Finite Group Databasebeta

← #15785299

Subgroups — #15785299

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718312C212yesmaximal
2C2×C4⋊C4×Dic13C211yesmaximal, characteristic
3#13113097C212yesmaximal
4#13113096C212yesmaximal
5#13113066C211yesmaximal, characteristic
6#13113065C211yesmaximal, characteristic
7#13113065C211yesmaximal, characteristic
8#13113065C211yesmaximal, characteristic
9#13113062C212yesmaximal
10C4×#88071C211yesmaximal, characteristic
11C13×C4⋊#95C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4×Dic13C2211yescharacteristic
18C22×C4×Dic13C2212yes—
19C22×C4×Dic13C2211yescharacteristic
20C2×C13×#95C2212yes—
21C2×C13×#95C2212yes—
22C2×#88071C2211yescharacteristic
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C4⋊C4×Dic13C418yescomplemented
36#11718312—28no—
37C23×C4×C13C2312yes—
38C23×C4×C13C2312yes—
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×Dic13C2312yes—
43C23×Dic13C2312yes—
44C23×Dic13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C2×C13×C4⋊C4—22no—
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4C2×C414yes—
54C2×C42×C13—22no—
55C2×C42×C13—22no—
56C2×C42×C13—22no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—22no—
60C2×C4⋊Dic13—22no—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13C2×C414yes—
63C2×C4×Dic13—22no—
64C2×C4×Dic13—22no—
65C2×C4×Dic13—24no—
66C2×C4×Dic13—24no—
67C2×C4×Dic13—22no—
68C2×C4×Dic13—22no—
69C2×C4×Dic13—22no—
70C2×C4×Dic13C2×C414yes—
71C2×C4×Dic13C2×C418yes—
72C13×#95—24no—
73C13×#95—42no—
74#88071—24no—
75#88071—22no—
76#88071—24no—
77#88071—24no—
78#88071—24no—
79#88071—24no—
80#88071—22no—
81#88071—24no—
82#88071—22no—
83#88071—42no—
84#88071—42no—
85#88071C2×C418yes—
86#88071D414yes—
87#13921—131nomaximal, Sylow
88C24×C13C2411yescharacteristic
89C22×C4×C13—22no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—22no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
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×C13C22×C414yes—
115C22×C4×C13C22×C412yes—
116C22×C4×C13C2×D412yes—
117C22×C4×C13#4112yes—
118C22×C4×C13#4112yes—
119C22×C4×C13#4112yes—
120C22×C4×C13#4112yes—
121C22×C4×C13#4112yes—
122C22×C4×C13#4112yes—
123C22×C4×C13#4112yes—
124C22×Dic13—21no—
125C22×Dic13—21no—
126C22×Dic13—21no—
127C22×Dic13—21no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13C22×C412yes—
160C22×Dic13C22×C414yes—
161C22×Dic13C22×C412yes—
162C22×Dic13C2×D412yes—
163C22×Dic13C2×D412yes—
164C22×Dic13#4112yes—
165C22×Dic13#4112yes—
166C13×C4⋊C4—28no—
167C13×C4⋊C4—44no—
168C42×C13—44no—
169C4⋊Dic13—28no—
170C4⋊Dic13—44no—
171C4×Dic13—28no—
172C4×Dic13—216no—
173C4×Dic13—44no—
174C2×#383—132no—
175C2×C4×C4⋊C4—131no—
176#1443—132no—
177#1443—132no—
178C4⋊#95—131no—
179C4⋊#95—131no—
180C4⋊#95—131no—
181C4⋊#95—131no—
182C4⋊#95D1311yescharacteristic
183#1434—132no—
184C4×#95—131no—
185C23×C13C23×C411yescharacteristic
186C23×C13C22×D411yescharacteristic
187C23×C13C2×#4111yescharacteristic
188C23×C13C2×#4111yescharacteristic
189C23×C13C2×#4111yescharacteristic
190C23×C13C2×#4111yescharacteristic
191C23×C13C2×#4111yescharacteristic
192C23×C13C2×#4111yescharacteristic
193C23×C13C2×#4111yescharacteristic
194C23×C13C2×#4111yescharacteristic
195C23×C13C2×#4111yescharacteristic
196C23×C13H(5,𝔽2)11yescharacteristic
197C23×C132−1+411yescharacteristic
198C23×C132−1+411yescharacteristic
199C23×C132−1+411yescharacteristic
200C2×C4×C13—24no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—42no—
218C2×C4×C13—41no—
219C2×C4×C13—42no—
220C2×C4×C13—41no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13#11714yes—
229C2×C4×C13#11714yes—
230C2×C4×C13#11714yes—
231C2×C4×C13#12614yes—
232C2×C4×C13#12614yes—
233C2×C4×C13#12614yes—
234C2×C4×C13#12614yes—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—22no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—24no—
243C2×Dic13—24no—
244C2×Dic13—22no—
245C2×Dic13—24no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
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×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13C4×D414yes—
277C22×C4⋊C4—131no—
278C22×C4⋊C4—131no—
279C22×C4⋊C4C2×D1311yescharacteristic
280C22×C4⋊C4C2×D1311yescharacteristic
281C22×C42—131no—
282C22×C42—132no—
283C22×C42—131no—
284C22×C42C2×D1311yescharacteristic
285#383—268no—
286C4×C4⋊C4—138no—
287C2×#95—131no—
288C2×#95—132no—
289C2×#95—131no—
290C2×#95—131no—
291C2×#95—131no—
292C2×#95—132no—
293C2×#95—132no—
294C2×#95—132no—
295C2×#95—132no—
296C2×#95—132no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95—132no—
300C2×#95C2×D1312yes—
301C2×#95C2×D1312yes—
302C22×C13C2×#11711yescharacteristic
303C22×C13C2×#11711yescharacteristic
304C22×C13C2×#11711yescharacteristic
305C22×C13C2×C4×D411yescharacteristic
306C22×C13C4×#4111yescharacteristic
307C22×C13#51911yescharacteristic
308C22×C13#52011yescharacteristic
309C22×C13C2×#12611yescharacteristic
310C22×C13C2×#12611yescharacteristic
311C22×C13C2×#12611yescharacteristic
312C22×C13C2×#12611yescharacteristic
313C22×C13#52911yescharacteristic
314C22×C13#52911yescharacteristic
315C22×C13#53211yescharacteristic
316C22×C13#53211yescharacteristic
317C22×C13#54111yescharacteristic
318C22×C13#54111yescharacteristic
319C22×C13#54211yescharacteristic
320C22×C13#54211yescharacteristic
321C22×C13#54711yescharacteristic
322C22×C13#54711yescharacteristic
323C22×C13#54711yescharacteristic
324C22×C13#55011yescharacteristic
325C22×C13#55211yescharacteristic
326C22×C13#55211yescharacteristic
327C22×C13#55211yescharacteristic
328C22×C13#55211yescharacteristic
329C22×C13#55311yescharacteristic
330C22×C13#55311yescharacteristic
331C22×C13#55511yescharacteristic
332C22×C13#55611yescharacteristic
333C22×C13#55611yescharacteristic
334C22×C13#55611yescharacteristic
335C22×C13#55611yescharacteristic
336C22×C13#55611yescharacteristic
337C4×C13—44no—
338C4×C13—42no—
339C4×C13—42no—
340C4×C13—82no—
341C4×C13#38318yescomplemented
342Dic13—24no—
343Dic13—42no—
344Dic13—42no—
345Dic13—42no—
346Dic13—44no—
347Dic13—82no—
348C23×C4—131no—
349C23×C4—132no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—131no—
353C23×C4—132no—
354C23×C4C22×D1312yes—
355C23×C4C22×D1312yes—
356C23×C4C22×D1311yescharacteristic
357C23×C4C22×D1311yescharacteristic
358C23×C4C22×D1311yescharacteristic
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—134no—
365C2×C4⋊C4—262no—
366C2×C4⋊C4—262no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4C4×D1314yes—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—138no—
375C2×C42—134no—
376C2×C42—264no—
377C2×C42—264no—
378C2×C42—262no—
379C2×C42—262no—
380C2×C42—262no—
381C2×C42—262no—
382C2×C42—262no—
383#95—24no—
384#95—42no—
385#95—138no—
386#95—134no—
387#95—262no—
388#95—262no—
389#95—264no—
390#95—264no—
391#95—264no—
392#95—264no—
393#95—264no—
394#95—262no—
395#95—264no—
396#95—522no—
397#95—522no—
398C2×C13C2×#38311yescharacteristic
399C2×C13#229311yescharacteristic
400C2×C13#232011yescharacteristic
401C2×C13#234411yescharacteristic
402C2×C13#234711yescharacteristic
403C2×C13#235411yescharacteristic
404C2×C13#235611yescharacteristic
405C2×C13#249511yescharacteristic
406C2×C13#249511yescharacteristic
407C2×C13#249611yescharacteristic
408C2×C13#249611yescharacteristic
409C2×C13#251211yescharacteristic
410C2×C13#251211yescharacteristic
411C2×C13#251411yescharacteristic
412C2×C13#251411yescharacteristic
413C24C23×D1311yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—132no—
440C22×C4—132no—
441C22×C4—132no—
442C22×C4—132no—
443C22×C4—134no—
444C22×C4—132no—
445C22×C4—132no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—262no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—262no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—262no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—262no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—262no—
469C22×C4—261no—
470C22×C4—262no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4C2×C4×D1314yes—
482C22×C4C2×C4×D1312yes—
483C22×C4#612712yes—
484C22×C4#612712yes—
485C22×C4D4×D1312yes—
486C22×C4#612912yes—
487C22×C4#612912yes—
488C22×C4#612912yes—
489C22×C4#613112yes—
490C22×C4#613112yes—
491C4⋊C4—28no—
492C4⋊C4—44no—
493C4⋊C4—268no—
494C4⋊C4—524no—
495C42—44no—
496C42—2616no—
497C42—268no—
498C42—524no—
499C13#1392111yescharacteristic, complemented, Sylow
500C23C22×C4×D1311yescharacteristic
501C23C2×#612711yescharacteristic
502C23C2×#612711yescharacteristic
503C23C2×D4×D1311yescharacteristic
504C23C2×#612911yescharacteristic
505C23C2×#612911yescharacteristic
506C23C2×#612911yescharacteristic
507C23#8825111yescharacteristic
508C23C2×#613111yescharacteristic
509C23C2×#613111yescharacteristic
510C23#8825411yescharacteristic
511C23#41×D1311yescharacteristic
512C23#41×D1311yescharacteristic
513C23#8825711yescharacteristic
514C23#8825711yescharacteristic
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—134no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—262no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—262no—
552C2×C4—264no—
553C2×C4—264no—
554C2×C4—262no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—262no—
558C2×C4—264no—
559C2×C4—262no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—522no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—522no—
573C2×C4—521no—
574C2×C4—522no—
575C2×C4—521no—
576C2×C4—522no—
577C2×C4—521no—
578C2×C4—522no—
579C2×C4—522no—
580C2×C4—522no—
581C2×C4—522no—
582C2×C4—522no—
583C2×C4—522no—
584C2×C4—522no—
585C2×C4#8812614yes—
586C2×C4#8813114yes—
587C2×C4#8813314yes—
588C2×C4#8813314yes—
589C2×C4#8814614yes—
590C2×C4#8815214yes—
591C2×C4#8815214yes—
592C22C2×#8812611yescharacteristic
593C22C2×#8813111yescharacteristic
594C22C2×#8813311yescharacteristic
595C22C2×#8813311yescharacteristic
596C22C2×#8814611yescharacteristic
597C22#1171921211yescharacteristic
598C22C2×#8815211yescharacteristic
599C22C2×#8815211yescharacteristic
600C22#1171921911yescharacteristic
601C22#1171923411yescharacteristic
602C22#1171923811yescharacteristic
603C22C4×D4×D1311yescharacteristic
604C22#1171925111yescharacteristic
605C22#1171925611yescharacteristic
606C22#1171926311yescharacteristic
607C22#1171927711yescharacteristic
608C22C4×#613111yescharacteristic
609C22#1171928611yescharacteristic
610C22#1171928911yescharacteristic
611C22#1171930111yescharacteristic
612C22#1171930811yescharacteristic
613C22#1171931611yescharacteristic
614C22#1171932111yescharacteristic
615C22#1171932911yescharacteristic
616C22#1171933011yescharacteristic
617C22#1171934411yescharacteristic
618C22#1171934711yescharacteristic
619C22#1171937611yescharacteristic
620C22#1171937611yescharacteristic
621C22#1171939611yescharacteristic
622C22#1171940211yescharacteristic
623C22#1171942311yescharacteristic
624C22#1171943011yescharacteristic
625C22#1171943711yescharacteristic
626C22#1171943811yescharacteristic
627C4—42no—
628C4—42no—
629C4—44no—
630C4—82no—
631C4—264no—
632C4—522no—
633C4—522no—
634C4—522no—
635C4—524no—
636C4—1042no—
637C4#1171831218yescomplemented
638C2C2×#1171831211yescharacteristic
639C2#1311729411yescharacteristic
640C2#1311748311yescharacteristic
641C2#1311770111yescharacteristic
642C2#1311772511yescharacteristic
643C2#1311778411yescharacteristic
644C2#1311780011yescharacteristic
645C2#1311924311yescharacteristic
646C2#1311924511yescharacteristic
647C2#1311925411yescharacteristic
648C2#1311925611yescharacteristic
649C2#1311941811yescharacteristic
650C2#1311942011yescharacteristic
651C2#1311944011yescharacteristic
652C2#1311944211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, prime radical, cosocleC24×C13C24
hypercenterC4⋊#95D13
hypocenterC13#13921
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
35. C4⋊C4×Dic13C4semidirect
341. C4×C13#383semidirect
499. C13#13921semidirect
637. C4#11718312semidirect

Maximal subgroups

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

subgroupindex
C2×#117183122
C2×C4⋊C4×Dic132
#131130972
#131130962
#131130662
#131130652
#131130622
C4×#880712
C13×C4⋊#952
#1392113