Finite Group Databasebeta

← #15881933

Subgroups — #15881933

Order 3328.

1052 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718586C211yesmaximal, characteristic, complemented
2C2×D13×C4⋊C8C211yesmaximal, characteristic, complemented
3C42×C22⋊D13C211yesmaximal, characteristic
4#13115439C212yesmaximal, complemented
5#13115391C212yesmaximal, complemented
6#13115125C212yesmaximal
7#13114952C211yesmaximal, characteristic, complemented
8#13114813C211yesmaximal, characteristic, complemented
9C4⋊C8×Dic13C211yesmaximal, characteristic, complemented
10#13114606C212yesmaximal, complemented
11C13×#1797C211yesmaximal, characteristic, complemented
12C22×C42×C13C2211yescharacteristic
13C2×C4×C22⋊D13C411yescharacteristic
14C2×C4×C22⋊D13C411yescharacteristic
15C2×C4×C22⋊D13C2211yescharacteristic
16C22×C8×D13C2212yes—
17C2×C42×D13C2211yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C13×C22⋊C8C2212yes—
21C4×C22⋊Dic13C411yescharacteristic
22C4×C22⋊Dic13C411yescharacteristic
23C4×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊#1055C2212yes—
25C2×#88060C2212yes—
26C2×#88054C2212yes—
27C2×C8×Dic13C2212yes—
28C4×#6103C411yescharacteristic
29C4×#6103C411yescharacteristic
30C4×#6103C2211yescharacteristic
31C4×#6101C411yescharacteristic
32C4×#6101C411yescharacteristic
33C4×#6101C2211yescharacteristic
34C42×Dic13C2211yescharacteristic
35#11718586—24no—
36C2×C4⋊#1055C2211yescharacteristic
37C2×C4⋊#1055C2211yescharacteristic
38C2×C4×#1055C2212yes—
39D13×C4⋊C8—24no—
40C13×#336C2212yes—
41#11718142C2212yes—
42#11718142C2212yes—
43#11718142C2212yes—
44#11718142C2212yes—
45C23×C4×C13C2×C411yescharacteristic
46C23×C4×C13C2×C411yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C22×C22⋊D13C2×C411yescharacteristic
49C22×C4×D13C2×C411yescharacteristic
50C22×C4×D13C2×C411yescharacteristic
51C22×C4×D13C2311yescharacteristic
52C22×C8×C13C2312yes—
53C22×C8×C13C2312yes—
54C2×C42×C13—22no—
55C2×C42×C13—22no—
56C2×C42×C13C2×C411yescharacteristic
57C2×C42×C13C2×C411yescharacteristic
58C2×C42×C13C2311yescharacteristic
59C2×C42×C13C2311yescharacteristic
60C2×C22⋊Dic13C2×C411yescharacteristic
61C2×C22⋊Dic13C2×C411yescharacteristic
62C2×C22⋊Dic13C2×C411yescharacteristic
63C4×C22⋊D13—22no—
64C4×C22⋊D13—22no—
65C4×C22⋊D13—24no—
66C4×C22⋊D13C818yescomplemented
67C2×#6103C2×C411yescharacteristic
68C2×#6103C2×C411yescharacteristic
69C2×#6103C2×C411yescharacteristic
70C2×#6101C2×C411yescharacteristic
71C2×#6101C2×C411yescharacteristic
72C2×#6101C2×C411yescharacteristic
73C2×C4×Dic13C2×C411yescharacteristic
74C2×C4×Dic13C2×C411yescharacteristic
75C2×C4×Dic13C2×C411yescharacteristic
76C2×C4×Dic13C2×C411yescharacteristic
77C2×C4×Dic13C2×C411yescharacteristic
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13C2311yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C22×#1055C2312yes—
83C22×#1055C2312yes—
84C2×C8×D13—24no—
85C2×C8×D13—24no—
86C2×C8×D13—42no—
87C42×D13—22no—
88C42×D13—22no—
89C13×C4⋊C8—22no—
90C13×C4⋊C8—22no—
91C13×C22⋊C8—42no—
92#88071C2×C411yescharacteristic
93#88071C2×C411yescharacteristic
94#88071C2×C411yescharacteristic
95#88071C2×C411yescharacteristic
96#88071C2×C411yescharacteristic
97#88071C2×C411yescharacteristic
98C22⋊#1055—24no—
99#88060—24no—
100#88054—24no—
101C8×Dic13—42no—
102C4⋊#1055—22no—
103C4⋊#1055D414yescomplemented
104C4×#1055—24no—
105#22748—131nomaximal, Sylow
106C24×C13C22×C411yescharacteristic
107C23×D13C22×C411yescharacteristic
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—41no—
119C22×C4×C13C2×C814yescomplemented
120C22×C4×C13C22×C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C2411yescharacteristic
126C2×C22⋊D13—22no—
127C2×C22⋊D13—22no—
128C2×C22⋊D13C2×C814yes—
129C22×Dic13C22×C411yescharacteristic
130C22×Dic13C22×C411yescharacteristic
131C22×Dic13C22×C411yescharacteristic
132C22×Dic13C22×C411yescharacteristic
133C22×Dic13C22×C411yescharacteristic
134C22×Dic13C22×C411yescharacteristic
135C22×Dic13C22×C411yescharacteristic
136C2×C4×D13—22no—
137C2×C4×D13—22no—
138C2×C4×D13—21no—
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13—21no—
142C2×C4×D13—22no—
143C2×C4×D13—22no—
144C2×C4×D13—41no—
145C2×C4×D13C2×C814yes—
146C2×C4×D13#4112yes—
147C2×C4×D13#4112yes—
148C2×C8×C13—22no—
149C2×C8×C13—22no—
150C2×C8×C13—22no—
151C2×C8×C13—22no—
152C2×C8×C13—22no—
153C2×C8×C13—22no—
154C42×C13—22no—
155C42×C13—22no—
156C42×C13—21no—
157C42×C13—21no—
158C42×C13C2×D412yes—
159C42×C13#4112yes—
160C22⋊Dic13—22no—
161C22⋊Dic13—22no—
162C22⋊Dic13C2×C814yescomplemented
163#6103—22no—
164#6103C2×C814yes—
165#6103M1614yes—
166#6101—22no—
167#6101—22no—
168#6101C2×C814yescomplemented
169C4×Dic13—22no—
170C4×Dic13—22no—
171C4×Dic13—22no—
172C4×Dic13—21no—
173C4×Dic13—21no—
174C4×Dic13—21no—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13—21no—
178C4×Dic13—22no—
179C4×Dic13—41no—
180C4×Dic13C2×C814yescomplemented
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055—22no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#1055C2×D414yes—
187C8×D13—48no—
188C2×#431—131no—
189C22×C4⋊C8—131no—
190C42×D4—131no—
191#1923—132no—
192#1916—132no—
193#1869—132no—
194#1831—131no—
195#1797—131no—
196#1797D1311yescharacteristic, complemented
197C4×C4⋊C8—131no—
198C8×C22⋊C4—132no—
199C23×C13—21no—
200C23×C13—21no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—21no—
204C23×C13—21no—
205C23×C13C22×C812yes—
206C23×C13C23×C411yescharacteristic
207C22×D13—21no—
208C22×D13—21no—
209C22×D13—21no—
210C22×D13—21no—
211C22×D13#11712yes—
212C22×D13C22×C812yes—
213C22×D13C2×M1612yes—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—28no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—44no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13C4×D412yes—
230C2×C4×C13C4×D412yes—
231C2×C4×C13C22×C812yes—
232C2×C4×C13C22×C812yes—
233C2×C4×C13C2×M1612yes—
234C2×C4×C13#13112yes—
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C13H(5,𝔽2)11yescharacteristic
240C2×C4×C132−1+411yescharacteristic
241C22⋊D13—28no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13#11712yes—
259C2×Dic13C22×C812yes—
260C2×Dic13C22×C812yes—
261C2×Dic13C22×C812yes—
262C2×Dic13C2×M1612yes—
263C4×D13—22no—
264C4×D13—22no—
265C4×D13—22no—
266C4×D13—22no—
267C4×D13—28no—
268C4×D13—44no—
269C8×C13—42no—
270C8×C13—42no—
271#1055—24no—
272#1055—42no—
273C23×C8—132no—
274C2×C4×D4—131no—
275C2×C4×D4—131no—
276C2×C4×D4—131no—
277C22×C42—131no—
278C22×C42C2×D1311yescharacteristic
279#431—264no—
280C2×C4⋊C8—131no—
281C2×C4⋊C8—132no—
282C2×C4⋊C8—131no—
283C2×C4⋊C8—264no—
284C2×C4⋊C8C2×D1311yescharacteristic
285C2×C4⋊C8C2×D1311yescharacteristic
286C2×C22⋊C8—132no—
287C2×C22⋊C8—132no—
288C2×C22⋊C8C2×D1312yes—
289C2×C4×C8—132no—
290C2×C4×C8—132no—
291C4×C4⋊C4—131no—
292C4×C4⋊C4—131no—
293C4×C4⋊C4—131no—
294C4×C22⋊C4—131no—
295C4×C22⋊C4—131no—
296C4×C22⋊C4—131no—
297C4×C22⋊C4—131no—
298C4×C22⋊C4—131no—
299C4×C22⋊C4—131no—
300C43—131no—
301#336—132no—
302#336—132no—
303#336—132no—
304#336—132no—
305#336C2×D1312yes—
306C22×C13—22no—
307C22×C13—22no—
308C22×C13—22no—
309C22×C13—41no—
310C22×C13—41no—
311C22×C13—41no—
312C22×C13—41no—
313C22×C13C2×#11711yescharacteristic
314C22×C13C2×C4×D411yescharacteristic
315C22×C13#52011yescharacteristic
316C22×C13C23×C811yescharacteristic
317C22×C13C22×M1611yescharacteristic
318C22×C13C2×#13111yescharacteristic
319C22×C13#56811yescharacteristic
320C2×D13—22no—
321C2×D13—22no—
322C2×D13—22no—
323C2×D13—22no—
324C2×D13—22no—
325C2×D13—22no—
326C2×D13#43114yescomplemented
327C4×C13—22no—
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—41no—
331C4×C13C8×D414yes—
332C4×C13#54611yescharacteristic
333C4×C13#54811yescharacteristic
334C4×C13#55211yescharacteristic
335C4×C13#55311yescharacteristic
336Dic13—22no—
337Dic13—22no—
338Dic13—22no—
339Dic13—22no—
340Dic13—22no—
341Dic13—41no—
342Dic13—41no—
343C22×D4—131no—
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—131no—
347C23×C4C4×D1311yescharacteristic
348C23×C4C4×D1311yescharacteristic
349C23×C4C22×D1311yescharacteristic
350C22×C8—132no—
351C22×C8—132no—
352C22×C8—264no—
353C22×C8—264no—
354C22×C8—522no—
355C22×C8C22×D1312yes—
356C22×C8C22×D1312yes—
357C4×D4—138no—
358C4×D4—264no—
359C4×D4—262no—
360C4×D4—262no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C22⋊C4—131no—
365C2×C22⋊C4—131no—
366C2×C22⋊C4—131no—
367C2×C22⋊C4—131no—
368C2×C22⋊C4—131no—
369C2×C22⋊C4—131no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—131no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C2×C42—262no—
382C2×C42—262no—
383C2×C42C4×D1311yescharacteristic
384C2×C42C4×D1311yescharacteristic
385C2×C42C22×D1311yescharacteristic
386C2×C42C22×D1311yescharacteristic
387C4⋊C8—22no—
388C4⋊C8—22no—
389C4⋊C8—134no—
390C4⋊C8—264no—
391C4⋊C8—262no—
392C22⋊C8—42no—
393C22⋊C8—264no—
394C22⋊C8—264no—
395C4×C8—264no—
396C4×C8—522no—
397#95—131no—
398#95—131no—
399#95—131no—
400#95—131no—
401#95—131no—
402#95—131no—
403C2×C13—42no—
404C2×C13#235211yescharacteristic
405C2×C13C2×#43111yescharacteristic
406C2×C13#292511yescharacteristic
407C2×C13C2×C8×D411yescharacteristic
408C2×C13D4×M1611yescharacteristic
409C2×C13#298811yescharacteristic
410C2×C13#299011yescharacteristic
411D13—24no—
412C24—131no—
413C24C2×C4×D1311yescharacteristic
414C2×D4—134no—
415C2×D4—262no—
416C2×D4—262no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—41no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—134no—
434C22×C4—132no—
435C22×C4—132no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—262no—
446C22×C4—521no—
447C22×C4C8×D1314yescomplemented
448C22×C4C2×C4×D1311yescharacteristic
449C22×C4C2×C4×D1311yescharacteristic
450C22×C4C2×C4×D1311yescharacteristic
451C22×C4C2×C4×D1311yescharacteristic
452C22×C4C2×C4×D1311yescharacteristic
453C22×C4C23×D1311yescharacteristic
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—134no—
461C2×C8—262no—
462C2×C8—262no—
463C2×C8—262no—
464C2×C8—262no—
465C2×C8—262no—
466C2×C8—528no—
467C4⋊C4—134no—
468C4⋊C4—262no—
469C4⋊C4—262no—
470C22⋊C4—134no—
471C22⋊C4—134no—
472C22⋊C4—134no—
473C22⋊C4—262no—
474C22⋊C4—262no—
475C22⋊C4—262no—
476C42—22no—
477C42—22no—
478C42—21no—
479C42—21no—
480C42—134no—
481C42—262no—
482C42—262no—
483C42—262no—
484C42—262no—
485C42—261no—
486C42—261no—
487C42—261no—
488C42—261no—
489C42—261no—
490C42—261no—
491C42—521no—
492C42D4×D1312yes—
493C42#612912yes—
494C13#2274811yescharacteristic, complemented, Sylow
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—132no—
502C23—132no—
503C23—132no—
504C23—261no—
505C23—261no—
506C23—261no—
507C23—261no—
508C23C2×C8×D1312yes—
509C23C22×C4×D1311yescharacteristic
510D4—268no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—28no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—44no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—132no—
527C2×C4—132no—
528C2×C4—132no—
529C2×C4—132no—
530C2×C4—132no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
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—268no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—524no—
553C2×C4#8813512yes—
554C2×C4#8813512yes—
555C2×C4C2×C8×D1312yes—
556C2×C4C2×C8×D1312yes—
557C2×C4M16×D1312yes—
558C2×C4#8816112yes—
559C2×C4C2×D4×D1311yescharacteristic
560C2×C4C2×#612911yescharacteristic
561C2×C4#8825111yescharacteristic
562C2×C4#8825411yescharacteristic
563C2×C4#41×D1311yescharacteristic
564C2×C4#41×D1311yescharacteristic
565C8—42no—
566C8—42no—
567C8—264no—
568C8—522no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—134no—
577C22—262no—
578C22—262no—
579C22—262no—
580C22—262no—
581C22—262no—
582C22—262no—
583C22C2×#8813511yescharacteristic
584C22#1171920911yescharacteristic
585C22D13×#11711yescharacteristic
586C22C22×C8×D1311yescharacteristic
587C22C2×M16×D1311yescharacteristic
588C22C2×#8816111yescharacteristic
589C22#1171945011yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—41no—
594C4—262no—
595C4—262no—
596C4—262no—
597C4—262no—
598C4—262no—
599C4—521no—
600C4—521no—
601C4#1171838614yes—
602C4#1171931711yescharacteristic
603C4#1171931911yescharacteristic
604C4#1171933811yescharacteristic
605C4#1171934411yescharacteristic
606C2—42no—
607C2—264no—
608C2#1311775811yescharacteristic
609C2D13×#43111yescharacteristic
610C2#1312350311yescharacteristic
611C2C2×#1171838611yescharacteristic
612C2#1312356811yescharacteristic
613C2#1312394511yescharacteristic
614C2#1312396211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC13×#1797C2
socleC23×C13C23×C4
prime radicalC22×C22⋊D13C2×C4
cosocleC22×C4×C13C24
hypercenter#1797D13
hypocenterC13#22748
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
1. C2×#11718586C2semidirect
2. C2×D13×C4⋊C8C2semidirect
4. #13115439C2semidirect
5. #13115391C2semidirect
7. #13114952C2semidirect
8. #13114813C2semidirect
9. C4⋊C8×Dic13C2semidirect
10. #13114606C2semidirect
11. C13×#1797C2semidirect
66. C4×C22⋊D13C8semidirect
103. C4⋊#1055D4semidirect
119. C22×C4×C13C2×C8semidirect
162. C22⋊Dic13C2×C8semidirect
168. #6101C2×C8semidirect
180. C4×Dic13C2×C8semidirect
196. #1797D13semidirect
326. C2×D13#431semidirect
447. C22×C4C8×D13semidirect
494. C13#22748semidirect

Maximal subgroups

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

subgroupindex
C2×#117185862
C2×D13×C4⋊C82
C42×C22⋊D132
#131154392
#131153912
#131151252
#131149522
#131148132
C4⋊C8×Dic132
#131146062
C13×#17972
#2274813