Finite Group Databasebeta

← #15883300

Subgroups — #15883300

Order 3328.

1134 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×#11718825C211yesmaximal, characteristic, complemented
2C2×#11718893C211yesmaximal, characteristic
3#13117845C211yesmaximal, characteristic, complemented
4#13117666C211yesmaximal, characteristic
5#13115698C211yesmaximal, characteristic, complemented
6#13115528C211yesmaximal, characteristic, complemented
7#13115479C211yesmaximal, characteristic, complemented
8#13115270C211yesmaximal, characteristic, complemented
9#13115179C211yesmaximal, characteristic, complemented
10#13115172C211yesmaximal, characteristic, complemented
11#13115085C211yesmaximal, characteristic, complemented
12#13115026C211yesmaximal, characteristic, complemented
13#102×Dic13C211yesmaximal, characteristic, complemented
14#13114622C211yesmaximal, characteristic, complemented
15C2×C13×#452C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C22×C13×Q16C2211yescharacteristic
18C22×C13×SD16C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×Q8×Dic13C2211yescharacteristic
21C2×D4×Dic13C2211yescharacteristic
22C2×D4×Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C13×#452C418yescomplemented
26C2×C13×#103C2211yescharacteristic
27C2×C13×#102C2211yescharacteristic
28C2×C13×C22⋊C8C2211yescharacteristic
29#11718893—24no—
30#11718891C2211yescharacteristic
31#11718891C2211yescharacteristic
32#11718891C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37#11718881—21no—
38#11718881—21no—
39C2×#88072C2211yescharacteristic
40C2×#88072C2211yescharacteristic
41#11718873C2211yescharacteristic
42#11718872—21no—
43C4×C22⋊Dic13C2211yescharacteristic
44C2×#88071—21no—
45#11718825—24no—
46C2×#88058C2211yescharacteristic
47C2×#88058C2211yescharacteristic
48C2×#88055C2211yescharacteristic
49C2×C8×Dic13C2211yescharacteristic
50#11718646—21no—
51#11718646C2211yescharacteristic
52#11718642—21no—
53C4⋊C4×Dic13C2211yescharacteristic
54#11718611—21no—
55C22⋊C4×Dic13—21no—
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C2×C13×#41—22no—
63C2×C13×#41—22no—
64C2×C13×#41—22no—
65C2×C13×#41—41no—
66C2×C13×#41—41no—
67C2×C13×#41C2×C414yes—
68C22×Q8×C13C2311yescharacteristic
69C22×Q8×C13C2311yescharacteristic
70C22×D4×C13—21no—
71C22×D4×C13C2311yescharacteristic
72C23×C4×C13—21no—
73C23×C4×C13C2311yescharacteristic
74C23×Dic13—21no—
75C23×Dic13—21no—
76C23×Dic13—21no—
77C2×C13×Q16—41no—
78C2×C13×Q16—41no—
79C2×C13×Q16C2×C414yescomplemented
80C2×C13×SD16—22no—
81C2×C13×SD16—22no—
82C2×C13×SD16C2×C414yescomplemented
83C22×C8×C13C2311yescharacteristic
84C22×C8×C13C2311yescharacteristic
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8C2×C414yescomplemented
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C22⋊C4—21no—
90C2×C22⋊Dic13—21no—
91C2×C22⋊Dic13—21no—
92C2×C22⋊Dic13—21no—
93C2×C22⋊Dic13D411yescharacteristic
94C2×C22⋊Dic13D411yescharacteristic
95Q8×Dic13—22no—
96Q8×Dic13—41no—
97D4×Dic13—22no—
98D4×Dic13—22no—
99D4×Dic13—41no—
100D4×Dic13—41no—
101C2×C4⋊Dic13—22no—
102C2×C4⋊Dic13—21no—
103C2×C4⋊Dic13—21no—
104C2×C4⋊Dic13—21no—
105C2×C4⋊Dic13—41no—
106C2×C4⋊Dic13C2311yescharacteristic
107C2×C4⋊Dic13C2311yescharacteristic
108C2×C4⋊Dic13C2311yescharacteristic
109C2×C4⋊Dic13C2311yescharacteristic
110C2×C4×Dic13—21no—
111C2×C4×Dic13—21no—
112C2×C4×Dic13C2311yescharacteristic
113C2×C4×Dic13C2311yescharacteristic
114C2×#6099—22no—
115C2×#6099—22no—
116C2×#6099—41no—
117C22×#1055C2311yescharacteristic
118C22×#1055C2311yescharacteristic
119C13×#103C2×C414yescomplemented
120C13×#102C2×C414yescomplemented
121C13×C22⋊C8C2×C414yescomplemented
122#88075—22no—
123#88075—22no—
124#88075—22no—
125#88075—41no—
126#88072—22no—
127#88072D414yes—
128#88071—21no—
129#88071—21no—
130#88071—21no—
131#88071—21no—
132#88071—21no—
133#88071—21no—
134#88071—21no—
135#88071—21no—
136#88071—21no—
137#88071D411yescharacteristic
138#88071D411yescharacteristic
139#88058—22no—
140#88058—41no—
141#88055—22no—
142C8×Dic13—41no—
143#22862—131nomaximal, Sylow
144C24×C13—21no—
145C24×C13C2×D411yescharacteristic
146C13×#41—28no—
147C13×#41—44no—
148C13×#41—44no—
149C13×#41—44no—
150C2×Q8×C13—21no—
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13—21no—
158C2×Q8×C13—21no—
159C2×Q8×C13—21no—
160C2×Q8×C13C22×C412yes—
161C2×Q8×C13C22×C412yes—
162C2×D4×C13—24no—
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13—21no—
166C2×D4×C13—42no—
167C2×D4×C13—42no—
168C2×D4×C13C22×C412yes—
169C2×D4×C13C2×D412yes—
170C2×D4×C13#4112yes—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—24no—
179C22×C4×C13—42no—
180C22×C4×C13—42no—
181C22×C4×C13C22×C412yes—
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13#4112yes—
184C22×C4×C13C2411yescharacteristic
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—42no—
190C22×Dic13—42no—
191C22×Dic13—42no—
192C22×Dic13—42no—
193C22×Dic13—42no—
194C22×Dic13—42no—
195C22×Dic13—81no—
196C22×Dic13—81no—
197C22×Dic13—81no—
198C22×Dic13C2×D411yescharacteristic
199C22×Dic13C2×D411yescharacteristic
200C22×Dic13C2×D411yescharacteristic
201C22×Dic13C2×D411yescharacteristic
202C13×Q16—44no—
203C13×SD16—28no—
204C2×C8×C13—21no—
205C2×C8×C13—21no—
206C2×C8×C13—21no—
207C2×C8×C13—21no—
208C2×C8×C13C22×C412yes—
209C2×C8×C13C22×C412yes—
210C13×C4⋊C4—24no—
211C13×C4⋊C4—21no—
212C13×C4⋊C4C22×C412yes—
213C13×C22⋊C4—24no—
214C22⋊Dic13—22no—
215C22⋊Dic13—41no—
216C22⋊Dic13—42no—
217C22⋊Dic13—42no—
218C22⋊Dic13—81no—
219C4⋊Dic13—21no—
220C4⋊Dic13—21no—
221C4⋊Dic13—21no—
222C4⋊Dic13—21no—
223C4⋊Dic13—21no—
224C4⋊Dic13—21no—
225C4⋊Dic13—21no—
226C4⋊Dic13—42no—
227C4⋊Dic13—42no—
228C4⋊Dic13—81no—
229C4⋊Dic13C2×D412yes—
230C4×Dic13—21no—
231C4×Dic13—21no—
232C4×Dic13—21no—
233C4×Dic13—21no—
234C4×Dic13—42no—
235C4×Dic13—81no—
236#6099—44no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055C2×D412yes—
243C2×#452D1311yescharacteristic
244C2×#440—131no—
245C2×#417—131no—
246#2360—131no—
247#2339—131no—
248#1969—131no—
249#1935—131no—
250#1928—131no—
251#1894—131no—
252#1878—131no—
253#1877—131no—
254#1862—131no—
255#1852—131no—
256C4×#102—131no—
257#1753—131no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—21no—
261C23×C13—22no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13C4×D412yes—
272C23×C13C22×D411yescharacteristic
273Q8×C13—22no—
274Q8×C13—22no—
275Q8×C13—22no—
276Q8×C13—22no—
277Q8×C13—41no—
278Q8×C13—41no—
279Q8×C13—41no—
280Q8×C13—41no—
281D4×C13—22no—
282D4×C13—22no—
283D4×C13—22no—
284D4×C13—48no—
285D4×C13C4×D414yes—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—48no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13C4×D412yes—
303C2×C4×C13C23×C411yescharacteristic
304C2×C4×C13C22×D411yescharacteristic
305C2×C4×C13C2×#4111yescharacteristic
306C2×C4×C13C2×#4111yescharacteristic
307C2×C4×C13H(5,𝔽2)11yescharacteristic
308C2×C4×C13H(5,𝔽2)11yescharacteristic
309C2×Dic13—21no—
310C2×Dic13—21no—
311C2×Dic13—21no—
312C2×Dic13—21no—
313C2×Dic13—22no—
314C2×Dic13—21no—
315C2×Dic13—21no—
316C2×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—21no—
319C2×Dic13—21no—
320C2×Dic13—21no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—84no—
333C2×Dic13—84no—
334C2×Dic13—84no—
335C2×Dic13#13712yes—
336C8×C13—22no—
337C8×C13—22no—
338#1055—22no—
339#1055—41no—
340C22×#41C2×D1311yescharacteristic
341C22×Q16C2×D1311yescharacteristic
342C22×SD16C2×D1311yescharacteristic
343C22×M16—131no—
344C2×C22⋊Q8C2×D1311yescharacteristic
345C2×C4×Q8—131no—
346C2×C4×D4—131no—
347C2×C4×D4—131no—
348C22×C4⋊C4—131no—
349#452Dic1318yescomplemented
350#440—264no—
351C2×#107—131no—
352C2×#107—131no—
353#417—264no—
354C2×#103—131no—
355C2×#103—131no—
356C2×#103—131no—
357C2×#103—131no—
358C2×#103C2×D1311yescharacteristic
359C2×#102—131no—
360C2×#102—131no—
361C2×#102C2×D1311yescharacteristic
362C2×C22⋊C8C2×D1311yescharacteristic
363C2×#97—131no—
364C2×C4×C8—131no—
365#391—131no—
366#391—131no—
367#391—131no—
368#389—131no—
369#389—261no—
370#387—261no—
371#386—261no—
372#386—261no—
373#385—261no—
374#381—261no—
375#380—131no—
376C4×C4⋊C4—131no—
377C4×C22⋊C4—131no—
378C4×C22⋊C4—261no—
379C2×#95—261no—
380#340—131no—
381#340—131no—
382#340—131no—
383#340—131no—
384#336—131no—
385#336—131no—
386C22×C13—22no—
387C22×C13—24no—
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—42no—
391C22×C13—42no—
392C22×C13—41no—
393C22×C13—42no—
394C22×C13—41no—
395C22×C13—42no—
396C22×C13—42no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13—42no—
400C22×C13C2×C4×D411yescharacteristic
401C22×C13D4211yescharacteristic
402C22×C13#54611yescharacteristic
403C22×C13C2×#13711yescharacteristic
404C22×C13#57511yescharacteristic
405C22×C13#57611yescharacteristic
406C22×C13#57811yescharacteristic
407C4×C13—22no—
408C4×C13—42no—
409C4×C13—42no—
410C4×C13—42no—
411C4×C13C2×C4×D411yescharacteristic
412C4×C13#51811yescharacteristic
413C4×C13#54611yescharacteristic
414C4×C13#55111yescharacteristic
415Dic13—22no—
416Dic13—41no—
417Dic13—42no—
418Dic13—41no—
419Dic13—41no—
420Dic13—81no—
421Dic13—81no—
422Dic13—81no—
423C2×#41—22no—
424C2×#41—22no—
425C2×#41—22no—
426C2×#41—41no—
427C2×#41—41no—
428C2×#41C2×Dic1314yes—
429C22×Q8C22×D1311yescharacteristic
430C22×Q8C22×D1311yescharacteristic
431C22×D4—21no—
432C22×D4C22×D1311yescharacteristic
433C23×C4—21no—
434C23×C4—261no—
435C23×C4—261no—
436C23×C4—261no—
437C23×C4C22×D1311yescharacteristic
438C2×Q16—41no—
439C2×Q16—41no—
440C2×Q16C2×Dic1314yescomplemented
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16C2×Dic1314yescomplemented
444C2×M16—262no—
445C2×M16—262no—
446C2×M16—521no—
447C22×C8—131no—
448C22×C8—131no—
449C22×C8C22×D1311yescharacteristic
450C22×C8C22×D1311yescharacteristic
451C22⋊Q8—22no—
452C22⋊Q8C2×Dic1314yescomplemented
453C4×Q8—262no—
454C4×Q8—521no—
455C4×D4—262no—
456C4×D4—262no—
457C4×D4—521no—
458C4×D4—521no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—131no—
461C2×C4⋊C4—131no—
462C2×C4⋊C4—131no—
463C2×C4⋊C4—131no—
464C2×C4⋊C4—262no—
465C2×C4⋊C4—261no—
466C2×C4⋊C4—261no—
467C2×C4⋊C4—261no—
468C2×C4⋊C4—521no—
469C2×C4⋊C4C22×D1311yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—131no—
472C2×C22⋊C4—131no—
473C2×C22⋊C4—261no—
474C2×C22⋊C4—261no—
475C2×C22⋊C4—261no—
476C2×C42—131no—
477C2×C42—131no—
478C2×C42—261no—
479C2×C42—261no—
480#107—262no—
481#107—521no—
482#103—262no—
483#103—262no—
484#103—262no—
485#103—521no—
486#103C2×Dic1314yescomplemented
487#102—134no—
488#102—262no—
489#102C2×Dic1314yescomplemented
490C22⋊C8C2×Dic1314yescomplemented
491#97—262no—
492C4×C8—521no—
493#95—131no—
494#95—131no—
495#95—261no—
496#95—261no—
497#95—261no—
498#95—261no—
499#95—261no—
500#95—261no—
501#95—261no—
502#95—261no—
503#95—261no—
504C2×C13—42no—
505C2×C13—44no—
506C2×C13#235811yescharacteristic
507C2×C13C4×#13711yescharacteristic
508C2×C13#295111yescharacteristic
509C2×C13#327311yescharacteristic
510C2×C13#327611yescharacteristic
511C2×C13#331411yescharacteristic
512C2×C13#331511yescharacteristic
513C24—21no—
514C24D4×D1311yescharacteristic
515#41—28no—
516#41—44no—
517#41—44no—
518#41—44no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8C22×Dic1312yes—
530C2×Q8C22×Dic1312yes—
531C2×D4—24no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4D4×D1312yes—
538C2×D4#612912yes—
539C2×D4C22×Dic1312yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—131no—
551C22×C4—131no—
552C22×C4—131no—
553C22×C4—131no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—522no—
559C22×C4—522no—
560C22×C4—522no—
561C22×C4—522no—
562C22×C4—522no—
563C22×C4—522no—
564C22×C4—1041no—
565C22×C4—1041no—
566C22×C4—1041no—
567C22×C4D4×D1311yescharacteristic
568C22×C4#612912yes—
569C22×C4C22×Dic1312yes—
570C22×C4C23×D1311yescharacteristic
571Q16—44no—
572SD16—28no—
573M16—524no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—132no—
579C2×C8—261no—
580C2×C8—261no—
581C2×C8—261no—
582C2×C8—261no—
583C2×C8—261no—
584C2×C8C22×Dic1312yes—
585C2×C8C22×Dic1312yes—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—132no—
589C4⋊C4—261no—
590C4⋊C4—261no—
591C4⋊C4—261no—
592C4⋊C4—261no—
593C4⋊C4—261no—
594C4⋊C4—261no—
595C4⋊C4—261no—
596C4⋊C4—522no—
597C4⋊C4—522no—
598C4⋊C4—1041no—
599C4⋊C4C22×Dic1312yes—
600C22⋊C4—24no—
601C22⋊C4—262no—
602C22⋊C4—521no—
603C22⋊C4—522no—
604C22⋊C4—522no—
605C22⋊C4—1041no—
606C42—261no—
607C42—261no—
608C42—261no—
609C42—261no—
610C42—522no—
611C42—1041no—
612C13#2286211yescharacteristic, complemented, Sylow
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—22no—
619C23—21no—
620C23—22no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23D4×Dic1312yes—
627C23C2×D4×D1311yescharacteristic
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—48no—
640D4D4×Dic1314yes—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—48no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—132no—
658C2×C4—261no—
659C2×C4—261no—
660C2×C4—261no—
661C2×C4—261no—
662C2×C4—261no—
663C2×C4—261no—
664C2×C4—261no—
665C2×C4—261no—
666C2×C4—261no—
667C2×C4—261no—
668C2×C4—262no—
669C2×C4—261no—
670C2×C4—521no—
671C2×C4—521no—
672C2×C4—521no—
673C2×C4—521no—
674C2×C4—521no—
675C2×C4—521no—
676C2×C4—521no—
677C2×C4—521no—
678C2×C4—521no—
679C2×C4—521no—
680C2×C4—521no—
681C2×C4—1044no—
682C2×C4—1044no—
683C2×C4—1044no—
684C2×C4D4×Dic1312yes—
685C2×C4C2×D4×D1311yescharacteristic
686C2×C4C2×#612911yescharacteristic
687C2×C4C2×#612911yescharacteristic
688C2×C4#8825111yescharacteristic
689C2×C4#8825111yescharacteristic
690C2×C4C23×Dic1311yescharacteristic
691C8—22no—
692C8—22no—
693C8—262no—
694C8—521no—
695C22—22no—
696C22—22no—
697C22—24no—
698C22—22no—
699C22—41no—
700C22—42no—
701C22—41no—
702C22—42no—
703C22—42no—
704C22—41no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—41no—
709C22#1171929511yescharacteristic
710C22#1171929611yescharacteristic
711C22#1171947411yescharacteristic
712C22#1171947611yescharacteristic
713C22D13×#13711yescharacteristic
714C22#1171948211yescharacteristic
715C22C2×D4×Dic1311yescharacteristic
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—262no—
721C4—521no—
722C4—521no—
723C4—522no—
724C4—521no—
725C4—1041no—
726C4—1041no—
727C4—1041no—
728C4#1171929211yescharacteristic
729C4#1171929611yescharacteristic
730C4C2×D4×Dic1311yescharacteristic
731C4#1171950311yescharacteristic
732C2—42no—
733C2—44no—
734C2#1311782011yescharacteristic
735C2#137×Dic1311yescharacteristic
736C2#1312371211yescharacteristic
737C2#1312644011yescharacteristic
738C2#1312648011yescharacteristic
739C2#1312691011yescharacteristic
740C2#1312692511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#452C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenterC2×#452D13
hypocenterC13#22862
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×#11718825C2semidirect
3. #13117845C2semidirect
5. #13115698C2semidirect
6. #13115528C2semidirect
7. #13115479C2semidirect
8. #13115270C2semidirect
9. #13115179C2semidirect
10. #13115172C2semidirect
11. #13115085C2semidirect
12. #13115026C2semidirect
13. #102×Dic13C2semidirect
14. #13114622C2semidirect
25. C13×#452C4semidirect
79. C2×C13×Q16C2×C4semidirect
82. C2×C13×SD16C2×C4semidirect
86. C13×C22⋊Q8C2×C4semidirect
119. C13×#103C2×C4semidirect
120. C13×#102C2×C4semidirect
121. C13×C22⋊C8C2×C4semidirect
349. #452Dic13semidirect
440. C2×Q16C2×Dic13semidirect
443. C2×SD16C2×Dic13semidirect
452. C22⋊Q8C2×Dic13semidirect
486. #103C2×Dic13semidirect
489. #102C2×Dic13semidirect
490. C22⋊C8C2×Dic13semidirect
612. C13#22862semidirect

Maximal subgroups

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

subgroupindex
C2×#117188252
C2×#117188932
#131178452
#131176662
#131156982
#131155282
#131154792
#131152702
#131151792
#131151722
#131150852
#131150262
#102×Dic132
#131146222
C2×C13×#4522
#2286213