Finite Group Databasebeta

← #15785591

Subgroups — #15785591

Order 3328.

1630 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718308C212yesmaximal
2C2×#11718633C212yesmaximal
3C2×#11718311C211yesmaximal, characteristic
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic
5C2×#11718310C211yesmaximal, characteristic
6#13113101C211yesmaximal, characteristic
7#13113100C211yesmaximal, characteristic
8#13113099C211yesmaximal, characteristic
9#13113065C212yesmaximal
10#13113064C212yesmaximal
11C13×#1444C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4⋊Dic13C2212yes—
16C22×#6101C2211yescharacteristic
17C22×#6101C2211yescharacteristic
18C22×#6101C2212yes—
19C22×#6101C2212yes—
20C22×#6101C2212yes—
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2212yes—
26C2×C13×#95C2211yescharacteristic
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C4⋊C4×Dic13—24no—
36#11718633—28no—
37#11718311—24no—
38#11718310C418yescomplemented
39#11718308—28no—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—24no—
55C2×C13×C4⋊C4—42no—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13—24no—
58C2×C4⋊Dic13—24no—
59C2×C4⋊Dic13—24no—
60C2×C4⋊Dic13—42no—
61C2×#6101—24no—
62C2×#6101—24no—
63C2×#6101—24no—
64C2×#6101—22no—
65C2×#6101—22no—
66C2×#6101—24no—
67C2×#6101—24no—
68C2×#6101—24no—
69C2×#6101—42no—
70C2×#6101—42no—
71C2×#6101C2×C418yes—
72C2×#6101D418yes—
73C2×#6101Q818yes—
74C2×C4×Dic13—24no—
75C2×C4×Dic13—24no—
76C2×C4×Dic13—24no—
77C2×C4×Dic13—42no—
78C2×C4×Dic13—42no—
79C2×C4×Dic13C2×C418yes—
80C2×C4×Dic13C2×C414yes—
81C2×C4×Dic13D414yes—
82C2×C4×Dic13Q814yes—
83C13×#95—24no—
84C13×#95—22no—
85C13×#95C2×C414yes—
86#88071—22no—
87#88071—24no—
88#88071—24no—
89#88071—22no—
90#88071—22no—
91#88071—24no—
92#88071—24no—
93#88071C2×C414yes—
94#13954—131nomaximal, Sylow
95C24×C13C2411yescharacteristic
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—21no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13C22×C412yes—
119C22×C4×C13C22×C414yes—
120C22×C4×C13C2×D412yes—
121C22×C4×C13C2×D414yes—
122C22×C4×C13C2×Q812yes—
123C22×C4×C13C2×Q814yes—
124C22×C4×C13#4114yes—
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—21no—
128C22×Dic13—21no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13C22×C414yes—
150C22×Dic13C22×C412yes—
151C22×Dic13C22×C412yes—
152C22×Dic13C2×D412yes—
153C22×Dic13C2×D414yes—
154C22×Dic13C2×D412yes—
155C22×Dic13C2×D414yes—
156C22×Dic13C2×Q812yes—
157C22×Dic13C2×Q814yes—
158C22×Dic13C2×Q812yes—
159C22×Dic13C2×Q814yes—
160C22×Dic13#4114yes—
161C13×C4⋊C4—28no—
162C13×C4⋊C4—48no—
163C4⋊Dic13—28no—
164C4⋊Dic13—48no—
165#6101—48no—
166#6101—48no—
167#6101—44no—
168#6101—44no—
169#6101C4⋊C4132yescomplemented
170C4×Dic13—48no—
171C4×Dic13—48no—
172C4×Dic13C4⋊C4116yescomplemented
173C2×#389—132no—
174C2×#389—132no—
175C2×#382—131no—
176C2×C4×C4⋊C4—131no—
177C2×C4×C4⋊C4—131no—
178#1444—131no—
179#1444—131no—
180#1444—131no—
181#1444D1311yescharacteristic
182C4⋊#95—132no—
183C4⋊#95—132no—
184C23×C13C23×C411yescharacteristic
185C23×C13C22×D411yescharacteristic
186C23×C13C22×D412yes—
187C23×C13C22×Q811yescharacteristic
188C23×C13C22×Q812yes—
189C23×C13C2×#4112yes—
190C23×C13C2×#4112yes—
191C23×C13H(5,𝔽2)11yescharacteristic
192C23×C13H(5,𝔽2)11yescharacteristic
193C23×C132−1+411yescharacteristic
194C23×C132−1+411yescharacteristic
195C2×C4×C13—24no—
196C2×C4×C13—24no—
197C2×C4×C13—24no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—24no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—24no—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13C2×C4⋊C414yes—
223C2×C4×C13C2×C4⋊C418yes—
224C2×Dic13—24no—
225C2×Dic13—22no—
226C2×Dic13—24no—
227C2×Dic13—22no—
228C2×Dic13—22no—
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—22no—
232C2×Dic13—24no—
233C2×Dic13—24no—
234C2×Dic13—24no—
235C2×Dic13—24no—
236C2×Dic13—24no—
237C2×Dic13—24no—
238C2×Dic13—24no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—41no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13C2×C4⋊C414yes—
254C2×Dic13C2×C4⋊C418yes—
255C2×Dic13C2×C4⋊C414yes—
256C2×Dic13C2×C4⋊C418yes—
257C2×Dic13#12714yes—
258C2×Dic13C4⋊Q814yes—
259C2×Dic13C4⋊Q818yes—
260C22×C4⋊C4—132no—
261C22×C4⋊C4—131no—
262C22×C4⋊C4—131no—
263C22×C4⋊C4—131no—
264C22×C4⋊C4—132no—
265C22×C4⋊C4—132no—
266C22×C4⋊C4—132no—
267C22×C4⋊C4C2×D1311yescharacteristic
268C22×C4⋊C4C2×D1312yes—
269C22×C42—131no—
270C22×C42—132no—
271C22×C42—132no—
272#389—268no—
273#389—268no—
274#382—264no—
275C4×C4⋊C4—138no—
276C4×C4⋊C4—264no—
277C2×#95—131no—
278C2×#95—132no—
279C2×#95—131no—
280C2×#95—131no—
281C2×#95—132no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—131no—
285C2×#95C2×D1312yes—
286C2×#95C2×D1311yescharacteristic
287C2×#95C2×D1311yescharacteristic
288C22×C13C22×C4⋊C411yescharacteristic
289C22×C13C22×C4⋊C412yes—
290C22×C13C4×#4112yes—
291C22×C13#51811yescharacteristic
292C22×C13#51911yescharacteristic
293C22×C13#52511yescharacteristic
294C22×C13#52511yescharacteristic
295C22×C13C2×#12711yescharacteristic
296C22×C13C2×C4⋊Q811yescharacteristic
297C22×C13C2×C4⋊Q812yes—
298C22×C13#53312yes—
299C22×C13#53711yescharacteristic
300C22×C13#53711yescharacteristic
301C22×C13#54411yescharacteristic
302C22×C13#54411yescharacteristic
303C22×C13#54612yes—
304C22×C13#54612yes—
305C22×C13#54812yes—
306C22×C13#54812yes—
307C22×C13#55412yes—
308C22×C13#55412yes—
309C22×C13#55712yes—
310C22×C13#55712yes—
311C4×C13—28no—
312C4×C13—24no—
313C4×C13—44no—
314C4×C13—81no—
315C4×C13—81no—
316Dic13—24no—
317Dic13—28no—
318Dic13—44no—
319Dic13—81no—
320Dic13—81no—
321Dic13#38418yes—
322C23×C4—131no—
323C23×C4—132no—
324C23×C4—131no—
325C23×C4—132no—
326C23×C4—131no—
327C23×C4—131no—
328C23×C4C22×D1311yescharacteristic
329C23×C4C22×D1311yescharacteristic
330C23×C4C22×D1312yes—
331C23×C4C22×D1312yes—
332C23×C4C22×D1311yescharacteristic
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—138no—
339C2×C4⋊C4—138no—
340C2×C4⋊C4—138no—
341C2×C4⋊C4—264no—
342C2×C4⋊C4—262no—
343C2×C4⋊C4—264no—
344C2×C4⋊C4—262no—
345C2×C4⋊C4—262no—
346C2×C4⋊C4—264no—
347C2×C4⋊C4—264no—
348C2×C4⋊C4—264no—
349C2×C4⋊C4—264no—
350C2×C4⋊C4—264no—
351C2×C4⋊C4—264no—
352C2×C4⋊C4—264no—
353C2×C4⋊C4—522no—
354C2×C4⋊C4—522no—
355C2×C4⋊C4—522no—
356C2×C42—134no—
357C2×C42—134no—
358C2×C42—134no—
359C2×C42—138no—
360C2×C42—264no—
361C2×C42—264no—
362C2×C42—264no—
363C2×C42—522no—
364C2×C42—522no—
365#95—22no—
366#95—24no—
367#95—134no—
368#95—264no—
369#95—262no—
370#95—262no—
371#95—264no—
372#95—264no—
373#95—262no—
374#95—264no—
375#95C4×D1314yes—
376C2×C13C2×#38411yescharacteristic
377C2×C13#229611yescharacteristic
378C2×C13#231611yescharacteristic
379C2×C13#234912yes—
380C2×C13#235112yes—
381C2×C13#254011yescharacteristic
382C2×C13#254011yescharacteristic
383C2×C13#255012yes—
384C2×C13#255012yes—
385C2×C13#258411yescharacteristic
386C2×C13#258411yescharacteristic
387C24C23×D1311yescharacteristic
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—132no—
411C22×C4—132no—
412C22×C4—134no—
413C22×C4—132no—
414C22×C4—134no—
415C22×C4—134no—
416C22×C4—132no—
417C22×C4—132no—
418C22×C4—134no—
419C22×C4—132no—
420C22×C4—134no—
421C22×C4—134no—
422C22×C4—262no—
423C22×C4—261no—
424C22×C4—262no—
425C22×C4—261no—
426C22×C4—262no—
427C22×C4—261no—
428C22×C4—262no—
429C22×C4—261no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—262no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4C2×C4×D1312yes—
447C22×C4C2×C4×D1314yes—
448C22×C4D4×D1312yes—
449C22×C4D4×D1314yes—
450C22×C4#612914yes—
451C22×C4Q8×D1312yes—
452C22×C4Q8×D1314yes—
453C4⋊C4—28no—
454C4⋊C4—48no—
455C4⋊C4—1332no—
456C4⋊C4—268no—
457C4⋊C4—528no—
458C4⋊C4—528no—
459C4⋊C4—524no—
460C4⋊C4—524no—
461C4⋊C4—528no—
462C42—1316no—
463C42—528no—
464C42—528no—
465C13#1395411yescharacteristic, complemented, Sylow
466C23C22×C4×D1311yescharacteristic
467C23C2×D4×D1311yescharacteristic
468C23C2×D4×D1312yes—
469C23C2×#612912yes—
470C23#8825111yescharacteristic
471C23C2×Q8×D1312yes—
472C23C2×Q8×D1311yescharacteristic
473C23#8825411yescharacteristic
474C23#41×D1312yes—
475C23#8825611yescharacteristic
476C23#8825711yescharacteristic
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—138no—
505C2×C4—134no—
506C2×C4—134no—
507C2×C4—138no—
508C2×C4—134no—
509C2×C4—134no—
510C2×C4—138no—
511C2×C4—262no—
512C2×C4—264no—
513C2×C4—262no—
514C2×C4—264no—
515C2×C4—262no—
516C2×C4—264no—
517C2×C4—262no—
518C2×C4—262no—
519C2×C4—264no—
520C2×C4—264no—
521C2×C4—264no—
522C2×C4—262no—
523C2×C4—264no—
524C2×C4—264no—
525C2×C4—264no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—522no—
530C2×C4—521no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4C4⋊C4×D1314yes—
541C2×C4C4⋊C4×D1318yes—
542C22C2×C4⋊C4×D1311yescharacteristic
543C22C2×C4⋊C4×D1312yes—
544C22C4×#612912yes—
545C22#1171925011yescharacteristic
546C22#1171927711yescharacteristic
547C22#1171929111yescharacteristic
548C22#1171929612yes—
549C22#1171930312yes—
550C22#1171931311yescharacteristic
551C22#1171932712yes—
552C22#1171933411yescharacteristic
553C22#1171933812yes—
554C22#1171934012yes—
555C22#1171934112yes—
556C22#1171935912yes—
557C22#1171936111yescharacteristic
558C22#1171939012yes—
559C22#1171939411yescharacteristic
560C22D13×#12711yescharacteristic
561C22#1171942612yes—
562C22D13×C4⋊Q812yes—
563C22D13×C4⋊Q811yescharacteristic
564C22#1171943411yescharacteristic
565C4—28no—
566C4—24no—
567C4—44no—
568C4—81no—
569C4—81no—
570C4—138no—
571C4—264no—
572C4—268no—
573C4—524no—
574C4—1041no—
575C4—1041no—
576C2D13×#38411yescharacteristic
577C2#1311731511yescharacteristic
578C2#1311745111yescharacteristic
579C2#1311774212yes—
580C2#1311775512yes—
581C2#1311976911yescharacteristic
582C2#1311977111yescharacteristic
583C2#1311985012yes—
584C2#1311985212yes—
585C2#1312021811yescharacteristic
586C2#1312022011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1444C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1444D13
hypocenterC13#13954
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
38. #11718310C4semidirect
169. #6101C4⋊C4semidirect
172. C4×Dic13C4⋊C4semidirect
465. C13#13954semidirect

Maximal subgroups

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

subgroupindex
C2×#117183082
C2×#117186332
C2×#117183112
C2×C4⋊C4×Dic132
C2×#117183102
#131131012
#131131002
#131130992
#131130652
#131130642
C13×#14442
#1395413