Finite Group Databasebeta

← #15861611

Subgroups — #15861611

Order 3328.

1210 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718387C211yesmaximal, characteristic
2C2×D13×C22⋊C8C211yesmaximal, characteristic
3#13117215C211yesmaximal, characteristic
4#13114621C211yesmaximal, characteristic, complemented
5#13114619C211yesmaximal, characteristic, complemented
6#13114618C211yesmaximal, characteristic, complemented
7#13114616C211yesmaximal, characteristic, complemented
8#13114613C211yesmaximal, characteristic, complemented
9#13114611C211yesmaximal, characteristic, complemented
10C8×#6103C211yesmaximal, characteristic, complemented
11#13114606C211yesmaximal, characteristic, complemented
12#13114604C211yesmaximal, characteristic, complemented
13#13114604C211yesmaximal, characteristic, complemented
14#13114602C211yesmaximal, characteristic, complemented
15C13×#1750C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C22×#6094C2211yescharacteristic
20C22×#6094C2211yescharacteristic
21C22×C8×D13C2211yescharacteristic
22C22×C8×D13C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25C2×C13×#97C2211yescharacteristic, complemented
26C2×C4×C8×C13C2211yescharacteristic, complemented
27C2×C22⋊#1055C2211yescharacteristic
28C2×C22⋊#1055C2211yescharacteristic
29C2×#88060C2211yescharacteristic
30C2×#88060C2211yescharacteristic
31C2×#88060C2211yescharacteristic
32C2×#88060C2211yescharacteristic
33C2×#88055C2211yescharacteristic, complemented
34C2×#88055C2211yescharacteristic, complemented
35C2×C8×Dic13C2211yescharacteristic, complemented
36C2×C8×Dic13C2211yescharacteristic, complemented
37#11718648C412yes—
38#11718648C412yes—
39#11718616C412yes—
40#11718604C412yes—
41C4×#6103C2211yescharacteristic
42C4×#6103C2211yescharacteristic
43C4×#6103C2211yescharacteristic
44C4×#6103C2211yescharacteristic
45C2×#88043C2211yescharacteristic, complemented
46C2×C4×#1055C2211yescharacteristic, complemented
47#11718387C418yescomplemented
48D13×C22⋊C8C418yescomplemented
49C13×#336C2211yescharacteristic, complemented
50C13×#336C2211yescharacteristic, complemented
51#11718142C2211yescharacteristic, complemented
52#11718142C2211yescharacteristic, complemented
53#11718142C2211yescharacteristic, complemented
54#11718142C2211yescharacteristic, complemented
55#11718116C2211yescharacteristic, complemented
56#11718116C2211yescharacteristic, complemented
57C24×D13C2×C411yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×Dic13C2×C411yescharacteristic
60C22×C4×D13—41no—
61C22×C4×D13—41no—
62C22×C4×D13—41no—
63C22×C4×D13—41no—
64C22×C4×D13C2×C411yescharacteristic
65C22×C4×D13C2×C411yescharacteristic
66C22×C4×D13C2×C414yes—
67C22×C4×D13C2×C414yes—
68C22×C4×D13C2311yescharacteristic
69C22×C4×D13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C13×#117—41no—
75C13×#117—41no—
76C2×C13×C4⋊C4C2×C412yes—
77C2×C13×C22⋊C4C2×C412yes—
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C22⋊Dic13C2×C412yes—
81C2×#6103C2×C412yes—
82C2×#6103C2×C412yes—
83C2×#6103C2×C412yes—
84C2×#6103C2×C412yes—
85#88180—41no—
86#88180—41no—
87C2×C4⋊Dic13C2×C412yes—
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C2×#6094—41no—
95C2×#6094—41no—
96C2×#6094—41no—
97C2×#6094—41no—
98C2×#6094C2×C414yes—
99C2×#6094C2×C414yes—
100C2×C8×D13—41no—
101C2×C8×D13—41no—
102C2×C8×D13—41no—
103C2×C8×D13—41no—
104C2×C8×D13C2×C414yes—
105C2×C8×D13C2×C414yes—
106C13×C22⋊C8C2×C414yes—
107C13×C22⋊C8C2×C414yes—
108C13×#97—41no—
109C4×C8×C13—41no—
110#88071C2×C412yes—
111#88071C2×C412yes—
112#88071C2×C412yes—
113#88071C2×C412yes—
114C22⋊#1055C2×C414yes—
115C22⋊#1055C2×C414yes—
116#88060C2×C414yes—
117#88060C2×C414yes—
118#88060C2×C414yes—
119#88060C2×C414yes—
120#88055—41no—
121#88055—41no—
122C8×Dic13—41no—
123C8×Dic13—41no—
124#88043—41no—
125C4×#1055—41no—
126#20527—131nomaximal, Sylow
127C24×C13C22×C411yescharacteristic
128C23×D13—24no—
129C23×D13—41no—
130C23×D13—41no—
131C23×D13—42no—
132C23×D13C4214yes—
133C23×D13C22×C411yescharacteristic
134C23×D13C22×C411yescharacteristic
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13C22×C412yes—
140C22×C4×C13C22×C412yes—
141C22×C4×C13C22×C411yescharacteristic
142C22×C4×C13C22×C412yes—
143C22×C4×C13C22×C412yes—
144C22×C4×C13C2411yescharacteristic
145C22×Dic13—41no—
146C22×Dic13—41no—
147C22×Dic13C4214yes—
148C22×Dic13C22×C412yes—
149C22×Dic13C22×C412yes—
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C2×C4×D13—21no—
153C2×C4×D13—21no—
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—44no—
161C2×C4×D13—44no—
162C2×C4×D13—44no—
163C2×C4×D13—44no—
164C2×C4×D13—41no—
165C2×C4×D13—41no—
166C2×C4×D13—41no—
167C2×C4×D13—41no—
168C2×C4×D13C4214yes—
169C2×C4×D13C4214yes—
170C2×C4×D13C22×C412yes—
171C2×C4×D13C22×C412yes—
172C2×C4×D13C22×C412yes—
173C2×C4×D13C22×C412yes—
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—21no—
182C2×C8×C13C22×C412yes—
183C2×C8×C13C22×C412yes—
184C2×C8×C13C22×C412yes—
185C2×C8×C13C22×C412yes—
186C13×C4⋊C4—42no—
187C13×C22⋊C4—42no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C22⋊Dic13—42no—
193#6103—24no—
194#6103—24no—
195#6103—42no—
196#6103—42no—
197C4⋊Dic13—42no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055C22×C412yes—
211C2×#1055C22×C412yes—
212C2×#1055C22×C412yes—
213C2×#1055C22×C412yes—
214#6094—44no—
215#6094—44no—
216C8×D13—44no—
217C8×D13—44no—
218C2×#407—131no—
219C22×C22⋊C8—131no—
220#2280—131no—
221#1753—131no—
222#1753—131no—
223#1753—131no—
224#1753—131no—
225#1752—131no—
226#1752—131no—
227C8×C22⋊C4—131no—
228C8×C22⋊C4—131no—
229#1750—131no—
230#1750—131no—
231#1750—131no—
232#1750D1311yescharacteristic, complemented
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13C2×C4212yes—
238C23×C13C23×C411yescharacteristic
239C22×D13—21no—
240C22×D13—21no—
241C22×D13—22no—
242C22×D13—21no—
243C22×D13—21no—
244C22×D13—22no—
245C22×D13—22no—
246C22×D13—28no—
247C22×D13—44no—
248C22×D13—44no—
249C22×D13—48no—
250C22×D13—48no—
251C22×D13C2×C4212yes—
252C22×D13C2×C4212yes—
253C22×D13#13114yes—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13C2×C4212yes—
267C2×C4×C13C23×C411yescharacteristic
268C2×C4×C13C23×C411yescharacteristic
269C2×C4×C13H(5,𝔽2)11yescharacteristic
270C2×C4×C13H(5,𝔽2)11yescharacteristic
271C2×C4×C13H(5,𝔽2)11yescharacteristic
272C2×C4×C13H(5,𝔽2)11yescharacteristic
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—22no—
283C2×Dic13—44no—
284C2×Dic13C2×C4212yes—
285C2×Dic13C2×C4212yes—
286C4×D13—22no—
287C4×D13—22no—
288C4×D13—22no—
289C4×D13—22no—
290C4×D13—22no—
291C4×D13—22no—
292C4×D13—22no—
293C4×D13—22no—
294C4×D13—44no—
295C4×D13—44no—
296C8×C13—22no—
297C8×C13—22no—
298C8×C13—22no—
299C8×C13—22no—
300#1055—22no—
301#1055—22no—
302#1055—22no—
303#1055—22no—
304C24×C4—131no—
305C22×M16—131no—
306C22×M16—131no—
307C23×C8—131no—
308C23×C8—131no—
309C2×#117—131no—
310C2×#117C2×D1311yescharacteristic
311#407—138no—
312C2×C22⋊C8—131no—
313C2×C22⋊C8—131no—
314C2×C22⋊C8—131no—
315C2×C22⋊C8—131no—
316C2×C22⋊C8—131no—
317C2×C22⋊C8—131no—
318C2×C22⋊C8—138no—
319C2×C22⋊C8C2×D1311yescharacteristic
320C2×C22⋊C8C2×D1311yescharacteristic
321C2×#97—131no—
322C2×#97—131no—
323C2×#97—131no—
324C2×#97C2×D1311yescharacteristic, complemented
325C2×C4×C8—131no—
326C2×C4×C8—131no—
327C2×C4×C8—131no—
328C2×C4×C8C2×D1311yescharacteristic, complemented
329#381—132no—
330#380—132no—
331#380—132no—
332#379—132no—
333C4×C22⋊C4—131no—
334C4×C22⋊C4—131no—
335C4×C22⋊C4—131no—
336C4×C22⋊C4—131no—
337#336—131no—
338#336—131no—
339#336—131no—
340#336—131no—
341#336—131no—
342#336—131no—
343#336C2×D1311yescharacteristic, complemented
344#336C2×D1311yescharacteristic, complemented
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—42no—
349C22×C13—42no—
350C22×C13C22×C4211yescharacteristic
351C22×C13#51811yescharacteristic
352C22×C13#51811yescharacteristic
353C22×C13C2×#13112yes—
354C22×C13#56812yes—
355C2×D13—22no—
356C2×D13—24no—
357C2×D13—24no—
358C2×D13—22no—
359C2×D13—22no—
360C2×D13—22no—
361C2×D13—22no—
362C2×D13—416no—
363C2×D13—42no—
364C2×D13—42no—
365C2×D13#40514yes—
366C4×C13—22no—
367C4×C13—42no—
368C4×C13—42no—
369C4×C13#51811yescharacteristic
370C4×C13#51811yescharacteristic
371C4×C13#51811yescharacteristic
372C4×C13#51811yescharacteristic
373Dic13—22no—
374Dic13—22no—
375Dic13—42no—
376Dic13—42no—
377C25—131no—
378C23×C4—131no—
379C23×C4—131no—
380C23×C4—131no—
381C23×C4—131no—
382C23×C4—131no—
383C23×C4—134no—
384C23×C4—134no—
385C23×C4—521no—
386C23×C4—521no—
387C23×C4—521no—
388C23×C4—521no—
389C23×C4C22×D1311yescharacteristic
390C2×M16—134no—
391C2×M16—134no—
392C2×M16—521no—
393C2×M16—521no—
394C2×M16—521no—
395C2×M16—521no—
396C22×C8—131no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8—134no—
401C22×C8—134no—
402C22×C8—521no—
403C22×C8—521no—
404C22×C8—521no—
405C22×C8—521no—
406C22×C8C22×D1311yescharacteristic
407C22×C8C22×D1311yescharacteristic
408C22×C8C22×D1311yescharacteristic
409C22×C8C22×D1311yescharacteristic
410#117—41no—
411#117—41no—
412#117—521no—
413#117—521no—
414C2×C4⋊C4—132no—
415C2×C4⋊C4C4×D1312yes—
416C2×C22⋊C4—132no—
417C2×C22⋊C4—132no—
418C2×C22⋊C4—132no—
419C2×C22⋊C4—132no—
420C2×C22⋊C4—132no—
421C2×C22⋊C4C4×D1312yes—
422C2×C42—131no—
423C2×C42—131no—
424C2×C42C22×D1311yescharacteristic
425C2×C42C22×D1311yescharacteristic
426C22⋊C8—134no—
427C22⋊C8—134no—
428C22⋊C8—134no—
429C22⋊C8—134no—
430C22⋊C8—134no—
431C22⋊C8—134no—
432C22⋊C8C4×D1314yes—
433C22⋊C8C4×D1314yes—
434#97—41no—
435#97—521no—
436#97—521no—
437#97—521no—
438C4×C8—41no—
439C4×C8—521no—
440C4×C8—521no—
441C4×C8—521no—
442#95—132no—
443#95—132no—
444#95—132no—
445#95—132no—
446C2×C13—42no—
447C2×C13#227311yescharacteristic
448C2×C13C2×#40511yescharacteristic
449C2×C13#287311yescharacteristic
450C2×C13#297612yes—
451C2×C13#297612yes—
452D13—24no—
453D13—42no—
454C24—131no—
455C24—131no—
456C24—134no—
457C24—264no—
458C24—521no—
459C24—521no—
460C24—522no—
461C24C2×C4×D1311yescharacteristic
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—131no—
467C22×C4—131no—
468C22×C4—134no—
469C22×C4—132no—
470C22×C4—132no—
471C22×C4—132no—
472C22×C4—132no—
473C22×C4—134no—
474C22×C4—134no—
475C22×C4—132no—
476C22×C4—132no—
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—524no—
486C22×C4—524no—
487C22×C4—524no—
488C22×C4—524no—
489C22×C4—521no—
490C22×C4—521no—
491C22×C4—521no—
492C22×C4—521no—
493C22×C4—521no—
494C22×C4—521no—
495C22×C4C2×C4×D1312yes—
496C22×C4C2×C4×D1312yes—
497C22×C4C2×C4×D1311yescharacteristic
498C22×C4C2×C4×D1312yes—
499C22×C4C2×C4×D1312yes—
500C22×C4C23×D1311yescharacteristic
501M16—524no—
502M16—524no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—132no—
512C2×C8—132no—
513C2×C8—132no—
514C2×C8—132no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—524no—
524C2×C8—524no—
525C2×C8C2×C4×D1312yes—
526C2×C8C2×C4×D1312yes—
527C2×C8C2×C4×D1312yes—
528C2×C8C2×C4×D1312yes—
529C4⋊C4—42no—
530C4⋊C4—522no—
531C22⋊C4—42no—
532C22⋊C4—264no—
533C22⋊C4—264no—
534C22⋊C4—522no—
535C22⋊C4—522no—
536C22⋊C4—522no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—261no—
542C42—261no—
543C42—261no—
544C42—261no—
545C13#2052711yescharacteristic, complemented, Sylow
546C23—21no—
547C23—22no—
548C23—22no—
549C23—21no—
550C23—132no—
551C23—134no—
552C23—132no—
553C23—268no—
554C23—261no—
555C23—262no—
556C23—261no—
557C23—261no—
558C23—262no—
559C23—262no—
560C23—261no—
561C23—524no—
562C23—524no—
563C23—528no—
564C23—528no—
565C23C42×D1312yes—
566C23C22×C4×D1311yescharacteristic
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—132no—
580C2×C4—132no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—261no—
584C2×C4—261no—
585C2×C4—262no—
586C2×C4—262no—
587C2×C4—262no—
588C2×C4—262no—
589C2×C4—262no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—262no—
596C2×C4—262no—
597C2×C4—262no—
598C2×C4—262no—
599C2×C4—524no—
600C2×C4—524no—
601C2×C4—524no—
602C2×C4C42×D1312yes—
603C2×C4C22×C4×D1311yescharacteristic
604C2×C4C22×C4×D1311yescharacteristic
605C2×C4#8825111yescharacteristic
606C2×C4#8825111yescharacteristic
607C2×C4#8825611yescharacteristic
608C2×C4#8825611yescharacteristic
609C8—22no—
610C8—22no—
611C8—22no—
612C8—22no—
613C8—262no—
614C8—262no—
615C8—262no—
616C8—262no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—42no—
621C22—42no—
622C22—134no—
623C22—262no—
624C22—264no—
625C22—264no—
626C22—262no—
627C22—262no—
628C22—262no—
629C22—262no—
630C22—5216no—
631C22—522no—
632C22—522no—
633C22C2×C42×D1311yescharacteristic
634C22#1171919111yescharacteristic
635C22#1171922611yescharacteristic
636C22D13×#13112yes—
637C22#1171945512yes—
638C4—22no—
639C4—42no—
640C4—42no—
641C4—262no—
642C4—262no—
643C4—522no—
644C4—522no—
645C4#1171925011yescharacteristic
646C4#1171925011yescharacteristic
647C4#1171925011yescharacteristic
648C4#1171925011yescharacteristic
649C2—42no—
650C2—264no—
651C2—522no—
652C2#1311718811yescharacteristic
653C2D13×#40511yescharacteristic
654C2#1312325211yescharacteristic
655C2#1312387912yes—
656C2#1312388212yes—
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C22×C42
FittingC13×#1750C2
socleC23×C13C23×C4
prime radicalC24×D13C2×C4
cosocleC22×C4×C13C24
hypercenter#1750D13
hypocenterC13#20527
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
4. #13114621C2semidirect
5. #13114619C2semidirect
6. #13114618C2semidirect
7. #13114616C2semidirect
8. #13114613C2semidirect
9. #13114611C2semidirect
10. C8×#6103C2semidirect
11. #13114606C2semidirect
12. #13114604C2semidirect
13. #13114604C2semidirect
14. #13114602C2semidirect
15. C13×#1750C2semidirect
25. C2×C13×#97C22semidirect
26. C2×C4×C8×C13C22semidirect
33. C2×#88055C22semidirect
34. C2×#88055C22semidirect
35. C2×C8×Dic13C22semidirect
36. C2×C8×Dic13C22semidirect
45. C2×#88043C22semidirect
46. C2×C4×#1055C22semidirect
47. #11718387C4semidirect
48. D13×C22⋊C8C4semidirect
49. C13×#336C22semidirect
50. C13×#336C22semidirect
51. #11718142C22semidirect
52. #11718142C22semidirect
53. #11718142C22semidirect
54. #11718142C22semidirect
55. #11718116C22semidirect
56. #11718116C22semidirect
232. #1750D13semidirect
324. C2×#97C2×D13semidirect
328. C2×C4×C8C2×D13semidirect
343. #336C2×D13semidirect
344. #336C2×D13semidirect
545. C13#20527semidirect

Maximal subgroups

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

subgroupindex
C2×#117183872
C2×D13×C22⋊C82
#131172152
#131146212
#131146192
#131146182
#131146162
#131146132
#131146112
C8×#61032
#131146062
#131146042
#131146022
C13×#17502
#2052713