Finite Group Databasebeta

← #15897264

Subgroups — #15897264

Order 3328.

1394 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718755C211yesmaximal, characteristic, complemented
2C2×#11718736C211yesmaximal, characteristic, complemented
3C4×#88178C211yesmaximal, characteristic, complemented
4#13116022C212yesmaximal, complemented
5#13115839C212yesmaximal, complemented
6#13115789C211yesmaximal, characteristic, complemented
7#13115764C211yesmaximal, characteristic, complemented
8#13115170C212yesmaximal, complemented
9#13115097C212yesmaximal, complemented
10#13114816C211yesmaximal, characteristic, complemented
11C2×C13×#532C211yesmaximal, characteristic
12C22×C13×#41—21no—
13C13×#532—24no—
14C13×#532—24no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#127C2211yescharacteristic
17C2×C13×#124—21no—
18C2×C13×#121—21no—
19C2×C13×#121C2212yes—
20C2×C4×D4×C13—21no—
21C2×C4×D4×C13C2212yes—
22C22×C42×C13C2211yescharacteristic
23C22×#6105C2212yes—
24C2×#88178C2211yescharacteristic
25C2×C4×Dic26C2211yescharacteristic
26C2×#88072C2212yes—
27C2×#88072C2212yes—
28C2×#88072C2212yes—
29#11718873C2211yescharacteristic
30#11718871—21no—
31C4×C22⋊Dic13—21no—
32C2×C22⋊#1055C2212yes—
33#11718755—24no—
34#11718736—24no—
35C2×#88050C2212yes—
36C2×#88048C2212yes—
37C4×C4⋊Dic13C2211yescharacteristic
38#11718594—21no—
39C4×#6101—21no—
40#11718590C2211yescharacteristic
41#11718589C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C2×C13×#41—28no—
48C2×C13×#41—44no—
49C2×C13×#41—44no—
50C22×Q8×C13—21no—
51C22×D4×C13—22no—
52C22×D4×C13—21no—
53C22×D4×C13—21no—
54C22×D4×C13C2312yes—
55C23×C4×C13—22no—
56C23×C4×C13D411yescharacteristic
57C23×C4×C13D411yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C22×Dic26C2311yescharacteristic
60C13×C4⋊Q8—22no—
61C13×C4⋊Q8D414yes—
62C13×#127—22no—
63C13×#127D414yes—
64C13×#124—28no—
65C13×#121—28no—
66C13×#121—24no—
67C13×#121—24no—
68C4×D4×C13—28no—
69C4×D4×C13—24no—
70C4×D4×C13—24no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—22no—
75C2×C42×C13—22no—
76C2×C42×C13—22no—
77C2×C42×C13D411yescharacteristic
78C2×C42×C13D411yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83C2×#6105—24no—
84C2×#6105—24no—
85C2×#6105—42no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89#88178—22no—
90#88178—22no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C22×#1055C2312yes—
97C22×#1055C2312yes—
98C4×Dic26—22no—
99C4×Dic26—22no—
100#88072—24no—
101#88072—24no—
102#88072—42no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108C22⋊#1055—42no—
109#88050—24no—
110#88048—24no—
111C4⋊#1055—22no—
112C4⋊#1055—22no—
113#24154—131nomaximal, Sylow
114C24×C13—22no—
115C24×C13C2×D411yescharacteristic
116C13×#41—432no—
117C2×Q8×C13—24no—
118C2×Q8×C13—42no—
119C2×Q8×C13—42no—
120C2×D4×C13—28no—
121C2×D4×C13—24no—
122C2×D4×C13—24no—
123C2×D4×C13—22no—
124C2×D4×C13—22no—
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13—22no—
128C2×D4×C13—42no—
129C2×D4×C13—42no—
130C2×D4×C13—44no—
131C2×D4×C13—44no—
132C2×D4×C13—42no—
133C2×D4×C13—42no—
134C2×D4×C13C2×D414yes—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—28no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—41no—
147C22×C4×C13—41no—
148C22×C4×C13—44no—
149C22×C4×C13—44no—
150C22×C4×C13SD1614yescomplemented
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2411yescharacteristic
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26—21no—
166C2×Dic26#4112yescomplemented
167C13×C4⋊C4—24no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4C2×D414yes—
170C13×C22⋊C4—28no—
171C13×C22⋊C4—28no—
172C42×C13—22no—
173C42×C13—22no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13C2×D412yes—
177C42×C13C2×D412yes—
178C22⋊Dic13—24no—
179C22⋊Dic13—42no—
180#6105—48no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13#4112yescomplemented
187#6101—24no—
188#6101—42no—
189#6101—42no—
190C4×Dic13—42no—
191C4×Dic13—42no—
192C2×#1055—22no—
193C2×#1055—22no—
194C2×#1055—22no—
195C2×#1055—22no—
196C2×#1055—22no—
197C2×#1055—22no—
198C2×#532D1311yescharacteristic
199C2×#475—131no—
200C2×#460—131no—
201C4×C22⋊Q8—131no—
202#2034—132no—
203#2000—132no—
204#1988—131no—
205#1982—131no—
206#1877—132no—
207#1864—132no—
208#1797—131no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—24no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13—42no—
222C23×C13C2×SD1612yes—
223C23×C13C22×D411yescharacteristic
224Q8×C13—48no—
225D4×C13—24no—
226D4×C13—24no—
227D4×C13—48no—
228D4×C13—416no—
229D4×C13—42no—
230D4×C13—42no—
231D4×C13—48no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—28no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—24no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—44no—
245C2×C4×C13—416no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13#12012yes—
253C2×C4×C13#12012yes—
254C2×C4×C13C2×SD1612yes—
255C2×C4×C13C2×SD1612yes—
256C2×C4×C13AGL(1,ℤ/8)12yes—
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C22×D411yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13H(5,𝔽2)11yescharacteristic
262C2×C4×C132−1+411yescharacteristic
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275Dic26—22no—
276Dic26—22no—
277Dic26—41no—
278Dic26—41no—
279#1055—42no—
280#1055—42no—
281C22×#41—21no—
282C22×SD16—132no—
283#532—24no—
284#532—24no—
285C2×C4⋊Q8C2×D1311yescharacteristic
286C2×#127C2×D1311yescharacteristic
287C2×#124—21no—
288C2×C22⋊Q8—131no—
289C2×#121—21no—
290C2×#121C2×D1312yes—
291C2×C4×Q8—131no—
292C2×C4×D4—21no—
293C2×C4×D4C2×D1312yes—
294C22×C42C2×D1311yescharacteristic
295#475—264no—
296#460—264no—
297C2×#106—132no—
298C2×C4⋊C8—131no—
299C2×C4⋊C8—131no—
300C2×#103—132no—
301C2×#102—132no—
302C2×#102—132no—
303C2×#102—132no—
304C2×C22⋊C8—132no—
305#391—131no—
306#389—131no—
307#387—261no—
308#385—261no—
309#380—131no—
310C4×C4⋊C4—131no—
311C4×C4⋊C4—261no—
312C4×C22⋊C4—261no—
313#340—132no—
314#340—132no—
315#336—132no—
316C22×C13—22no—
317C22×C13—22no—
318C22×C13—22no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—44no—
324C22×C13—44no—
325C22×C13—44no—
326C22×C13—82no—
327C22×C13—82no—
328C22×C13—82no—
329C22×C13—82no—
330C22×C13C2×#12011yescharacteristic
331C22×C13#52511yescharacteristic
332C22×C13#53711yescharacteristic
333C22×C13C22×SD1611yescharacteristic
334C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C13#57511yescharacteristic
336C22×C13#57511yescharacteristic
337C4×C13—22no—
338C4×C13—22no—
339C4×C13—41no—
340C4×C13—44no—
341C4×C13—41no—
342C4×C13#45014yes—
343C4×C13#54611yescharacteristic
344C4×C13#54711yescharacteristic
345C4×C13#54811yescharacteristic
346C4×C13#55011yescharacteristic
347Dic13—42no—
348Dic13—42no—
349Dic13—81no—
350Dic13—81no—
351C2×#41—28no—
352C2×#41—44no—
353C2×#41—44no—
354C22×Q8—21no—
355C22×Q8—131no—
356C22×D4—22no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4C22×D1312yes—
360C23×C4—22no—
361C23×C4C22⋊D1311yescharacteristic
362C23×C4C22⋊D1311yescharacteristic
363C23×C4C22×D1311yescharacteristic
364C2×SD16—264no—
365C2×SD16—264no—
366C2×SD16—522no—
367C22×C8—132no—
368C22×C8—132no—
369C4⋊Q8—22no—
370C4⋊Q8C22⋊D1314yes—
371#127—22no—
372#127C22⋊D1314yes—
373#124—28no—
374C22⋊Q8—262no—
375C22⋊Q8—262no—
376#121—28no—
377#121—24no—
378#121—24no—
379C4×Q8—262no—
380C4×Q8—262no—
381C4×D4—28no—
382C4×D4—24no—
383C4×D4—24no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4C22×D1312yes—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—261no—
399C2×C42—261no—
400C2×C42C22⋊D1311yescharacteristic
401C2×C42C22⋊D1311yescharacteristic
402C2×C42C22×D1311yescharacteristic
403C2×C42C22×D1311yescharacteristic
404#106—264no—
405C4⋊C8—262no—
406C4⋊C8—262no—
407#103—264no—
408#102—264no—
409#102—264no—
410#102—522no—
411C22⋊C8—522no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417C2×C13—42no—
418C2×C13—84no—
419C2×C13#240711yescharacteristic
420C2×C13C2×#45011yescharacteristic
421C2×C13#300511yescharacteristic
422C2×C13#310311yescharacteristic
423C2×C13#311511yescharacteristic
424C2×C13#324611yescharacteristic
425C2×C13#325111yescharacteristic
426C24—22no—
427C24C2×C22⋊D1311yescharacteristic
428#41—432no—
429C2×Q8—24no—
430C2×Q8—42no—
431C2×Q8—42no—
432C2×Q8—132no—
433C2×Q8—261no—
434C2×Q8—261no—
435C2×Q8—261no—
436C2×Q8—261no—
437C2×Q8—261no—
438C2×D4—28no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4C2×C22⋊D1314yes—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—28no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4#610514yescomplemented
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C2×C22⋊D1311yescharacteristic
478C22×C4C23×D1311yescharacteristic
479SD16—528no—
480C2×C8—262no—
481C2×C8—262no—
482C2×C8—262no—
483C2×C8—262no—
484C2×C8—262no—
485C2×C8—262no—
486C4⋊C4—24no—
487C4⋊C4—22no—
488C4⋊C4—132no—
489C4⋊C4—264no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—522no—
496C4⋊C4—522no—
497C4⋊C4C2×C22⋊D1314yes—
498C22⋊C4—28no—
499C22⋊C4—28no—
500C22⋊C4—264no—
501C22⋊C4—522no—
502C42—22no—
503C42—22no—
504C42—21no—
505C42—21no—
506C42—522no—
507C42—522no—
508C42C2×C22⋊D1312yes—
509C42C2×C22⋊D1312yes—
510C13#2415411yescharacteristic, complemented, Sylow
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—24no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23C2×#610512yes—
525C23C22×C22⋊D1311yescharacteristic
526Q8—48no—
527Q8—262no—
528Q8—262no—
529Q8—521no—
530Q8—521no—
531D4—24no—
532D4—24no—
533D4—48no—
534D4—416no—
535D4—42no—
536D4—42no—
537D4—48no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—28no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—24no—
550C2×C4—44no—
551C2×C4—416no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—262no—
559C2×C4—262no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4#8818612yes—
571C2×C4C2×#610512yes—
572C2×C4C2×#610512yes—
573C2×C4#8820712yes—
574C2×C4#8820712yes—
575C2×C4#41×D1311yescharacteristic
576C2×C4#41×D1311yescharacteristic
577C2×C4#8825611yescharacteristic
578C2×C4#8825711yescharacteristic
579C2×C4C22×C22⋊D1311yescharacteristic
580C2×C4C22×C22⋊D1311yescharacteristic
581C8—522no—
582C8—522no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22C2×#8818611yescharacteristic
598C22C22×#610511yescharacteristic
599C22#1171952711yescharacteristic
600C22#1171952711yescharacteristic
601C22#1171953311yescharacteristic
602C22#1171953811yescharacteristic
603C22C2×#8820711yescharacteristic
604C4—22no—
605C4—22no—
606C4—44no—
607C4—41no—
608C4—41no—
609C4—522no—
610C4—522no—
611C4—1041no—
612C4—1041no—
613C4#1171887914yes—
614C4#1171952911yescharacteristic
615C4#1171953411yescharacteristic
616C4#1171953611yescharacteristic
617C4#1171953911yescharacteristic
618C2—42no—
619C2—84no—
620C2#1311817511yescharacteristic
621C2C2×#1171887911yescharacteristic
622C2#1312407811yescharacteristic
623C2#1312486311yescharacteristic
624C2#1312498111yescharacteristic
625C2#1312615211yescharacteristic
626C2#1312619211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#532C2
socleC23×C13C22×D4
hypercenterC2×#532D13
hypocenterC13#24154
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#11718755C2semidirect
2. C2×#11718736C2semidirect
3. C4×#88178C2semidirect
4. #13116022C2semidirect
5. #13115839C2semidirect
6. #13115789C2semidirect
7. #13115764C2semidirect
8. #13115170C2semidirect
9. #13115097C2semidirect
10. #13114816C2semidirect
150. C22×C4×C13SD16semidirect
166. C2×Dic26#41semidirect
186. C4⋊Dic13#41semidirect
472. C22×C4#6105semidirect
510. C13#24154semidirect

Maximal subgroups

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

subgroupindex
C2×#117187552
C2×#117187362
C4×#881782
#131160222
#131158392
#131157892
#131157642
#131151702
#131150972
#131148162
C2×C13×#5322
#2415413