Finite Group Databasebeta

← #15828830

Subgroups — #15828830

Order 3328.

1210 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719251C211yesmaximal, characteristic
2#13123865C211yesmaximal, characteristic, complemented
3#13113179C212yesmaximal, complemented
4#13113172C212yesmaximal, complemented
5#13113168C212yesmaximal, complemented
6#13113165C212yesmaximal, complemented
7#13113152C212yesmaximal, complemented
8C2×#11718061C212yesmaximal, complemented
9C13×#2973C211yesmaximal, characteristic, complemented
10C22×#6129C411yescharacteristic
11C2×C4×D4×C13C2211yescharacteristic
12C2×D4×Dic13C411yescharacteristic
13C2×C4×C22⋊D13C2211yescharacteristic
14C2×C4×C22⋊D13C2211yescharacteristic
15C22×#6101C2211yescharacteristic
16C22×#6101C2211yescharacteristic
17#11719251—24no—
18#11719251—24no—
19C2×C4⋊C4×D13C411yescharacteristic
20C2×#88141C411yescharacteristic
21C2×#88135C411yescharacteristic
22C2×#88135C411yescharacteristic
23C2×#88131C411yescharacteristic
24C2×#88131C411yescharacteristic
25C2×#88126C2211yescharacteristic
26C2×C4×Dic26C2211yescharacteristic
27C13×#435—24no—
28C13×#432C2212yes—
29C13×#407C2212yes—
30C2×C13×C22⋊C8C2212yes—
31#11718868C2212yes—
32C2×C22⋊#1055C2212yes—
33#11718672—24no—
34#11718587C2212yes—
35#11718061C2214yes—
36#11718061C2214yes—
37#11718061C2214yes—
38#11718060C2214yes—
39C22×D4×C13C2×C411yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C22×C22⋊D13C2×C411yescharacteristic
43C22×C22⋊D13C2×C411yescharacteristic
44C23×Dic13C2×C411yescharacteristic
45C23×Dic13C2×C411yescharacteristic
46C23×Dic13C2×C411yescharacteristic
47C23×Dic13C2×C411yescharacteristic
48C2×#6129—24no—
49C2×#6129—24no—
50C2×#6129—24no—
51C22×C4×D13C2×C411yescharacteristic
52C22×C4×D13C2×C411yescharacteristic
53C22×C4×D13C2×C411yescharacteristic
54C22×Dic26C2×C411yescharacteristic
55C2×C13×M16—22no—
56C22×C8×C13—22no—
57C4×D4×C13D414yes—
58C4×D4×C13D414yes—
59C2×C13×C4⋊C4C2×C411yescharacteristic
60C2×C13×C22⋊C4C2×C411yescharacteristic
61C2×C13×C22⋊C4C2×C411yescharacteristic
62C2×C42×C13C2311yescharacteristic
63C2×C22⋊Dic13C2×C411yescharacteristic
64C2×C22⋊Dic13C2×C411yescharacteristic
65D4×Dic13—24no—
66C4×C22⋊D13—22no—
67C4×C22⋊D13—22no—
68C4×C22⋊D13—22no—
69C4×C22⋊D13—22no—
70C2×#6103C2×C411yescharacteristic
71C2×#6103C2311yescharacteristic
72C2×C4⋊Dic13C2×C411yescharacteristic
73C2×#6101—22no—
74C2×#6101—22no—
75C2×#6101—22no—
76C2×#6101—22no—
77C2×#6101C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×#6101C2311yescharacteristic
83C2×#6101C2311yescharacteristic
84C2×#6101C2311yescharacteristic
85C2×C4×Dic13C2×C411yescharacteristic
86C2×C4×Dic13C2×C411yescharacteristic
87C2×C4×Dic13C2×C411yescharacteristic
88C2×C4×Dic13C2×C411yescharacteristic
89C2×C4×Dic13C2×C411yescharacteristic
90C2×#6099—22no—
91C22×#1055—22no—
92C4⋊C4×D13—24no—
93#88141—24no—
94#88135—24no—
95#88135—24no—
96#88131—24no—
97#88131—24no—
98#88126—22no—
99#88126—22no—
100C4×Dic26—22no—
101C4×Dic26—22no—
102C13×C4⋊C8—22no—
103C13×C22⋊C8—22no—
104C13×C22⋊C8—22no—
105C13×C22⋊C8C2314yes—
106C13×#97—22no—
107C22⋊#1055—22no—
108C22⋊#1055—22no—
109C22⋊#1055C2314yes—
110C4⋊#1055—22no—
111#88043—22no—
112#17368—131nomaximal, Sylow
113C24×C13C22×C411yescharacteristic
114C24×C13C22×C411yescharacteristic
115C23×D13C22×C411yescharacteristic
116C2×D4×C13—22no—
117C2×D4×C13—22no—
118C2×D4×C13C22⋊C414yes—
119C22×C4×C13—81no—
120C22×C4×C13—81no—
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C2×D412yes—
126C22×C4×C13C2×D412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×D412yes—
129C22×C4×C13C2411yescharacteristic
130C2×C22⋊D13—22no—
131C2×C22⋊D13—22no—
132C2×C22⋊D13—22no—
133C2×C22⋊D13—22no—
134C2×C22⋊D13—22no—
135C2×C22⋊D13M1614yescomplemented
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—81no—
144C22×Dic13—81no—
145C22×Dic13M1614yescomplemented
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153#6129—232no—
154C2×C4×D13—22no—
155C2×C4×D13—22no—
156C2×C4×D13—22no—
157C2×C4×D13—22no—
158C2×C4×D13—22no—
159C2×C4×D13—81no—
160C2×C4×D13—81no—
161C2×Dic26—22no—
162C2×Dic26—22no—
163C2×Dic26—22no—
164C13×M16—82no—
165C2×C8×C13—24no—
166C2×C8×C13—82no—
167C13×C4⋊C4C22⋊C414yes—
168C13×C22⋊C4C22⋊C414yes—
169C13×C22⋊C4C22⋊C414yes—
170C42×C13C2×D412yes—
171C42×C13C2×D412yes—
172C22⋊Dic13—22no—
173C22⋊Dic13—22no—
174#6103—22no—
175#6103—21no—
176#6103—21no—
177C4⋊Dic13—22no—
178#6101—22no—
179#6101—22no—
180#6101—22no—
181#6101—22no—
182#6101—22no—
183#6101—21no—
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189C4×Dic13—22no—
190C4×Dic13—22no—
191C4×Dic13—22no—
192C4×Dic13—22no—
193C4×Dic13—22no—
194#6099—82no—
195C2×#1055—24no—
196C2×#1055—82no—
197C2×#520—131no—
198#2973—131no—
199#2973D1311yescharacteristic, complemented
200#1467—132no—
201#1465—132no—
202#1464—132no—
203#1463—132no—
204#1459—132no—
205C2×#324—132no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13C2×C22⋊C412yes—
213C23×C13C2×C22⋊C412yes—
214C23×C13C2×M1612yes—
215C23×C13C2×M1612yes—
216C23×C13C23×C411yescharacteristic
217C22×D13—21no—
218C22×D13—21no—
219C22×D13—41no—
220C22×D13—41no—
221C22×D13C2×M1612yes—
222D4×C13—28no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13C2×C22⋊C412yes—
234C2×C4×C13C2×C22⋊C412yes—
235C2×C4×C13C2×C22⋊C412yes—
236C2×C4×C13C2×C22⋊C412yes—
237C2×C4×C13C22×D411yescharacteristic
238C2×C4×C13C22×D411yescharacteristic
239C22⋊D13—28no—
240C22⋊D13—28no—
241C2×Dic13—28no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—28no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—82no—
258C2×Dic13—82no—
259C2×Dic13C2×M1612yes—
260C2×Dic13C2×M1612yes—
261C2×Dic13C2×M1612yes—
262C4×D13—28no—
263C4×D13—82no—
264C4×D13—82no—
265Dic26—28no—
266C8×C13—44no—
267#1055—44no—
268C22×#41—131no—
269#520—264no—
270#520—264no—
271C2×C4×Q8—131no—
272C2×C4×Q8—131no—
273C2×C4×D4—131no—
274C2×C4×D4—131no—
275C2×C4×D4—131no—
276C2×C4×D4—131no—
277C2×C4×D4—131no—
278C2×C4×D4C2×D1311yescharacteristic
279C2×#117—131no—
280C2×#117—131no—
281C2×#117—131no—
282C22×C4⋊C4—131no—
283C22×C4⋊C4—131no—
284C22×C4⋊C4—131no—
285#435—24no—
286#435—264no—
287#432—132no—
288#432C2×D1312yes—
289#407—132no—
290#407C2×D1312yes—
291C2×C22⋊C8—132no—
292C2×C22⋊C8C2×D1312yes—
293#324—134no—
294#324—134no—
295#324—134no—
296#323—134no—
297C22×C13—21no—
298C22×C13—22no—
299C22×C13—21no—
300C22×C13—22no—
301C22×C13—22no—
302C22×C13—22no—
303C22×C13—22no—
304C22×C13—42no—
305C22×C13—42no—
306C22×C13—42no—
307C22×C13—42no—
308C22×C13#40714yes—
309C22×C13C22×C22⋊C411yescharacteristic
310C22×C13C22×M1611yescharacteristic
311C22×C13C22×M1611yescharacteristic
312C2×D13—22no—
313C2×D13—42no—
314C2×D13—41no—
315C2×D13—41no—
316C2×D13—42no—
317C4×C13—22no—
318C4×C13—21no—
319C4×C13—21no—
320C4×C13—22no—
321C4×C13—22no—
322C4×C13—22no—
323Dic13—22no—
324Dic13—22no—
325Dic13—22no—
326Dic13—41no—
327Dic13—41no—
328Dic13—41no—
329Dic13—41no—
330C2×#41—264no—
331C2×#41—264no—
332C2×#41—264no—
333C22×Q8—131no—
334C22×D4—131no—
335C22×D4—131no—
336C22×D4C4×D1311yescharacteristic
337C23×C4—131no—
338C23×C4—131no—
339C23×C4—131no—
340C23×C4—131no—
341C23×C4—131no—
342C23×C4—131no—
343C23×C4—131no—
344C23×C4C22×D1311yescharacteristic
345C23×C4C22×D1311yescharacteristic
346C2×M16—22no—
347C2×M16—262no—
348C22×C8—22no—
349C22×C8—262no—
350C4×Q8—264no—
351C4×Q8—262no—
352C4×Q8—262no—
353C4×D4—264no—
354C4×D4—262no—
355C4×D4—262no—
356C4×D4—262no—
357C4×D4—262no—
358C4×D4—264no—
359C4×D4—264no—
360C4×D4D5214yes—
361C4×D4C22⋊D1314yes—
362#117—264no—
363#117—264no—
364#117—262no—
365#117—262no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—262no—
378C2×C4⋊C4—262no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4C4×D1311yescharacteristic
381C2×C22⋊C4—131no—
382C2×C22⋊C4—131no—
383C2×C22⋊C4—131no—
384C2×C22⋊C4—131no—
385C2×C22⋊C4C4×D1311yescharacteristic
386C2×C22⋊C4C4×D1311yescharacteristic
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42C22×D1311yescharacteristic
393C4⋊C8—22no—
394C4⋊C8—262no—
395C22⋊C8—22no—
396C22⋊C8—22no—
397C22⋊C8—134no—
398C22⋊C8—262no—
399C22⋊C8—262no—
400C22⋊C8C22×D1314yes—
401#97—22no—
402#97—262no—
403C2×C13—21no—
404C2×C13—21no—
405C2×C13—24no—
406C2×C13—42no—
407C2×C13C2×#40711yescharacteristic
408C2×C13#288311yescharacteristic
409C2×C13#288911yescharacteristic
410D13—42no—
411C24—131no—
412C24C2×C4×D1311yescharacteristic
413C24C2×C4×D1311yescharacteristic
414#41—2632no—
415C2×Q8—262no—
416C2×Q8—262no—
417C2×Q8—262no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—134no—
421C2×D4—262no—
422C2×D4—262no—
423C2×D4—262no—
424C2×D4—262no—
425C2×D4—262no—
426C2×D4#610314yes—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4—134no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—131no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—1041no—
450C22×C4—1041no—
451C22×C4—1041no—
452C22×C4—1041no—
453C22×C4C2×C4×D1311yescharacteristic
454C22×C4C2×C4×D1311yescharacteristic
455C22×C4C2×C4×D1311yescharacteristic
456C22×C4C2×C4×D1311yescharacteristic
457C22×C4C2×D5212yes—
458C22×C4C2×D5212yes—
459C22×C4C2×C22⋊D1312yes—
460C22×C4C2×C22⋊D1312yes—
461C22×C4C23×D1311yescharacteristic
462M16—82no—
463M16—1042no—
464C2×C8—24no—
465C2×C8—82no—
466C2×C8—264no—
467C2×C8—1042no—
468C4⋊C4—262no—
469C4⋊C4—262no—
470C4⋊C4—262no—
471C4⋊C4—262no—
472C4⋊C4—262no—
473C4⋊C4—262no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4#610314yes—
481C22⋊C4—262no—
482C22⋊C4—262no—
483C22⋊C4—262no—
484C22⋊C4—261no—
485C22⋊C4—261no—
486C22⋊C4#610314yes—
487C22⋊C4#610314yes—
488C42—262no—
489C42—262no—
490C42—262no—
491C42—262no—
492C42—262no—
493C42C2×D5212yes—
494C42C2×C22⋊D1312yes—
495C13#1736811yescharacteristic, complemented, Sylow
496C23—21no—
497C23—21no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—132no—
503C23—261no—
504C23—261no—
505C23—521no—
506C23—521no—
507C23M16×D1312yes—
508C23M16×D1312yes—
509C23C2×#610312yes—
510C23C2×#610312yes—
511C23C22×C4×D1311yescharacteristic
512Q8—268no—
513D4—28no—
514D4—268no—
515D4—268no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—132no—
527C2×C4—132no—
528C2×C4—132no—
529C2×C4—268no—
530C2×C4—268no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—268no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—1042no—
547C2×C4—1042no—
548C2×C4—1042no—
549C2×C4—1042no—
550C2×C4C2×#610312yes—
551C2×C4C2×#610312yes—
552C2×C4C2×#610312yes—
553C2×C4C2×#610312yes—
554C2×C4C22×D5211yescharacteristic
555C2×C4C22×C22⋊D1311yescharacteristic
556C8—44no—
557C8—524no—
558C22—21no—
559C22—22no—
560C22—21no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—262no—
570C22—522no—
571C22—522no—
572C22—521no—
573C22—521no—
574C22#1171878714yes—
575C22C2×M16×D1311yescharacteristic
576C22C2×M16×D1311yescharacteristic
577C22C22×#610311yescharacteristic
578C4—22no—
579C4—21no—
580C4—21no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—262no—
585C4—262no—
586C4—262no—
587C4—521no—
588C4—521no—
589C4—521no—
590C4—521no—
591C2—21no—
592C2—21no—
593C2—24no—
594C2—42no—
595C2—522no—
596C2C2×#1171878711yescharacteristic
597C2#1312329611yescharacteristic
598C2#1312331811yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2973C2
socleC22×C13C22×C22⋊C4
prime radicalC22×#6129C4
cosocleC22×C4×C13C24
hypercenter#2973D13
hypocenterC13#17368
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13123865C2semidirect
3. #13113179C2semidirect
4. #13113172C2semidirect
5. #13113168C2semidirect
6. #13113165C2semidirect
7. #13113152C2semidirect
8. C2×#11718061C2semidirect
9. C13×#2973C2semidirect
135. C2×C22⋊D13M16semidirect
145. C22×Dic13M16semidirect
199. #2973D13semidirect
495. C13#17368semidirect

Maximal subgroups

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

subgroupindex
C2×#117192512
#131238652
#131131792
#131131722
#131131682
#131131652
#131131522
C2×#117180612
C13×#29732
#1736813