Finite Group Databasebeta

← #15785593

Subgroups — #15785593

Order 3328.

1630 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718308C212yesmaximal
2C2×#11718633C212yesmaximal
3C2×#11718311C211yesmaximal, characteristic
4C2×C4×#6101C211yesmaximal, characteristic
5C2×#11718310C211yesmaximal, characteristic
6#13113100C212yesmaximal
7#13113099C212yesmaximal
8#13113066C211yesmaximal, characteristic
9#13113064C211yesmaximal, characteristic
10#13113064C211yesmaximal, characteristic
11C13×C4⋊#95C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2212yes—
13C22×C42×C13C2211yescharacteristic
14C22×C4⋊Dic13C2212yes—
15C22×#6101C2212yes—
16C22×#6101C2212yes—
17C22×#6101C2212yes—
18C22×#6101C2212yes—
19C22×#6101C2211yescharacteristic
20C22×#6101C2211yescharacteristic
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C2×C13×#95C2212yes—
25C2×C13×#95C2211yescharacteristic
26C2×C13×#95C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35#11718633—28no—
36C4×#6101C418yescomplemented
37#11718311—24no—
38#11718310—24no—
39#11718308—28no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C2×C13×C4⋊C4—24no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—42no—
54C2×C42×C13—42no—
55C2×C42×C13C2×C414yes—
56C2×C4⋊Dic13—24no—
57C2×C4⋊Dic13—24no—
58C2×C4⋊Dic13—42no—
59C2×#6101—24no—
60C2×#6101—24no—
61C2×#6101—24no—
62C2×#6101—24no—
63C2×#6101—24no—
64C2×#6101—24no—
65C2×#6101—24no—
66C2×#6101—24no—
67C2×#6101—24no—
68C2×#6101—24no—
69C2×#6101—42no—
70C2×#6101—42no—
71C2×#6101C2×C414yes—
72C2×#6101C2×C414yes—
73C2×#6101D414yes—
74C2×#6101D414yes—
75C2×#6101Q814yes—
76C2×#6101Q814yes—
77C2×C4×Dic13—24no—
78C2×C4×Dic13—24no—
79C2×C4×Dic13—24no—
80C2×C4×Dic13—42no—
81C2×C4×Dic13C2×C414yes—
82C2×C4×Dic13C2×C414yes—
83C2×C4×Dic13D414yes—
84C2×C4×Dic13Q814yes—
85C13×#95—24no—
86C13×#95—22no—
87C13×#95—22no—
88#88071—22no—
89#88071—22no—
90#88071—24no—
91#88071—24no—
92#88071—24no—
93#88071—24no—
94#88071C2×C414yes—
95#88071C2×C414yes—
96#13954—131nomaximal, Sylow
97C24×C13C2411yescharacteristic
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13C22×C412yes—
118C22×C4×C13C22×C412yes—
119C22×C4×C13C22×C412yes—
120C22×C4×C13C2×D412yes—
121C22×C4×C13C2×D412yes—
122C22×C4×C13C2×D412yes—
123C22×C4×C13C2×Q812yes—
124C22×C4×C13C2×Q812yes—
125C22×C4×C13C2×Q812yes—
126C22×C4×C13#4114yes—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13C22×C412yes—
147C22×Dic13C22×C412yes—
148C22×Dic13C22×C412yes—
149C22×Dic13C22×C412yes—
150C22×Dic13C2×D412yes—
151C22×Dic13C2×D412yes—
152C22×Dic13C2×D412yes—
153C22×Dic13C2×D412yes—
154C22×Dic13C2×D412yes—
155C22×Dic13C2×D412yes—
156C22×Dic13C2×Q812yes—
157C22×Dic13C2×Q812yes—
158C22×Dic13C2×Q812yes—
159C22×Dic13C2×Q812yes—
160C22×Dic13C2×Q812yes—
161C22×Dic13C2×Q812yes—
162C22×Dic13#4114yes—
163C13×C4⋊C4—48no—
164C42×C13—44no—
165C4⋊Dic13—48no—
166#6101—216no—
167#6101—48no—
168#6101—48no—
169#6101—48no—
170#6101C4⋊C4116yescomplemented
171#6101C4⋊C4116yescomplemented
172C4×Dic13—44no—
173C4×Dic13—48no—
174C4×Dic13C4⋊C4116yescomplemented
175C2×#389—132no—
176C2×#389—132no—
177C2×#382—131no—
178C2×C4×C4⋊C4—131no—
179C2×C4×C4⋊C4—131no—
180#1444—132no—
181#1444—132no—
182C4⋊#95—131no—
183C4⋊#95—131no—
184C4⋊#95—131no—
185C4⋊#95D1311yescharacteristic
186C23×C13C23×C411yescharacteristic
187C23×C13C22×D411yescharacteristic
188C23×C13C22×D411yescharacteristic
189C23×C13C22×D411yescharacteristic
190C23×C13C22×Q811yescharacteristic
191C23×C13C22×Q811yescharacteristic
192C23×C13C22×Q811yescharacteristic
193C23×C13C2×#4112yes—
194C23×C13C2×#4112yes—
195C23×C13H(5,𝔽2)12yes—
196C23×C132−1+412yes—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—24no—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—24no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13C2×C4⋊C414yes—
224C2×C4×C13C2×C4⋊C414yes—
225C2×C4×C13C2×C4⋊C414yes—
226C2×Dic13—22no—
227C2×Dic13—22no—
228C2×Dic13—22no—
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—22no—
232C2×Dic13—24no—
233C2×Dic13—24no—
234C2×Dic13—24no—
235C2×Dic13—24no—
236C2×Dic13—24no—
237C2×Dic13—24no—
238C2×Dic13—24no—
239C2×Dic13—24no—
240C2×Dic13—24no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13C2×C4⋊C414yes—
253C2×Dic13C2×C4⋊C414yes—
254C2×Dic13C2×C4⋊C414yes—
255C2×Dic13C2×C4⋊C414yes—
256C2×Dic13C2×C4⋊C414yes—
257C2×Dic13C2×C4⋊C414yes—
258C2×Dic13#12714yes—
259C2×Dic13C4⋊Q814yes—
260C2×Dic13C4⋊Q814yes—
261C2×Dic13C4⋊Q814yes—
262C22×C4⋊C4—131no—
263C22×C4⋊C4—131no—
264C22×C4⋊C4—132no—
265C22×C4⋊C4—132no—
266C22×C4⋊C4—132no—
267C22×C4⋊C4—132no—
268C22×C4⋊C4—132no—
269C22×C4⋊C4C2×D1312yes—
270C22×C42—131no—
271C22×C42—131no—
272C22×C42—132no—
273C22×C42C2×D1311yescharacteristic
274#389—268no—
275#389—268no—
276#382—264no—
277C4×C4⋊C4—138no—
278C4×C4⋊C4—264no—
279C2×#95—131no—
280C2×#95—131no—
281C2×#95—131no—
282C2×#95—131no—
283C2×#95—132no—
284C2×#95—132no—
285C2×#95—132no—
286C2×#95—132no—
287C2×#95C2×D1311yescharacteristic
288C2×#95C2×D1311yescharacteristic
289C2×#95C2×D1312yes—
290C22×C13C22×C4⋊C411yescharacteristic
291C22×C13C22×C4⋊C411yescharacteristic
292C22×C13C22×C4⋊C411yescharacteristic
293C22×C13C4×#4111yescharacteristic
294C22×C13C4×#4111yescharacteristic
295C22×C13#51811yescharacteristic
296C22×C13#51911yescharacteristic
297C22×C13#52512yes—
298C22×C13C2×#12711yescharacteristic
299C22×C13C2×C4⋊Q811yescharacteristic
300C22×C13C2×C4⋊Q811yescharacteristic
301C22×C13C2×C4⋊Q811yescharacteristic
302C22×C13#53312yes—
303C22×C13#53712yes—
304C22×C13#54412yes—
305C22×C13#54612yes—
306C22×C13#54612yes—
307C22×C13#54812yes—
308C22×C13#54812yes—
309C22×C13#55412yes—
310C22×C13#55412yes—
311C22×C13#55712yes—
312C22×C13#55712yes—
313C4×C13—24no—
314C4×C13—24no—
315C4×C13—24no—
316C4×C13—44no—
317C4×C13—82no—
318Dic13—24no—
319Dic13—24no—
320Dic13—24no—
321Dic13—44no—
322Dic13—82no—
323Dic13#38418yes—
324C23×C4—131no—
325C23×C4—131no—
326C23×C4—131no—
327C23×C4—131no—
328C23×C4—132no—
329C23×C4—132no—
330C23×C4C22×D1312yes—
331C23×C4C22×D1312yes—
332C23×C4C22×D1311yescharacteristic
333C23×C4C22×D1311yescharacteristic
334C23×C4C22×D1311yescharacteristic
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—134no—
339C2×C4⋊C4—134no—
340C2×C4⋊C4—134no—
341C2×C4⋊C4—134no—
342C2×C4⋊C4—134no—
343C2×C4⋊C4—134no—
344C2×C4⋊C4—264no—
345C2×C4⋊C4—264no—
346C2×C4⋊C4—264no—
347C2×C4⋊C4—264no—
348C2×C4⋊C4—264no—
349C2×C4⋊C4—264no—
350C2×C4⋊C4—264no—
351C2×C4⋊C4—264no—
352C2×C4⋊C4—264no—
353C2×C4⋊C4—264no—
354C2×C4⋊C4—264no—
355C2×C4⋊C4—264no—
356C2×C4⋊C4—522no—
357C2×C4⋊C4—522no—
358C2×C4⋊C4—522no—
359C2×C42—42no—
360C2×C42—134no—
361C2×C42—134no—
362C2×C42—134no—
363C2×C42—134no—
364C2×C42—264no—
365C2×C42—264no—
366C2×C42—264no—
367C2×C42—522no—
368C2×C42C4×D1314yes—
369#95—22no—
370#95—22no—
371#95—24no—
372#95—134no—
373#95—134no—
374#95—264no—
375#95—264no—
376#95—264no—
377#95—262no—
378#95—262no—
379#95—264no—
380C2×C13C2×#38411yescharacteristic
381C2×C13#229611yescharacteristic
382C2×C13#231611yescharacteristic
383C2×C13#234911yescharacteristic
384C2×C13#234911yescharacteristic
385C2×C13#235111yescharacteristic
386C2×C13#235111yescharacteristic
387C2×C13#254012yes—
388C2×C13#255012yes—
389C2×C13#255012yes—
390C2×C13#258412yes—
391C24C23×D1311yescharacteristic
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—132no—
412C22×C4—132no—
413C22×C4—132no—
414C22×C4—132no—
415C22×C4—132no—
416C22×C4—132no—
417C22×C4—132no—
418C22×C4—132no—
419C22×C4—132no—
420C22×C4—132no—
421C22×C4—132no—
422C22×C4—132no—
423C22×C4—132no—
424C22×C4—132no—
425C22×C4—132no—
426C22×C4—132no—
427C22×C4—134no—
428C22×C4—262no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4C2×C4×D1312yes—
448C22×C4C2×C4×D1312yes—
449C22×C4C2×C4×D1312yes—
450C22×C4#612714yes—
451C22×C4D4×D1312yes—
452C22×C4D4×D1312yes—
453C22×C4D4×D1312yes—
454C22×C4Q8×D1312yes—
455C22×C4Q8×D1312yes—
456C22×C4Q8×D1312yes—
457C4⋊C4—48no—
458C4⋊C4—1316no—
459C4⋊C4—1316no—
460C4⋊C4—2616no—
461C4⋊C4—528no—
462C4⋊C4—528no—
463C4⋊C4—528no—
464C4⋊C4—528no—
465C42—44no—
466C42—1316no—
467C42—524no—
468C42—528no—
469C13#1395411yescharacteristic, complemented, Sylow
470C23C22×C4×D1311yescharacteristic
471C23C2×#612712yes—
472C23C2×D4×D1311yescharacteristic
473C23C2×D4×D1311yescharacteristic
474C23C2×D4×D1311yescharacteristic
475C23#8825112yes—
476C23C2×Q8×D1311yescharacteristic
477C23C2×Q8×D1311yescharacteristic
478C23C2×Q8×D1311yescharacteristic
479C23#41×D1312yes—
480C23#8825712yes—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—134no—
508C2×C4—134no—
509C2×C4—134no—
510C2×C4—134no—
511C2×C4—134no—
512C2×C4—134no—
513C2×C4—134no—
514C2×C4—134no—
515C2×C4—134no—
516C2×C4—134no—
517C2×C4—262no—
518C2×C4—262no—
519C2×C4—262no—
520C2×C4—262no—
521C2×C4—264no—
522C2×C4—264no—
523C2×C4—262no—
524C2×C4—262no—
525C2×C4—264no—
526C2×C4—264no—
527C2×C4—264no—
528C2×C4—264no—
529C2×C4—264no—
530C2×C4—264no—
531C2×C4—264no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—522no—
540C2×C4—522no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4C4⋊C4×D1314yes—
544C2×C4C4⋊C4×D1314yes—
545C2×C4C4⋊C4×D1314yes—
546C22C4×#612711yescharacteristic
547C22#1171919111yescharacteristic
548C22#1171919512yes—
549C22C2×C4⋊C4×D1311yescharacteristic
550C22C2×C4⋊C4×D1311yescharacteristic
551C22C2×C4⋊C4×D1311yescharacteristic
552C22#1171921612yes—
553C22#1171922111yescharacteristic
554C22#1171922711yescharacteristic
555C22#1171925212yes—
556C22#1171925712yes—
557C22#1171927212yes—
558C22#1171928312yes—
559C22#1171930212yes—
560C22#1171931512yes—
561C22#1171932812yes—
562C22#1171934112yes—
563C22#1171938212yes—
564C22#1171939012yes—
565C22D13×#12711yescharacteristic
566C22D13×C4⋊Q811yescharacteristic
567C22D13×C4⋊Q811yescharacteristic
568C22D13×C4⋊Q811yescharacteristic
569C4—24no—
570C4—24no—
571C4—24no—
572C4—44no—
573C4—82no—
574C4—138no—
575C4—264no—
576C4—264no—
577C4—264no—
578C4—524no—
579C4—1042no—
580C2D13×#38411yescharacteristic
581C2#1311731611yescharacteristic
582C2#1311745311yescharacteristic
583C2#1311774011yescharacteristic
584C2#1311774311yescharacteristic
585C2#1311775311yescharacteristic
586C2#1311775611yescharacteristic
587C2#1311977312yes—
588C2#1311985412yes—
589C2#1311985612yes—
590C2#1312022212yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, prime radical, cosocleC24×C13C24
hypercenterC4⋊#95D13
hypocenterC13#13954
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
36. C4×#6101C4semidirect
170. #6101C4⋊C4semidirect
171. #6101C4⋊C4semidirect
174. C4×Dic13C4⋊C4semidirect
469. C13#13954semidirect

Maximal subgroups

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

subgroupindex
C2×#117183082
C2×#117186332
C2×#117183112
C2×C4×#61012
C2×#117183102
#131131002
#131130992
#131130662
#131130642
C13×C4⋊#952
#1395413