Finite Group Databasebeta

← #15892951

Subgroups — #15892951

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88184C211yesmaximal, characteristic
2#13116403C211yesmaximal, characteristic, complemented
3#13116360C211yesmaximal, characteristic, complemented
4#13116318C211yesmaximal, characteristic, complemented
5#13116272C211yesmaximal, characteristic, complemented
6#13116267C211yesmaximal, characteristic, complemented
7#13116250C211yesmaximal, characteristic, complemented
8#13116025C211yesmaximal, characteristic
9#13116018C211yesmaximal, characteristic
10C4×#88047C211yesmaximal, characteristic, complemented
11C4×#88048C211yesmaximal, characteristic, complemented
12C4×#88049C211yesmaximal, characteristic, complemented
13C4×#88049C211yesmaximal, characteristic, complemented
14C4×C22⋊#1055C211yesmaximal, characteristic, complemented
15C13×#2283C211yesmaximal, characteristic, complemented
16C22×C42×C13C2211yescharacteristic
17C2×#88184C2211yescharacteristic
18C2×C4×C22⋊D13—21no—
19C2×C4×D52C2211yescharacteristic
20C13×#383—21no—
21C13×#382C2211yescharacteristic
22C13×#382C2211yescharacteristic
23C13×#381—21no—
24C13×#380C2211yescharacteristic
25C13×#380C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C13×#376—21no—
30#11718874—21no—
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42#11718601—21no—
43#11718600C2211yescharacteristic
44C4×#6103—21no—
45C4×C4⋊Dic13C2211yescharacteristic
46#11718589C2211yescharacteristic
47C2×C4×#1055C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13D411yescharacteristic
60C23×C4×C13D411yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—21no—
71C2×C42×C13—22no—
72C2×C42×C13—22no—
73C2×C42×C13—21no—
74C2×C42×C13—21no—
75C2×C42×C13D411yescharacteristic
76C2×C42×C13D411yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C22⋊Dic13—21no—
80#88184—22no—
81#88184—22no—
82C4×C22⋊D13—44no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×C4×Dic13—21no—
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C4×D52—22no—
97C4×D52—22no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109C22⋊#1055—22no—
110C22⋊#1055—22no—
111#88049—22no—
112#88049—22no—
113#88049—22no—
114#88049—22no—
115#88048—22no—
116#88048—22no—
117#88047—22no—
118#88047—22no—
119C4×#1055—22no—
120C4×#1055—22no—
121#23758—131nomaximal, Sylow
122C24×C13C2×D411yescharacteristic
123C23×D13—21no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—41no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2411yescharacteristic
146C2×C22⋊D13—24no—
147C2×C22⋊D13—42no—
148C2×C22⋊D13—42no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52—21no—
157C2×D52#4112yes—
158C2×C4×D13—42no—
159C2×C4×D13—42no—
160C2×C4×D13—42no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C22⋊C4—42no—
170C13×C22⋊C4—42no—
171C42×C13—22no—
172C42×C13—22no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—42no—
176C42×C13—42no—
177C42×C13#4112yes—
178C42×C13#4112yes—
179C22⋊Dic13—42no—
180#6103—24no—
181#6103—42no—
182#6103—42no—
183#6103—42no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13#4112yes—
190#6101—42no—
191C4×Dic13—42no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055#4112yes—
203C2×#1055#4112yes—
204C4×#121—131no—
205#2283D1311yescharacteristic, complemented
206#2101—131no—
207#2092—131no—
208#2085—131no—
209#2077—131no—
210#2076—131no—
211#2073—131no—
212#2034—131no—
213#2033—131no—
214C4×#107—131no—
215C4×#106—131no—
216C4×#102—131no—
217C4×#102—131no—
218C4×C22⋊C8—131no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13#13512yes—
226C23×C13C22×D411yescharacteristic
227C22×D13—22no—
228C22×D13—41no—
229C22×D13—41no—
230C22×D13—41no—
231C22×D13—41no—
232C22×D13—41no—
233C22×D13—41no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—44no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—44no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13#12312yes—
264C2×C4×C13#12312yes—
265C2×C4×C13#13512yes—
266C2×C4×C13AGL(1,ℤ/8)12yes—
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C22⋊D13—48no—
274C2×Dic13—22no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283D52—22no—
284D52—22no—
285D52—41no—
286D52—41no—
287C4×D13—84no—
288#1055—22no—
289#1055—22no—
290#1055—41no—
291#1055—41no—
292C2×#121—131no—
293C2×C4×D4—131no—
294C2×C4×D4—261no—
295C22×C42C2×D1311yescharacteristic
296C2×#107—131no—
297C2×#107—131no—
298C2×#106—131no—
299C2×#106—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×#102—131no—
303C2×#102—131no—
304C2×C22⋊C8—131no—
305C2×C22⋊C8—131no—
306C2×C4×C8—131no—
307C2×C4×C8—131no—
308#390—131no—
309#389—131no—
310#388—261no—
311#386—261no—
312#383—21no—
313#382C2×D1311yescharacteristic
314#382C2×D1311yescharacteristic
315#381—21no—
316#380—131no—
317#380C2×D1311yescharacteristic
318#380C2×D1311yescharacteristic
319C4×C4⋊C4—131no—
320C4×C4⋊C4C2×D1311yescharacteristic
321C4×C4⋊C4C2×D1311yescharacteristic
322C4×C22⋊C4—21no—
323C4×C22⋊C4—261no—
324#376—21no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#336—131no—
334#336—131no—
335C22×C13—22no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13C2×#12311yescharacteristic
343C22×C13#52511yescharacteristic
344C22×C13#53211yescharacteristic
345C22×C13C2×#13511yescharacteristic
346C22×C13C2×#13511yescharacteristic
347C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C13#57511yescharacteristic
349C2×D13—42no—
350C2×D13—42no—
351C2×D13—42no—
352C2×D13—81no—
353C2×D13—81no—
354C2×D13—81no—
355C2×D13—81no—
356C4×C13—22no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13—41no—
360C4×C13—81no—
361C4×C13—81no—
362C4×C13—81no—
363C4×C13—81no—
364C4×C13#48214yes—
365C4×C13#52911yescharacteristic
366C4×C13#52911yescharacteristic
367C4×C13#52911yescharacteristic
368C4×C13#52911yescharacteristic
369Dic13—42no—
370Dic13—81no—
371Dic13—81no—
372C22×D4—131no—
373C22×D4—261no—
374C23×C4—261no—
375C23×C4C22⋊D1311yescharacteristic
376C23×C4C22⋊D1311yescharacteristic
377C23×C4C22×D1311yescharacteristic
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381C22×C8—131no—
382#121—262no—
383#121—262no—
384C4×D4—262no—
385C4×D4—262no—
386C4×D4—524no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C4⋊C4C22×D1311yescharacteristic
393C2×C4⋊C4C22×D1311yescharacteristic
394C2×C4⋊C4C22×D1311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—261no—
398C2×C22⋊C4—261no—
399C2×C22⋊C4—261no—
400C2×C22⋊C4—261no—
401C2×C22⋊C4—261no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—261no—
407C2×C42C22⋊D1311yescharacteristic
408C2×C42C22⋊D1311yescharacteristic
409C2×C42C22×D1311yescharacteristic
410C2×C42C22×D1311yescharacteristic
411#107—262no—
412#107—262no—
413#106—262no—
414#106—262no—
415#102—262no—
416#102—262no—
417#102—262no—
418#102—262no—
419C22⋊C8—262no—
420C22⋊C8—262no—
421C4×C8—262no—
422C4×C8—262no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—261no—
432#95—261no—
433#95—261no—
434C2×C13—42no—
435C2×C13#239511yescharacteristic
436C2×C13C2×#48211yescharacteristic
437C2×C13#309111yescharacteristic
438C2×C13#310211yescharacteristic
439C2×C13#310511yescharacteristic
440C2×C13#316811yescharacteristic
441C2×C13#317111yescharacteristic
442D13—82no—
443C24—261no—
444C24C2×C22⋊D1311yescharacteristic
445C2×D4—132no—
446C2×D4—264no—
447C2×D4—261no—
448C2×D4—261no—
449C2×D4—261no—
450C2×D4—261no—
451C2×D4—261no—
452C2×D4—522no—
453C2×D4—522no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—41no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—522no—
474C22×C4—522no—
475C22×C4—522no—
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C2×C22⋊D1311yescharacteristic
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C2×C22⋊D1311yescharacteristic
480C22×C4C2×C22⋊D1311yescharacteristic
481C22×C4C23×D1311yescharacteristic
482C2×C8—132no—
483C2×C8—132no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—132no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—522no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—264no—
512C22⋊C4—522no—
513C22⋊C4—522no—
514C22⋊C4—522no—
515C22⋊C4—522no—
516C42—22no—
517C42—22no—
518C42—21no—
519C42—21no—
520C42—42no—
521C42—42no—
522C42—522no—
523C42#612712yes—
524C42#612712yes—
525C13#2375811yescharacteristic, complemented, Sylow
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—262no—
533C23—521no—
534C23—521no—
535C23—521no—
536C23—521no—
537C23—521no—
538C23—521no—
539C23#8820412yes—
540C23C22×C22⋊D1311yescharacteristic
541D4—262no—
542D4—262no—
543D4—528no—
544D4—521no—
545D4—521no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—262no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—1044no—
585C2×C4#8818312yes—
586C2×C4#8818312yes—
587C2×C4#8820312yes—
588C2×C4#8820412yes—
589C2×C4C2×#612711yescharacteristic
590C2×C4C2×#612711yescharacteristic
591C2×C4#41×D1311yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4#41×D1311yescharacteristic
594C2×C4#41×D1311yescharacteristic
595C8—262no—
596C8—262no—
597C8—521no—
598C8—521no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—522no—
607C22—522no—
608C22—522no—
609C22—1041no—
610C22—1041no—
611C22—1041no—
612C22—1041no—
613C22C2×#8818311yescharacteristic
614C22C2×#8820311yescharacteristic
615C22C2×#8820411yescharacteristic
616C22C2×#8820411yescharacteristic
617C22#1171952711yescharacteristic
618C22#1171953311yescharacteristic
619C22#1171953711yescharacteristic
620C4—22no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—522no—
629C4—1041no—
630C4—1041no—
631C4#1171866414yes—
632C4#1171923311yescharacteristic
633C4#1171923311yescharacteristic
634C4#1171923311yescharacteristic
635C4#1171923311yescharacteristic
636C2—42no—
637C2—1042no—
638C2#1311809311yescharacteristic
639C2C2×#1171866411yescharacteristic
640C2#1312474911yescharacteristic
641C2#1312484811yescharacteristic
642C2#1312487911yescharacteristic
643C2#1312540011yescharacteristic
644C2#1312543211yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2283C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2283D13
hypocenterC13#23758
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
2. #13116403C2semidirect
3. #13116360C2semidirect
4. #13116318C2semidirect
5. #13116272C2semidirect
6. #13116267C2semidirect
7. #13116250C2semidirect
10. C4×#88047C2semidirect
11. C4×#88048C2semidirect
12. C4×#88049C2semidirect
13. C4×#88049C2semidirect
14. C4×C22⋊#1055C2semidirect
15. C13×#2283C2semidirect
205. #2283D13semidirect
525. C13#23758semidirect

Maximal subgroups

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

subgroupindex
C4×#881842
#131164032
#131163602
#131163182
#131162722
#131162672
#131162502
#131160252
#131160182
C4×#880472
C4×#880482
C4×#880492
C4×C22⋊#10552
C13×#22832
#2375813