Finite Group Databasebeta

← #15870861

Subgroups — #15870861

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×#11718367C211yesmaximal, characteristic
2#13118119C211yesmaximal, characteristic
3#13115773C211yesmaximal, characteristic, complemented
4#13115629C211yesmaximal, characteristic
5#13115448C211yesmaximal, characteristic, complemented
6#13115448C211yesmaximal, characteristic, complemented
7#13115441C211yesmaximal, characteristic, complemented
8#13115441C211yesmaximal, characteristic, complemented
9#13114955C211yesmaximal, characteristic, complemented
10#13114621C211yesmaximal, characteristic, complemented
11#13114619C211yesmaximal, characteristic, complemented
12#13114613C211yesmaximal, characteristic, complemented
13C8×#6103C211yesmaximal, characteristic, complemented
14#13114524C211yesmaximal, characteristic, complemented
15C2×C13×#446C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C22×#6094C2211yescharacteristic
18C22×C8×D13C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C13×#446—24no—
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×#97C2211yescharacteristic
25C2×C13×#97C2211yescharacteristic
26C2×C4×C8×C13C2211yescharacteristic
27#11718892C411yescharacteristic
28#11718892C411yescharacteristic
29C2×#88060C2211yescharacteristic
30C2×#88060C2211yescharacteristic
31C2×#88060C2211yescharacteristic
32C2×#88060C2211yescharacteristic
33C2×#88060C2211yescharacteristic
34C2×#88060C2211yescharacteristic
35C2×#88055C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×C8×Dic13C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39#11718654C411yescharacteristic
40#11718654C411yescharacteristic
41#11718652C411yescharacteristic
42#11718652C411yescharacteristic
43#11718647C411yescharacteristic
44#11718647C411yescharacteristic
45C4×#6103C2211yescharacteristic
46C4×#6103C2211yescharacteristic
47C4×#6103C2211yescharacteristic
48C4×#6103C2211yescharacteristic
49#11718593C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51C2×C4×#1055C2211yescharacteristic
52#11718367—24no—
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13C2×C411yescharacteristic
62C22×D52C2×C411yescharacteristic
63C22×C4×D13C2311yescharacteristic
64C22×C4×D13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C4×Q8×C13—22no—
70C4×Q8×C13—22no—
71C2×C13×C4⋊C4C2×C411yescharacteristic
72C2×C13×C4⋊C4C2×C411yescharacteristic
73C2×C13×C4⋊C4C2×C411yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×C42×C13C2311yescharacteristic
77C2×#6103C2×C411yescharacteristic
78C2×#6103C2×C411yescharacteristic
79C2×#6103C2×C411yescharacteristic
80C2×#6103C2×C411yescharacteristic
81C2×#6103C2×C411yescharacteristic
82C2×#6103C2×C411yescharacteristic
83C2×#6103C2×C411yescharacteristic
84C2×#6103C2×C411yescharacteristic
85C2×#6103C2×C411yescharacteristic
86C2×#6103C2×C411yescharacteristic
87C2×C4⋊Dic13C2×C411yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C2×#6094—22no—
95C2×#6094—22no—
96C2×#6094—22no—
97C2×C8×D13—22no—
98C2×C8×D13—22no—
99C2×C8×D13—22no—
100C4×D52—22no—
101C4×D52—22no—
102C13×C4⋊C8—22no—
103C13×C4⋊C8—22no—
104C13×C4⋊C8—22no—
105C13×#97—22no—
106C13×#97D414yes—
107C4×C8×C13—22no—
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
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#88060—22no—
121#88060—22no—
122#88060—22no—
123#88060—22no—
124#88060—22no—
125#88060—22no—
126#88055—22no—
127#88055—22no—
128C8×Dic13—22no—
129C8×Dic13—22no—
130C4⋊#1055—22no—
131C4×#1055—22no—
132#21637—131nomaximal, Sylow
133C23×D13C22×C411yescharacteristic
134C23×D13C22×C411yescharacteristic
135C2×Q8×C13—22no—
136C2×Q8×C13—22no—
137C2×Q8×C13—41no—
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×C13C2411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C22×C411yescharacteristic
151C2×D52—22no—
152C2×D52—22no—
153C2×D52—41no—
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—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C8×C13—21no—
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×C13C2×D412yes—
175C2×C8×C13C2×D412yes—
176C2×C8×C13#4112yes—
177C2×C8×C13#4112yes—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—22no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13C2×D412yes—
186C42×C13#4112yes—
187#6103—22no—
188#6103—22no—
189#6103—22no—
190#6103—22no—
191#6103—22no—
192#6103—22no—
193#6103—41no—
194#6103—41no—
195#6103—41no—
196#6103—41no—
197C4⋊Dic13—22no—
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×#1055—21no—
211C2×#1055—21no—
212C2×#1055#4112yes—
213C2×#1055#4112yes—
214#6094—44no—
215C8×D13—44no—
216C2×#446D1311yescharacteristic, complemented
217C2×#435—131no—
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×C13C23×C411yescharacteristic
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—21no—
235C22×D13—21no—
236C22×D13—21no—
237C22×D13—21no—
238C22×D13—21no—
239C22×D13—21no—
240C22×D13—21no—
241C22×D13—21no—
242C22×D13—21no—
243C22×D13—21no—
244C22×D13—21no—
245C22×D13#13112yes—
246Q8×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—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13C4×D412yes—
263C2×C4×C13C4×D412yes—
264C2×C4×C13#13112yes—
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×Dic13—21no—
272C2×Dic13—21no—
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—
289D52—44no—
290C4×D13—41no—
291C4×D13—41no—
292C4×D13—41no—
293C4×D13—41no—
294C4×D13—41no—
295C4×D13—41no—
296C4×D13—41no—
297C4×D13—41no—
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×M16—131no—
307C23×C8—131no—
308C2×C4×Q8C2×D1311yescharacteristic
309C2×C4×D4—131no—
310#446—24no—
311#435—264no—
312C2×C4⋊C8—131no—
313C2×C4⋊C8C2×D1311yescharacteristic
314C2×C4⋊C8C2×D1311yescharacteristic
315C2×C4⋊C8C2×D1311yescharacteristic
316C2×C22⋊C8—131no—
317C2×C22⋊C8—131no—
318C2×C22⋊C8—131no—
319C2×C22⋊C8—131no—
320C2×C22⋊C8—131no—
321C2×C22⋊C8—131no—
322C2×#97—131no—
323C2×#97—131no—
324C2×#97C2×D1311yescharacteristic
325C2×#97C2×D1311yescharacteristic
326C2×C4×C8—131no—
327C2×C4×C8—131no—
328C2×C4×C8—131no—
329C2×C4×C8C2×D1311yescharacteristic
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×C13C2×C4×D411yescharacteristic
352C22×C13C4×#4111yescharacteristic
353C22×C13C4×#4111yescharacteristic
354C22×C13C2×#13111yescharacteristic
355C22×C13C2×#13111yescharacteristic
356C22×C13#56811yescharacteristic
357C22×C13#56811yescharacteristic
358C2×D13—22no—
359C2×D13—22no—
360C2×D13—22no—
361C2×D13—41no—
362C2×D13—41no—
363C2×D13—41no—
364C2×D13—41no—
365C2×D13—41no—
366C2×D13—41no—
367C2×D13—41no—
368C2×D13—41no—
369C2×D13—41no—
370C2×D13—41no—
371C2×D13—41no—
372C4×C13—22no—
373C4×C13—22no—
374C4×C13—22no—
375C4×C13—41no—
376C4×C13—41no—
377C4×C13—41no—
378C4×C13C2×#12411yescharacteristic
379C4×C13#52911yescharacteristic
380C4×C13#52911yescharacteristic
381C4×C13#53211yescharacteristic
382Dic13—41no—
383Dic13—41no—
384Dic13—41no—
385Dic13—41no—
386Dic13—41no—
387Dic13—41no—
388C22×Q8C4×D1311yescharacteristic
389C22×D4—131no—
390C23×C4—131no—
391C23×C4—131no—
392C2×M16—262no—
393C2×M16—262no—
394C2×M16—262no—
395C22×C8—131no—
396C22×C8—131no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—262no—
400C22×C8—262no—
401C22×C8—262no—
402C22×C8C22×D1311yescharacteristic
403C22×C8C22×D1311yescharacteristic
404C22×C8C22×D1311yescharacteristic
405C22×C8C22×D1311yescharacteristic
406C4×Q8—22no—
407C4×Q8—22no—
408C4×D4—262no—
409C4×D4—262no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4C4×D1311yescharacteristic
412C2×C4⋊C4C4×D1311yescharacteristic
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⋊C4—131no—
423C2×C22⋊C4—131no—
424C2×C42—131no—
425C2×C42—131no—
426C2×C42C22×D1311yescharacteristic
427C2×C42C22×D1311yescharacteristic
428C2×C42C22×D1311yescharacteristic
429C4⋊C8—22no—
430C4⋊C8—22no—
431C4⋊C8—22no—
432C4⋊C8—262no—
433C22⋊C8—262no—
434C22⋊C8—262no—
435C22⋊C8—262no—
436C22⋊C8—262no—
437C22⋊C8—262no—
438C22⋊C8—262no—
439#97—22no—
440#97—262no—
441#97—262no—
442#97C22⋊D1314yes—
443C4×C8—22no—
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×C13C4×#12411yescharacteristic
460C2×C13#293311yescharacteristic
461C2×C13#293311yescharacteristic
462C2×C13#296611yescharacteristic
463C2×C13#296711yescharacteristic
464C2×C13#296811yescharacteristic
465C2×C13#296911yescharacteristic
466D13—42no—
467D13—81no—
468C24—131no—
469C24—131no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—41no—
473C2×D4—262no—
474C2×D4—262no—
475C2×D4—521no—
476C22×C4—131no—
477C22×C4—131no—
478C22×C4—131no—
479C22×C4—131no—
480C22×C4—131no—
481C22×C4—131no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4C2×C4×D1311yescharacteristic
495C22×C4C2×C4×D1311yescharacteristic
496C22×C4C2×C4×D1311yescharacteristic
497C22×C4C2×C4×D1311yescharacteristic
498C22×C4C2×C4×D1311yescharacteristic
499C22×C4C2×C4×D1311yescharacteristic
500C22×C4C23×D1311yescharacteristic
501M16—524no—
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—132no—
511C2×C8—132no—
512C2×C8—261no—
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—524no—
523C2×C8#613112yes—
524C2×C8#613112yes—
525C2×C8C2×C22⋊D1312yes—
526C2×C8C2×C22⋊D1312yes—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—262no—
531C22⋊C4—262no—
532C22⋊C4—262no—
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—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—261no—
546C42—261no—
547C42—261no—
548C42—261no—
549C42#612712yes—
550C42C2×C22⋊D1312yes—
551C13#2163711yescharacteristic, complemented, Sylow
552C23—132no—
553C23—261no—
554C23—261no—
555C23—261no—
556C23—261no—
557C23—261no—
558C23—261no—
559C23—261no—
560C23—261no—
561C23—261no—
562C23—261no—
563C23—261no—
564C23—261no—
565C23—261no—
566C23C22×C4×D1311yescharacteristic
567Q8—44no—
568D4—524no—
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—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—261no—
585C2×C4—261no—
586C2×C4—261no—
587C2×C4—261no—
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—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4#8816112yes—
611C2×C4C4×C22⋊D1312yes—
612C2×C4C4×C22⋊D1312yes—
613C2×C4C2×#612711yescharacteristic
614C2×C4C2×#613111yescharacteristic
615C2×C4C2×#613111yescharacteristic
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#8820114yes—
627C22—262no—
628C22—262no—
629C22—262no—
630C22—521no—
631C22—521no—
632C22—521no—
633C22—521no—
634C22—521no—
635C22—521no—
636C22—521no—
637C22—521no—
638C22—521no—
639C22—521no—
640C22—521no—
641C22C4×#613111yescharacteristic
642C22C4×#613111yescharacteristic
643C22C2×#8816111yescharacteristic
644C22#1171945011yescharacteristic
645C22D13×#13111yescharacteristic
646C22#1171945511yescharacteristic
647C22C2×C4×C22⋊D1311yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—521no—
655C4—521no—
656C4—521no—
657C4—521no—
658C4—521no—
659C4—521no—
660C4#1171928511yescharacteristic
661C4#1171928511yescharacteristic
662C4C2×#8820111yescharacteristic
663C4#1171953711yescharacteristic
664C2—522no—
665C2—1041no—
666C2C4×#8820111yescharacteristic
667C2#1312355811yescharacteristic
668C2#1312356111yescharacteristic
669C2#1312381011yescharacteristic
670C2#1312382011yescharacteristic
671C2#1312382911yescharacteristic
672C2#1312384211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#446C2
prime radicalC22×D52C2×C4
cosocleC22×C4×C13C24
hypercenterC2×#446D13
hypocenterC13#21637
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
3. #13115773C2semidirect
5. #13115448C2semidirect
6. #13115448C2semidirect
7. #13115441C2semidirect
8. #13115441C2semidirect
9. #13114955C2semidirect
10. #13114621C2semidirect
11. #13114619C2semidirect
12. #13114613C2semidirect
13. C8×#6103C2semidirect
14. #13114524C2semidirect
15. C2×C13×#446C2semidirect
216. C2×#446D13semidirect
551. C13#21637semidirect

Maximal subgroups

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

subgroupindex
C2×#117183672
#131181192
#131157732
#131156292
#131154482
#131154412
#131149552
#131146212
#131146192
#131146132
C8×#61032
#131145242
C2×C13×#4462
#2163713