Finite Group Databasebeta

← C2×#20273208 #27351189

Subgroups — C2×#20273208 #27351189

Order 13568.

1474 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811168C211yesmaximal, characteristic
2C2×#16810673C211yesmaximal, characteristic, complemented
3C2×#16810474C211yesmaximal, characteristic, complemented
4#20273208C218yesmaximal, direct product factor
5C2×#16810358C211yesmaximal, characteristic, complemented
6C2×#16810357C211yesmaximal, characteristic, complemented
7C2×#16810356C211yesmaximal, characteristic, complemented
8C2×C53×#327C211yesmaximal, characteristic, complemented
9C22×#11719947—21no—
10#16811168—22no—
11#16811168—22no—
12#16811168C414yescomplemented
13#16811168C2214yes—
14C2×#13133216C411yescharacteristic, complemented
15C2×#13133213C411yescharacteristic, complemented
16C2×#13133203—21no—
17C2×#13133191C2211yescharacteristic
18C2×#13133189—21no—
19C2×D4×Dic53C411yescharacteristic, complemented
20C2×#13133179C411yescharacteristic, complemented
21C2×#13133177—21no—
22C22×#11719919—21no—
23C22×C4×Dic53—21no—
24C22×C4×Dic53C2211yescharacteristic
25#16810673—22no—
26#16810673C2214yescomplemented
27C2×#13133146—21no—
28C2×C22⋊#88322C2211yescharacteristic
29C2×C8×Dic53—21no—
30#16810474—22no—
31#16810474C2214yescomplemented
32C2×#13133124C2211yescharacteristic
33#16810358C2214yescomplemented
34#16810357C2214yescomplemented
35#16810356C2214yescomplemented
36C2×#121×C53C2211yescharacteristic
37C2×C22⋊C8×C53C2211yescharacteristic
38C2×#95×C53C2211yescharacteristic
39C53×#327C2214yescomplemented
40C2×#11719947—24no—
41C2×#11719947—24no—
42C2×#11719947—44no—
43C2×#11719947—44no—
44C22×Dic106—21no—
45C22×D212C2×C411yescharacteristic
46C22×C22⋊D53—21no—
47C22×C22⋊D53—21no—
48C22×C22⋊D53—21no—
49C23×Dic53—21no—
50C23×Dic53—21no—
51C23×Dic53D411yescharacteristic
52C23×Dic53D411yescharacteristic
53C22×C4×D53—21no—
54C22×#88322—21no—
55#13133216—22no—
56#13133216C2×C414yescomplemented
57#13133213—22no—
58#13133213C2×C414yescomplemented
59#13133203—24no—
60#13133203—24no—
61#13133191—21no—
62#13133191—21no—
63#13133191C2×C412yes—
64#13133191C2312yes—
65#13133189—24no—
66#13133189—24no—
67D4×Dic53—22no—
68D4×Dic53C2×C414yescomplemented
69#13133179—22no—
70#13133179C2×C414yescomplemented
71#13133177—24no—
72#13133177—24no—
73C2×C4⋊Dic53C2×C411yescharacteristic
74C2×#11719919—28no—
75C2×#11719919—21no—
76C2×#11719919—24no—
77C2×C22⋊Dic53—21no—
78C2×#11719921—21no—
79C2×#11719921—21no—
80C2×C4×Dic53—24no—
81C2×C4×Dic53—44no—
82C2×C4×Dic53C2×C411yescharacteristic
83C2×C4×Dic53C2×C411yescharacteristic
84C2×C4×Dic53C2×C412yes—
85C2×C4×Dic53D411yescharacteristic
86C2×C4×Dic53D411yescharacteristic
87C2×C4×Dic53D412yes—
88C2×C4×Dic53D412yes—
89C2×C4×Dic53C2312yes—
90#13133146—24no—
91C22⋊#88322—21no—
92C22⋊#88322C2312yes—
93C8×Dic53—24no—
94#13133124—21no—
95#13133124C2312yes—
96C22×D4×C53—21no—
97C22×D4×C53C2×C411yescharacteristic
98C23×C4×C53—21no—
99C23×C4×C53C2311yescharacteristic
100C22×C8×C53—21no—
101#121×C53—21no—
102#121×C53—21no—
103#121×C53C2×C412yes—
104#121×C53C2312yes—
105C2×C4⋊C4×C53C2×C411yescharacteristic
106C2×C22⋊C4×C53—21no—
107C22⋊C8×C53—21no—
108C22⋊C8×C53C2312yes—
109#95×C53—21no—
110#95×C53C2312yes—
111C24×C53—21no—
112C24×C53C2×D411yescharacteristic
113C23×D53—21no—
114C2×D4×C53—22no—
115C2×D4×C53—22no—
116C2×D4×C53—21no—
117C2×D4×C53—42no—
118C2×D4×C53—42no—
119C2×D4×C53—42no—
120C2×D4×C53C22×C412yes—
121C22×C4×C53—24no—
122C22×C4×C53—21no—
123C22×C4×C53—22no—
124C22×C4×C53—42no—
125C22×C4×C53—42no—
126C22×C4×C53—42no—
127C22×C4×C53C22×C411yescharacteristic
128C22×C4×C53C22×C411yescharacteristic
129C22×C4×C53C2×D411yescharacteristic
130C22×C4×C53C2×D411yescharacteristic
131C22×C4×C53C2×D411yescharacteristic
132C22×C4×C53C2411yescharacteristic
133C2×C22⋊D53—22no—
134C2×C22⋊D53—22no—
135C2×C22⋊D53—24no—
136C2×C22⋊D53—24no—
137C2×C22⋊D53—42no—
138C2×C22⋊D53—42no—
139C2×C22⋊D53—44no—
140C2×C22⋊D53—44no—
141C22×Dic53—24no—
142C22×Dic53—24no—
143C22×Dic53—21no—
144C22×Dic53—22no—
145C22×Dic53—24no—
146C22×Dic53—42no—
147C22×Dic53—42no—
148C22×Dic53—44no—
149C22×Dic53C22⋊C411yescharacteristic
150C22×Dic53C22⋊C412yes—
151C22×Dic53C22⋊C411yescharacteristic
152C22×Dic53C22⋊C411yescharacteristic
153C22×Dic53C22⋊C412yes—
154C22×Dic53C22⋊C411yescharacteristic
155C22×Dic53D814yes—
156C22×Dic53SD1614yes—
157C22×Dic53C2×D412yes—
158C22×Dic53C2×D412yes—
159#11719947—416no—
160#11719947—48no—
161#11719947—48no—
162C2×D212—21no—
163C2×D212—42no—
164C2×D212C22×C412yes—
165C2×C4×D53—24no—
166C2×C4×D53—44no—
167C2×Dic106—24no—
168C2×Dic106—44no—
169C2×C8×C53—22no—
170C2×C8×C53—42no—
171C4⋊C4×C53—21no—
172C4⋊C4×C53C22×C412yes—
173C22⋊C4×C53—22no—
174C22⋊C4×C53—22no—
175C22⋊Dic53—24no—
176#11719921—22no—
177#11719921—22no—
178#11719921—24no—
179C4⋊Dic53—21no—
180C4⋊Dic53C22×C412yes—
181#11719919—216no—
182#11719919—24no—
183C4×Dic53—48no—
184C4×Dic53C22⋊C412yes—
185C4×Dic53C22⋊C412yes—
186C4×Dic53C22⋊C412yes—
187C4×Dic53C22⋊C412yes—
188C4×Dic53C22×C412yes—
189C4×Dic53C22×C412yes—
190C4×Dic53C2×D412yes—
191C4×Dic53C2×D412yes—
192C2×#88322—22no—
193C2×#88322—42no—
194C23×C53—22no—
195C23×C53—22no—
196C23×C53—22no—
197C23×C53—42no—
198C23×C53—42no—
199C23×C53—42no—
200C23×C53C2×C22⋊C411yescharacteristic
201C23×C53C2×C22⋊C411yescharacteristic
202C23×C53C2×D812yes—
203C23×C53C2×SD1612yes—
204C23×C53C22×D411yescharacteristic
205C22×D53—22no—
206C22×D53—42no—
207C22×D53—42no—
208C22×D53—42no—
209D4×C53—42no—
210D4×C53—42no—
211D4×C53—42no—
212D4×C53—42no—
213D4×C53—44no—
214C2×C4×C53—22no—
215C2×C4×C53—22no—
216C2×C4×C53—24no—
217C2×C4×C53—22no—
218C2×C4×C53—41no—
219C2×C4×C53—41no—
220C2×C4×C53—41no—
221C2×C4×C53—41no—
222C2×C4×C53—42no—
223C2×C4×C53—48no—
224C2×C4×C53—42no—
225C2×C4×C53—42no—
226C2×C4×C53C2×C22⋊C411yescharacteristic
227C2×C4×C53C2×C22⋊C411yescharacteristic
228C2×C4×C53C23×C411yescharacteristic
229C2×C4×C53C22×D411yescharacteristic
230C22⋊D53—42no—
231C22⋊D53—42no—
232C22⋊D53—44no—
233C22⋊D53—48no—
234C22⋊D53—48no—
235C2×Dic53—22no—
236C2×Dic53—24no—
237C2×Dic53—24no—
238C2×Dic53—24no—
239C2×Dic53—22no—
240C2×Dic53—42no—
241C2×Dic53—48no—
242C2×Dic53—42no—
243C2×Dic53—42no—
244C2×Dic53—48no—
245C2×Dic53#10214yes—
246C2×Dic53#10214yes—
247C2×Dic53#10218yes—
248C2×Dic53#10414yes—
249C2×Dic53C2×C22⋊C412yes—
250C2×Dic53C2×C22⋊C412yes—
251C2×Dic53C2×C22⋊C412yes—
252C2×Dic53C2×C22⋊C412yes—
253C2×Dic53C2×D814yes—
254C2×Dic53C2×SD1614yes—
255D212—42no—
256D212—42no—
257C4×D53—48no—
258Dic106—48no—
259C8×C53—42no—
260#88322—42no—
261C2×#1502—531nomaximal, Sylow
262C22×C53—21no—
263C22×C53—21no—
264C22×C53—21no—
265C22×C53—21no—
266C22×C53—24no—
267C22×C53—24no—
268C22×C53—42no—
269C22×C53—42no—
270C22×C53—42no—
271C22×C53—84no—
272C22×C53#41012yes—
273C22×C53C2×#10212yes—
274C22×C53C2×#10212yes—
275C22×C53C2×#10412yes—
276C22×C53C22×C22⋊C411yescharacteristic
277C22×C53C22×D811yescharacteristic
278C22×C53C22×SD1611yescharacteristic
279C2×D53—42no—
280C2×D53—42no—
281C2×D53—42no—
282C2×D53—84no—
283C4×C53—21no—
284C4×C53—21no—
285C4×C53—21no—
286C4×C53—21no—
287C4×C53—44no—
288C4×C53—42no—
289Dic53—22no—
290Dic53—44no—
291Dic53—42no—
292Dic53C2×#10214yes—
293Dic53C2×#10214yes—
294Dic53C2×#10414yes—
295C2×#532—531no—
296C2×#431—531no—
297C2×C4×C4⋊C4—531no—
298#1502—538no—
299C2×#327—531no—
300C2×#327—531no—
301C2×#327—531no—
302C2×#327D5311yescharacteristic, complemented
303C2×C53—21no—
304C2×C53—21no—
305C2×C53—22no—
306C2×C53—82no—
307C2×C53#150214yescomplemented
308C2×C53C2×#41011yescharacteristic
309C2×C53C22×#10211yescharacteristic
310C2×C53C22×#10411yescharacteristic
311D53—82no—
312C22×#41—1061no—
313#532—534no—
314#532—534no—
315#532—1062no—
316#532—1062no—
317C2×C4⋊Q8—531no—
318C2×#127—531no—
319C2×#124—1061no—
320C2×#121—531no—
321C2×#121—1061no—
322C2×#121C2×D5311yescharacteristic
323C2×C4×D4—531no—
324C2×C4×D4—531no—
325C2×C4×D4—1061no—
326C22×C4⋊C4—1061no—
327C22×C42—531no—
328C22×C42—1061no—
329#431—534no—
330#431—1062no—
331C2×C4⋊C8—1061no—
332C2×C22⋊C8—531no—
333C2×C22⋊C8C2×D5311yescharacteristic
334C2×C4×C8—1061no—
335C4×C4⋊C4—534no—
336C4×C4⋊C4—1062no—
337C2×#95—531no—
338C2×#95C2×D5311yescharacteristic
339#327—534no—
340#327—534no—
341#327—534no—
342#327C2×D5314yescomplemented
343C53C2×#150211yescharacteristic, complemented, Sylow
344C2×#41—1064no—
345C2×#41—1064no—
346C2×#41—2124no—
347C2×#41—2124no—
348C22×Q8—1061no—
349C22×D4—21no—
350C22×D4—531no—
351C22×D4—1061no—
352C22×D4—1061no—
353C22×D4—1061no—
354C22×D4C4×D5311yescharacteristic
355C23×C4—21no—
356C23×C4—531no—
357C23×C4—531no—
358C23×C4—1061no—
359C23×C4—1061no—
360C23×C4—1061no—
361C23×C4C22×D5311yescharacteristic
362C22×C8—21no—
363C22×C8—1061no—
364C4⋊Q8—534no—
365C4⋊Q8—1062no—
366#127—534no—
367#127—1062no—
368#124—1064no—
369#124—1064no—
370#121—21no—
371#121—21no—
372#121—532no—
373#121—532no—
374#121—1064no—
375#121—1064no—
376#121—1061no—
377#121—1061no—
378#121C4×D5312yes—
379#121C22×D5312yes—
380C4×D4—534no—
381C4×D4—534no—
382C4×D4—1064no—
383C4×D4—1064no—
384C4×D4—1062no—
385C4×D4—1062no—
386C2×C4⋊C4—531no—
387C2×C4⋊C4—1064no—
388C2×C4⋊C4—1061no—
389C2×C4⋊C4—1068no—
390C2×C4⋊C4C4×D5311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—1061no—
393C2×C22⋊C4—1061no—
394C2×C22⋊C4—1061no—
395C2×C42—531no—
396C2×C42—531no—
397C2×C42—532no—
398C2×C42—531no—
399C2×C42—531no—
400C2×C42—532no—
401C2×C42—532no—
402C2×C42—532no—
403C2×C42—1064no—
404C2×C42—2124no—
405C4⋊C8—1064no—
406C22⋊C8—21no—
407C22⋊C8—532no—
408C22⋊C8—1061no—
409C22⋊C8C22×D5312yes—
410C4×C8—1064no—
411#95—21no—
412#95—532no—
413#95—1061no—
414#95C22×D5312yes—
415C24—21no—
416C24—1061no—
417C24D4×D5311yescharacteristic
418#41—21216no—
419#41—2128no—
420#41—2128no—
421C2×Q8—1064no—
422C2×Q8—2124no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—532no—
430C2×D4—1064no—
431C2×D4—1064no—
432C2×D4—1062no—
433C2×D4—1062no—
434C2×D4—1061no—
435C2×D4—2122no—
436C2×D4—2124no—
437C2×D4—2124no—
438C2×D4—2122no—
439C2×D4—2122no—
440C2×D4C2×C4×D5312yes—
441C22×C4—24no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—532no—
448C22×C4—531no—
449C22×C4—531no—
450C22×C4—531no—
451C22×C4—534no—
452C22×C4—534no—
453C22×C4—532no—
454C22×C4—532no—
455C22×C4—531no—
456C22×C4—532no—
457C22×C4—1064no—
458C22×C4—1064no—
459C22×C4—1064no—
460C22×C4—1064no—
461C22×C4—1061no—
462C22×C4—1062no—
463C22×C4—2124no—
464C22×C4—2124no—
465C22×C4—2122no—
466C22×C4—2122no—
467C22×C4C2×C4×D5311yescharacteristic
468C22×C4C2×C4×D5311yescharacteristic
469C22×C4D4×D5311yescharacteristic
470C22×C4D4×D5311yescharacteristic
471C22×C4D4×D5311yescharacteristic
472C22×C4C23×D5311yescharacteristic
473C2×C8—22no—
474C2×C8—42no—
475C2×C8—1062no—
476C2×C8—2122no—
477C4⋊C4—21no—
478C4⋊C4—532no—
479C4⋊C4—1064no—
480C4⋊C4—10616no—
481C4⋊C4—1061no—
482C4⋊C4C2×C4×D5312yes—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—1064no—
486C22⋊C4—1064no—
487C22⋊C4—1062no—
488C22⋊C4—1062no—
489C42—532no—
490C42—532no—
491C42—532no—
492C42—532no—
493C42—532no—
494C42—532no—
495C42—532no—
496C42—532no—
497C42—2128no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—1062no—
505C23—2122no—
506C23—2122no—
507C23—2122no—
508C23C22⋊C4×D5311yescharacteristic
509C23C22⋊C4×D5311yescharacteristic
510C23D8×D5312yes—
511C23SD16×D5312yes—
512C23C2×D4×D5311yescharacteristic
513Q8—2128no—
514D4—42no—
515D4—42no—
516D4—44no—
517D4—42no—
518D4—42no—
519D4—2122no—
520D4—2122no—
521D4—2128no—
522D4—2128no—
523D4—2124no—
524D4—2122no—
525D4—2122no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—48no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—532no—
539C2×C4—532no—
540C2×C4—532no—
541C2×C4—534no—
542C2×C4—534no—
543C2×C4—538no—
544C2×C4—534no—
545C2×C4—534no—
546C2×C4—534no—
547C2×C4—532no—
548C2×C4—1064no—
549C2×C4—1064no—
550C2×C4—1062no—
551C2×C4—1064no—
552C2×C4—1062no—
553C2×C4—2128no—
554C2×C4—2128no—
555C2×C4—2122no—
556C2×C4—2128no—
557C2×C4—2122no—
558C2×C4—2122no—
559C2×C4C22⋊C4×D5311yescharacteristic
560C2×C4C22⋊C4×D5311yescharacteristic
561C2×C4C22×C4×D5311yescharacteristic
562C2×C4C2×D4×D5311yescharacteristic
563C8—42no—
564C8—2122no—
565C22—21no—
566C22—21no—
567C22—24no—
568C22—24no—
569C22—21no—
570C22—21no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—84no—
575C22—4244no—
576C22—2122no—
577C22—2122no—
578C22—2122no—
579C22#1681059512yes—
580C22#102×D5312yes—
581C22#102×D5312yes—
582C22#104×D5312yes—
583C22C2×C22⋊C4×D5311yescharacteristic
584C22C2×D8×D5311yescharacteristic
585C22C2×SD16×D5311yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—44no—
591C4—42no—
592C4—534no—
593C4—534no—
594C4—534no—
595C4—1062no—
596C4—2124no—
597C4—2122no—
598C2—21no—
599C2—22no—
600C2—21no—
601C2—82no—
602C2—4242no—
603C2#2027320814yesdirect product factor
604C2C2×#1681059511yescharacteristic
605C2C2×#102×D5311yescharacteristic
606C2C2×#104×D5311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#327C2
socleC23×C53C2×C22⋊C4
prime radicalC2×#16811168C2
cosocleC22×C4×C53C24
hypercenterC2×#327D53
hypocenterC53C2×#1502
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#16810673C2semidirect
3. C2×#16810474C2semidirect
4. #20273208C2direct (N × H)
5. C2×#16810358C2semidirect
6. C2×#16810357C2semidirect
7. C2×#16810356C2semidirect
8. C2×C53×#327C2semidirect
12. #16811168C4semidirect
14. C2×#13133216C4semidirect
15. C2×#13133213C4semidirect
19. C2×D4×Dic53C4semidirect
20. C2×#13133179C4semidirect
26. #16810673C22semidirect
31. #16810474C22semidirect
33. #16810358C22semidirect
34. #16810357C22semidirect
35. #16810356C22semidirect
39. C53×#327C22semidirect
56. #13133216C2×C4semidirect
58. #13133213C2×C4semidirect
68. D4×Dic53C2×C4semidirect
70. #13133179C2×C4semidirect
302. C2×#327D53semidirect
307. C2×C53#1502semidirect
342. #327C2×D53semidirect
343. C53C2×#1502semidirect
603. C2#20273208direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111682
C2×#168106732
C2×#168104742
#202732082
C2×#168103582
C2×#168103572
C2×#168103562
C2×C53×#3272
C2×#150253