Finite Group Databasebeta

← C2×#13127416 #16741619

Subgroups — C2×#13127416 #16741619

Order 3328.

2082 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719238C211yesmaximal, characteristic, complemented
2C2×#11719212C211yesmaximal, characteristic
3#13127416C2116yesmaximal, direct product factor
4C2×#11718535C211yesmaximal, characteristic, complemented
5C2×#11718545C211yesmaximal, characteristic, complemented
6C2×#11718631C211yesmaximal, characteristic, complemented
7C2×#11718527C211yesmaximal, characteristic, complemented
8C2×#11718664C211yesmaximal, characteristic, complemented
9C2×#11718515C211yesmaximal, characteristic, complemented
10C2×#11718551C211yesmaximal, characteristic, complemented
11C2×#11718547C211yesmaximal, characteristic, complemented
12C2×#11718795C211yesmaximal, characteristic, complemented
13C2×#11718513C211yesmaximal, characteristic, complemented
14C2×#11718789C211yesmaximal, characteristic, complemented
15C2×#11718522C211yesmaximal, characteristic, complemented
16C2×C13×#428C211yesmaximal, characteristic, complemented
17C22×#6127—21no—
18C22×C13×M16C2211yescharacteristic
19C2×C13×#117C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C2×#88184C2211yescharacteristic
22C2×#88183—21no—
23C2×C4×C22⋊D13C2211yescharacteristic
24C2×#88178C2211yescharacteristic
25C22×#6095C2211yescharacteristic
26C22×#6094C2211yescharacteristic
27#11719238—24no—
28#11719238C2218yescomplemented
29C2×#88151C2211yescharacteristic
30C2×#88150—21no—
31#11719212—24no—
32#11719212C2218yes—
33C2×#88149C2211yescharacteristic
34C2×#88148—21no—
35C2×#88147C2211yescharacteristic
36C2×#88146C2211yescharacteristic
37C2×C4⋊C4×D13C2211yescharacteristic
38C2×#88142C2211yescharacteristic
39C2×#88142C2211yescharacteristic
40C2×#88141C2211yescharacteristic
41C2×#88139—21no—
42C2×#88133—21no—
43C2×#88130—21no—
44C2×C4×Dic26—21no—
45C13×#428C2218yescomplemented
46C2×C13×#107C2211yescharacteristic
47C2×C13×#107C2211yescharacteristic
48C2×C13×#106C2211yescharacteristic
49C2×C13×#106C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51#11718795C2218yescomplemented
52#11718789C2218yescomplemented
53C2×#88061C2211yescharacteristic
54C2×#88060C2211yescharacteristic
55C2×#88058C2211yescharacteristic
56C2×#88056C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58C2×C8×Dic13C2211yescharacteristic
59#11718664C2218yescomplemented
60#11718631C2218yescomplemented
61C2×#88050C2211yescharacteristic
62C2×#88050C2211yescharacteristic
63C2×#88049C2211yescharacteristic
64C2×#88049C2211yescharacteristic
65C2×#88048C2211yescharacteristic
66C2×#88047C2211yescharacteristic
67C2×#88047C2211yescharacteristic
68C2×#88047C2211yescharacteristic
69#11718551C2218yescomplemented
70#11718547C2218yescomplemented
71#11718545C2218yescomplemented
72#11718535C2218yescomplemented
73#11718527C2218yescomplemented
74#11718522C2218yescomplemented
75#11718515C2218yescomplemented
76#11718513C2218yescomplemented
77C23×C4×C13—21no—
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13—21no—
80C22×C22⋊D13D411yescharacteristic
81C2×#6127—28no—
82C2×#6127—48no—
83C22×D52—21no—
84C22×D52C2311yescharacteristic
85C22×C4×D13—21no—
86C22×C4×D13—21no—
87C22×C4×D13C2311yescharacteristic
88C22×Dic26—21no—
89C22×Dic26—21no—
90C22×Dic26C2311yescharacteristic
91C2×C13×M16—24no—
92C2×C13×M16C2314yes—
93C22×C8×C13C2311yescharacteristic
94C22×C8×C13C2311yescharacteristic
95C13×#117—22no—
96C13×#117C2314yes—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4C2311yescharacteristic
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2314yes—
104C2×C13×C22⋊C4—21no—
105C2×C42×C13—21no—
106C2×C22⋊Dic13—21no—
107C2×C22⋊Dic13D411yescharacteristic
108#88184—22no—
109#88184C2314yes—
110#88183—28no—
111C4×C22⋊D13D414yes—
112C4×C22⋊D13C2314yes—
113C2×#6103—21no—
114C2×#6103—21no—
115C2×#6103—21no—
116C2×#6103—21no—
117C2×#6103—21no—
118C2×#6103D411yescharacteristic
119C2×C4⋊Dic13—21no—
120C2×C4⋊Dic13C2311yescharacteristic
121C2×C4⋊Dic13C2311yescharacteristic
122#88178—22no—
123#88178C2314yes—
124C2×#6101—21no—
125C2×#6101—21no—
126C2×#6101—21no—
127C2×#6101—21no—
128C2×#6101—21no—
129C2×#6101D411yescharacteristic
130C2×C4×Dic13—21no—
131C2×C4×Dic13—21no—
132C2×C4×Dic13C2311yescharacteristic
133C22×#1055C2311yescharacteristic
134C22×#1055C2311yescharacteristic
135C2×#6095—24no—
136C2×#6095C2314yes—
137C2×#6094—24no—
138C2×#6094C2314yes—
139#88151—22no—
140#88151C2314yes—
141#88150—28no—
142#88149—22no—
143#88149C2314yes—
144#88148—28no—
145#88147—22no—
146#88147C2314yes—
147#88146—22no—
148#88146C2314yes—
149C4⋊C4×D13—22no—
150C4⋊C4×D13C2314yes—
151#88142—22no—
152#88142—22no—
153#88142C2314yes—
154#88142C2314yes—
155#88141—22no—
156#88141C2314yes—
157#88139—28no—
158#88133—28no—
159#88130—28no—
160C4×Dic26—28no—
161C13×#107C2314yes—
162C13×#107C2314yes—
163C13×#106C2314yes—
164C13×#106C2314yes—
165C22⋊#1055C2314yes—
166#88061C2314yes—
167#88060C2314yes—
168#88058C2314yes—
169#88056C2314yes—
170#88054C2314yes—
171C8×Dic13C2314yes—
172#88050C2314yes—
173#88050C2314yes—
174#88049C2314yes—
175#88049C2314yes—
176#88048C2314yes—
177#88047C2314yes—
178#88047C2314yes—
179#88047C2314yes—
180C2×#3353—131nomaximal, Sylow
181C24×C13C2×D411yescharacteristic
182C23×D13—21no—
183C23×D13C2×D411yescharacteristic
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—24no—
191C22×C4×C13—44no—
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13C2×D412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2411yescharacteristic
196C2×C22⋊D13—24no—
197C2×C22⋊D13—24no—
198C2×C22⋊D13—44no—
199C2×C22⋊D13C2×D414yes—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13C2×D411yescharacteristic
204C22×Dic13C2×D411yescharacteristic
205C22×Dic13C2×D411yescharacteristic
206#6127—432no—
207C2×D52—22no—
208C2×D52—22no—
209C2×D52—24no—
210C2×D52—21no—
211C2×D52—44no—
212C2×D52C2412yes—
213C2×C4×D13—22no—
214C2×C4×D13—22no—
215C2×C4×D13—24no—
216C2×C4×D13—24no—
217C2×C4×D13—44no—
218C2×C4×D13—44no—
219C2×C4×D13C2×D412yes—
220C2×C4×D13C2412yes—
221C2×Dic26—22no—
222C2×Dic26—22no—
223C2×Dic26—21no—
224C2×Dic26—24no—
225C2×Dic26—24no—
226C2×Dic26—44no—
227C2×Dic26—44no—
228C2×Dic26C2412yes—
229C13×M16—28no—
230C2×C8×C13—22no—
231C2×C8×C13#4114yescomplemented
232C2×C8×C13C2412yes—
233C2×C8×C13C2412yes—
234C13×C4⋊C4—21no—
235C13×C4⋊C4—21no—
236C13×C4⋊C4—21no—
237C13×C4⋊C4—21no—
238C13×C4⋊C4—24no—
239C13×C4⋊C4C2412yes—
240C13×C4⋊C4C2412yes—
241C13×C4⋊C4C2412yes—
242C13×C4⋊C4C2412yes—
243C13×C22⋊C4—24no—
244C42×C13—24no—
245C22⋊Dic13—24no—
246C22⋊Dic13C2×D414yes—
247#6103—24no—
248#6103—24no—
249#6103—24no—
250#6103—24no—
251#6103—24no—
252#6103C2×D414yes—
253C4⋊Dic13—21no—
254C4⋊Dic13—21no—
255C4⋊Dic13—24no—
256C4⋊Dic13C2412yes—
257C4⋊Dic13C2412yes—
258#6101—24no—
259#6101—24no—
260#6101—24no—
261#6101—24no—
262#6101—24no—
263#6101C2×D414yes—
264C4×Dic13—24no—
265C4×Dic13—24no—
266C4×Dic13C2×D412yes—
267C4×Dic13C2412yes—
268C2×#1055—22no—
269C2×#1055—22no—
270C2×#1055C2412yes—
271C2×#1055C2412yes—
272#6095—28no—
273#6094—28no—
274C2×#556—131no—
275C2×#547—131no—
276#3353—1316no—
277C2×#500—131no—
278C2×#484—131no—
279C2×#484—131no—
280C2×#482—131no—
281C2×#482—131no—
282C2×#475—131no—
283C2×#474—131no—
284C2×#468—131no—
285C2×#468—131no—
286C2×C4×SD16—131no—
287C2×#436—131no—
288C2×#428—131no—
289C2×#428D1311yescharacteristic, complemented
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13C22×D412yes—
294C23×C13C22×D411yescharacteristic
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—42no—
300C22×D13—42no—
301C22×D13—42no—
302C22×D13C22×D412yes—
303C2×C4×C13—22no—
304C2×C4×C13—24no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—48no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13C22×D412yes—
317C2×C4×C13C22×D411yescharacteristic
318C2×C4×C13C2×#4112yes—
319C2×C4×C132−1+412yes—
320C2×C4×C13C2511yescharacteristic
321C22⋊D13—28no—
322C22⋊D13—48no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—42no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13AGL(1,ℤ/8)14yes—
332C2×Dic13C22×D412yes—
333C2×Dic13C22×D412yes—
334C2×Dic13C22×D412yes—
335D52—22no—
336D52—22no—
337D52—48no—
338D52—42no—
339C4×D13—24no—
340C4×D13—22no—
341C4×D13—22no—
342C4×D13—48no—
343C4×D13—48no—
344Dic26—22no—
345Dic26—22no—
346Dic26—42no—
347Dic26—48no—
348Dic26—48no—
349C8×C13—22no—
350C8×C13C2×#4114yescomplemented
351#1055—22no—
352#1055—22no—
353C22×#41—261no—
354C22×SD16—131no—
355C22×M16—131no—
356C22×M16C2×D1311yescharacteristic
357#556—138no—
358#556—264no—
359#547—138no—
360#547—264no—
361C2×C4⋊Q8—131no—
362C2×C4⋊Q8—131no—
363C2×#126—261no—
364C2×#126—261no—
365C2×#124—261no—
366C2×#123—261no—
367C2×#123—261no—
368C2×C22⋊Q8—131no—
369C2×C22⋊Q8—131no—
370C2×C22⋊Q8—261no—
371C2×#121—131no—
372C2×#121—131no—
373C2×C4×Q8—131no—
374C2×C4×Q8—261no—
375C2×C4×D4—131no—
376C2×C4×D4—131no—
377C2×#117—131no—
378C2×#117C2×D1311yescharacteristic
379C22×C4⋊C4—131no—
380C22×C4⋊C4C2×D1311yescharacteristic
381#500—138no—
382#484—138no—
383#484—138no—
384#482—138no—
385#482—138no—
386#475—138no—
387#474—138no—
388#468—138no—
389#468—138no—
390C4×SD16—138no—
391#436—138no—
392#428—138no—
393#428C2×D1318yescomplemented
394C2×#107—131no—
395C2×#107—131no—
396C2×#107—131no—
397C2×#107—131no—
398C2×#107C2×D1311yescharacteristic
399C2×#107C2×D1311yescharacteristic
400C2×#106—131no—
401C2×#106C2×D1311yescharacteristic
402C2×#106C2×D1311yescharacteristic
403C2×C4⋊C8—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#102—131no—
408C2×#102—131no—
409C2×#102—131no—
410C2×C22⋊C8—131no—
411C2×C22⋊C8—131no—
412C2×C4×C8—131no—
413C22×C13—22no—
414C22×C13—22no—
415C22×C13—22no—
416C22×C13—44no—
417C22×C13#54712yes—
418C22×C13C2×AGL(1,ℤ/8)12yes—
419C22×C13#57812yes—
420C22×C13C23×D411yescharacteristic
421C2×D13—22no—
422C2×D13—22no—
423C2×D13—22no—
424C2×D13—44no—
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—42no—
428C2×D13—84no—
429C4×C13—22no—
430C4×C13—42no—
431C4×C13—42no—
432C4×C13—42no—
433C4×C13—42no—
434C4×C13#54712yes—
435C4×C13C22×#4111yescharacteristic
436C4×C13C2×2−1+411yescharacteristic
437Dic13—22no—
438Dic13—22no—
439Dic13—42no—
440Dic13—42no—
441Dic13—42no—
442Dic13C2×AGL(1,ℤ/8)14yes—
443C2×#41—268no—
444C2×#41—528no—
445C22×Q8—131no—
446C22×Q8—261no—
447C22×Q8—261no—
448C22×D4—131no—
449C22×D4—131no—
450C22×D4—261no—
451C22×D4—261no—
452C23×C4—21no—
453C23×C4—131no—
454C23×C4—261no—
455C23×C4—261no—
456C23×C4C22×D1311yescharacteristic
457C2×SD16—134no—
458C2×SD16—264no—
459C2×M16—24no—
460C2×M16—134no—
461C2×M16—264no—
462C2×M16C22×D1314yes—
463C22×C8—131no—
464C22×C8—131no—
465C22×C8C22×D1311yescharacteristic
466C22×C8C22×D1311yescharacteristic
467C4⋊Q8—134no—
468C4⋊Q8—134no—
469C4⋊Q8—262no—
470C4⋊Q8—262no—
471#126—268no—
472#126—268no—
473#124—268no—
474#123—268no—
475#123—268no—
476C22⋊Q8—134no—
477C22⋊Q8—134no—
478C22⋊Q8—268no—
479C22⋊Q8—262no—
480C22⋊Q8—262no—
481#121—134no—
482#121—134no—
483#121—262no—
484#121—262no—
485C4×Q8—134no—
486C4×Q8—268no—
487C4×Q8—262no—
488C4×D4—134no—
489C4×D4—134no—
490C4×D4—134no—
491C4×D4—262no—
492#117—22no—
493#117—134no—
494#117—262no—
495#117C22×D1314yes—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—131no—
499C2×C4⋊C4—131no—
500C2×C4⋊C4—131no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—262no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4C22×D1311yescharacteristic
510C2×C4⋊C4C22×D1311yescharacteristic
511C2×C4⋊C4C22×D1314yes—
512C2×C4⋊C4C22×D1311yescharacteristic
513C2×C4⋊C4C22×D1311yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—131no—
516C2×C22⋊C4—131no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C22⋊C4—261no—
523C2×C42—21no—
524C2×C42—131no—
525C2×C42—261no—
526C2×C42—261no—
527#107—134no—
528#107—134no—
529#107—134no—
530#107—134no—
531#107C22×D1314yes—
532#107C22×D1314yes—
533#106—134no—
534#106C22×D1314yes—
535#106C22×D1314yes—
536C4⋊C8—134no—
537#103—134no—
538#103—134no—
539#103—134no—
540#102—134no—
541#102—134no—
542#102—134no—
543C22⋊C8—134no—
544C22⋊C8—134no—
545C4×C8—134no—
546C2×C13—42no—
547C2×C13#335314yescomplemented
548C2×C13C2×#54711yescharacteristic
549C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
550C2×C13C2×#57811yescharacteristic
551D13—42no—
552D13—82no—
553C24—131no—
554C24—261no—
555C24D4×D1311yescharacteristic
556#41—5232no—
557C2×Q8—132no—
558C2×Q8—264no—
559C2×Q8—264no—
560C2×Q8—261no—
561C2×Q8—262no—
562C2×Q8—262no—
563C2×Q8—524no—
564C2×Q8—524no—
565C2×D4—134no—
566C2×D4—132no—
567C2×D4—264no—
568C2×D4—264no—
569C2×D4—264no—
570C2×D4—262no—
571C2×D4—261no—
572C2×D4—262no—
573C2×D4—524no—
574C2×D4—524no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—44no—
583C22×C4—131no—
584C22×C4—131no—
585C22×C4—131no—
586C22×C4—132no—
587C22×C4—132no—
588C22×C4—264no—
589C22×C4—264no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4—261no—
595C22×C4—524no—
596C22×C4—524no—
597C22×C4D4×D1312yes—
598C22×C4D4×D1311yescharacteristic
599C22×C4C23×D1312yes—
600C22×C4C23×D1311yescharacteristic
601SD16—268no—
602M16—28no—
603M16—268no—
604C2×C8—22no—
605C2×C8—132no—
606C2×C8—132no—
607C2×C8—262no—
608C2×C8—262no—
609C2×C8#612714yescomplemented
610C2×C8C23×D1312yes—
611C2×C8C23×D1312yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—134no—
618C4⋊C4—132no—
619C4⋊C4—132no—
620C4⋊C4—264no—
621C4⋊C4—264no—
622C4⋊C4—264no—
623C4⋊C4—264no—
624C4⋊C4—264no—
625C4⋊C4—261no—
626C4⋊C4—261no—
627C4⋊C4—264no—
628C4⋊C4C23×D1312yes—
629C4⋊C4C23×D1312yes—
630C4⋊C4C23×D1312yes—
631C4⋊C4C23×D1312yes—
632C22⋊C4—24no—
633C22⋊C4—134no—
634C22⋊C4—134no—
635C22⋊C4—264no—
636C22⋊C4—264no—
637C22⋊C4—264no—
638C22⋊C4—264no—
639C22⋊C4—264no—
640C22⋊C4—264no—
641C42—24no—
642C42—132no—
643C42—132no—
644C42—264no—
645C42—264no—
646C13C2×#335311yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—132no—
651C23—262no—
652C23—262no—
653C23—262no—
654C23—262no—
655C23—522no—
656C23—522no—
657C23—522no—
658C23C2×D4×D1312yes—
659C23C2×D4×D1311yescharacteristic
660Q8—262no—
661Q8—262no—
662Q8—528no—
663Q8—528no—
664Q8—522no—
665D4—268no—
666D4—262no—
667D4—262no—
668D4—528no—
669D4—528no—
670D4—522no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—48no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—134no—
685C2×C4—132no—
686C2×C4—132no—
687C2×C4—132no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—264no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—262no—
696C2×C4—528no—
697C2×C4—528no—
698C2×C4—522no—
699C2×C4—522no—
700C2×C4—522no—
701C2×C4C2×#612712yes—
702C2×C4C2×D4×D1312yes—
703C2×C4C2×D4×D1311yescharacteristic
704C2×C4#8825412yes—
705C2×C4C24×D1311yescharacteristic
706C8—22no—
707C8—262no—
708C8—262no—
709C8C2×#612714yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—262no—
715C22—262no—
716C22—262no—
717C22—524no—
718C22—522no—
719C22—522no—
720C22—522no—
721C22—1044no—
722C22#1171921212yes—
723C22D13×AGL(1,ℤ/8)12yes—
724C22#1171948412yes—
725C22C22×D4×D1311yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—134no—
732C4—262no—
733C4—262no—
734C4—522no—
735C4—522no—
736C4—522no—
737C4#1171921212yes—
738C4C22×#612711yescharacteristic
739C4C2×#8825411yescharacteristic
740C2—42no—
741C2—522no—
742C2—1042no—
743C2#1312741614yesdirect product factor
744C2C2×#1171921211yescharacteristic
745C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
746C2C2×#1171948411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#428C2
socleC23×C13C22×D4
prime radicalC2×#11719212C2
hypercenterC2×#428D13
hypocenterC13C2×#3353
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#11719238C2semidirect
3. #13127416C2direct (N × H)
4. C2×#11718535C2semidirect
5. C2×#11718545C2semidirect
6. C2×#11718631C2semidirect
7. C2×#11718527C2semidirect
8. C2×#11718664C2semidirect
9. C2×#11718515C2semidirect
10. C2×#11718551C2semidirect
11. C2×#11718547C2semidirect
12. C2×#11718795C2semidirect
13. C2×#11718513C2semidirect
14. C2×#11718789C2semidirect
15. C2×#11718522C2semidirect
16. C2×C13×#428C2semidirect
28. #11719238C22semidirect
45. C13×#428C22semidirect
51. #11718795C22semidirect
52. #11718789C22semidirect
59. #11718664C22semidirect
60. #11718631C22semidirect
69. #11718551C22semidirect
70. #11718547C22semidirect
71. #11718545C22semidirect
72. #11718535C22semidirect
73. #11718527C22semidirect
74. #11718522C22semidirect
75. #11718515C22semidirect
76. #11718513C22semidirect
231. C2×C8×C13#41semidirect
289. C2×#428D13semidirect
350. C8×C13C2×#41semidirect
393. #428C2×D13semidirect
547. C2×C13#3353semidirect
609. C2×C8#6127semidirect
646. C13C2×#3353semidirect
709. C8C2×#6127semidirect
743. C2#13127416direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192382
C2×#117192122
#131274162
C2×#117185352
C2×#117185452
C2×#117186312
C2×#117185272
C2×#117186642
C2×#117185152
C2×#117185512
C2×#117185472
C2×#117187952
C2×#117185132
C2×#117187892
C2×#117185222
C2×C13×#4282
C2×#335313