Finite Group Databasebeta

← C2×#20286085 #28256945

Subgroups — C2×#20286085 #28256945

Order 13568.

1898 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811177C211yesmaximal, characteristic, complemented
2C2×#16811152C211yesmaximal, characteristic
3#20286085C2116yesmaximal, direct product factor
4C2×#16810931C211yesmaximal, characteristic, complemented
5C2×#16810930C211yesmaximal, characteristic, complemented
6C2×#16810916C211yesmaximal, characteristic, complemented
7C2×#16810911C211yesmaximal, characteristic, complemented
8C2×#16810880C211yesmaximal, characteristic, complemented
9C2×#16810878C211yesmaximal, characteristic, complemented
10C2×#16810868C211yesmaximal, characteristic
11C2×#16810866C211yesmaximal, characteristic
12C2×#16810842C211yesmaximal, characteristic, complemented
13C2×#16810831C211yesmaximal, characteristic, complemented
14C2×#16810826C211yesmaximal, characteristic, complemented
15C2×#16810645C211yesmaximal, characteristic, complemented
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×#11719912C2211yescharacteristic
21#16811177—24no—
22#16811177C2218yescomplemented
23C2×#13133216C2211yescharacteristic
24C2×#13133215C2211yescharacteristic
25#16811152—24no—
26#16811152C2218yes—
27C2×#13133210—21no—
28C2×#13133209C2211yescharacteristic
29C2×#13133207—21no—
30C2×#13133199—21no—
31C2×#13133197C2211yescharacteristic
32C2×#13133195—21no—
33C2×#13133193C2211yescharacteristic
34C2×#13133193C2211yescharacteristic
35C2×#13133188C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×C4×Dic106—21no—
38C2×C4×Dic106C2211yescharacteristic
39C2×D4×Dic53C2211yescharacteristic
40C2×#13133177—21no—
41C2×#13133174—21no—
42C2×#13133173—21no—
43C2×C42×D53C2211yescharacteristic
44#16810931C2218yescomplemented
45#16810930C2218yescomplemented
46#16810916C2218yescomplemented
47#16810911C2218yescomplemented
48#16810880C2218yescomplemented
49#16810878C2218yescomplemented
50#16810868C2218yes—
51#16810866C2218yes—
52#16810842C2218yescomplemented
53#16810831C2218yescomplemented
54#16810826C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59#16810645C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×#13133141C2211yescharacteristic
67C2×#13133141C2211yescharacteristic
68C2×#13133138C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C53×#464C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×C22⋊D53—21no—
80C23×Dic53—21no—
81C22×C4×D53D411yescharacteristic
82C22×C4×D53D411yescharacteristic
83C22×C4×D53C2311yescharacteristic
84C2×#11719925—42no—
85C2×#11719925C2314yes—
86C2×#11719923—42no—
87C2×#11719923C2314yes—
88C2×#11719912—42no—
89C2×#11719912—42no—
90C2×#11719912C2314yes—
91C2×#11719912C2314yes—
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94#13133216—22no—
95#13133216C2314yes—
96#13133215—22no—
97#13133215C2314yes—
98#13133210—28no—
99#13133209—22no—
100#13133209C2314yes—
101#13133207—28no—
102#13133199—28no—
103#13133197—22no—
104#13133197C2314yes—
105#13133195—28no—
106#13133193—22no—
107#13133193—22no—
108#13133193C2314yes—
109#13133193C2314yes—
110#13133188—22no—
111#13133188C2314yes—
112Q8×Dic53—22no—
113Q8×Dic53C2314yes—
114C4×Dic106—22no—
115C4×Dic106—28no—
116C4×Dic106C2314yes—
117D4×Dic53—22no—
118D4×Dic53C2314yes—
119#13133177—28no—
120#13133174—28no—
121#13133173—28no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53D411yescharacteristic
143C2×C4×Dic53D411yescharacteristic
144C2×C4×Dic53C2311yescharacteristic
145C42×D53D414yes—
146C42×D53C2314yes—
147#13133151C2314yes—
148#13133150C2314yes—
149#13133149C2314yes—
150#13133148C2314yes—
151C4⋊#88322C2314yes—
152#13133146C2314yes—
153#13133146C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133141C2314yes—
157#13133141C2314yes—
158#13133141C2314yes—
159#13133138C2314yes—
160C22×Q8×C53C2311yescharacteristic
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C2×Q16×C53—42no—
164C2×Q16×C53C2314yes—
165C2×SD16×C53—42no—
166C2×SD16×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169#124×C53—22no—
170#124×C53C2314yes—
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C42×C53—21no—
178C2×C42×C53C2311yescharacteristic
179C4⋊C8×C53C2314yes—
180#103×C53C2314yes—
181#102×C53C2314yes—
182C24×C53—21no—
183C23×D53C2×D411yescharacteristic
184C2×Q8×C53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C2×Q8×C53C2412yes—
192C2×D4×C53—21no—
193C2×D4×C53—22no—
194C2×D4×C53—22no—
195C2×D4×C53C2412yes—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2411yescharacteristic
202C2×C22⋊D53—24no—
203C2×C22⋊D53—44no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—24no—
209C22×Dic53—44no—
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C2×C4×D53—22no—
214C2×C4×D53—22no—
215C2×C4×D53—24no—
216C2×C4×D53—42no—
217C2×C4×D53C2×D412yes—
218C2×C4×D53C2×D414yes—
219C2×C4×D53C2×D414yes—
220C2×C4×D53C2412yes—
221C2×Dic106—22no—
222C2×Dic106—22no—
223C2×Dic106—21no—
224C2×Dic106—24no—
225C2×Dic106—44no—
226C2×Dic106C2412yes—
227Q16×C53—44no—
228SD16×C53—44no—
229C2×C8×C53—22no—
230C2×C8×C53—22no—
231C2×C8×C53C2412yes—
232C2×C8×C53C2412yes—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2412yes—
236C22⋊C4×C53—24no—
237C22⋊C4×C53—24no—
238C42×C53—24no—
239C42×C53C2×D412yes—
240C42×C53C2412yes—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243#11719925—44no—
244#11719923—44no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248C4⋊Dic53—21no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C4×Dic53C2×D412yes—
267C4×Dic53C2×D414yes—
268C4×Dic53C2×D414yes—
269C4×Dic53C2412yes—
270C2×#88322—22no—
271C2×#88322—22no—
272C2×#88322C2412yes—
273C2×#88322C2412yes—
274#11719912—44no—
275#11719912—44no—
276C23×C53—22no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53C22×D411yescharacteristic
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53C22×D412yes—
285Q8×C53—22no—
286Q8×C53—22no—
287Q8×C53—22no—
288Q8×C53—22no—
289Q8×C53—42no—
290Q8×C53—42no—
291D4×C53—22no—
292D4×C53—22no—
293D4×C53—42no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53H(5,𝔽2)12yes—
306C2×C4×C532−1+412yes—
307C2×C4×C53C2511yescharacteristic
308C22⋊D53—48no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—48no—
320C2×Dic53#13714yes—
321C2×Dic53C22×D412yes—
322C2×Dic53C22×D412yes—
323C2×Dic53C22×D412yes—
324C4×D53—24no—
325C4×D53—22no—
326C4×D53—22no—
327C4×D53—28no—
328C4×D53—44no—
329Dic106—22no—
330Dic106—22no—
331Dic106—48no—
332Dic106—42no—
333C8×C53—22no—
334C8×C53—22no—
335#88322—22no—
336#88322—22no—
337C2×#3252—531nomaximal, Sylow
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—84no—
342C22×C53#53712yes—
343C22×C53C2×#13712yes—
344C22×C53#57512yes—
345C22×C53C23×D411yescharacteristic
346C2×D53—22no—
347C2×D53—22no—
348C2×D53—22no—
349C2×D53—44no—
350C4×C53—22no—
351C4×C53—22no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53#53712yes—
356C4×C53C2×H(5,𝔽2)11yescharacteristic
357C4×C53C2×2−1+411yescharacteristic
358Dic53—22no—
359Dic53—22no—
360Dic53—42no—
361Dic53—42no—
362Dic53—42no—
363Dic53—42no—
364Dic53C2×#13714yes—
365C2×#533—531no—
366C2×#529—531no—
367#3252—5316no—
368C2×#479—531no—
369C2×#479—531no—
370C2×#477—531no—
371C2×#476—531no—
372C2×#470—531no—
373C2×#470—531no—
374C2×#468—531no—
375C2×#468—531no—
376C2×#464—531no—
377C2×#464D5311yescharacteristic, complemented
378C2×#462—531no—
379C2×#461—531no—
380C2×#423—531no—
381C2×C53—82no—
382C2×C53#325214yescomplemented
383C2×C53C2×#53711yescharacteristic
384C2×C53C22×#13711yescharacteristic
385C2×C53C2×#57511yescharacteristic
386D53—42no—
387C22×Q16—531no—
388C22×Q16C2×D5311yescharacteristic
389C22×SD16—531no—
390C22×SD16C2×D5311yescharacteristic
391C22×M16—531no—
392C22×M16—531no—
393#533—538no—
394#533—1064no—
395C2×C4⋊Q8—531no—
396C2×C4⋊Q8—531no—
397#529—538no—
398#529—1064no—
399C2×#126—1061no—
400C2×#125—531no—
401C2×#125—1061no—
402C2×#124C2×D5311yescharacteristic
403C2×#123—1061no—
404C2×C22⋊Q8—531no—
405C2×C22⋊Q8—531no—
406C2×C22⋊Q8—531no—
407C2×C22⋊Q8—1061no—
408C2×#121—531no—
409C2×C4×Q8—531no—
410C2×C4×Q8—531no—
411C2×C4×Q8—1061no—
412C2×C4×Q8C2×D5311yescharacteristic
413C2×C4×D4—531no—
414C2×C4×D4—1061no—
415C2×#117—1061no—
416C2×#117—1061no—
417C22×C42—531no—
418#479—538no—
419#479—538no—
420#477—538no—
421#476—538no—
422#470—538no—
423#470—538no—
424#468—538no—
425#468—538no—
426#464—538no—
427#464C2×D5318yescomplemented
428#462—538no—
429#461—538no—
430C2×#107—531no—
431C2×#107—531no—
432C2×#106—531no—
433C2×#106—531no—
434#423—538no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8—531no—
437C2×C4⋊C8—531no—
438C2×C4⋊C8C2×D5311yescharacteristic
439C2×#103—531no—
440C2×#103—531no—
441C2×#103—531no—
442C2×#103—531no—
443C2×#103—531no—
444C2×#103C2×D5311yescharacteristic
445C2×#102—531no—
446C2×#102C2×D5311yescharacteristic
447C53C2×#325211yescharacteristic, complemented, Sylow
448C22×Q8—531no—
449C22×Q8—1061no—
450C22×Q8C22×D5311yescharacteristic
451C22×Q8C22×D5311yescharacteristic
452C22×D4—1061no—
453C22×D4C22×D5311yescharacteristic
454C23×C4—531no—
455C23×C4—531no—
456C23×C4—531no—
457C23×C4—1061no—
458C2×Q16—42no—
459C2×Q16—534no—
460C2×Q16—2122no—
461C2×Q16C22×D5314yes—
462C2×SD16—42no—
463C2×SD16—534no—
464C2×SD16—2122no—
465C2×SD16C22×D5314yes—
466C2×M16—534no—
467C2×M16—534no—
468C2×M16—2122no—
469C2×M16—2122no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8C22×D5311yescharacteristic
473C22×C8C22×D5311yescharacteristic
474C4⋊Q8—534no—
475C4⋊Q8—534no—
476C4⋊Q8—1062no—
477C4⋊Q8—1062no—
478#126—1068no—
479#125—534no—
480#125—1068no—
481#125—1062no—
482#124—22no—
483#124C22×D5314yes—
484#123—1068no—
485C22⋊Q8—534no—
486C22⋊Q8—534no—
487C22⋊Q8—534no—
488C22⋊Q8—1062no—
489C22⋊Q8—1068no—
490C22⋊Q8—1062no—
491C22⋊Q8—1062no—
492#121—534no—
493#121—1062no—
494C4×Q8—22no—
495C4×Q8—534no—
496C4×Q8—534no—
497C4×Q8—1068no—
498C4×Q8—1062no—
499C4×Q8—1062no—
500C4×Q8C22×D5314yes—
501C4×D4—534no—
502C4×D4—1062no—
503C4×D4—1068no—
504#117—1068no—
505#117—1068no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C42—21no—
529C2×C42—531no—
530C2×C42—531no—
531C2×C42—531no—
532C2×C42—534no—
533C2×C42—534no—
534C2×C42—1061no—
535C2×C42—1061no—
536C2×C42C22×D5311yescharacteristic
537#107—534no—
538#107—534no—
539#106—534no—
540#106—534no—
541C4⋊C8—534no—
542C4⋊C8—534no—
543C4⋊C8—534no—
544C4⋊C8C22×D5314yes—
545#103—534no—
546#103—534no—
547#103—534no—
548#103—534no—
549#103—534no—
550#103C22×D5314yes—
551#102—534no—
552#102C22×D5314yes—
553C24—21no—
554C24—531no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—532no—
562C2×Q8—1064no—
563C2×Q8—1061no—
564C2×Q8—1062no—
565C2×Q8—1062no—
566C2×Q8—2124no—
567C2×Q8C23×D5312yes—
568C2×Q8C23×D5312yes—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—1064no—
573C2×D4—2124no—
574C2×D4C23×D5312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—531no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—534no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—534no—
585C22×C4—1064no—
586C22×C4—1064no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—2122no—
594C22×C4—2124no—
595C22×C4D4×D5311yescharacteristic
596C22×C4D4×D5311yescharacteristic
597C22×C4C23×D5311yescharacteristic
598Q16—44no—
599Q16—2124no—
600SD16—44no—
601SD16—2124no—
602M16—2124no—
603M16—2124no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—532no—
607C2×C8—532no—
608C2×C8—1062no—
609C2×C8—1062no—
610C2×C8C23×D5312yes—
611C2×C8C23×D5312yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—532no—
615C4⋊C4—532no—
616C4⋊C4—532no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1061no—
625C4⋊C4—1061no—
626C4⋊C4—1061no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4C23×D5312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1064no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C42—24no—
639C42—534no—
640C42—532no—
641C42—534no—
642C42—532no—
643C42—1064no—
644C42—1064no—
645C42D4×D5312yes—
646C42C23×D5312yes—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—532no—
652C23—1062no—
653C23—1062no—
654C23—1062no—
655C23C2×D4×D5311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—1062no—
663Q8—1062no—
664Q8—2128no—
665Q8—2122no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—2128no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—534no—
679C2×C4—532no—
680C2×C4—532no—
681C2×C4—532no—
682C2×C4—1068no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1064no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—2124no—
693C2×C4—2128no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4—2122no—
698C2×C4C2×D4×D5312yes—
699C2×C4C2×D4×D5312yes—
700C2×C4C2×D4×D5311yescharacteristic
701C2×C4#1313326212yes—
702C2×C4#1313326412yes—
703C2×C4C24×D5311yescharacteristic
704C8—22no—
705C8—22no—
706C8—1062no—
707C8—1062no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—84no—
712C22—1062no—
713C22—1062no—
714C22—1062no—
715C22—2124no—
716C22#1681120212yes—
717C22#137×D5312yes—
718C22#1681142012yes—
719C22C22×D4×D5311yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—534no—
726C4—1062no—
727C4—1062no—
728C4—2122no—
729C4—2122no—
730C4—2122no—
731C4—2122no—
732C4#1681120212yes—
733C4C2×#1313326211yescharacteristic
734C4C2×#1313326411yescharacteristic
735C2—82no—
736C2—2122no—
737C2#2028608514yesdirect product factor
738C2C2×#1681120211yescharacteristic
739C2C2×#137×D5311yescharacteristic
740C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
prime radicalC2×#13133188C22
hypercenterC2×#464D53
hypocenterC53C2×#3252
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#16811177C2semidirect
3. #20286085C2direct (N × H)
4. C2×#16810931C2semidirect
5. C2×#16810930C2semidirect
6. C2×#16810916C2semidirect
7. C2×#16810911C2semidirect
8. C2×#16810880C2semidirect
9. C2×#16810878C2semidirect
12. C2×#16810842C2semidirect
13. C2×#16810831C2semidirect
14. C2×#16810826C2semidirect
15. C2×#16810645C2semidirect
16. C2×C53×#464C2semidirect
22. #16811177C22semidirect
44. #16810931C22semidirect
45. #16810930C22semidirect
46. #16810916C22semidirect
47. #16810911C22semidirect
48. #16810880C22semidirect
49. #16810878C22semidirect
52. #16810842C22semidirect
53. #16810831C22semidirect
54. #16810826C22semidirect
59. #16810645C22semidirect
73. C53×#464C22semidirect
377. C2×#464D53semidirect
382. C2×C53#3252semidirect
427. #464C2×D53semidirect
447. C53C2×#3252semidirect
737. C2#20286085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111772
C2×#168111522
#202860852
C2×#168109312
C2×#168109302
C2×#168109162
C2×#168109112
C2×#168108802
C2×#168108782
C2×#168108682
C2×#168108662
C2×#168108422
C2×#168108312
C2×#168108262
C2×#168106452
C2×C53×#4642
C2×#325253