Finite Group Databasebeta

← C2×#13125906 #16734260

Subgroups — C2×#13125906 #16734260

Order 3328.

2214 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719330C211yesmaximal, characteristic, complemented
2C2×#11719535C211yesmaximal, characteristic
3#13125906C2116yesmaximal, direct product factor
4C2×#11718851C211yesmaximal, characteristic, complemented
5C2×#11718836C211yesmaximal, characteristic, complemented
6C2×#11718425C211yesmaximal, characteristic, complemented
7C2×#11718461C211yesmaximal, characteristic, complemented
8C2×#11718459C211yesmaximal, characteristic, complemented
9C2×#11718846C211yesmaximal, characteristic, complemented
10C2×#11718423C211yesmaximal, characteristic, complemented
11C2×#11718824C211yesmaximal, characteristic, complemented
12C2×#11718900C211yesmaximal, characteristic, complemented
13C2×#11718392C211yesmaximal, characteristic, complemented
14C2×#11718707C211yesmaximal, characteristic, complemented
15C2×#11718381C211yesmaximal, characteristic, complemented
16C2×C13×#452C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C23×D52C2211yescharacteristic
19C22×C13×Q16C2211yescharacteristic, complemented
20C22×C13×SD16C2211yescharacteristic, complemented
21C2×C13×C22⋊Q8C2211yescharacteristic
22#11719535—24no—
23#11719535C2218yes—
24C2×#88201C2211yescharacteristic
25C2×#88201C2211yescharacteristic
26C2×Q8×Dic13C2211yescharacteristic, complemented
27C2×#88198C2211yescharacteristic, complemented
28C22×#6107C2211yescharacteristic, complemented
29C22×#6106C2211yescharacteristic
30C22×#6106C2211yescharacteristic
31C2×#88194C2211yescharacteristic
32C2×#88194C2211yescharacteristic
33C2×#88191—21no—
34C2×#88191—21no—
35C22×#6105C2211yescharacteristic, complemented
36C2×#88184—21no—
37C2×#88184—21no—
38C2×#88180C2211yescharacteristic
39C2×#88178C2211yescharacteristic
40C22×#6095C2211yescharacteristic
41C22×#6095C2211yescharacteristic
42#11719330—24no—
43#11719330C2218yescomplemented
44C2×#88144—21no—
45C2×#88144C2211yescharacteristic, complemented
46C2×#88143—21no—
47C2×#88141C2211yescharacteristic, complemented
48C2×#88133—21no—
49C2×#88133—21no—
50C13×#452C2218yescomplemented
51C2×C13×#103C2211yescharacteristic, complemented
52C2×C13×#102C2211yescharacteristic, complemented
53C2×C13×C22⋊C8C2211yescharacteristic
54#11718900C2218yescomplemented
55C2×#88075C2211yescharacteristic, complemented
56C2×#88072C2211yescharacteristic, complemented
57C2×C22⋊#1055C2211yescharacteristic
58#11718851C2218yescomplemented
59#11718846C2218yescomplemented
60#11718836C2218yescomplemented
61#11718824C2218yescomplemented
62C2×#88061C2211yescharacteristic
63C2×#88061C2211yescharacteristic
64C2×#88055C2211yescharacteristic, complemented
65C2×#88054C2211yescharacteristic, complemented
66C2×#88054C2211yescharacteristic, complemented
67C2×C8×Dic13C2211yescharacteristic, complemented
68#11718707C2218yescomplemented
69C2×#88049C2211yescharacteristic
70C2×#88049C2211yescharacteristic
71#11718461C2218yescomplemented
72#11718459C2218yescomplemented
73#11718425C2218yescomplemented
74#11718423C2218yescomplemented
75#11718392C2218yescomplemented
76#11718381C2218yescomplemented
77C24×D13—21no—
78C2×C13×#41—22no—
79C2×C13×#41—42no—
80C2×C13×#41—42no—
81C2×C13×#41C2314yes—
82C22×Q8×C13C2311yescharacteristic
83C22×Q8×C13C2311yescharacteristic
84C22×D4×C13—21no—
85C22×D4×C13C2311yescharacteristic
86C23×C4×C13—21no—
87C23×C4×C13C2311yescharacteristic
88C22×C22⋊D13—21no—
89C22×C22⋊D13—21no—
90C22×C22⋊D13—21no—
91C22×C22⋊D13—21no—
92C22×D52—21no—
93C22×D52—22no—
94C22×D52—42no—
95C22×D52—42no—
96C22×D52C2311yescharacteristic
97C22×D52C2311yescharacteristic
98C22×D52C2314yes—
99C22×Dic26C2311yescharacteristic
100C2×C13×Q16—42no—
101C2×C13×Q16C2314yescomplemented
102C2×C13×SD16—42no—
103C2×C13×SD16C2314yescomplemented
104C22×C8×C13C2311yescharacteristic
105C22×C8×C13C2311yescharacteristic
106C13×C22⋊Q8—22no—
107C13×C22⋊Q8C2314yes—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C22⋊C4—21no—
111C2×C22⋊Dic13—21no—
112C2×C22⋊Dic13D411yescharacteristic
113C2×C22⋊Dic13D411yescharacteristic
114#88201—22no—
115#88201—22no—
116#88201C2314yes—
117#88201C2314yes—
118Q8×Dic13—22no—
119Q8×Dic13C2314yescomplemented
120#88198—22no—
121#88198C2314yescomplemented
122C2×#6107—42no—
123C2×#6107C2314yescomplemented
124C2×#6106—42no—
125C2×#6106—42no—
126C2×#6106C2314yes—
127C2×#6106C2314yes—
128#88194—22no—
129#88194—22no—
130#88194C2314yes—
131#88194C2314yes—
132#88191—28no—
133#88191—28no—
134C2×#6105—42no—
135C2×#6105C2314yescomplemented
136#88184—28no—
137#88184—28no—
138C2×#6103—21no—
139C2×#6103—21no—
140C2×#6103—21no—
141C2×#6103—21no—
142#88180D414yes—
143#88180C2314yes—
144C2×C4⋊Dic13—21no—
145C2×C4⋊Dic13—21no—
146C2×C4⋊Dic13D411yescharacteristic
147C2×C4⋊Dic13D411yescharacteristic
148C2×C4⋊Dic13C2311yescharacteristic
149#88178—22no—
150#88178C2314yes—
151C2×#6101—21no—
152C2×#6101—21no—
153C2×#6101—21no—
154C2×#6101—21no—
155C2×#6101—21no—
156C2×C4×Dic13—21no—
157C2×C4×Dic13—21no—
158C2×C4×Dic13C2311yescharacteristic
159C2×C4×Dic13C2311yescharacteristic
160C22×#1055C2311yescharacteristic
161C22×#1055C2311yescharacteristic
162C2×#6095—42no—
163C2×#6095—42no—
164C2×#6095C2314yes—
165C2×#6095C2314yes—
166#88144—28no—
167#88144—22no—
168#88144C2314yescomplemented
169#88143—28no—
170#88141—22no—
171#88141C2314yescomplemented
172#88133—28no—
173#88133—28no—
174C13×#103C2314yescomplemented
175C13×#102C2314yescomplemented
176C13×C22⋊C8C2314yes—
177#88075C2314yescomplemented
178#88072C2314yescomplemented
179C22⋊#1055C2314yes—
180#88061C2314yes—
181#88061C2314yes—
182#88055C2314yescomplemented
183#88054C2314yescomplemented
184#88054C2314yescomplemented
185C8×Dic13C2314yescomplemented
186#88049C2314yes—
187#88049C2314yes—
188C2×#3222—131nomaximal, Sylow
189C24×C13—21no—
190C24×C13C2×D411yescharacteristic
191C23×D13—21no—
192C23×D13—21no—
193C23×D13—24no—
194C23×D13—44no—
195C23×D13—82no—
196C23×D13—82no—
197C13×#41—44no—
198C13×#41—44no—
199C13×#41—48no—
200C2×Q8×C13—21no—
201C2×Q8×C13—21no—
202C2×Q8×C13—22no—
203C2×Q8×C13—22no—
204C2×Q8×C13—22no—
205C2×Q8×C13—22no—
206C2×Q8×C13C2412yes—
207C2×Q8×C13C2412yes—
208C2×D4×C13—24no—
209C2×D4×C13—21no—
210C2×D4×C13—22no—
211C2×D4×C13—22no—
212C2×D4×C13—44no—
213C2×D4×C13C2412yes—
214C22×C4×C13—22no—
215C22×C4×C13—22no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—24no—
220C22×C4×C13—44no—
221C22×C4×C13C2×D411yescharacteristic
222C22×C4×C13C2×D412yes—
223C22×C4×C13C2412yes—
224C22×C4×C13C2411yescharacteristic
225C2×C22⋊D13—24no—
226C2×C22⋊D13—24no—
227C2×C22⋊D13—24no—
228C2×C22⋊D13—24no—
229C2×C22⋊D13—82no—
230C2×C22⋊D13—82no—
231C2×C22⋊D13—82no—
232C2×C22⋊D13—82no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13C2×D411yescharacteristic
236C22×Dic13C2×D411yescharacteristic
237C22×Dic13C2×D411yescharacteristic
238C22×Dic13C2×D411yescharacteristic
239C2×D52—22no—
240C2×D52—22no—
241C2×D52—22no—
242C2×D52—22no—
243C2×D52—24no—
244C2×D52—21no—
245C2×D52—21no—
246C2×D52—44no—
247C2×D52—44no—
248C2×D52—44no—
249C2×D52—48no—
250C2×D52C2412yes—
251C2×D52C2412yes—
252C2×Dic26—22no—
253C2×Dic26—22no—
254C2×Dic26—21no—
255C2×Dic26C2412yes—
256C13×Q16—44no—
257C13×SD16—44no—
258C2×C8×C13—22no—
259C2×C8×C13—22no—
260C2×C8×C13C2412yes—
261C2×C8×C13C2412yes—
262C13×C4⋊C4—21no—
263C13×C4⋊C4—24no—
264C13×C4⋊C4C2412yes—
265C13×C22⋊C4—24no—
266C22⋊Dic13—24no—
267C22⋊Dic13C2×D414yes—
268C22⋊Dic13C2×D414yes—
269#6107—44no—
270#6106—44no—
271#6106—44no—
272#6105—44no—
273#6103—24no—
274#6103—24no—
275#6103—24no—
276#6103—24no—
277C4⋊Dic13—21no—
278C4⋊Dic13—24no—
279C4⋊Dic13—24no—
280C4⋊Dic13C2×D414yes—
281C4⋊Dic13C2×D414yes—
282C4⋊Dic13C2412yes—
283#6101—24no—
284#6101—24no—
285#6101—24no—
286#6101—24no—
287#6101—24no—
288C4×Dic13—24no—
289C4×Dic13—24no—
290C4×Dic13C2×D412yes—
291C4×Dic13C2×D412yes—
292C4×Dic13C2412yes—
293C4×Dic13C2412yes—
294C2×#1055—22no—
295C2×#1055—22no—
296C2×#1055C2412yes—
297C2×#1055C2412yes—
298#6095—44no—
299#6095—44no—
300C2×#541—131no—
301C2×#535—131no—
302#3222—1316no—
303C2×#497—131no—
304C2×#492—131no—
305C2×#490—131no—
306C2×#488—131no—
307C2×#464—131no—
308C2×#464—131no—
309C2×#460—131no—
310C2×#460—131no—
311C2×#452—131no—
312C2×#452D1311yescharacteristic, complemented
313C2×#450—131no—
314C2×#450—131no—
315C2×#433—131no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—42no—
321C23×C13—42no—
322C23×C13—42no—
323C23×C13C22×D412yes—
324C23×C13C22×D411yescharacteristic
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—48no—
328C22×D13—42no—
329C22×D13—42no—
330C22×D13—42no—
331C22×D13—42no—
332C22×D13—42no—
333C22×D13—42no—
334C22×D13—84no—
335C22×D13—84no—
336C22×D13—816no—
337Q8×C13—22no—
338Q8×C13—22no—
339Q8×C13—22no—
340Q8×C13—22no—
341Q8×C13—42no—
342Q8×C13—42no—
343D4×C13—22no—
344D4×C13—22no—
345D4×C13—48no—
346D4×C13—42no—
347C2×C4×C13—22no—
348C2×C4×C13—24no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—48no—
355C2×C4×C13—42no—
356C2×C4×C13—42no—
357C2×C4×C13—42no—
358C2×C4×C13C22×D412yes—
359C2×C4×C13C22×D411yescharacteristic
360C2×C4×C13H(5,𝔽2)12yes—
361C2×C4×C13H(5,𝔽2)12yes—
362C2×C4×C13C2511yescharacteristic
363C22⋊D13—84no—
364C22⋊D13—84no—
365C22⋊D13—84no—
366C22⋊D13—84no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—42no—
374C2×Dic13—42no—
375C2×Dic13C22×D412yes—
376C2×Dic13C22×D412yes—
377C2×Dic13C22×D412yes—
378C2×Dic13C22×D412yes—
379D52—22no—
380D52—22no—
381D52—22no—
382D52—22no—
383D52—48no—
384D52—42no—
385D52—42no—
386Dic26—22no—
387Dic26—22no—
388Dic26—42no—
389C8×C13—22no—
390C8×C13—22no—
391#1055—22no—
392#1055—22no—
393C22×#41C2×D1311yescharacteristic
394C23×D4—131no—
395C22×Q16—131no—
396C22×Q16C2×D1311yescharacteristic, complemented
397C22×SD16—131no—
398C22×SD16—131no—
399C22×SD16—131no—
400C22×SD16—131no—
401C22×SD16—131no—
402C22×SD16C2×D1311yescharacteristic, complemented
403#541—138no—
404#541—264no—
405#535—138no—
406#535—264no—
407C2×C4⋊Q8—131no—
408C2×#127—131no—
409C2×#127—131no—
410C2×#126—261no—
411C2×#126—261no—
412C2×#125—131no—
413C2×#125—261no—
414C2×#125—261no—
415C2×#124—131no—
416C2×#124—131no—
417C2×C22⋊Q8—131no—
418C2×C22⋊Q8C2×D1311yescharacteristic
419C2×#121—261no—
420C2×#121—261no—
421C2×#120—261no—
422C2×#120—261no—
423C2×C4×Q8—131no—
424C2×C4×Q8—131no—
425C2×#117—131no—
426#497—138no—
427#492—138no—
428#490—138no—
429#488—138no—
430#464—138no—
431#464—138no—
432#460—138no—
433#460—138no—
434#452—138no—
435#452C2×D1318yescomplemented
436#450—138no—
437#450—138no—
438#433—138no—
439C2×C4⋊C8—131no—
440C2×C4⋊C8—131no—
441C2×#103—131no—
442C2×#103C2×D1311yescharacteristic, complemented
443C2×#102—131no—
444C2×#102—131no—
445C2×#102—131no—
446C2×#102—131no—
447C2×#102—131no—
448C2×#102C2×D1311yescharacteristic, complemented
449C2×C22⋊C8—131no—
450C2×C22⋊C8C2×D1311yescharacteristic
451C2×#97—131no—
452C2×C4×C8—131no—
453C22×C13—22no—
454C22×C13—22no—
455C22×C13—22no—
456C22×C13—44no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—84no—
461C22×C13#53512yes—
462C22×C13#57712yes—
463C22×C13#57712yes—
464C22×C13C23×D411yescharacteristic
465C2×D13—42no—
466C2×D13—42no—
467C2×D13—42no—
468C2×D13—42no—
469C2×D13—42no—
470C2×D13—42no—
471C2×D13—816no—
472C2×D13—84no—
473C2×D13—84no—
474C4×C13—22no—
475C4×C13—42no—
476C4×C13—42no—
477C4×C13—42no—
478C4×C13#53512yes—
479C4×C13C2×H(5,𝔽2)11yescharacteristic
480C4×C13C2×H(5,𝔽2)11yescharacteristic
481Dic13—22no—
482Dic13—22no—
483Dic13—22no—
484Dic13—22no—
485Dic13—42no—
486Dic13—42no—
487C25—261no—
488C2×#41—22no—
489C2×#41—42no—
490C2×#41—42no—
491C2×#41C22×D1314yes—
492C22×Q8—131no—
493C22×Q8C22×D1311yescharacteristic
494C22×Q8C22×D1311yescharacteristic
495C22×D4—21no—
496C22×D4—131no—
497C22×D4—131no—
498C22×D4—134no—
499C22×D4—261no—
500C22×D4—261no—
501C22×D4—261no—
502C22×D4—261no—
503C22×D4—261no—
504C22×D4—262no—
505C22×D4—522no—
506C22×D4—522no—
507C22×D4C22×D1311yescharacteristic
508C23×C4—21no—
509C23×C4C22×D1311yescharacteristic
510C2×Q16—42no—
511C2×Q16—134no—
512C2×Q16—522no—
513C2×Q16C22×D1314yescomplemented
514C2×SD16—42no—
515C2×SD16—134no—
516C2×SD16—134no—
517C2×SD16—134no—
518C2×SD16—134no—
519C2×SD16—134no—
520C2×SD16—522no—
521C2×SD16—522no—
522C2×SD16—522no—
523C2×SD16—522no—
524C2×SD16—522no—
525C2×SD16C22×D1314yescomplemented
526C22×C8—131no—
527C22×C8—131no—
528C22×C8C22×D1311yescharacteristic
529C22×C8C22×D1311yescharacteristic
530C4⋊Q8—134no—
531C4⋊Q8—262no—
532#127—134no—
533#127—134no—
534#127—262no—
535#127—262no—
536#126—268no—
537#126—268no—
538#125—134no—
539#125—262no—
540#125—268no—
541#125—268no—
542#124—134no—
543#124—134no—
544#124—262no—
545#124—262no—
546C22⋊Q8—22no—
547C22⋊Q8—134no—
548C22⋊Q8—262no—
549C22⋊Q8C22×D1314yes—
550#121—268no—
551#121—268no—
552#120—268no—
553#120—268no—
554C4×Q8—134no—
555C4×Q8—134no—
556C4×Q8—262no—
557C4×Q8—262no—
558#117—134no—
559#117—134no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—131no—
562C2×C4⋊C4—131no—
563C2×C4⋊C4—131no—
564C2×C4⋊C4—261no—
565C2×C4⋊C4—261no—
566C2×C4⋊C4—261no—
567C2×C4⋊C4—261no—
568C2×C4⋊C4—261no—
569C2×C4⋊C4—261no—
570C2×C4⋊C4—261no—
571C2×C4⋊C4C22×D1311yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—131no—
574C2×C22⋊C4—131no—
575C2×C22⋊C4—261no—
576C2×C22⋊C4—261no—
577C2×C22⋊C4—261no—
578C2×C22⋊C4—261no—
579C2×C22⋊C4—261no—
580C2×C42—131no—
581C2×C42—131no—
582C2×C42—261no—
583C2×C42—261no—
584C4⋊C8—134no—
585C4⋊C8—134no—
586#103—134no—
587#103C22×D1314yescomplemented
588#102—134no—
589#102—134no—
590#102—134no—
591#102—134no—
592#102—134no—
593#102C22×D1314yescomplemented
594C22⋊C8—134no—
595C22⋊C8C22×D1314yes—
596#97—134no—
597C4×C8—134no—
598C2×C13—42no—
599C2×C13—82no—
600C2×C13#322214yescomplemented
601C2×C13C2×#53511yescharacteristic
602C2×C13C2×#57711yescharacteristic
603C2×C13C2×#57711yescharacteristic
604D13—82no—
605D13—82no—
606C24—21no—
607C24—261no—
608C24—261no—
609C24—264no—
610C24—524no—
611C24—1042no—
612C24—1042no—
613C24D4×D1311yescharacteristic
614#41—44no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—132no—
624C2×Q8—261no—
625C2×Q8—262no—
626C2×Q8—262no—
627C2×Q8C23×D1312yes—
628C2×Q8C23×D1312yes—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—44no—
634C2×D4—132no—
635C2×D4—132no—
636C2×D4—264no—
637C2×D4—264no—
638C2×D4—264no—
639C2×D4—264no—
640C2×D4—264no—
641C2×D4—261no—
642C2×D4—261no—
643C2×D4—262no—
644C2×D4—262no—
645C2×D4—262no—
646C2×D4—262no—
647C2×D4—524no—
648C2×D4—524no—
649C2×D4—524no—
650C2×D4—528no—
651C2×D4—1042no—
652C2×D4—1042no—
653C2×D4—1042no—
654C2×D4—1042no—
655C2×D4C23×D1312yes—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—44no—
663C22×C4—131no—
664C22×C4—131no—
665C22×C4—131no—
666C22×C4—131no—
667C22×C4—261no—
668C22×C4—261no—
669C22×C4D4×D1312yes—
670C22×C4D4×D1311yescharacteristic
671C22×C4C23×D1312yes—
672C22×C4C23×D1311yescharacteristic
673Q16—44no—
674Q16—524no—
675SD16—44no—
676SD16—524no—
677SD16—524no—
678SD16—524no—
679SD16—524no—
680SD16—524no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—132no—
684C2×C8—132no—
685C2×C8—262no—
686C2×C8—262no—
687C2×C8C23×D1312yes—
688C2×C8C23×D1312yes—
689C4⋊C4—24no—
690C4⋊C4—21no—
691C4⋊C4—134no—
692C4⋊C4—134no—
693C4⋊C4—132no—
694C4⋊C4—264no—
695C4⋊C4—264no—
696C4⋊C4—264no—
697C4⋊C4—264no—
698C4⋊C4—264no—
699C4⋊C4—264no—
700C4⋊C4—261no—
701C4⋊C4—264no—
702C4⋊C4C23×D1312yes—
703C22⋊C4—24no—
704C22⋊C4—134no—
705C22⋊C4—134no—
706C22⋊C4—264no—
707C22⋊C4—264no—
708C22⋊C4—264no—
709C22⋊C4—264no—
710C22⋊C4—264no—
711C42—132no—
712C42—132no—
713C42—132no—
714C42—132no—
715C42—264no—
716C42—264no—
717C13C2×#322211yescharacteristic, complemented, Sylow
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—262no—
726C23—262no—
727C23—528no—
728C23—522no—
729C23—522no—
730C23—522no—
731C23—522no—
732C23—522no—
733C23—522no—
734C23—1044no—
735C23—1044no—
736C23—10416no—
737C23C2×D4×D1312yes—
738C23C2×D4×D1311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—42no—
745Q8—262no—
746Q8—262no—
747Q8—522no—
748D4—22no—
749D4—22no—
750D4—48no—
751D4—42no—
752D4—262no—
753D4—262no—
754D4—262no—
755D4—262no—
756D4—528no—
757D4—522no—
758D4—522no—
759D4—1044no—
760D4—1044no—
761D4—1044no—
762D4—1044no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—48no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—132no—
775C2×C4—132no—
776C2×C4—132no—
777C2×C4—132no—
778C2×C4—262no—
779C2×C4—262no—
780C2×C4—262no—
781C2×C4—262no—
782C2×C4—262no—
783C2×C4—262no—
784C2×C4—522no—
785C2×C4—522no—
786C2×C4C2×D4×D1312yes—
787C2×C4C2×D4×D1311yescharacteristic
788C2×C4#8825112yes—
789C2×C4#8825112yes—
790C2×C4C24×D1311yescharacteristic
791C8—22no—
792C8—22no—
793C8—262no—
794C8—262no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—84no—
803C22—522no—
804C22—522no—
805C22—522no—
806C22—522no—
807C22—522no—
808C22—522no—
809C22—10416no—
810C22—1044no—
811C22—1044no—
812C22#1171929712yes—
813C22#1171947512yes—
814C22#1171948312yes—
815C22C22×D4×D1311yescharacteristic
816C4—22no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—262no—
821C4—262no—
822C4—262no—
823C4—262no—
824C4—522no—
825C4—522no—
826C4#1171929712yes—
827C4C2×#8825111yescharacteristic
828C4C2×#8825111yescharacteristic
829C2—42no—
830C2—82no—
831C2—1042no—
832C2—1042no—
833C2#1312590614yesdirect product factor
834C2C2×#1171929711yescharacteristic
835C2C2×#1171947511yescharacteristic
836C2C2×#1171948311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#452C2
socleC23×C13C22×D4
prime radicalC2×#11719535C2
hypercenterC2×#452D13
hypocenterC13C2×#3222
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#11719330C2semidirect
3. #13125906C2direct (N × H)
4. C2×#11718851C2semidirect
5. C2×#11718836C2semidirect
6. C2×#11718425C2semidirect
7. C2×#11718461C2semidirect
8. C2×#11718459C2semidirect
9. C2×#11718846C2semidirect
10. C2×#11718423C2semidirect
11. C2×#11718824C2semidirect
12. C2×#11718900C2semidirect
13. C2×#11718392C2semidirect
14. C2×#11718707C2semidirect
15. C2×#11718381C2semidirect
16. C2×C13×#452C2semidirect
19. C22×C13×Q16C22semidirect
20. C22×C13×SD16C22semidirect
26. C2×Q8×Dic13C22semidirect
27. C2×#88198C22semidirect
28. C22×#6107C22semidirect
35. C22×#6105C22semidirect
43. #11719330C22semidirect
45. C2×#88144C22semidirect
47. C2×#88141C22semidirect
50. C13×#452C22semidirect
51. C2×C13×#103C22semidirect
52. C2×C13×#102C22semidirect
54. #11718900C22semidirect
55. C2×#88075C22semidirect
56. C2×#88072C22semidirect
58. #11718851C22semidirect
59. #11718846C22semidirect
60. #11718836C22semidirect
61. #11718824C22semidirect
64. C2×#88055C22semidirect
65. C2×#88054C22semidirect
66. C2×#88054C22semidirect
67. C2×C8×Dic13C22semidirect
68. #11718707C22semidirect
71. #11718461C22semidirect
72. #11718459C22semidirect
73. #11718425C22semidirect
74. #11718423C22semidirect
75. #11718392C22semidirect
76. #11718381C22semidirect
101. C2×C13×Q16C23semidirect
103. C2×C13×SD16C23semidirect
119. Q8×Dic13C23semidirect
121. #88198C23semidirect
123. C2×#6107C23semidirect
135. C2×#6105C23semidirect
168. #88144C23semidirect
171. #88141C23semidirect
174. C13×#103C23semidirect
175. C13×#102C23semidirect
177. #88075C23semidirect
178. #88072C23semidirect
182. #88055C23semidirect
183. #88054C23semidirect
184. #88054C23semidirect
185. C8×Dic13C23semidirect
312. C2×#452D13semidirect
396. C22×Q16C2×D13semidirect
402. C22×SD16C2×D13semidirect
435. #452C2×D13semidirect
442. C2×#103C2×D13semidirect
448. C2×#102C2×D13semidirect
513. C2×Q16C22×D13semidirect
525. C2×SD16C22×D13semidirect
587. #103C22×D13semidirect
593. #102C22×D13semidirect
600. C2×C13#3222semidirect
717. C13C2×#3222semidirect
833. C2#13125906direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193302
C2×#117195352
#131259062
C2×#117188512
C2×#117188362
C2×#117184252
C2×#117184612
C2×#117184592
C2×#117188462
C2×#117184232
C2×#117188242
C2×#117189002
C2×#117183922
C2×#117187072
C2×#117183812
C2×C13×#4522
C2×#322213