Finite Group Databasebeta

← C2×#20253462 #27084354

Subgroups — C2×#20253462 #27084354

Order 12032.

2170 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689678C211yesmaximal, characteristic, complemented
2C2×C4×#10625354C211yesmaximal, characteristic
3#20253462C2116yesmaximal, direct product factor
4C2×#15689467C212yesmaximal, complemented
5C2×#15689400C211yesmaximal, characteristic, complemented
6C2×#15689333C211yesmaximal, characteristic, complemented
7C2×#15689329C211yesmaximal, characteristic, complemented
8C2×#15689288C212yesmaximal
9C2×#15689215C212yesmaximal, complemented
10C2×#15689210C212yesmaximal, complemented
11C2×#15689175C211yesmaximal, characteristic, complemented
12C2×C47×#475C211yesmaximal, characteristic, complemented
13C22×#10625354C2211yescharacteristic
14C22×#10625337C2212yes—
15C22×#10625325C2212yes—
16#15689678—24no—
17#15689678C2218yescomplemented
18C2×#13094024C2211yescharacteristic
19C2×#13094015—21no—
20C2×#13094004C2212yes—
21C2×#13094000—21no—
22C4×#10625354—24no—
23C4×#10625354C2218yes—
24C2×Q8×Dic47—21no—
25C2×Q8×Dic47C2211yescharacteristic
26C2×#13093989C2212yes—
27C2×C4×D188—21no—
28C2×C4×D188C2211yescharacteristic
29C2×#13093986—21no—
30C2×#13093986C2211yescharacteristic
31C2×#13093982—21no—
32C2×#13093982—21no—
33C2×#13093982C2211yescharacteristic
34C2×C42×D47—21no—
35C2×C42×D47C2211yescharacteristic
36#15689467C22116yescomplemented
37#15689400C2218yescomplemented
38#15689333C2218yescomplemented
39#15689329C2218yescomplemented
40#15689288C22116yes—
41#15689215C22116yescomplemented
42#15689210C22116yescomplemented
43#15689175C2218yescomplemented
44C2×#13093957C2212yes—
45C2×C4⋊(C47⋊C8)C2211yescharacteristic
46C2×#13093949C2212yes—
47C2×#13093947C2212yes—
48C2×#13093944C2212yes—
49C2×(C2×D47)⋊C8C2212yes—
50C2×C8×Dic47C2212yes—
51C2×C4⋊Q8×C47C2211yescharacteristic
52C2×C4×Q8×C47C2211yescharacteristic
53C47×#475C2218yescomplemented
54C2×#106×C47C2212yes—
55C2×C4⋊C8×C47C2211yescharacteristic
56C2×#103×C47C2212yes—
57C2×#10625354—24no—
58C2×#10625354—24no—
59C2×#10625354—22no—
60C2×#10625354C2314yes—
61C22×Dic94C2312yes—
62C22×D188—21no—
63C22×D188C2311yescharacteristic
64C22×C4×D47—21no—
65C22×C4×D47—21no—
66C22×C4×D47—21no—
67C22×C4×D47D411yescharacteristic
68C22×C4×D47D411yescharacteristic
69C22×C4×D47C2311yescharacteristic
70C2×#10625337—28no—
71C2×#10625337C2318yes—
72C2×#10625325—28no—
73C2×#10625325C2318yes—
74C22×C47⋊C8C2312yes—
75#13094024—22no—
76#13094024C2314yes—
77#13094015—28no—
78#13094004—24no—
79#13094004C2318yes—
80#13094000—28no—
81Q8×Dic47—28no—
82Q8×Dic47—22no—
83Q8×Dic47C2314yes—
84#13093989—24no—
85#13093989C2318yes—
86C4×D188—28no—
87C4×D188—22no—
88C4×D188C2314yes—
89#13093986—28no—
90#13093986—22no—
91#13093986C2314yes—
92#13093982—28no—
93#13093982—22no—
94#13093982—28no—
95#13093982C2314yes—
96C2×C4⋊Dic47—21no—
97C2×C4⋊Dic47—21no—
98C2×C4⋊Dic47—21no—
99C2×C4⋊Dic47—22no—
100C2×C4⋊Dic47C2311yescharacteristic
101C2×Dic47⋊C4—22no—
102C2×(C2×D47)⋊C4—22no—
103C2×(C2×D47)⋊C4—21no—
104C2×(C2×D47)⋊C4—21no—
105C2×(C2×D47)⋊C4—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47—21no—
108C2×C4×Dic47—22no—
109C2×C4×Dic47D411yescharacteristic
110C2×C4×Dic47D411yescharacteristic
111C2×C4×Dic47C2311yescharacteristic
112C42×D47—28no—
113C42×D47D414yes—
114C42×D47C2314yes—
115#13093957C2318yes—
116C4⋊(C47⋊C8)C2314yes—
117#13093949C2318yes—
118#13093947C2318yes—
119#13093944C2318yes—
120(C2×D47)⋊C8C2318yes—
121C8×Dic47C2318yes—
122C22×Q8×C47—21no—
123C22×Q8×C47C2311yescharacteristic
124C22×C8×C47C2312yes—
125C4⋊Q8×C47—22no—
126C4⋊Q8×C47C2314yes—
127C4×Q8×C47—22no—
128C4×Q8×C47C2314yes—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C4⋊C4×C47C2312yes—
133C2×C42×C47—21no—
134C2×C42×C47C2311yescharacteristic
135#106×C47C2318yes—
136C4⋊C8×C47C2314yes—
137#103×C47C2318yes—
138C23×D47—21no—
139C23×D47C2×D411yescharacteristic
140C2×Q8×C47—21no—
141C2×Q8×C47—24no—
142C2×Q8×C47—22no—
143C2×Q8×C47—44no—
144C2×Q8×C47#4114yes—
145C2×Q8×C47C2412yes—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—22no—
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2411yescharacteristic
152C22×Dic47—21no—
153C22×Dic47—22no—
154C22×Dic47C2×D411yescharacteristic
155C22×Dic47C2×D411yescharacteristic
156C22×Dic47C2×D411yescharacteristic
157#10625354—216no—
158#10625354—28no—
159#10625354—28no—
160C2×D188—28no—
161C2×D188—24no—
162C2×D188—21no—
163C2×D188—22no—
164C2×D188#4114yes—
165C2×D188C2412yes—
166C2×C4×D47—28no—
167C2×C4×D47—24no—
168C2×C4×D47—22no—
169C2×C4×D47—22no—
170C2×C4×D47—24no—
171C2×C4×D47—24no—
172C2×C4×D47—24no—
173C2×C4×D47—24no—
174C2×C4×D47—44no—
175C2×C4×D47—44no—
176C2×C4×D47C2×D412yes—
177C2×C4×D47C2×D414yes—
178C2×C4×D47C2×D414yes—
179C2×C4×D47C2412yes—
180C2×Dic94—24no—
181C2×Dic94—24no—
182C2×Dic94—22no—
183C2×Dic94C2414yes—
184C2×C8×C47—24no—
185C2×C8×C47C2414yes—
186C4⋊C4×C47—24no—
187C4⋊C4×C47—24no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—22no—
190C4⋊C4×C47C2414yes—
191C4⋊C4×C47C2412yes—
192C42×C47—24no—
193C42×C47C2×D412yes—
194C42×C47C2412yes—
195#10625337—216no—
196(C2×D47)⋊C4—28no—
197(C2×D47)⋊C4—24no—
198(C2×D47)⋊C4—24no—
199(C2×D47)⋊C4—24no—
200C4⋊Dic47—24no—
201C4⋊Dic47—24no—
202C4⋊Dic47—21no—
203C4⋊Dic47—24no—
204C4⋊Dic47—28no—
205C4⋊Dic47C2412yes—
206Dic47⋊C4—28no—
207C4×Dic47—24no—
208C4×Dic47—24no—
209C4×Dic47—28no—
210C4×Dic47C2×D414yes—
211C4×Dic47C2×D412yes—
212C4×Dic47C2×D414yes—
213C4×Dic47C2412yes—
214C2×C47⋊C8—24no—
215C2×C47⋊C8C2414yes—
216#10625325—216no—
217C23×C47C22×D411yescharacteristic
218C22×D47—22no—
219C22×D47—24no—
220C22×D47—22no—
221C22×D47—22no—
222C22×D47—22no—
223C22×D47—42no—
224C22×D47—42no—
225C22×D47C22×D412yes—
226Q8×C47—24no—
227Q8×C47—22no—
228Q8×C47—48no—
229Q8×C47C2×#4114yes—
230C2×C4×C47—24no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—24no—
234C2×C4×C47—22no—
235C2×C4×C47—44no—
236C2×C4×C47—42no—
237C2×C4×C47#13514yes—
238C2×C4×C47C22×D412yes—
239C2×C4×C47C22×D411yescharacteristic
240C2×C4×C47C22×D412yes—
241C2×C4×C47C2×#4112yes—
242C2×C4×C47C2×#4112yes—
243C2×C4×C47C2511yescharacteristic
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—24no—
248C2×Dic47—44no—
249C2×Dic47—42no—
250C2×Dic47#13714yes—
251C2×Dic47C22×D412yes—
252C2×Dic47C22×D412yes—
253C2×Dic47C22×D412yes—
254D188—216no—
255D188—24no—
256D188—22no—
257D188C2×#4114yes—
258C4×D47—216no—
259C4×D47—24no—
260C4×D47—28no—
261C4×D47—22no—
262C4×D47—22no—
263C4×D47—28no—
264C4×D47—48no—
265C4×D47—48no—
266Dic94—24no—
267Dic94—24no—
268Dic94—44no—
269C8×C47—24no—
270C47⋊C8—24no—
271C2×#3107—471nomaximal, Sylow
272C22×C47#52512yes—
273C22×C47C2×#13512yes—
274C22×C47C2×#13712yes—
275C22×C47C23×D411yescharacteristic
276C2×D47—22no—
277C2×D47—24no—
278C2×D47—22no—
279C2×D47—22no—
280C2×D47—44no—
281C2×D47—48no—
282C2×D47—42no—
283C2×D47—42no—
284C4×C47—24no—
285C4×C47—22no—
286C4×C47—44no—
287C4×C47—42no—
288C4×C47#52512yes—
289C4×C47C2×#13514yes—
290C4×C47C22×#4111yescharacteristic
291C4×C47C22×#4111yescharacteristic
292Dic47—22no—
293Dic47—22no—
294Dic47—44no—
295Dic47—42no—
296Dic47C2×#13714yes—
297C2×#533—471no—
298C2×C4×#41—471no—
299#3107—4716no—
300C2×#485—472no—
301C2×#475D4711yescharacteristic, complemented
302C2×#474—471no—
303C2×#462—471no—
304C2×#461—471no—
305C2×#452—472no—
306C2×C4×Q16—472no—
307C2×C4×SD16—472no—
308C2×#431—471no—
309C2×C47#310714yescomplemented
310C2×C47C2×#52511yescharacteristic
311C2×C47C22×#13511yescharacteristic
312C2×C47C22×#13711yescharacteristic
313D47—42no—
314D47—44no—
315C22×#41—471no—
316C22×Q16—472no—
317C22×SD16—472no—
318#533—478no—
319#533—944no—
320C2×C4⋊Q8—471no—
321C2×C4⋊Q8C2×D4711yescharacteristic
322C2×#125—941no—
323C2×C22⋊Q8—472no—
324C2×C22⋊Q8—941no—
325C4×#41—478no—
326C4×#41—944no—
327C2×C4×Q8—471no—
328C2×C4×Q8—472no—
329C2×C4×Q8—941no—
330C2×C4×Q8C2×D4711yescharacteristic
331C2×C4×D4—471no—
332C2×C4×D4—471no—
333C2×C4×D4—941no—
334C2×C4×D4—941no—
335C2×#117—471no—
336C2×#117—941no—
337C2×#117—941no—
338C22×C42—471no—
339C22×C42—941no—
340#485—4716no—
341#475C2×D4718yescomplemented
342#474—478no—
343#462—478no—
344#461—478no—
345#452—4716no—
346C4×Q16—4716no—
347C4×SD16—4716no—
348#431—478no—
349C2×#107—472no—
350C2×#106C2×D4712yes—
351C2×C4⋊C8—471no—
352C2×C4⋊C8C2×D4711yescharacteristic
353C2×#103—472no—
354C2×#103—472no—
355C2×#103C2×D4712yes—
356C2×#102—472no—
357C2×C22⋊C8—472no—
358C2×C4×C8—472no—
359C47C2×#310711yescharacteristic, complemented, Sylow
360C2×#41—474no—
361C2×#41—942no—
362C2×#41—944no—
363C2×#41—944no—
364C22×Q8—21no—
365C22×Q8—472no—
366C22×Q8C22×D4711yescharacteristic
367C22×D4—471no—
368C22×D4—941no—
369C23×C4—471no—
370C23×C4—471no—
371C23×C4—471no—
372C23×C4—941no—
373C23×C4—941no—
374C23×C4—941no—
375C2×Q16—478no—
376C2×Q16—948no—
377C2×SD16—478no—
378C2×SD16—948no—
379C22×C8—472no—
380C22×C8C22×D4712yes—
381C4⋊Q8—22no—
382C4⋊Q8—474no—
383C4⋊Q8—942no—
384C4⋊Q8C22×D4714yes—
385#125—948no—
386C22⋊Q8—478no—
387C22⋊Q8—944no—
388C22⋊Q8—948no—
389C4×Q8—22no—
390C4×Q8—474no—
391C4×Q8—478no—
392C4×Q8—944no—
393C4×Q8—942no—
394C4×Q8—948no—
395C4×Q8C22×D4714yes—
396C4×D4—474no—
397C4×D4—474no—
398C4×D4—948no—
399C4×D4—942no—
400C4×D4—948no—
401C4×D4—942no—
402#117—474no—
403#117—948no—
404#117—942no—
405#117—948no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—471no—
409C2×C4⋊C4—941no—
410C2×C4⋊C4—942no—
411C2×C4⋊C4—942no—
412C2×C4⋊C4—941no—
413C2×C4⋊C4—941no—
414C2×C4⋊C4C22×D4711yescharacteristic
415C2×C4⋊C4C22×D4712yes—
416C2×C22⋊C4—941no—
417C2×C22⋊C4—941no—
418C2×C22⋊C4—942no—
419C2×C22⋊C4—941no—
420C2×C42—21no—
421C2×C42—471no—
422C2×C42—471no—
423C2×C42—471no—
424C2×C42—474no—
425C2×C42—474no—
426C2×C42—948no—
427C2×C42—941no—
428C2×C42—942no—
429C2×C42—941no—
430C2×C42C22×D4711yescharacteristic
431#107—478no—
432#106C22×D4718yes—
433C4⋊C8—474no—
434C4⋊C8C22×D4714yes—
435#103—478no—
436#103—478no—
437#103C22×D4718yes—
438#102—478no—
439C22⋊C8—478no—
440C4×C8—478no—
441C24—471no—
442C24—941no—
443#41—948no—
444#41—9416no—
445#41—948no—
446C2×Q8—21no—
447C2×Q8—24no—
448C2×Q8—22no—
449C2×Q8—44no—
450C2×Q8—474no—
451C2×Q8—942no—
452C2×Q8—944no—
453C2×Q8—944no—
454C2×Q8#1062535414yes—
455C2×Q8C23×D4712yes—
456C2×D4—474no—
457C2×D4—472no—
458C2×D4—944no—
459C2×D4—948no—
460C2×D4—941no—
461C2×D4—942no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—471no—
466C22×C4—471no—
467C22×C4—471no—
468C22×C4—474no—
469C22×C4—472no—
470C22×C4—474no—
471C22×C4—472no—
472C22×C4—944no—
473C22×C4—944no—
474C22×C4—944no—
475C22×C4—948no—
476C22×C4—944no—
477C22×C4—942no—
478C22×C4—942no—
479C22×C4—941no—
480C22×C4—942no—
481C22×C4—944no—
482C22×C4—1884no—
483C22×C4—1884no—
484C22×C4D4×D4711yescharacteristic
485C22×C4D4×D4711yescharacteristic
486C22×C4C23×D4711yescharacteristic
487Q16—9416no—
488SD16—9416no—
489C2×C8—24no—
490C2×C8—474no—
491C2×C8—944no—
492C2×C8C23×D4714yes—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—472no—
498C4⋊C4—948no—
499C4⋊C4—944no—
500C4⋊C4—948no—
501C4⋊C4—941no—
502C4⋊C4—944no—
503C4⋊C4—944no—
504C4⋊C4C23×D4714yes—
505C4⋊C4C23×D4712yes—
506C22⋊C4—944no—
507C22⋊C4—944no—
508C22⋊C4—948no—
509C22⋊C4—944no—
510C42—24no—
511C42—474no—
512C42—474no—
513C42—472no—
514C42—472no—
515C42—944no—
516C42—944no—
517C42—948no—
518C42D4×D4712yes—
519C42C23×D4712yes—
520C23—472no—
521C23—944no—
522C23—942no—
523C23—942no—
524C23—942no—
525C23—942no—
526C23—1882no—
527C23—1882no—
528C23C2×D4×D4711yescharacteristic
529Q8—24no—
530Q8—22no—
531Q8—48no—
532Q8—944no—
533Q8—944no—
534Q8—1884no—
535Q8C2×#1062535414yes—
536D4—474no—
537D4—9416no—
538D4—944no—
539D4—942no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—474no—
548C2×C4—472no—
549C2×C4—472no—
550C2×C4—472no—
551C2×C4—948no—
552C2×C4—9416no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—944no—
556C2×C4—948no—
557C2×C4—942no—
558C2×C4—942no—
559C2×C4—942no—
560C2×C4—944no—
561C2×C4—1888no—
562C2×C4—1884no—
563C2×C4—1882no—
564C2×C4—1888no—
565C2×C4#1309404514yes—
566C2×C4C2×D4×D4712yes—
567C2×C4C2×D4×D4711yescharacteristic
568C2×C4C2×D4×D4712yes—
569C2×C4#41×D4712yes—
570C2×C4C2×#1062535412yes—
571C2×C4C24×D4711yescharacteristic
572C8—24no—
573C8—944no—
574C22—942no—
575C22—942no—
576C22—944no—
577C22—942no—
578C22—1884no—
579C22—1888no—
580C22—1882no—
581C22—1882no—
582C22#1568963612yes—
583C22C2×#1309404512yes—
584C22#137×D4712yes—
585C22C22×D4×D4711yescharacteristic
586C4—22no—
587C4—24no—
588C4—44no—
589C4—42no—
590C4—474no—
591C4—942no—
592C4—942no—
593C4—1882no—
594C4—1884no—
595C4#1568963612yes—
596C4C2×#1309404514yes—
597C4C2×#41×D4711yescharacteristic
598C4C22×#1062535411yescharacteristic
599C2—1882no—
600C2—1884no—
601C2#2025346214yesdirect product factor
602C2C2×#1568963611yescharacteristic
603C2C22×#1309404511yescharacteristic
604C2C2×#137×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#475C2
socleC23×C47C22×D4
prime radicalC22×#10625354C22
hypercenterC2×#475D47
hypocenterC47C2×#3107
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#15689678C2semidirect
3. #20253462C2direct (N × H)
4. C2×#15689467C2semidirect
5. C2×#15689400C2semidirect
6. C2×#15689333C2semidirect
7. C2×#15689329C2semidirect
9. C2×#15689215C2semidirect
10. C2×#15689210C2semidirect
11. C2×#15689175C2semidirect
12. C2×C47×#475C2semidirect
17. #15689678C22semidirect
36. #15689467C22semidirect
37. #15689400C22semidirect
38. #15689333C22semidirect
39. #15689329C22semidirect
41. #15689215C22semidirect
42. #15689210C22semidirect
43. #15689175C22semidirect
53. C47×#475C22semidirect
301. C2×#475D47semidirect
309. C2×C47#3107semidirect
341. #475C2×D47semidirect
359. C47C2×#3107semidirect
601. C2#20253462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896782
C2×C4×#106253542
#202534622
C2×#156894672
C2×#156894002
C2×#156893332
C2×#156893292
C2×#156892882
C2×#156892152
C2×#156892102
C2×#156891752
C2×C47×#4752
C2×#310747