Finite Group Databasebeta

← #15867793

Subgroups — #15867793

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718496C211yesmaximal, characteristic
2#13117229C211yesmaximal, characteristic
3C4×C4⋊C4×D13C211yesmaximal, characteristic
4#13115606C211yesmaximal, characteristic, complemented
5#13115604C211yesmaximal, characteristic, complemented
6#13115602C211yesmaximal, characteristic, complemented
7#13115030C211yesmaximal, characteristic
8#13115027C211yesmaximal, characteristic
9#13115025C211yesmaximal, characteristic
10#13115022C211yesmaximal, characteristic
11#13114736C211yesmaximal, characteristic, complemented
12#13114735C211yesmaximal, characteristic, complemented
13#13114732C211yesmaximal, characteristic, complemented
14#13114732C211yesmaximal, characteristic, complemented
15C13×#1949C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D13C2211yescharacteristic
17C2×C4⋊C4×D13C2211yescharacteristic
18C2×C42×D13—21no—
19C2×C42×D13C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C13×#382C2211yescharacteristic
24C4×C13×C4⋊C4C2211yescharacteristic
25C2×#88060C2211yescharacteristic
26C2×#88060C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88057C2211yescharacteristic
29C2×#88055C2211yescharacteristic
30C2×#88055C2211yescharacteristic
31#11718648C2211yescharacteristic
32#11718648C2211yescharacteristic
33C4⋊C4×Dic13C2211yescharacteristic
34C4⋊C4×Dic13C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718597C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43C4×#6101—21no—
44C2×C4⋊#1055C2211yescharacteristic
45#11718496C418yescomplemented
46#11718327—21no—
47#11718325—21no—
48D13×#95—21no—
49#11718312—21no—
50#11718310—21no—
51#11718309—21no—
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×C4×D13D411yescharacteristic
63C22×C4×D13D411yescharacteristic
64C22×C4×D13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C42×C13—21no—
72C2×C42×C13C2311yescharacteristic
73C2×#6103—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13C2311yescharacteristic
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×#6101—21no—
80C2×#6101—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13D411yescharacteristic
87C2×C4×Dic13D411yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C4⋊C4×D13—22no—
92C4⋊C4×D13—22no—
93C4⋊C4×D13—22no—
94C4⋊C4×D13—22no—
95C42×D13—44no—
96C42×D13C2×C414yes—
97C42×D13Q814yes—
98C13×#107—22no—
99C13×#106—22no—
100C13×C4⋊C8C2×C414yescomplemented
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88060C2×C414yes—
114#88060C2×C414yes—
115#88058—22no—
116#88057—22no—
117#88055C2×C414yescomplemented
118#88055C2×C414yescomplemented
119#88048—22no—
120#88048—22no—
121#88047—22no—
122#88047—22no—
123C4⋊#1055C2×C414yescomplemented
124#21363—131nomaximal, Sylow
125C23×D13C2×D411yescharacteristic
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C22×Dic13C2×D411yescharacteristic
140C2×C4×D13—22no—
141C2×C4×D13—22no—
142C2×C4×D13—21no—
143C2×C4×D13—21no—
144C2×C4×D13—21no—
145C2×C4×D13—21no—
146C2×C4×D13—24no—
147C2×C4×D13—24no—
148C2×C4×D13—41no—
149C2×C4×D13—41no—
150C2×C4×D13—42no—
151C2×C4×D13—42no—
152C2×C4×D13—42no—
153C2×C4×D13—42no—
154C2×C4×D13C4⋊C414yes—
155C2×C4×D13C4⋊C414yes—
156C2×C4×D13C22×C412yes—
157C2×C4×D13C2×Q812yes—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13C22×C412yes—
163C2×C8×C13C22×C412yes—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4#4112yes—
171C13×C4⋊C4#4112yes—
172C42×C13—42no—
173C42×C13C22×C412yes—
174C42×C13C2×Q812yes—
175#6103—42no—
176#6103—42no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13#4112yes—
184C4⋊Dic13#4112yes—
185#6101—24no—
186#6101—24no—
187C4×Dic13—42no—
188C4×Dic13—42no—
189C4×Dic13—42no—
190C4×Dic13—42no—
191C4×Dic13—42no—
192C4×Dic13C4⋊C414yes—
193C4×Dic13C4⋊C414yes—
194C4×Dic13C22×C412yes—
195C4×Dic13C2×Q812yes—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055C22×C412yes—
201C2×#1055C22×C412yes—
202C2×#432—131no—
203#2283—131no—
204C2×C4×C4⋊C4—131no—
205#1949—131no—
206#1949—131no—
207#1949—131no—
208#1949D1311yescharacteristic, complemented
209#1853—131no—
210#1853—131no—
211#1852—131no—
212#1852—131no—
213#1776—131no—
214#1776—131no—
215#1776—131no—
216#1776—131no—
217C23×C13C22×D411yescharacteristic
218C22×D13—21no—
219C22×D13—21no—
220C22×D13—21no—
221C22×D13—21no—
222C22×D13C2×C4⋊C412yes—
223C22×D13AGL(1,ℤ/8)12yes—
224C22×D13#13712yes—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13C2×C4⋊C412yes—
242C2×C4×C13C2×C4⋊C412yes—
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×Q811yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13C2×C4⋊C412yes—
268C2×Dic13C2×C4⋊C412yes—
269C2×Dic13C2×C4⋊C412yes—
270C4×D13—28no—
271C4×D13—22no—
272C4×D13—22no—
273C4×D13—22no—
274C4×D13—22no—
275C4×D13—44no—
276C4×D13—48no—
277C4×D13—48no—
278C8×C13—22no—
279C8×C13—22no—
280#1055—22no—
281#1055—22no—
282C22×C4⋊C4—131no—
283C22×C4⋊C4—131no—
284C22×C42—131no—
285C22×C42—261no—
286#432—138no—
287C2×#107—131no—
288C2×#107—131no—
289C2×#107—131no—
290C2×#107C2×D1311yescharacteristic
291C2×#106—131no—
292C2×#106—131no—
293C2×#106—131no—
294C2×#106C2×D1311yescharacteristic
295C2×C4⋊C8—131no—
296C2×C4⋊C8C2×D1311yescharacteristic
297C2×C22⋊C8—131no—
298C2×C22⋊C8—131no—
299C2×#97—131no—
300C2×#97—131no—
301#383—261no—
302#382—131no—
303#382C2×D1311yescharacteristic
304#381—261no—
305#380—131no—
306#380—131no—
307C4×C4⋊C4—131no—
308C4×C4⋊C4—131no—
309C4×C4⋊C4—131no—
310C4×C4⋊C4—131no—
311C4×C4⋊C4—131no—
312C4×C4⋊C4—261no—
313C4×C4⋊C4—261no—
314C4×C4⋊C4C2×D1311yescharacteristic
315C4×C22⋊C4—261no—
316#376—261no—
317C2×#95—261no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340C2×D1311yescharacteristic
325#340C2×D1311yescharacteristic
326C22×C13C22×C4⋊C411yescharacteristic
327C22×C13#52511yescharacteristic
328C22×C13#52511yescharacteristic
329C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C13C2×#13711yescharacteristic
331C22×C13#57511yescharacteristic
332C22×C13#57511yescharacteristic
333C2×D13—22no—
334C2×D13—22no—
335C2×D13—22no—
336C2×D13—22no—
337C2×D13—22no—
338C2×D13—22no—
339C2×D13#42814yes—
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—42no—
343C4×C13—42no—
344C4×C13—81no—
345C4×C13—81no—
346C4×C13C4×#4111yescharacteristic
347C4×C13C4×#4111yescharacteristic
348C4×C13#53311yescharacteristic
349C4×C13#53311yescharacteristic
350Dic13—22no—
351Dic13—22no—
352Dic13—22no—
353Dic13—42no—
354Dic13—42no—
355Dic13—81no—
356Dic13—81no—
357C23×C4—131no—
358C23×C4—131no—
359C23×C4—131no—
360C23×C4—261no—
361C23×C4—261no—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8C22×D1311yescharacteristic
365C22×C8C22×D1311yescharacteristic
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—262no—
371C2×C4⋊C4—262no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—262no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C22⋊C4—261no—
381C2×C22⋊C4—261no—
382C2×C42—21no—
383C2×C42—131no—
384C2×C42—131no—
385C2×C42—131no—
386C2×C42—134no—
387C2×C42—134no—
388C2×C42—261no—
389C2×C42—261no—
390C2×C42—261no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42—524no—
394C2×C42C22×D1311yescharacteristic
395#107—22no—
396#107—262no—
397#107—262no—
398#107—262no—
399#106—22no—
400#106—262no—
401#106—262no—
402#106—262no—
403C4⋊C8—134no—
404C4⋊C8C4×D1314yescomplemented
405C22⋊C8—134no—
406C22⋊C8—134no—
407#97—134no—
408#97—134no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421C2×C13#229611yescharacteristic
422C2×C13C2×#42811yescharacteristic
423C2×C13#291111yescharacteristic
424C2×C13#311411yescharacteristic
425C2×C13#311411yescharacteristic
426C2×C13#311711yescharacteristic
427C2×C13#311711yescharacteristic
428D13—24no—
429C24—131no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—134no—
438C22×C4—132no—
439C22×C4—132no—
440C22×C4—134no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—264no—
444C22×C4—264no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—521no—
454C22×C4—521no—
455C22×C4—522no—
456C22×C4—522no—
457C22×C4—522no—
458C22×C4—522no—
459C22×C4D4×D1311yescharacteristic
460C22×C4D4×D1311yescharacteristic
461C22×C4C23×D1311yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—132no—
467C2×C8—132no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8C2×C4×D1312yes—
473C2×C8C2×C4×D1312yes—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—132no—
481C4⋊C4—132no—
482C4⋊C4—264no—
483C4⋊C4—264no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4#612912yes—
491C4⋊C4#613112yes—
492C22⋊C4—522no—
493C22⋊C4—522no—
494C42—42no—
495C42—134no—
496C42—134no—
497C42—132no—
498C42—132no—
499C42—522no—
500C42—522no—
501C42—522no—
502C42—522no—
503C42—522no—
504C42C2×C4×D1312yes—
505C42Q8×D1312yes—
506C13#2136311yescharacteristic, complemented, Sylow
507C23—132no—
508C23—132no—
509C23—132no—
510C23—261no—
511C23—261no—
512C23—261no—
513C23—261no—
514C23C2×D4×D1311yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—132no—
532C2×C4—132no—
533C2×C4—132no—
534C2×C4—268no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—524no—
548C2×C4—528no—
549C2×C4—528no—
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×C4—521no—
559C2×C4—521no—
560C2×C4C4⋊C4×D1312yes—
561C2×C4C4⋊C4×D1312yes—
562C2×C4C22×C4×D1311yescharacteristic
563C2×C4C2×#612911yescharacteristic
564C2×C4C2×Q8×D1311yescharacteristic
565C2×C4C2×#613111yescharacteristic
566C2×C4#41×D1311yescharacteristic
567C2×C4#41×D1311yescharacteristic
568C8—22no—
569C8—22no—
570C8—262no—
571C8—262no—
572C22—134no—
573C22—262no—
574C22—262no—
575C22—262no—
576C22—262no—
577C22—262no—
578C22—262no—
579C22C2×C4⋊C4×D1311yescharacteristic
580C22#1171931111yescharacteristic
581C22#1171933211yescharacteristic
582C22#1171947311yescharacteristic
583C22#1171947311yescharacteristic
584C22D13×AGL(1,ℤ/8)11yescharacteristic
585C22D13×#13711yescharacteristic
586C4—22no—
587C4—22no—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—81no—
592C4—262no—
593C4—262no—
594C4—262no—
595C4—522no—
596C4—522no—
597C4—1041no—
598C4—1041no—
599C4C4×#612911yescharacteristic
600C4C4×#613111yescharacteristic
601C4#1171939311yescharacteristic
602C4#1171943311yescharacteristic
603C2—264no—
604C2#1311731711yescharacteristic
605C2D13×#42811yescharacteristic
606C2#1312342411yescharacteristic
607C2#1312497311yescharacteristic
608C2#1312497911yescharacteristic
609C2#1312500611yescharacteristic
610C2#1312501211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1949C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1949D13
hypocenterC13#21363
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #13115606C2semidirect
5. #13115604C2semidirect
6. #13115602C2semidirect
11. #13114736C2semidirect
12. #13114735C2semidirect
13. #13114732C2semidirect
14. #13114732C2semidirect
15. C13×#1949C2semidirect
45. #11718496C4semidirect
100. C13×C4⋊C8C2×C4semidirect
117. #88055C2×C4semidirect
118. #88055C2×C4semidirect
123. C4⋊#1055C2×C4semidirect
208. #1949D13semidirect
404. C4⋊C8C4×D13semidirect
506. C13#21363semidirect

Maximal subgroups

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

subgroupindex
C2×#117184962
#131172292
C4×C4⋊C4×D132
#131156062
#131156042
#131156022
#131150302
#131150272
#131150252
#131150222
#131147362
#131147352
#131147322
C13×#19492
#2136313