Finite Group Databasebeta

← #15907257

Subgroups — #15907257

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119144C211yesmaximal, characteristic
2D4×C4⋊Dic13C211yesmaximal, characteristic
3#13116395C211yesmaximal, characteristic, complemented
4#13116309C211yesmaximal, characteristic, complemented
5#13116259C211yesmaximal, characteristic, complemented
6#13116259C211yesmaximal, characteristic, complemented
7#13115408C211yesmaximal, characteristic, complemented
8#13115408C211yesmaximal, characteristic, complemented
9#13115026C211yesmaximal, characteristic, complemented
10#13115026C211yesmaximal, characteristic, complemented
11#13114923C211yesmaximal, characteristic, complemented
12#13114923C211yesmaximal, characteristic, complemented
13#13114865C211yesmaximal, characteristic, complemented
14C2×#11718143C211yesmaximal, characteristic, complemented
15C13×#1869C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×#88189—21no—
19C2×D4×Dic13—21no—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26#11718873C2211yescharacteristic
27#11718873C2211yescharacteristic
28#11718873C2211yescharacteristic
29#11718873C2211yescharacteristic
30#11718873C2211yescharacteristic
31C2×#88058C2211yescharacteristic
32C2×#88058C2211yescharacteristic
33C2×#88058C2211yescharacteristic
34C2×#88058C2211yescharacteristic
35#11718646—21no—
36#11718644—21no—
37#11718614—21no—
38#11718611—21no—
39#11718611—21no—
40#11718604—21no—
41#11718596C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45C13×#336C2211yescharacteristic
46C13×#336C2211yescharacteristic
47#11718143C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59C22×D4×C13D411yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13—21no—
63C23×Dic13—21no—
64C23×Dic13—21no—
65C22×C8×C13—22no—
66C22×C8×C13—22no—
67C22×C8×C13—41no—
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C4×D4×C13—22no—
73C4×D4×C13—22no—
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C22⋊C4D411yescharacteristic
76C2×C13×C22⋊C4D411yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83#88189—44no—
84D4×Dic13—44no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—41no—
95C2×C4⋊Dic13—41no—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×C4⋊Dic13C2311yescharacteristic
102C2×C4⋊Dic13C2311yescharacteristic
103C2×C4⋊Dic13C2311yescharacteristic
104C2×#6101—21no—
105C2×#6101—21no—
106C2×C4×Dic13—21no—
107C13×C22⋊C8—22no—
108C13×C22⋊C8—22no—
109C13×C22⋊C8—41no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88058—22no—
119#88058—22no—
120#88058—41no—
121#88058—41no—
122#24933—131nomaximal, Sylow
123C24×C13C2×D411yescharacteristic
124C24×C13C2×D411yescharacteristic
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13D814yes—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13#4112yes—
143C22×C4×C13#4112yes—
144C22×C4×C13C2411yescharacteristic
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—42no—
154C22×Dic13—42no—
155C22×Dic13—42no—
156C22×Dic13—42no—
157C22×Dic13—42no—
158C22×Dic13—42no—
159C22×Dic13—42no—
160C22×Dic13—81no—
161C22×Dic13—81no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—44no—
174C2×C8×C13#4112yes—
175C13×C4⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—22no—
178C42×C13—21no—
179C42×C13—21no—
180C22⋊Dic13—42no—
181C22⋊Dic13—42no—
182C22⋊Dic13—42no—
183C22⋊Dic13—42no—
184C22⋊Dic13—42no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—42no—
201C4⋊Dic13—42no—
202C4⋊Dic13—42no—
203C4⋊Dic13—42no—
204C4⋊Dic13—81no—
205C4⋊Dic13#4112yes—
206#6101—42no—
207#6101—42no—
208C4×Dic13—42no—
209#2486—131no—
210D4×C4⋊C4—131no—
211#2099—131no—
212#2083—131no—
213#2075—131no—
214#2075—131no—
215#1918—131no—
216#1918—131no—
217#1869D1311yescharacteristic
218#1852—131no—
219#1852—131no—
220#1823—131no—
221#1823—131no—
222#1808—131no—
223C2×#340—131no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13#12312yes—
235C23×C13C2×D812yes—
236C23×C13C2×D812yes—
237C23×C13#13712yes—
238C23×C13C22×D411yescharacteristic
239D4×C13—28no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13#12312yes—
259C2×C4×C13C2×D812yes—
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13H(5,𝔽2)11yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C2×Dic13—22no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—84no—
291C2×Dic13—84no—
292C2×Dic13—84no—
293C8×C13—22no—
294C8×C13—41no—
295C8×C13—41no—
296C8×C13—41no—
297C23×C8C2×D1311yescharacteristic
298C2×#123—261no—
299C2×C4×D4—261no—
300C2×C4×D4C2×D1311yescharacteristic
301C22×C4⋊C4—131no—
302C22×C4⋊C4—131no—
303C22×C4⋊C4—131no—
304C2×#107—131no—
305C2×#107—131no—
306C2×#107—131no—
307C2×#107—131no—
308C2×C22⋊C8C2×D1311yescharacteristic
309C2×C22⋊C8C2×D1311yescharacteristic
310C2×C22⋊C8C2×D1311yescharacteristic
311#398—261no—
312#397—261no—
313#389—131no—
314#389—131no—
315#389—261no—
316#385—261no—
317#385—261no—
318#384—131no—
319#381—261no—
320#380—131no—
321#380—131no—
322#380—131no—
323#380—131no—
324#380—131no—
325C4×C4⋊C4—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#336C2×D1311yescharacteristic
339#336C2×D1311yescharacteristic
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—22no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13#48014yes—
354C22×C13C2×#12311yescharacteristic
355C22×C13#54611yescharacteristic
356C22×C13#54711yescharacteristic
357C22×C13C22×D811yescharacteristic
358C22×C13C2×#13711yescharacteristic
359C22×C13#57711yescharacteristic
360C22×C13#57811yescharacteristic
361C4×C13—22no—
362C4×C13—22no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13#52911yescharacteristic
366C4×C13#53911yescharacteristic
367C4×C13#55111yescharacteristic
368C4×C13#55211yescharacteristic
369Dic13—42no—
370Dic13—81no—
371Dic13—81no—
372Dic13—81no—
373Dic13—81no—
374Dic13—81no—
375Dic13—81no—
376Dic13—81no—
377C22×D4D5211yescharacteristic
378C23×C4—261no—
379C23×C4—261no—
380C23×C4—261no—
381C23×C4C22×D1311yescharacteristic
382C23×C4C22×D1311yescharacteristic
383C22×C8—22no—
384C22×C8—22no—
385C22×C8—41no—
386C22×C8C22×D1311yescharacteristic
387C22×C8C22×D1311yescharacteristic
388C22×C8C22×D1311yescharacteristic
389C22×C8C22×D1311yescharacteristic
390#123—524no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—524no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—131no—
398C2×C4⋊C4—131no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—262no—
403C2×C4⋊C4—262no—
404C2×C4⋊C4—262no—
405C2×C4⋊C4—262no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4—521no—
414C2×C4⋊C4—521no—
415C2×C4⋊C4D5211yescharacteristic
416C2×C22⋊C4—261no—
417C2×C22⋊C4—261no—
418C2×C22⋊C4—261no—
419C2×C22⋊C4—261no—
420C2×C22⋊C4—261no—
421C2×C22⋊C4D5211yescharacteristic
422C2×C22⋊C4D5211yescharacteristic
423C2×C42—261no—
424C2×C42C22×D1311yescharacteristic
425#107—262no—
426#107—262no—
427#107—521no—
428#107—521no—
429C22⋊C8—22no—
430C22⋊C8—22no—
431C22⋊C8—41no—
432#95—261no—
433#95—261no—
434#95—261no—
435#95—261no—
436#95—261no—
437#95—261no—
438#95—261no—
439#95—261no—
440C2×C13—24no—
441C2×C13—42no—
442C2×C13#241911yescharacteristic
443C2×C13C2×#48011yescharacteristic
444C2×C13#309711yescharacteristic
445C2×C13#329411yescharacteristic
446C2×C13#331211yescharacteristic
447C2×C13#333411yescharacteristic
448C2×C13#334411yescharacteristic
449C24C2×D5211yescharacteristic
450C24C2×D5211yescharacteristic
451C2×D4—22no—
452C2×D4—22no—
453C2×D4D10414yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—522no—
473C22×C4—522no—
474C22×C4—522no—
475C22×C4—522no—
476C22×C4—522no—
477C22×C4—522no—
478C22×C4—522no—
479C22×C4—1041no—
480C22×C4—1041no—
481C22×C4C2×D5211yescharacteristic
482C22×C4C2×D5211yescharacteristic
483C22×C4C2×D5211yescharacteristic
484C22×C4C2×D5211yescharacteristic
485C22×C4#612912yes—
486C22×C4#612912yes—
487C22×C4C23×D1311yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—44no—
500C2×C8#612912yes—
501C4⋊C4—22no—
502C4⋊C4—132no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4—522no—
519C4⋊C4—522no—
520C4⋊C4—522no—
521C4⋊C4—522no—
522C4⋊C4—522no—
523C4⋊C4—522no—
524C4⋊C4—1041no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—522no—
528C22⋊C4—522no—
529C22⋊C4—522no—
530C22⋊C4—522no—
531C22⋊C4—522no—
532C42—21no—
533C42—21no—
534C42—522no—
535C13#2493311yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23#8814012yes—
547C23C2×D10412yes—
548C23C2×D10412yes—
549C23#8816312yes—
550C23C22×D5211yescharacteristic
551D4—28no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—262no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—1044no—
595C2×C4—1044no—
596C2×C4—1044no—
597C2×C4#8814012yes—
598C2×C4C2×D10412yes—
599C2×C4C2×#612911yescharacteristic
600C2×C4C2×#612911yescharacteristic
601C2×C4C2×#612911yescharacteristic
602C2×C4#8825111yescharacteristic
603C2×C4#41×D1311yescharacteristic
604C2×C4#8825711yescharacteristic
605C8—22no—
606C8—41no—
607C8—41no—
608C8—41no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22#1171839714yes—
623C22C2×#8814011yescharacteristic
624C22#1171925911yescharacteristic
625C22#1171926011yescharacteristic
626C22C22×D10411yescharacteristic
627C22C2×#8816311yescharacteristic
628C22#1171945611yescharacteristic
629C22#1171945811yescharacteristic
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—522no—
635C4—1041no—
636C4—1041no—
637C4—1041no—
638C4—1041no—
639C4—1041no—
640C4—1041no—
641C4—1041no—
642C4#1171929211yescharacteristic
643C4#1171930511yescharacteristic
644C4#1171930711yescharacteristic
645C4#1171935511yescharacteristic
646C2—24no—
647C2—42no—
648C2#1311831111yescharacteristic
649C2C2×#1171839711yescharacteristic
650C2#1312480611yescharacteristic
651C2#1312665011yescharacteristic
652C2#1312688911yescharacteristic
653C2#1312718411yescharacteristic
654C2#1312729311yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1869C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#1869D13
hypocenterC13#24933
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1869

Complements

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

NH ≅ G/Ntype
3. #13116395C2semidirect
4. #13116309C2semidirect
5. #13116259C2semidirect
6. #13116259C2semidirect
7. #13115408C2semidirect
8. #13115408C2semidirect
9. #13115026C2semidirect
10. #13115026C2semidirect
11. #13114923C2semidirect
12. #13114923C2semidirect
13. #13114865C2semidirect
14. C2×#11718143C2semidirect
535. C13#24933semidirect

Maximal subgroups

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

subgroupindex
#131191442
D4×C4⋊Dic132
#131163952
#131163092
#131162592
#131154082
#131150262
#131149232
#131148652
C2×#117181432
C13×#18692
#2493313