Finite Group Databasebeta

← #15869942

Subgroups — #15869942

Order 3328.

924 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718673C211yesmaximal, characteristic
2C2×M16×Dic13C211yesmaximal, characteristic, complemented
3C4×#88189C211yesmaximal, characteristic
4#13115452C211yesmaximal, characteristic, complemented
5#13115445C211yesmaximal, characteristic, complemented
6#13115403C211yesmaximal, characteristic, complemented
7#13115396C211yesmaximal, characteristic, complemented
8#13115019C211yesmaximal, characteristic, complemented
9#13114902C211yesmaximal, characteristic, complemented
10#13114707C211yesmaximal, characteristic, complemented
11#13114697C211yesmaximal, characteristic, complemented
12#13114622C211yesmaximal, characteristic, complemented
13#13114622C211yesmaximal, characteristic, complemented
14#13114622C211yesmaximal, characteristic, complemented
15C13×#1870C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×#88189C411yescharacteristic
19C22×C4×Dic13C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25#11718881C411yescharacteristic
26C4×C22⋊Dic13C2211yescharacteristic
27C4×C22⋊Dic13C2211yescharacteristic
28C4×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31M16×Dic13—24no—
32C2×#88055C2211yescharacteristic
33C2×#88055C2211yescharacteristic
34C2×#88055C2211yescharacteristic
35C2×#88054C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×C8×Dic13C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39C2×C8×Dic13C2211yescharacteristic
40#11718673—24no—
41#11718639C411yescharacteristic
42#11718639C411yescharacteristic
43#11718607C411yescharacteristic
44#11718605C411yescharacteristic
45#11718605C411yescharacteristic
46#11718604C411yescharacteristic
47C4×#6101C2211yescharacteristic
48C4×#6101C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51C13×#336C2211yescharacteristic
52C13×#336C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61C22×D4×C13C2×C411yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2×C411yescharacteristic
65C23×Dic13C2×C411yescharacteristic
66C2×C13×M16—22no—
67C2×C13×M16—22no—
68C2×C13×M16—22no—
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C4×D4×C13—22no—
74C4×D4×C13—22no—
75C2×C13×C4⋊C4C2×C411yescharacteristic
76C2×C13×C22⋊C4C2×C411yescharacteristic
77C2×C13×C22⋊C4C2×C411yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C22⋊Dic13C2×C411yescharacteristic
80C2×C22⋊Dic13C2×C411yescharacteristic
81C2×C22⋊Dic13C2×C411yescharacteristic
82C2×C22⋊Dic13C2×C411yescharacteristic
83C2×C22⋊Dic13C2×C411yescharacteristic
84C2×C22⋊Dic13C2×C411yescharacteristic
85#88189—24no—
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×#6101C2×C411yescharacteristic
90C2×C4×Dic13—22no—
91C2×C4×Dic13—22no—
92C2×C4×Dic13C2×C411yescharacteristic
93C2×C4×Dic13C2×C411yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C2×#6099—22no—
99C2×#6099—22no—
100C2×#6099—22no—
101C2×#6099—22no—
102C2×#6099—22no—
103C2×#6099D414yes—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C13×C22⋊C8—22no—
109C13×C22⋊C8—22no—
110C13×C22⋊C8—22no—
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88071C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#88071C2×C411yescharacteristic
121C22⋊#1055—22no—
122C22⋊#1055—22no—
123#88055—22no—
124#88055—22no—
125#88055—22no—
126#88054—22no—
127#88054—22no—
128C8×Dic13—22no—
129C8×Dic13—22no—
130C8×Dic13—22no—
131C4⋊#1055—22no—
132C4×#1055—22no—
133#21565—131nomaximal, Sylow
134C24×C13C22×C411yescharacteristic
135C24×C13C22×C411yescharacteristic
136C2×D4×C13—22no—
137C2×D4×C13—22no—
138C2×D4×C13—41no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C2×D412yes—
154C22×C4×C13#4112yes—
155C22×C4×C13C2411yescharacteristic
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—41no—
161C22×Dic13—41no—
162C22×Dic13C22×C411yescharacteristic
163C22×Dic13C22×C411yescharacteristic
164C22×Dic13C22×C411yescharacteristic
165C22×Dic13C22×C411yescharacteristic
166C22×Dic13C22×C411yescharacteristic
167C22×Dic13C22×C411yescharacteristic
168C22×Dic13C22×C411yescharacteristic
169C22×Dic13C22×C411yescharacteristic
170C13×M16—28no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C2×C8×C13#4112yes—
182C2×C8×C13#4112yes—
183C13×C4⋊C4—22no—
184C13×C22⋊C4—22no—
185C13×C22⋊C4—22no—
186C42×C13—21no—
187C42×C13—21no—
188C22⋊Dic13—22no—
189C22⋊Dic13—22no—
190C22⋊Dic13—22no—
191C22⋊Dic13—22no—
192C22⋊Dic13—41no—
193C22⋊Dic13—41no—
194#6101—22no—
195#6101—22no—
196#6101—41no—
197#6101M1614yescomplemented
198C4×Dic13—22no—
199C4×Dic13—22no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13—21no—
207C4×Dic13—21no—
208#6099—28no—
209#6099—44no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055C2×D412yes—
219C2×#1055C2×D412yes—
220C2×#1055#4112yes—
221C2×#1055#4112yes—
222C2×#436—131no—
223C2×C4×M16—131no—
224C4×#123—131no—
225#1924—131no—
226#1923—131no—
227#1917—131no—
228#1916—131no—
229#1870D1311yescharacteristic
230#1851—131no—
231#1817—131no—
232#1771—131no—
233C8×C4⋊C4—131no—
234#1753—131no—
235#1753—131no—
236#1753—131no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13—21no—
249C23×C13—21no—
250C23×C13C4×D412yes—
251C23×C13C23×C411yescharacteristic
252D4×C13—44no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
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—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13C4×D412yes—
272C2×C4×C13C2×M1612yes—
273C2×C4×C13C22×D411yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
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—21no—
291C2×Dic13—21no—
292C2×Dic13—21no—
293C2×Dic13—21no—
294C2×Dic13—21no—
295C2×Dic13—21no—
296C2×Dic13—21no—
297C2×Dic13—21no—
298C2×Dic13—21no—
299C2×Dic13—21no—
300C2×Dic13—44no—
301C2×Dic13—44no—
302C2×Dic13C2×M1612yes—
303C2×Dic13C2×M1612yes—
304C2×Dic13#13112yes—
305C8×C13—22no—
306C8×C13—22no—
307C8×C13—41no—
308C8×C13—41no—
309#1055—22no—
310#1055—41no—
311#1055—41no—
312#1055#12314yescomplemented
313C22×M16—131no—
314C22×M16—131no—
315C22×M16C2×D1311yescharacteristic
316C2×#123—131no—
317C2×C4×D4C2×D1311yescharacteristic
318C22×C42—131no—
319#436—264no—
320C2×C4⋊C8—131no—
321C2×C4⋊C8—131no—
322C2×C4⋊C8—131no—
323C2×C22⋊C8—131no—
324C2×C22⋊C8—131no—
325C2×C22⋊C8C2×D1311yescharacteristic
326C2×C22⋊C8C2×D1311yescharacteristic
327C2×C22⋊C8C2×D1311yescharacteristic
328C4×M16—264no—
329C2×#97—131no—
330C2×#97—131no—
331C2×#97—131no—
332C2×C4×C8—131no—
333C2×C4×C8—131no—
334C2×C4×C8—131no—
335C2×C4×C8—131no—
336#388—131no—
337#388—131no—
338#387—131no—
339#387—131no—
340#386—131no—
341#385—131no—
342#381—131no—
343C4×C4⋊C4—131no—
344C4×C4⋊C4—131no—
345C4×C22⋊C4—131no—
346C4×C22⋊C4—131no—
347C4×C22⋊C4—131no—
348#336—131no—
349#336—131no—
350#336—131no—
351#336—131no—
352#336—131no—
353#336—131no—
354#336—131no—
355#336—131no—
356#336C2×D1311yescharacteristic
357#336C2×D1311yescharacteristic
358C22×C13—22no—
359C22×C13—22no—
360C22×C13—22no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13—41no—
370C22×C13—41no—
371C22×C13—41no—
372C22×C13C2×C4×D411yescharacteristic
373C22×C13C4×#4111yescharacteristic
374C22×C13C4×#4111yescharacteristic
375C22×C13C22×M1611yescharacteristic
376C22×C13C2×#13111yescharacteristic
377C22×C13#56811yescharacteristic
378C22×C13#56811yescharacteristic
379C4×C13—22no—
380C4×C13—22no—
381C4×C13—41no—
382C4×C13—41no—
383C4×C13C2×#12311yescharacteristic
384C4×C13#52511yescharacteristic
385C4×C13#52911yescharacteristic
386C4×C13#52911yescharacteristic
387Dic13—22no—
388Dic13—22no—
389Dic13—22no—
390Dic13—41no—
391Dic13—41no—
392Dic13—41no—
393Dic13—41no—
394Dic13—41no—
395C22×D4C4×D1311yescharacteristic
396C23×C4—131no—
397C23×C4—131no—
398C23×C4C22×D1311yescharacteristic
399C23×C4C22×D1311yescharacteristic
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—22no—
403C2×M16—134no—
404C2×M16—262no—
405C2×M16—262no—
406C2×M16—262no—
407C2×M16—262no—
408C2×M16—262no—
409C22×C8—131no—
410C22×C8—131no—
411C22×C8—131no—
412C22×C8—131no—
413C22×C8C22×D1311yescharacteristic
414C22×C8C22×D1311yescharacteristic
415C22×C8C22×D1311yescharacteristic
416C22×C8C22×D1311yescharacteristic
417#123—264no—
418C4×D4—22no—
419C4×D4—22no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—131no—
422C2×C4⋊C4—131no—
423C2×C4⋊C4—131no—
424C2×C4⋊C4C4×D1311yescharacteristic
425C2×C22⋊C4—131no—
426C2×C22⋊C4—131no—
427C2×C22⋊C4—131no—
428C2×C22⋊C4—131no—
429C2×C22⋊C4—131no—
430C2×C22⋊C4—131no—
431C2×C22⋊C4C4×D1311yescharacteristic
432C2×C22⋊C4C4×D1311yescharacteristic
433C2×C42—131no—
434C2×C42—131no—
435C2×C42—131no—
436C2×C42—131no—
437C2×C42—131no—
438C2×C42—131no—
439C2×C42—262no—
440C2×C42—262no—
441C2×C42C22×D1311yescharacteristic
442C4⋊C8—262no—
443C4⋊C8—262no—
444C4⋊C8—262no—
445C22⋊C8—22no—
446C22⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8—262no—
449C22⋊C8—262no—
450#97—262no—
451#97—262no—
452#97—262no—
453C4×C8—262no—
454C4×C8—262no—
455C4×C8—262no—
456C4×C8—262no—
457#95—131no—
458#95—131no—
459#95—131no—
460#95—131no—
461#95—131no—
462#95—131no—
463#95—131no—
464#95—131no—
465#95—131no—
466#95—131no—
467C2×C13—42no—
468C2×C13—81no—
469C2×C13C4×#12311yescharacteristic
470C2×C13#293311yescharacteristic
471C2×C13D4×M1611yescharacteristic
472C2×C13#296511yescharacteristic
473C2×C13#296711yescharacteristic
474C2×C13#296911yescharacteristic
475C2×C13#297111yescharacteristic
476C24C2×C4×D1311yescharacteristic
477C24C2×C4×D1311yescharacteristic
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—41no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—131no—
492C22×C4—131no—
493C22×C4—131no—
494C22×C4—131no—
495C22×C4—131no—
496C22×C4—131no—
497C22×C4—131no—
498C22×C4—131no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—521no—
504C22×C4—521no—
505C22×C4C2×C4×D1311yescharacteristic
506C22×C4C2×C4×D1311yescharacteristic
507C22×C4C2×C4×D1311yescharacteristic
508C22×C4C2×C4×D1311yescharacteristic
509C22×C4D4×D1312yes—
510C22×C4#612912yes—
511C22×C4C23×D1311yescharacteristic
512M16—28no—
513M16—268no—
514M16—524no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—132no—
526C2×C8—132no—
527C2×C8—132no—
528C2×C8—132no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C2×C8#612912yes—
538C2×C8#612912yes—
539C4⋊C4—22no—
540C4⋊C4—134no—
541C4⋊C4—262no—
542C4⋊C4—262no—
543C4⋊C4—521no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—262no—
547C22⋊C4—262no—
548C22⋊C4—262no—
549C22⋊C4—262no—
550C22⋊C4—521no—
551C22⋊C4—521no—
552C42—21no—
553C42—21no—
554C42—262no—
555C42—262no—
556C42—261no—
557C42—261no—
558C42—261no—
559C42—261no—
560C42—261no—
561C42—261no—
562C42—261no—
563C42—261no—
564C13#2156511yescharacteristic, complemented, Sylow
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23#8813512yes—
579C23C22×C4×D1311yescharacteristic
580D4—44no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—132no—
600C2×C4—132no—
601C2×C4—132no—
602C2×C4—261no—
603C2×C4—261no—
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—261no—
614C2×C4—261no—
615C2×C4—261no—
616C2×C4—261no—
617C2×C4—261no—
618C2×C4—261no—
619C2×C4—261no—
620C2×C4—261no—
621C2×C4—261no—
622C2×C4—261no—
623C2×C4—524no—
624C2×C4—524no—
625C2×C4#8813512yes—
626C2×C4M16×D1312yes—
627C2×C4C2×D4×D1311yescharacteristic
628C2×C4C2×#612911yescharacteristic
629C2×C4C2×#612911yescharacteristic
630C2×C4C2×#612911yescharacteristic
631C2×C4#41×D1311yescharacteristic
632C2×C4#41×D1311yescharacteristic
633C8—22no—
634C8—22no—
635C8—41no—
636C8—41no—
637C8—134no—
638C8—262no—
639C8—521no—
640C8—521no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22C2×#8813511yescharacteristic
656C22C4×#612911yescharacteristic
657C22C4×#612911yescharacteristic
658C22C2×M16×D1311yescharacteristic
659C22#1171945011yescharacteristic
660C22D13×#13111yescharacteristic
661C22#1171945511yescharacteristic
662C4—22no—
663C4—22no—
664C4—41no—
665C4—41no—
666C4—262no—
667C4—262no—
668C4—262no—
669C4—521no—
670C4—521no—
671C4—521no—
672C4—521no—
673C4—521no—
674C4#1171929111yescharacteristic
675C4#1171930511yescharacteristic
676C4#1171930511yescharacteristic
677C4D13×#12311yescharacteristic
678C2—42no—
679C2—81no—
680C2#1311736111yescharacteristic
681C2#1312356611yescharacteristic
682C2#1312356811yescharacteristic
683C2#1312379911yescharacteristic
684C2#1312381511yescharacteristic
685C2#1312383311yescharacteristic
686C2#1312385211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1870C2
prime radicalC22×D4×C13C2×C4
cosocleC22×C4×C13C24
hypercenter#1870D13
hypocenterC13#21565
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×M16×Dic13C2semidirect
4. #13115452C2semidirect
5. #13115445C2semidirect
6. #13115403C2semidirect
7. #13115396C2semidirect
8. #13115019C2semidirect
9. #13114902C2semidirect
10. #13114707C2semidirect
11. #13114697C2semidirect
12. #13114622C2semidirect
13. #13114622C2semidirect
14. #13114622C2semidirect
197. #6101M16semidirect
312. #1055#123semidirect
564. C13#21565semidirect

Maximal subgroups

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

subgroupindex
C2×#117186732
C2×M16×Dic132
C4×#881892
#131154522
#131154452
#131154032
#131153962
#131150192
#131149022
#131147072
#131146972
#131146222
C13×#18702
#2156513