Finite Group Databasebeta

← #15925448

Subgroups — #15925448

Order 3328.

882 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718512C211yesmaximal, characteristic, complemented
2C22×#88057C211yesmaximal, characteristic
3#13118538C211yesmaximal, characteristic
4#13117839C211yesmaximal, characteristic
5#13116378C211yesmaximal, characteristic, complemented
6#13116334C211yesmaximal, characteristic, complemented
7#13116216C211yesmaximal, characteristic, complemented
8#13116170C211yesmaximal, characteristic, complemented
9#13115600C211yesmaximal, characteristic, complemented
10#13115415C211yesmaximal, characteristic, complemented
11#13115259C211yesmaximal, characteristic
12#13115141C211yesmaximal, characteristic
13#13115107C211yesmaximal, characteristic, complemented
14#13115031C211yesmaximal, characteristic
15C13×#1850C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C2×#88132—21no—
21C2×#88123C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26C4×C13×C22⋊C4C2211yescharacteristic
27#11718873C2211yescharacteristic
28C2×#88057—24no—
29C2×#88057C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31C2×#88057C2211yescharacteristic
32C2×#88057C2211yescharacteristic
33C2×#88057C2211yescharacteristic
34C2×#88057C2211yescharacteristic
35C2×#88056C2211yescharacteristic
36C2×#88056C2211yescharacteristic
37C2×#88056C2211yescharacteristic
38C2×#88056C2211yescharacteristic
39#11718611—21no—
40#11718607—21no—
41C22⋊C4×Dic13—21no—
42#11718596C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44#11718590C2211yescharacteristic
45#11718589C2211yescharacteristic
46#11718589C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718512—24no—
49#11718322—21no—
50#11718317—21no—
51#11718316—21no—
52#11718308—21no—
53C13×#336C2211yescharacteristic
54C13×#336C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60#11718143C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13—21no—
63C23×Dic13—21no—
64C22×Dic26—21no—
65C22×Dic26C2311yescharacteristic
66C22×C8×C13—22no—
67C22×C8×C13—22no—
68C22×C8×C13—22no—
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C2×C13×C22⋊C4D411yescharacteristic
74C2×C13×C22⋊C4D411yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×C42×C13C2311yescharacteristic
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—41no—
87C2×C4⋊Dic13—41no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95#88178—22no—
96#88178Q814yescomplemented
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—21no—
101C2×#6101—21no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13—21no—
104#88132—44no—
105#88123—22no—
106#88123—41no—
107C4×Dic26—22no—
108C4×Dic26—41no—
109C13×C4⋊C8—22no—
110C13×C4⋊C8—22no—
111C13×C22⋊C8—22no—
112C13×#95D411yescharacteristic
113C13×#95D411yescharacteristic
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88057—22no—
122#88057—22no—
123#88057—22no—
124#88057—22no—
125#88057—41no—
126#88057D414yes—
127#88056—22no—
128#88056—22no—
129#88056—22no—
130#88056—41no—
131#26340—131nomaximal, Sylow
132C24×C13C2×D411yescharacteristic
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×Q812yes—
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—81no—
158C22×Dic13—81no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—42no—
165C2×Dic26—42no—
166C2×Dic26—81no—
167C2×Dic26C2×Q812yes—
168C2×C8×C13—28no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13C2×D412yes—
180C2×C8×C13#4112yes—
181C13×C22⋊C4—22no—
182C13×C22⋊C4SD1614yes—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—21no—
187C22⋊Dic13—24no—
188C22⋊Dic13—42no—
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⋊Dic13C2×D412yes—
206C4⋊Dic13C2×D412yes—
207C4⋊Dic13C2×Q812yes—
208#6101—24no—
209#6101—42no—
210#6101—42no—
211#6101—42no—
212#6101—81no—
213C4×Dic13—42no—
214C4×Dic13—81no—
215C2×#475—131no—
216C22×#106—131no—
217#2440—131no—
218#2360—131no—
219#2096—131no—
220#2088—131no—
221#2066—131no—
222#2058—131no—
223#1948—131no—
224#1919—131no—
225#1892—131no—
226#1872—131no—
227#1865—131no—
228#1853—131no—
229#1850D1311yescharacteristic
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13C22⋊Q812yes—
235C23×C13C2×SD1612yes—
236C23×C13#13712yes—
237C23×C13C22×D411yescharacteristic
238C2×C4×C13—21no—
239C2×C4×C13—21no—
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×C13C22⋊Q812yes—
255C2×C4×C13C2×SD1612yes—
256C2×C4×C13C2×SD1612yes—
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C22×Q811yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13H(5,𝔽2)11yescharacteristic
262C2×C4×C132−1+411yescharacteristic
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—22no—
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—84no—
288C2×Dic13—84no—
289Dic26—22no—
290Dic26—22no—
291Dic26—41no—
292Dic26—41no—
293Dic26—84no—
294C8×C13—22no—
295C8×C13—22no—
296C8×C13—41no—
297C8×C13—41no—
298C23×C8C2×D1311yescharacteristic
299C2×C4⋊Q8—131no—
300C2×C22⋊Q8—131no—
301C2×C22⋊Q8—261no—
302C2×C4×Q8—131no—
303C22×C4⋊C4—131no—
304C22×C4⋊C4—131no—
305#475—264no—
306C2×#106—131no—
307C2×#106—131no—
308C2×#106—131no—
309C2×#106—131no—
310C2×#106—131no—
311C2×#106—131no—
312C2×#106—264no—
313C2×C4⋊C8C2×D1311yescharacteristic
314C2×C4⋊C8C2×D1311yescharacteristic
315C2×#103—131no—
316C2×#103—131no—
317C2×#103—131no—
318C2×#103—131no—
319C2×C22⋊C8C2×D1311yescharacteristic
320#398—261no—
321#395—261no—
322#391—131no—
323#389—131no—
324#389—131no—
325#389—131no—
326#389—261no—
327#387—261no—
328#385—261no—
329#385—261no—
330#384—131no—
331#380—131no—
332C4×C4⋊C4—131no—
333C4×C22⋊C4—261no—
334C4×C22⋊C4C2×D1311yescharacteristic
335#340—131no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#336C2×D1311yescharacteristic
342#336C2×D1311yescharacteristic
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—22no—
349C22×C13#47514yescomplemented
350C22×C13C2×C22⋊Q811yescharacteristic
351C22×C13D4211yescharacteristic
352C22×C13#54711yescharacteristic
353C22×C13C22×SD1611yescharacteristic
354C22×C13C2×#13711yescharacteristic
355C22×C13#57711yescharacteristic
356C22×C13#57711yescharacteristic
357C4×C13—22no—
358C4×C13—22no—
359C4×C13—22no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13#52511yescharacteristic
363C4×C13#53911yescharacteristic
364C4×C13D4×Q811yescharacteristic
365C4×C13#55411yescharacteristic
366Dic13—42no—
367Dic13—42no—
368Dic13—42no—
369Dic13—42no—
370Dic13—81no—
371Dic13—81no—
372Dic13—81no—
373Dic13—81no—
374C22×Q8—131no—
375C22×Q8—261no—
376C23×C4—261no—
377C23×C4—261no—
378C23×C4C22×D1311yescharacteristic
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—22no—
382C22×C8C22×D1311yescharacteristic
383C22×C8C22×D1311yescharacteristic
384C22×C8C22×D1311yescharacteristic
385C22×C8C22×D1311yescharacteristic
386C4⋊Q8—262no—
387C4⋊Q8—521no—
388C22⋊Q8—134no—
389C22⋊Q8—262no—
390C22⋊Q8—524no—
391C4×Q8—262no—
392C4×Q8—521no—
393C2×C4⋊C4—131no—
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—262no—
401C2×C4⋊C4—262no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
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—521no—
413C2×C4⋊C4—521no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4D5211yescharacteristic
417C2×C22⋊C4D5211yescharacteristic
418C2×C42—261no—
419C2×C42—261no—
420C2×C42C22×D1311yescharacteristic
421C2×C42C22×D1311yescharacteristic
422#106—134no—
423#106—262no—
424#106—262no—
425#106—262no—
426#106—262no—
427#106—521no—
428C4⋊C8—22no—
429C4⋊C8—22no—
430#103—262no—
431#103—262no—
432#103—262no—
433#103—521no—
434C22⋊C8—22no—
435#95—261no—
436#95—261no—
437#95—261no—
438#95—261no—
439#95—261no—
440#95—261no—
441#95—261no—
442#95D5211yescharacteristic
443#95D5211yescharacteristic
444C2×C13—24no—
445C2×C13#244911yescharacteristic
446C2×C13C2×#47511yescharacteristic
447C2×C13#308411yescharacteristic
448C2×C13#326611yescharacteristic
449C2×C13D4×SD1611yescharacteristic
450C2×C13#333511yescharacteristic
451C2×C13#334411yescharacteristic
452C24C2×D5211yescharacteristic
453C2×Q8—132no—
454C2×Q8—261no—
455C2×Q8—261no—
456C2×Q8—261no—
457C2×Q8—261no—
458C2×Q8—261no—
459C2×Q8—522no—
460C2×Q8—522no—
461C2×Q8—1041no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—522no—
475C22×C4—522no—
476C22×C4—522no—
477C22×C4—522no—
478C22×C4—1041no—
479C22×C4—1041no—
480C22×C4C2×D5211yescharacteristic
481C22×C4C2×D5211yescharacteristic
482C22×C4C2×D5211yescharacteristic
483C22×C4C2×D5211yescharacteristic
484C22×C4C2×D5211yescharacteristic
485C22×C4#612912yes—
486C22×C4Q8×D1312yes—
487C22×C4C23×D1311yescharacteristic
488C2×C8—28no—
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×C8D4×D1312yes—
500C2×C8#612912yes—
501C4⋊C4—132no—
502C4⋊C4—132no—
503C4⋊C4—132no—
504C4⋊C4—264no—
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—522no—
517C4⋊C4—522no—
518C4⋊C4—522no—
519C4⋊C4—522no—
520C4⋊C4—522no—
521C4⋊C4—522no—
522C4⋊C4—522no—
523C4⋊C4—1041no—
524C4⋊C4—1041no—
525C22⋊C4—22no—
526C22⋊C4—264no—
527C22⋊C4—522no—
528C22⋊C4#609514yes—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—522no—
534C42—1041no—
535C13#2634011yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23#8815112yes—
541C23C2×#609512yes—
542C23#8816312yes—
543C23C22×D5211yescharacteristic
544Q8—262no—
545Q8—262no—
546Q8—521no—
547Q8—521no—
548Q8—1044no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—521no—
570C2×C4—521no—
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—1044no—
590C2×C4—1044no—
591C2×C4#8815112yes—
592C2×C4C2×#609512yes—
593C2×C4C2×#609512yes—
594C2×C4C2×D4×D1311yescharacteristic
595C2×C4C2×#612911yescharacteristic
596C2×C4C2×#612911yescharacteristic
597C2×C4C2×Q8×D1311yescharacteristic
598C2×C4#8825611yescharacteristic
599C2×C4#8825711yescharacteristic
600C8—22no—
601C8—22no—
602C8—41no—
603C8—41no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22#1171851214yescomplemented
611C22C2×#8815111yescharacteristic
612C22D4×D5211yescharacteristic
613C22#1171926011yescharacteristic
614C22C22×#609511yescharacteristic
615C22C2×#8816311yescharacteristic
616C22#1171945611yescharacteristic
617C22#1171945611yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—41no—
622C4—41no—
623C4—522no—
624C4—522no—
625C4—522no—
626C4—522no—
627C4—1041no—
628C4—1041no—
629C4—1041no—
630C4—1041no—
631C4#1171929111yescharacteristic
632C4#1171933711yescharacteristic
633C4#1171934011yescharacteristic
634C4#1171937011yescharacteristic
635C2—24no—
636C2#1311864311yescharacteristic
637C2C2×#1171851211yescharacteristic
638C2#1312470011yescharacteristic
639C2#1312635111yescharacteristic
640C2D4×#609511yescharacteristic
641C2#1312719411yescharacteristic
642C2#1312729311yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1850C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1850D13
hypocenterC13#26340
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#11718512C2semidirect
5. #13116378C2semidirect
6. #13116334C2semidirect
7. #13116216C2semidirect
8. #13116170C2semidirect
9. #13115600C2semidirect
10. #13115415C2semidirect
13. #13115107C2semidirect
96. #88178Q8semidirect
349. C22×C13#475semidirect
535. C13#26340semidirect
610. C22#11718512semidirect

Maximal subgroups

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

subgroupindex
C2×#117185122
C22×#880572
#131185382
#131178392
#131163782
#131163342
#131162162
#131161702
#131156002
#131154152
#131152592
#131151412
#131151072
#131150312
C13×#18502
#2634013