Finite Group Databasebeta

← C2×#13127391 #16741592

Subgroups — C2×#13127391 #16741592

Order 3328.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719323C211yesmaximal, characteristic
2C2×#11719344C211yesmaximal, characteristic, complemented
3#13127391C2116yesmaximal, direct product factor
4C2×#11718539C211yesmaximal, characteristic, complemented
5C2×#11718438C211yesmaximal, characteristic, complemented
6C2×#11718475C211yesmaximal, characteristic, complemented
7C2×#11718696C211yesmaximal, characteristic, complemented
8C2×#11718704C211yesmaximal, characteristic, complemented
9C2×#11718460C211yesmaximal, characteristic, complemented
10C2×#11718427C211yesmaximal, characteristic, complemented
11C2×#11718835C211yesmaximal, characteristic, complemented
12C2×SD16×Dic13C211yesmaximal, characteristic, complemented
13C2×#11718789C211yesmaximal, characteristic, complemented
14C2×#11718782C211yesmaximal, characteristic, complemented
15C2×#11718542C211yesmaximal, characteristic, complemented
16C2×C13×#468C211yesmaximal, characteristic, complemented
17C22×C13×SD16C2211yescharacteristic
18C22×C13×M16C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×#121C2211yescharacteristic
21C2×#88200C2211yescharacteristic
22C2×Q8×Dic13C2211yescharacteristic
23C2×#88193—21no—
24C2×#88192C2211yescharacteristic
25C2×D4×Dic13—21no—
26C2×D4×Dic13C2211yescharacteristic
27C2×C4×C22⋊D13C2211yescharacteristic
28C2×#88180C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×#6094C2211yescharacteristic
31#11719344—24no—
32#11719344C2218yescomplemented
33#11719323—24no—
34#11719323C2218yes—
35C2×#88146—21no—
36C2×#88146C2211yescharacteristic
37C2×C4⋊C4×D13C2211yescharacteristic
38C2×#88144C2211yescharacteristic
39C2×#88144C2211yescharacteristic
40C2×#88143—21no—
41C2×#88140—21no—
42C2×#88137—21no—
43C2×#88133—21no—
44C2×#88133—21no—
45C13×#468C2218yescomplemented
46C2×C13×#107C2211yescharacteristic
47C2×C13×#103C2211yescharacteristic
48C2×C13×#102C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88075C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×#88072C2211yescharacteristic
53C2×C22⋊#1055C2211yescharacteristic
54#11718835C2218yescomplemented
55SD16×Dic13C2218yescomplemented
56#11718789C2218yescomplemented
57#11718782C2218yescomplemented
58C2×#88060C2211yescharacteristic
59C2×#88058C2211yescharacteristic
60C2×#88058C2211yescharacteristic
61C2×#88057C2211yescharacteristic
62C2×#88057C2211yescharacteristic
63C2×#88054C2211yescharacteristic
64C2×C8×Dic13C2211yescharacteristic
65#11718704C2218yescomplemented
66#11718696C2218yescomplemented
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71#11718542C2218yescomplemented
72#11718539C2218yescomplemented
73#11718475C2218yescomplemented
74#11718460C2218yescomplemented
75#11718438C2218yescomplemented
76#11718427C2218yescomplemented
77C22×Q8×C13C2311yescharacteristic
78C22×D4×C13—21no—
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13—21no—
82C22×C22⋊D13D411yescharacteristic
83C23×Dic13—21no—
84C23×Dic13—21no—
85C22×C4×D13—21no—
86C22×C4×D13C2311yescharacteristic
87C2×C13×SD16—24no—
88C2×C13×SD16C2314yes—
89C2×C13×M16—24no—
90C2×C13×M16C2314yes—
91C22×C8×C13C2311yescharacteristic
92C22×C8×C13C2311yescharacteristic
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8C2314yes—
95C13×#121—22no—
96C13×#121C2314yes—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C4⋊C4C2311yescharacteristic
100C2×C13×C22⋊C4—21no—
101C2×C13×C22⋊C4—21no—
102C2×C22⋊Dic13—21no—
103C2×C22⋊Dic13—21no—
104C2×C22⋊Dic13—21no—
105C2×C22⋊Dic13D411yescharacteristic
106#88200—22no—
107#88200C2314yes—
108Q8×Dic13—22no—
109Q8×Dic13C2314yes—
110#88193—28no—
111#88192—22no—
112#88192C2314yes—
113D4×Dic13—28no—
114D4×Dic13—22no—
115D4×Dic13C2314yes—
116C4×C22⋊D13D414yes—
117C4×C22⋊D13C2314yes—
118C2×#6103—21no—
119C2×#6103—21no—
120C2×#6103D411yescharacteristic
121#88180—22no—
122#88180C2314yes—
123C2×C4⋊Dic13—21no—
124C2×C4⋊Dic13—22no—
125C2×C4⋊Dic13—21no—
126C2×C4⋊Dic13—21no—
127C2×C4⋊Dic13—21no—
128C2×C4⋊Dic13C2311yescharacteristic
129C2×C4⋊Dic13C2311yescharacteristic
130C2×C4⋊Dic13C2311yescharacteristic
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2314yes—
133C2×#6101—21no—
134C2×#6101—21no—
135C2×#6101—21no—
136C2×#6101—21no—
137C2×#6101D411yescharacteristic
138C2×C4×Dic13—21no—
139C2×C4×Dic13—21no—
140C2×C4×Dic13—21no—
141C2×C4×Dic13C2311yescharacteristic
142C22×#1055C2311yescharacteristic
143C22×#1055C2311yescharacteristic
144C2×#6094—24no—
145C2×#6094C2314yes—
146#88146—22no—
147#88146—28no—
148#88146C2314yes—
149C4⋊C4×D13—22no—
150C4⋊C4×D13C2314yes—
151#88144—22no—
152#88144—22no—
153#88144C2314yes—
154#88144C2314yes—
155#88143—28no—
156#88140—28no—
157#88137—28no—
158#88133—28no—
159#88133—28no—
160C13×#107C2314yes—
161C13×#103C2314yes—
162C13×#102C2314yes—
163#88075C2314yes—
164#88075C2314yes—
165#88072C2314yes—
166#88072C2314yes—
167C22⋊#1055C2314yes—
168#88060C2314yes—
169#88058C2314yes—
170#88058C2314yes—
171#88057C2314yes—
172#88057C2314yes—
173#88054C2314yes—
174C8×Dic13C2314yes—
175#88048C2314yes—
176#88048C2314yes—
177#88048C2314yes—
178#88047C2314yes—
179C2×#3351—131nomaximal, Sylow
180C24×C13—21no—
181C24×C13C2×D411yescharacteristic
182C23×D13C2×D411yescharacteristic
183C2×Q8×C13—21no—
184C2×Q8×C13—22no—
185C2×Q8×C13—22no—
186C2×Q8×C13C2412yes—
187C2×D4×C13—24no—
188C2×D4×C13—21no—
189C2×D4×C13—22no—
190C2×D4×C13—22no—
191C2×D4×C13—44no—
192C2×D4×C13C2412yes—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2411yescharacteristic
202C2×C22⋊D13—24no—
203C2×C22⋊D13—42no—
204C2×C22⋊D13—82no—
205C2×C22⋊D13C2×D414yes—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—24no—
211C22×Dic13—24no—
212C22×Dic13—82no—
213C22×Dic13—82no—
214C22×Dic13C2×D411yescharacteristic
215C22×Dic13C2×D411yescharacteristic
216C22×Dic13C2×D411yescharacteristic
217C2×C4×D13—22no—
218C2×C4×D13—22no—
219C2×C4×D13—24no—
220C2×C4×D13—44no—
221C2×C4×D13C2×D412yes—
222C2×C4×D13C2412yes—
223C13×SD16—28no—
224C13×M16—28no—
225C2×C8×C13—22no—
226C2×C8×C13#4114yes—
227C2×C8×C13C2412yes—
228C2×C8×C13C2412yes—
229C13×C4⋊C4—24no—
230C13×C4⋊C4—21no—
231C13×C4⋊C4—21no—
232C13×C4⋊C4C2412yes—
233C13×C4⋊C4C2412yes—
234C13×C22⋊C4—24no—
235C13×C22⋊C4—24no—
236C22⋊Dic13—24no—
237C22⋊Dic13—24no—
238C22⋊Dic13—24no—
239C22⋊Dic13C2×D414yes—
240#6103—24no—
241#6103—24no—
242#6103C2×D414yes—
243C4⋊Dic13—24no—
244C4⋊Dic13—21no—
245C4⋊Dic13—21no—
246C4⋊Dic13—21no—
247C4⋊Dic13—21no—
248C4⋊Dic13—24no—
249C4⋊Dic13—24no—
250C4⋊Dic13—24no—
251C4⋊Dic13C2412yes—
252C4⋊Dic13C2412yes—
253C4⋊Dic13C2412yes—
254C4⋊Dic13C2412yes—
255#6101—24no—
256#6101—24no—
257#6101—24no—
258#6101—24no—
259#6101C2×D414yes—
260C4×Dic13—24no—
261C4×Dic13—24no—
262C4×Dic13—24no—
263C4×Dic13C2×D412yes—
264C4×Dic13C2412yes—
265C2×#1055—22no—
266C2×#1055—22no—
267C2×#1055C2412yes—
268C2×#1055C2412yes—
269#6094—28no—
270C2×#553—131no—
271C2×#552—131no—
272#3351—1316no—
273C2×#499—131no—
274C2×#481—131no—
275C2×#485—131no—
276C2×#482—131no—
277C2×#483—131no—
278C2×#479—131no—
279C2×#478—131no—
280C2×#468—131no—
281C2×#468D1311yescharacteristic, complemented
282C2×C4×SD16—131no—
283C2×#436—131no—
284C2×#428—131no—
285C2×#428—131no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—42no—
291C23×C13—42no—
292C23×C13—42no—
293C23×C13C22×D412yes—
294C23×C13C22×D411yescharacteristic
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13C22×D412yes—
299Q8×C13—22no—
300Q8×C13—22no—
301Q8×C13—42no—
302D4×C13—22no—
303D4×C13—22no—
304D4×C13—48no—
305D4×C13—42no—
306C2×C4×C13—22no—
307C2×C4×C13—24no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
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—44no—
322C22⋊D13—84no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—84no—
335C2×Dic13—84no—
336C2×Dic13C22×D412yes—
337C2×Dic13C22×D412yes—
338C2×Dic13C22×D412yes—
339C4×D13—24no—
340C4×D13—22no—
341C4×D13—22no—
342C4×D13—48no—
343C8×C13—22no—
344C8×C13C2×#4114yes—
345#1055—22no—
346#1055—22no—
347C22×SD16C2×D1311yescharacteristic
348C22×M16—131no—
349C22×M16C2×D1311yescharacteristic
350#553—138no—
351#553—264no—
352#552—138no—
353#552—264no—
354C2×#126—261no—
355C2×#126—261no—
356C2×#125—131no—
357C2×#125—131no—
358C2×#125—261no—
359C2×#123—261no—
360C2×#123—261no—
361C2×C22⋊Q8—131no—
362C2×C22⋊Q8C2×D1311yescharacteristic
363C2×#121—131no—
364C2×#121—261no—
365C2×#121C2×D1311yescharacteristic
366C2×C4×Q8—131no—
367C2×C4×D4—131no—
368C2×C4×D4—131no—
369C2×C4×D4—261no—
370C2×#117—131no—
371C2×#117—131no—
372C2×#117—261no—
373C22×C4⋊C4—131no—
374C22×C4⋊C4—131no—
375#499—138no—
376#485—138no—
377#483—138no—
378#482—138no—
379#481—138no—
380#479—138no—
381#478—138no—
382#468—138no—
383#468C2×D1318yescomplemented
384C4×SD16—138no—
385#436—138no—
386#428—138no—
387#428—138no—
388C2×#107—131no—
389C2×#107—131no—
390C2×#107—131no—
391C2×#107C2×D1311yescharacteristic
392C2×#106—131no—
393C2×#106—131no—
394C2×#106—131no—
395C2×#106—131no—
396C2×#106—131no—
397C2×C4⋊C8—131no—
398C2×#103—131no—
399C2×#103—131no—
400C2×#103C2×D1311yescharacteristic
401C2×#102—131no—
402C2×#102—131no—
403C2×#102C2×D1311yescharacteristic
404C2×C22⋊C8—131no—
405C2×C22⋊C8—131no—
406C2×C4×C8—131no—
407C22×C13—22no—
408C22×C13—22no—
409C22×C13—22no—
410C22×C13—44no—
411C22×C13—42no—
412C22×C13—42no—
413C22×C13—42no—
414C22×C13—84no—
415C22×C13#54712yes—
416C22×C13#57512yes—
417C22×C13#57712yes—
418C22×C13C23×D411yescharacteristic
419C2×D13—22no—
420C2×D13—22no—
421C2×D13—22no—
422C2×D13—44no—
423C4×C13—22no—
424C4×C13—42no—
425C4×C13—42no—
426C4×C13—42no—
427C4×C13#54712yes—
428C4×C13C22×#4111yescharacteristic
429C4×C13C2×2−1+411yescharacteristic
430Dic13—22no—
431Dic13—22no—
432Dic13—22no—
433Dic13—42no—
434Dic13—42no—
435Dic13—42no—
436Dic13—42no—
437C22×Q8C22×D1311yescharacteristic
438C22×D4—21no—
439C22×D4—131no—
440C22×D4—261no—
441C22×D4C22×D1311yescharacteristic
442C23×C4—131no—
443C23×C4—261no—
444C23×C4—261no—
445C23×C4—261no—
446C23×C4C22×D1311yescharacteristic
447C2×SD16—24no—
448C2×SD16C22×D1314yes—
449C2×M16—24no—
450C2×M16—134no—
451C2×M16—264no—
452C2×M16C22×D1314yes—
453C22×C8—131no—
454C22×C8—131no—
455C22×C8C22×D1311yescharacteristic
456C22×C8C22×D1311yescharacteristic
457#126—268no—
458#126—268no—
459#125—134no—
460#125—134no—
461#125—262no—
462#125—262no—
463#125—268no—
464#123—268no—
465#123—268no—
466C22⋊Q8—22no—
467C22⋊Q8—134no—
468C22⋊Q8—262no—
469C22⋊Q8C22×D1314yes—
470#121—22no—
471#121—134no—
472#121—262no—
473#121—268no—
474#121C22×D1314yes—
475C4×Q8—134no—
476C4×Q8—262no—
477C4×D4—134no—
478C4×D4—134no—
479C4×D4—134no—
480C4×D4—262no—
481C4×D4—268no—
482#117—134no—
483#117—134no—
484#117—268no—
485#117—262no—
486#117—262no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—131no—
491C2×C4⋊C4—131no—
492C2×C4⋊C4—134no—
493C2×C4⋊C4—131no—
494C2×C4⋊C4—134no—
495C2×C4⋊C4—262no—
496C2×C4⋊C4—261no—
497C2×C4⋊C4—261no—
498C2×C4⋊C4—261no—
499C2×C4⋊C4—261no—
500C2×C4⋊C4—261no—
501C2×C4⋊C4—261no—
502C2×C4⋊C4—261no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—262no—
505C2×C4⋊C4C22×D1311yescharacteristic
506C2×C4⋊C4C22×D1311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—131no—
510C2×C22⋊C4—131no—
511C2×C22⋊C4—261no—
512C2×C22⋊C4—261no—
513C2×C22⋊C4—261no—
514C2×C22⋊C4—261no—
515C2×C22⋊C4—261no—
516C2×C42—131no—
517C2×C42—261no—
518C2×C42—261no—
519C2×C42—261no—
520#107—134no—
521#107—134no—
522#107—134no—
523#107C22×D1314yes—
524#106—134no—
525#106—134no—
526#106—134no—
527#106—134no—
528#106—134no—
529C4⋊C8—134no—
530#103—134no—
531#103—134no—
532#103C22×D1314yes—
533#102—134no—
534#102—134no—
535#102C22×D1314yes—
536C22⋊C8—134no—
537C22⋊C8—134no—
538C4×C8—134no—
539C2×C13—42no—
540C2×C13—82no—
541C2×C13#335114yescomplemented
542C2×C13C2×#54711yescharacteristic
543C2×C13C2×#57511yescharacteristic
544C2×C13C2×#57711yescharacteristic
545D13—42no—
546C24—21no—
547C24—131no—
548C24D4×D1311yescharacteristic
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8C23×D1312yes—
553C2×D4—24no—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—44no—
558C2×D4—134no—
559C2×D4—264no—
560C2×D4—522no—
561C2×D4—1042no—
562C2×D4C23×D1312yes—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—131no—
569C22×C4—131no—
570C22×C4—131no—
571C22×C4—132no—
572C22×C4—132no—
573C22×C4—264no—
574C22×C4—264no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—264no—
582C22×C4—524no—
583C22×C4—1042no—
584C22×C4—1042no—
585C22×C4D4×D1312yes—
586C22×C4D4×D1311yescharacteristic
587C22×C4C23×D1312yes—
588C22×C4C23×D1311yescharacteristic
589SD16—28no—
590M16—28no—
591M16—268no—
592C2×C8—22no—
593C2×C8—132no—
594C2×C8—132no—
595C2×C8—262no—
596C2×C8—262no—
597C2×C8#612914yes—
598C2×C8C23×D1312yes—
599C2×C8C23×D1312yes—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—134no—
604C4⋊C4—132no—
605C4⋊C4—132no—
606C4⋊C4—132no—
607C4⋊C4—132no—
608C4⋊C4—264no—
609C4⋊C4—264no—
610C4⋊C4—264no—
611C4⋊C4—264no—
612C4⋊C4—264no—
613C4⋊C4—264no—
614C4⋊C4—264no—
615C4⋊C4—261no—
616C4⋊C4—261no—
617C4⋊C4—261no—
618C4⋊C4—264no—
619C4⋊C4—261no—
620C4⋊C4C23×D1312yes—
621C4⋊C4C23×D1312yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—134no—
625C22⋊C4—134no—
626C22⋊C4—264no—
627C22⋊C4—264no—
628C22⋊C4—264no—
629C22⋊C4—264no—
630C22⋊C4—264no—
631C42—132no—
632C42—132no—
633C42—264no—
634C42—264no—
635C42—264no—
636C13C2×#335111yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—132no—
645C23—262no—
646C23—262no—
647C23—262no—
648C23C2×D4×D1312yes—
649C23C2×D4×D1311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—42no—
657D4—524no—
658D4—1044no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—132no—
670C2×C4—132no—
671C2×C4—132no—
672C2×C4—262no—
673C2×C4—262no—
674C2×C4—262no—
675C2×C4—264no—
676C2×C4—262no—
677C2×C4—262no—
678C2×C4—262no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—528no—
683C2×C4—522no—
684C2×C4—522no—
685C2×C4—522no—
686C2×C4—522no—
687C2×C4—1044no—
688C2×C4—1044no—
689C2×C4C2×D4×D1312yes—
690C2×C4C2×D4×D1311yescharacteristic
691C2×C4C2×#612912yes—
692C2×C4#8825712yes—
693C2×C4C24×D1311yescharacteristic
694C8—22no—
695C8—262no—
696C8—262no—
697C8C2×#612914yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—84no—
706C22—262no—
707C22—262no—
708C22—262no—
709C22—524no—
710C22#1171931612yes—
711C22#1171947812yes—
712C22#1171948312yes—
713C22C22×D4×D1311yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—262no—
719C4—262no—
720C4—262no—
721C4—522no—
722C4—522no—
723C4—522no—
724C4—522no—
725C4#1171931612yes—
726C4C22×#612911yescharacteristic
727C4C2×#8825711yescharacteristic
728C2—42no—
729C2—82no—
730C2—522no—
731C2#1312739114yesdirect product factor
732C2C2×#1171931611yescharacteristic
733C2C2×#1171947811yescharacteristic
734C2C2×#1171948311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#468C2
socleC23×C13C22×D4
prime radicalC2×#11719323C2
hypercenterC2×#468D13
hypocenterC13C2×#3351
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#11719344C2semidirect
3. #13127391C2direct (N × H)
4. C2×#11718539C2semidirect
5. C2×#11718438C2semidirect
6. C2×#11718475C2semidirect
7. C2×#11718696C2semidirect
8. C2×#11718704C2semidirect
9. C2×#11718460C2semidirect
10. C2×#11718427C2semidirect
11. C2×#11718835C2semidirect
12. C2×SD16×Dic13C2semidirect
13. C2×#11718789C2semidirect
14. C2×#11718782C2semidirect
15. C2×#11718542C2semidirect
16. C2×C13×#468C2semidirect
32. #11719344C22semidirect
45. C13×#468C22semidirect
54. #11718835C22semidirect
55. SD16×Dic13C22semidirect
56. #11718789C22semidirect
57. #11718782C22semidirect
65. #11718704C22semidirect
66. #11718696C22semidirect
71. #11718542C22semidirect
72. #11718539C22semidirect
73. #11718475C22semidirect
74. #11718460C22semidirect
75. #11718438C22semidirect
76. #11718427C22semidirect
281. C2×#468D13semidirect
383. #468C2×D13semidirect
541. C2×C13#3351semidirect
636. C13C2×#3351semidirect
731. C2#13127391direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193232
C2×#117193442
#131273912
C2×#117185392
C2×#117184382
C2×#117184752
C2×#117186962
C2×#117187042
C2×#117184602
C2×#117184272
C2×#117188352
C2×SD16×Dic132
C2×#117187892
C2×#117187822
C2×#117185422
C2×C13×#4682
C2×#335113