Finite Group Databasebeta

← #15786153

Subgroups — #15786153

Order 3328.

1470 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718646C211yesmaximal, characteristic
2C2×#11718634C211yesmaximal, characteristic
3C2×#11718634C211yesmaximal, characteristic
4C2×#11718638C211yesmaximal, characteristic
5C2×C4×C4⋊Dic13C211yesmaximal, characteristic
6#13113094C212yesmaximal
7#13113090C212yesmaximal
8#13113070C212yesmaximal
9#13113064C212yesmaximal
10C4×#88071C211yesmaximal, characteristic
11C13×C4⋊#95C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×C4⋊Dic13C2212yes—
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×#6101C2212yes—
19C22×#6101C2212yes—
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C2×C13×#95C2212yes—
24C2×C13×#95C2212yes—
25C2×#88071C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35#11718646—24no—
36#11718638—24no—
37#11718634—24no—
38#11718634C418yescomplemented
39C4×C4⋊Dic13—24no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4C2×C414yes—
57C2×C42×C13—22no—
58C2×C42×C13—22no—
59C2×C42×C13Q814yes—
60C2×C4⋊Dic13—22no—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13—24no—
63C2×C4⋊Dic13—24no—
64C2×C4⋊Dic13—42no—
65C2×C4⋊Dic13C2×C414yes—
66C2×C4⋊Dic13D414yes—
67C2×C4⋊Dic13D414yes—
68C2×C4⋊Dic13Q814yes—
69C2×#6101—24no—
70C2×#6101—24no—
71C2×#6101—42no—
72C2×#6101—42no—
73C2×#6101—42no—
74C2×#6101C2×C418yes—
75C2×C4×Dic13—22no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13—22no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13—22no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—42no—
83C2×C4×Dic13C2×C414yes—
84C13×#95—24no—
85C13×#95—42no—
86#88071—22no—
87#88071—22no—
88#88071—24no—
89#88071—24no—
90#88071—24no—
91#88071—24no—
92#88071—24no—
93#88071—22no—
94#88071—22no—
95#88071C2×C418yes—
96#14006—131nomaximal, Sylow
97C24×C13C2411yescharacteristic
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—22no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
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×C13C22×C414yes—
122C22×C4×C13C22×C412yes—
123C22×C4×C13C2×D412yes—
124C22×C4×C13C2×D412yes—
125C22×C4×C13C2×Q812yes—
126C22×C4×C13C2×Q812yes—
127C22×C4×C13C2×Q812yes—
128C22×C4×C13C2×Q812yes—
129C22×C4×C13#4112yes—
130C22×C4×C13#4112yes—
131C22×C4×C13#4112yes—
132C22×C4×C13#4112yes—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—22no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
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—21no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—22no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13C22×C412yes—
168C22×Dic13C22×C412yes—
169C22×Dic13C22×C414yes—
170C22×Dic13C2×D414yes—
171C22×Dic13C2×D414yes—
172C22×Dic13C2×Q814yes—
173C22×Dic13#4112yes—
174C22×Dic13#4112yes—
175C13×C4⋊C4—28no—
176C13×C4⋊C4—44no—
177C42×C13—28no—
178C4⋊Dic13—28no—
179C4⋊Dic13—48no—
180C4⋊Dic13C4⋊C4116yescomplemented
181#6101—48no—
182#6101—48no—
183C4×Dic13—28no—
184C4×Dic13—48no—
185C4×Dic13—44no—
186C2×#389—131no—
187C2×#389—131no—
188C2×#389—131no—
189C2×#382—131no—
190C2×C4×C4⋊C4—131no—
191#1442—132no—
192#1441—132no—
193#1436—132no—
194C4⋊#95—132no—
195C4⋊#95D1311yescharacteristic
196C4×#95—131no—
197C23×C13C23×C411yescharacteristic
198C23×C13C22×D411yescharacteristic
199C23×C13C22×D411yescharacteristic
200C23×C13C22×Q811yescharacteristic
201C23×C13C22×Q811yescharacteristic
202C23×C13C2×#4111yescharacteristic
203C23×C13C2×#4111yescharacteristic
204C23×C13C2×#4111yescharacteristic
205C23×C13C2×#4111yescharacteristic
206C23×C13C2×#4111yescharacteristic
207C23×C13C2×#4111yescharacteristic
208C23×C13H(5,𝔽2)11yescharacteristic
209C23×C13H(5,𝔽2)11yescharacteristic
210C23×C132−1+411yescharacteristic
211C23×C132−1+411yescharacteristic
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—24no—
219C2×C4×C13—24no—
220C2×C4×C13—24no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—42no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
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×C4⋊C414yes—
240C2×C4×C13C4×D414yes—
241C2×C4×C13C4×Q814yes—
242C2×C4×C13#12114yes—
243C2×C4×C13C22⋊Q814yes—
244C2×C4×C13#12514yes—
245C2×C4×C13#12514yes—
246C2×C4×C13C4⋊Q814yes—
247C2×Dic13—24no—
248C2×Dic13—24no—
249C2×Dic13—24no—
250C2×Dic13—24no—
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—24no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—42no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—42no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13C2×C4⋊C418yes—
289C22×C4⋊C4—131no—
290C22×C4⋊C4—131no—
291C22×C4⋊C4—132no—
292C22×C4⋊C4—132no—
293C22×C4⋊C4—132no—
294C22×C4⋊C4C2×D1311yescharacteristic
295C22×C4⋊C4C2×D1311yescharacteristic
296C22×C42—131no—
297C22×C42—131no—
298C22×C42—132no—
299C22×C42C2×D1311yescharacteristic
300#389—138no—
301#389—264no—
302#389—264no—
303#382—264no—
304C4×C4⋊C4—264no—
305C2×#95—132no—
306C2×#95—131no—
307C2×#95—131no—
308C2×#95—131no—
309C2×#95—131no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95—132no—
313C2×#95—132no—
314C2×#95—132no—
315C2×#95C2×D1312yes—
316C2×#95C2×D1312yes—
317C22×C13C22×C4⋊C411yescharacteristic
318C22×C13C2×C4×D411yescharacteristic
319C22×C13C2×C4×Q811yescharacteristic
320C22×C13C4×#4111yescharacteristic
321C22×C13C4×#4111yescharacteristic
322C22×C13#51811yescharacteristic
323C22×C13#51911yescharacteristic
324C22×C13C2×#12111yescharacteristic
325C22×C13C2×C22⋊Q811yescharacteristic
326C22×C13C2×#12511yescharacteristic
327C22×C13C2×#12511yescharacteristic
328C22×C13#52911yescharacteristic
329C22×C13#52911yescharacteristic
330C22×C13C2×C4⋊Q811yescharacteristic
331C22×C13#53311yescharacteristic
332C22×C13#54211yescharacteristic
333C22×C13#54211yescharacteristic
334C22×C13#54411yescharacteristic
335C22×C13#54411yescharacteristic
336C22×C13#54611yescharacteristic
337C22×C13#54611yescharacteristic
338C22×C13#54611yescharacteristic
339C22×C13#54711yescharacteristic
340C22×C13#54811yescharacteristic
341C22×C13#54811yescharacteristic
342C22×C13#54811yescharacteristic
343C22×C13#55011yescharacteristic
344C22×C13#55211yescharacteristic
345C22×C13#55311yescharacteristic
346C22×C13#55411yescharacteristic
347C22×C13#55411yescharacteristic
348C22×C13#55511yescharacteristic
349C22×C13#55611yescharacteristic
350C22×C13#55711yescharacteristic
351C22×C13#55711yescharacteristic
352C4×C13—24no—
353C4×C13—44no—
354C4×C13—42no—
355C4×C13—82no—
356C4×C13#38918yes—
357Dic13—28no—
358Dic13—42no—
359Dic13—42no—
360Dic13—42no—
361Dic13—44no—
362Dic13—42no—
363C23×C4—132no—
364C23×C4—131no—
365C23×C4—132no—
366C23×C4—131no—
367C23×C4—131no—
368C23×C4—131no—
369C23×C4C22×D1312yes—
370C23×C4C22×D1311yescharacteristic
371C23×C4C22×D1312yes—
372C23×C4C22×D1311yescharacteristic
373C23×C4C22×D1311yescharacteristic
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—134no—
380C2×C4⋊C4—134no—
381C2×C4⋊C4—134no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—138no—
384C2×C4⋊C4—262no—
385C2×C4⋊C4—262no—
386C2×C4⋊C4—264no—
387C2×C4⋊C4—264no—
388C2×C4⋊C4—264no—
389C2×C4⋊C4—264no—
390C2×C4⋊C4—522no—
391C2×C4⋊C4—522no—
392C2×C4⋊C4—522no—
393C2×C4⋊C4—522no—
394C2×C4⋊C4C4×D1314yes—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—134no—
398C2×C42—262no—
399C2×C42—262no—
400C2×C42—264no—
401C2×C42—262no—
402C2×C42—262no—
403C2×C42—262no—
404C2×C42—264no—
405C2×C42—522no—
406C2×C42Dic2614yes—
407#95—24no—
408#95—42no—
409#95—138no—
410#95—262no—
411#95—262no—
412#95—264no—
413#95—264no—
414#95—264no—
415#95—264no—
416#95—264no—
417#95—262no—
418#95—262no—
419C2×C13C2×#38911yescharacteristic
420C2×C13C4×#12511yescharacteristic
421C2×C13#233111yescharacteristic
422C2×C13#234911yescharacteristic
423C2×C13#235111yescharacteristic
424C2×C13#236211yescharacteristic
425C2×C13#236311yescharacteristic
426C2×C13#242611yescharacteristic
427C2×C13#242711yescharacteristic
428C2×C13#243911yescharacteristic
429C2×C13#244211yescharacteristic
430C2×C13#250811yescharacteristic
431C2×C13#250911yescharacteristic
432C2×C13#255011yescharacteristic
433C2×C13#255211yescharacteristic
434C24C23×D1311yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—134no—
459C22×C4—134no—
460C22×C4—134no—
461C22×C4—132no—
462C22×C4—132no—
463C22×C4—134no—
464C22×C4—132no—
465C22×C4—132no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—262no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—262no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4C2×Dic2612yes—
501C22×C4C2×Dic2612yes—
502C22×C4C2×Dic2612yes—
503C22×C4C2×C4×D1314yes—
504C22×C4C2×C4×D1312yes—
505C22×C4#612712yes—
506C22×C4D4×D1312yes—
507C22×C4D4×D1312yes—
508C22×C4#612912yes—
509C22×C4#612912yes—
510C22×C4Q8×D1312yes—
511C22×C4#613112yes—
512C4⋊C4—28no—
513C4⋊C4—44no—
514C4⋊C4—1316no—
515C4⋊C4—268no—
516C4⋊C4—528no—
517C4⋊C4—528no—
518C4⋊C4—528no—
519C42—28no—
520C42—268no—
521C42—528no—
522C42—524no—
523C13#1400611yescharacteristic, complemented, Sylow
524C23C22×Dic2611yescharacteristic
525C23C22×C4×D1311yescharacteristic
526C23C2×#612711yescharacteristic
527C23C2×D4×D1311yescharacteristic
528C23C2×D4×D1311yescharacteristic
529C23C2×#612911yescharacteristic
530C23C2×#612911yescharacteristic
531C23#8825111yescharacteristic
532C23C2×Q8×D1311yescharacteristic
533C23C2×#613111yescharacteristic
534C23#8825411yescharacteristic
535C23#41×D1311yescharacteristic
536C23#41×D1311yescharacteristic
537C23#8825611yescharacteristic
538C23#8825711yescharacteristic
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—138no—
567C2×C4—264no—
568C2×C4—264no—
569C2×C4—264no—
570C2×C4—264no—
571C2×C4—264no—
572C2×C4—264no—
573C2×C4—264no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—264no—
577C2×C4—262no—
578C2×C4—262no—
579C2×C4—262no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—262no—
584C2×C4—262no—
585C2×C4—262no—
586C2×C4—264no—
587C2×C4—262no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—522no—
594C2×C4—521no—
595C2×C4—522no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—522no—
600C2×C4—521no—
601C2×C4—522no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4C4×Dic2614yes—
609C2×C4#8813214yes—
610C2×C4#8813514yes—
611C2×C4#8813814yes—
612C2×C4#8814214yes—
613C2×C4#8814314yes—
614C2×C4#8814414yes—
615C2×C4C4⋊C4×D1314yes—
616C22C2×C4×Dic2611yescharacteristic
617C22C2×#8813211yescharacteristic
618C22C2×#8813511yescharacteristic
619C22C2×#8813811yescharacteristic
620C22C2×#8814211yescharacteristic
621C22C2×#8814311yescharacteristic
622C22C2×#8814411yescharacteristic
623C22#1171920511yescharacteristic
624C22C2×C4⋊C4×D1311yescharacteristic
625C22#1171922211yescharacteristic
626C22#1171922411yescharacteristic
627C22C4×#612911yescharacteristic
628C22#1171925011yescharacteristic
629C22#1171926211yescharacteristic
630C22#1171926611yescharacteristic
631C22#1171927711yescharacteristic
632C22C4×#613111yescharacteristic
633C22#1171928511yescharacteristic
634C22#1171928711yescharacteristic
635C22#1171930311yescharacteristic
636C22#1171931711yescharacteristic
637C22#1171932111yescharacteristic
638C22#1171932311yescharacteristic
639C22#1171933511yescharacteristic
640C22#1171933811yescharacteristic
641C22#1171934611yescharacteristic
642C22#1171934711yescharacteristic
643C22#1171938111yescharacteristic
644C22#1171938211yescharacteristic
645C22#1171939011yescharacteristic
646C22#1171939511yescharacteristic
647C22#1171942311yescharacteristic
648C22#1171942611yescharacteristic
649C22#1171943111yescharacteristic
650C22#1171943511yescharacteristic
651C4—24no—
652C4—42no—
653C4—44no—
654C4—82no—
655C4—268no—
656C4—522no—
657C4—522no—
658C4—522no—
659C4—524no—
660C4—522no—
661C4#1171830818yes—
662C2C2×#1171830811yescharacteristic
663C2C4×#8814411yescharacteristic
664C2#1311758011yescharacteristic
665C2#1311774511yescharacteristic
666C2#1311775511yescharacteristic
667C2#1311786811yescharacteristic
668C2#1311787911yescharacteristic
669C2#1311840311yescharacteristic
670C2#1311841411yescharacteristic
671C2#1311852811yescharacteristic
672C2#1311856111yescharacteristic
673C2#1311937511yescharacteristic
674C2#1311938611yescharacteristic
675C2#1311985811yescharacteristic
676C2#1311987211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, prime radical, cosocleC24×C13C24
hypercenterC4⋊#95D13
hypocenterC13#14006
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
38. #11718634C4semidirect
180. C4⋊Dic13C4⋊C4semidirect
523. C13#14006semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×#117186342
C2×#117186382
C2×C4×C4⋊Dic132
#131130942
#131130902
#131130702
#131130642
C4×#880712
C13×C4⋊#952
#1400613