Finite Group Databasebeta

← #15896861

Subgroups — #15896861

Order 3328.

1154 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718752C211yesmaximal, characteristic, complemented
2C2×C4×#6105C211yesmaximal, characteristic, complemented
3#13119758C211yesmaximal, characteristic, complemented
4#13116015C212yesmaximal, complemented
5#13115839C212yesmaximal, complemented
6#13115798C211yesmaximal, characteristic, complemented
7#13115631C211yesmaximal, characteristic, complemented
8#13115148C212yesmaximal, complemented
9#13115035C212yesmaximal, complemented
10#13114836C211yesmaximal, characteristic, complemented
11C2×C13×#555C211yesmaximal, characteristic
12C13×#555—24no—
13C13×#555—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#124—22no—
16C2×C13×#121—21no—
17C2×C13×#121C2212yes—
18C2×C4×D4×C13C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C2×C13×#117—21no—
21C2×C13×#117C2212yes—
22C22×#6105C2211yescharacteristic
23C2×#88178C2212yes—
24C2×C4×Dic26C2211yescharacteristic
25#11718882—21no—
26C2×#88072C2211yescharacteristic
27C2×#88072C2212yes—
28#11718873C2212yes—
29C2×C22⋊#1055C2212yes—
30C2×C22⋊#1055C2212yes—
31#11718752—24no—
32C4×#6105—24no—
33#11718634—21no—
34C2×#88050C2211yescharacteristic
35C2×#88050C2212yes—
36C2×#88048C2211yescharacteristic
37C2×#88047C2212yes—
38#11718609—22no—
39#11718596C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×C4×#1055C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C22×Q8×C13—21no—
46C22×D4×C13—22no—
47C22×D4×C13D411yescharacteristic
48C22×D4×C13C2311yescharacteristic
49C23×C4×C13—21no—
50C23×C4×C13C2312yes—
51C22×Dic26C2311yescharacteristic
52C13×C4⋊Q8—22no—
53C13×C4⋊Q8D414yes—
54C13×#124—216no—
55C13×#121—28no—
56C13×#121—24no—
57C13×#121—24no—
58C4×D4×C13—22no—
59C4×D4×C13—22no—
60C4×D4×C13—22no—
61C4×D4×C13D414yes—
62C13×#117—28no—
63C13×#117—24no—
64C13×#117—24no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4D411yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2312yes—
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4D412yes—
73C2×C42×C13—22no—
74C2×C42×C13C2311yescharacteristic
75C2×C22⋊Dic13—22no—
76C2×C22⋊Dic13—22no—
77C2×#6105—22no—
78C2×#6105—22no—
79C2×#6105—22no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2312yes—
84#88178—24no—
85#88178—42no—
86C2×#6101—21no—
87C2×#6101—22no—
88C2×C4×Dic13—21no—
89C22×#1055C2311yescharacteristic
90C22×#1055C2312yes—
91C22×#1055C2311yescharacteristic
92C4×Dic26—22no—
93C4×Dic26—22no—
94#88072—22no—
95#88072—42no—
96#88071—22no—
97C22⋊#1055—24no—
98C22⋊#1055—42no—
99#88050—22no—
100#88050—24no—
101#88048—22no—
102#88047—24no—
103C4⋊#1055—22no—
104C4×#1055—22no—
105#24121—131nomaximal, Sylow
106C24×C13—21no—
107C24×C13C2×D412yes—
108C2×Q8×C13—24no—
109C2×Q8×C13—81no—
110C2×Q8×C13—81no—
111C2×D4×C13—28no—
112C2×D4×C13—22no—
113C2×D4×C13—22no—
114C2×D4×C13—22no—
115C2×D4×C13—21no—
116C2×D4×C13—21no—
117C2×D4×C13—21no—
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—82no—
121C2×D4×C13—82no—
122C2×D4×C13C2×D412yes—
123C22×C4×C13—21no—
124C22×C4×C13—22no—
125C22×C4×C13—24no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2411yescharacteristic
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—22no—
141C2×Dic26—21no—
142C2×Dic26—21no—
143C2×Dic26—21no—
144C2×Dic26—21no—
145C2×Dic26—21no—
146C2×Dic26#4112yes—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4C2×D412yes—
152C13×C4⋊C4C2×D414yes—
153C13×C22⋊C4—28no—
154C13×C22⋊C4—28no—
155C13×C22⋊C4—24no—
156C13×C22⋊C4—24no—
157C42×C13—28no—
158C42×C13C2×D412yes—
159C42×C13C2×D412yes—
160C22⋊Dic13—44no—
161C22⋊Dic13—82no—
162#6105—28no—
163C4⋊Dic13—21no—
164C4⋊Dic13—21no—
165C4⋊Dic13—22no—
166C4⋊Dic13—22no—
167C4⋊Dic13—42no—
168C4⋊Dic13—81no—
169#6101—44no—
170#6101—42no—
171C4×Dic13—42no—
172C2×#1055—21no—
173C2×#1055—21no—
174C2×#1055—21no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—21no—
178C2×#1055—22no—
179C2×#1055—21no—
180C2×#1055#4112yes—
181C2×#555D1311yescharacteristic
182C2×#477—131no—
183C2×C4×SD16—131no—
184#2538—131no—
185#2033—132no—
186#2000—132no—
187#1990—131no—
188#1954—131no—
189#1873—132no—
190#1854—132no—
191#1802—131no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—41no—
201C23×C13—41no—
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13C22×D411yescharacteristic
207Q8×C13—84no—
208D4×C13—22no—
209D4×C13—22no—
210D4×C13—41no—
211D4×C13—41no—
212D4×C13—44no—
213D4×C13—88no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—24no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—48no—
230C2×C4×C13#12012yes—
231C2×C4×C13#12012yes—
232C2×C4×C13#13512yes—
233C2×C4×C13#13712yes—
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13H(5,𝔽2)11yescharacteristic
239C2×C4×C132−1+411yescharacteristic
240C2×Dic13—22no—
241C2×Dic13—41no—
242C2×Dic13—41no—
243C2×Dic13—41no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249Dic26—22no—
250Dic26—22no—
251Dic26—41no—
252Dic26—41no—
253#1055—22no—
254#1055—41no—
255#1055—42no—
256C22×SD16—131no—
257#555—24no—
258#555—24no—
259C2×C4⋊Q8C2×D1311yescharacteristic
260C2×#124—22no—
261C2×C22⋊Q8—132no—
262C2×#121—21no—
263C2×#121C2×D1312yes—
264C2×C4×Q8—131no—
265C2×C4×D4C2×D1311yescharacteristic
266C2×C4×D4C2×D1311yescharacteristic
267C2×#117—21no—
268C2×#117C2×D1312yes—
269#477—264no—
270C4×SD16—264no—
271C2×#107—132no—
272C2×#106—131no—
273C2×C4⋊C8—131no—
274C2×#103—132no—
275C2×#103—131no—
276C2×#102—131no—
277C2×#102—132no—
278C2×C22⋊C8—132no—
279C2×C22⋊C8—132no—
280C2×C4×C8—131no—
281#396—262no—
282#390—261no—
283#389—261no—
284#384—131no—
285#380—132no—
286#340—132no—
287#340—132no—
288#340—132no—
289C22×C13—42no—
290C22×C13—42no—
291C22×C13—42no—
292C22×C13—42no—
293C22×C13—42no—
294C22×C13—42no—
295C22×C13—42no—
296C22×C13—42no—
297C22×C13—42no—
298C22×C13—42no—
299C22×C13—81no—
300C22×C13—81no—
301C22×C13—81no—
302C22×C13—81no—
303C22×C13C2×#12011yescharacteristic
304C22×C13#54611yescharacteristic
305C22×C13#54711yescharacteristic
306C22×C13C2×#13511yescharacteristic
307C22×C13C2×#13711yescharacteristic
308C22×C13#57611yescharacteristic
309C22×C13#57711yescharacteristic
310C4×C13—22no—
311C4×C13—42no—
312C4×C13—42no—
313C4×C13—44no—
314C4×C13#45214yes—
315C4×C13#52511yescharacteristic
316C4×C13#53711yescharacteristic
317C4×C13#54811yescharacteristic
318C4×C13#55011yescharacteristic
319Dic13—42no—
320Dic13—81no—
321Dic13—82no—
322C22×Q8—21no—
323C22×Q8—131no—
324C22×D4—22no—
325C22×D4C22⋊D1311yescharacteristic
326C22×D4C22×D1311yescharacteristic
327C23×C4—21no—
328C23×C4C22×D1312yes—
329C2×SD16—262no—
330C2×SD16—262no—
331C2×SD16—262no—
332C22×C8—131no—
333C22×C8—131no—
334C22×C8—132no—
335C4⋊Q8—22no—
336C4⋊Q8C22⋊D1314yes—
337#124—216no—
338C22⋊Q8—264no—
339C22⋊Q8—522no—
340#121—28no—
341#121—24no—
342#121—24no—
343C4×Q8—262no—
344C4×Q8—262no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4C22⋊D1314yes—
349#117—28no—
350#117—24no—
351#117—24no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—131no—
354C2×C4⋊C4—132no—
355C2×C4⋊C4—261no—
356C2×C4⋊C4—262no—
357C2×C4⋊C4—261no—
358C2×C4⋊C4—261no—
359C2×C4⋊C4C22⋊D1311yescharacteristic
360C2×C4⋊C4C22×D1311yescharacteristic
361C2×C4⋊C4C22×D1312yes—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—262no—
366C2×C22⋊C4—262no—
367C2×C22⋊C4C22⋊D1312yes—
368C2×C42—22no—
369C2×C42—261no—
370C2×C42C22×D1311yescharacteristic
371#107—264no—
372#106—262no—
373C4⋊C8—262no—
374#103—262no—
375#103—264no—
376#102—262no—
377#102—522no—
378C22⋊C8—264no—
379C22⋊C8—522no—
380C4×C8—262no—
381#95—262no—
382C2×C13—82no—
383C2×C13—82no—
384C2×C13#240711yescharacteristic
385C2×C13C2×#45211yescharacteristic
386C2×C13#301211yescharacteristic
387C2×C13#330511yescharacteristic
388C2×C13#332911yescharacteristic
389C2×C13#334011yescharacteristic
390C2×C13#335711yescharacteristic
391C24—21no—
392C24C2×C22⋊D1312yes—
393C2×Q8—24no—
394C2×Q8—81no—
395C2×Q8—81no—
396C2×Q8—132no—
397C2×Q8—261no—
398C2×Q8—261no—
399C2×Q8—261no—
400C2×Q8—261no—
401C2×Q8—261no—
402C2×D4—28no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—82no—
412C2×D4—82no—
413C2×D4C2×C22⋊D1312yes—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4—262no—
428C22×C4C2×C22⋊D1312yes—
429C22×C4C2×C22⋊D1311yescharacteristic
430C22×C4C2×C22⋊D1311yescharacteristic
431C22×C4C23×D1311yescharacteristic
432SD16—268no—
433C2×C8—132no—
434C2×C8—261no—
435C2×C8—261no—
436C2×C8—262no—
437C2×C8—261no—
438C2×C8—262no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—262no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—262no—
447C4⋊C4—262no—
448C4⋊C4—261no—
449C4⋊C4—261no—
450C4⋊C4—524no—
451C4⋊C4—522no—
452C4⋊C4—522no—
453C4⋊C4—1041no—
454C4⋊C4C2×C22⋊D1312yes—
455C4⋊C4C2×C22⋊D1314yes—
456C22⋊C4—28no—
457C22⋊C4—28no—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—524no—
461C22⋊C4—1042no—
462C42—28no—
463C42—522no—
464C42C2×C22⋊D1312yes—
465C42C2×C22⋊D1312yes—
466C13#2412111yescharacteristic, complemented, Sylow
467C23—22no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23C22×C22⋊D1311yescharacteristic
482Q8—84no—
483Q8—262no—
484Q8—262no—
485Q8—521no—
486Q8—521no—
487D4—22no—
488D4—22no—
489D4—41no—
490D4—41no—
491D4—44no—
492D4—88no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—48no—
509C2×C4—262no—
510C2×C4—521no—
511C2×C4—521no—
512C2×C4—522no—
513C2×C4—522no—
514C2×C4—521no—
515C2×C4—522no—
516C2×C4—521no—
517C2×C4—521no—
518C2×C4#8820412yes—
519C2×C4#8820512yes—
520C2×C4#8820712yes—
521C2×C4#8820712yes—
522C2×C4#41×D1311yescharacteristic
523C2×C4#41×D1311yescharacteristic
524C2×C4#8825611yescharacteristic
525C2×C4#8825711yescharacteristic
526C2×C4C22×C22⋊D1311yescharacteristic
527C2×C4C22×C22⋊D1311yescharacteristic
528C8—262no—
529C8—521no—
530C8—522no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22C2×#8820411yescharacteristic
546C22C2×#8820511yescharacteristic
547C22#1171952911yescharacteristic
548C22#1171953411yescharacteristic
549C22#1171954011yescharacteristic
550C22#1171954111yescharacteristic
551C22C2×#8820711yescharacteristic
552C4—22no—
553C4—44no—
554C4—42no—
555C4—42no—
556C4—522no—
557C4—1041no—
558C4—1042no—
559C4#1171890014yes—
560C4#1171953311yescharacteristic
561C4#1171953611yescharacteristic
562C4#1171953811yescharacteristic
563C4#1171953911yescharacteristic
564C2—82no—
565C2—82no—
566C2#1311817511yescharacteristic
567C2C2×#1171890011yescharacteristic
568C2#1312414011yescharacteristic
569C2#1312678011yescharacteristic
570C2#1312712411yescharacteristic
571C2#1312724911yescharacteristic
572C2#1312745611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#555C2
socleC23×C13C22×D4
hypercenterC2×#555D13
hypocenterC13#24121
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#11718752C2semidirect
2. C2×C4×#6105C2semidirect
3. #13119758C2semidirect
4. #13116015C2semidirect
5. #13115839C2semidirect
6. #13115798C2semidirect
7. #13115631C2semidirect
8. #13115148C2semidirect
9. #13115035C2semidirect
10. #13114836C2semidirect
466. C13#24121semidirect

Maximal subgroups

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

subgroupindex
C2×#117187522
C2×C4×#61052
#131197582
#131160152
#131158392
#131157982
#131156312
#131151482
#131150352
#131148362
C2×C13×#5552
#2412113