Finite Group Databasebeta

← #15799675

Subgroups — #15799675

Order 3328.

1410 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718641C211yesmaximal, characteristic
2C2×#11718633C212yesmaximal
3C2×#11718633C211yesmaximal, characteristic
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic
5#13113095C212yesmaximal
6#13113094C212yesmaximal
7#13113090C211yesmaximal, characteristic
8#13113089C211yesmaximal, characteristic
9#13113064C212yesmaximal
10#13113064C211yesmaximal, characteristic
11C2×C13×#398C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101C2211yescharacteristic
17C22×#6101C2211yescharacteristic
18C22×#6101C2212yes—
19C22×#6101C2211yescharacteristic
20C22×#6101C2212yes—
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C13×#398—24no—
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36#11718641—24no—
37C4⋊C4×Dic13—24no—
38#11718633—28no—
39#11718633—24no—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—42no—
59C2×C13×C4⋊C4D414yes—
60C2×C4⋊Dic13—22no—
61C2×C4⋊Dic13—24no—
62C2×#6101—22no—
63C2×#6101—24no—
64C2×#6101—22no—
65C2×#6101—24no—
66C2×#6101—22no—
67C2×#6101—24no—
68C2×#6101—22no—
69C2×#6101—22no—
70C2×#6101—24no—
71C2×#6101—22no—
72C2×#6101—24no—
73C2×#6101—42no—
74C2×#6101D414yes—
75C2×#6101Q818yes—
76C2×C4×Dic13—24no—
77C2×C4×Dic13—24no—
78C2×C4×Dic13—24no—
79C2×C4×Dic13—24no—
80C2×C4×Dic13D414yes—
81C13×#95—22no—
82C13×#95—24no—
83#88071—24no—
84#88071—22no—
85#88071—24no—
86#88071—24no—
87#88071—22no—
88#88071—22no—
89#88071—24no—
90#88071—24no—
91#88071—24no—
92#88071—42no—
93#15149—131nomaximal, Sylow
94C24×C13C2411yescharacteristic
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—21no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13C2×D412yes—
121C22×C4×C13C2×D412yes—
122C22×C4×C13C2×D414yes—
123C22×C4×C13C2×D412yes—
124C22×C4×C13C2×Q814yes—
125C22×C4×C13#4112yes—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—21no—
130C22×Dic13—22no—
131C22×Dic13—21no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—21no—
136C22×Dic13—22no—
137C22×Dic13—21no—
138C22×Dic13—22no—
139C22×Dic13—21no—
140C22×Dic13—22no—
141C22×Dic13—21no—
142C22×Dic13—22no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—22no—
151C22×Dic13—21no—
152C22×Dic13—22no—
153C22×Dic13C2×D412yes—
154C22×Dic13C2×D412yes—
155C22×Dic13C2×D412yes—
156C22×Dic13C2×D412yes—
157C22×Dic13C2×Q814yes—
158C22×Dic13C2×Q814yes—
159C22×Dic13#4114yes—
160C22×Dic13#4112yes—
161C22×Dic13#4114yes—
162C13×C4⋊C4—28no—
163C13×C4⋊C4—48no—
164C13×C4⋊C4—44no—
165C4⋊Dic13—28no—
166#6101—28no—
167#6101—216no—
168#6101—48no—
169#6101—44no—
170#6101—44no—
171C4×Dic13—28no—
172C4×Dic13—48no—
173C2×#398—131no—
174C2×#398D1311yescharacteristic
175C2×#389—132no—
176C2×#389—131no—
177C2×C4×C4⋊C4—131no—
178#1442—132no—
179#1442—132no—
180#1441—131no—
181#1441—131no—
182C4⋊#95—131no—
183C4⋊#95—132no—
184C23×C13C22×D411yescharacteristic
185C23×C13C22×D411yescharacteristic
186C23×C13C22×D411yescharacteristic
187C23×C13C22×Q812yes—
188C23×C13C2×#4111yescharacteristic
189C23×C13C2×#4111yescharacteristic
190C23×C13C2×#4112yes—
191C23×C13C2×#4112yes—
192C23×C13H(5,𝔽2)11yescharacteristic
193C23×C132−1+412yes—
194C23×C132−1+411yescharacteristic
195C2×C4×C13—22no—
196C2×C4×C13—22no—
197C2×C4×C13—24no—
198C2×C4×C13—24no—
199C2×C4×C13—22no—
200C2×C4×C13—24no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—22no—
204C2×C4×C13—24no—
205C2×C4×C13—22no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—42no—
209C2×C4×C13—41no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—41no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—41no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13#12114yes—
226C2×Dic13—22no—
227C2×Dic13—24no—
228C2×Dic13—22no—
229C2×Dic13—24no—
230C2×Dic13—22no—
231C2×Dic13—22no—
232C2×Dic13—22no—
233C2×Dic13—22no—
234C2×Dic13—24no—
235C2×Dic13—24no—
236C2×Dic13—24no—
237C2×Dic13—24no—
238C2×Dic13—42no—
239C2×Dic13—41no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—41no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—41no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13#12114yes—
258C2×Dic13C22⋊Q818yes—
259C2×Dic13#12314yes—
260C2×Dic13#12518yes—
261C2×Dic13C4⋊Q814yes—
262C22×C4⋊C4—132no—
263C22×C4⋊C4—131no—
264C22×C4⋊C4—131no—
265C22×C4⋊C4—131no—
266C22×C4⋊C4—131no—
267C22×C4⋊C4—132no—
268C22×C4⋊C4C2×D1311yescharacteristic
269C22×C4⋊C4C2×D1312yes—
270C22×C4⋊C4C2×D1311yescharacteristic
271C22×C42—131no—
272C22×C42—132no—
273#398—24no—
274#398—264no—
275#389—264no—
276#389—268no—
277C4×C4⋊C4—264no—
278C2×#95—131no—
279C2×#95—132no—
280C2×#95—132no—
281C2×#95—132no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—132no—
285C2×#95—131no—
286C2×#95—131no—
287C2×#95—132no—
288C2×#95C2×D1311yescharacteristic
289C2×#95C2×D1312yes—
290C22×C13C2×#12111yescharacteristic
291C22×C13C2×#12111yescharacteristic
292C22×C13C2×C22⋊Q812yes—
293C22×C13C2×#12311yescharacteristic
294C22×C13#52511yescharacteristic
295C22×C13C2×#12512yes—
296C22×C13#52912yes—
297C22×C13C2×C4⋊Q811yescharacteristic
298C22×C13#53212yes—
299C22×C13#53611yescharacteristic
300C22×C13#53711yescharacteristic
301C22×C13#54112yes—
302C22×C13#54212yes—
303C22×C13D4211yescharacteristic
304C22×C13#54711yescharacteristic
305C22×C13#54711yescharacteristic
306C22×C13#54812yes—
307C22×C13D4×Q812yes—
308C22×C13#55212yes—
309C22×C13#55412yes—
310C22×C13#55511yescharacteristic
311C22×C13#55712yes—
312C22×C13#55712yes—
313C4×C13—24no—
314C4×C13—44no—
315C4×C13—42no—
316C4×C13—44no—
317C4×C13—81no—
318Dic13—42no—
319Dic13—44no—
320Dic13—44no—
321Dic13—42no—
322Dic13—81no—
323Dic13#39818yescomplemented
324C23×C4—131no—
325C23×C4—131no—
326C23×C4—132no—
327C23×C4—132no—
328C23×C4—131no—
329C23×C4—131no—
330C23×C4C22×D1311yescharacteristic
331C23×C4C22×D1311yescharacteristic
332C23×C4C22×D1312yes—
333C23×C4C22×D1312yes—
334C23×C4C22×D1311yescharacteristic
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—134no—
344C2×C4⋊C4—138no—
345C2×C4⋊C4—262no—
346C2×C4⋊C4—264no—
347C2×C4⋊C4—262no—
348C2×C4⋊C4—264no—
349C2×C4⋊C4—264no—
350C2×C4⋊C4—262no—
351C2×C4⋊C4—264no—
352C2×C4⋊C4—264no—
353C2×C4⋊C4—262no—
354C2×C4⋊C4—262no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4—264no—
357C2×C4⋊C4—262no—
358C2×C4⋊C4—522no—
359C2×C4⋊C4C22⋊D1314yes—
360C2×C42—134no—
361C2×C42—264no—
362C2×C42—264no—
363C2×C42—264no—
364C2×C42—264no—
365#95—22no—
366#95—24no—
367#95—264no—
368#95—264no—
369#95—264no—
370#95—262no—
371#95—264no—
372#95—262no—
373#95—264no—
374#95—262no—
375#95—264no—
376#95—522no—
377C2×C13C2×#39811yescharacteristic
378C2×C13#245212yes—
379C2×C13#245312yes—
380C2×C13#250612yes—
381C2×C13#250812yes—
382C2×C13#253611yescharacteristic
383C2×C13#253711yescharacteristic
384C2×C13#254611yescharacteristic
385C2×C13#258411yescharacteristic
386C2×C13#262511yescharacteristic
387C2×C13#285411yescharacteristic
388C24C23×D1311yescharacteristic
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—132no—
415C22×C4—132no—
416C22×C4—134no—
417C22×C4—132no—
418C22×C4—134no—
419C22×C4—132no—
420C22×C4—132no—
421C22×C4—134no—
422C22×C4—134no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—261no—
426C22×C4—262no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—262no—
430C22×C4—261no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—261no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—262no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—261no—
450C22×C4D4×D1312yes—
451C22×C4D4×D1312yes—
452C22×C4#612912yes—
453C22×C4Q8×D1314yes—
454C22×C4C2×C22⋊D1314yes—
455C22×C4C2×C22⋊D1312yes—
456C4⋊C4—28no—
457C4⋊C4—48no—
458C4⋊C4—44no—
459C4⋊C4—268no—
460C4⋊C4—2616no—
461C4⋊C4—268no—
462C4⋊C4—528no—
463C4⋊C4—524no—
464C4⋊C4—524no—
465C42—268no—
466C42—528no—
467C13#1514911yescharacteristic, complemented, Sylow
468C23C2×D4×D1311yescharacteristic
469C23C2×D4×D1311yescharacteristic
470C23C2×#612911yescharacteristic
471C23#8825111yescharacteristic
472C23C2×Q8×D1312yes—
473C23#8825412yes—
474C23#41×D1311yescharacteristic
475C23#41×D1312yes—
476C23#41×D1312yes—
477C23#8825711yescharacteristic
478C23C22×C22⋊D1311yescharacteristic
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—134no—
510C2×C4—134no—
511C2×C4—138no—
512C2×C4—134no—
513C2×C4—138no—
514C2×C4—262no—
515C2×C4—262no—
516C2×C4—264no—
517C2×C4—262no—
518C2×C4—262no—
519C2×C4—262no—
520C2×C4—264no—
521C2×C4—264no—
522C2×C4—264no—
523C2×C4—262no—
524C2×C4—264no—
525C2×C4—264no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—522no—
540C2×C4—521no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4#8819314yes—
546C22D13×#12111yescharacteristic
547C22#1171931311yescharacteristic
548C22#1171931611yescharacteristic
549C22#1171932111yescharacteristic
550C22D13×C22⋊Q812yes—
551C22#1171933812yes—
552C22#1171934112yes—
553C22#1171934512yes—
554C22#1171935412yes—
555C22D13×#12311yescharacteristic
556C22#1171936111yescharacteristic
557C22#1171939012yes—
558C22D13×#12512yes—
559C22#1171939812yes—
560C22#1171940112yes—
561C22#1171942612yes—
562C22D13×C4⋊Q811yescharacteristic
563C22#1171942911yescharacteristic
564C22D4×C22⋊D1311yescharacteristic
565C22C2×#8819311yescharacteristic
566C22Q8×C22⋊D1312yes—
567C22#1171952911yescharacteristic
568C22#1171953712yes—
569C4—24no—
570C4—42no—
571C4—44no—
572C4—44no—
573C4—81no—
574C4—138no—
575C4—522no—
576C4—522no—
577C4—524no—
578C4—524no—
579C4—1041no—
580C2D13×#39811yescharacteristic
581C2#1311868512yes—
582C2#1311869212yes—
583C2#1311935112yes—
584C2#1311936912yes—
585C2#1311974211yescharacteristic
586C2#1311975011yescharacteristic
587C2#1311982211yescharacteristic
588C2#1312022011yescharacteristic
589C2#1312063911yescharacteristic
590C2#1312316511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, prime radical, cosocleC24×C13C24
FittingC2×C13×#398C2
hypercenterC2×#398D13
hypocenterC13#15149
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
323. Dic13#398semidirect
467. C13#15149semidirect

Maximal subgroups

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

subgroupindex
C2×#117186412
C2×#117186332
C2×C4⋊C4×Dic132
#131130952
#131130942
#131130902
#131130892
#131130642
C2×C13×#3982
#1514913