Finite Group Databasebeta

← #15874179

Subgroups — #15874179

Order 3328.

1084 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718698C211yesmaximal, characteristic
2#13117326C211yesmaximal, characteristic, complemented
3#13115716C211yesmaximal, characteristic, complemented
4#13115711C211yesmaximal, characteristic, complemented
5#13115532C211yesmaximal, characteristic, complemented
6#13115525C211yesmaximal, characteristic, complemented
7#13115470C211yesmaximal, characteristic, complemented
8#13115456C211yesmaximal, characteristic, complemented
9#13115184C211yesmaximal, characteristic, complemented
10#13115170C211yesmaximal, characteristic, complemented
11#13115159C211yesmaximal, characteristic, complemented
12#13115033C211yesmaximal, characteristic, complemented
13#13114774C211yesmaximal, characteristic, complemented
14#13114598C211yesmaximal, characteristic, complemented
15C4×C13×#121C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C2×C13×#121C2211yescharacteristic
18C2×C4×D4×C13—21no—
19C2×C4×D4×C13C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×#6105C2211yescharacteristic
22C22×#6104C2211yescharacteristic
23C2×#88180C2211yescharacteristic
24C13×#390C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#388—21no—
27C13×#386—21no—
28C13×#380C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C4×C13×C22⋊C4—21no—
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33#11718874—21no—
34#11718874—21no—
35C2×C22⋊#1055C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718698C418yescomplemented
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C2×#88049C2211yescharacteristic
43C2×#88049C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46#11718600C2211yescharacteristic
47#11718600C2211yescharacteristic
48C4×#6103—21no—
49C4×#6103—21no—
50#11718590C2211yescharacteristic
51#11718590C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53C2×#88043C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D4×C13—21no—
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13D411yescharacteristic
64C23×C4×C13D411yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C22×C22⋊D13—21no—
67C2×#6127—22no—
68C2×#6127—41no—
69C2×#6127—41no—
70C2×#6127—41no—
71C2×#6127—41no—
72C2×#6127C2×C414yescomplemented
73C22×D52C2311yescharacteristic
74C22×C4×D13—21no—
75C22×Dic26C2311yescharacteristic
76C13×#121—22no—
77C13×#121C2×C414yes—
78C4×D4×C13—41no—
79C4×D4×C13—41no—
80C4×D4×C13—44no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—21no—
90C2×C42×C13—21no—
91C2×C42×C13—41no—
92C2×C42×C13—41no—
93C2×C42×C13D411yescharacteristic
94C2×C42×C13D411yescharacteristic
95C2×C42×C13C2311yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×C22⋊Dic13—21no—
98C2×#6105—41no—
99C2×#6105—41no—
100C2×#6105C2×C414yescomplemented
101C2×#6104—41no—
102C2×#6104—41no—
103C2×#6104C2×C414yescomplemented
104C2×#6103—21no—
105C2×#6103—21no—
106C2×#6103—21no—
107C2×#6103—21no—
108#88180—41no—
109#88180—41no—
110C2×C4⋊Dic13C2311yescharacteristic
111C2×C4⋊Dic13C2311yescharacteristic
112C2×C4×Dic13—21no—
113C22×#1055C2311yescharacteristic
114C22×#1055C2311yescharacteristic
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C13×#95—21no—
118C13×#95—21no—
119C13×#95—21no—
120#88072—41no—
121#88072—41no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126C22⋊#1055—22no—
127C22⋊#1055C2×C414yescomplemented
128#88050—41no—
129#88050—41no—
130#88050C2×C414yescomplemented
131#88049—41no—
132#88049—41no—
133#88049C2×C414yescomplemented
134#88048—41no—
135#88047—41no—
136#88043—41no—
137#88043—41no—
138#22051—131nomaximal, Sylow
139C24×C13—21no—
140C24×C13C2×D411yescharacteristic
141C23×D13—21no—
142C2×D4×C13—24no—
143C2×D4×C13—21no—
144C2×D4×C13—21no—
145C2×D4×C13—21no—
146C2×D4×C13—21no—
147C2×D4×C13—21no—
148C2×D4×C13—42no—
149C2×D4×C13—42no—
150C2×D4×C13C22×C412yes—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—22no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—41no—
160C22×C4×C13—41no—
161C22×C4×C13—41no—
162C22×C4×C13—41no—
163C22×C4×C13—41no—
164C22×C4×C13—42no—
165C22×C4×C13—42no—
166C22×C4×C13—42no—
167C22×C4×C13C22×C412yes—
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13#4112yes—
174C22×C4×C13C2411yescharacteristic
175C2×C22⋊D13—24no—
176C2×C22⋊D13—42no—
177C2×C22⋊D13—42no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181#6127—44no—
182#6127—44no—
183#6127—44no—
184#6127—44no—
185C2×D52—21no—
186C2×D52—21no—
187C2×D52—21no—
188C2×D52—21no—
189C2×D52—21no—
190C2×D52C22×C412yes—
191C2×C4×D13—24no—
192C2×C4×D13—42no—
193C2×C4×D13—42no—
194C2×Dic26—21no—
195C2×Dic26—21no—
196C2×Dic26—21no—
197C2×Dic26—21no—
198C2×Dic26—21no—
199C2×Dic26C22×C412yes—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—42no—
206C13×C4⋊C4C22×C412yes—
207C13×C22⋊C4—24no—
208C13×C22⋊C4—42no—
209C13×C22⋊C4—42no—
210C13×C22⋊C4—42no—
211C13×C22⋊C4—42no—
212C42×C13—21no—
213C42×C13—21no—
214C42×C13—21no—
215C42×C13—21no—
216C42×C13—41no—
217C42×C13—41no—
218C42×C13—42no—
219C22⋊Dic13—42no—
220#6105—44no—
221#6104—44no—
222#6103—42no—
223#6103—42no—
224#6103—42no—
225#6103—42no—
226C4⋊Dic13—21no—
227C4⋊Dic13—21no—
228C4⋊Dic13—21no—
229C4⋊Dic13—21no—
230C4×Dic13—42no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055C22×C412yes—
242C2×#1055C22×C412yes—
243C2×#449—131no—
244C4×#121D1311yescharacteristic, complemented
245#2297—131no—
246#1973—131no—
247#1972—131no—
248#1936—131no—
249#1935—131no—
250#1927—131no—
251#1925—131no—
252#1879—131no—
253#1877—131no—
254#1875—131no—
255#1854—131no—
256#1788—131no—
257#1749—131no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—22no—
265C23×C13—41no—
266C23×C13—41no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13C4×D412yes—
272C23×C13C22×D411yescharacteristic
273C22×D13—22no—
274C22×D13—41no—
275C22×D13—41no—
276C22×D13—41no—
277C22×D13—41no—
278C22×D13—41no—
279C22×D13—41no—
280D4×C13—22no—
281D4×C13—22no—
282D4×C13—48no—
283D4×C13—41no—
284D4×C13—41no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—21no—
299C2×C4×C13—21no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—44no—
304C2×C4×C13—44no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—84no—
314C2×C4×C13C4×D412yes—
315C2×C4×C13AGL(1,ℤ/8)12yes—
316C2×C4×C13C23×C411yescharacteristic
317C2×C4×C13C2×#4111yescharacteristic
318C2×C4×C13H(5,𝔽2)11yescharacteristic
319C2×C4×C13H(5,𝔽2)11yescharacteristic
320C2×C4×C13H(5,𝔽2)11yescharacteristic
321C2×C4×C13H(5,𝔽2)11yescharacteristic
322C22⋊D13—48no—
323C2×Dic13—22no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332D52—22no—
333D52—22no—
334D52—41no—
335D52—41no—
336C4×D13—48no—
337Dic26—22no—
338Dic26—22no—
339Dic26—41no—
340Dic26—41no—
341#1055—22no—
342#1055—22no—
343#1055—41no—
344#1055—41no—
345C22×#41—131no—
346C22×SD16—131no—
347C22×D8—131no—
348C2×#121C2×D1311yescharacteristic
349C2×C4×D4—21no—
350C2×C4×D4C2×D1311yescharacteristic
351C2×#117—131no—
352C22×C42C2×D1311yescharacteristic
353#449—138no—
354C2×#107—131no—
355C2×#106—131no—
356C2×#103—131no—
357C2×#103—131no—
358C2×#103—131no—
359C2×#102—131no—
360C2×#102—131no—
361C2×#102—131no—
362C2×#102—131no—
363C2×#102—131no—
364C2×C22⋊C8—131no—
365C2×C22⋊C8—131no—
366C2×#97—131no—
367C2×#97—131no—
368#391—131no—
369#391—131no—
370#390—131no—
371#390—131no—
372#390C2×D1311yescharacteristic
373#389C2×D1311yescharacteristic
374#388—21no—
375#386—21no—
376#386—261no—
377#386—261no—
378#380C2×D1311yescharacteristic
379C4×C4⋊C4C2×D1311yescharacteristic
380C4×C22⋊C4—21no—
381C4×C22⋊C4—261no—
382C4×C22⋊C4—261no—
383#340—131no—
384#340—131no—
385#340—131no—
386#340—131no—
387#336—131no—
388#336—131no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—41no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—42no—
397C22×C13—42no—
398C22×C13—42no—
399C22×C13—81no—
400C22×C13—81no—
401C22×C13—81no—
402C22×C13—81no—
403C22×C13C2×C4×D411yescharacteristic
404C22×C13#53411yescharacteristic
405C22×C13#53511yescharacteristic
406C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
407C22×C13#57511yescharacteristic
408C22×C13#57511yescharacteristic
409C22×C13#57511yescharacteristic
410C2×D13—42no—
411C2×D13—42no—
412C2×D13—42no—
413C2×D13—81no—
414C2×D13—81no—
415C2×D13—81no—
416C2×D13—81no—
417C4×C13—22no—
418C4×C13—22no—
419C4×C13—41no—
420C4×C13—41no—
421C4×C13—41no—
422C4×C13—42no—
423C4×C13—81no—
424C4×C13—81no—
425C4×C13#51811yescharacteristic
426C4×C13#51811yescharacteristic
427C4×C13#53811yescharacteristic
428C4×C13#53811yescharacteristic
429Dic13—42no—
430Dic13—81no—
431Dic13—81no—
432C2×#41—134no—
433C2×#41—262no—
434C2×#41—521no—
435C2×#41—521no—
436C2×#41—521no—
437C2×#41—521no—
438C22×Q8—131no—
439C22×D4—21no—
440C22×D4—131no—
441C22×D4—261no—
442C22×D4C22×D1311yescharacteristic
443C23×C4—21no—
444C23×C4—261no—
445C23×C4C22⋊D1311yescharacteristic
446C23×C4C22⋊D1311yescharacteristic
447C23×C4C22×D1311yescharacteristic
448C2×SD16—134no—
449C2×SD16—521no—
450C2×SD16—521no—
451C2×D8—134no—
452C2×D8—521no—
453C2×D8—521no—
454C22×C8—131no—
455C22×C8—131no—
456C22×C8—131no—
457C22×C8—131no—
458#121—22no—
459#121C4×D1314yes—
460C4×D4—41no—
461C4×D4—41no—
462C4×D4—44no—
463#117—521no—
464#117—521no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4C22×D1311yescharacteristic
469C2×C4⋊C4C22×D1311yescharacteristic
470C2×C4⋊C4C22×D1311yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—261no—
477C2×C22⋊C4—261no—
478C2×C22⋊C4—261no—
479C2×C22⋊C4—261no—
480C2×C22⋊C4—261no—
481C2×C42—21no—
482C2×C42—41no—
483C2×C42—41no—
484C2×C42—261no—
485C2×C42C22⋊D1311yescharacteristic
486C2×C42C22⋊D1311yescharacteristic
487C2×C42C22×D1311yescharacteristic
488C2×C42C22×D1311yescharacteristic
489#107—521no—
490#106—521no—
491#103—134no—
492#103—521no—
493#103—521no—
494#102—134no—
495#102—521no—
496#102—521no—
497#102—521no—
498#102—521no—
499C22⋊C8—134no—
500C22⋊C8—262no—
501#97—521no—
502#97—521no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—261no—
507#95—261no—
508#95—261no—
509#95—261no—
510C2×C13—42no—
511C2×C13—82no—
512C2×C13#232111yescharacteristic
513C2×C13#294311yescharacteristic
514C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
515C2×C13#319411yescharacteristic
516C2×C13#319711yescharacteristic
517C2×C13#321411yescharacteristic
518C2×C13#321911yescharacteristic
519D13—82no—
520C24—21no—
521C24—261no—
522C24C2×C22⋊D1311yescharacteristic
523#41—524no—
524#41—524no—
525#41—524no—
526#41—524no—
527C2×Q8—132no—
528C2×Q8—261no—
529C2×Q8—261no—
530C2×Q8—261no—
531C2×Q8—261no—
532C2×Q8—261no—
533C2×D4—24no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—132no—
542C2×D4—264no—
543C2×D4—261no—
544C2×D4—261no—
545C2×D4—261no—
546C2×D4—261no—
547C2×D4—261no—
548C2×D4—522no—
549C2×D4—522no—
550C2×D4C2×C4×D1312yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—261no—
568C22×C4—264no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—522no—
572C22×C4—522no—
573C22×C4C2×C4×D1312yes—
574C22×C4#612712yes—
575C22×C4C2×C22⋊D1311yescharacteristic
576C22×C4C2×C22⋊D1311yescharacteristic
577C22×C4C2×C22⋊D1311yescharacteristic
578C22×C4C2×C22⋊D1311yescharacteristic
579C22×C4C2×C22⋊D1311yescharacteristic
580C22×C4C23×D1311yescharacteristic
581SD16—524no—
582D8—524no—
583C2×C8—132no—
584C2×C8—132no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—261no—
590C2×C8—261no—
591C2×C8—261no—
592C2×C8—261no—
593C2×C8—261no—
594C2×C8—261no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—42no—
601C4⋊C4—261no—
602C4⋊C4—261no—
603C4⋊C4—261no—
604C4⋊C4—261no—
605C4⋊C4C2×C4×D1312yes—
606C22⋊C4—24no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—522no—
612C22⋊C4—522no—
613C22⋊C4—522no—
614C22⋊C4—522no—
615C22⋊C4—522no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—41no—
621C42—41no—
622C42—42no—
623C42—522no—
624C13#2205111yescharacteristic, complemented, Sylow
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—262no—
639C23—521no—
640C23—521no—
641C23—521no—
642C23—521no—
643C23—521no—
644C23—521no—
645C23C4×C22⋊D1312yes—
646C23C22×C22⋊D1311yescharacteristic
647Q8—262no—
648Q8—262no—
649Q8—521no—
650Q8—521no—
651D4—22no—
652D4—22no—
653D4—48no—
654D4—41no—
655D4—41no—
656D4—262no—
657D4—262no—
658D4—528no—
659D4—521no—
660D4—521no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—262no—
691C2×C4—528no—
692C2×C4—521no—
693C2×C4—521no—
694C2×C4—521no—
695C2×C4—521no—
696C2×C4—521no—
697C2×C4—521no—
698C2×C4—521no—
699C2×C4—521no—
700C2×C4C4×C22⋊D1312yes—
701C2×C4#8818612yes—
702C2×C4C22×C4×D1311yescharacteristic
703C2×C4C2×#612711yescharacteristic
704C2×C4#8825111yescharacteristic
705C2×C4#8825111yescharacteristic
706C2×C4#8825611yescharacteristic
707C2×C4#8825611yescharacteristic
708C8—262no—
709C8—262no—
710C8—521no—
711C8—521no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—522no—
727C22—522no—
728C22—522no—
729C22—1041no—
730C22—1041no—
731C22—1041no—
732C22—1041no—
733C22C2×C4×C22⋊D1311yescharacteristic
734C22C2×#8818611yescharacteristic
735C22#1171950911yescharacteristic
736C22#1171952711yescharacteristic
737C22#1171952711yescharacteristic
738C22#1171952711yescharacteristic
739C22#1171953511yescharacteristic
740C4—22no—
741C4—22no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—522no—
749C4—1041no—
750C4—1041no—
751C4#1171925011yescharacteristic
752C4#1171925011yescharacteristic
753C4#1171926511yescharacteristic
754C4#1171926511yescharacteristic
755C2—42no—
756C2—82no—
757C2—1042no—
758C2#1311749011yescharacteristic
759C2#1312363411yescharacteristic
760C2C4×#8818611yescharacteristic
761C2#1312565011yescharacteristic
762C2#1312567311yescharacteristic
763C2#1312582711yescharacteristic
764C2#1312586911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#121C2
socleC23×C13C22×D4
prime radicalC2×#11718698C2
cosocleC22×C4×C13C24
hypercenterC4×#121D13
hypocenterC13#22051
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. #13117326C2semidirect
3. #13115716C2semidirect
4. #13115711C2semidirect
5. #13115532C2semidirect
6. #13115525C2semidirect
7. #13115470C2semidirect
8. #13115456C2semidirect
9. #13115184C2semidirect
10. #13115170C2semidirect
11. #13115159C2semidirect
12. #13115033C2semidirect
13. #13114774C2semidirect
14. #13114598C2semidirect
15. C4×C13×#121C2semidirect
37. #11718698C4semidirect
72. C2×#6127C2×C4semidirect
100. C2×#6105C2×C4semidirect
103. C2×#6104C2×C4semidirect
127. C22⋊#1055C2×C4semidirect
130. #88050C2×C4semidirect
133. #88049C2×C4semidirect
244. C4×#121D13semidirect
624. C13#22051semidirect

Maximal subgroups

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

subgroupindex
C2×#117186982
#131173262
#131157162
#131157112
#131155322
#131155252
#131154702
#131154562
#131151842
#131151702
#131151592
#131150332
#131147742
#131145982
C4×C13×#1212
#2205113