Finite Group Databasebeta

← #15935632

Subgroups — #15935632

Order 3328.

728 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117839C211yesmaximal, characteristic
2#13116245C211yesmaximal, characteristic, complemented
3#13116214C211yesmaximal, characteristic, complemented
4#13116032C211yesmaximal, characteristic
5#13116032C211yesmaximal, characteristic
6#13115597C211yesmaximal, characteristic, complemented
7#13115561C211yesmaximal, characteristic, complemented
8#13115444C211yesmaximal, characteristic
9#13115421C211yesmaximal, characteristic, complemented
10#13115411C211yesmaximal, characteristic, complemented
11#13115103C211yesmaximal, characteristic, complemented
12#13115028C211yesmaximal, characteristic
13#13114924C211yesmaximal, characteristic
14C4×#88050C211yesmaximal, characteristic, complemented
15C13×#2496C211yesmaximal, characteristic
16C2×C13×#126—21no—
17C22×C4⋊Dic13C2211yescharacteristic
18C2×#88178C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C13×#400—21no—
21C13×#397—21no—
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#387—21no—
25C13×#384C2211yescharacteristic
26C13×#380C2211yescharacteristic
27C13×#380C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88050C2211yescharacteristic
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40#11718607—21no—
41C22⋊C4×Dic13—21no—
42C4×C4⋊Dic13C2211yescharacteristic
43#11718590C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718316—21no—
48#11718308—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C22×Dic26C2311yescharacteristic
62C13×#126—44no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4D411yescharacteristic
74C2×C13×C22⋊C4D411yescharacteristic
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C22⋊Dic13—21no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—41no—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85#88178—22no—
86#88178—22no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C4×Dic26—22no—
97C4×Dic26—41no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95D411yescharacteristic
104C13×#95D411yescharacteristic
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109C22⋊#1055—22no—
110C22⋊#1055—41no—
111#88050—22no—
112#88050—22no—
113#88050—22no—
114#88050—41no—
115#88048—22no—
116#88048—22no—
117#88048—22no—
118#88048—41no—
119C4⋊#1055—22no—
120C4×#1055—41no—
121#27034—131nomaximal, Sylow
122C24×C13C2×D411yescharacteristic
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
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×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2411yescharacteristic
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—42no—
144C22×Dic13—42no—
145C22×Dic13—81no—
146C2×Dic26—21no—
147C2×Dic26—21no—
148C2×Dic26—21no—
149C2×Dic26—21no—
150C2×Dic26—21no—
151C2×Dic26#4112yes—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4—42no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4—42no—
164C13×C22⋊C4—41no—
165C13×C22⋊C4—42no—
166C13×C22⋊C4—42no—
167C13×C22⋊C4SD1614yes—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—42no—
173C22⋊Dic13—24no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—42no—
179C4⋊Dic13#4112yes—
180C4⋊Dic13#4112yes—
181#6101—24no—
182#6101—42no—
183#6101—81no—
184C4×Dic13—42no—
185C4×Dic13—81no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055#4112yes—
198#2496D1311yescharacteristic
199#2360—131no—
200#2072—131no—
201#2066—131no—
202#2035—131no—
203#2035—131no—
204#1948—131no—
205#1941—131no—
206#1923—131no—
207#1920—131no—
208#1919—131no—
209#1865—131no—
210#1853—131no—
211#1824—131no—
212C4×#103—131no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13C2×SD1612yes—
220C23×C13C22×D411yescharacteristic
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13C2×SD1612yes—
251C2×C4×C13C2×SD1612yes—
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13H(5,𝔽2)11yescharacteristic
257C2×C4×C132−1+411yescharacteristic
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—84no—
271Dic26—22no—
272Dic26—22no—
273Dic26—41no—
274Dic26—41no—
275#1055—22no—
276#1055—41no—
277#1055—41no—
278#1055—41no—
279C2×#126—21no—
280C2×C22⋊Q8—131no—
281C2×C4×Q8—131no—
282C22×C4⋊C4—131no—
283C2×#106—131no—
284C2×#106—131no—
285C2×#106—131no—
286C2×#106—131no—
287C2×C4⋊C8—131no—
288C2×#103—131no—
289C2×#103—131no—
290C2×#103—131no—
291C2×#103—131no—
292C2×C22⋊C8—131no—
293C2×C22⋊C8—131no—
294C2×C4×C8—131no—
295#400—21no—
296#397—21no—
297#391—131no—
298#389—131no—
299#389—261no—
300#389C2×D1311yescharacteristic
301#389C2×D1311yescharacteristic
302#387—21no—
303#387—261no—
304#385—261no—
305#384C2×D1311yescharacteristic
306#380C2×D1311yescharacteristic
307#380C2×D1311yescharacteristic
308C4×C4⋊C4—131no—
309C4×C4⋊C4C2×D1311yescharacteristic
310C4×C22⋊C4—261no—
311C4×C22⋊C4C2×D1311yescharacteristic
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#336—131no—
321#336—131no—
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13#52511yescharacteristic
330C22×C13#54611yescharacteristic
331C22×C13#54711yescharacteristic
332C22×C13C22×SD1611yescharacteristic
333C22×C13#57511yescharacteristic
334C22×C13#57711yescharacteristic
335C22×C13#57811yescharacteristic
336C4×C13—22no—
337C4×C13—22no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—81no—
342C4×C13—81no—
343C4×C13—81no—
344C4×C13—81no—
345C4×C13#52911yescharacteristic
346C4×C13#53911yescharacteristic
347C4×C13#55311yescharacteristic
348C4×C13#55611yescharacteristic
349Dic13—42no—
350Dic13—42no—
351Dic13—42no—
352Dic13—81no—
353C22×Q8—131no—
354C23×C4—261no—
355C23×C4C22×D1311yescharacteristic
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—131no—
360#126—44no—
361C22⋊Q8—262no—
362C22⋊Q8—262no—
363C4×Q8—262no—
364C4×Q8—521no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—262no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—521no—
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4C22⋊D1311yescharacteristic
386C2×C22⋊C4C22⋊D1311yescharacteristic
387C2×C42—21no—
388C2×C42—261no—
389C2×C42—261no—
390C2×C42C22×D1311yescharacteristic
391C2×C42C22×D1311yescharacteristic
392#106—262no—
393#106—262no—
394#106—262no—
395#106—521no—
396C4⋊C8—262no—
397#103—262no—
398#103—262no—
399#103—262no—
400#103—521no—
401C22⋊C8—262no—
402C22⋊C8—521no—
403C4×C8—521no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95C22⋊D1311yescharacteristic
414#95C22⋊D1311yescharacteristic
415C2×C13—42no—
416C2×C13#246611yescharacteristic
417C2×C13#310311yescharacteristic
418C2×C13#312011yescharacteristic
419C2×C13#329811yescharacteristic
420C2×C13#331111yescharacteristic
421C2×C13#333511yescharacteristic
422C2×C13#335211yescharacteristic
423C24C2×C22⋊D1311yescharacteristic
424C2×Q8—132no—
425C2×Q8—261no—
426C2×Q8—261no—
427C2×Q8—261no—
428C2×Q8—261no—
429C2×Q8—261no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—522no—
445C22×C4—522no—
446C22×C4—1041no—
447C22×C4C2×C22⋊D1311yescharacteristic
448C22×C4C2×C22⋊D1311yescharacteristic
449C22×C4C2×C22⋊D1311yescharacteristic
450C22×C4C2×C22⋊D1311yescharacteristic
451C22×C4C2×C22⋊D1311yescharacteristic
452C22×C4C23×D1311yescharacteristic
453C2×C8—132no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—132no—
478C4⋊C4—132no—
479C4⋊C4—264no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—522no—
485C4⋊C4—522no—
486C4⋊C4—1041no—
487C22⋊C4—41no—
488C22⋊C4—42no—
489C22⋊C4—42no—
490C22⋊C4—264no—
491C22⋊C4#610514yes—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—42no—
497C42—522no—
498C42—1041no—
499C13#2703411yescharacteristic, complemented, Sylow
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23C2×#610512yes—
507C23C22×C22⋊D1311yescharacteristic
508Q8—262no—
509Q8—262no—
510Q8—521no—
511Q8—521no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—1044no—
554C2×C4C2×#610512yes—
555C2×C4C2×#610512yes—
556C2×C4#41×D1311yescharacteristic
557C2×C4#41×D1311yescharacteristic
558C2×C4#41×D1311yescharacteristic
559C2×C4#41×D1311yescharacteristic
560C2×C4#8825611yescharacteristic
561C2×C4#8825711yescharacteristic
562C8—262no—
563C8—521no—
564C8—521no—
565C8—521no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22C22×#610511yescharacteristic
574C22#1171952711yescharacteristic
575C22#1171952911yescharacteristic
576C22#1171953311yescharacteristic
577C22#1171953411yescharacteristic
578C22#1171954211yescharacteristic
579C22#1171954311yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—522no—
590C4—522no—
591C4—522no—
592C4—1041no—
593C4#1171940711yescharacteristic
594C4#1171941111yescharacteristic
595C4#1171941211yescharacteristic
596C4#1171941411yescharacteristic
597C2—42no—
598C2#1311886811yescharacteristic
599C2#1312486311yescharacteristic
600C2#1312504411yescharacteristic
601C2#1312669511yescharacteristic
602C2#1312686611yescharacteristic
603C2#1312719311yescharacteristic
604C2#1312740511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2496C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2496D13
hypocenterC13#27034
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2496

Complements

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

NH ≅ G/Ntype
2. #13116245C2semidirect
3. #13116214C2semidirect
6. #13115597C2semidirect
7. #13115561C2semidirect
9. #13115421C2semidirect
10. #13115411C2semidirect
11. #13115103C2semidirect
14. C4×#88050C2semidirect
499. C13#27034semidirect

Maximal subgroups

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

subgroupindex
#131178392
#131162452
#131162142
#131160322
#131155972
#131155612
#131154442
#131154212
#131154112
#131151032
#131150282
#131149242
C4×#880502
C13×#24962
#2703413