Finite Group Databasebeta

← #15867297

Subgroups — #15867297

Order 3328.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718679C211yesmaximal, characteristic
2#13117488C211yesmaximal, characteristic, complemented
3#13115716C211yesmaximal, characteristic
4#13115689C211yesmaximal, characteristic
5#13115571C211yesmaximal, characteristic, complemented
6#13115566C211yesmaximal, characteristic, complemented
7#13115536C211yesmaximal, characteristic
8#13115525C211yesmaximal, characteristic, complemented
9#13115522C211yesmaximal, characteristic
10#13115511C211yesmaximal, characteristic, complemented
11#13114734C211yesmaximal, characteristic, complemented
12C4×#88050C211yesmaximal, characteristic, complemented
13C4×#88072C211yesmaximal, characteristic
14#13114523C211yesmaximal, characteristic, complemented
15C13×#2319C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C22×#6105C2211yescharacteristic
18C2×C4×Dic26C2211yescharacteristic
19C13×#390C2211yescharacteristic
20C13×#390C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#388—21no—
24C13×#388—21no—
25C13×#381—21no—
26C13×#380—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C13×#376C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718679C418yescomplemented
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718590C2211yescharacteristic
41#11718590C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718589C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45C2×#88043C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47C2×C4×#1055C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718313—21no—
51#11718313—21no—
52#11718312—21no—
53#11718311—21no—
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C22×Dic26C2311yescharacteristic
63C4×D4×C13—22no—
64C4×D4×C13C2×C414yes—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C22⋊C4—21no—
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×#6105—22no—
80C2×#6105—22no—
81C2×#6105C2×C414yes—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C4×Dic26—22no—
95C4×Dic26C2×C414yes—
96C13×#95—21no—
97C13×#95—21no—
98C13×#95—21no—
99C13×#95D411yescharacteristic
100C13×#95D411yescharacteristic
101C13×#95D411yescharacteristic
102C13×#95D411yescharacteristic
103#88072—22no—
104#88072—22no—
105#88072C2×C414yes—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88050—22no—
114#88050—22no—
115#88050C2×C414yes—
116#88048—22no—
117#88047—22no—
118#88047C2×C414yes—
119#88043—22no—
120#88043—22no—
121#88043C2×C414yes—
122C4×#1055—22no—
123C4×#1055—22no—
124C4×#1055—22no—
125#21291—131nomaximal, Sylow
126C24×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13C22×C412yes—
133C22×C4×C13—21no—
134C22×C4×C13—24no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—81no—
138C22×C4×C13—81no—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2411yescharacteristic
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26C22×C412yes—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—81no—
162C13×C4⋊C4—81no—
163C13×C4⋊C4C22×C412yes—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—81no—
166C13×C22⋊C4—81no—
167C13×C22⋊C4—81no—
168C13×C22⋊C4—81no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—81no—
174C42×C13C22×C412yes—
175C42×C13#4112yes—
176#6105—28no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13C22×C412yes—
183#6101—24no—
184#6101—81no—
185#6101—81no—
186C4×Dic13—24no—
187C4×Dic13—81no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055C22×C412yes—
195C2×#1055C22×C412yes—
196C2×#1055#4112yes—
197C2×#1055#4112yes—
198C2×#1055#4112yes—
199C2×#1055#4112yes—
200C2×#440—131no—
201#2320—131no—
202#2319D1311yescharacteristic
203#1973—131no—
204#1968—131no—
205#1943—131no—
206#1942—131no—
207#1936—131no—
208#1935—131no—
209#1934—131no—
210#1933—131no—
211#1776—131no—
212C4×#103—131no—
213C4×#102—131no—
214#1726—131no—
215C23×C13—22no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13C22×D411yescharacteristic
223D4×C13—22no—
224D4×C13—22no—
225D4×C13—41no—
226D4×C13—41no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—22no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
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—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—84no—
253C2×C4×C13C4×D412yes—
254C2×C4×C13C4×D412yes—
255C2×C4×C13C23×C411yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273Dic26—22no—
274Dic26—22no—
275Dic26—41no—
276Dic26—41no—
277#1055—22no—
278#1055—22no—
279#1055—22no—
280#1055#11714yes—
281C22×SD16—131no—
282C2×C4×Q8—131no—
283C2×C4×D4C2×D1311yescharacteristic
284#440—138no—
285C2×#107—131no—
286C2×#107—131no—
287C2×#106—131no—
288C2×#103—131no—
289C2×#103—131no—
290C2×#103—131no—
291C2×#102—131no—
292C2×#102—131no—
293C2×#102—131no—
294C2×#97—131no—
295C2×#97—131no—
296C2×#97—131no—
297C2×C4×C8—131no—
298C2×C4×C8—131no—
299C2×C4×C8—131no—
300#391—131no—
301#391—131no—
302#390C2×D1311yescharacteristic
303#390C2×D1311yescharacteristic
304#389—131no—
305#389—131no—
306#389C2×D1311yescharacteristic
307#389C2×D1311yescharacteristic
308#388—21no—
309#388—21no—
310#387—261no—
311#387—261no—
312#383—261no—
313#382—261no—
314#381—21no—
315#380—21no—
316C4×C4⋊C4—131no—
317C4×C4⋊C4C2×D1311yescharacteristic
318#376C2×D1311yescharacteristic
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—42no—
328C22×C13—81no—
329C22×C13—81no—
330C22×C13—81no—
331C22×C13—81no—
332C22×C13C2×C4×D411yescharacteristic
333C22×C13#53211yescharacteristic
334C22×C13#53211yescharacteristic
335C22×C13#57611yescharacteristic
336C22×C13#57711yescharacteristic
337C22×C13#57711yescharacteristic
338C22×C13#57811yescharacteristic
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13—42no—
346C4×C13—81no—
347C4×C13—81no—
348C4×C13C2×#11711yescharacteristic
349C4×C13C4×#4111yescharacteristic
350C4×C13#52911yescharacteristic
351C4×C13#52911yescharacteristic
352Dic13—42no—
353Dic13—42no—
354Dic13—81no—
355Dic13—81no—
356C22×Q8—131no—
357C22×D4C22×D1311yescharacteristic
358C23×C4—21no—
359C2×SD16—134no—
360C2×SD16—262no—
361C2×SD16—262no—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8—131no—
365C22×C8—131no—
366C4×Q8—134no—
367C4×Q8—262no—
368C4×D4—22no—
369C4×D4C4×D1314yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—21no—
387C2×C42—261no—
388C2×C42—261no—
389C2×C42C22×D1311yescharacteristic
390C2×C42C22×D1311yescharacteristic
391C2×C42C22×D1311yescharacteristic
392#107—134no—
393#107—262no—
394#106—262no—
395#103—134no—
396#103—262no—
397#103—262no—
398#102—134no—
399#102—262no—
400#102—262no—
401#97—134no—
402#97—262no—
403#97—262no—
404C4×C8—262no—
405C4×C8—262no—
406C4×C8—262no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95C22⋊D1311yescharacteristic
418#95C22⋊D1311yescharacteristic
419#95C22⋊D1311yescharacteristic
420#95C22⋊D1311yescharacteristic
421C2×C13—82no—
422C2×C13#229311yescharacteristic
423C2×C13#294611yescharacteristic
424C2×C13#294711yescharacteristic
425C2×C13#317411yescharacteristic
426C2×C13#317511yescharacteristic
427C2×C13#317811yescharacteristic
428C2×C13#317911yescharacteristic
429C24—21no—
430C2×Q8—132no—
431C2×Q8—261no—
432C2×Q8—261no—
433C2×Q8—261no—
434C2×Q8—261no—
435C2×Q8—261no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×C4×D1312yes—
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—81no—
447C22×C4—81no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4C2×C22⋊D1311yescharacteristic
453C22×C4C2×C22⋊D1311yescharacteristic
454C22×C4C2×C22⋊D1311yescharacteristic
455C22×C4C2×C22⋊D1311yescharacteristic
456C22×C4C2×C22⋊D1311yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459SD16—268no—
460C2×C8—132no—
461C2×C8—132no—
462C2×C8—132no—
463C2×C8—132no—
464C2×C8—132no—
465C2×C8—132no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—132no—
480C4⋊C4—264no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—1041no—
487C4⋊C4—1041no—
488C4⋊C4C2×C4×D1312yes—
489C22⋊C4—24no—
490C22⋊C4—81no—
491C22⋊C4—81no—
492C22⋊C4—81no—
493C22⋊C4—81no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—81no—
499C42—264no—
500C42—1041no—
501C42C2×C4×D1312yes—
502C42#612712yes—
503C13#2129111yescharacteristic, complemented, Sylow
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×C22⋊D1311yescharacteristic
512Q8—262no—
513Q8—262no—
514Q8—521no—
515Q8—521no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4C4×C22⋊D1312yes—
559C2×C4C4×C22⋊D1312yes—
560C2×C4C22×C4×D1311yescharacteristic
561C2×C4C2×#612711yescharacteristic
562C2×C4#41×D1311yescharacteristic
563C2×C4#41×D1311yescharacteristic
564C2×C4#41×D1311yescharacteristic
565C2×C4#41×D1311yescharacteristic
566C8—134no—
567C8—262no—
568C8—262no—
569C8—262no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×C4×C22⋊D1311yescharacteristic
578C22#1171953711yescharacteristic
579C22#1171953711yescharacteristic
580C22#1171954011yescharacteristic
581C22#1171954111yescharacteristic
582C22#1171954111yescharacteristic
583C22#1171954311yescharacteristic
584C4—22no—
585C4—22no—
586C4—41no—
587C4—42no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—522no—
594C4—522no—
595C4—1041no—
596C4—1041no—
597C4D13×#11711yescharacteristic
598C4#1171922711yescharacteristic
599C4#1171923311yescharacteristic
600C4#1171923311yescharacteristic
601C2—82no—
602C2#1311729511yescharacteristic
603C2#1312366811yescharacteristic
604C2#1312367511yescharacteristic
605C2#1312545811yescharacteristic
606C2#1312546911yescharacteristic
607C2#1312549811yescharacteristic
608C2#1312552111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2319C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#2319D13
hypocenterC13#21291
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #13117488C2semidirect
5. #13115571C2semidirect
6. #13115566C2semidirect
8. #13115525C2semidirect
10. #13115511C2semidirect
11. #13114734C2semidirect
12. C4×#88050C2semidirect
14. #13114523C2semidirect
32. #11718679C4semidirect
503. C13#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#117186792
#131174882
#131157162
#131156892
#131155712
#131155662
#131155362
#131155252
#131155222
#131155112
#131147342
C4×#880502
C4×#880722
#131145232
C13×#23192
#2129113