Finite Group Databasebeta

← #15869976

Subgroups — #15869976

Order 3328.

878 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718788C211yesmaximal, characteristic
2#13118093C211yesmaximal, characteristic
3#13115449C211yesmaximal, characteristic, complemented
4#13115442C211yesmaximal, characteristic, complemented
5#13115400C211yesmaximal, characteristic, complemented
6#13115393C211yesmaximal, characteristic, complemented
7#13115128C211yesmaximal, characteristic
8#13115014C211yesmaximal, characteristic, complemented
9#13114907C211yesmaximal, characteristic, complemented
10#13114710C211yesmaximal, characteristic, complemented
11#13114704C211yesmaximal, characteristic, complemented
12#13114617C211yesmaximal, characteristic, complemented
13#13114613C211yesmaximal, characteristic, complemented
14C8×#6103C211yesmaximal, characteristic, complemented
15C2×C13×#405C211yesmaximal, characteristic, complemented
16C22×C13×M16C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×C4×C22⋊D13C2211yescharacteristic
20C22×C8×D13C2211yescharacteristic
21C13×#405—24no—
22C2×C13×#97C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C2×C4×C8×C13C2211yescharacteristic
26C4×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊#1055C2211yescharacteristic
28C2×C22⋊#1055C2211yescharacteristic
29#11718788—24no—
30C2×#88060C2211yescharacteristic
31C2×#88060C2211yescharacteristic
32C2×#88060C2211yescharacteristic
33C2×#88055C2211yescharacteristic
34C2×#88055C2211yescharacteristic
35C2×#88054C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39#11718654C411yescharacteristic
40#11718653C411yescharacteristic
41#11718643C411yescharacteristic
42#11718641C411yescharacteristic
43#11718620C411yescharacteristic
44#11718620C411yescharacteristic
45#11718613C411yescharacteristic
46#11718613C411yescharacteristic
47C4×#6103C2211yescharacteristic
48C4×#6103C2211yescharacteristic
49C4×#6101C2211yescharacteristic
50C4×#6101C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13C2×C411yescharacteristic
63C22×C4×D13C2311yescharacteristic
64C2×C13×M16—22no—
65C2×C13×M16—22no—
66C2×C13×M16D414yes—
67C22×C8×C13—22no—
68C22×C8×C13—22no—
69C22×C8×C13—22no—
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C13×#117—22no—
75C13×#117—22no—
76C2×C13×C4⋊C4C2×C411yescharacteristic
77C2×C13×C4⋊C4C2×C411yescharacteristic
78C2×C13×C22⋊C4C2×C411yescharacteristic
79C2×C13×C22⋊C4C2×C411yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C22⋊Dic13C2×C411yescharacteristic
83C2×C22⋊Dic13C2×C411yescharacteristic
84C2×C22⋊Dic13C2×C411yescharacteristic
85C4×C22⋊D13—22no—
86C4×C22⋊D13—22no—
87C2×#6103C2×C411yescharacteristic
88C2×#6103C2×C411yescharacteristic
89C2×#6103C2×C411yescharacteristic
90C2×#6103C2×C411yescharacteristic
91C2×#6103C2×C411yescharacteristic
92C2×#6101C2×C411yescharacteristic
93C2×#6101C2×C411yescharacteristic
94C2×#6101C2×C411yescharacteristic
95C2×#6101C2×C411yescharacteristic
96C2×#6101C2×C411yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C2×C8×D13—22no—
105C2×C8×D13—22no—
106C2×C8×D13—22no—
107C13×#97—22no—
108C13×#97—22no—
109C4×C8×C13—22no—
110C4×C8×C13—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#88060—22no—
124#88060—22no—
125#88060—22no—
126#88055—22no—
127#88055—22no—
128#88054—22no—
129#88054—22no—
130#88054—22no—
131C8×Dic13—22no—
132#21568—131nomaximal, Sylow
133C24×C13C22×C411yescharacteristic
134C23×D13C22×C411yescharacteristic
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C22×C411yescharacteristic
142C22×C4×C13C22×C411yescharacteristic
143C22×C4×C13C22×C411yescharacteristic
144C22×C4×C13C2×D412yes—
145C22×C4×C13#4112yes—
146C22×C4×C13C2411yescharacteristic
147C2×C22⋊D13—22no—
148C2×C22⋊D13—22no—
149C2×C22⋊D13—41no—
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C411yescharacteristic
154C22×Dic13C22×C411yescharacteristic
155C22×Dic13C22×C411yescharacteristic
156C22×Dic13C22×C411yescharacteristic
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C13×M16—28no—
164C2×C8×C13—28no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13C2×D412yes—
172C2×C8×C13C2×D412yes—
173C2×C8×C13#4112yes—
174C2×C8×C13#4112yes—
175C2×C8×C13#4112yes—
176C2×C8×C13#4112yes—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C22⋊Dic13—22no—
186C22⋊Dic13—22no—
187C22⋊Dic13—41no—
188#6103—22no—
189#6103—22no—
190#6103—22no—
191#6103—22no—
192#6103—41no—
193#6101—22no—
194#6101—22no—
195#6101—41no—
196#6101—41no—
197#6101—41no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C8×D13—44no—
217C2×#435—131no—
218C2×#405D1311yescharacteristic, complemented
219#2395—131no—
220#1924—131no—
221#1923—131no—
222#1917—131no—
223#1916—131no—
224#1869—131no—
225#1850—131no—
226#1818—131no—
227#1771—131no—
228#1770—131no—
229#1753—131no—
230#1752—131no—
231C8×C22⋊C4—131no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13C4×D412yes—
239C23×C13C23×C411yescharacteristic
240C22×D13—21no—
241C22×D13—21no—
242C22×D13—21no—
243C22×D13—21no—
244C22×D13—21no—
245C22×D13—21no—
246C22×D13#13112yes—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
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×C13C4×D412yes—
266C2×C4×C13C22×D411yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C22⋊D13—44no—
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—21no—
291C2×Dic13—21no—
292C2×Dic13—21no—
293C2×Dic13#13112yes—
294C4×D13—41no—
295C4×D13—41no—
296C4×D13—41no—
297C4×D13—41no—
298C8×C13—22no—
299C8×C13—22no—
300C8×C13—22no—
301C8×C13#12314yes—
302#1055—41no—
303#1055—41no—
304#1055—41no—
305#1055—41no—
306C22×M16C2×D1311yescharacteristic
307C23×C8—131no—
308C23×C8C2×D1311yescharacteristic
309C2×C4×D4—131no—
310C2×#117C2×D1311yescharacteristic
311#435—264no—
312C2×C4⋊C8—131no—
313C2×C4⋊C8—131no—
314C2×C4⋊C8—131no—
315C2×C22⋊C8—131no—
316C2×C22⋊C8—131no—
317C2×C22⋊C8—131no—
318C2×C22⋊C8—131no—
319C2×C22⋊C8—131no—
320#405—24no—
321C2×#97—131no—
322C2×#97—131no—
323C2×#97C2×D1311yescharacteristic
324C2×#97C2×D1311yescharacteristic
325C2×C4×C8—131no—
326C2×C4×C8C2×D1311yescharacteristic
327C2×C4×C8C2×D1311yescharacteristic
328#400—131no—
329#399—131no—
330#398—131no—
331#397—131no—
332#397—131no—
333#397—131no—
334#394—131no—
335#394—131no—
336C4×C4⋊C4—131no—
337C4×C4⋊C4—131no—
338C4×C22⋊C4—131no—
339C4×C22⋊C4—131no—
340C4×C22⋊C4—131no—
341#336—131no—
342#336—131no—
343#336—131no—
344#336—131no—
345#336—131no—
346#336—131no—
347#336—131no—
348#336—131no—
349#336—131no—
350#336—131no—
351C22×C13—22no—
352C22×C13—22no—
353C22×C13—22no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13C2×C4×D411yescharacteristic
359C22×C13C4×#4111yescharacteristic
360C22×C13C4×#4111yescharacteristic
361C22×C13C2×#13111yescharacteristic
362C22×C13C2×#13111yescharacteristic
363C22×C13#56811yescharacteristic
364C22×C13#56811yescharacteristic
365C2×D13—22no—
366C2×D13—22no—
367C2×D13—22no—
368C2×D13—41no—
369C2×D13—41no—
370C2×D13—41no—
371C2×D13—41no—
372C4×C13—22no—
373C4×C13—41no—
374C4×C13—41no—
375C4×C13—41no—
376C4×C13—41no—
377C4×C13C2×#12311yescharacteristic
378C4×C13#52511yescharacteristic
379C4×C13#52911yescharacteristic
380C4×C13#52911yescharacteristic
381Dic13—22no—
382Dic13—41no—
383Dic13—41no—
384Dic13—41no—
385Dic13—41no—
386Dic13—41no—
387Dic13—41no—
388C22×D4—131no—
389C23×C4—131no—
390C23×C4C22×D1311yescharacteristic
391C2×M16—22no—
392C2×M16—22no—
393C2×M16C22⋊D1314yes—
394C22×C8—22no—
395C22×C8—22no—
396C22×C8—22no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8—131no—
401C22×C8—262no—
402C22×C8—262no—
403C22×C8—262no—
404C22×C8C22×D1311yescharacteristic
405C22×C8C22×D1311yescharacteristic
406C22×C8C22×D1311yescharacteristic
407C22×C8C22×D1311yescharacteristic
408C4×D4—262no—
409C4×D4—262no—
410#117—22no—
411#117—22no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4C4×D1311yescharacteristic
418C2×C4⋊C4C4×D1311yescharacteristic
419C2×C22⋊C4—131no—
420C2×C22⋊C4—131no—
421C2×C22⋊C4—131no—
422C2×C22⋊C4—131no—
423C2×C22⋊C4—131no—
424C2×C22⋊C4—131no—
425C2×C22⋊C4—131no—
426C2×C22⋊C4—131no—
427C2×C22⋊C4C4×D1311yescharacteristic
428C2×C22⋊C4C4×D1311yescharacteristic
429C2×C42—131no—
430C2×C42—131no—
431C2×C42—131no—
432C2×C42C22×D1311yescharacteristic
433C2×C42C22×D1311yescharacteristic
434C4⋊C8—262no—
435C4⋊C8—262no—
436C4⋊C8—262no—
437C22⋊C8—262no—
438C22⋊C8—262no—
439C22⋊C8—262no—
440C22⋊C8—262no—
441C22⋊C8—262no—
442#97—22no—
443#97—22no—
444#97—262no—
445#97—262no—
446C4×C8—22no—
447C4×C8—22no—
448C4×C8—262no—
449#95—131no—
450#95—131no—
451#95—131no—
452#95—131no—
453#95—131no—
454#95—131no—
455#95—131no—
456#95—131no—
457#95—131no—
458#95—131no—
459C2×C13—42no—
460C2×C13C4×#12311yescharacteristic
461C2×C13#293311yescharacteristic
462C2×C13#293511yescharacteristic
463C2×C13#296611yescharacteristic
464C2×C13#296711yescharacteristic
465C2×C13#296811yescharacteristic
466C2×C13#296811yescharacteristic
467D13—42no—
468C24—131no—
469C24C2×C4×D1311yescharacteristic
470C2×D4—262no—
471C2×D4—262no—
472C2×D4—521no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—131no—
478C22×C4—131no—
479C22×C4—131no—
480C22×C4—131no—
481C22×C4—131no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4C2×C4×D1311yescharacteristic
491C22×C4C2×C4×D1311yescharacteristic
492C22×C4C2×C4×D1311yescharacteristic
493C22×C4C2×C4×D1311yescharacteristic
494C22×C4C2×C4×D1311yescharacteristic
495C22×C4#612712yes—
496C22×C4C2×C22⋊D1312yes—
497C22×C4C23×D1311yescharacteristic
498M16—28no—
499C2×C8—28no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—524no—
519C2×C8#612712yes—
520C2×C8#612712yes—
521C2×C8#612712yes—
522C2×C8#612712yes—
523C2×C8C2×C22⋊D1312yes—
524C2×C8C2×C22⋊D1312yes—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—262no—
528C4⋊C4—262no—
529C4⋊C4—521no—
530C4⋊C4—521no—
531C4⋊C4—521no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—262no—
535C22⋊C4—262no—
536C22⋊C4—262no—
537C22⋊C4—262no—
538C22⋊C4—262no—
539C22⋊C4—262no—
540C22⋊C4—521no—
541C22⋊C4—521no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—261no—
547C42—261no—
548C42—261no—
549C42—261no—
550C42—261no—
551C42—261no—
552C13#2156811yescharacteristic, complemented, Sylow
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—132no—
560C23—261no—
561C23—261no—
562C23—261no—
563C23—261no—
564C23—261no—
565C23—261no—
566C23C4×C22⋊D1312yes—
567C23C22×C4×D1311yescharacteristic
568D4—524no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—132no—
588C2×C4—261no—
589C2×C4—261no—
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—261no—
599C2×C4—261no—
600C2×C4—261no—
601C2×C4—261no—
602C2×C4—261no—
603C2×C4—261no—
604C2×C4—261no—
605C2×C4—261no—
606C2×C4—261no—
607C2×C4—261no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4C4×C22⋊D1312yes—
613C2×C4C2×#612711yescharacteristic
614C2×C4C2×#612711yescharacteristic
615C2×C4C2×#612711yescharacteristic
616C2×C4C2×#612711yescharacteristic
617C2×C4C2×#612711yescharacteristic
618C2×C4C22×C22⋊D1311yescharacteristic
619C8—22no—
620C8—22no—
621C8—22no—
622C8—521no—
623C8—521no—
624C8—521no—
625C8—521no—
626C8#8818314yes—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—262no—
635C22—262no—
636C22—262no—
637C22—521no—
638C22—521no—
639C22—521no—
640C22—521no—
641C22C4×#612711yescharacteristic
642C22C4×#612711yescharacteristic
643C22D13×#13111yescharacteristic
644C22D13×#13111yescharacteristic
645C22#1171945511yescharacteristic
646C22#1171945511yescharacteristic
647C22C2×C4×C22⋊D1311yescharacteristic
648C4—22no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—262no—
654C4—521no—
655C4—521no—
656C4—521no—
657C4—521no—
658C4—521no—
659C4—521no—
660C4#1171918411yescharacteristic
661C4#1171918411yescharacteristic
662C4C2×#8818311yescharacteristic
663C4#1171949611yescharacteristic
664C2—42no—
665C2—522no—
666C2C4×#8818311yescharacteristic
667C2#1312355811yescharacteristic
668C2#1312357811yescharacteristic
669C2#1312380711yescharacteristic
670C2#1312381711yescharacteristic
671C2#1312382611yescharacteristic
672C2#1312382611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#405C2
prime radicalC22×C22⋊D13C2×C4
cosocleC22×C4×C13C24
hypercenterC2×#405D13
hypocenterC13#21568
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
3. #13115449C2semidirect
4. #13115442C2semidirect
5. #13115400C2semidirect
6. #13115393C2semidirect
8. #13115014C2semidirect
9. #13114907C2semidirect
10. #13114710C2semidirect
11. #13114704C2semidirect
12. #13114617C2semidirect
13. #13114613C2semidirect
14. C8×#6103C2semidirect
15. C2×C13×#405C2semidirect
218. C2×#405D13semidirect
552. C13#21568semidirect

Maximal subgroups

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

subgroupindex
C2×#117187882
#131180932
#131154492
#131154422
#131154002
#131153932
#131151282
#131150142
#131149072
#131147102
#131147042
#131146172
#131146132
C8×#61032
C2×C13×#4052
#2156813