Finite Group Databasebeta

← #15907493

Subgroups — #15907493

Order 3328.

800 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119133C211yesmaximal, characteristic
2#13116398C211yesmaximal, characteristic, complemented
3#13116313C211yesmaximal, characteristic, complemented
4#13116272C211yesmaximal, characteristic, complemented
5#13116262C211yesmaximal, characteristic, complemented
6#13115428C211yesmaximal, characteristic, complemented
7#13115414C211yesmaximal, characteristic, complemented
8#13115134C211yesmaximal, characteristic
9#13115029C211yesmaximal, characteristic, complemented
10#13115029C211yesmaximal, characteristic, complemented
11#13114928C211yesmaximal, characteristic, complemented
12#13114922C211yesmaximal, characteristic, complemented
13#13114867C211yesmaximal, characteristic, complemented
14#13114555C211yesmaximal, characteristic, complemented
15D4×C13×C4⋊C4C211yesmaximal, characteristic
16C2×C4×D4×C13—21no—
17C2×C4×D4×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C13×#389—21no—
23C13×#385—21no—
24C13×#385—21no—
25C13×#384C2211yescharacteristic
26C13×#380C2211yescharacteristic
27C13×#380C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29#11718883—21no—
30#11718873C2211yescharacteristic
31#11718873C2211yescharacteristic
32#11718873C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36#11718639—21no—
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718613—21no—
42#11718605—21no—
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45#11718121C2211yescharacteristic
46#11718121C2211yescharacteristic
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D4×C13D411yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13—21no—
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C4×D4×C13—22no—
65C4×D4×C13—22no—
66C4×D4×C13—44no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—41no—
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C42×C13—21no—
85C2×C42×C13C2311yescharacteristic
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89C2×C22⋊Dic13—21no—
90#88180—22no—
91#88180—22no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C2×#6099—22no—
100C2×#6099—22no—
101C2×#6099—41no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114C22⋊#1055—22no—
115C22⋊#1055—22no—
116C22⋊#1055—41no—
117#88048—22no—
118#88048—41no—
119#88048—41no—
120#88047—22no—
121#24949—131nomaximal, Sylow
122C24×C13C2×D411yescharacteristic
123C24×C13C2×D411yescharacteristic
124C2×D4×C13—22no—
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—42no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—81no—
146C22×C4×C13—81no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4112yes—
152C22×C4×C13#4112yes—
153C22×C4×C13C2411yescharacteristic
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4—42no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4—81no—
170C13×C4⋊C4#4112yes—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—42no—
174C13×C22⋊C4—42no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—42no—
178C22⋊Dic13—42no—
179C22⋊Dic13—42no—
180C22⋊Dic13—81no—
181C22⋊Dic13—81no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190#6101—42no—
191#6101—81no—
192C4×Dic13—42no—
193#6099—44no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055#4112yes—
206#2485—131no—
207D4×C4⋊C4D1311yescharacteristic
208#2100—131no—
209#2084—131no—
210#2077—131no—
211#2075—131no—
212#1921—131no—
213#1919—131no—
214#1870—131no—
215#1853—131no—
216#1853—131no—
217#1825—131no—
218#1823—131no—
219#1809—131no—
220#1736—131no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13#12312yes—
234C23×C13AGL(1,ℤ/8)12yes—
235C23×C13C22×D411yescharacteristic
236D4×C13—28no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—22no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—84no—
268C2×C4×C13—84no—
269C2×C4×C13#12312yes—
270C2×C4×C13#13712yes—
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13H(5,𝔽2)11yescharacteristic
276C2×C4×C132−1+411yescharacteristic
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289#1055—22no—
290#1055—41no—
291#1055—41no—
292#1055—41no—
293C22×M16—131no—
294C2×C4×D4—21no—
295C2×C4×D4C2×D1311yescharacteristic
296C2×#117—131no—
297C22×C4⋊C4C2×D1311yescharacteristic
298C22×C4⋊C4C2×D1311yescharacteristic
299C2×#107—131no—
300C2×#106—131no—
301C2×#106—131no—
302C2×#106—131no—
303C2×C22⋊C8—131no—
304C2×C22⋊C8—131no—
305C2×C22⋊C8—131no—
306#397—261no—
307#394—261no—
308#389—21no—
309#389—131no—
310#389—131no—
311#388—261no—
312#387—261no—
313#385—21no—
314#385—21no—
315#384C2×D1311yescharacteristic
316#380—131no—
317#380—131no—
318#380—131no—
319#380C2×D1311yescharacteristic
320#380C2×D1311yescharacteristic
321C4×C4⋊C4C2×D1311yescharacteristic
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#336—131no—
335#336—131no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13C2×#12311yescharacteristic
351C22×C13#54611yescharacteristic
352C22×C13#54711yescharacteristic
353C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C13C2×#13711yescharacteristic
355C22×C13#57711yescharacteristic
356C22×C13#57711yescharacteristic
357C4×C13—22no—
358C4×C13—22no—
359C4×C13—41no—
360C4×C13—41no—
361C4×C13—42no—
362C4×C13—81no—
363C4×C13—81no—
364C4×C13—81no—
365C4×C13#52911yescharacteristic
366C4×C13#53911yescharacteristic
367C4×C13#55111yescharacteristic
368C4×C13#55211yescharacteristic
369Dic13—81no—
370Dic13—81no—
371Dic13—81no—
372Dic13—81no—
373C22×D4C22⋊D1311yescharacteristic
374C23×C4—21no—
375C23×C4—21no—
376C23×C4C22×D1311yescharacteristic
377C23×C4C22×D1311yescharacteristic
378C2×M16—262no—
379C2×M16—262no—
380C2×M16—521no—
381C22×C8—131no—
382C22×C8—131no—
383C22×C8—131no—
384C22×C8—131no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—44no—
388#117—262no—
389#117—262no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—41no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—131no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4C22⋊D1311yescharacteristic
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—261no—
412C2×C22⋊C4—261no—
413C2×C22⋊C4—261no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4C22⋊D1311yescharacteristic
416C2×C22⋊C4C22⋊D1311yescharacteristic
417C2×C42—21no—
418C2×C42—261no—
419C2×C42C22×D1311yescharacteristic
420#107—262no—
421#106—262no—
422#106—521no—
423#106—521no—
424C22⋊C8—262no—
425C22⋊C8—262no—
426C22⋊C8—521no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434#95—261no—
435C2×C13—42no—
436C2×C13—42no—
437C2×C13#241911yescharacteristic
438C2×C13#309211yescharacteristic
439C2×C13#309911yescharacteristic
440C2×C13#331011yescharacteristic
441C2×C13#332911yescharacteristic
442C2×C13#334511yescharacteristic
443C2×C13#335611yescharacteristic
444C24C2×C22⋊D1311yescharacteristic
445C24C2×C22⋊D1311yescharacteristic
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—81no—
468C22×C4—81no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4#612712yes—
474C22×C4#612712yes—
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C2×C22⋊D1311yescharacteristic
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C23×D1311yescharacteristic
480M16—524no—
481C2×C8—132no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—81no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—522no—
514C4⋊C4—1041no—
515C4⋊C4#612912yes—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—522no—
521C22⋊C4—522no—
522C22⋊C4—1041no—
523C22⋊C4—1041no—
524C42—21no—
525C42—21no—
526C42—42no—
527C42—522no—
528C13#2494911yescharacteristic, complemented, Sylow
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23#8818312yes—
542C23#8818612yes—
543C23C22×C22⋊D1311yescharacteristic
544D4—28no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4—84no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4#8818312yes—
590C2×C4#8819612yes—
591C2×C4C2×#612711yescharacteristic
592C2×C4C2×#612711yescharacteristic
593C2×C4C2×#612911yescharacteristic
594C2×C4#8825111yescharacteristic
595C2×C4#41×D1311yescharacteristic
596C2×C4#8825711yescharacteristic
597C8—262no—
598C8—521no—
599C8—521no—
600C8—521no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22C2×#8818311yescharacteristic
616C22C2×#8818611yescharacteristic
617C22#1171951111yescharacteristic
618C22C2×#8819611yescharacteristic
619C22#1171952911yescharacteristic
620C22#1171954111yescharacteristic
621C22#1171954211yescharacteristic
622C4—22no—
623C4—22no—
624C4—41no—
625C4—42no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—81no—
630C4—1041no—
631C4—1041no—
632C4—1041no—
633C4—1041no—
634C4#1171924311yescharacteristic
635C4#1171924611yescharacteristic
636C4#1171926111yescharacteristic
637C4#1171926911yescharacteristic
638C2—42no—
639C2—42no—
640C2#1311830711yescharacteristic
641C2#1312475911yescharacteristic
642C2#1312482511yescharacteristic
643C2#1312685711yescharacteristic
644C2#1312713011yescharacteristic
645C2#1312730611yescharacteristic
646C2#1312745111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterD4×C4⋊C4D13
hypocenterC13#24949
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13116398C2semidirect
3. #13116313C2semidirect
4. #13116272C2semidirect
5. #13116262C2semidirect
6. #13115428C2semidirect
7. #13115414C2semidirect
9. #13115029C2semidirect
10. #13115029C2semidirect
11. #13114928C2semidirect
12. #13114922C2semidirect
13. #13114867C2semidirect
14. #13114555C2semidirect
528. C13#24949semidirect

Maximal subgroups

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

subgroupindex
#131191332
#131163982
#131163132
#131162722
#131162622
#131154282
#131154142
#131151342
#131150292
#131149282
#131149222
#131148672
#131145552
D4×C13×C4⋊C42
#2494913