Finite Group Databasebeta

← #15793669

Subgroups — #15793669

Order 3328.

1130 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718644C211yesmaximal, characteristic
2C2×#11718634C211yesmaximal, characteristic
3C2×#11718642C211yesmaximal, characteristic
4#13113105C211yesmaximal, characteristic
5#13113102C212yesmaximal
6#13113095C211yesmaximal, characteristic
7#13113092C212yesmaximal
8#13113091C212yesmaximal
9#13113087C212yesmaximal
10#13113061C211yesmaximal, characteristic
11C13×#1441C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101C2212yes—
17C22×#6101C2212yes—
18C22×C4×Dic13C2211yescharacteristic
19C2×C13×#95C2211yescharacteristic
20C2×C13×#95C2212yes—
21C2×C13×#95C2212yes—
22C2×#88071C2211yescharacteristic
23C2×#88071C2212yes—
24C2×#88071C2211yescharacteristic
25C2×#88071C2211yescharacteristic
26C2×#88071C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35#11718644C418yescomplemented
36#11718642—24no—
37#11718634—24no—
38C23×C4×C13C2312yes—
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×Dic13C2311yescharacteristic
44C23×Dic13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—42no—
53C2×C13×C4⋊C4C2×C414yes—
54C2×C4⋊Dic13—22no—
55C2×C4⋊Dic13—22no—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13—42no—
58C2×C4⋊Dic13C2×C414yes—
59C2×#6101—24no—
60C2×#6101—42no—
61C2×#6101—42no—
62C2×#6101—42no—
63C2×#6101—42no—
64C2×#6101C2×C418yes—
65C2×C4×Dic13—42no—
66C2×C4×Dic13D414yes—
67C13×#95—22no—
68C13×#95—42no—
69C13×#95—42no—
70#88071—22no—
71#88071—24no—
72#88071—22no—
73#88071—22no—
74#88071—22no—
75#88071—42no—
76#88071—42no—
77#88071—42no—
78#88071—42no—
79#88071—42no—
80#88071—42no—
81#88071C2×C414yes—
82#88071C2×C418yes—
83#14631—131nomaximal, Sylow
84C24×C13C2411yescharacteristic
85C22×C4×C13—22no—
86C22×C4×C13—22no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13C22×C412yes—
112C22×C4×C13C22×C412yes—
113C22×C4×C13C22×C412yes—
114C22×C4×C13C2×D412yes—
115C22×C4×C13#4112yes—
116C22×Dic13—22no—
117C22×Dic13—22no—
118C22×Dic13—22no—
119C22×Dic13—21no—
120C22×Dic13—22no—
121C22×Dic13—22no—
122C22×Dic13—22no—
123C22×Dic13—22no—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—21no—
128C22×Dic13—21no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—21no—
146C22×Dic13C22×C414yes—
147C22×Dic13C22×C414yes—
148C22×Dic13C2×D412yes—
149C22×Dic13C2×D412yes—
150C13×C4⋊C4—28no—
151C13×C4⋊C4—44no—
152C4⋊Dic13—28no—
153C4⋊Dic13—44no—
154#6101—48no—
155#6101—48no—
156C4×Dic13—44no—
157C2×#398—131no—
158C2×#389—131no—
159C2×#387—131no—
160#1445—132no—
161#1445—131no—
162#1442—132no—
163#1442—132no—
164#1442—131no—
165#1441—132no—
166#1441D1311yescharacteristic
167#1434—131no—
168C23×C13C23×C411yescharacteristic
169C23×C13C22×D411yescharacteristic
170C23×C13C2×#4111yescharacteristic
171C23×C13H(5,𝔽2)11yescharacteristic
172C23×C13H(5,𝔽2)11yescharacteristic
173C23×C13H(5,𝔽2)12yes—
174C23×C13H(5,𝔽2)11yescharacteristic
175C23×C132−1+412yes—
176C23×C132−1+412yes—
177C23×C132−1+412yes—
178C23×C132−1+411yescharacteristic
179C2×C4×C13—24no—
180C2×C4×C13—22no—
181C2×C4×C13—22no—
182C2×C4×C13—24no—
183C2×C4×C13—22no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—24no—
187C2×C4×C13—22no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—42no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—42no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13C4×D414yes—
210C2×Dic13—24no—
211C2×Dic13—24no—
212C2×Dic13—24no—
213C2×Dic13—24no—
214C2×Dic13—24no—
215C2×Dic13—24no—
216C2×Dic13—22no—
217C2×Dic13—22no—
218C2×Dic13—22no—
219C2×Dic13—22no—
220C2×Dic13—22no—
221C2×Dic13—22no—
222C2×Dic13—42no—
223C2×Dic13—42no—
224C2×Dic13—42no—
225C2×Dic13—42no—
226C2×Dic13—42no—
227C2×Dic13—42no—
228C2×Dic13—42no—
229C2×Dic13—42no—
230C2×Dic13—42no—
231C2×Dic13—42no—
232C2×Dic13—42no—
233C2×Dic13—42no—
234C2×Dic13—41no—
235C2×Dic13—41no—
236C2×Dic13—41no—
237C2×Dic13—41no—
238C2×Dic13—41no—
239C2×Dic13—41no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C22×C4⋊C4—131no—
245C22×C4⋊C4—132no—
246C22×C4⋊C4—132no—
247C22×C4⋊C4—131no—
248C22×C4⋊C4C2×D1311yescharacteristic
249C22×C4⋊C4C2×D1311yescharacteristic
250C22×C42—131no—
251#398—138no—
252#389—264no—
253#387—264no—
254C2×#95—131no—
255C2×#95—132no—
256C2×#95—131no—
257C2×#95—131no—
258C2×#95—131no—
259C2×#95—132no—
260C2×#95—131no—
261C2×#95—132no—
262C2×#95—132no—
263C2×#95—132no—
264C2×#95—132no—
265C2×#95—132no—
266C2×#95—132no—
267C2×#95C2×D1311yescharacteristic
268C2×#95C2×D1312yes—
269C2×#95C2×D1312yes—
270C22×C13C2×C4×D411yescharacteristic
271C22×C13#51811yescharacteristic
272C22×C13#51912yes—
273C22×C13#52011yescharacteristic
274C22×C13#52012yes—
275C22×C13#53411yescharacteristic
276C22×C13#53511yescharacteristic
277C22×C13#53611yescharacteristic
278C22×C13#53611yescharacteristic
279C22×C13#53611yescharacteristic
280C22×C13#53711yescharacteristic
281C22×C13#53912yes—
282C22×C13#54011yescharacteristic
283C22×C13#54112yes—
284C22×C13#54211yescharacteristic
285C22×C13#56212yes—
286C22×C13#56212yes—
287C22×C13#56212yes—
288C22×C13#56312yes—
289C22×C13#56312yes—
290C22×C13#56312yes—
291C22×C13#56312yes—
292C22×C13#56412yes—
293C4×C13—24no—
294C4×C13—42no—
295C4×C13—42no—
296C4×C13—82no—
297C4×C13—82no—
298Dic13—42no—
299Dic13—44no—
300Dic13—44no—
301Dic13—42no—
302Dic13—81no—
303Dic13—81no—
304C23×C4—132no—
305C23×C4—131no—
306C23×C4—132no—
307C23×C4—131no—
308C23×C4—131no—
309C23×C4—131no—
310C23×C4C22×D1312yes—
311C23×C4C22×D1312yes—
312C23×C4C22×D1311yescharacteristic
313C23×C4C22×D1311yescharacteristic
314C23×C4C22×D1311yescharacteristic
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—134no—
320C2×C4⋊C4—138no—
321C2×C4⋊C4—262no—
322C2×C4⋊C4—262no—
323C2×C4⋊C4—264no—
324C2×C4⋊C4—262no—
325C2×C4⋊C4—522no—
326C2×C4⋊C4—522no—
327C2×C4⋊C4—522no—
328C2×C4⋊C4—522no—
329C2×C4⋊C4—522no—
330C2×C4⋊C4C4×D1314yes—
331C2×C42—134no—
332C2×C42—522no—
333#95—22no—
334#95—42no—
335#95—42no—
336#95—134no—
337#95—138no—
338#95—262no—
339#95—262no—
340#95—262no—
341#95—264no—
342#95—262no—
343#95—522no—
344#95—522no—
345#95—522no—
346#95—522no—
347#95—522no—
348#95—522no—
349C2×C13#232211yescharacteristic
350C2×C13#232411yescharacteristic
351C2×C13#232711yescharacteristic
352C2×C13#237812yes—
353C2×C13#238212yes—
354C2×C13#281411yescharacteristic
355C2×C13#281611yescharacteristic
356C2×C13#282111yescharacteristic
357C2×C13#282211yescharacteristic
358C2×C13#283612yes—
359C2×C13#283912yes—
360C24C23×D1311yescharacteristic
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—134no—
388C22×C4—134no—
389C22×C4—132no—
390C22×C4—132no—
391C22×C4—262no—
392C22×C4—262no—
393C22×C4—262no—
394C22×C4—262no—
395C22×C4—262no—
396C22×C4—262no—
397C22×C4—261no—
398C22×C4—262no—
399C22×C4—262no—
400C22×C4—262no—
401C22×C4—261no—
402C22×C4—261no—
403C22×C4—262no—
404C22×C4—262no—
405C22×C4—262no—
406C22×C4—262no—
407C22×C4—261no—
408C22×C4—262no—
409C22×C4—262no—
410C22×C4—262no—
411C22×C4—261no—
412C22×C4—261no—
413C22×C4—261no—
414C22×C4—262no—
415C22×C4—262no—
416C22×C4—262no—
417C22×C4—261no—
418C22×C4—261no—
419C22×C4—261no—
420C22×C4—262no—
421C22×C4C2×C4×D1312yes—
422C22×C4C2×C4×D1312yes—
423C22×C4C2×C4×D1312yes—
424C22×C4D4×D1312yes—
425C22×C4#612912yes—
426C4⋊C4—28no—
427C4⋊C4—44no—
428C4⋊C4—268no—
429C4⋊C4—528no—
430C4⋊C4—528no—
431C4⋊C4—524no—
432C42—524no—
433C13#1463111yescharacteristic, complemented, Sylow
434C23C22×C4×D1311yescharacteristic
435C23C2×D4×D1311yescharacteristic
436C23C2×#612911yescharacteristic
437C23#8825112yes—
438C23#8825111yescharacteristic
439C23#8825412yes—
440C23#8825411yescharacteristic
441C23#8825611yescharacteristic
442C23#8825611yescharacteristic
443C23#8825712yes—
444C23#8825712yes—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—262no—
476C2×C4—264no—
477C2×C4—264no—
478C2×C4—264no—
479C2×C4—264no—
480C2×C4—264no—
481C2×C4—264no—
482C2×C4—262no—
483C2×C4—262no—
484C2×C4—262no—
485C2×C4—262no—
486C2×C4—262no—
487C2×C4—522no—
488C2×C4—522no—
489C2×C4—522no—
490C2×C4—522no—
491C2×C4—522no—
492C2×C4—522no—
493C2×C4—522no—
494C2×C4—522no—
495C2×C4—522no—
496C2×C4—522no—
497C2×C4—522no—
498C2×C4—522no—
499C2×C4—521no—
500C2×C4—521no—
501C2×C4—522no—
502C2×C4—521no—
503C2×C4—521no—
504C2×C4—521no—
505C2×C4—522no—
506C2×C4—522no—
507C2×C4—521no—
508C2×C4—522no—
509C2×C4#8813514yes—
510C22C2×#8813511yescharacteristic
511C22#1171920911yescharacteristic
512C22#1171922611yescharacteristic
513C22#1171925112yes—
514C22#1171927712yes—
515C22#1171929411yescharacteristic
516C22#1171930712yes—
517C22#1171931211yescharacteristic
518C22#1171932411yescharacteristic
519C22#1171932612yes—
520C22#1171933012yes—
521C22#1171933411yescharacteristic
522C22#1171934811yescharacteristic
523C22#1171935112yes—
524C22#1171935212yes—
525C22#1171935311yescharacteristic
526C22#1171937212yes—
527C22#1171938011yescharacteristic
528C22C13⋊#56412yes—
529C22#1171940412yes—
530C22#1171941712yes—
531C22#1171942911yescharacteristic
532C22#1171944012yes—
533C4—24no—
534C4—42no—
535C4—42no—
536C4—82no—
537C4—82no—
538C4—522no—
539C4—524no—
540C4—522no—
541C4—524no—
542C4—1041no—
543C4—1041no—
544C2#1311751011yescharacteristic
545C2#1311752511yescharacteristic
546C2#1311755411yescharacteristic
547C2#1311800012yes—
548C2#1311801812yes—
549C2#1312284811yescharacteristic
550C2#1312286711yescharacteristic
551C2#1312289611yescharacteristic
552C2#1312290511yescharacteristic
553C2#1312303712yes—
554C2#1312308212yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1441D13
hypocenterC13#14631
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
35. #11718644C4semidirect
433. C13#14631semidirect

Maximal subgroups

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

subgroupindex
C2×#117186442
C2×#117186342
C2×#117186422
#131131052
#131131022
#131130952
#131130922
#131130912
#131130872
#131130612
C13×#14412
#1463113