Finite Group Databasebeta

← #15870853

Subgroups — #15870853

Order 3328.

848 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×#11718362C211yesmaximal, characteristic, complemented
2#13118120C211yesmaximal, characteristic
3#13115771C211yesmaximal, characteristic, complemented
4#13115631C211yesmaximal, characteristic
5#13115452C211yesmaximal, characteristic, complemented
6#13115452C211yesmaximal, characteristic, complemented
7#13115445C211yesmaximal, characteristic, complemented
8#13115445C211yesmaximal, characteristic, complemented
9#13114955C211yesmaximal, characteristic, complemented
10#13114617C211yesmaximal, characteristic, complemented
11#13114617C211yesmaximal, characteristic, complemented
12#13114612C211yesmaximal, characteristic, complemented
13C8×C22⋊Dic13C211yesmaximal, characteristic, complemented
14#13114524C211yesmaximal, characteristic, complemented
15C2×C13×#435C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C13×#435—24no—
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C2×C13×#97C2211yescharacteristic
25#11718883C411yescharacteristic
26#11718883C411yescharacteristic
27C4×C22⋊Dic13C2211yescharacteristic
28C4×C22⋊Dic13C2211yescharacteristic
29C4×C22⋊Dic13C2211yescharacteristic
30C4×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×#88055C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×#88055C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39C2×#88054C2211yescharacteristic
40C2×C8×Dic13C2211yescharacteristic
41C2×C8×Dic13C2211yescharacteristic
42C2×C8×Dic13C2211yescharacteristic
43#11718643C411yescharacteristic
44#11718643C411yescharacteristic
45#11718614C411yescharacteristic
46#11718614C411yescharacteristic
47#11718608C411yescharacteristic
48#11718608C411yescharacteristic
49#11718593C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51C2×C4×#1055C2211yescharacteristic
52#11718362—24no—
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
64C22×Dic26C2×C411yescharacteristic
65C2×C13×M16—22no—
66C2×C13×M16—22no—
67C2×C13×M16—22no—
68C22×C8×C13—22no—
69C22×C8×C13—22no—
70C22×C8×C13—22no—
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C4×D4×C13—22no—
76C4×D4×C13—22no—
77C2×C13×C4⋊C4C2×C411yescharacteristic
78C2×C13×C22⋊C4C2×C411yescharacteristic
79C2×C13×C22⋊C4C2×C411yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C22⋊Dic13C2×C411yescharacteristic
82C2×C22⋊Dic13C2×C411yescharacteristic
83C2×C22⋊Dic13C2×C411yescharacteristic
84C2×C22⋊Dic13C2×C411yescharacteristic
85C2×C22⋊Dic13C2×C411yescharacteristic
86C2×C22⋊Dic13C2×C411yescharacteristic
87C2×C22⋊Dic13C2×C411yescharacteristic
88C2×C22⋊Dic13C2×C411yescharacteristic
89C2×C4⋊Dic13C2×C411yescharacteristic
90C2×#6101C2×C411yescharacteristic
91C2×#6101C2×C411yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C4×Dic26—22no—
101C4×Dic26—22no—
102C13×C4⋊C8—22no—
103C13×C22⋊C8—22no—
104C13×C22⋊C8—22no—
105C13×#97D414yes—
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88071C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118C22⋊#1055—22no—
119C22⋊#1055—22no—
120C22⋊#1055—22no—
121C22⋊#1055—22no—
122#88055—22no—
123#88055—22no—
124#88055—22no—
125#88054—22no—
126#88054—22no—
127C8×Dic13—22no—
128C8×Dic13—22no—
129C8×Dic13—22no—
130C4⋊#1055—22no—
131C4×#1055—22no—
132#21637—131nomaximal, Sylow
133C24×C13C22×C411yescharacteristic
134C24×C13C22×C411yescharacteristic
135C2×D4×C13—22no—
136C2×D4×C13—22no—
137C2×D4×C13—41no—
138C22×C4×C13—21no—
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×C13—21no—
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C2411yescharacteristic
155C22×Dic13C22×C411yescharacteristic
156C22×Dic13C22×C411yescharacteristic
157C22×Dic13C22×C411yescharacteristic
158C22×Dic13C22×C411yescharacteristic
159C22×Dic13C22×C411yescharacteristic
160C22×Dic13C22×C411yescharacteristic
161C22×Dic13C22×C411yescharacteristic
162C22×Dic13C22×C411yescharacteristic
163C2×Dic26—22no—
164C2×Dic26—22no—
165C2×Dic26—41no—
166C13×M16—44no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—44no—
176C2×C8×C13C2×D412yes—
177C2×C8×C13C2×D412yes—
178C2×C8×C13#4112yes—
179C2×C8×C13#4112yes—
180C13×C4⋊C4—22no—
181C13×C22⋊C4—22no—
182C13×C22⋊C4—22no—
183C42×C13C2×D412yes—
184C42×C13#4112yes—
185C22⋊Dic13—22no—
186C22⋊Dic13—22no—
187C22⋊Dic13—22no—
188C22⋊Dic13—22no—
189C22⋊Dic13—41no—
190C22⋊Dic13—41no—
191C22⋊Dic13—41no—
192C22⋊Dic13—41no—
193C4⋊Dic13—22no—
194#6101—22no—
195#6101—22no—
196C4×Dic13—21no—
197C4×Dic13—21no—
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#4112yes—
215C2×#1055#4112yes—
216C2×#446—131no—
217C2×#435D1311yescharacteristic
218#2398—131no—
219#1984—131no—
220#1954—131no—
221#1924—131no—
222#1924—131no—
223#1923—131no—
224#1923—131no—
225#1832—131no—
226#1753—131no—
227#1753—131no—
228#1752—131no—
229C8×C22⋊C4—131no—
230#1726—131no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13#13112yes—
245C23×C13C23×C411yescharacteristic
246D4×C13—44no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13C4×D412yes—
266C2×C4×C13C4×D412yes—
267C2×C4×C13C22×D411yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
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—21no—
294C2×Dic13—21no—
295C2×Dic13—21no—
296C2×Dic13#13112yes—
297Dic26—44no—
298C8×C13—22no—
299C8×C13—41no—
300C8×C13—41no—
301C8×C13#12414yes—
302#1055—22no—
303#1055—22no—
304#1055—41no—
305#1055—41no—
306C22×M16C2×D1311yescharacteristic
307C23×C8C2×D1311yescharacteristic
308C2×C4×Q8—131no—
309C2×C4×D4C2×D1311yescharacteristic
310#446—264no—
311#435—24no—
312C2×C4⋊C8—131no—
313C2×C4⋊C8—131no—
314C2×C4⋊C8—131no—
315C2×C4⋊C8C2×D1311yescharacteristic
316C2×C22⋊C8—131no—
317C2×C22⋊C8—131no—
318C2×C22⋊C8—131no—
319C2×C22⋊C8—131no—
320C2×C22⋊C8C2×D1311yescharacteristic
321C2×C22⋊C8C2×D1311yescharacteristic
322C2×#97—131no—
323C2×#97—131no—
324C2×#97—131no—
325C2×#97C2×D1311yescharacteristic
326C2×C4×C8—131no—
327C2×C4×C8—131no—
328C2×C4×C8—131no—
329C2×C4×C8—131no—
330#400—131no—
331#400—131no—
332#397—131no—
333#397—131no—
334#394—131no—
335#394—131no—
336#393—131no—
337#393—131no—
338C4×C22⋊C4—131no—
339C4×C22⋊C4—131no—
340C4×C22⋊C4—131no—
341C4×C22⋊C4—131no—
342#376—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×C13—41no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13C2×C4×D411yescharacteristic
366C22×C13C4×#4111yescharacteristic
367C22×C13C4×#4111yescharacteristic
368C22×C13C2×#13111yescharacteristic
369C22×C13C2×#13111yescharacteristic
370C22×C13#56811yescharacteristic
371C22×C13#56811yescharacteristic
372C4×C13—22no—
373C4×C13—22no—
374C4×C13—41no—
375C4×C13—41no—
376C4×C13C2×#12411yescharacteristic
377C4×C13#52911yescharacteristic
378C4×C13#52911yescharacteristic
379C4×C13#53211yescharacteristic
380Dic13—22no—
381Dic13—41no—
382Dic13—41no—
383Dic13—41no—
384Dic13—41no—
385Dic13—41no—
386Dic13—41no—
387Dic13—41no—
388C22×Q8—131no—
389C22×D4C4×D1311yescharacteristic
390C23×C4C22×D1311yescharacteristic
391C23×C4C22×D1311yescharacteristic
392C2×M16—22no—
393C2×M16—22no—
394C2×M16—22no—
395C22×C8—22no—
396C22×C8—22no—
397C22×C8—22no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8—131no—
401C22×C8—131no—
402C22×C8C22×D1311yescharacteristic
403C22×C8C22×D1311yescharacteristic
404C22×C8C22×D1311yescharacteristic
405C22×C8C22×D1311yescharacteristic
406C4×Q8—262no—
407C4×Q8—262no—
408C4×D4—22no—
409C4×D4—22no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4C4×D1311yescharacteristic
414C2×C22⋊C4—131no—
415C2×C22⋊C4—131no—
416C2×C22⋊C4—131no—
417C2×C22⋊C4—131no—
418C2×C22⋊C4—131no—
419C2×C22⋊C4—131no—
420C2×C22⋊C4—131no—
421C2×C22⋊C4—131no—
422C2×C22⋊C4C4×D1311yescharacteristic
423C2×C22⋊C4C4×D1311yescharacteristic
424C2×C42—131no—
425C2×C42—131no—
426C2×C42—131no—
427C2×C42—131no—
428C2×C42C22×D1311yescharacteristic
429C4⋊C8—22no—
430C4⋊C8—262no—
431C4⋊C8—262no—
432C4⋊C8—262no—
433C22⋊C8—22no—
434C22⋊C8—22no—
435C22⋊C8—262no—
436C22⋊C8—262no—
437C22⋊C8—262no—
438C22⋊C8—262no—
439#97—262no—
440#97—262no—
441#97—262no—
442#97C22⋊D1314yes—
443C4×C8—262no—
444C4×C8—262no—
445C4×C8—262no—
446C4×C8—262no—
447#95—131no—
448#95—131no—
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×C13—81no—
461C2×C13C4×#12411yescharacteristic
462C2×C13#293311yescharacteristic
463C2×C13#293311yescharacteristic
464C2×C13#296611yescharacteristic
465C2×C13#296711yescharacteristic
466C2×C13#296811yescharacteristic
467C2×C13#296911yescharacteristic
468C24C2×C4×D1311yescharacteristic
469C24C2×C4×D1311yescharacteristic
470C2×Q8—262no—
471C2×Q8—262no—
472C2×Q8—521no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—41no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—131no—
489C22×C4—131no—
490C22×C4—131no—
491C22×C4—131no—
492C22×C4—131no—
493C22×C4—131no—
494C22×C4—131no—
495C22×C4—131no—
496C22×C4C2×C4×D1311yescharacteristic
497C22×C4C2×C4×D1311yescharacteristic
498C22×C4C2×C4×D1311yescharacteristic
499C22×C4C2×C4×D1311yescharacteristic
500C22×C4C23×D1311yescharacteristic
501M16—44no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—44no—
511C2×C8—132no—
512C2×C8—132no—
513C2×C8—261no—
514C2×C8—261no—
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#612912yes—
524C2×C8#612912yes—
525C2×C8C2×C22⋊D1312yes—
526C2×C8C2×C22⋊D1312yes—
527C4⋊C4—22no—
528C4⋊C4—262no—
529C4⋊C4—262no—
530C4⋊C4—262no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—262no—
534C22⋊C4—262no—
535C22⋊C4—262no—
536C22⋊C4—262no—
537C22⋊C4—521no—
538C22⋊C4—521no—
539C22⋊C4—521no—
540C22⋊C4—521no—
541C42—261no—
542C42—261no—
543C42—261no—
544C42—261no—
545C42—261no—
546C42—261no—
547C42—261no—
548C42—261no—
549C42#612712yes—
550C42C2×C22⋊D1312yes—
551C13#2163711yescharacteristic, complemented, Sylow
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23#8816112yes—
566C23C22×C4×D1311yescharacteristic
567Q8—524no—
568D4—44no—
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—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
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—261no—
609C2×C4—261no—
610C2×C4—261no—
611C2×C4C4×C22⋊D1312yes—
612C2×C4C4×C22⋊D1312yes—
613C2×C4C2×#612711yescharacteristic
614C2×C4C2×#612911yescharacteristic
615C2×C4C2×#612911yescharacteristic
616C2×C4#41×D1311yescharacteristic
617C2×C4#41×D1311yescharacteristic
618C2×C4C22×C22⋊D1311yescharacteristic
619C8—22no—
620C8—41no—
621C8—41no—
622C8—262no—
623C8—262no—
624C8—521no—
625C8—521no—
626C8#8819014yes—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C4×#612911yescharacteristic
642C22C4×#612911yescharacteristic
643C22C2×#8816111yescharacteristic
644C22#1171945011yescharacteristic
645C22D13×#13111yescharacteristic
646C22#1171945511yescharacteristic
647C22C2×C4×C22⋊D1311yescharacteristic
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—262no—
653C4—521no—
654C4—521no—
655C4—521no—
656C4—521no—
657C4—521no—
658C4—521no—
659C4—521no—
660C4#1171926211yescharacteristic
661C4#1171926211yescharacteristic
662C4C2×#8819011yescharacteristic
663C4#1171953711yescharacteristic
664C2—42no—
665C2—81no—
666C2C4×#8819011yescharacteristic
667C2#1312355811yescharacteristic
668C2#1312356111yescharacteristic
669C2#1312380611yescharacteristic
670C2#1312381511yescharacteristic
671C2#1312383111yescharacteristic
672C2#1312383311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#435C2
prime radicalC22×D4×C13C2×C4
cosocleC22×C4×C13C24
hypercenterC2×#435D13
hypocenterC13#21637
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#11718362C2semidirect
3. #13115771C2semidirect
5. #13115452C2semidirect
6. #13115452C2semidirect
7. #13115445C2semidirect
8. #13115445C2semidirect
9. #13114955C2semidirect
10. #13114617C2semidirect
11. #13114617C2semidirect
12. #13114612C2semidirect
13. C8×C22⋊Dic13C2semidirect
14. #13114524C2semidirect
551. C13#21637semidirect

Maximal subgroups

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

subgroupindex
C2×#117183622
#131181202
#131157712
#131156312
#131154522
#131154452
#131149552
#131146172
#131146122
C8×C22⋊Dic132
#131145242
C2×C13×#4352
#2163713