Finite Group Databasebeta

← #15883191

Subgroups — #15883191

Order 3328.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718888C211yesmaximal, characteristic
2C2×#11718478C211yesmaximal, characteristic, complemented
3#13117852C211yesmaximal, characteristic
4Q8×C22⋊Dic13C211yesmaximal, characteristic, complemented
5#13115714C211yesmaximal, characteristic, complemented
6#13115523C211yesmaximal, characteristic, complemented
7#13115480C211yesmaximal, characteristic, complemented
8#13115264C211yesmaximal, characteristic
9#13115189C211yesmaximal, characteristic, complemented
10#13115167C211yesmaximal, characteristic, complemented
11#13115088C211yesmaximal, characteristic, complemented
12#13115024C211yesmaximal, characteristic, complemented
13#13114668C211yesmaximal, characteristic, complemented
14#13114612C211yesmaximal, characteristic, complemented
15C22×C13×#103C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×Q8×Dic13C2211yescharacteristic
20C2×Q8×Dic13C2211yescharacteristic
21C22×#6106C2211yescharacteristic
22C22×#6106C2211yescharacteristic
23C2×#88184C2211yescharacteristic
24C2×C4×C22⋊D13—21no—
25C2×#88147C2211yescharacteristic
26C2×C13×#103—24no—
27C2×C13×#103C2211yescharacteristic
28C2×C13×#103C2211yescharacteristic
29C2×C13×#103C2211yescharacteristic
30C2×C13×#103C2211yescharacteristic
31#11718891—21no—
32#11718891—21no—
33#11718891C2211yescharacteristic
34#11718891C2211yescharacteristic
35#11718888C418yescomplemented
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38#11718874—21no—
39#11718873—21no—
40#11718873C2211yescharacteristic
41C4×C22⋊Dic13—21no—
42C4×C22⋊Dic13C2211yescharacteristic
43C2×C22⋊#1055C2211yescharacteristic
44C2×#88061C2211yescharacteristic
45C2×#88061C2211yescharacteristic
46C2×#88055C2211yescharacteristic
47C2×#88055C2211yescharacteristic
48#11718651—21no—
49#11718650—21no—
50#11718649C2211yescharacteristic
51C4⋊C4×Dic13C2211yescharacteristic
52#11718634C2211yescharacteristic
53C2×#88047C2211yescharacteristic
54C2×#88047C2211yescharacteristic
55#11718478—24no—
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13—21no—
63C22×Q8×C13—22no—
64C22×Q8×C13—22no—
65C22×Q8×C13—22no—
66C22×Q8×C13—41no—
67C22×Q8×C13—41no—
68C22×Q8×C13C2×C414yescomplemented
69C22×Q8×C13C2311yescharacteristic
70C22×Q8×C13C2311yescharacteristic
71C23×C4×C13—21no—
72C23×C4×C13—21no—
73C23×C4×C13C2311yescharacteristic
74C22×C22⋊D13—21no—
75C22×D52C2311yescharacteristic
76C22×C4×D13—21no—
77C22×C8×C13—22no—
78C22×C8×C13—22no—
79C22×C8×C13—41no—
80C22×C8×C13C2311yescharacteristic
81C22×C8×C13C2311yescharacteristic
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—41no—
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13D411yescharacteristic
89C2×C22⋊Dic13D411yescharacteristic
90Q8×Dic13—22no—
91Q8×Dic13—22no—
92Q8×Dic13—41no—
93Q8×Dic13—41no—
94C2×#6106—22no—
95C2×#6106—22no—
96C2×#6106—41no—
97C2×#6106—41no—
98C2×#6106C2×C414yescomplemented
99C2×#6106C2×C414yescomplemented
100#88184—22no—
101#88184C2×C414yes—
102C4×C22⋊D13—44no—
103C2×#6103—21no—
104C2×#6103—21no—
105C2×#6103—21no—
106C2×#6103—21no—
107C2×C4⋊Dic13—21no—
108C2×C4⋊Dic13—21no—
109C2×C4⋊Dic13C2311yescharacteristic
110C2×C4⋊Dic13C2311yescharacteristic
111C2×C4⋊Dic13C2311yescharacteristic
112C2×#6101—21no—
113C2×C4×Dic13—21no—
114C2×C4×Dic13—21no—
115C2×C4×Dic13—21no—
116C2×C4×Dic13C2311yescharacteristic
117C2×C4×Dic13C2311yescharacteristic
118C22×#1055C2311yescharacteristic
119C22×#1055C2311yescharacteristic
120#88147—22no—
121#88147—41no—
122C13×#103—22no—
123C13×#103—22no—
124C13×#103—22no—
125C13×#103D414yescomplemented
126#88075C2×C414yescomplemented
127#88075C2×C414yescomplemented
128#88071—21no—
129#88071—21no—
130#88071—21no—
131#88071—21no—
132#88071—21no—
133#88071—21no—
134#88071—21no—
135#88071D411yescharacteristic
136#88071D411yescharacteristic
137C22⋊#1055C2×C414yescomplemented
138#88061—22no—
139#88061—41no—
140#88055—22no—
141#88055—41no—
142#88047—22no—
143#88047—41no—
144#22855—131nomaximal, Sylow
145C24×C13C2×D411yescharacteristic
146C23×D13—21no—
147C2×Q8×C13—24no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—21no—
151C2×Q8×C13—21no—
152C2×Q8×C13—28no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13—42no—
158C2×Q8×C13—42no—
159C2×Q8×C13—44no—
160C2×Q8×C13—44no—
161C2×Q8×C13—44no—
162C2×Q8×C13C22×C412yes—
163C2×Q8×C13C22×C412yes—
164C2×Q8×C13C2×D412yes—
165C2×Q8×C13#4112yes—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—24no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—42no—
176C22×C4×C13—42no—
177C22×C4×C13—42no—
178C22×C4×C13—42no—
179C22×C4×C13—81no—
180C22×C4×C13C22×C412yes—
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13#4112yes—
183C22×C4×C13C2411yescharacteristic
184C2×C22⋊D13—24no—
185C2×C22⋊D13—42no—
186C2×C22⋊D13—42no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13C2×D411yescharacteristic
191C22×Dic13C2×D411yescharacteristic
192C22×Dic13C2×D411yescharacteristic
193C22×Dic13C2×D411yescharacteristic
194C2×D52—21no—
195C2×D52—21no—
196C2×D52—21no—
197C2×D52—21no—
198C2×D52—21no—
199C2×D52C22×C412yes—
200C2×C4×D13—42no—
201C2×C4×D13—42no—
202C2×C4×D13—81no—
203C2×C8×C13—21no—
204C2×C8×C13—21no—
205C2×C8×C13—21no—
206C2×C8×C13—21no—
207C2×C8×C13—21no—
208C2×C8×C13—44no—
209C2×C8×C13C2×D412yes—
210C13×C4⋊C4—21no—
211C13×C4⋊C4—21no—
212C13×C4⋊C4—21no—
213C13×C4⋊C4—42no—
214C13×C4⋊C4C2×D412yes—
215C22⋊Dic13—22no—
216C22⋊Dic13—22no—
217C22⋊Dic13—42no—
218#6106—28no—
219#6106—44no—
220#6103—24no—
221#6103—42no—
222#6103—42no—
223#6103—81no—
224C4⋊Dic13—21no—
225C4⋊Dic13—21no—
226C4⋊Dic13—21no—
227C4⋊Dic13—21no—
228C4⋊Dic13—21no—
229C4⋊Dic13—42no—
230C4⋊Dic13—42no—
231C4⋊Dic13C22×C412yes—
232#6101—42no—
233C4×Dic13—21no—
234C4×Dic13—21no—
235C4×Dic13—21no—
236C4×Dic13—21no—
237C4×Dic13—42no—
238C4×Dic13—42no—
239C4×Dic13—42no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—21no—
244C2×#1055C22×C412yes—
245C2×#1055C22×C412yes—
246C2×#448—131no—
247C2×#440—131no—
248C22×#103D1311yescharacteristic, complemented
249#2361—131no—
250Q8×C22⋊C4—131no—
251#1973—131no—
252#1935—131no—
253#1928—131no—
254#1893—131no—
255#1880—131no—
256#1877—131no—
257#1863—131no—
258#1852—131no—
259#1763—131no—
260#1752—131no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13C4×D412yes—
266C23×C13AGL(1,ℤ/8)12yes—
267C23×C13#13712yes—
268C23×C13C22×D411yescharacteristic
269C22×D13—22no—
270C22×D13—41no—
271C22×D13—41no—
272C22×D13—41no—
273C22×D13—41no—
274C22×D13—41no—
275C22×D13—41no—
276Q8×C13—22no—
277Q8×C13—22no—
278Q8×C13—22no—
279Q8×C13—22no—
280Q8×C13—22no—
281Q8×C13—48no—
282Q8×C13—41no—
283Q8×C13—41no—
284Q8×C13C4×D414yescomplemented
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—21no—
288C2×C4×C13—22no—
289C2×C4×C13—21no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—48no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—84no—
305C2×C4×C13C4×D412yes—
306C2×C4×C13C23×C411yescharacteristic
307C2×C4×C13C22×D411yescharacteristic
308C2×C4×C13C2×#4111yescharacteristic
309C2×C4×C13C2×#4111yescharacteristic
310C2×C4×C13H(5,𝔽2)11yescharacteristic
311C2×C4×C13H(5,𝔽2)11yescharacteristic
312C22⋊D13—48no—
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—21no—
322C2×Dic13—21no—
323C2×Dic13—21no—
324C2×Dic13—21no—
325C2×Dic13—21no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334D52—22no—
335D52—22no—
336D52—41no—
337D52—41no—
338C4×D13—84no—
339C8×C13—22no—
340C8×C13—41no—
341#1055—22no—
342#1055—22no—
343C23×Q8C2×D1311yescharacteristic
344C22×SD16—131no—
345C22×SD16—131no—
346C23×C8C2×D1311yescharacteristic
347C2×#121—131no—
348C2×C4×Q8—131no—
349C2×C4×Q8—131no—
350C2×C4×D4—131no—
351C2×C4×D4—261no—
352C22×C4⋊C4C2×D1311yescharacteristic
353#448—138no—
354#440—264no—
355C2×#107—131no—
356C2×#107—131no—
357C2×#103—24no—
358C2×#103—131no—
359C2×#103—131no—
360C2×#103C2×D1311yescharacteristic
361C2×#103C2×D1311yescharacteristic
362C2×#103C2×D1311yescharacteristic
363C2×#103C2×D1311yescharacteristic
364C2×#102—131no—
365C2×#102—131no—
366C2×C22⋊C8—131no—
367C2×#97—131no—
368C2×#97—131no—
369#391—131no—
370#391—131no—
371#391—261no—
372#391—261no—
373#390—131no—
374#389—131no—
375#388—261no—
376#386—261no—
377#385—261no—
378#380—131no—
379#380—261no—
380C4×C4⋊C4—131no—
381C4×C22⋊C4—131no—
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—22no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13#44014yescomplemented
396C22×C13C2×C4×D411yescharacteristic
397C22×C13D4211yescharacteristic
398C22×C13#54611yescharacteristic
399C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C13C2×#13711yescharacteristic
401C22×C13#57711yescharacteristic
402C22×C13#57811yescharacteristic
403C2×D13—42no—
404C2×D13—42no—
405C2×D13—42no—
406C2×D13—81no—
407C2×D13—81no—
408C2×D13—81no—
409C2×D13—81no—
410C4×C13—22no—
411C4×C13—24no—
412C4×C13—42no—
413C4×C13—42no—
414C4×C13—81no—
415C4×C13C2×C4×D411yescharacteristic
416C4×C13#51811yescharacteristic
417C4×C13#54611yescharacteristic
418C4×C13#55111yescharacteristic
419Dic13—42no—
420Dic13—41no—
421Dic13—41no—
422Dic13—41no—
423Dic13—41no—
424Dic13—81no—
425Dic13—81no—
426C22×Q8—21no—
427C22×Q8—22no—
428C22×Q8—22no—
429C22×Q8—22no—
430C22×Q8—41no—
431C22×Q8—41no—
432C22×Q8C4×D1314yescomplemented
433C22×Q8C22×D1311yescharacteristic
434C22×Q8C22×D1311yescharacteristic
435C22×D4—131no—
436C22×D4—261no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—261no—
440C23×C4C22×D1311yescharacteristic
441C2×SD16—134no—
442C2×SD16—134no—
443C2×SD16—262no—
444C2×SD16—262no—
445C2×SD16—521no—
446C2×SD16—521no—
447C22×C8—22no—
448C22×C8—22no—
449C22×C8—41no—
450C22×C8—131no—
451C22×C8—131no—
452C22×C8C22×D1311yescharacteristic
453C22×C8C22×D1311yescharacteristic
454#121—134no—
455#121—262no—
456C4×Q8—262no—
457C4×Q8—262no—
458C4×Q8—521no—
459C4×Q8—521no—
460C4×D4—262no—
461C4×D4—521no—
462C4×D4—524no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—41no—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—261no—
470C2×C4⋊C4—261no—
471C2×C4⋊C4—261no—
472C2×C4⋊C4C22×D1311yescharacteristic
473C2×C4⋊C4C22×D1311yescharacteristic
474C2×C22⋊C4—131no—
475C2×C22⋊C4—131no—
476C2×C22⋊C4—261no—
477C2×C22⋊C4—261no—
478C2×C22⋊C4—261no—
479C2×C22⋊C4—261no—
480C2×C22⋊C4—261no—
481C2×C42—131no—
482C2×C42—131no—
483C2×C42—261no—
484C2×C42—261no—
485C2×C42—261no—
486#107—262no—
487#107—521no—
488#103—22no—
489#103—22no—
490#103—22no—
491#103—134no—
492#103—134no—
493#103C22⋊D1314yescomplemented
494#102—262no—
495#102—521no—
496C22⋊C8—134no—
497#97—262no—
498#97—521no—
499#95—131no—
500#95—131no—
501#95—261no—
502#95—261no—
503#95—261no—
504#95—261no—
505#95—261no—
506#95—261no—
507#95—261no—
508C2×C13—24no—
509C2×C13#235811yescharacteristic
510C2×C13C2×#44011yescharacteristic
511C2×C13#294711yescharacteristic
512C2×C13#326511yescharacteristic
513C2×C13#327011yescharacteristic
514C2×C13#330811yescharacteristic
515C2×C13#332011yescharacteristic
516D13—82no—
517C24—261no—
518C24D4×D1311yescharacteristic
519C2×Q8—24no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—28no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—44no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8C2×C4×D1312yes—
535C2×Q8C2×C4×D1312yes—
536C2×Q8#612712yes—
537C2×Q8C2×C22⋊D1312yes—
538C2×D4—132no—
539C2×D4—264no—
540C2×D4—261no—
541C2×D4—261no—
542C2×D4—261no—
543C2×D4—261no—
544C2×D4—261no—
545C2×D4—522no—
546C2×D4—522no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—81no—
561C22×C4—131no—
562C22×C4—131no—
563C22×C4—131no—
564C22×C4—131no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—522no—
569C22×C4—522no—
570C22×C4—1041no—
571C22×C4C2×C4×D1312yes—
572C22×C4D4×D1311yescharacteristic
573C22×C4#612912yes—
574C22×C4C23×D1311yescharacteristic
575SD16—268no—
576SD16—524no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—44no—
583C2×C8—132no—
584C2×C8—132no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8C2×C22⋊D1312yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—132no—
595C4⋊C4—261no—
596C4⋊C4—261no—
597C4⋊C4—261no—
598C4⋊C4—261no—
599C4⋊C4—261no—
600C4⋊C4—522no—
601C4⋊C4—522no—
602C4⋊C4—522no—
603C4⋊C4C2×C22⋊D1312yes—
604C22⋊C4—262no—
605C22⋊C4—262no—
606C22⋊C4—264no—
607C22⋊C4—522no—
608C22⋊C4—522no—
609C22⋊C4—522no—
610C22⋊C4—1041no—
611C42—261no—
612C42—261no—
613C42—261no—
614C42—261no—
615C42—522no—
616C42—522no—
617C42—522no—
618C13#2285511yescharacteristic, complemented, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—262no—
624C23—521no—
625C23—521no—
626C23—521no—
627C23—521no—
628C23—521no—
629C23—521no—
630C23#8813512yes—
631C23#8816812yes—
632C23#8817212yes—
633C23C2×D4×D1311yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8C4×C22⋊D1314yescomplemented
643D4—262no—
644D4—262no—
645D4—528no—
646D4—521no—
647D4—521no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—262no—
669C2×C4—261no—
670C2×C4—261no—
671C2×C4—261no—
672C2×C4—261no—
673C2×C4—261no—
674C2×C4—261no—
675C2×C4—261no—
676C2×C4—261no—
677C2×C4—261no—
678C2×C4—261no—
679C2×C4—261no—
680C2×C4—261no—
681C2×C4—521no—
682C2×C4—521no—
683C2×C4—521no—
684C2×C4—521no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4—521no—
688C2×C4—521no—
689C2×C4—1044no—
690C2×C4#8813512yes—
691C2×C4C22×C4×D1311yescharacteristic
692C2×C4C2×#612711yescharacteristic
693C2×C4C2×#612911yescharacteristic
694C2×C4#8825111yescharacteristic
695C2×C4#8825111yescharacteristic
696C2×C4C22×C22⋊D1311yescharacteristic
697C8—22no—
698C8—41no—
699C8—262no—
700C8—262no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—522no—
708C22—522no—
709C22—522no—
710C22—1041no—
711C22—1041no—
712C22—1041no—
713C22—1041no—
714C22#1171847814yescomplemented
715C22C2×#8813511yescharacteristic
716C22#1171919511yescharacteristic
717C22C2×#8816811yescharacteristic
718C22#1171946711yescharacteristic
719C22C2×#8817211yescharacteristic
720C22#1171947111yescharacteristic
721C22D4×C22⋊D1311yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—81no—
727C4—521no—
728C4—522no—
729C4—521no—
730C4—521no—
731C4—521no—
732C4—1041no—
733C4—1041no—
734C4#1171919111yescharacteristic
735C4#1171920011yescharacteristic
736C4C2×C4×C22⋊D1311yescharacteristic
737C4#1171951111yescharacteristic
738C2—24no—
739C2—1042no—
740C2#1311781511yescharacteristic
741C2C2×#1171847811yescharacteristic
742C2#1312367311yescharacteristic
743C2#1312633111yescharacteristic
744C2#1312640611yescharacteristic
745C2#1312682311yescharacteristic
746C2#1312700311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#103C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
cosocleC22×C4×C13C24
hypercenterC22×#103D13
hypocenterC13#22855
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C2×#11718478C2semidirect
4. Q8×C22⋊Dic13C2semidirect
5. #13115714C2semidirect
6. #13115523C2semidirect
7. #13115480C2semidirect
9. #13115189C2semidirect
10. #13115167C2semidirect
11. #13115088C2semidirect
12. #13115024C2semidirect
13. #13114668C2semidirect
14. #13114612C2semidirect
15. C22×C13×#103C2semidirect
35. #11718888C4semidirect
68. C22×Q8×C13C2×C4semidirect
98. C2×#6106C2×C4semidirect
99. C2×#6106C2×C4semidirect
125. C13×#103D4semidirect
126. #88075C2×C4semidirect
127. #88075C2×C4semidirect
137. C22⋊#1055C2×C4semidirect
248. C22×#103D13semidirect
284. Q8×C13C4×D4semidirect
395. C22×C13#440semidirect
432. C22×Q8C4×D13semidirect
493. #103C22⋊D13semidirect
618. C13#22855semidirect
642. Q8C4×C22⋊D13semidirect
714. C22#11718478semidirect

Maximal subgroups

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

subgroupindex
C2×#117188882
C2×#117184782
#131178522
Q8×C22⋊Dic132
#131157142
#131155232
#131154802
#131152642
#131151892
#131151672
#131150882
#131150242
#131146682
#131146122
C22×C13×#1032
#2285513