Finite Group Databasebeta

← C2×#13125538 #16732835

Subgroups — C2×#13125538 #16732835

Order 3328.

1998 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×#11719327C211yesmaximal, characteristic, complemented
2C2×#11719305C211yesmaximal, characteristic
3#13125538C2116yesmaximal, direct product factor
4C2×#11718517C211yesmaximal, characteristic, complemented
5C2×#11718828C211yesmaximal, characteristic, complemented
6C2×#11718458C211yesmaximal, characteristic, complemented
7C2×#11718426C211yesmaximal, characteristic, complemented
8C2×#11718777C211yesmaximal, characteristic, complemented
9C2×#11718712C211yesmaximal, characteristic, complemented
10C2×#11718702C211yesmaximal, characteristic
11C2×#11718514C211yesmaximal, characteristic, complemented
12C2×#11718450C211yesmaximal, characteristic, complemented
13C2×#11718825C211yesmaximal, characteristic, complemented
14C2×#11718418C211yesmaximal, characteristic, complemented
15C22×#88055C211yesmaximal, characteristic, complemented
16C2×C13×#465C211yesmaximal, characteristic
17C22×C13×SD16C2211yescharacteristic
18C23×C8×C13C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×#121C2211yescharacteristic
21C2×Q8×Dic13C2211yescharacteristic
22C2×#88198C2211yescharacteristic
23C22×#6107C2211yescharacteristic
24C2×#88190C2211yescharacteristic
25C2×#88189—21no—
26C2×D4×Dic13—21no—
27C2×D4×Dic13C2211yescharacteristic
28C22×#6105C2211yescharacteristic
29C2×#88178C2211yescharacteristic
30C2×#88178C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C23×#1055C2211yescharacteristic
33C22×Dic52C2211yescharacteristic
34#11719327—24no—
35#11719327C2218yescomplemented
36#11719305—24no—
37#11719305C2218yes—
38C2×#88144C2211yescharacteristic
39C2×#88143—21no—
40C2×#88142C2211yescharacteristic
41C2×#88141—21no—
42C2×#88141C2211yescharacteristic
43C2×#88141C2211yescharacteristic
44C2×#88133—21no—
45C2×#88132—21no—
46C2×#88131—21no—
47C2×#88131—21no—
48C13×#465C2218yes—
49C2×C13×#106C2211yescharacteristic
50C2×C13×#103C2211yescharacteristic
51C2×C13×#102C2211yescharacteristic
52C2×#88075C2211yescharacteristic
53C2×#88072C2211yescharacteristic
54#11718828C2218yescomplemented
55#11718825C2218yescomplemented
56#11718777C2218yescomplemented
57C2×#88058C2211yescharacteristic
58C2×#88056C2211yescharacteristic
59C2×#88056C2211yescharacteristic
60C2×#88055C2211yescharacteristic
61C2×#88055C2211yescharacteristic
62C2×#88055C2211yescharacteristic
63C2×#88055C2211yescharacteristic
64C2×#88055C2218yescomplemented
65#11718712C2218yescomplemented
66#11718702C2218yes—
67C2×#88050C2211yescharacteristic
68C2×#88050C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71#11718517C2218yescomplemented
72#11718514C2218yescomplemented
73#11718458C2218yescomplemented
74#11718450C2218yescomplemented
75#11718426C2218yescomplemented
76#11718418C2218yescomplemented
77C22×Q8×C13C2311yescharacteristic
78C22×D4×C13—21no—
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×Dic13—21no—
82C23×Dic13D411yescharacteristic
83C23×Dic13D411yescharacteristic
84C22×Dic26—21no—
85C22×Dic26C2311yescharacteristic
86C22×Dic26C2311yescharacteristic
87C2×C13×SD16—24no—
88C2×C13×SD16C2314yes—
89C22×C8×C13—24no—
90C22×C8×C13C2311yescharacteristic
91C22×C8×C13C2314yes—
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⋊Dic13—21no—
106C2×C22⋊Dic13—21no—
107Q8×Dic13—22no—
108Q8×Dic13C2314yes—
109#88198—22no—
110#88198C2314yes—
111C2×#6107—24no—
112C2×#6107C2314yes—
113#88190—22no—
114#88190C2314yes—
115#88189—28no—
116D4×Dic13—28no—
117D4×Dic13—22no—
118D4×Dic13C2314yes—
119C2×#6105—24no—
120C2×#6105C2314yes—
121C2×C4⋊Dic13—21no—
122C2×C4⋊Dic13—21no—
123C2×C4⋊Dic13C2311yescharacteristic
124C2×C4⋊Dic13C2311yescharacteristic
125#88178—22no—
126#88178—22no—
127#88178C2314yes—
128#88178C2314yes—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×#6101—21no—
132C2×#6101—21no—
133C2×#6101—21no—
134C2×#6101—21no—
135C2×#6101—21no—
136C2×#6101—21no—
137C2×C4×Dic13—21no—
138C2×C4×Dic13—21no—
139C2×C4×Dic13—21no—
140C2×C4×Dic13D411yescharacteristic
141C2×C4×Dic13D411yescharacteristic
142C2×C4×Dic13D414yes—
143C2×C4×Dic13C2311yescharacteristic
144C2×C4×Dic13C2311yescharacteristic
145C2×C4×Dic13C2314yes—
146C22×#1055—24no—
147C22×#1055C2314yes—
148C22×#1055C2311yescharacteristic
149C22×#1055C2311yescharacteristic
150C2×Dic52—24no—
151C2×Dic52C2314yes—
152#88144—22no—
153#88144C2314yes—
154#88143—28no—
155#88142—22no—
156#88142C2314yes—
157#88141—28no—
158#88141—22no—
159#88141—22no—
160#88141C2314yes—
161#88141C2314yes—
162#88133—28no—
163#88132—28no—
164#88131—28no—
165#88131—28no—
166C13×#106C2314yes—
167C13×#103C2314yes—
168C13×#102C2314yes—
169#88075C2314yes—
170#88072C2314yes—
171#88058C2314yes—
172#88056C2314yes—
173#88056C2314yes—
174#88055C2314yes—
175#88055C2314yes—
176#88055C2314yes—
177#88055C2314yes—
178#88050C2314yes—
179#88050C2314yes—
180#88048C2314yes—
181#88047C2314yes—
182C2×#3181—131nomaximal, Sylow
183C24×C13—21no—
184C24×C13C2×D411yescharacteristic
185C2×Q8×C13—21no—
186C2×Q8×C13—22no—
187C2×Q8×C13—22no—
188C2×Q8×C13C2412yes—
189C2×D4×C13—24no—
190C2×D4×C13—21no—
191C2×D4×C13—22no—
192C2×D4×C13—22no—
193C2×D4×C13—44no—
194C2×D4×C13C2412yes—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2411yescharacteristic
204C22×Dic13—24no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—24no—
210C22×Dic13—42no—
211C22×Dic13—44no—
212C22×Dic13C2×D414yes—
213C22×Dic13C2×D411yescharacteristic
214C22×Dic13C2×D411yescharacteristic
215C22×Dic13C2×D411yescharacteristic
216C22×Dic13C2×D411yescharacteristic
217C22×Dic13C2×D414yes—
218C2×Dic26—22no—
219C2×Dic26—22no—
220C2×Dic26—22no—
221C2×Dic26—22no—
222C2×Dic26—21no—
223C2×Dic26—21no—
224C2×Dic26—24no—
225C2×Dic26—44no—
226C2×Dic26C2412yes—
227C2×Dic26C2412yes—
228C13×SD16—28no—
229C2×C8×C13—22no—
230C2×C8×C13—28no—
231C2×C8×C13#4114yes—
232C2×C8×C13C2412yes—
233C2×C8×C13C2412yes—
234C13×C4⋊C4—21no—
235C13×C4⋊C4—24no—
236C13×C4⋊C4—21no—
237C13×C4⋊C4C2412yes—
238C13×C4⋊C4C2412yes—
239C13×C22⋊C4—24no—
240C13×C22⋊C4—24no—
241C22⋊Dic13—24no—
242C22⋊Dic13—24no—
243C22⋊Dic13—24no—
244C22⋊Dic13—24no—
245C22⋊Dic13—24no—
246#6107—28no—
247#6105—28no—
248C4⋊Dic13—21no—
249C4⋊Dic13—21no—
250C4⋊Dic13—24no—
251C4⋊Dic13—24no—
252C4⋊Dic13C2412yes—
253C4⋊Dic13C2412yes—
254#6101—24no—
255#6101—24no—
256#6101—24no—
257#6101—24no—
258#6101—24no—
259#6101—24no—
260#6101—24no—
261#6101—24no—
262C4×Dic13—24no—
263C4×Dic13—24no—
264C4×Dic13—24no—
265C4×Dic13C2×D414yes—
266C4×Dic13C2×D414yes—
267C4×Dic13C2×D412yes—
268C4×Dic13C2×D412yes—
269C4×Dic13C2412yes—
270C4×Dic13C2412yes—
271C2×#1055—22no—
272C2×#1055—28no—
273C2×#1055#4114yes—
274C2×#1055C2412yes—
275C2×#1055C2412yes—
276Dic52—28no—
277C2×#533—131no—
278C2×#529—131no—
279#3181—1316no—
280C2×#501—131no—
281C2×#497—131no—
282C2×#491—131no—
283C2×#489—131no—
284C2×#467—131no—
285C2×#467—131no—
286C2×#465—131no—
287C2×#465D1311yescharacteristic
288C2×#441—131no—
289C2×#441—131no—
290C2×#440—131no—
291C2×#440—131no—
292C22×#97—131no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—42no—
297C23×C13—42no—
298C23×C13—42no—
299C23×C13#13714yes—
300C23×C13C22×D412yes—
301C23×C13C22×D411yescharacteristic
302Q8×C13—22no—
303Q8×C13—22no—
304Q8×C13—42no—
305D4×C13—22no—
306D4×C13—22no—
307D4×C13—48no—
308D4×C13—42no—
309C2×C4×C13—22no—
310C2×C4×C13—24no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13C22×D412yes—
320C2×C4×C13C22×D411yescharacteristic
321C2×C4×C13C2×#4112yes—
322C2×C4×C13C2×#4112yes—
323C2×C4×C13C2511yescharacteristic
324C2×Dic13—28no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—44no—
334C2×Dic13—48no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13C22×D412yes—
340C2×Dic13C22×D412yes—
341C2×Dic13C22×D412yes—
342C2×Dic13C22×D412yes—
343Dic26—22no—
344Dic26—22no—
345Dic26—22no—
346Dic26—22no—
347Dic26—48no—
348Dic26—42no—
349Dic26—42no—
350C8×C13—22no—
351C8×C13C2×#4114yes—
352#1055—22no—
353#1055C2×#4114yes—
354C22×Q16—131no—
355C22×Q16—131no—
356C22×SD16—131no—
357C22×SD16C2×D1311yescharacteristic
358C23×C8—131no—
359C23×C8C2×D1311yescharacteristic
360#533—138no—
361#533—264no—
362C2×C4⋊Q8—131no—
363C2×C4⋊Q8—131no—
364#529—138no—
365#529—264no—
366C2×#126—261no—
367C2×#125—131no—
368C2×#125—261no—
369C2×#124—131no—
370C2×#123—261no—
371C2×C22⋊Q8—131no—
372C2×C22⋊Q8—131no—
373C2×C22⋊Q8—261no—
374C2×C22⋊Q8C2×D1311yescharacteristic
375C2×#121C2×D1311yescharacteristic
376C2×C4×Q8—131no—
377C2×C4×Q8—131no—
378C2×C4×Q8—131no—
379C2×C4×Q8—261no—
380C2×C4×D4—131no—
381C2×C4×D4—261no—
382C2×#117—261no—
383C2×#117—261no—
384C22×C42—131no—
385#501—138no—
386#497—138no—
387#491—138no—
388#489—138no—
389#467—138no—
390#467—138no—
391#465—138no—
392#465C2×D1318yes—
393#441—138no—
394#441—138no—
395#440—138no—
396#440—138no—
397C2×#107—131no—
398C2×#107—131no—
399C2×#106—131no—
400C2×#106C2×D1311yescharacteristic
401C2×#103—131no—
402C2×#103—131no—
403C2×#103—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103C2×D1311yescharacteristic
407C2×#102—131no—
408C2×#102C2×D1311yescharacteristic
409C2×#97—131no—
410C2×#97—131no—
411C2×#97—131no—
412C2×#97—131no—
413C2×#97—138no—
414C22×C13—28no—
415C22×C13—22no—
416C22×C13—22no—
417C22×C13—42no—
418C22×C13—42no—
419C22×C13—42no—
420C22×C13—84no—
421C22×C13#53212yes—
422C22×C13C2×#13714yes—
423C22×C13C2×#13712yes—
424C22×C13#57512yes—
425C22×C13C23×D411yescharacteristic
426C4×C13—22no—
427C4×C13—42no—
428C4×C13—42no—
429C4×C13—42no—
430C4×C13#53212yes—
431C4×C13C22×#4111yescharacteristic
432C4×C13C22×#4111yescharacteristic
433Dic13—22no—
434Dic13—22no—
435Dic13—22no—
436Dic13—22no—
437Dic13—42no—
438Dic13—42no—
439Dic13—42no—
440Dic13—42no—
441C22×Q8—131no—
442C22×Q8—131no—
443C22×Q8—261no—
444C22×Q8C22×D1311yescharacteristic
445C22×D4—21no—
446C22×D4C22×D1311yescharacteristic
447C23×C4—131no—
448C23×C4—131no—
449C23×C4—261no—
450C23×C4C22×D1311yescharacteristic
451C2×Q16—134no—
452C2×Q16—134no—
453C2×Q16—264no—
454C2×Q16—264no—
455C2×SD16—24no—
456C2×SD16—134no—
457C2×SD16—264no—
458C2×SD16C22×D1314yes—
459C22×C8—24no—
460C22×C8—131no—
461C22×C8—131no—
462C22×C8—134no—
463C22×C8—264no—
464C22×C8C22×D1311yescharacteristic
465C22×C8C22×D1314yes—
466C22×C8C22×D1311yescharacteristic
467C4⋊Q8—134no—
468C4⋊Q8—134no—
469C4⋊Q8—262no—
470C4⋊Q8—262no—
471#126—268no—
472#125—134no—
473#125—262no—
474#125—268no—
475#124—134no—
476#124—262no—
477#123—268no—
478C22⋊Q8—22no—
479C22⋊Q8—134no—
480C22⋊Q8—134no—
481C22⋊Q8—268no—
482C22⋊Q8—262no—
483C22⋊Q8—262no—
484C22⋊Q8C22×D1314yes—
485#121—22no—
486#121C22×D1314yes—
487C4×Q8—134no—
488C4×Q8—134no—
489C4×Q8—134no—
490C4×Q8—262no—
491C4×Q8—262no—
492C4×Q8—268no—
493C4×Q8—262no—
494C4×D4—134no—
495C4×D4—262no—
496C4×D4—268no—
497#117—268no—
498#117—268no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—131no—
501C2×C4⋊C4—131no—
502C2×C4⋊C4—261no—
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⋊C4—261no—
510C2×C4⋊C4—261no—
511C2×C4⋊C4—261no—
512C2×C4⋊C4C22×D1311yescharacteristic
513C2×C4⋊C4C22×D1311yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—261no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C42—131no—
522C2×C42—131no—
523C2×C42—134no—
524C2×C42—131no—
525C2×C42—131no—
526C2×C42—134no—
527C2×C42—261no—
528C2×C42—261no—
529C2×C42—261no—
530#107—134no—
531#107—134no—
532#106—134no—
533#106C22×D1314yes—
534#103—134no—
535#103—134no—
536#103—134no—
537#103—134no—
538#103—134no—
539#103C22×D1314yes—
540#102—134no—
541#102C22×D1314yes—
542#97—134no—
543#97—134no—
544#97—134no—
545#97—134no—
546C2×C13—24no—
547C2×C13—82no—
548C2×C13#318114yescomplemented
549C2×C13C2×#53211yescharacteristic
550C2×C13C22×#13711yescharacteristic
551C2×C13C2×#57511yescharacteristic
552C24—21no—
553C24D4×D1311yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—132no—
558C2×Q8—132no—
559C2×Q8—264no—
560C2×Q8—261no—
561C2×Q8—261no—
562C2×Q8—262no—
563C2×Q8—262no—
564C2×Q8—262no—
565C2×Q8—262no—
566C2×Q8—524no—
567C2×Q8C23×D1312yes—
568C2×D4—24no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—44no—
573C2×D4C23×D1312yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—134no—
580C22×C4—131no—
581C22×C4—131no—
582C22×C4—131no—
583C22×C4—131no—
584C22×C4—134no—
585C22×C4—264no—
586C22×C4—264no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—522no—
592C22×C4—524no—
593C22×C4D4×D1312yes—
594C22×C4D4×D1311yescharacteristic
595C22×C4C23×D1312yes—
596C22×C4C23×D1311yescharacteristic
597Q16—268no—
598Q16—268no—
599SD16—28no—
600SD16—268no—
601C2×C8—22no—
602C2×C8—28no—
603C2×C8—134no—
604C2×C8—132no—
605C2×C8—132no—
606C2×C8—268no—
607C2×C8—262no—
608C2×C8#612914yes—
609C2×C8C23×D1312yes—
610C2×C8C23×D1312yes—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—132no—
615C4⋊C4—132no—
616C4⋊C4—264no—
617C4⋊C4—264no—
618C4⋊C4—264no—
619C4⋊C4—264no—
620C4⋊C4—264no—
621C4⋊C4—264no—
622C4⋊C4—264no—
623C4⋊C4—264no—
624C4⋊C4—261no—
625C4⋊C4—261no—
626C4⋊C4—264no—
627C4⋊C4—264no—
628C4⋊C4C23×D1312yes—
629C4⋊C4C23×D1312yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—264no—
633C22⋊C4—264no—
634C22⋊C4—264no—
635C22⋊C4—264no—
636C22⋊C4—264no—
637C42—134no—
638C42—132no—
639C42—134no—
640C42—132no—
641C42—132no—
642C42—132no—
643C42—264no—
644C42—264no—
645C42—264no—
646C13C2×#318111yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23#8816914yes—
654C23C2×D4×D1312yes—
655C23C2×D4×D1311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—262no—
660Q8—262no—
661Q8—262no—
662Q8—262no—
663Q8—528no—
664Q8—522no—
665Q8—522no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—132no—
681C2×C4—132no—
682C2×C4—132no—
683C2×C4—132no—
684C2×C4—268no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—524no—
694C2×C4—528no—
695C2×C4—522no—
696C2×C4—522no—
697C2×C4—522no—
698C2×C4—522no—
699C2×C4C2×D4×D1312yes—
700C2×C4C2×D4×D1311yescharacteristic
701C2×C4C2×#612912yes—
702C2×C4#41×D1312yes—
703C2×C4C24×D1311yescharacteristic
704C8—22no—
705C8—134no—
706C8—262no—
707C8C2×#612914yes—
708C22—22no—
709C22—28no—
710C22—22no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—84no—
715C22#1171930112yes—
716C22C2×#8816914yes—
717C22C2×#8816912yes—
718C22#1171947312yes—
719C22C22×D4×D1311yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—262no—
725C4—262no—
726C4—262no—
727C4—262no—
728C4—522no—
729C4—522no—
730C4—522no—
731C4—522no—
732C4#1171930112yes—
733C4C22×#612911yescharacteristic
734C4C2×#41×D1311yescharacteristic
735C2—24no—
736C2—82no—
737C2#1312553814yesdirect product factor
738C2C2×#1171930111yescharacteristic
739C2C22×#8816911yescharacteristic
740C2C2×#1171947311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#465C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenterC2×#465D13
hypocenterC13C2×#3181
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#11719327C2semidirect
3. #13125538C2direct (N × H)
4. C2×#11718517C2semidirect
5. C2×#11718828C2semidirect
6. C2×#11718458C2semidirect
7. C2×#11718426C2semidirect
8. C2×#11718777C2semidirect
9. C2×#11718712C2semidirect
11. C2×#11718514C2semidirect
12. C2×#11718450C2semidirect
13. C2×#11718825C2semidirect
14. C2×#11718418C2semidirect
15. C22×#88055C2semidirect
35. #11719327C22semidirect
54. #11718828C22semidirect
55. #11718825C22semidirect
56. #11718777C22semidirect
64. C2×#88055C22semidirect
65. #11718712C22semidirect
71. #11718517C22semidirect
72. #11718514C22semidirect
73. #11718458C22semidirect
74. #11718450C22semidirect
75. #11718426C22semidirect
76. #11718418C22semidirect
548. C2×C13#3181semidirect
646. C13C2×#3181semidirect
737. C2#13125538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193272
C2×#117193052
#131255382
C2×#117185172
C2×#117188282
C2×#117184582
C2×#117184262
C2×#117187772
C2×#117187122
C2×#117187022
C2×#117185142
C2×#117184502
C2×#117188252
C2×#117184182
C22×#880552
C2×C13×#4652
C2×#318113