Finite Group Databasebeta

← #15866034

Subgroups — #15866034

Order 3328.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718679C211yesmaximal, characteristic
2#13117199C211yesmaximal, characteristic, complemented
3#13115460C211yesmaximal, characteristic
4#13115453C211yesmaximal, characteristic
5#13115425C211yesmaximal, characteristic, complemented
6#13115404C211yesmaximal, characteristic, complemented
7#13115194C211yesmaximal, characteristic
8#13115194C211yesmaximal, characteristic
9#13115103C211yesmaximal, characteristic, complemented
10#13115089C211yesmaximal, characteristic, complemented
11#13114734C211yesmaximal, characteristic, complemented
12C4×#88050C211yesmaximal, characteristic, complemented
13C4×#88072C211yesmaximal, characteristic
14#13114588C211yesmaximal, characteristic, complemented
15C13×#2319C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C22×#6105C2211yescharacteristic
18C2×C4×Dic26C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C2×C4×Dic26C2211yescharacteristic
21C13×#390C2211yescharacteristic
22C13×#390C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#388—21no—
26C13×#388—21no—
27C13×#381—21no—
28C13×#380—21no—
29C4×C13×C4⋊C4C2211yescharacteristic
30C13×#376C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34#11718679C418yescomplemented
35C2×#88050C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45C2×C4×#1055C2211yescharacteristic
46#11718310—21no—
47#11718310—21no—
48#11718310—21no—
49#11718309—21no—
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
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—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C4×Dic26—22no—
99C4×Dic26—22no—
100C4×Dic26—22no—
101C4×Dic26—22no—
102C4×Dic26—22no—
103C4×Dic26C2×C414yes—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109C13×#95D411yescharacteristic
110C13×#95D411yescharacteristic
111#88072—22no—
112#88072—22no—
113#88072C2×C414yes—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88050—22no—
118#88050—22no—
119#88050C2×C414yes—
120#88048—22no—
121#88047—22no—
122#88047C2×C414yes—
123#88043C2×C414yes—
124C4×#1055—22no—
125#21128—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×Dic26C22×C412yes—
154C2×Dic26#4112yes—
155C2×Dic26#4112yes—
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⋊Dic13C22×C412yes—
181C4⋊Dic13#4112yes—
182C4⋊Dic13#4112yes—
183#6101—24no—
184#6101—24no—
185#6101—24no—
186C4×Dic13—24no—
187C4×Dic13—24no—
188C4×Dic13—24no—
189C4×Dic13—81no—
190C4×Dic13—81no—
191C4×Dic13—81no—
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×#1055C22×C412yes—
203C2×#1055C22×C412yes—
204C2×#440—131no—
205#2319D1311yescharacteristic
206#2276—131no—
207#1926—131no—
208#1925—131no—
209#1921—131no—
210#1918—131no—
211#1880—131no—
212#1880—131no—
213#1865—131no—
214#1863—131no—
215#1776—131no—
216C4×#103—131no—
217C4×#102—131no—
218#1746—131no—
219C23×C13—22no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13C22×D411yescharacteristic
227D4×C13—22no—
228D4×C13—22no—
229D4×C13—41no—
230D4×C13—41no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—22no—
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—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—84no—
257C2×C4×C13C4×D412yes—
258C2×C4×C13C4×D412yes—
259C2×C4×C13C23×C411yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277Dic26—22no—
278Dic26—22no—
279Dic26—22no—
280Dic26#11714yes—
281#1055—22no—
282#1055—22no—
283#1055—41no—
284#1055—41no—
285C22×SD16—131no—
286C2×C4×Q8—131no—
287C2×C4×Q8—131no—
288C2×C4×Q8—131no—
289C2×C4×D4C2×D1311yescharacteristic
290#440—138no—
291C2×#107—131no—
292C2×#107—131no—
293C2×#106—131no—
294C2×#103—131no—
295C2×#103—131no—
296C2×#103—131no—
297C2×#102—131no—
298C2×#102—131no—
299C2×#102—131no—
300C2×#97—131no—
301C2×C4×C8—131no—
302#390C2×D1311yescharacteristic
303#390C2×D1311yescharacteristic
304#389C2×D1311yescharacteristic
305#389C2×D1311yescharacteristic
306#388—21no—
307#388—21no—
308#381—21no—
309#380—21no—
310C4×C4⋊C4—131no—
311C4×C4⋊C4—131no—
312C4×C4⋊C4—131no—
313C4×C4⋊C4—261no—
314C4×C4⋊C4—261no—
315C4×C4⋊C4—261no—
316C4×C4⋊C4C2×D1311yescharacteristic
317#376—261no—
318#376C2×D1311yescharacteristic
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#336—131no—
326#336—131no—
327#336—131no—
328#336—131no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—42no—
332C22×C13—81no—
333C22×C13—81no—
334C22×C13—81no—
335C22×C13—81no—
336C22×C13C2×C4×D411yescharacteristic
337C22×C13#52511yescharacteristic
338C22×C13#52511yescharacteristic
339C22×C13#57611yescharacteristic
340C22×C13#57711yescharacteristic
341C22×C13#57711yescharacteristic
342C22×C13#57811yescharacteristic
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—41no—
349C4×C13—42no—
350C4×C13—81no—
351C4×C13—81no—
352C4×C13C2×#11711yescharacteristic
353C4×C13C4×#4111yescharacteristic
354C4×C13#52911yescharacteristic
355C4×C13#52911yescharacteristic
356Dic13—24no—
357Dic13—42no—
358Dic13—42no—
359Dic13—42no—
360C22×Q8—131no—
361C22×D4C22×D1311yescharacteristic
362C23×C4—21no—
363C2×SD16—134no—
364C2×SD16—262no—
365C2×SD16—262no—
366C22×C8—131no—
367C22×C8—131no—
368C22×C8—131no—
369C22×C8—131no—
370C4×Q8—134no—
371C4×Q8—262no—
372C4×Q8—262no—
373C4×Q8—262no—
374C4×Q8—262no—
375C4×Q8—262no—
376C4×D4—22no—
377C4×D4C4×D1314yes—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395C2×C42—261no—
396C2×C42—261no—
397C2×C42—261no—
398C2×C42—261no—
399C2×C42—261no—
400C2×C42—261no—
401C2×C42C22×D1311yescharacteristic
402C2×C42C22×D1311yescharacteristic
403C2×C42C22×D1311yescharacteristic
404#107—134no—
405#107—262no—
406#106—262no—
407#103—134no—
408#103—262no—
409#103—262no—
410#102—134no—
411#102—262no—
412#102—262no—
413#97—134no—
414C4×C8—262no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—261no—
419#95—261no—
420#95—261no—
421#95C22⋊D1311yescharacteristic
422#95C22⋊D1311yescharacteristic
423#95C22⋊D1311yescharacteristic
424#95C22⋊D1311yescharacteristic
425C2×C13—82no—
426C2×C13#229011yescharacteristic
427C2×C13#294611yescharacteristic
428C2×C13#294711yescharacteristic
429C2×C13#311911yescharacteristic
430C2×C13#312111yescharacteristic
431C2×C13#312411yescharacteristic
432C2×C13#312611yescharacteristic
433C24—21no—
434C2×Q8—132no—
435C2×Q8—132no—
436C2×Q8—132no—
437C2×Q8—261no—
438C2×Q8—261no—
439C2×Q8—261no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4C2×C4×D1312yes—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4C2×C22⋊D1311yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C23×D1311yescharacteristic
463SD16—268no—
464C2×C8—132no—
465C2×C8—132no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—132no—
484C4⋊C4—132no—
485C4⋊C4—132no—
486C4⋊C4—264no—
487C4⋊C4—264no—
488C4⋊C4—264no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4C2×C4×D1312yes—
493C22⋊C4—24no—
494C22⋊C4—81no—
495C22⋊C4—81no—
496C22⋊C4—81no—
497C22⋊C4—81no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—81no—
503C42—264no—
504C42—264no—
505C42—264no—
506C42—1041no—
507C42—1041no—
508C42—1041no—
509C42C2×C4×D1312yes—
510C42#612712yes—
511C13#2112811yescharacteristic, complemented, Sylow
512C23—22no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23C22×C22⋊D1311yescharacteristic
520Q8—134no—
521Q8—262no—
522Q8—262no—
523Q8—262no—
524D4—22no—
525D4—22no—
526D4—41no—
527D4—41no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—84no—
554C2×C4—262no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—262no—
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×C4C4×C22⋊D1312yes—
567C2×C4C4×C22⋊D1312yes—
568C2×C4C22×C4×D1311yescharacteristic
569C2×C4C2×#612711yescharacteristic
570C2×C4#41×D1311yescharacteristic
571C2×C4#41×D1311yescharacteristic
572C2×C4#41×D1311yescharacteristic
573C2×C4#41×D1311yescharacteristic
574C8—262no—
575C8—262no—
576C8—521no—
577C8—521no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22C2×C4×C22⋊D1311yescharacteristic
586C22#1171953311yescharacteristic
587C22#1171953311yescharacteristic
588C22#1171954011yescharacteristic
589C22#1171954111yescharacteristic
590C22#1171954111yescharacteristic
591C22#1171954311yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—264no—
602C4—522no—
603C4—522no—
604C4—522no—
605C4D13×#11711yescharacteristic
606C4#1171922711yescharacteristic
607C4#1171923311yescharacteristic
608C4#1171923311yescharacteristic
609C2—82no—
610C2#1311727311yescharacteristic
611C2#1312366811yescharacteristic
612C2#1312367511yescharacteristic
613C2#1312502911yescharacteristic
614C2#1312505911yescharacteristic
615C2#1312509211yescharacteristic
616C2#1312512211yescharacteristic
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#21128
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. #13117199C2semidirect
5. #13115425C2semidirect
6. #13115404C2semidirect
9. #13115103C2semidirect
10. #13115089C2semidirect
11. #13114734C2semidirect
12. C4×#88050C2semidirect
14. #13114588C2semidirect
34. #11718679C4semidirect
511. C13#21128semidirect

Maximal subgroups

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

subgroupindex
C2×#117186792
#131171992
#131154602
#131154532
#131154252
#131154042
#131151942
#131151032
#131150892
#131147342
C4×#880502
C4×#880722
#131145882
C13×#23192
#2112813