Finite Group Databasebeta

← #15926020

Subgroups — #15926020

Order 3328.

848 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic
2C2×C4×#6105C211yesmaximal, characteristic
3#13118697C211yesmaximal, characteristic, complemented
4#13116387C211yesmaximal, characteristic, complemented
5#13116318C211yesmaximal, characteristic, complemented
6#13116214C211yesmaximal, characteristic, complemented
7#13116174C211yesmaximal, characteristic, complemented
8#13115561C211yesmaximal, characteristic, complemented
9#13115395C211yesmaximal, characteristic, complemented
10#13115170C211yesmaximal, characteristic
11#13115170C211yesmaximal, characteristic
12#13115097C211yesmaximal, characteristic
13#13115089C211yesmaximal, characteristic, complemented
14#13115083C211yesmaximal, characteristic
15C13×#2349C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×#6105C2211yescharacteristic
20C2×#88124C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#385—21no—
25C13×#385—21no—
26C13×#382C2211yescharacteristic
27C13×#380—21no—
28C4×C13×C4⋊C4C2211yescharacteristic
29C2×C13×#95—21no—
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C4×#6105—24no—
34#11718670—24no—
35#11718641—21no—
36#11718633—21no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718590C2211yescharacteristic
46#11718590C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718319—21no—
52#11718313—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C22×Dic26C2311yescharacteristic
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—41no—
71C4×D4×C13—41no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×#6105—22no—
86C2×#6105—22no—
87C2×#6105Q814yes—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×C4×Dic13—21no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101#88124—22no—
102#88124—41no—
103C4×Dic26—22no—
104C4×Dic26—41no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95D411yescharacteristic
110C13×#95D411yescharacteristic
111#88072—22no—
112#88072—22no—
113#88072D414yes—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88050—22no—
121#88050—22no—
122#88050—41no—
123#88048—22no—
124#88048—22no—
125#88048—22no—
126#88047—22no—
127#88047—41no—
128C4⋊#1055—22no—
129C4×#1055—22no—
130#26378—131nomaximal, Sylow
131C24×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13C2×D412yes—
136C2×D4×C13C2×Q812yes—
137C2×D4×C13#4112yes—
138C22×C4×C13—21no—
139C22×C4×C13—24no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—81no—
147C22×C4×C13—81no—
148C22×C4×C13—81no—
149C22×C4×C13—81no—
150C22×C4×C13C2×D411yescharacteristic
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×Dic26C2×Q812yes—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—41no—
174C13×C4⋊C4—81no—
175C13×C4⋊C4—81no—
176C13×C4⋊C4#4112yes—
177C13×C22⋊C4—24no—
178C13×C22⋊C4—42no—
179C13×C22⋊C4—42no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186#6105—28no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13C2×D412yes—
193#6101—42no—
194#6101—42no—
195#6101—42no—
196#6101—42no—
197#6101—42no—
198C4×Dic13—42no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055C2×D412yes—
210C2×#1055C2×Q812yes—
211C2×#478—131no—
212C2×C4×SD16—131no—
213#2453—131no—
214#2349D1311yescharacteristic
215#2097—131no—
216#2085—131no—
217#2066—131no—
218#2059—131no—
219#1941—131no—
220#1916—131no—
221#1877—131no—
222#1877—131no—
223#1864—131no—
224#1863—131no—
225#1862—131no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13—41no—
232C23×C13—41no—
233C23×C13C22×D411yescharacteristic
234D4×C13—22no—
235D4×C13—22no—
236D4×C13—22no—
237D4×C13C22⋊Q814yes—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—22no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
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—41no—
264C2×C4×C13—84no—
265C2×C4×C13—84no—
266C2×C4×C13—84no—
267C2×C4×C13#13512yes—
268C2×C4×C13C22×D411yescharacteristic
269C2×C4×C13C22×Q811yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13H(5,𝔽2)11yescharacteristic
273C2×C4×C132−1+411yescharacteristic
274C2×Dic13—22no—
275C2×Dic13—22no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286Dic26—22no—
287Dic26—22no—
288Dic26—41no—
289Dic26—41no—
290#1055—22no—
291#1055—22no—
292#1055—41no—
293#1055—41no—
294C22×SD16—131no—
295C2×#125—131no—
296C2×C4×Q8—131no—
297C2×C4×D4C2×D1311yescharacteristic
298C2×C4×D4C2×D1311yescharacteristic
299C2×C4×D4C2×D1311yescharacteristic
300#478—264no—
301C4×SD16—264no—
302C2×#107—131no—
303C2×#107—131no—
304C2×#106—131no—
305C2×#106—131no—
306C2×#106—131no—
307C2×C4⋊C8—131no—
308C2×#103—131no—
309C2×#103—131no—
310C2×#103—131no—
311C2×#102—131no—
312C2×#102—131no—
313C2×#102—131no—
314C2×C4×C8—131no—
315#400—261no—
316#398—261no—
317#391—131no—
318#391—131no—
319#389—131no—
320#389—131no—
321#389—261no—
322#389C2×D1311yescharacteristic
323#389C2×D1311yescharacteristic
324#387—261no—
325#385—21no—
326#385—21no—
327#382C2×D1311yescharacteristic
328#380—21no—
329C4×C4⋊C4C2×D1311yescharacteristic
330C2×#95—21no—
331#340—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#336—131no—
336#336—131no—
337#336—131no—
338#336—131no—
339C22×C13—24no—
340C22×C13—42no—
341C22×C13—42no—
342C22×C13—42no—
343C22×C13—42no—
344C22×C13—42no—
345C22×C13—42no—
346C22×C13#52511yescharacteristic
347C22×C13D4211yescharacteristic
348C22×C13D4×Q811yescharacteristic
349C22×C13C2×#13511yescharacteristic
350C22×C13#57511yescharacteristic
351C22×C13#57711yescharacteristic
352C22×C13#57711yescharacteristic
353C4×C13—22no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—42no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13—41no—
360C4×C13—81no—
361C4×C13—81no—
362C4×C13C2×C22⋊Q811yescharacteristic
363C4×C13#53911yescharacteristic
364C4×C13#54711yescharacteristic
365C4×C13#55411yescharacteristic
366Dic13—42no—
367Dic13—42no—
368Dic13—81no—
369Dic13—81no—
370C22×Q8—131no—
371C22×D4C22×D1311yescharacteristic
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—21no—
375C2×SD16—134no—
376C2×SD16—262no—
377C2×SD16—262no—
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381C22×C8—131no—
382#125—262no—
383#125—521no—
384C4×Q8—262no—
385C4×Q8—521no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—41no—
391C4×D4—41no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4C22⋊D1311yescharacteristic
403C2×C4⋊C4C22⋊D1311yescharacteristic
404C2×C4⋊C4C22×D1311yescharacteristic
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C42—261no—
411C2×C42C22×D1311yescharacteristic
412C2×C42C22×D1311yescharacteristic
413C2×C42C22×D1311yescharacteristic
414#107—262no—
415#107—521no—
416#106—262no—
417#106—262no—
418#106—262no—
419C4⋊C8—262no—
420#103—262no—
421#103—262no—
422#103—521no—
423#102—134no—
424#102—262no—
425#102—262no—
426C4×C8—262no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—261no—
432#95—261no—
433#95—261no—
434#95—261no—
435#95—261no—
436#95—261no—
437#95C22⋊D1311yescharacteristic
438#95C22⋊D1311yescharacteristic
439C2×C13—44no—
440C2×C13#244911yescharacteristic
441C2×C13#310211yescharacteristic
442C2×C13#312311yescharacteristic
443C2×C13#326711yescharacteristic
444C2×C13#328211yescharacteristic
445C2×C13#338111yescharacteristic
446C2×C13#338811yescharacteristic
447C24—21no—
448C2×Q8—132no—
449C2×Q8—261no—
450C2×Q8—261no—
451C2×Q8—261no—
452C2×Q8—261no—
453C2×Q8—261no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4#612712yes—
458C2×D4D4×D1312yes—
459C2×D4Q8×D1312yes—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4—81no—
470C22×C4—81no—
471C22×C4—81no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C2×C22⋊D1311yescharacteristic
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C2×C22⋊D1311yescharacteristic
480C22×C4C2×C22⋊D1311yescharacteristic
481C22×C4C2×C22⋊D1311yescharacteristic
482C22×C4C23×D1311yescharacteristic
483SD16—268no—
484C2×C8—132no—
485C2×C8—132no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—41no—
503C4⋊C4—81no—
504C4⋊C4—81no—
505C4⋊C4—132no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—522no—
512C4⋊C4—522no—
513C4⋊C4—522no—
514C4⋊C4—522no—
515C4⋊C4—522no—
516C4⋊C4#612712yes—
517C22⋊C4—24no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—522no—
527C13#2637811yescharacteristic, complemented, Sylow
528C23—22no—
529C23—22no—
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23C22×C22⋊D1311yescharacteristic
536Q8—262no—
537Q8—262no—
538Q8—521no—
539Q8—521no—
540D4—22no—
541D4—22no—
542D4—22no—
543D4#8815014yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
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—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
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—84no—
571C2×C4—84no—
572C2×C4—84no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—521no—
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—521no—
585C2×C4#8820412yes—
586C2×C4C2×#612711yescharacteristic
587C2×C4C2×#612711yescharacteristic
588C2×C4C2×D4×D1311yescharacteristic
589C2×C4#8825111yescharacteristic
590C2×C4C2×Q8×D1311yescharacteristic
591C2×C4#8825411yescharacteristic
592C8—262no—
593C8—262no—
594C8—521no—
595C8—521no—
596C22—24no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22#1171949611yescharacteristic
604C22D4×C22⋊D1311yescharacteristic
605C22Q8×C22⋊D1311yescharacteristic
606C22C2×#8820411yescharacteristic
607C22#1171952711yescharacteristic
608C22#1171954111yescharacteristic
609C22#1171954111yescharacteristic
610C4—22no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—42no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4—522no—
620C4—522no—
621C4—1041no—
622C4—1041no—
623C4#1171921211yescharacteristic
624C4C2×#8815011yescharacteristic
625C4#1171921611yescharacteristic
626C4#1171922011yescharacteristic
627C2—44no—
628C2#1311864511yescharacteristic
629C2#1312485411yescharacteristic
630C2#1312508811yescharacteristic
631C2#1312635711yescharacteristic
632C2#1312653911yescharacteristic
633C2#1312771111yescharacteristic
634C2#1312778111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2349C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2349D13
hypocenterC13#26378
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #13118697C2semidirect
4. #13116387C2semidirect
5. #13116318C2semidirect
6. #13116214C2semidirect
7. #13116174C2semidirect
8. #13115561C2semidirect
9. #13115395C2semidirect
13. #13115089C2semidirect
527. C13#26378semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
C2×C4×#61052
#131186972
#131163872
#131163182
#131162142
#131161742
#131155612
#131153952
#131151702
#131150972
#131150892
#131150832
C13×#23492
#2637813