
383C2×C47⋊C8C2412yes—
384C8×D47—24no—
385C8×D47—24no—
386C23×C47C22×D411yescharacteristic
387C22×D47—22no—
388C22×D47—22no—
389C22×D47—22no—
390C22×D47C22×D411yescharacteristic
391C22×D47C22×D411yescharacteristic
392Q8×C47—24no—
393Q8×C47—42no—
394Q8×C47—42no—
395Q8×C47—42no—
396C2×C4×C47—22no—
397C2×C4×C47—22no—
398C2×C4×C47—22no—
399C2×C4×C47—22no—
400C2×C4×C47—22no—
401C2×C4×C47—22no—
402C2×C4×C47—22no—
403C2×C4×C47C22×D411yescharacteristic
404C2×C4×C47C22×D411yescharacteristic
405C2×C4×C47C22×D411yescharacteristic
406C2×C4×C47C22×D411yescharacteristic
407C2×C4×C47C22×D411yescharacteristic
408C2×C4×C47C2511yescharacteristic
409C2×Dic47—22no—
410C2×Dic47—22no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—22no—
414C2×Dic47—22no—
415C2×Dic47—22no—
416C2×Dic47C22×D411yescharacteristic
417C2×Dic47C22×D411yescharacteristic
418C2×Dic47C22×D411yescharacteristic
419C2×Dic47C22×D411yescharacteristic
420C2×Dic47C22×D411yescharacteristic
421C2×Dic47C22×D411yescharacteristic
422C4×D47—22no—
423C4×D47—22no—
424C4×D47—22no—
425C4×D47—22no—
426C4×D47—22no—
427C4×D47—22no—
428C4×D47—22no—
429C4×D47—22no—
430C4×D47—22no—
431C4×D47—44no—
432C4×D47—44no—
433C4×D47—44no—
434C4×D47—44no—
435C4×D47#13514yes—
436C4×D47#13714yes—
437C4×D472−1+414yes—
438Dic94—24no—
439Dic94—42no—
440Dic94—42no—
441Dic94—42no—
442Dic94—44no—
443Dic94—44no—
444Dic94—44no—
445Dic94—44no—
446C8×C47—22no—
447C8×C47—22no—
448C47⋊C8—22no—
449C47⋊C8—22no—
450C2×#3231—471nomaximal, Sylow
451C22×C47—21no—
452C22×C47—21no—
453C22×C47—21no—
454C22×C47C23×D411yescharacteristic
455C2×D47—21no—
456C2×D47—21no—
457C2×D47—21no—
458C2×D47—44no—
459C2×D47#53612yes—
460C2×D47C2×#13512yes—
461C2×D47C2×#13712yes—
462C4×C47—21no—
463C4×C47—21no—
464C4×C47—21no—
465C4×C47—42no—
466C4×C47—42no—
467C4×C47—42no—
468C4×C47—42no—
469C4×C47C2×#13512yes—
470C4×C47C2×#13712yes—
471C4×C47C2×2−1+412yes—
472Dic47—21no—
473Dic47—21no—
474Dic47—21no—
475Dic47—42no—
476Dic47—42no—
477Dic47—42no—
478Dic47—42no—
479Dic47#53612yes—
480Dic47C2×#13512yes—
481Dic47C2×#13712yes—
482C2×#533—471no—
483C2×#533—471no—
484#3231—471no—
485#3231—471no—
486#3231—471no—
487#3231—471no—
488#3231—474no—
489#3231—474no—
490#3231—471no—
491#3231—471no—
492#3231—471no—
493#3231D4711yescharacteristic, direct product factor
494C2×#500—471no—
495C2×#498—471no—
496C2×#487—471no—
497C2×#487—471no—
498C2×#485—474no—
499C2×#479—474no—
500C2×#431—471no—
501C2×C47—41no—
502C2×C47C2×#53611yescharacteristic
503C2×C47C22×#13511yescharacteristic
504C2×C47C22×#13711yescharacteristic
505D47—41no—
506D47#323114yesdirect product factor
507#533—471no—
508#533—471no—
509#533—472no—
510#533—472no—
511#533—471no—
512#533—471no—
513#533—472no—
514#533—472no—
515#533—471no—
516#533—471no—
517#533—941no—
518#533—941no—
519#533—941no—
520#533—941no—
521#533—941no—
522#533—941no—
523#533—941no—
524#533—941no—
525#533C2×D4711yescharacteristic
526#533C2×D4711yescharacteristic
527C2×C4⋊Q8—471no—
528C2×C4⋊Q8—471no—
529C2×C4⋊Q8—471no—
530C2×C4⋊Q8—471no—
531C2×#125—472no—
532C2×#125—941no—
533C2×C22⋊Q8—472no—
534C2×C22⋊Q8—941no—
535C2×C22⋊Q8—941no—
536C2×C22⋊Q8—941no—
537C2×C4×Q8—472no—
538C2×C4×Q8—941no—
539C2×C4×Q8—941no—
540C2×C4×Q8—941no—
541C2×#117—472no—
542C2×#117—941no—
543C22×C42—471no—
544#500—471no—
545#500—471no—
546#500—474no—
547#500—471no—
548#500C2×D4711yescharacteristic, complemented
549#498—471no—
550#498—471no—
551#498—474no—
552#498—471no—
553#498C2×D4711yescharacteristic, complemented
554#487—471no—
555#487—471no—
556#487—471no—
557#487—471no—
558#487—474no—
559#487—474no—
560#487—471no—
561#487—471no—
562#487C2×D4711yescharacteristic, complemented
563#487C2×D4711yescharacteristic, complemented
564#485—474no—
565#485—474no—
566#485—474no—
567#485—474no—
568#485—474no—
569#485—474no—
570#485—474no—
571#485C2×D4714yes—
572#479—474no—
573#479—474no—
574#479—474no—
575#479—474no—
576#479—474no—
577#479—474no—
578#479—474no—
579#479C2×D4714yescomplemented
580#431—471no—
581#431—472no—
582#431—472no—
583#431—471no—
584#431—471no—
585#431C2×D4711yescharacteristic
586C2×#107—474no—
587C2×#106—474no—
588C2×C4⋊C8—472no—
589C2×#103—474no—
590C2×#103—474no—
591C2×C22⋊C8—472no—
592C2×C4×C8—471no—
593C2×C4×C8—471no—
594C47C2×#323111yescharacteristic, complemented, Sylow
595C22×Q8—472no—
596C22×Q8—941no—
597C22×Q8—941no—
598C22×Q8—941no—
599C23×C4—471no—
600C23×C4—471no—
601C23×C4—471no—
602C22×C8—472no—
603C22×C8—472no—
604C4⋊Q8—472no—
605C4⋊Q8—472no—
606C4⋊Q8—472no—
607C4⋊Q8—472no—
608C4⋊Q8—471no—
609C4⋊Q8—471no—
610C4⋊Q8—471no—
611C4⋊Q8—471no—
612C4⋊Q8—941no—
613C4⋊Q8—941no—
614C4⋊Q8—941no—
615C4⋊Q8—941no—
616C4⋊Q8—941no—
617C4⋊Q8—941no—
618C4⋊Q8—941no—
619C4⋊Q8—941no—
620C4⋊Q8C22×D4711yescharacteristic
621C4⋊Q8C22×D4711yescharacteristic
622C4⋊Q8C22×D4711yescharacteristic
623C4⋊Q8C22×D4711yescharacteristic
624#125—21no—
625#125—472no—
626#125—472no—
627#125—472no—
628#125—942no—
629#125—942no—
630#125—942no—
631#125—942no—
632#125—941no—
633#125—941no—
634#125—941no—
635#125C22×D4712yes—
636C22⋊Q8—21no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—472no—
640C22⋊Q8—472no—
641C22⋊Q8—472no—
642C22⋊Q8—942no—
643C22⋊Q8—942no—
644C22⋊Q8—942no—
645C22⋊Q8—942no—
646C22⋊Q8—942no—
647C22⋊Q8—942no—
648C22⋊Q8—942no—
649C22⋊Q8—942no—
650C22⋊Q8—941no—
651C22⋊Q8—941no—
652C22⋊Q8—941no—
653C22⋊Q8—941no—
654C22⋊Q8—941no—
655C22⋊Q8—941no—
656C22⋊Q8—941no—
657C22⋊Q8—941no—
658C22⋊Q8—941no—
659C22⋊Q8C22×D4712yes—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8—21no—
663C4×Q8—472no—
664C4×Q8—472no—
665C4×Q8—472no—
666C4×Q8—942no—
667C4×Q8—942no—
668C4×Q8—942no—
669C4×Q8—942no—
670C4×Q8—942no—
671C4×Q8—942no—
672C4×Q8—941no—
673C4×Q8—941no—
674C4×Q8—942no—
675C4×Q8—942no—
676C4×Q8—941no—
677C4×Q8—941no—
678C4×Q8—941no—
679C4×Q8—941no—
680C4×Q8—941no—
681C4×Q8—941no—
682C4×Q8—941no—
683C4×Q8C22×D4712yes—
684#117—21no—
685#117—472no—
686#117—472no—
687#117—472no—
688#117—942no—
689#117—942no—
690#117—942no—
691#117—942no—
692#117—941no—
693#117—941no—
694#117—941no—
695#117C22×D4712yes—
696C2×C4⋊C4—472no—
697C2×C4⋊C4—472no—
698C2×C4⋊C4—472no—
699C2×C4⋊C4—941no—
700C2×C4⋊C4—941no—
701C2×C4⋊C4—942no—
702C2×C4⋊C4—942no—
703C2×C4⋊C4—942no—
704C2×C4⋊C4—942no—
705C2×C4⋊C4—941no—
706C2×C4⋊C4—941no—
707C2×C4⋊C4—941no—
708C2×C22⋊C4—942no—
709C2×C22⋊C4—942no—
710C2×C42—471no—
711C2×C42—471no—
712C2×C42—471no—
713C2×C42—471no—
714C2×C42—471no—
715C2×C42—471no—
716C2×C42—471no—
717C2×C42—471no—
718C2×C42—471no—
719C2×C42—471no—
720C2×C42—471no—
721C2×C42—942no—
722C2×C42—942no—
723C2×C42C22×D4711yescharacteristic
724#107—474no—
725#107—474no—
726#107—474no—
727#107C22×D4714yes—
728#106—474no—
729#106—474no—
730#106—474no—
731#106C22×D4714yes—
732C4⋊C8—472no—
733C4⋊C8—472no—
734C4⋊C8—472no—
735C4⋊C8C22×D4712yes—
736#103—474no—
737#103—474no—
738#103—474no—
739#103—474no—
740#103—474no—
741#103—474no—
742#103C22×D4714yes—
743#103C22×D4714yes—
744C22⋊C8—472no—
745C22⋊C8—472no—
746C22⋊C8—472no—
747C22⋊C8C22×D4712yes—
748C4×C8—472no—
749C4×C8—472no—
750C4×C8—471no—
751C4×C8—471no—
752C4×C8C22×D4711yescharacteristic
753C4×C8C22×D4711yescharacteristic
754C24—471no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—472no—
759C2×Q8—942no—
760C2×Q8—942no—
761C2×Q8—942no—
762C2×Q8—942no—
763C2×Q8—948no—
764C2×Q8—941no—
765C2×Q8—941no—
766C2×Q8—941no—
767C2×Q8—1884no—
768C2×Q8—1884no—
769C2×Q8—1884no—
770C2×Q8C23×D4712yes—
771C22×C4—471no—
772C22×C4—471no—
773C22×C4—471no—
774C22×C4—471no—
775C22×C4—471no—
776C22×C4—471no—
777C22×C4—471no—
778C22×C4—471no—
779C22×C4—471no—
780C22×C4—471no—
781C22×C4—471no—
782C22×C4—471no—
783C22×C4—471no—
784C22×C4—471no—
785C22×C4—471no—
786C22×C4—944no—
787C22×C4—944no—
788C22×C4—944no—
789C22×C4—942no—
790C22×C4—942no—
791C22×C4—942no—
792C22×C4—942no—
793C22×C4D4×D4711yescharacteristic
794C22×C4D4×D4711yescharacteristic
795C22×C4C23×D4711yescharacteristic
796C2×C8—472no—
797C2×C8—472no—
798C2×C8—944no—
799C2×C8—944no—
800C2×C8C23×D4712yes—
801C2×C8C23×D4712yes—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—472no—
812C4⋊C4—472no—
813C4⋊C4—472no—
814C4⋊C4—942no—
815C4⋊C4—942no—
816C4⋊C4—942no—
817C4⋊C4—942no—
818C4⋊C4—942no—
819C4⋊C4—942no—
820C4⋊C4—942no—
821C4⋊C4—942no—
822C4⋊C4—942no—
823C4⋊C4—942no—
824C4⋊C4—942no—
825C4⋊C4—942no—
826C4⋊C4—942no—
827C4⋊C4—942no—
828C4⋊C4—942no—
829C4⋊C4—942no—
830C4⋊C4—942no—
831C4⋊C4—942no—
832C4⋊C4—942no—
833C4⋊C4—942no—
834C4⋊C4—941no—
835C4⋊C4—941no—
836C4⋊C4—941no—
837C4⋊C4—941no—
838C4⋊C4—941no—
839C4⋊C4C23×D4712yes—
840C4⋊C4C23×D4712yes—
841C4⋊C4C23×D4712yes—
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—942no—
845C22⋊C4—942no—
846C22⋊C4—942no—
847C22⋊C4—942no—
848C22⋊C4—942no—
849C22⋊C4—942no—
850C42—22no—
851C42—22no—
852C42—471no—
853C42—471no—
854C42—471no—
855C42—471no—
856C42—471no—
857C42—471no—
858C42—471no—
859C42—471no—
860C42—471no—
861C42—471no—
862C42—471no—
863C42—471no—
864C42—942no—
865C42—942no—
866C42—942no—
867C42—942no—
868C42—942no—
869C42—942no—
870C42D4×D4711yescharacteristic
871C42D4×D4711yescharacteristic
872C42C23×D4711yescharacteristic
873C42C23×D4711yescharacteristic
874C23—471no—
875C23—471no—
876C23—942no—
877C23—942no—
878C23—942no—
879C23C2×D4×D4711yescharacteristic
880Q8—24no—
881Q8—42no—
882Q8—42no—
883Q8—42no—
884Q8—944no—
885Q8—1884no—
886Q8—1884no—
887Q8—1884no—
888Q8—1884no—
889Q8—1882no—
890Q8—1882no—
891Q8—1882no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—471no—
900C2×C4—471no—
901C2×C4—471no—
902C2×C4—474no—
903C2×C4—474no—
904C2×C4—474no—
905C2×C4—471no—
906C2×C4—471no—
907C2×C4—471no—
908C2×C4—942no—
909C2×C4—942no—
910C2×C4—942no—
911C2×C4—942no—
912C2×C4—942no—
913C2×C4—942no—
914C2×C4—942no—
915C2×C4—942no—
916C2×C4—942no—
917C2×C4—942no—
918C2×C4—942no—
919C2×C4—942no—
920C2×C4—942no—
921C2×C4—942no—
922C2×C4—942no—
923C2×C4—942no—
924C2×C4—1884no—
925C2×C4—1884no—
926C2×C4—1884no—
927C2×C4—1884no—
928C2×C4C2×D4×D4711yescharacteristic
929C2×C4C2×D4×D4711yescharacteristic
930C2×C4C2×D4×D4711yescharacteristic
931C2×C4C2×D4×D4711yescharacteristic
932C2×C4C2×D4×D4711yescharacteristic
933C2×C4C24×D4711yescharacteristic
934C8—22no—
935C8—22no—
936C8—942no—
937C8—942no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—472no—
942C22—472no—
943C22—472no—
944C22—941no—
945C22—941no—
946C22—941no—
947C22—1884no—
948C22C22×D4×D4711yescharacteristic
949C4—21no—
950C4—21no—
951C4—21no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—472no—
957C4—472no—
958C4—472no—
959C4—941no—
960C4—941no—
961C4—941no—
962C4—1882no—
963C4—1882no—
964C4—1882no—
965C4—1882no—
966C4#135×D4712yes—
967C4#137×D4712yes—
968C42−1+4×D4712yes—
969C2—41no—
970C2—474no—
971C2—1881no—
972C2#536×D4711yescharacteristic
973C2C2×#135×D4711yescharacteristic
974C2C2×#137×D4711yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3231C2
socleC22×C47C23×D4
prime radicalC23×D47C2×D4
hypercenter#3231D47
hypocenterC47C2×#3231
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
3. #20254550C2semidirect
4. #20254549C2semidirect
5. #20254548C2semidirect
6. #20254547C2semidirect
7. #20254546C2semidirect
8. #20254545C2semidirect
9. #20254544C2semidirect
10. #20254543C2semidirect
11. #20254542C2semidirect
12. #500×D47C2semidirect
13. #498×D47C2semidirect
14. #487×D47C2semidirect
15. #487×D47C2semidirect
17. #479×D47C2semidirect
19. C47×#3231C2semidirect
55. #15689528C22semidirect
56. #15689527C22semidirect
57. #15689526C22semidirect
58. #15689526C22semidirect
59. #15689521C22semidirect
60. #15689520C22semidirect
61. #15689519C22semidirect
62. #15689519C22semidirect
63. #15689475C22semidirect
64. #15689475C22semidirect
65. #15689474C22semidirect
66. #15689474C22semidirect
67. #15689473C22semidirect
68. #15689473C22semidirect
69. #15689472C22semidirect
70. #15689472C22semidirect
78. #15689433C22semidirect
79. #15689432C22semidirect
80. #15689431C22semidirect
81. #15689430C22semidirect
82. #15689429C22semidirect
83. #15689428C22semidirect
84. #15689427C22semidirect
100. C47×#500C22semidirect
101. C47×#498C22semidirect
102. C47×#487C22semidirect
103. C47×#487C22semidirect
105. C47×#479C22semidirect
493. #3231D47direct (N × H)
506. D47#3231direct (N × H)
548. #500C2×D47semidirect
553. #498C2×D47semidirect
562. #487C2×D47semidirect
563. #487C2×D47semidirect
579. #479C2×D47semidirect
594. C47C2×#3231semidirect

Maximal subgroups

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

subgroupindex
#533×D472
#202545502
#202545492
#202545482
#202545472
#202545462
#202545452
#202545442
#202545432
#202545422
#500×D472
#498×D472
#487×D472
#485×D472
#479×D472
#431×D472
C47×#32312
C2×#323147