Finite Group Databasebeta

← #15878377

Subgroups — #15878377

Order 3328.

1490 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#1055C211yesmaximal, characteristic, complemented
2C2×#11718894C212yesmaximal, complemented
3#13117785C211yesmaximal, characteristic, complemented
4#13115760C211yesmaximal, characteristic, complemented
5#13115639C211yesmaximal, characteristic, complemented
6#13115260C212yesmaximal, complemented
7#13115149C212yesmaximal, complemented
8#13114836C211yesmaximal, characteristic, complemented
9#13114776C212yesmaximal, complemented
10C4×#88072C211yesmaximal, characteristic, complemented
11C2×C13×#547C211yesmaximal, characteristic
12C22×C13×#41C2212yes—
13C13×#547—24no—
14C13×#547C418yescomplemented
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#123—22no—
17C2×C13×C22⋊Q8C2212yes—
18C2×C13×#121—21no—
19C2×C4×D4×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C22×C13×C4⋊C4—21no—
22C2×#88180C2212yes—
23C23×#1055C2212yes—
24#11718894—28no—
25C2×#88075C2212yes—
26C2×#88075C2212yes—
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29#11718882—21no—
30C2×#88072C2212yes—
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33#11718873C2212yes—
34C2×C22⋊#1055C2212yes—
35D4×#1055—24no—
36C4⋊C4×Dic13—21no—
37#11718612—22no—
38#11718596C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×C4×#1055C2211yescharacteristic
42#11718121C2211yescharacteristic
43#11718121C2212yes—
44#11718121C2211yescharacteristic
45C2×C13×#41—24no—
46C2×C13×#41—24no—
47C2×C13×#41—24no—
48C2×C13×#41—42no—
49C2×C13×#41—42no—
50C2×C13×#41C2×C418yes—
51C22×Q8×C13C2312yes—
52C22×D4×C13—22no—
53C22×D4×C13D411yescharacteristic
54C22×D4×C13C2311yescharacteristic
55C23×C4×C13—21no—
56C23×C4×C13—22no—
57C23×C4×C13C2312yes—
58C13×C4⋊Q8—22no—
59C13×C4⋊Q8C2×C414yes—
60C13×#123—216no—
61C13×C22⋊Q8—24no—
62C13×C22⋊Q8C2×C418yes—
63C13×#121—28no—
64C4×D4×C13—22no—
65C4×D4×C13C2×C414yes—
66C4×D4×C13C2×C414yes—
67C4×D4×C13D414yes—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—28no—
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4D412yes—
77C2×C42×C13C2311yescharacteristic
78C2×C22⋊Dic13—22no—
79C2×C22⋊Dic13—22no—
80#88180—24no—
81#88180—42no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13C2312yes—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4×Dic13—22no—
88C2×C4×Dic13—21no—
89C22×#1055—24no—
90C22×#1055—24no—
91C22×#1055—42no—
92C22×#1055C2312yes—
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95#88075—24no—
96#88075—24no—
97#88075—42no—
98#88075—42no—
99#88072—24no—
100#88072—22no—
101#88072D414yescomplemented
102#88071—21no—
103#88071—22no—
104C22⋊#1055—24no—
105C4⋊#1055—22no—
106C4×#1055—22no—
107#22417—131nomaximal, Sylow
108C24×C13—21no—
109C24×C13C2×D412yes—
110C13×#41—216no—
111C13×#41—48no—
112C13×#41—48no—
113C13×#41—48no—
114C2×Q8×C13—22no—
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13C22×C414yes—
120C2×D4×C13—28no—
121C2×D4×C13—22no—
122C2×D4×C13—22no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—44no—
127C2×D4×C13—44no—
128C2×D4×C13C22⋊C414yes—
129C2×D4×C13C22×C412yes—
130C2×D4×C13C2×D412yes—
131C2×D4×C13#4112yes—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—24no—
139C22×C4×C13—28no—
140C22×C4×C13—44no—
141C22×C4×C13—44no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13C22×C414yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D414yes—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2411yescharacteristic
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—22no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—28no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4C22⋊C414yes—
158C13×C4⋊C4C22×C412yes—
159C13×C22⋊C4—28no—
160C13×C22⋊C4—24no—
161C13×C22⋊C4C22⋊C418yes—
162C42×C13C22×C412yes—
163C42×C13C2×D412yes—
164C22⋊Dic13—44no—
165C22⋊Dic13—82no—
166C4⋊Dic13—21no—
167C4⋊Dic13—22no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—22no—
171C4⋊Dic13—42no—
172C4⋊Dic13—81no—
173C4⋊Dic13C2×D412yes—
174C4×Dic13—44no—
175C4×Dic13—42no—
176C2×#1055—21no—
177C2×#1055—21no—
178C2×#1055—21no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×#1055—21no—
182C2×#1055—21no—
183C2×#1055—22no—
184C2×#1055—48no—
185C2×#1055C2×D412yes—
186C2×#547D1311yescharacteristic
187C2×C8×D4—131no—
188C2×#416—132no—
189#2354—131no—
190#1981—131no—
191#1956—131no—
192#1892—132no—
193#1873—132no—
194#1802—131no—
195#1788—132no—
196C4×#102—131no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—22no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—22no—
205C23×C13—22no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13C2×C22⋊C414yes—
211C23×C13C22×D411yescharacteristic
212Q8×C13—24no—
213Q8×C13—24no—
214Q8×C13—42no—
215Q8×C13—42no—
216D4×C13—22no—
217D4×C13—22no—
218D4×C13—22no—
219D4×C13—28no—
220D4×C13—416no—
221D4×C13C4×D414yes—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—416no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—48no—
238C2×C4×C13C2×C22⋊C412yes—
239C2×C4×C13C2×C22⋊C414yes—
240C2×C4×C13C2×C22⋊C412yes—
241C2×C4×C13#13512yes—
242C2×C4×C13#13512yes—
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13H(5,𝔽2)11yescharacteristic
248C2×C4×C13H(5,𝔽2)11yescharacteristic
249C2×Dic13—22no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—42no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—41no—
258#1055—22no—
259#1055—42no—
260#1055—41no—
261C22×#41C2×D1312yes—
262C23×C8—132no—
263#547—24no—
264#547Dic1318yescomplemented
265C2×C4⋊Q8C2×D1311yescharacteristic
266C2×#123—22no—
267C2×C22⋊Q8C2×D1312yes—
268C2×#121—21no—
269C2×C4×D4C2×D1311yescharacteristic
270C2×C4×D4C2×D1311yescharacteristic
271C2×#117—132no—
272C22×C4⋊C4—21no—
273C8×D4—264no—
274C2×C4⋊C8—131no—
275#416—268no—
276C2×#103—132no—
277C2×#103—132no—
278C2×#103—132no—
279C2×#103—132no—
280C2×#102—131no—
281C2×#102—132no—
282C2×#102—131no—
283C2×C22⋊C8—132no—
284C2×C4×C8—131no—
285#390—261no—
286#388—262no—
287#384—131no—
288#380—132no—
289C4×C4⋊C4—131no—
290C4×C4⋊C4—261no—
291#340—132no—
292#340—131no—
293#340—131no—
294C22×C13—24no—
295C22×C13—24no—
296C22×C13—24no—
297C22×C13—24no—
298C22×C13—42no—
299C22×C13—42no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—42no—
305C22×C13—42no—
306C22×C13—42no—
307C22×C13—42no—
308C22×C13C22×C22⋊C411yescharacteristic
309C22×C13D4211yescharacteristic
310C22×C13#54611yescharacteristic
311C22×C13C2×#13511yescharacteristic
312C22×C13C2×#13511yescharacteristic
313C22×C13#57711yescharacteristic
314C22×C13#57811yescharacteristic
315C4×C13—24no—
316C4×C13—22no—
317C4×C13—44no—
318C4×C13—42no—
319C4×C13#41614yescomplemented
320C4×C13C2×C4×D411yescharacteristic
321C4×C13#51811yescharacteristic
322C4×C13D4211yescharacteristic
323C4×C13#54611yescharacteristic
324Dic13—42no—
325Dic13—82no—
326Dic13—81no—
327C2×#41—24no—
328C2×#41—24no—
329C2×#41—24no—
330C2×#41—42no—
331C2×#41—42no—
332C2×#41C2×Dic1318yes—
333C22×Q8C22×D1312yes—
334C22×D4—22no—
335C22×D4C22⋊D1311yescharacteristic
336C22×D4C22×D1311yescharacteristic
337C23×C4—21no—
338C23×C4—22no—
339C23×C4C22×D1312yes—
340C22×C8—131no—
341C22×C8—132no—
342C22×C8—131no—
343C22×C8—264no—
344C22×C8—264no—
345C22×C8—522no—
346C4⋊Q8—22no—
347C4⋊Q8C2×Dic1314yes—
348#123—216no—
349C22⋊Q8—24no—
350C22⋊Q8C2×Dic1318yes—
351#121—28no—
352C4×D4—22no—
353C4×D4C2×Dic1314yes—
354C4×D4C2×Dic1314yes—
355C4×D4C22⋊D1314yes—
356#117—264no—
357#117—522no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—132no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4C22⋊D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C22⋊C4—22no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—262no—
372C2×C22⋊C4—262no—
373C2×C22⋊C4C22⋊D1312yes—
374C2×C42—262no—
375C2×C42—261no—
376C2×C42C22×D1311yescharacteristic
377C4⋊C8—262no—
378#103—264no—
379#103—264no—
380#103—522no—
381#103—522no—
382#102—134no—
383#102—264no—
384#102—262no—
385C22⋊C8—264no—
386C4×C8—262no—
387#95—261no—
388#95—262no—
389C2×C13—44no—
390C2×C13—44no—
391C2×C13D4×C22⋊C411yescharacteristic
392C2×C13C2×#41611yescharacteristic
393C2×C13#289811yescharacteristic
394C2×C13#328311yescharacteristic
395C2×C13#328411yescharacteristic
396C2×C13#330211yescharacteristic
397C2×C13#330311yescharacteristic
398C24—21no—
399C24C2×C22⋊D1312yes—
400#41—216no—
401#41—48no—
402#41—48no—
403#41—48no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8C22×Dic1314yes—
410C2×D4—28no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4C22⋊Dic1314yes—
419C2×D4D4×D1312yes—
420C2×D4#612912yes—
421C2×D4C22×Dic1312yes—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—28no—
430C22×C4—44no—
431C22×C4—44no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—262no—
437C22×C4C22×Dic1314yes—
438C22×C4C2×C22⋊D1312yes—
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C2×C22⋊D1314yes—
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C23×D1311yescharacteristic
443C2×C8—132no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—262no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—262no—
450C2×C8—261no—
451C2×C8—262no—
452C2×C8—528no—
453C4⋊C4—24no—
454C4⋊C4—28no—
455C4⋊C4—24no—
456C4⋊C4—21no—
457C4⋊C4—132no—
458C4⋊C4—261no—
459C4⋊C4—262no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—262no—
463C4⋊C4—522no—
464C4⋊C4—1041no—
465C4⋊C4C22⋊Dic1314yes—
466C4⋊C4C22×Dic1312yes—
467C22⋊C4—28no—
468C22⋊C4—24no—
469C22⋊C4—524no—
470C22⋊C4—1042no—
471C22⋊C4C22⋊Dic1318yes—
472C42—524no—
473C42—522no—
474C42C22×Dic1312yes—
475C42C2×C22⋊D1312yes—
476C13#2241711yescharacteristic, complemented, Sylow
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C2×C22⋊Dic1314yes—
491C23C22×C22⋊D1311yescharacteristic
492Q8—24no—
493Q8—24no—
494Q8—42no—
495Q8—42no—
496D4—22no—
497D4—22no—
498D4—22no—
499D4—28no—
500D4—416no—
501D4D4×Dic1314yes—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—416no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—48no—
518C2×C4—262no—
519C2×C4—521no—
520C2×C4—521no—
521C2×C4—522no—
522C2×C4—521no—
523C2×C4—521no—
524C2×C4—522no—
525C2×C4—521no—
526C2×C4—522no—
527C2×C4#8820412yes—
528C2×C4#8820412yes—
529C2×C4C2×C22⋊Dic1312yes—
530C2×C4C2×C22⋊Dic1314yes—
531C2×C4C2×C22⋊Dic1312yes—
532C2×C4C2×D4×D1311yescharacteristic
533C2×C4C2×#612911yescharacteristic
534C2×C4#8825111yescharacteristic
535C2×C4#8825111yescharacteristic
536C2×C4C23×Dic1311yescharacteristic
537C2×C4C22×C22⋊D1311yescharacteristic
538C8—262no—
539C8—522no—
540C8—521no—
541C22—24no—
542C22—24no—
543C22—24no—
544C22—24no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22D4×C22⋊D1311yescharacteristic
556C22#1171951111yescharacteristic
557C22C2×#8820411yescharacteristic
558C22C2×#8820411yescharacteristic
559C22#1171954211yescharacteristic
560C22#1171954311yescharacteristic
561C22C22×C22⋊Dic1311yescharacteristic
562C4—22no—
563C4—24no—
564C4—42no—
565C4—44no—
566C4—522no—
567C4—1041no—
568C4—1042no—
569C4#1171889414yescomplemented
570C4C2×D4×Dic1311yescharacteristic
571C4#1171950311yescharacteristic
572C4D4×C22⋊D1311yescharacteristic
573C4#1171951111yescharacteristic
574C2—44no—
575C2—44no—
576C2D4×C22⋊Dic1311yescharacteristic
577C2C2×#1171889411yescharacteristic
578C2#1312336911yescharacteristic
579C2#1312655411yescharacteristic
580C2#1312656211yescharacteristic
581C2#1312675311yescharacteristic
582C2#1312676411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#547C2
socleC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×#547D13
hypocenterC13#22417
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×D4×#1055C2semidirect
2. C2×#11718894C2semidirect
3. #13117785C2semidirect
4. #13115760C2semidirect
5. #13115639C2semidirect
6. #13115260C2semidirect
7. #13115149C2semidirect
8. #13114836C2semidirect
9. #13114776C2semidirect
10. C4×#88072C2semidirect
14. C13×#547C4semidirect
101. #88072D4semidirect
264. #547Dic13semidirect
319. C4×C13#416semidirect
476. C13#22417semidirect
569. C4#11718894semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#10552
C2×#117188942
#131177852
#131157602
#131156392
#131152602
#131151492
#131148362
#131147762
C4×#880722
C2×C13×#5472
#2241713