Finite Group Databasebeta

← #15785473

Subgroups — #15785473

Order 3328.

1766 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88141C211yesmaximal, characteristic
2C2×#11718307C212yesmaximal
3C2×#11718311C211yesmaximal, characteristic
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic
5#13113090C211yesmaximal, characteristic
6#13113089C211yesmaximal, characteristic
7#13113086C211yesmaximal, characteristic
8#13113064C212yesmaximal
9#13113062C212yesmaximal
10#13113061C212yesmaximal
11C13×#1441C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101C2212yes—
17C22×#6101C2211yescharacteristic
18C22×#6101C2211yescharacteristic
19C22×C4×Dic13C2212yes—
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C2×#88141—24no—
24C2×#88141—24no—
25C2×#88141C418yescomplemented
26C2×C13×#95C2211yescharacteristic
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C4⋊C4×Dic13—24no—
39#11718311—24no—
40#11718307—28no—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C22×Dic26—22no—
53C22×Dic26—22no—
54C22×Dic26—22no—
55C22×Dic26—22no—
56C22×Dic26C2×C414yes—
57C22×Dic26D414yes—
58C22×Dic26Q814yes—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—24no—
63C2×C13×C4⋊C4C2×C414yes—
64C2×C4⋊Dic13—22no—
65C2×C4⋊Dic13—24no—
66C2×#6101—22no—
67C2×#6101—22no—
68C2×#6101—22no—
69C2×#6101—22no—
70C2×#6101—24no—
71C2×#6101—24no—
72C2×#6101—24no—
73C2×#6101C2×C414yes—
74C2×#6101C2×C414yes—
75C2×C4×Dic13—22no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13—22no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13—24no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13C2×C414yes—
83C2×C4×Dic13C2×C414yes—
84C2×C4×Dic13C2×C414yes—
85C2×C4×Dic13D414yes—
86C2×C4×Dic13D414yes—
87#88141—232no—
88C13×#95—24no—
89C13×#95—22no—
90C13×#95—24no—
91#88071—24no—
92#88071—22no—
93#88071—24no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—24no—
98#88071—24no—
99#88071—24no—
100#13942—131nomaximal, Sylow
101C24×C13C2411yescharacteristic
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13C22×C412yes—
126C22×C4×C13C22×C412yes—
127C22×C4×C13C22×C412yes—
128C22×C4×C13C2×D412yes—
129C22×C4×C13C2×D412yes—
130C22×C4×C13C2×D412yes—
131C22×C4×C13C2×Q812yes—
132C22×C4×C13#4114yes—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13C22×C412yes—
157C22×Dic13C22×C412yes—
158C22×Dic13C22×C412yes—
159C22×Dic13C22×C412yes—
160C22×Dic13C2×D412yes—
161C22×Dic13C2×D412yes—
162C22×Dic13C2×D412yes—
163C22×Dic13C2×D412yes—
164C22×Dic13C2×D412yes—
165C22×Dic13C2×D412yes—
166C22×Dic13C2×Q812yes—
167C22×Dic13C2×Q812yes—
168C22×Dic13#4114yes—
169C22×Dic13#4112yes—
170C22×Dic13#4112yes—
171C2×Dic26—28no—
172C2×Dic26—28no—
173C2×Dic26—28no—
174C2×Dic26—28no—
175C2×Dic26—28no—
176C2×Dic26—28no—
177C2×Dic26C4⋊C4116yescomplemented
178C13×C4⋊C4—28no—
179C13×C4⋊C4—28no—
180C4⋊Dic13—28no—
181#6101—28no—
182#6101—28no—
183#6101—48no—
184C4×Dic13—28no—
185C4×Dic13—28no—
186C4×Dic13—48no—
187C4×Dic13C22⋊C4116yes—
188C22×C4×Q8—131no—
189C2×#391—132no—
190C2×#382—131no—
191C2×C4×C4⋊C4—131no—
192#1441—131no—
193#1441—131no—
194#1441—131no—
195#1441D1311yescharacteristic
196C4⋊#95—132no—
197#1434—132no—
198#1434—132no—
199C23×C13C23×C411yescharacteristic
200C23×C13C22×D411yescharacteristic
201C23×C13C22×D411yescharacteristic
202C23×C13C22×D411yescharacteristic
203C23×C13C22×Q811yescharacteristic
204C23×C13C2×#4111yescharacteristic
205C23×C13C2×#4111yescharacteristic
206C23×C13C2×#4112yes—
207C23×C13C2×#4112yes—
208C23×C132−1+412yes—
209C23×C132−1+412yes—
210C2×C4×C13—22no—
211C2×C4×C13—22no—
212C2×C4×C13—24no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—24no—
220C2×C4×C13—22no—
221C2×C4×C13—24no—
222C2×C4×C13—24no—
223C2×C4×C13—24no—
224C2×C4×C13—24no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13C2×C22⋊C414yes—
240C2×C4×C13C2×C4⋊C414yes—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—24no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—24no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—24no—
253C2×Dic13—24no—
254C2×Dic13—24no—
255C2×Dic13—24no—
256C2×Dic13—42no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—42no—
270C2×Dic13C2×C22⋊C414yes—
271C2×Dic13C2×C22⋊C414yes—
272C2×Dic13C2×C4⋊C414yes—
273C2×Dic13C2×C4⋊C414yes—
274C2×Dic13#11714yes—
275C2×Dic13#12114yes—
276C2×Dic13#12114yes—
277C2×Dic13C22⋊Q814yes—
278C2×Dic13C22⋊Q814yes—
279Dic26—232no—
280C23×Q8—131no—
281C2×C4×Q8—138no—
282C2×C4×Q8—264no—
283C2×C4×Q8—264no—
284C22×C4⋊C4—131no—
285C22×C4⋊C4—131no—
286C22×C4⋊C4—132no—
287C22×C4⋊C4—131no—
288C22×C4⋊C4C2×D1311yescharacteristic
289C22×C4⋊C4C2×D1311yescharacteristic
290C22×C42—131no—
291C22×C42—131no—
292C22×C42—131no—
293C22×C42—132no—
294#391—268no—
295#382—264no—
296C4×C4⋊C4—264no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95—132no—
300C2×#95—132no—
301C2×#95—132no—
302C2×#95—132no—
303C2×#95—132no—
304C2×#95—132no—
305C2×#95—131no—
306C2×#95C2×D1312yes—
307C2×#95C2×D1312yes—
308C2×#95C2×D1311yescharacteristic
309C22×C13C22×C22⋊C411yescharacteristic
310C22×C13C22×C4⋊C411yescharacteristic
311C22×C13C2×#11711yescharacteristic
312C22×C13C4×#4112yes—
313C22×C13#51912yes—
314C22×C13C2×#12111yescharacteristic
315C22×C13C2×#12111yescharacteristic
316C22×C13C2×C22⋊Q811yescharacteristic
317C22×C13C2×C22⋊Q811yescharacteristic
318C22×C13#52511yescharacteristic
319C22×C13#52511yescharacteristic
320C22×C13#53212yes—
321C22×C13#53611yescharacteristic
322C22×C13#53612yes—
323C22×C13#53611yescharacteristic
324C22×C13#54812yes—
325C22×C13#54812yes—
326C22×C13#55212yes—
327C22×C13#55212yes—
328C22×C13#55612yes—
329C22×C13#55612yes—
330C22×C13#55712yes—
331C22×C13#55712yes—
332C4×C13—24no—
333C4×C13—24no—
334C4×C13—44no—
335C4×C13—42no—
336C4×C13—82no—
337Dic13—24no—
338Dic13—24no—
339Dic13—44no—
340Dic13—42no—
341Dic13—82no—
342Dic13#38018yes—
343C22×Q8—134no—
344C22×Q8—134no—
345C22×Q8—134no—
346C22×Q8—262no—
347C22×Q8—262no—
348C22×Q8—262no—
349C22×Q8—262no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—131no—
353C23×C4—131no—
354C23×C4—132no—
355C23×C4—132no—
356C23×C4C22×D1312yes—
357C23×C4C22×D1311yescharacteristic
358C23×C4C22×D1312yes—
359C23×C4C22×D1311yescharacteristic
360C23×C4C22×D1311yescharacteristic
361C4×Q8—2632no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—134no—
367C2×C4⋊C4—134no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4—264no—
371C2×C4⋊C4—262no—
372C2×C4⋊C4—262no—
373C2×C4⋊C4—262no—
374C2×C4⋊C4—264no—
375C2×C4⋊C4—264no—
376C2×C4⋊C4—264no—
377C2×C4⋊C4C4×D1314yes—
378C2×C42—134no—
379C2×C42—134no—
380C2×C42—134no—
381C2×C42—134no—
382C2×C42—134no—
383C2×C42—262no—
384C2×C42—262no—
385C2×C42—262no—
386C2×C42—262no—
387C2×C42—264no—
388C2×C42—264no—
389C2×C42—264no—
390#95—22no—
391#95—24no—
392#95—24no—
393#95—264no—
394#95—264no—
395#95—264no—
396#95—264no—
397#95—264no—
398#95—264no—
399#95—262no—
400#95—264no—
401#95—264no—
402C2×C13C2×#38011yescharacteristic
403C2×C13#229711yescharacteristic
404C2×C13#231011yescharacteristic
405C2×C13#235112yes—
406C2×C13#235612yes—
407C2×C13#253611yescharacteristic
408C2×C13#253611yescharacteristic
409C2×C13#254512yes—
410C2×C13#256512yes—
411C2×C13#258111yescharacteristic
412C2×C13#258111yescharacteristic
413C24C23×D1311yescharacteristic
414C2×Q8—1316no—
415C2×Q8—268no—
416C2×Q8—268no—
417C2×Q8—268no—
418C2×Q8—268no—
419C2×Q8—268no—
420C2×Q8—268no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—132no—
445C22×C4—132no—
446C22×C4—132no—
447C22×C4—132no—
448C22×C4—132no—
449C22×C4—132no—
450C22×C4—132no—
451C22×C4—132no—
452C22×C4—132no—
453C22×C4—132no—
454C22×C4—132no—
455C22×C4—132no—
456C22×C4—132no—
457C22×C4—132no—
458C22×C4—134no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—262no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4C2×C4×D1312yes—
483C22×C4C2×C4×D1312yes—
484C22×C4C2×C4×D1312yes—
485C22×C4D4×D1312yes—
486C22×C4D4×D1312yes—
487C22×C4D4×D1312yes—
488C22×C4#612914yes—
489C22×C4Q8×D1312yes—
490C4⋊C4—28no—
491C4⋊C4—28no—
492C4⋊C4—268no—
493C4⋊C4—268no—
494C4⋊C4—268no—
495C4⋊C4—528no—
496C42—1316no—
497C42—268no—
498C42—268no—
499C42—528no—
500C13#1394211yescharacteristic, complemented, Sylow
501C23C22×C4×D1311yescharacteristic
502C23C2×D4×D1311yescharacteristic
503C23C2×D4×D1311yescharacteristic
504C23C2×D4×D1311yescharacteristic
505C23C2×#612912yes—
506C23C2×Q8×D1311yescharacteristic
507C23#8825412yes—
508C23#41×D1311yescharacteristic
509C23#41×D1311yescharacteristic
510C23#41×D1312yes—
511C23#8825712yes—
512Q8—2632no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
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—134no—
543C2×C4—134no—
544C2×C4—134no—
545C2×C4—134no—
546C2×C4—134no—
547C2×C4—134no—
548C2×C4—134no—
549C2×C4—134no—
550C2×C4—134no—
551C2×C4—262no—
552C2×C4—262no—
553C2×C4—262no—
554C2×C4—264no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—262no—
558C2×C4—262no—
559C2×C4—264no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—264no—
563C2×C4—264no—
564C2×C4—264no—
565C2×C4—264no—
566C2×C4—522no—
567C2×C4—521no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—522no—
571C2×C4—521no—
572C2×C4—522no—
573C2×C4—522no—
574C2×C4—522no—
575C2×C4—522no—
576C2×C4—522no—
577C2×C4—522no—
578C2×C4—522no—
579C2×C4—522no—
580C2×C4C22⋊C4×D1314yes—
581C2×C4C4⋊C4×D1314yes—
582C22C2×C22⋊C4×D1311yescharacteristic
583C22C2×C4⋊C4×D1311yescharacteristic
584C22D13×#11711yescharacteristic
585C22C4×#612912yes—
586C22#1171927712yes—
587C22#1171929111yescharacteristic
588C22#1171930112yes—
589C22#1171930312yes—
590C22D13×#12111yescharacteristic
591C22D13×#12111yescharacteristic
592C22D13×C22⋊Q811yescharacteristic
593C22D13×C22⋊Q811yescharacteristic
594C22#1171933312yes—
595C22#1171933812yes—
596C22#1171934612yes—
597C22#1171935512yes—
598C22#1171936111yescharacteristic
599C22#1171938011yescharacteristic
600C22#1171939012yes—
601C22#1171939812yes—
602C22#1171940712yes—
603C22#1171942612yes—
604C22#1171942911yescharacteristic
605C4—24no—
606C4—24no—
607C4—42no—
608C4—44no—
609C4—82no—
610C4—138no—
611C4—264no—
612C4—264no—
613C4—522no—
614C4—524no—
615C4—1042no—
616C2D13×#38011yescharacteristic
617C2#1311732111yescharacteristic
618C2#1311741911yescharacteristic
619C2#1311775512yes—
620C2#1311779812yes—
621C2#1311974011yescharacteristic
622C2#1311974211yescharacteristic
623C2#1311981112yes—
624C2#1312002212yes—
625C2#1312019711yescharacteristic
626C2#1312019911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1441D13
hypocenterC13#13942
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
25. C2×#88141C4semidirect
177. C2×Dic26C4⋊C4semidirect
500. C13#13942semidirect

Maximal subgroups

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

subgroupindex
C22×#881412
C2×#117183072
C2×#117183112
C2×C4⋊C4×Dic132
#131130902
#131130892
#131130862
#131130642
#131130622
#131130612
C13×#14412
#1394213