Finite Group Databasebeta

← #16791774

Subgroups — #16791774

Order 3328.

1226 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130022C212yesmaximal
2#13130021C212yesmaximal
3#13130015C212yesmaximal
4#13130014C211yesmaximal, characteristic
5#13130012C211yesmaximal, characteristic
6#13130012C211yesmaximal, characteristic
7#13130012C211yesmaximal, characteristic
8#13130012C211yesmaximal, characteristic
9#13130011C212yesmaximal
10C4×(C2×#261)⋊C4C211yesmaximal, characteristic
11C4×C4⋊C4×D13C211yesmaximal, characteristic
12C22×C4⋊#261C2212yes—
13C22×C4×#261C2212yes—
14C2×C4⋊C4×D13C2211yescharacteristic
15C2×C4⋊C4×D13C2211yescharacteristic
16C2×C42×D13C2211yescharacteristic
17C2×C42×D13C2211yescharacteristic
18C2×C42×D13C2211yescharacteristic
19C2×(C2×#261)⋊C4C2211yescharacteristic
20C2×(C2×#261)⋊C4C2212yes—
21C2×(C2×#261)⋊C4C2212yes—
22C2×(C2×#261)⋊C4C2212yes—
23C2×(C2×#261)⋊C4C2211yescharacteristic
24C2×(C2×#261)⋊C4C2211yescharacteristic
25C2×(C2×#261)⋊C4C2212yes—
26C2×(C2×#261)⋊C4C2212yes—
27C2×(C2×#261)⋊C4C2212yes—
28C2×(C2×#261)⋊C4C2212yes—
29C2×(C2×#261)⋊C4C2212yes—
30C2×(C2×#261)⋊C4C2212yes—
31C2×(C2×#261)⋊C4C2212yes—
32C2×(C2×#261)⋊C4C2211yescharacteristic
33C4×C13×C4⋊C4C411yescharacteristic, complemented
34C4⋊C4×Dic13C411yescharacteristic, complemented
35C4⋊C4×Dic13C411yescharacteristic, complemented
36C4×C4⋊Dic13C411yescharacteristic, complemented
37C4×#6101C411yescharacteristic, complemented
38C4×#6101C411yescharacteristic, complemented
39D13×#95C2211yescharacteristic
40D13×#95C2211yescharacteristic
41#11718310C411yescharacteristic, complemented
42#11718310C411yescharacteristic, complemented
43C23×#261C2312yes—
44C23×#261C2312yes—
45C23×#261C2312yes—
46C23×#261C2312yes—
47C22×C4×D13C2311yescharacteristic
48C22×C4×D13C2311yescharacteristic
49C22×C4×D13C2311yescharacteristic
50C22×C4×D13C2311yescharacteristic
51C22×C4×D13C2311yescharacteristic
52C22×C4×D13C2311yescharacteristic
53C22×C4×D13C2311yescharacteristic
54C2×C4⋊#261—24no—
55C2×C4⋊#261—42no—
56C2×C4⋊#261—42no—
57C2×C4×#261—24no—
58C2×C4×#261—24no—
59C2×C4×#261—42no—
60C2×C13×C4⋊C4C2×C411yescharacteristic
61C2×C13×C4⋊C4C2×C411yescharacteristic
62C2×C42×C13C2×C411yescharacteristic
63C2×C42×C13C2×C411yescharacteristic
64C2×C42×C13C2×C411yescharacteristic
65C2×C4⋊Dic13C2×C411yescharacteristic
66C2×C4⋊Dic13C2×C411yescharacteristic
67C2×#6101C2×C411yescharacteristic
68C2×#6101C2×C411yescharacteristic
69C2×#6101C2×C411yescharacteristic
70C2×#6101C2×C411yescharacteristic
71C2×C4×Dic13C2×C411yescharacteristic
72C2×C4×Dic13C2×C411yescharacteristic
73C2×C4×Dic13C2×C411yescharacteristic
74C2×C4×Dic13C2×C411yescharacteristic
75C2×C4×Dic13C2×C411yescharacteristic
76C2×C4×Dic13C2×C411yescharacteristic
77C2×C4×Dic13C2×C411yescharacteristic
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C4⋊C4×D13—22no—
81C4⋊C4×D13—24no—
82C4⋊C4×D13—22no—
83C42×D13—24no—
84C42×D13—42no—
85C42×D13—42no—
86(C2×#261)⋊C4—24no—
87(C2×#261)⋊C4—24no—
88(C2×#261)⋊C4—24no—
89(C2×#261)⋊C4—24no—
90(C2×#261)⋊C4—24no—
91(C2×#261)⋊C4—24no—
92(C2×#261)⋊C4—22no—
93(C2×#261)⋊C4—22no—
94(C2×#261)⋊C4—22no—
95(C2×#261)⋊C4—42no—
96(C2×#261)⋊C4—42no—
97(C2×#261)⋊C4—42no—
98(C2×#261)⋊C4—42no—
99(C2×#261)⋊C4Q814yes—
100C13×#95C2×C411yescharacteristic
101C13×#95C2×C411yescharacteristic
102#88071C2×C411yescharacteristic
103#88071C2×C411yescharacteristic
104#88071C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#13928—131nomaximal, Sylow
109C23×D13C2411yescharacteristic
110C22×#261—22no—
111C22×#261—22no—
112C22×#261—22no—
113C22×#261—22no—
114C22×#261—22no—
115C22×#261—22no—
116C22×#261—22no—
117C22×#261—22no—
118C22×#261—22no—
119C22×#261—22no—
120C22×#261—22no—
121C22×#261—22no—
122C22×#261—22no—
123C22×#261—22no—
124C22×#261—22no—
125C22×#261—22no—
126C22×#261—22no—
127C22×#261—22no—
128C22×#261—22no—
129C22×#261—22no—
130C22×#261—22no—
131C22×#261—22no—
132C22×#261—22no—
133C22×#261—22no—
134C22×#261—22no—
135C22×#261—22no—
136C22×#261C2×Q814yes—
137C22×#261#4114yes—
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C22×C411yescharacteristic
142C22×C4×C13C22×C411yescharacteristic
143C22×C4×C13C22×C411yescharacteristic
144C22×C4×C13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C2×C4×D13—22no—
153C2×C4×D13—22no—
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13—22no—
157C2×C4×D13—22no—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—22no—
163C2×C4×D13—22no—
164C2×C4×D13—22no—
165C2×C4×D13—22no—
166C2×C4×D13—21no—
167C2×C4×D13—21no—
168C2×C4×D13—21no—
169C2×C4×D13—21no—
170C2×C4×D13—22no—
171C2×C4×D13—22no—
172C2×C4×D13—21no—
173C2×C4×D13—21no—
174C2×C4×D13C2×Q812yes—
175C2×C4×D13#4114yes—
176C2×C4×D13#4112yes—
177C2×C4×D13#4114yes—
178C2×C4×D13#4112yes—
179C2×C4×D13#4112yes—
180C4⋊#261—48no—
181C4×#261—48no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C42×C13—22no—
185C42×C13—41no—
186C42×C13—41no—
187C4⋊Dic13—22no—
188C4⋊Dic13—22no—
189#6101—22no—
190#6101—22no—
191#6101—22no—
192#6101—22no—
193C4×Dic13—22no—
194C4×Dic13—22no—
195C4×Dic13—22no—
196C4×Dic13—41no—
197C4×Dic13—41no—
198C4×Dic13—41no—
199C4×Dic13—41no—
200C4×Dic13—41no—
201C4×Dic13—41no—
202C2×C4×C4⋊C4—131no—
203#1442—132no—
204#1441—132no—
205#1436—132no—
206C4⋊#95—131no—
207#1434—132no—
208#1434—131no—
209#1434—131no—
210#1434—131no—
211#1434—131no—
212C4×#95—131no—
213C23×C13C23×C411yescharacteristic
214C22×D13C22×Q811yescharacteristic
215C22×D13C2×#4112yes—
216C22×D13C2×#4111yescharacteristic
217C22×D13C2×#4112yes—
218C22×D13C2×#4111yescharacteristic
219C22×D13C2×#4111yescharacteristic
220C22×D13C2×#4112yes—
221C22×D13H(5,𝔽2)11yescharacteristic
222C22×D13H(5,𝔽2)12yes—
223C22×D132−1+411yescharacteristic
224C2×#261—24no—
225C2×#261—24no—
226C2×#261—24no—
227C2×#261—24no—
228C2×#261—24no—
229C2×#261—24no—
230C2×#261—42no—
231C2×#261—42no—
232C2×#261—42no—
233C2×#261—42no—
234C2×#261—42no—
235C2×#261—42no—
236C2×#261—42no—
237C2×#261—42no—
238C2×#261—42no—
239C2×#261—42no—
240C2×#261—42no—
241C2×#261—42no—
242C2×#261—42no—
243C2×#261—42no—
244C2×#261—42no—
245C2×#261—42no—
246C2×#261—42no—
247C2×#261—42no—
248C2×#261—42no—
249C2×#261—42no—
250C2×#261—42no—
251C2×#261—42no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13#11712yes—
270C2×C4×C13#11712yes—
271C2×C4×C13#11712yes—
272C2×C4×C13C4×Q812yes—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—21no—
285C2×Dic13—21no—
286C2×Dic13—21no—
287C2×Dic13—21no—
288C2×Dic13—21no—
289C2×Dic13—21no—
290C2×Dic13#11712yes—
291C2×Dic13#11712yes—
292C2×Dic13#11712yes—
293C2×Dic13C4×Q812yes—
294C4×D13—24no—
295C4×D13—24no—
296C4×D13—24no—
297C4×D13—24no—
298C4×D13—24no—
299C4×D13—24no—
300C4×D13—24no—
301C4×D13—24no—
302C4×D13—42no—
303C4×D13—42no—
304C4×D13—42no—
305C4×D13—42no—
306C4×D13—42no—
307C4×D13—42no—
308C22×C4⋊C4—131no—
309C22×C4⋊C4—131no—
310C22×C4⋊C4—132no—
311C22×C42—131no—
312C22×C42—131no—
313C22×C42—131no—
314C22×C42—132no—
315C4×C4⋊C4—131no—
316C4×C4⋊C4—131no—
317C4×C4⋊C4—131no—
318C4×C4⋊C4—131no—
319C4×C4⋊C4—131no—
320C4×C4⋊C4—131no—
321C4×C4⋊C4—131no—
322C4×C4⋊C4#26111yescharacteristic, complemented
323C2×#95—131no—
324C2×#95—131no—
325C2×#95—131no—
326C2×#95—131no—
327C2×#95—132no—
328C2×#95—131no—
329C2×#95—131no—
330C2×#95—132no—
331C2×#95—132no—
332C2×#95—132no—
333C2×#95—132no—
334C2×#95—132no—
335C2×#95—132no—
336C2×#95—132no—
337C2×#95—132no—
338C2×#95—132no—
339C22×C13C2×#11711yescharacteristic
340C22×C13C2×#11711yescharacteristic
341C22×C13C2×#11711yescharacteristic
342C22×C13C2×C4×Q811yescharacteristic
343C22×C13C4×#4111yescharacteristic
344C22×C13#51811yescharacteristic
345C22×C13#52011yescharacteristic
346C2×D13#52912yes—
347C2×D13#52912yes—
348C2×D13#52912yes—
349C2×D13#53312yes—
350C2×D13#53812yes—
351C2×D13#53912yes—
352C2×D13#55112yes—
353C2×D13#55212yes—
354C2×D13#55312yes—
355C2×D13#55312yes—
356C2×D13#55411yescharacteristic
357C2×D13#55412yes—
358C2×D13#55512yes—
359C2×D13#55611yescharacteristic
360C2×D13#55711yescharacteristic
361C2×D13#55911yescharacteristic
362#261—44no—
363#261—44no—
364#261—82no—
365#261—82no—
366C4×C13—22no—
367C4×C13—22no—
368C4×C13—22no—
369C4×C13—22no—
370C4×C13—41no—
371C4×C13—41no—
372C4×C13—41no—
373Dic13—22no—
374Dic13—22no—
375Dic13—22no—
376Dic13—22no—
377Dic13—41no—
378Dic13—41no—
379Dic13—41no—
380C23×C4—131no—
381C23×C4—131no—
382C23×C4—131no—
383C23×C4—131no—
384C23×C4—132no—
385C23×C4—132no—
386C23×C4—131no—
387C23×C4—131no—
388C23×C4—131no—
389C23×C4—132no—
390C23×C4—132no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—262no—
398C2×C4⋊C4—264no—
399C2×C4⋊C4—262no—
400C2×C4⋊C4—264no—
401C2×C4⋊C4—522no—
402C2×C4⋊C4—522no—
403C2×C4⋊C4C2×#26111yescharacteristic
404C2×C4⋊C4C2×#26111yescharacteristic
405C2×C42—131no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—131no—
409C2×C42—131no—
410C2×C42—131no—
411C2×C42—131no—
412C2×C42—131no—
413C2×C42—131no—
414C2×C42—264no—
415C2×C42—264no—
416C2×C42—264no—
417C2×C42—522no—
418C2×C42—522no—
419C2×C42—522no—
420C2×C42C2×#26111yescharacteristic
421C2×C42C2×#26111yescharacteristic
422C2×C42C2×#26111yescharacteristic
423#95—134no—
424#95—131no—
425#95—131no—
426#95—131no—
427#95—131no—
428#95—131no—
429#95—131no—
430#95—264no—
431#95—264no—
432#95—264no—
433#95—264no—
434#95—262no—
435#95—262no—
436#95—262no—
437#95—264no—
438#95—264no—
439#95—522no—
440#95—522no—
441#95—522no—
442#95—522no—
443#95C2×#26111yescharacteristic
444#95C2×#26111yescharacteristic
445C2×C13#228311yescharacteristic
446C2×C13#229511yescharacteristic
447C2×C13#231811yescharacteristic
448C2×C13#234511yescharacteristic
449C2×C13#234611yescharacteristic
450C2×C13#235311yescharacteristic
451C2×C13#235511yescharacteristic
452D13#257312yes—
453D13#257412yes—
454D13#258512yes—
455D13#259312yes—
456C24—131no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—134no—
462C22×C4—132no—
463C22×C4—134no—
464C22×C4—132no—
465C22×C4—132no—
466C22×C4—132no—
467C22×C4—134no—
468C22×C4—134no—
469C22×C4—131no—
470C22×C4—131no—
471C22×C4—131no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—262no—
487C22×C4—262no—
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—262no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—262no—
509C22×C4—262no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—262no—
513C22×C4—262no—
514C22×C4—262no—
515C22×C4—262no—
516C22×C4—262no—
517C22×C4—262no—
518C22×C4—262no—
519C22×C4—262no—
520C22×C4C22×#26111yescharacteristic
521C22×C4C22×#26111yescharacteristic
522C22×C4C22×#26111yescharacteristic
523C22×C4C22×#26111yescharacteristic
524C22×C4C22×#26111yescharacteristic
525C22×C4C22×#26111yescharacteristic
526C22×C4C22×#26111yescharacteristic
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—262no—
530C4⋊C4—262no—
531C4⋊C4—262no—
532C4⋊C4—262no—
533C4⋊C4—262no—
534C4⋊C4—262no—
535C4⋊C4—528no—
536C42—22no—
537C42—41no—
538C42—41no—
539C42—262no—
540C42—262no—
541C42—262no—
542C42—521no—
543C42—521no—
544C42—521no—
545C42—521no—
546C42—521no—
547C42—521no—
548C42—528no—
549C13#1392811yescharacteristic, complemented, Sylow
550C23—132no—
551C23—132no—
552C23—131no—
553C23—131no—
554C23—132no—
555C23—131no—
556C23—131no—
557C23—132no—
558C23—131no—
559C23—131no—
560C23C23×#26111yescharacteristic
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—132no—
579C2×C4—132no—
580C2×C4—132no—
581C2×C4—132no—
582C2×C4—264no—
583C2×C4—264no—
584C2×C4—264no—
585C2×C4—264no—
586C2×C4—264no—
587C2×C4—264no—
588C2×C4—264no—
589C2×C4—264no—
590C2×C4—261no—
591C2×C4—261no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—261no—
595C2×C4—261no—
596C2×C4—261no—
597C2×C4—261no—
598C2×C4—264no—
599C2×C4—264no—
600C2×C4—264no—
601C2×C4—264no—
602C2×C4—264no—
603C2×C4—264no—
604C2×C4—261no—
605C2×C4—261no—
606C2×C4—261no—
607C2×C4—261no—
608C2×C4—261no—
609C2×C4—261no—
610C2×C4—261no—
611C2×C4—261no—
612C2×C4—261no—
613C2×C4—522no—
614C2×C4—522no—
615C2×C4—522no—
616C2×C4—522no—
617C2×C4—522no—
618C2×C4—522no—
619C2×C4—522no—
620C2×C4—522no—
621C2×C4—522no—
622C2×C4—522no—
623C2×C4—522no—
624C2×C4—522no—
625C2×C4—522no—
626C2×C4—522no—
627C2×C4—522no—
628C2×C4—522no—
629C2×C4—522no—
630C2×C4—522no—
631C2×C4—522no—
632C2×C4—522no—
633C2×C4—522no—
634C2×C4—522no—
635C2×C4—522no—
636C2×C4—522no—
637C2×C4—522no—
638C2×C4—522no—
639C2×C4—522no—
640C2×C4—522no—
641C2×C4#8823712yes—
642C2×C4#8823712yes—
643C2×C4#8823712yes—
644C2×C4Q8×#26112yes—
645C22—132no—
646C22—132no—
647C22—132no—
648C22—132no—
649C22—132no—
650C22—132no—
651C22—132no—
652C22—132no—
653C22—132no—
654C22—132no—
655C22—132no—
656C22—132no—
657C22—131no—
658C22—131no—
659C22—131no—
660C22—131no—
661C22C2×#8823711yescharacteristic
662C22C2×#8823711yescharacteristic
663C22C2×#8823711yescharacteristic
664C22#1171962311yescharacteristic
665C22C2×Q8×#26111yescharacteristic
666C22#41×#26111yescharacteristic
667C22#1171963111yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—22no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—262no—
676C4—262no—
677C4—262no—
678C4—262no—
679C4—524no—
680C4—524no—
681C4—521no—
682C4—521no—
683C4—521no—
684C4—1042no—
685C4—1042no—
686C2—132no—
687C2—132no—
688C2—132no—
689C2—132no—
690C2#1313128311yescharacteristic
691C2#1313129511yescharacteristic
692C2#1313131811yescharacteristic
693C2#1313134511yescharacteristic
694C2#1313134611yescharacteristic
695C2#1313135311yescharacteristic
696C2#1313135511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC4×C13×C4⋊C4C4
prime radical, cosocleC23×D13C24
hypercenterC4×C4⋊C4#261
hypocenterC13#13928
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
33. C4×C13×C4⋊C4C4semidirect
34. C4⋊C4×Dic13C4semidirect
35. C4⋊C4×Dic13C4semidirect
36. C4×C4⋊Dic13C4semidirect
37. C4×#6101C4semidirect
38. C4×#6101C4semidirect
41. #11718310C4semidirect
42. #11718310C4semidirect
322. C4×C4⋊C4#261semidirect
549. C13#13928semidirect

Maximal subgroups

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

subgroupindex
#131300222
#131300212
#131300152
#131300142
#131300122
#131300112
C4×(C2×#261)⋊C42
C4×C4⋊C4×D132
#1392813