Finite Group Databasebeta

← #15785272

Subgroups — #15785272

Order 3328.

1426 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718646C211yesmaximal, characteristic
2C2×#11718638C212yesmaximal
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic
4#13113095C212yesmaximal
5#13113092C212yesmaximal
6#13113066C211yesmaximal, characteristic
7#13113065C211yesmaximal, characteristic
8#13113065C211yesmaximal, characteristic
9#13113062C212yesmaximal
10C4×#88071C211yesmaximal, characteristic
11C2×C13×#389C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2212yes—
18C22×C4⋊Dic13C2211yescharacteristic
19C22×C4×Dic13C2211yescharacteristic
20C22×C4×Dic13C2212yes—
21C22×C4×Dic13C2211yescharacteristic
22C13×#389—24no—
23C2×C13×#95C2212yes—
24C2×#88071C2211yescharacteristic
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36#11718646—24no—
37#11718638—28no—
38C4⋊C4×Dic13C418yescomplemented
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×Dic13C2312yes—
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C2×C13×C4⋊C4—24no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—42no—
56C2×C13×C4⋊C4C2×C414yes—
57C2×C13×C4⋊C4D414yes—
58C2×C13×C4⋊C4Q814yes—
59C2×C42×C13—22no—
60C2×C42×C13—22no—
61C2×C42×C13—22no—
62C2×C4⋊Dic13—22no—
63C2×C4⋊Dic13—22no—
64C2×C4⋊Dic13—24no—
65C2×C4⋊Dic13—22no—
66C2×C4⋊Dic13—22no—
67C2×C4⋊Dic13—22no—
68C2×C4⋊Dic13—24no—
69C2×C4⋊Dic13—42no—
70C2×C4⋊Dic13C2×C414yes—
71C2×C4×Dic13—22no—
72C2×C4×Dic13—22no—
73C2×C4×Dic13—24no—
74C2×C4×Dic13—24no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13—22no—
78C2×C4×Dic13C2×C414yes—
79C2×C4×Dic13C2×C418yes—
80C13×#95—24no—
81#88071—24no—
82#88071—24no—
83#88071—22no—
84#88071—24no—
85#88071—24no—
86#88071—24no—
87#88071—22no—
88#88071—24no—
89#88071—22no—
90#88071—42no—
91#88071C2×C418yes—
92#88071D414yes—
93#13918—131nomaximal, Sylow
94C24×C13C2411yescharacteristic
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
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×C13C22×C414yes—
119C22×C4×C13C22×C412yes—
120C22×C4×C13C2×D412yes—
121C22×C4×C13C2×D414yes—
122C22×C4×C13C2×D412yes—
123C22×C4×C13C2×Q814yes—
124C22×C4×C13C2×Q812yes—
125C22×C4×C13#4112yes—
126C22×C4×C13#4112yes—
127C22×C4×C13#4112yes—
128C22×C4×C13#4112yes—
129C22×C4×C13#4112yes—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—22no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—22no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13C22×C412yes—
166C22×Dic13C22×C414yes—
167C22×Dic13C22×C412yes—
168C22×Dic13C2×D412yes—
169C22×Dic13C2×D412yes—
170C22×Dic13#4112yes—
171C22×Dic13#4112yes—
172C13×C4⋊C4—48no—
173C13×C4⋊C4—44no—
174C13×C4⋊C4C4⋊C4116yes—
175C42×C13—44no—
176C4⋊Dic13—28no—
177C4⋊Dic13—48no—
178C4⋊Dic13—44no—
179C4×Dic13—28no—
180C4×Dic13—216no—
181C4×Dic13—44no—
182C2×#389—131no—
183C2×#389D1311yescharacteristic
184C2×#382—132no—
185C2×C4×C4⋊C4—131no—
186#1442—132no—
187#1442—132no—
188C4⋊#95—131no—
189C4⋊#95—131no—
190C4⋊#95—131no—
191#1434—132no—
192C4×#95—131no—
193C23×C13C23×C411yescharacteristic
194C23×C13C22×D411yescharacteristic
195C23×C13C22×D411yescharacteristic
196C23×C13C22×Q811yescharacteristic
197C23×C13C2×#4111yescharacteristic
198C23×C13C2×#4111yescharacteristic
199C23×C13C2×#4111yescharacteristic
200C23×C13C2×#4111yescharacteristic
201C23×C13C2×#4111yescharacteristic
202C23×C13C2×#4111yescharacteristic
203C23×C13C2×#4111yescharacteristic
204C23×C13H(5,𝔽2)11yescharacteristic
205C23×C132−1+411yescharacteristic
206C23×C132−1+411yescharacteristic
207C23×C132−1+411yescharacteristic
208C2×C4×C13—24no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
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×C13C2×C4⋊C418yes—
236C2×C4×C13C2×C4⋊C414yes—
237C2×C4×C13#11714yes—
238C2×C4×C13#11714yes—
239C2×C4×C13#12414yes—
240C2×C4×C13#12414yes—
241C2×C4×C13#12514yes—
242C2×C4×C13#12514yes—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—24no—
251C2×Dic13—24no—
252C2×Dic13—22no—
253C2×Dic13—24no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
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—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13C4×D414yes—
285C22×C4⋊C4—131no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4—132no—
288C22×C4⋊C4C2×D1311yescharacteristic
289C22×C4⋊C4C2×D1312yes—
290C22×C4⋊C4C2×D1311yescharacteristic
291C22×C42—131no—
292C22×C42—132no—
293C22×C42—131no—
294C22×C42C2×D1311yescharacteristic
295#389—24no—
296#389—264no—
297#382—268no—
298C4×C4⋊C4—138no—
299C2×#95—131no—
300C2×#95—132no—
301C2×#95—131no—
302C2×#95—131no—
303C2×#95—131no—
304C2×#95—132no—
305C2×#95—132no—
306C2×#95—132no—
307C2×#95—132no—
308C2×#95—132no—
309C2×#95—132no—
310C2×#95—132no—
311C2×#95C2×D1312yes—
312C22×C13C22×C4⋊C411yescharacteristic
313C22×C13C2×#11711yescharacteristic
314C22×C13C2×#11711yescharacteristic
315C22×C13C2×C4×D411yescharacteristic
316C22×C13C4×#4111yescharacteristic
317C22×C13#51911yescharacteristic
318C22×C13#52011yescharacteristic
319C22×C13C2×#12411yescharacteristic
320C22×C13C2×#12411yescharacteristic
321C22×C13C2×#12511yescharacteristic
322C22×C13C2×#12511yescharacteristic
323C22×C13#52911yescharacteristic
324C22×C13#52911yescharacteristic
325C22×C13#53211yescharacteristic
326C22×C13#53211yescharacteristic
327C22×C13#54111yescharacteristic
328C22×C13#54111yescharacteristic
329C22×C13#54211yescharacteristic
330C22×C13#54211yescharacteristic
331C22×C13D4211yescharacteristic
332C22×C13#54711yescharacteristic
333C22×C13#54711yescharacteristic
334C22×C13#54711yescharacteristic
335C22×C13#54811yescharacteristic
336C22×C13#54811yescharacteristic
337C22×C13D4×Q811yescharacteristic
338C22×C13#55211yescharacteristic
339C22×C13#55211yescharacteristic
340C22×C13#55211yescharacteristic
341C22×C13#55211yescharacteristic
342C22×C13#55411yescharacteristic
343C22×C13#55511yescharacteristic
344C22×C13#55511yescharacteristic
345C22×C13#55711yescharacteristic
346C22×C13#55711yescharacteristic
347C4×C13—28no—
348C4×C13—42no—
349C4×C13—42no—
350C4×C13—82no—
351C4×C13#38218yescomplemented
352Dic13—24no—
353Dic13—42no—
354Dic13—42no—
355Dic13—42no—
356Dic13—44no—
357Dic13—82no—
358C23×C4—131no—
359C23×C4—131no—
360C23×C4—132no—
361C23×C4—131no—
362C23×C4—131no—
363C23×C4—132no—
364C23×C4C22×D1312yes—
365C23×C4C22×D1311yescharacteristic
366C23×C4C22×D1311yescharacteristic
367C23×C4C22×D1312yes—
368C23×C4C22×D1311yescharacteristic
369C2×C4⋊C4—24no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—134no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—262no—
378C2×C4⋊C4—264no—
379C2×C4⋊C4—262no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4—264no—
382C2×C4⋊C4—262no—
383C2×C4⋊C4—522no—
384C2×C4⋊C4Dic2614yes—
385C2×C4⋊C4C4×D1314yes—
386C2×C4⋊C4C22⋊D1314yes—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—138no—
391C2×C42—134no—
392C2×C42—264no—
393C2×C42—264no—
394C2×C42—262no—
395C2×C42—262no—
396C2×C42—262no—
397C2×C42—262no—
398C2×C42—262no—
399#95—24no—
400#95—138no—
401#95—134no—
402#95—262no—
403#95—262no—
404#95—264no—
405#95—264no—
406#95—264no—
407#95—264no—
408#95—262no—
409#95—264no—
410#95—264no—
411#95—522no—
412C2×C13C2×#38211yescharacteristic
413C2×C13#229311yescharacteristic
414C2×C13#232011yescharacteristic
415C2×C13#234411yescharacteristic
416C2×C13#234611yescharacteristic
417C2×C13D4×C4⋊C411yescharacteristic
418C2×C13#235111yescharacteristic
419C2×C13#248911yescharacteristic
420C2×C13#248911yescharacteristic
421C2×C13#249111yescharacteristic
422C2×C13#249111yescharacteristic
423C2×C13#250611yescharacteristic
424C2×C13#250611yescharacteristic
425C2×C13#250811yescharacteristic
426C2×C13#250811yescharacteristic
427C24C23×D1311yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—132no—
452C22×C4—132no—
453C22×C4—132no—
454C22×C4—132no—
455C22×C4—134no—
456C22×C4—132no—
457C22×C4—132no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—262no—
463C22×C4—261no—
464C22×C4—262no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—262no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—262no—
476C22×C4—261no—
477C22×C4—262no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—262no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4C2×Dic2614yes—
494C22×C4C2×Dic2612yes—
495C22×C4C2×C4×D1314yes—
496C22×C4C2×C4×D1312yes—
497C22×C4D4×D1312yes—
498C22×C4#612912yes—
499C22×C4#612912yes—
500C22×C4#613112yes—
501C22×C4#613112yes—
502C22×C4#613112yes—
503C22×C4C2×C22⋊D1314yes—
504C22×C4C2×C22⋊D1312yes—
505C4⋊C4—48no—
506C4⋊C4—44no—
507C4⋊C4—268no—
508C4⋊C4—528no—
509C4⋊C4—524no—
510C4⋊C4#6101116yes—
511C42—44no—
512C42—2616no—
513C42—268no—
514C42—524no—
515C13#1391811yescharacteristic, complemented, Sylow
516C23C22×Dic2611yescharacteristic
517C23C22×C4×D1311yescharacteristic
518C23C2×D4×D1311yescharacteristic
519C23C2×#612911yescharacteristic
520C23C2×#612911yescharacteristic
521C23#8825111yescharacteristic
522C23C2×#613111yescharacteristic
523C23C2×#613111yescharacteristic
524C23C2×#613111yescharacteristic
525C23#8825411yescharacteristic
526C23#41×D1311yescharacteristic
527C23#41×D1311yescharacteristic
528C23#8825711yescharacteristic
529C23#8825711yescharacteristic
530C23C22×C22⋊D1311yescharacteristic
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—134no—
559C2×C4—262no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—262no—
564C2×C4—262no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—264no—
569C2×C4—264no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—262no—
573C2×C4—264no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—262no—
577C2×C4—522no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—522no—
586C2×C4—521no—
587C2×C4—522no—
588C2×C4—521no—
589C2×C4—522no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—522no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4#8814414yes—
601C2×C4#8814414yes—
602C2×C4#8814614yes—
603C2×C4#8814614yes—
604C2×C4C2×#610118yes—
605C2×C4C2×#610114yes—
606C2×C4#8819014yes—
607C2×C4#8820114yes—
608C22C2×#8814411yescharacteristic
609C22C2×#8814411yescharacteristic
610C22C2×#8814611yescharacteristic
611C22C2×#8814611yescharacteristic
612C22D4×Dic2611yescharacteristic
613C22#1171924411yescharacteristic
614C22C4×D4×D1311yescharacteristic
615C22#1171925111yescharacteristic
616C22#1171927411yescharacteristic
617C22#1171927511yescharacteristic
618C22#1171927711yescharacteristic
619C22C4×#613111yescharacteristic
620C22#1171930111yescharacteristic
621C22#1171930811yescharacteristic
622C22#1171931611yescharacteristic
623C22#1171932111yescharacteristic
624C22#1171932911yescharacteristic
625C22#1171933011yescharacteristic
626C22#1171934411yescharacteristic
627C22#1171934711yescharacteristic
628C22#1171939611yescharacteristic
629C22#1171939911yescharacteristic
630C22#1171939911yescharacteristic
631C22#1171940211yescharacteristic
632C22#1171943011yescharacteristic
633C22#1171943111yescharacteristic
634C22#1171943811yescharacteristic
635C22#1171943911yescharacteristic
636C22C22×#610111yescharacteristic
637C22C2×#8819011yescharacteristic
638C22D4×C22⋊D1311yescharacteristic
639C22C2×#8820111yescharacteristic
640C22#1171952211yescharacteristic
641C22#1171952911yescharacteristic
642C22#1171953611yescharacteristic
643C4—28no—
644C4—42no—
645C4—42no—
646C4—82no—
647C4—264no—
648C4—522no—
649C4—524no—
650C4—522no—
651C4—522no—
652C4—1042no—
653C4#1171863818yescomplemented
654C2C2×#1171863811yescharacteristic
655C2#1311729411yescharacteristic
656C2#1311748311yescharacteristic
657C2#1311770411yescharacteristic
658C2#1311772011yescharacteristic
659C2D4×#610111yescharacteristic
660C2#1311775411yescharacteristic
661C2#1311917911yescharacteristic
662C2#1311918011yescharacteristic
663C2#1311920111yescharacteristic
664C2#1311920211yescharacteristic
665C2#1311935411yescharacteristic
666C2#1311935511yescharacteristic
667C2#1311937611yescharacteristic
668C2#1311937711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#389D13
hypocenterC13#13918
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
38. C4⋊C4×Dic13C4semidirect
351. C4×C13#382semidirect
515. C13#13918semidirect
653. C4#11718638semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×#117186382
C2×C4⋊C4×Dic132
#131130952
#131130922
#131130662
#131130652
#131130622
C4×#880712
C2×C13×#3892
#1391813