Finite Group Databasebeta

← #15799587

Subgroups — #15799587

Order 3328.

1438 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718318C212yesmaximal
2C2×#11718646C211yesmaximal, characteristic
3C2×#11718589C211yesmaximal, characteristic
4C2×#11718634C211yesmaximal, characteristic
5C2×#11718637C211yesmaximal, characteristic
6#13113100C212yesmaximal
7#13113094C212yesmaximal
8#13113087C212yesmaximal
9#13113065C211yesmaximal, characteristic
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×#6101C2212yes—
21C22×#6101C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C2×C13×#95C2212yes—
25C2×C13×#95C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35#11718646—24no—
36#11718637—24no—
37#11718634—24no—
38#11718589—24no—
39#11718318—28no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
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⋊C4Q814yes—
57C2×C42×C13—22no—
58C2×C42×C13—22no—
59C2×C42×C13—22no—
60C2×C4⋊Dic13—22no—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13—22no—
63C2×C4⋊Dic13—22no—
64C2×C4⋊Dic13—24no—
65C2×C4⋊Dic13—24no—
66C2×C4⋊Dic13—42no—
67C2×C4⋊Dic13D414yes—
68C2×C4⋊Dic13D414yes—
69C2×#6101—24no—
70C2×#6101—24no—
71C2×#6101—24no—
72C2×#6101—24no—
73C2×#6101—24no—
74C2×#6101—24no—
75C2×#6101—24no—
76C2×#6101—24no—
77C2×#6101—42no—
78C2×#6101—42no—
79C2×#6101—42no—
80C2×#6101—42no—
81C2×C4×Dic13—22no—
82C2×C4×Dic13—22no—
83C2×C4×Dic13—22no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13Q814yes—
87C13×#95—24no—
88C13×#95—42no—
89#88071—24no—
90#88071—24no—
91#88071—24no—
92#88071—24no—
93#88071—24no—
94#88071—22no—
95#88071—22no—
96#88071D414yes—
97#88071Q814yes—
98#15137—131nomaximal, Sylow
99C24×C13C2411yescharacteristic
100C22×C4×C13—21no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
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×C13C2×D412yes—
126C22×C4×C13C2×D412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×Q814yes—
129C22×C4×C13C2×Q812yes—
130C22×C4×C13C2×Q812yes—
131C22×C4×C13C2×Q812yes—
132C22×C4×C13#4112yes—
133C22×C4×C13#4112yes—
134C22×C4×C13#4112yes—
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—21no—
148C22×Dic13—21no—
149C22×Dic13—22no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—22no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—21no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—21no—
164C22×Dic13—22no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13C2×D414yes—
168C22×Dic13C2×D414yes—
169C22×Dic13C2×D412yes—
170C22×Dic13C2×D412yes—
171C22×Dic13C2×Q812yes—
172C22×Dic13C2×Q812yes—
173C22×Dic13C2×Q812yes—
174C22×Dic13C2×Q812yes—
175C22×Dic13#4112yes—
176C22×Dic13#4112yes—
177C13×C4⋊C4—28no—
178C13×C4⋊C4—44no—
179C42×C13—44no—
180C4⋊Dic13—28no—
181C4⋊Dic13—28no—
182C4⋊Dic13—48no—
183#6101—48no—
184#6101—48no—
185#6101—48no—
186#6101—48no—
187C4×Dic13—28no—
188C4×Dic13—44no—
189C2×#398—132no—
190C2×#389—131no—
191C2×#389—131no—
192C2×#389—131no—
193C2×#384—131no—
194#1444—132no—
195#1442—132no—
196#1441—132no—
197C4⋊#95—131no—
198C4⋊#95D1311yescharacteristic
199C4×#95—131no—
200C23×C13C22×D411yescharacteristic
201C23×C13C22×D411yescharacteristic
202C23×C13C22×D411yescharacteristic
203C23×C13C22×Q811yescharacteristic
204C23×C13C22×Q811yescharacteristic
205C23×C13C22×Q811yescharacteristic
206C23×C13C2×#4111yescharacteristic
207C23×C13C2×#4111yescharacteristic
208C23×C13C2×#4111yescharacteristic
209C23×C13C2×#4111yescharacteristic
210C23×C13C2×#4111yescharacteristic
211C23×C13H(5,𝔽2)11yescharacteristic
212C23×C13H(5,𝔽2)11yescharacteristic
213C23×C132−1+411yescharacteristic
214C23×C132−1+411yescharacteristic
215C2×C4×C13—24no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—24no—
222C2×C4×C13—22no—
223C2×C4×C13—24no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—42no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—41no—
232C2×C4×C13—42no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13#12114yes—
244C2×C4×C13C22⋊Q814yes—
245C2×C4×C13C22⋊Q814yes—
246C2×C4×C13#12314yes—
247C2×C4×C13#12514yes—
248C2×C4×C13#12514yes—
249C2×C4×C13C4⋊Q814yes—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—24no—
267C2×Dic13—22no—
268C2×Dic13—24no—
269C2×Dic13—22no—
270C2×Dic13—24no—
271C2×Dic13—24no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—42no—
277C2×Dic13—42no—
278C2×Dic13—41no—
279C2×Dic13—42no—
280C2×Dic13—41no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—41no—
284C2×Dic13—42no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—42no—
288C2×Dic13—41no—
289C2×Dic13—42no—
290C2×Dic13#12514yes—
291C2×Dic13C4⋊Q814yes—
292C22×C4⋊C4—131no—
293C22×C4⋊C4—131no—
294C22×C4⋊C4—132no—
295C22×C4⋊C4—132no—
296C22×C4⋊C4—132no—
297C22×C4⋊C4—132no—
298C22×C4⋊C4—132no—
299C22×C4⋊C4C2×D1311yescharacteristic
300C22×C4⋊C4C2×D1311yescharacteristic
301C22×C42—131no—
302C22×C42—131no—
303C22×C42C2×D1311yescharacteristic
304#398—268no—
305#389—264no—
306#389—264no—
307#389—264no—
308#384—264no—
309C2×#95—131no—
310C2×#95—131no—
311C2×#95—132no—
312C2×#95—131no—
313C2×#95—131no—
314C2×#95—132no—
315C2×#95—132no—
316C2×#95—132no—
317C2×#95—132no—
318C2×#95C2×D1312yes—
319C2×#95C2×D1312yes—
320C22×C13C2×#12111yescharacteristic
321C22×C13C2×C22⋊Q811yescharacteristic
322C22×C13C2×C22⋊Q811yescharacteristic
323C22×C13C2×#12311yescharacteristic
324C22×C13C2×#12511yescharacteristic
325C22×C13C2×#12511yescharacteristic
326C22×C13C2×#12511yescharacteristic
327C22×C13C2×C4⋊Q811yescharacteristic
328C22×C13C2×C4⋊Q811yescharacteristic
329C22×C13#53211yescharacteristic
330C22×C13#53211yescharacteristic
331C22×C13#53311yescharacteristic
332C22×C13#53311yescharacteristic
333C22×C13#54011yescharacteristic
334C22×C13#54111yescharacteristic
335C22×C13#54211yescharacteristic
336C22×C13#54211yescharacteristic
337C22×C13#54411yescharacteristic
338C22×C13#54411yescharacteristic
339C22×C13D4211yescharacteristic
340C22×C13D4211yescharacteristic
341C22×C13#54611yescharacteristic
342C22×C13#54711yescharacteristic
343C22×C13#54711yescharacteristic
344C22×C13#54811yescharacteristic
345C22×C13D4×Q811yescharacteristic
346C22×C13D4×Q811yescharacteristic
347C22×C13D4×Q811yescharacteristic
348C22×C13#55011yescharacteristic
349C22×C13#55211yescharacteristic
350C22×C13#55311yescharacteristic
351C22×C13#55411yescharacteristic
352C22×C13#55411yescharacteristic
353C22×C13#55711yescharacteristic
354C22×C13Q8211yescharacteristic
355C4×C13—42no—
356C4×C13—42no—
357C4×C13—44no—
358C4×C13—82no—
359C4×C13#39818yescomplemented
360Dic13—24no—
361Dic13—24no—
362Dic13—44no—
363Dic13—44no—
364Dic13—42no—
365Dic13—42no—
366C23×C4—131no—
367C23×C4—131no—
368C23×C4—132no—
369C23×C4—131no—
370C23×C4—132no—
371C23×C4—131no—
372C23×C4C22×D1312yes—
373C23×C4C22×D1312yes—
374C23×C4C22×D1311yescharacteristic
375C23×C4C22×D1311yescharacteristic
376C23×C4C22×D1311yescharacteristic
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—134no—
384C2×C4⋊C4—262no—
385C2×C4⋊C4—262no—
386C2×C4⋊C4—262no—
387C2×C4⋊C4—262no—
388C2×C4⋊C4—264no—
389C2×C4⋊C4—264no—
390C2×C4⋊C4—264no—
391C2×C4⋊C4—264no—
392C2×C4⋊C4—264no—
393C2×C4⋊C4—264no—
394C2×C4⋊C4—264no—
395C2×C4⋊C4—264no—
396C2×C4⋊C4—264no—
397C2×C4⋊C4—264no—
398C2×C4⋊C4—522no—
399C2×C4⋊C4—522no—
400C2×C4⋊C4—522no—
401C2×C4⋊C4—522no—
402C2×C4⋊C4—522no—
403C2×C4⋊C4Dic2614yes—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—134no—
408C2×C42—262no—
409C2×C42—262no—
410C2×C42—262no—
411C2×C42—262no—
412C2×C42—262no—
413#95—24no—
414#95—42no—
415#95—134no—
416#95—134no—
417#95—262no—
418#95—264no—
419#95—262no—
420#95—264no—
421#95—264no—
422#95—264no—
423#95—264no—
424C2×C13C2×#39811yescharacteristic
425C2×C13#242211yescharacteristic
426C2×C13#242311yescharacteristic
427C2×C13#242811yescharacteristic
428C2×C13#242911yescharacteristic
429C2×C13#244011yescharacteristic
430C2×C13#244211yescharacteristic
431C2×C13#245111yescharacteristic
432C2×C13#245211yescharacteristic
433C2×C13#250611yescharacteristic
434C2×C13#250711yescharacteristic
435C2×C13#255111yescharacteristic
436C2×C13#255211yescharacteristic
437C2×C13#264711yescharacteristic
438C2×C13#285911yescharacteristic
439C24C23×D1311yescharacteristic
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—132no—
466C22×C4—132no—
467C22×C4—132no—
468C22×C4—132no—
469C22×C4—132no—
470C22×C4—132no—
471C22×C4—132no—
472C22×C4—134no—
473C22×C4—134no—
474C22×C4—132no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4—262no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—261no—
505C22×C4—262no—
506C22×C4—261no—
507C22×C4C2×Dic2614yes—
508C22×C4C2×Dic2612yes—
509C22×C4#612712yes—
510C22×C4#612712yes—
511C22×C4D4×D1312yes—
512C22×C4D4×D1312yes—
513C22×C4D4×D1312yes—
514C22×C4#612912yes—
515C22×C4Q8×D1312yes—
516C22×C4Q8×D1312yes—
517C4⋊C4—28no—
518C4⋊C4—44no—
519C4⋊C4—268no—
520C4⋊C4—268no—
521C4⋊C4—528no—
522C4⋊C4—528no—
523C4⋊C4—528no—
524C4⋊C4—528no—
525C4⋊C4—528no—
526C42—44no—
527C42—268no—
528C42—524no—
529C13#1513711yescharacteristic, complemented, Sylow
530C23C22×Dic2611yescharacteristic
531C23C2×#612711yescharacteristic
532C23C2×#612711yescharacteristic
533C23C2×D4×D1311yescharacteristic
534C23C2×D4×D1311yescharacteristic
535C23C2×D4×D1311yescharacteristic
536C23C2×#612911yescharacteristic
537C23#8825111yescharacteristic
538C23C2×Q8×D1311yescharacteristic
539C23C2×Q8×D1311yescharacteristic
540C23#8825411yescharacteristic
541C23#41×D1311yescharacteristic
542C23#41×D1311yescharacteristic
543C23#8825611yescharacteristic
544C23#8825711yescharacteristic
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—134no—
574C2×C4—134no—
575C2×C4—262no—
576C2×C4—262no—
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—262no—
587C2×C4—262no—
588C2×C4—264no—
589C2×C4—264no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—264no—
593C2×C4—262no—
594C2×C4—264no—
595C2×C4—262no—
596C2×C4—264no—
597C2×C4—264no—
598C2×C4—262no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—522no—
602C2×C4—522no—
603C2×C4—522no—
604C2×C4—521no—
605C2×C4—522no—
606C2×C4—521no—
607C2×C4—522no—
608C2×C4—522no—
609C2×C4—521no—
610C2×C4—522no—
611C2×C4—521no—
612C2×C4—522no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4#8812414yes—
616C2×C4#8813214yes—
617C2×C4#8813714yes—
618C2×C4#8813814yes—
619C2×C4#8814214yes—
620C2×C4#8814314yes—
621C2×C4#8815014yes—
622C22C2×#8812411yescharacteristic
623C22C2×#8813211yescharacteristic
624C22C2×#8813711yescharacteristic
625C22C2×#8813811yescharacteristic
626C22C2×#8814211yescharacteristic
627C22C2×#8814311yescharacteristic
628C22#1171921211yescharacteristic
629C22C2×#8815011yescharacteristic
630C22#1171921611yescharacteristic
631C22#1171923411yescharacteristic
632C22#1171923511yescharacteristic
633C22D4×Dic2611yescharacteristic
634C22#1171924411yescharacteristic
635C22#1171925311yescharacteristic
636C22#1171926711yescharacteristic
637C22Q8×Dic2611yescharacteristic
638C22#1171927411yescharacteristic
639C22#1171928311yescharacteristic
640C22#1171928811yescharacteristic
641C22#1171930111yescharacteristic
642C22#1171930411yescharacteristic
643C22#1171930811yescharacteristic
644C22#1171931411yescharacteristic
645C22#1171932711yescharacteristic
646C22#1171933611yescharacteristic
647C22#1171933711yescharacteristic
648C22#1171934811yescharacteristic
649C22#1171938111yescharacteristic
650C22#1171938211yescharacteristic
651C22D13×#12511yescharacteristic
652C22#1171939411yescharacteristic
653C22#1171942211yescharacteristic
654C22D13×C4⋊Q811yescharacteristic
655C22#1171943211yescharacteristic
656C22#1171943411yescharacteristic
657C4—42no—
658C4—42no—
659C4—44no—
660C4—82no—
661C4—264no—
662C4—264no—
663C4—524no—
664C4—524no—
665C4—522no—
666C4—522no—
667C4#1171831818yescomplemented
668C2C2×#1171831811yescharacteristic
669C2#1311835211yescharacteristic
670C2#1311836311yescharacteristic
671C2#1311842511yescharacteristic
672C2#1311843611yescharacteristic
673C2#1311854111yescharacteristic
674C2#1311856311yescharacteristic
675C2#1311867811yescharacteristic
676C2#1311868911yescharacteristic
677C2#1311934611yescharacteristic
678C2#1311935711yescharacteristic
679C2#1311986411yescharacteristic
680C2#1311987311yescharacteristic
681C2#1312081311yescharacteristic
682C2#1312319511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, prime radical, cosocleC24×C13C24
FittingC13×C4⋊#95C2
hypercenterC4⋊#95D13
hypocenterC13#15137
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
359. C4×C13#398semidirect
529. C13#15137semidirect
667. C4#11718318semidirect

Maximal subgroups

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

subgroupindex
C2×#117183182
C2×#117186462
C2×#117185892
C2×#117186342
C2×#117186372
#131131002
#131130942
#131130872
#131130652
C4×#880712
C13×C4⋊#952
#1513713