Finite Group Databasebeta

← C2×#13126089 #16735108

Subgroups — C2×#13126089 #16735108

Order 3328.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719240C211yesmaximal, characteristic
2#13126089C2116yesmaximal, direct product factor
3C2×#11718741C211yesmaximal, characteristic, complemented
4C2×#11718725C211yesmaximal, characteristic, complemented
5C2×#11718728C211yesmaximal, characteristic, complemented
6C2×#11718749C211yesmaximal, characteristic, complemented
7C2×#11718629C211yesmaximal, characteristic, complemented
8C2×#11718664C211yesmaximal, characteristic, complemented
9C2×#11718664C211yesmaximal, characteristic, complemented
10C2×#11718628C211yesmaximal, characteristic, complemented
11C2×#11718727C211yesmaximal, characteristic, complemented
12C2×#11718727C211yesmaximal, characteristic, complemented
13C2×#11718745C211yesmaximal, characteristic, complemented
14C2×#11718748C211yesmaximal, characteristic, complemented
15C2×#11718661C211yesmaximal, characteristic, complemented
16C2×C13×#544C211yesmaximal, characteristic, complemented
17C13×#544—24no—
18C13×#544C2218yescomplemented
19C2×C13×C4⋊Q8—21no—
20C2×C13×C4⋊Q8C2211yescharacteristic
21C2×C13×C4⋊Q8C2211yescharacteristic
22C2×C13×#125—21no—
23C2×C13×#125C2211yescharacteristic
24C2×C13×#125C2211yescharacteristic
25C2×C13×C22⋊Q8—21no—
26C2×C13×C22⋊Q8—21no—
27C2×C13×#117C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic
29C22×C13×C4⋊C4C2211yescharacteristic
30C2×#88184C2211yescharacteristic
31C2×#88184C2211yescharacteristic
32#11719240—24no—
33#11719240C2218yes—
34C2×#88148—21no—
35C2×#88148—21no—
36C2×#88138—21no—
37C2×#88138—21no—
38C2×#88128C2211yescharacteristic
39C2×C4×D52C2211yescharacteristic
40C2×C4×D52C2211yescharacteristic
41C2×#88124C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43C2×C22⋊#1055C2211yescharacteristic
44#11718749C2218yescomplemented
45#11718748C2218yescomplemented
46#11718745C2218yescomplemented
47#11718741C2218yescomplemented
48#11718728C2218yescomplemented
49#11718727C2218yescomplemented
50#11718727C2218yescomplemented
51#11718725C2218yescomplemented
52#11718664C2218yescomplemented
53#11718664C2218yescomplemented
54#11718661C2218yescomplemented
55#11718629C2218yescomplemented
56#11718628C2218yescomplemented
57C2×#88049C2211yescharacteristic
58C2×#88049C2211yescharacteristic
59C2×#88049C2211yescharacteristic
60C2×#88049C2211yescharacteristic
61C2×#88049C2211yescharacteristic
62C2×#88049C2211yescharacteristic
63C2×#88049C2211yescharacteristic
64C2×#88049C2211yescharacteristic
65C2×#88048C2211yescharacteristic
66C2×#88048C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88047C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×C4⋊#1055C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13—21no—
78C22×Q8×C13—21no—
79C23×C4×C13—21no—
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13—21no—
82C22×C22⋊D13—21no—
83C22×D52—21no—
84C22×D52—21no—
85C22×D52C2311yescharacteristic
86C22×D52C2311yescharacteristic
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C13×C4⋊Q8—28no—
90C13×C4⋊Q8—22no—
91C13×C4⋊Q8—22no—
92C13×C4⋊Q8C2314yes—
93C13×C4⋊Q8C2314yes—
94C13×#125—28no—
95C13×#125—22no—
96C13×#125—22no—
97C13×#125C2314yes—
98C13×#125C2314yes—
99C13×C22⋊Q8—28no—
100C13×C22⋊Q8—28no—
101C13×#117—22no—
102C13×#117D414yes—
103C13×#117C2314yes—
104C13×#117C2314yes—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4D411yescharacteristic
114C2×C13×C4⋊C4D411yescharacteristic
115C2×C13×C4⋊C4C2311yescharacteristic
116C2×C13×C4⋊C4C2311yescharacteristic
117C2×C13×C4⋊C4C2314yes—
118C2×C13×C4⋊C4C2311yescharacteristic
119C2×C13×C4⋊C4C2311yescharacteristic
120C2×C13×C22⋊C4—21no—
121C2×C13×C22⋊C4D411yescharacteristic
122C2×C13×C22⋊C4D411yescharacteristic
123C2×C42×C13—21no—
124C2×C42×C13C2311yescharacteristic
125C2×C42×C13C2311yescharacteristic
126#88184—22no—
127#88184—22no—
128#88184C2314yes—
129#88184C2314yes—
130C2×#6103—21no—
131C2×#6103—21no—
132C2×#6103—21no—
133C2×#6103—21no—
134C2×C4⋊Dic13C2311yescharacteristic
135C2×C4⋊Dic13C2311yescharacteristic
136C2×#6101—21no—
137C2×#6101—21no—
138C22×#1055C2311yescharacteristic
139C22×#1055C2311yescharacteristic
140C22×#1055C2311yescharacteristic
141C22×#1055C2311yescharacteristic
142#88148—28no—
143#88148—28no—
144#88138—28no—
145#88138—28no—
146#88128—22no—
147#88128C2314yes—
148C4×D52—22no—
149C4×D52—22no—
150C4×D52C2314yes—
151C4×D52C2314yes—
152#88124—22no—
153#88124C2314yes—
154C22⋊#1055C2314yes—
155C22⋊#1055C2314yes—
156#88049C2314yes—
157#88049C2314yes—
158#88049C2314yes—
159#88049C2314yes—
160#88049C2314yes—
161#88049C2314yes—
162#88049C2314yes—
163#88049C2314yes—
164#88048C2314yes—
165#88048C2314yes—
166#88048C2314yes—
167#88048C2314yes—
168#88047C2314yes—
169#88047C2314yes—
170#88047C2314yes—
171#88047C2314yes—
172C4⋊#1055C2314yes—
173C4⋊#1055C2314yes—
174#88043C2314yes—
175C4×#1055C2314yes—
176C2×#3241—131nomaximal, Sylow
177C24×C13C2×D411yescharacteristic
178C23×D13—21no—
179C23×D13—21no—
180C2×Q8×C13—24no—
181C2×Q8×C13—24no—
182C2×Q8×C13—82no—
183C2×Q8×C13—82no—
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—82no—
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13C2×D411yescharacteristic
194C22×C4×C13C2×D411yescharacteristic
195C22×C4×C13C2×D411yescharacteristic
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D412yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2411yescharacteristic
200C2×C22⋊D13—24no—
201C2×C22⋊D13—24no—
202C2×C22⋊D13—82no—
203C2×C22⋊D13—82no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C2×D52—22no—
207C2×D52—22no—
208C2×D52—22no—
209C2×D52—22no—
210C2×D52—21no—
211C2×D52—21no—
212C2×D52—24no—
213C2×D52—24no—
214C2×D52—82no—
215C2×D52—82no—
216C2×D52C2412yes—
217C2×D52C2412yes—
218C2×C4×D13—24no—
219C2×C4×D13—24no—
220C2×C4×D13—82no—
221C2×C4×D13—82no—
222C13×C4⋊C4—24no—
223C13×C4⋊C4—21no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—24no—
226C13×C4⋊C4—24no—
227C13×C4⋊C4—24no—
228C13×C4⋊C4—24no—
229C13×C4⋊C4—24no—
230C13×C4⋊C4—24no—
231C13×C4⋊C4—21no—
232C13×C4⋊C4—21no—
233C13×C4⋊C4C2×D414yes—
234C13×C4⋊C4C2×D414yes—
235C13×C4⋊C4C2412yes—
236C13×C4⋊C4C2412yes—
237C13×C4⋊C4C2412yes—
238C13×C4⋊C4C2412yes—
239C13×C22⋊C4—24no—
240C13×C22⋊C4C2×D414yes—
241C13×C22⋊C4C2×D414yes—
242C42×C13—24no—
243C42×C13C2×D412yes—
244C42×C13C2×D412yes—
245C42×C13C2412yes—
246C42×C13C2412yes—
247#6103—24no—
248#6103—24no—
249#6103—24no—
250#6103—24no—
251C4⋊Dic13—21no—
252C4⋊Dic13—21no—
253C4⋊Dic13C2412yes—
254C4⋊Dic13C2412yes—
255#6101—24no—
256#6101—24no—
257C2×#1055—22no—
258C2×#1055—22no—
259C2×#1055—22no—
260C2×#1055—22no—
261C2×#1055C2412yes—
262C2×#1055C2412yes—
263C2×#1055C2412yes—
264C2×#1055C2412yes—
265C2×#544D1311yescharacteristic, complemented
266C2×#540—131no—
267#3241—1316no—
268C2×#501—131no—
269C2×#499—131no—
270C2×#490—131no—
271C2×#486—131no—
272C2×#481—131no—
273C2×#482—131no—
274C2×#482—131no—
275C2×#480—131no—
276C2×#478—131no—
277C2×#478—131no—
278C2×#476—131no—
279C2×#474—131no—
280C2×#433—131no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13C22×D412yes—
285C23×C13C22×D411yescharacteristic
286C22×D13—22no—
287C22×D13—22no—
288C22×D13—42no—
289C22×D13—42no—
290C22×D13—42no—
291C22×D13—42no—
292C22×D13—42no—
293C22×D13—42no—
294Q8×C13—84no—
295Q8×C13—84no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—24no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—84no—
313C2×C4×C13C22×D412yes—
314C2×C4×C13C22×D412yes—
315C2×C4×C13C22×D412yes—
316C2×C4×C13C22×D412yes—
317C2×C4×C13C22×D412yes—
318C2×C4×C13C22×D411yescharacteristic
319C2×C4×C132−1+412yes—
320C2×C4×C132−1+412yes—
321C2×C4×C13C2511yescharacteristic
322C22⋊D13—84no—
323C22⋊D13—84no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328D52—22no—
329D52—22no—
330D52—22no—
331D52—22no—
332D52—42no—
333D52—42no—
334D52—84no—
335D52—84no—
336C4×D13—84no—
337C4×D13—84no—
338#1055—22no—
339#1055—22no—
340#1055—22no—
341#1055—22no—
342#544—24no—
343#544C2×D1318yescomplemented
344#540—138no—
345#540—264no—
346C2×C4⋊Q8—21no—
347C2×C4⋊Q8C2×D1311yescharacteristic
348C2×C4⋊Q8C2×D1311yescharacteristic
349C2×#127—131no—
350C2×#125—21no—
351C2×#125—131no—
352C2×#125C2×D1311yescharacteristic
353C2×#125C2×D1311yescharacteristic
354C2×#123—261no—
355C2×#123—261no—
356C2×C22⋊Q8—21no—
357C2×C22⋊Q8—21no—
358C2×#121—131no—
359C2×#121—131no—
360C2×#121—261no—
361C2×#121—261no—
362C2×C4×D4—131no—
363C2×C4×D4—131no—
364C2×#117C2×D1311yescharacteristic
365C2×#117C2×D1311yescharacteristic
366C22×C4⋊C4C2×D1311yescharacteristic
367#501—138no—
368#499—138no—
369#490—138no—
370#486—138no—
371#482—138no—
372#482—138no—
373#481—138no—
374#480—138no—
375#478—138no—
376#478—138no—
377#476—138no—
378#474—138no—
379#433—138no—
380C2×#107—131no—
381C2×#107—131no—
382C2×#107—131no—
383C2×#107—131no—
384C2×#106—131no—
385C2×#106—131no—
386C2×#106—131no—
387C2×#106—131no—
388C2×C4⋊C8—131no—
389C2×C4⋊C8—131no—
390C2×#102—131no—
391C2×#102—131no—
392C2×#102—131no—
393C2×#102—131no—
394C2×#102—131no—
395C2×#102—131no—
396C2×#102—131no—
397C2×#102—131no—
398C2×C22⋊C8—131no—
399C2×C22⋊C8—131no—
400C2×#97—131no—
401C2×C4×C8—131no—
402C22×C13—22no—
403C22×C13—22no—
404C22×C13—22no—
405C22×C13—44no—
406C22×C13#53612yes—
407C22×C13#57612yes—
408C22×C13#57712yes—
409C22×C13C23×D411yescharacteristic
410C2×D13—42no—
411C2×D13—42no—
412C2×D13—42no—
413C2×D13—42no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—84no—
417C2×D13—84no—
418C4×C13—22no—
419C4×C13—22no—
420C4×C13—22no—
421C4×C13—22no—
422C4×C13—22no—
423C4×C13—42no—
424C4×C13—42no—
425C4×C13—42no—
426C4×C13—42no—
427C4×C13#53612yes—
428C4×C13C2×2−1+411yescharacteristic
429C4×C13C2×2−1+411yescharacteristic
430Dic13—42no—
431Dic13—42no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×D4—131no—
435C22×D4—131no—
436C22×D4—261no—
437C22×D4—261no—
438C22×D4—261no—
439C22×D4—261no—
440C23×C4—21no—
441C23×C4—261no—
442C23×C4—261no—
443C23×C4C22×D1311yescharacteristic
444C22×C8—131no—
445C22×C8—131no—
446C22×C8—131no—
447C22×C8—131no—
448C4⋊Q8—28no—
449C4⋊Q8—22no—
450C4⋊Q8—22no—
451C4⋊Q8C22×D1314yes—
452C4⋊Q8C22×D1314yes—
453#127—134no—
454#127—262no—
455#125—28no—
456#125—22no—
457#125—22no—
458#125—134no—
459#125—262no—
460#125C22×D1314yes—
461#125C22×D1314yes—
462#123—268no—
463#123—268no—
464C22⋊Q8—28no—
465C22⋊Q8—28no—
466#121—134no—
467#121—134no—
468#121—262no—
469#121—262no—
470#121—268no—
471#121—268no—
472C4×D4—134no—
473C4×D4—134no—
474C4×D4—262no—
475C4×D4—262no—
476#117—22no—
477#117C22⋊D1314yes—
478#117C22×D1314yes—
479#117C22×D1314yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—261no—
491C2×C4⋊C4—261no—
492C2×C4⋊C4C22⋊D1311yescharacteristic
493C2×C4⋊C4C22⋊D1311yescharacteristic
494C2×C4⋊C4C22×D1311yescharacteristic
495C2×C4⋊C4C22×D1311yescharacteristic
496C2×C4⋊C4C22×D1314yes—
497C2×C4⋊C4C22×D1311yescharacteristic
498C2×C4⋊C4C22×D1311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—261no—
501C2×C22⋊C4—261no—
502C2×C22⋊C4—261no—
503C2×C22⋊C4—261no—
504C2×C22⋊C4C22⋊D1311yescharacteristic
505C2×C22⋊C4C22⋊D1311yescharacteristic
506C2×C42—21no—
507C2×C42C22×D1311yescharacteristic
508C2×C42C22×D1311yescharacteristic
509#107—134no—
510#107—134no—
511#107—134no—
512#107—134no—
513#106—134no—
514#106—134no—
515#106—134no—
516#106—134no—
517C4⋊C8—134no—
518C4⋊C8—134no—
519#102—134no—
520#102—134no—
521#102—134no—
522#102—134no—
523#102—134no—
524#102—134no—
525#102—134no—
526#102—134no—
527C22⋊C8—134no—
528C22⋊C8—134no—
529#97—134no—
530C4×C8—134no—
531C2×C13—42no—
532C2×C13#324114yescomplemented
533C2×C13C2×#53611yescharacteristic
534C2×C13C2×#57611yescharacteristic
535C2×C13C2×#57711yescharacteristic
536D13—82no—
537D13—82no—
538C24—261no—
539C24—261no—
540C24C2×C22⋊D1311yescharacteristic
541C2×Q8—24no—
542C2×Q8—24no—
543C2×Q8—82no—
544C2×Q8—82no—
545C2×D4—132no—
546C2×D4—132no—
547C2×D4—264no—
548C2×D4—264no—
549C2×D4—262no—
550C2×D4—262no—
551C2×D4—262no—
552C2×D4—262no—
553C2×D4—261no—
554C2×D4—261no—
555C2×D4—264no—
556C2×D4—264no—
557C2×D4—1042no—
558C2×D4—1042no—
559C2×D4—1042no—
560C2×D4—1042no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—264no—
572C22×C4—264no—
573C22×C4—1042no—
574C22×C4—1042no—
575C22×C4C2×C22⋊D1312yes—
576C22×C4C2×C22⋊D1311yescharacteristic
577C22×C4C2×C22⋊D1311yescharacteristic
578C22×C4C2×C22⋊D1311yescharacteristic
579C22×C4C2×C22⋊D1311yescharacteristic
580C22×C4C2×C22⋊D1311yescharacteristic
581C22×C4C23×D1312yes—
582C22×C4C23×D1311yescharacteristic
583C2×C8—132no—
584C2×C8—132no—
585C2×C8—132no—
586C2×C8—132no—
587C2×C8—262no—
588C2×C8—262no—
589C2×C8—262no—
590C2×C8—262no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—132no—
603C4⋊C4—132no—
604C4⋊C4—261no—
605C4⋊C4—261no—
606C4⋊C4—264no—
607C4⋊C4—264no—
608C4⋊C4C2×C22⋊D1314yes—
609C4⋊C4C2×C22⋊D1314yes—
610C4⋊C4C23×D1312yes—
611C4⋊C4C23×D1312yes—
612C4⋊C4C23×D1312yes—
613C4⋊C4C23×D1312yes—
614C22⋊C4—24no—
615C22⋊C4—264no—
616C22⋊C4—264no—
617C22⋊C4—264no—
618C22⋊C4—264no—
619C22⋊C4C2×C22⋊D1314yes—
620C22⋊C4C2×C22⋊D1314yes—
621C42—24no—
622C42C2×C22⋊D1312yes—
623C42C2×C22⋊D1312yes—
624C42C23×D1312yes—
625C42C23×D1312yes—
626C13C2×#324111yescharacteristic, complemented, Sylow
627C23—22no—
628C23—22no—
629C23—22no—
630C23—262no—
631C23—262no—
632C23—522no—
633C23—522no—
634C23—522no—
635C23—522no—
636C23—522no—
637C23—522no—
638C23C22×C22⋊D1312yes—
639C23C22×C22⋊D1311yescharacteristic
640Q8—84no—
641Q8—84no—
642D4—262no—
643D4—262no—
644D4—262no—
645D4—262no—
646D4—522no—
647D4—522no—
648D4—1044no—
649D4—1044no—
650D4—1044no—
651D4—1044no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—262no—
670C2×C4—262no—
671C2×C4—522no—
672C2×C4—522no—
673C2×C4—1044no—
674C2×C4—1044no—
675C2×C4#8825412yes—
676C2×C4#8825412yes—
677C2×C4C22×C22⋊D1312yes—
678C2×C4C22×C22⋊D1312yes—
679C2×C4C22×C22⋊D1312yes—
680C2×C4C22×C22⋊D1312yes—
681C2×C4C22×C22⋊D1312yes—
682C2×C4C22×C22⋊D1311yescharacteristic
683C2×C4C24×D1311yescharacteristic
684C8—262no—
685C8—262no—
686C8—262no—
687C8—262no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—522no—
693C22—522no—
694C22—522no—
695C22—522no—
696C22—522no—
697C22—522no—
698C22—1044no—
699C22—1044no—
700C22#1171952112yes—
701C22#1171954012yes—
702C22#1171954212yes—
703C22C23×C22⋊D1311yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—522no—
714C4—522no—
715C4#1171952112yes—
716C4C2×#8825411yescharacteristic
717C4C2×#8825411yescharacteristic
718C2—42no—
719C2—1042no—
720C2—1042no—
721C2#1312608914yesdirect product factor
722C2C2×#1171952111yescharacteristic
723C2C2×#1171954011yescharacteristic
724C2C2×#1171954211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#544C2
socleC23×C13C22×D4
prime radicalC2×#11719240C2
hypercenterC2×#544D13
hypocenterC13C2×#3241
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #13126089C2direct (N × H)
3. C2×#11718741C2semidirect
4. C2×#11718725C2semidirect
5. C2×#11718728C2semidirect
6. C2×#11718749C2semidirect
7. C2×#11718629C2semidirect
8. C2×#11718664C2semidirect
9. C2×#11718664C2semidirect
10. C2×#11718628C2semidirect
11. C2×#11718727C2semidirect
12. C2×#11718727C2semidirect
13. C2×#11718745C2semidirect
14. C2×#11718748C2semidirect
15. C2×#11718661C2semidirect
16. C2×C13×#544C2semidirect
18. C13×#544C22semidirect
44. #11718749C22semidirect
45. #11718748C22semidirect
46. #11718745C22semidirect
47. #11718741C22semidirect
48. #11718728C22semidirect
49. #11718727C22semidirect
50. #11718727C22semidirect
51. #11718725C22semidirect
52. #11718664C22semidirect
53. #11718664C22semidirect
54. #11718661C22semidirect
55. #11718629C22semidirect
56. #11718628C22semidirect
265. C2×#544D13semidirect
343. #544C2×D13semidirect
532. C2×C13#3241semidirect
626. C13C2×#3241semidirect
721. C2#13126089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192402
#131260892
C2×#117187412
C2×#117187252
C2×#117187282
C2×#117187492
C2×#117186292
C2×#117186642
C2×#117186282
C2×#117187272
C2×#117187452
C2×#117187482
C2×#117186612
C2×C13×#5442
C2×#324113