Finite Group Databasebeta

← #15785403

Subgroups — #15785403

Order 3328.

1370 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718646C211yesmaximal, characteristic
2C2×C4⋊C4×Dic13C211yesmaximal, characteristic
3#13113095C212yesmaximal
4#13113092C212yesmaximal
5#13113066C211yesmaximal, characteristic
6#13113065C211yesmaximal, characteristic
7#13113065C211yesmaximal, characteristic
8#13113065C212yesmaximal
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×Dic13C2211yescharacteristic
21C22×C4×Dic13C2212yes—
22C13×#389—24no—
23C2×C13×#95C2212yes—
24C2×#88071C2211yescharacteristic
25C2×#88071C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36#11718646—24no—
37C4⋊C4×Dic13C418yescomplemented
38C23×C4×C13C2312yes—
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×Dic13C2312yes—
44C23×Dic13C2312yes—
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C2×C13×C4⋊C4—24no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—24no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4C2×C414yes—
56C2×C13×C4⋊C4D414yes—
57C2×C13×C4⋊C4Q814yes—
58C2×C42×C13—22no—
59C2×C42×C13—22no—
60C2×C42×C13—22no—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13—22no—
63C2×C4⋊Dic13—24no—
64C2×C4⋊Dic13—22no—
65C2×C4⋊Dic13—22no—
66C2×C4⋊Dic13—22no—
67C2×C4⋊Dic13—24no—
68C2×C4⋊Dic13—42no—
69C2×C4⋊Dic13C2×C414yes—
70C2×C4×Dic13—22no—
71C2×C4×Dic13—22no—
72C2×C4×Dic13—22no—
73C2×C4×Dic13—22no—
74C2×C4×Dic13—22no—
75C2×C4×Dic13—42no—
76C2×C4×Dic13—42no—
77C2×C4×Dic13C2×C414yes—
78C2×C4×Dic13C2×C418yes—
79C13×#95—24no—
80#88071—24no—
81#88071—22no—
82#88071—22no—
83#88071—22no—
84#88071—24no—
85#88071—42no—
86#88071—42no—
87#88071—42no—
88#88071—42no—
89#88071—42no—
90#88071C2×C418yes—
91#88071Q814yes—
92#13933—131nomaximal, Sylow
93C24×C13C2411yescharacteristic
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
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—22no—
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×C13C22×C414yes—
118C22×C4×C13C22×C412yes—
119C22×C4×C13C2×D414yes—
120C22×C4×C13C2×D412yes—
121C22×C4×C13C2×Q814yes—
122C22×C4×C13C2×Q812yes—
123C22×C4×C13C2×Q812yes—
124C22×C4×C13#4112yes—
125C22×C4×C13#4112yes—
126C22×C4×C13#4112yes—
127C22×C4×C13#4112yes—
128C22×C4×C13#4112yes—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13C22×C412yes—
165C22×Dic13C22×C414yes—
166C22×Dic13C22×C412yes—
167C22×Dic13C2×Q812yes—
168C22×Dic13C2×Q812yes—
169C22×Dic13#4112yes—
170C22×Dic13#4112yes—
171C13×C4⋊C4—48no—
172C13×C4⋊C4—44no—
173C13×C4⋊C4C4⋊C4116yes—
174C42×C13—44no—
175C4⋊Dic13—28no—
176C4⋊Dic13—48no—
177C4⋊Dic13—44no—
178C4×Dic13—28no—
179C4×Dic13—48no—
180C4×Dic13—44no—
181C2×#389—131no—
182C2×#389D1311yescharacteristic
183C2×C4×C4⋊C4—131no—
184#1442—132no—
185#1442—132no—
186C4⋊#95—131no—
187C4⋊#95—131no—
188C4⋊#95—131no—
189C4⋊#95—132no—
190#1434—132no—
191C4×#95—131no—
192C23×C13C23×C411yescharacteristic
193C23×C13C22×D411yescharacteristic
194C23×C13C22×Q811yescharacteristic
195C23×C13C22×Q811yescharacteristic
196C23×C13C2×#4111yescharacteristic
197C23×C13C2×#4111yescharacteristic
198C23×C13C2×#4111yescharacteristic
199C23×C13C2×#4111yescharacteristic
200C23×C13C2×#4111yescharacteristic
201C23×C13C2×#4111yescharacteristic
202C23×C13C2×#4111yescharacteristic
203C23×C13H(5,𝔽2)11yescharacteristic
204C23×C13H(5,𝔽2)11yescharacteristic
205C23×C13H(5,𝔽2)11yescharacteristic
206C23×C132−1+411yescharacteristic
207C2×C4×C13—24no—
208C2×C4×C13—24no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
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—41no—
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—42no—
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×C13C2×C4⋊C418yes—
235C2×C4×C13C2×C4⋊C414yes—
236C2×C4×C13#11714yes—
237C2×C4×C13#11714yes—
238C2×C4×C13#12414yes—
239C2×C4×C13#12414yes—
240C2×C4×C13#12514yes—
241C2×C4×C13#12514yes—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—24no—
250C2×Dic13—22no—
251C2×Dic13—24no—
252C2×Dic13—24no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—41no—
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—42no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13C4×Q814yes—
284C22×C4⋊C4—131no—
285C22×C4⋊C4—131no—
286C22×C4⋊C4—132no—
287C22×C4⋊C4C2×D1311yescharacteristic
288C22×C4⋊C4C2×D1312yes—
289C22×C4⋊C4C2×D1311yescharacteristic
290C22×C42—131no—
291C22×C42—132no—
292C22×C42—131no—
293C22×C42C2×D1311yescharacteristic
294#389—24no—
295#389—264no—
296C4×C4⋊C4—138no—
297C2×#95—131no—
298C2×#95—132no—
299C2×#95—131no—
300C2×#95—131no—
301C2×#95—131no—
302C2×#95—132no—
303C2×#95—132no—
304C2×#95—132no—
305C2×#95—132no—
306C2×#95—132no—
307C2×#95—132no—
308C2×#95—132no—
309C2×#95C2×D1312yes—
310C22×C13C22×C4⋊C411yescharacteristic
311C22×C13C2×#11711yescharacteristic
312C22×C13C2×#11711yescharacteristic
313C22×C13C2×C4×Q811yescharacteristic
314C22×C13C4×#4111yescharacteristic
315C22×C13#51811yescharacteristic
316C22×C13#52011yescharacteristic
317C22×C13C2×#12411yescharacteristic
318C22×C13C2×#12411yescharacteristic
319C22×C13C2×#12511yescharacteristic
320C22×C13C2×#12511yescharacteristic
321C22×C13#52911yescharacteristic
322C22×C13#52911yescharacteristic
323C22×C13#53311yescharacteristic
324C22×C13#53311yescharacteristic
325C22×C13#54011yescharacteristic
326C22×C13#54011yescharacteristic
327C22×C13#54211yescharacteristic
328C22×C13#54211yescharacteristic
329C22×C13#54611yescharacteristic
330C22×C13#54611yescharacteristic
331C22×C13D4×Q811yescharacteristic
332C22×C13#55011yescharacteristic
333C22×C13#55311yescharacteristic
334C22×C13#55311yescharacteristic
335C22×C13#55311yescharacteristic
336C22×C13#55311yescharacteristic
337C22×C13#55411yescharacteristic
338C22×C13#55411yescharacteristic
339C22×C13#55411yescharacteristic
340C22×C13#55411yescharacteristic
341C22×C13#55611yescharacteristic
342C22×C13#55611yescharacteristic
343C22×C13#55711yescharacteristic
344C22×C13Q8211yescharacteristic
345C4×C13—28no—
346C4×C13—42no—
347C4×C13—42no—
348C4×C13—82no—
349C4×C13#38218yes—
350Dic13—24no—
351Dic13—44no—
352Dic13—42no—
353Dic13—42no—
354Dic13—42no—
355Dic13—82no—
356C23×C4—131no—
357C23×C4—131no—
358C23×C4—132no—
359C23×C4—131no—
360C23×C4—131no—
361C23×C4—132no—
362C23×C4C22×D1312yes—
363C23×C4C22×D1311yescharacteristic
364C23×C4C22×D1311yescharacteristic
365C23×C4C22×D1312yes—
366C23×C4C22×D1311yescharacteristic
367C2×C4⋊C4—24no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—134no—
374C2×C4⋊C4—262no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4—264no—
377C2×C4⋊C4—262no—
378C2×C4⋊C4—262no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4—522no—
382C2×C4⋊C4Dic2614yes—
383C2×C4⋊C4C4×D1314yes—
384C2×C4⋊C4C22⋊D1314yes—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—134no—
389C2×C42—138no—
390C2×C42—262no—
391C2×C42—262no—
392C2×C42—262no—
393C2×C42—262no—
394C2×C42—262no—
395C2×C42—522no—
396C2×C42—522no—
397#95—24no—
398#95—138no—
399#95—134no—
400#95—262no—
401#95—262no—
402#95—264no—
403#95—262no—
404#95—264no—
405#95—522no—
406#95—522no—
407#95—522no—
408#95—522no—
409#95—522no—
410C2×C13C2×#38211yescharacteristic
411C2×C13#229511yescharacteristic
412C2×C13#231911yescharacteristic
413C2×C13#234511yescharacteristic
414C2×C13#234711yescharacteristic
415C2×C13#234911yescharacteristic
416C2×C13Q8×C4⋊C411yescharacteristic
417C2×C13#249011yescharacteristic
418C2×C13#249011yescharacteristic
419C2×C13#249211yescharacteristic
420C2×C13#249211yescharacteristic
421C2×C13#250711yescharacteristic
422C2×C13#250711yescharacteristic
423C2×C13#250911yescharacteristic
424C2×C13#250911yescharacteristic
425C24C23×D1311yescharacteristic
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
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—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—132no—
450C22×C4—132no—
451C22×C4—132no—
452C22×C4—132no—
453C22×C4—134no—
454C22×C4—132no—
455C22×C4—132no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—262no—
464C22×C4—261no—
465C22×C4—262no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—262no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—262no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—262no—
479C22×C4—261no—
480C22×C4—262no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4C2×Dic2614yes—
492C22×C4C2×Dic2612yes—
493C22×C4C2×C4×D1314yes—
494C22×C4C2×C4×D1312yes—
495C22×C4#612912yes—
496C22×C4#612912yes—
497C22×C4#612912yes—
498C22×C4Q8×D1312yes—
499C22×C4#613112yes—
500C22×C4#613112yes—
501C22×C4C2×C22⋊D1314yes—
502C22×C4C2×C22⋊D1312yes—
503C4⋊C4—48no—
504C4⋊C4—44no—
505C4⋊C4—268no—
506C4⋊C4—528no—
507C4⋊C4—524no—
508C4⋊C4#6101116yes—
509C42—44no—
510C42—268no—
511C42—528no—
512C42—524no—
513C13#1393311yescharacteristic, complemented, Sylow
514C23C22×Dic2611yescharacteristic
515C23C22×C4×D1311yescharacteristic
516C23C2×#612911yescharacteristic
517C23C2×#612911yescharacteristic
518C23C2×#612911yescharacteristic
519C23#8825111yescharacteristic
520C23C2×Q8×D1311yescharacteristic
521C23C2×#613111yescharacteristic
522C23C2×#613111yescharacteristic
523C23#8825411yescharacteristic
524C23#41×D1311yescharacteristic
525C23#41×D1311yescharacteristic
526C23#8825611yescharacteristic
527C23#8825611yescharacteristic
528C23C22×C22⋊D1311yescharacteristic
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—134no—
557C2×C4—262no—
558C2×C4—262no—
559C2×C4—262no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—262no—
564C2×C4—262no—
565C2×C4—262no—
566C2×C4—264no—
567C2×C4—262no—
568C2×C4—264no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—264no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—522no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—522no—
585C2×C4—521no—
586C2×C4—522no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—522no—
590C2×C4—521no—
591C2×C4—522no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—522no—
598C2×C4#8814414yes—
599C2×C4#8814414yes—
600C2×C4#8814614yes—
601C2×C4#8814614yes—
602C2×C4C2×#610118yes—
603C2×C4C2×#610114yes—
604C2×C4#8819014yes—
605C2×C4#8820114yes—
606C22C2×#8814411yescharacteristic
607C22C2×#8814411yescharacteristic
608C22C2×#8814611yescharacteristic
609C22C2×#8814611yescharacteristic
610C22C4×#612911yescharacteristic
611C22#1171924411yescharacteristic
612C22#1171924811yescharacteristic
613C22#1171925011yescharacteristic
614C22Q8×Dic2611yescharacteristic
615C22#1171927411yescharacteristic
616C22C4×Q8×D1311yescharacteristic
617C22#1171927911yescharacteristic
618C22#1171930511yescharacteristic
619C22#1171931911yescharacteristic
620C22#1171932311yescharacteristic
621C22#1171932411yescharacteristic
622C22#1171932711yescharacteristic
623C22#1171934011yescharacteristic
624C22#1171934611yescharacteristic
625C22#1171934811yescharacteristic
626C22#1171939611yescharacteristic
627C22#1171940011yescharacteristic
628C22#1171940011yescharacteristic
629C22#1171940311yescharacteristic
630C22#1171943311yescharacteristic
631C22#1171943511yescharacteristic
632C22#1171943711yescharacteristic
633C22#1171943811yescharacteristic
634C22C22×#610111yescharacteristic
635C22C2×#8819011yescharacteristic
636C22#1171951111yescharacteristic
637C22C2×#8820111yescharacteristic
638C22Q8×C22⋊D1311yescharacteristic
639C22#1171953411yescharacteristic
640C22#1171953911yescharacteristic
641C4—28no—
642C4—42no—
643C4—42no—
644C4—82no—
645C4—264no—
646C4—522no—
647C4—524no—
648C4—522no—
649C4—522no—
650C4—1042no—
651C4#1171863818yes—
652C2C2×#1171863811yescharacteristic
653C2#1311730711yescharacteristic
654C2#1311747511yescharacteristic
655C2#1311771211yescharacteristic
656C2#1311772811yescharacteristic
657C2#1311774111yescharacteristic
658C2Q8×#610111yescharacteristic
659C2#1311919011yescharacteristic
660C2#1311919111yescharacteristic
661C2#1311921211yescharacteristic
662C2#1311921311yescharacteristic
663C2#1311936511yescharacteristic
664C2#1311936611yescharacteristic
665C2#1311938711yescharacteristic
666C2#1311938811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#389D13
hypocenterC13#13933
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
37. C4⋊C4×Dic13C4semidirect
513. C13#13933semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×C4⋊C4×Dic132
#131130952
#131130922
#131130662
#131130652
#131130622
C4×#880712
C2×C13×#3892
#1393313