Finite Group Databasebeta

← #15881937

Subgroups — #15881937

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×#11718494C211yesmaximal, characteristic, complemented
2C2×D13×C4⋊C8C211yesmaximal, characteristic, complemented
3C42×D52C211yesmaximal, characteristic
4#13115440C212yesmaximal, complemented
5#13115392C212yesmaximal, complemented
6#13115127C212yesmaximal
7#13114813C211yesmaximal, characteristic, complemented
8#13114813C211yesmaximal, characteristic, complemented
9C4×C4⋊#1055C211yesmaximal, characteristic, complemented
10#13114606C212yesmaximal, complemented
11C13×#1831C211yesmaximal, characteristic, complemented
12C22×C8×D13C2212yes—
13C2×C4×D52C411yescharacteristic
14C2×C4×D52C411yescharacteristic
15C2×C4×D52C2211yescharacteristic
16C2×C42×D13C2211yescharacteristic
17C2×C42×D13C2211yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C43×C13C2211yescharacteristic
21C2×#88060C2212yes—
22C2×#88060C2212yes—
23C2×#88060C2212yes—
24C2×#88054C2212yes—
25C2×C8×Dic13C2212yes—
26C4×#6103C411yescharacteristic
27C4×#6103C411yescharacteristic
28C4×#6103C411yescharacteristic
29C4×#6103C411yescharacteristic
30C4×#6103C2211yescharacteristic
31C4×#6103C2211yescharacteristic
32C4×C4⋊Dic13C411yescharacteristic
33C4×C4⋊Dic13C411yescharacteristic
34C4×C4⋊Dic13C2211yescharacteristic
35C2×C4⋊#1055C2211yescharacteristic
36C2×C4⋊#1055C2211yescharacteristic
37C2×C4×#1055C2212yes—
38#11718494—24no—
39D13×C4⋊C8—24no—
40C13×#336C2212yes—
41C13×#336C2212yes—
42#11718142C2212yes—
43#11718142C2212yes—
44#11718116C2212yes—
45C22×D52C2×C411yescharacteristic
46C22×C4×D13C2×C411yescharacteristic
47C22×C4×D13C2×C411yescharacteristic
48C22×C4×D13C2×C411yescharacteristic
49C22×C4×D13C2×C411yescharacteristic
50C22×C4×D13C2311yescharacteristic
51C22×C4×D13C2311yescharacteristic
52C22×C8×C13C2312yes—
53C22×C8×C13C2312yes—
54C2×C42×C13C2×C411yescharacteristic
55C2×C42×C13C2×C411yescharacteristic
56C2×C42×C13C2×C411yescharacteristic
57C2×C42×C13C2×C411yescharacteristic
58C2×C42×C13C2311yescharacteristic
59C2×C42×C13C2311yescharacteristic
60C2×C42×C13C2311yescharacteristic
61C2×#6103C2×C411yescharacteristic
62C2×#6103C2×C411yescharacteristic
63C2×#6103C2×C411yescharacteristic
64C2×#6103C2×C411yescharacteristic
65C2×#6103C2×C411yescharacteristic
66C2×#6103C2×C411yescharacteristic
67C2×C4⋊Dic13C2×C411yescharacteristic
68C2×C4⋊Dic13C2×C411yescharacteristic
69C2×C4⋊Dic13C2×C411yescharacteristic
70C2×C4×Dic13C2×C411yescharacteristic
71C2×C4×Dic13C2×C411yescharacteristic
72C2×C4×Dic13C2×C411yescharacteristic
73C2×C4×Dic13C2×C411yescharacteristic
74C2×C4×Dic13C2311yescharacteristic
75C2×C4×Dic13C2311yescharacteristic
76C22×#1055C2312yes—
77C22×#1055C2312yes—
78C2×C8×D13—24no—
79C2×C8×D13—24no—
80C2×C8×D13—42no—
81C4×D52—22no—
82C4×D52—22no—
83C4×D52—24no—
84C4×D52C818yescomplemented
85C42×D13—22no—
86C42×D13—22no—
87C42×D13—22no—
88C42×D13—22no—
89C13×C4⋊C8—22no—
90C13×C4⋊C8—22no—
91#88071C2×C411yescharacteristic
92#88071C2×C411yescharacteristic
93#88071C2×C411yescharacteristic
94#88071C2×C411yescharacteristic
95#88071C2×C411yescharacteristic
96#88071C2×C411yescharacteristic
97#88060—24no—
98#88060—24no—
99#88060—42no—
100#88054—24no—
101C8×Dic13—24no—
102C4⋊#1055—22no—
103C4⋊#1055D414yescomplemented
104C4×#1055—42no—
105#22748—131nomaximal, Sylow
106C23×D13C22×C411yescharacteristic
107C23×D13C22×C411yescharacteristic
108C22×C4×C13C22×C411yescharacteristic
109C22×C4×C13C22×C411yescharacteristic
110C22×C4×C13C22×C411yescharacteristic
111C22×C4×C13C22×C411yescharacteristic
112C22×C4×C13C22×C411yescharacteristic
113C22×C4×C13C22×C411yescharacteristic
114C22×C4×C13C2411yescharacteristic
115C22×Dic13C22×C411yescharacteristic
116C22×Dic13C22×C411yescharacteristic
117C22×Dic13C22×C411yescharacteristic
118C22×Dic13C22×C411yescharacteristic
119C22×Dic13C22×C411yescharacteristic
120C22×Dic13C22×C411yescharacteristic
121C2×D52—22no—
122C2×D52—22no—
123C2×D52C2×C814yes—
124C2×C4×D13—22no—
125C2×C4×D13—22no—
126C2×C4×D13—22no—
127C2×C4×D13—22no—
128C2×C4×D13—21no—
129C2×C4×D13—21no—
130C2×C4×D13—21no—
131C2×C4×D13—21no—
132C2×C4×D13—22no—
133C2×C4×D13—22no—
134C2×C4×D13—22no—
135C2×C4×D13—21no—
136C2×C4×D13—21no—
137C2×C4×D13—21no—
138C2×C4×D13—21no—
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13—22no—
142C2×C4×D13—41no—
143C2×C4×D13—41no—
144C2×C4×D13C2×C814yes—
145C2×C4×D13C2×C814yescomplemented
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×C13—21no—
159C42×C13—21no—
160C42×C13—41no—
161C42×C13C2×C814yescomplemented
162C42×C13C2×D412yes—
163C42×C13#4112yes—
164#6103—22no—
165#6103—22no—
166#6103—22no—
167#6103C2×C814yes—
168#6103C2×C814yescomplemented
169#6103M1614yes—
170C4⋊Dic13—22no—
171C4⋊Dic13—22no—
172C4⋊Dic13C2×C814yescomplemented
173C4×Dic13—22no—
174C4×Dic13—22no—
175C4×Dic13—22no—
176C4×Dic13—22no—
177C4×Dic13—21no—
178C4×Dic13—21no—
179C4×Dic13—21no—
180C4×Dic13—21no—
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#1831D1311yescharacteristic, complemented
195#1797—131no—
196#1797—131no—
197C4×C4⋊C8—131no—
198C8×C22⋊C4—132no—
199C23×C13C23×C411yescharacteristic
200C22×D13—21no—
201C22×D13—21no—
202C22×D13—21no—
203C22×D13—21no—
204C22×D13—21no—
205C22×D13—21no—
206C22×D13—21no—
207C22×D13—21no—
208C22×D13—21no—
209C22×D13—21no—
210C22×D13#11712yes—
211C22×D13C22×C812yes—
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—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13C4×D412yes—
226C2×C4×C13C4×D412yes—
227C2×C4×C13C22×C812yes—
228C2×C4×C13C22×C812yes—
229C2×C4×C13C22×C812yes—
230C2×C4×C13C2×M1612yes—
231C2×C4×C13#13112yes—
232C2×C4×C13C22×D411yescharacteristic
233C2×C4×C13C2×#4111yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13H(5,𝔽2)11yescharacteristic
237C2×C4×C132−1+411yescharacteristic
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
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#11712yes—
253C2×Dic13C22×C812yes—
254C2×Dic13C22×C812yes—
255C2×Dic13C2×M1612yes—
256D52—28no—
257C4×D13—22no—
258C4×D13—22no—
259C4×D13—22no—
260C4×D13—22no—
261C4×D13—28no—
262C4×D13—28no—
263C4×D13—44no—
264C4×D13—44no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
268C4×D13—41no—
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×C42—131no—
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⋊C8—132no—
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—
300C43C2×D1311yescharacteristic
301#336—132no—
302#336—132no—
303#336—132no—
304#336C2×D1312yes—
305#336C2×D1312yes—
306C22×C13C2×#11711yescharacteristic
307C22×C13C2×C4×D411yescharacteristic
308C22×C13#52011yescharacteristic
309C22×C13C23×C811yescharacteristic
310C22×C13C22×M1611yescharacteristic
311C22×C13C2×#13111yescharacteristic
312C22×C13#56811yescharacteristic
313C2×D13—22no—
314C2×D13—22no—
315C2×D13—22no—
316C2×D13—22no—
317C2×D13—22no—
318C2×D13—22no—
319C2×D13—22no—
320C2×D13—22no—
321C2×D13—22no—
322C2×D13—41no—
323C2×D13—41no—
324C2×D13—41no—
325C2×D13—41no—
326C2×D13#43114yescomplemented
327C4×C13—22no—
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—22no—
331C4×C13—41no—
332C4×C13C8×D414yes—
333C4×C13#54611yescharacteristic
334C4×C13#54811yescharacteristic
335C4×C13#55211yescharacteristic
336C4×C13#55311yescharacteristic
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×C4—131no—
348C23×C4—131no—
349C23×C4—131no—
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—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42—131no—
376C2×C42—262no—
377C2×C42—262no—
378C2×C42—262no—
379C2×C42—262no—
380C2×C42C4×D1311yescharacteristic
381C2×C42C4×D1311yescharacteristic
382C2×C42C4×D1311yescharacteristic
383C2×C42C4×D1311yescharacteristic
384C2×C42C22×D1311yescharacteristic
385C2×C42C22×D1311yescharacteristic
386C2×C42C22×D1311yescharacteristic
387C4⋊C8—22no—
388C4⋊C8—22no—
389C4⋊C8—134no—
390C4⋊C8—264no—
391C4⋊C8—262no—
392C22⋊C8—264no—
393C22⋊C8—264no—
394C22⋊C8—522no—
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#235211yescharacteristic
404C2×C13C2×#43111yescharacteristic
405C2×C13#292511yescharacteristic
406C2×C13C2×C8×D411yescharacteristic
407C2×C13D4×M1611yescharacteristic
408C2×C13#298811yescharacteristic
409C2×C13#299011yescharacteristic
410D13—24no—
411D13—42no—
412C24—131no—
413C24—131no—
414C2×D4—134no—
415C2×D4—262no—
416C2×D4—262no—
417C22×C4—131no—
418C22×C4—131no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—134no—
422C22×C4—134no—
423C22×C4—132no—
424C22×C4—132no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—521no—
446C22×C4—521no—
447C22×C4C2×C4×D1311yescharacteristic
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—21no—
481C42—21no—
482C42—41no—
483C42—262no—
484C42—262no—
485C42—262no—
486C42—262no—
487C42—261no—
488C42—261no—
489C42—261no—
490C42—261no—
491C42C8×D1314yescomplemented
492C42D4×D1312yes—
493C42#613112yes—
494C13#2274811yescharacteristic, complemented, Sylow
495C23—132no—
496C23—132no—
497C23—132no—
498C23—132no—
499C23—261no—
500C23—261no—
501C23—261no—
502C23—261no—
503C23—261no—
504C23—261no—
505C23—261no—
506C23—261no—
507C23—261no—
508C23—261no—
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—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—132no—
523C2×C4—132no—
524C2×C4—132no—
525C2×C4—132no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—268no—
535C2×C4—268no—
536C2×C4—262no—
537C2×C4—262no—
538C2×C4—262no—
539C2×C4—262no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—524no—
547C2×C4—524no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4#8814712yes—
553C2×C4#8814712yes—
554C2×C4C2×C8×D1312yes—
555C2×C4C2×C8×D1312yes—
556C2×C4C2×C8×D1312yes—
557C2×C4M16×D1312yes—
558C2×C4#8816112yes—
559C2×C4C2×D4×D1311yescharacteristic
560C2×C4C2×#613111yescharacteristic
561C2×C4#41×D1311yescharacteristic
562C2×C4#41×D1311yescharacteristic
563C2×C4#8825611yescharacteristic
564C2×C4#8825711yescharacteristic
565C8—42no—
566C8—42no—
567C8—264no—
568C8—522no—
569C22—134no—
570C22—262no—
571C22—262no—
572C22—262no—
573C22—262no—
574C22—262no—
575C22—262no—
576C22—262no—
577C22—262no—
578C22—262no—
579C22—521no—
580C22—521no—
581C22—521no—
582C22—521no—
583C22C2×#8814711yescharacteristic
584C22D13×#11711yescharacteristic
585C22#1171922811yescharacteristic
586C22C22×C8×D1311yescharacteristic
587C22C2×M16×D1311yescharacteristic
588C22C2×#8816111yescharacteristic
589C22#1171945011yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—262no—
596C4—262no—
597C4—262no—
598C4—262no—
599C4—521no—
600C4—521no—
601C4#1171849514yes—
602C4#1171938111yescharacteristic
603C4#1171938211yescharacteristic
604C4#1171939911yescharacteristic
605C4#1171940011yescharacteristic
606C2—264no—
607C2—522no—
608C2#1311776211yescharacteristic
609C2D13×#43111yescharacteristic
610C2#1312350311yescharacteristic
611C2C2×#1171849511yescharacteristic
612C2#1312357111yescharacteristic
613C2#1312394411yescharacteristic
614C2#1312396311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC13×#1831C2
socleC23×C13C23×C4
prime radicalC22×D52C2×C4
cosocleC22×C4×C13C24
hypercenter#1831D13
hypocenterC13#22748
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1831

Complements

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

NH ≅ G/Ntype
1. C2×#11718494C2semidirect
2. C2×D13×C4⋊C8C2semidirect
4. #13115440C2semidirect
5. #13115392C2semidirect
7. #13114813C2semidirect
8. #13114813C2semidirect
9. C4×C4⋊#1055C2semidirect
10. #13114606C2semidirect
11. C13×#1831C2semidirect
84. C4×D52C8semidirect
103. C4⋊#1055D4semidirect
145. C2×C4×D13C2×C8semidirect
161. C42×C13C2×C8semidirect
168. #6103C2×C8semidirect
172. C4⋊Dic13C2×C8semidirect
194. #1831D13semidirect
326. C2×D13#431semidirect
491. C42C8×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×#117184942
C2×D13×C4⋊C82
C42×D522
#131154402
#131153922
#131151272
#131148132
C4×C4⋊#10552
#131146062
C13×#18312
#2274813