Finite Group Databasebeta

← #15873476

Subgroups — #15873476

Order 3328.

858 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718366C211yesmaximal, characteristic
2#13117241C211yesmaximal, characteristic
3D13×#382C211yesmaximal, characteristic
4#13115607C212yesmaximal, complemented
5#13115603C212yesmaximal, complemented
6#13115030C212yesmaximal
7#13115025C212yesmaximal
8#13115005C211yesmaximal, characteristic, complemented
9#13115004C211yesmaximal, characteristic, complemented
10#13114971C211yesmaximal, characteristic, complemented
11C13×#1836C211yesmaximal, characteristic, complemented
12C2×#88146—21no—
13C2×C4⋊C4×D13C2211yescharacteristic
14C2×C4⋊C4×D13C2211yescharacteristic
15C2×C42×D13C2211yescharacteristic
16C2×C13×#97C2211yescharacteristic
17C13×#384C2211yescharacteristic
18C13×#382C2211yescharacteristic
19C2×#88060C2212yes—
20C2×#88058C2212yes—
21C2×#88057C2212yes—
22C2×#88054C2212yes—
23#11718648—21no—
24#11718648C2212yes—
25#11718638—21no—
26#11718638C2211yescharacteristic
27#11718638C2211yescharacteristic
28C4⋊C4×Dic13—21no—
29C4⋊C4×Dic13C2212yes—
30C2×#88048C2212yes—
31C2×#88047C2212yes—
32#11718597C2211yescharacteristic
33#11718596C2211yescharacteristic
34C2×#88043C2211yescharacteristic
35#11718366C418yescomplemented
36D13×#95—21no—
37D13×#95—21no—
38#11718311—21no—
39#11718311—21no—
40C13×#340C2212yes—
41C13×#340C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C22×C4×D13—21no—
45C22×C4×D13—21no—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13C2311yescharacteristic
49C22×C8×C13C2312yes—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4C2311yescharacteristic
53C2×C13×C4⋊C4C2311yescharacteristic
54C2×C13×C4⋊C4C2312yes—
55C2×C42×C13C2311yescharacteristic
56C2×#6103—22no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13C2311yescharacteristic
60C2×C4⋊Dic13C2311yescharacteristic
61C2×C4⋊Dic13C2312yes—
62C2×#6101—21no—
63C2×#6101—21no—
64C2×C4×Dic13—22no—
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13C2311yescharacteristic
68C22×#1055C2312yes—
69#88146—44no—
70C4⋊C4×D13—42no—
71C4⋊C4×D13—42no—
72C42×D13C2×C414yes—
73C42×D13Q814yes—
74C13×#97C2×C414yescomplemented
75C13×#95—21no—
76C13×#95—21no—
77#88071—21no—
78#88071—21no—
79#88071—21no—
80#88071—21no—
81#88071—21no—
82#88071—21no—
83#88071—22no—
84#88071—22no—
85#88060C2×C418yes—
86#88058—42no—
87#88057—42no—
88#88054C2×C418yescomplemented
89#88048—42no—
90#88047—42no—
91#88043C2×C414yescomplemented
92#21986—131nomaximal, Sylow
93C23×D13C2×D411yescharacteristic
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2411yescharacteristic
100C22×Dic13—21no—
101C22×Dic13—21no—
102C22×Dic13—22no—
103C22×Dic13C2×D411yescharacteristic
104C22×Dic13C2×D411yescharacteristic
105C22×Dic13C2×D411yescharacteristic
106C2×C4×D13—22no—
107C2×C4×D13—22no—
108C2×C4×D13—22no—
109C2×C4×D13—22no—
110C2×C4×D13—41no—
111C2×C4×D13—41no—
112C2×C4×D13—42no—
113C2×C4×D13—42no—
114C2×C4×D13—42no—
115C2×C4×D13—42no—
116C2×C4×D13—42no—
117C2×C4×D13—42no—
118C2×C4×D13C4⋊C414yes—
119C2×C4×D13C4⋊C414yes—
120C2×C4×D13C22×C412yes—
121C2×C4×D13C2×Q812yes—
122C2×C8×C13—22no—
123C2×C8×C13—22no—
124C2×C8×C13C22×C414yes—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—24no—
128C13×C4⋊C4—42no—
129C13×C4⋊C4—42no—
130C42×C13C22×C412yes—
131C42×C13C2×Q812yes—
132#6103—44no—
133C4⋊Dic13—22no—
134C4⋊Dic13—22no—
135C4⋊Dic13—22no—
136C4⋊Dic13—22no—
137C4⋊Dic13—42no—
138C4⋊Dic13—42no—
139#6101—42no—
140#6101—42no—
141C4×Dic13—44no—
142C4×Dic13C4⋊C414yes—
143C4×Dic13C4⋊C414yes—
144C4×Dic13C22×C412yes—
145C4×Dic13C2×Q812yes—
146C2×#1055—22no—
147C2×#1055—22no—
148C2×#1055C22×C414yes—
149C2×#432—131no—
150#2285—131no—
151C2×#382—131no—
152#1949—132no—
153#1949—132no—
154#1853—132no—
155#1852—132no—
156#1847—131no—
157#1847—131no—
158#1836—131no—
159#1836D1311yescharacteristic, complemented
160C23×C13C22×D411yescharacteristic
161C22×D13—21no—
162C22×D13—21no—
163C22×D13—21no—
164C22×D13—21no—
165C22×D13C2×C4⋊C412yes—
166C22×D13AGL(1,ℤ/8)12yes—
167C22×D13#13712yes—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—42no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13C2×C4⋊C412yes—
182C2×C4×C13C2×C4⋊C412yes—
183C2×C4×C13C23×C411yescharacteristic
184C2×C4×C13C22×Q811yescharacteristic
185C2×C4×C13H(5,𝔽2)12yes—
186C2×C4×C132−1+412yes—
187C2×Dic13—21no—
188C2×Dic13—21no—
189C2×Dic13—21no—
190C2×Dic13—21no—
191C2×Dic13—21no—
192C2×Dic13—21no—
193C2×Dic13—41no—
194C2×Dic13—41no—
195C2×Dic13—42no—
196C2×Dic13—42no—
197C2×Dic13—41no—
198C2×Dic13—41no—
199C2×Dic13—42no—
200C2×Dic13—41no—
201C2×Dic13—41no—
202C2×Dic13C2×C4⋊C412yes—
203C2×Dic13C2×C4⋊C412yes—
204C2×Dic13C2×C4⋊C412yes—
205C4×D13—28no—
206C4×D13—24no—
207C4×D13—24no—
208C4×D13—44no—
209C4×D13—84no—
210C4×D13—84no—
211C8×C13—24no—
212#1055—24no—
213C2×#117—261no—
214C22×C4⋊C4—131no—
215C22×C4⋊C4—131no—
216C22×C42—131no—
217#432—138no—
218C2×#107—132no—
219C2×#107—132no—
220C2×#106—132no—
221C2×#106—132no—
222C2×C4⋊C8—132no—
223C2×C22⋊C8—132no—
224C2×#97—131no—
225C2×#97C2×D1311yescharacteristic
226#384—131no—
227#384C2×D1311yescharacteristic
228#382—131no—
229#382—131no—
230#382—131no—
231#382—261no—
232#382—261no—
233#382—261no—
234#382C2×D1311yescharacteristic
235#380—132no—
236#380—261no—
237C4×C4⋊C4—132no—
238C4×C4⋊C4—261no—
239C2×#95—261no—
240C2×#95—261no—
241#340—132no—
242#340—132no—
243#340C2×D1312yes—
244#340C2×D1312yes—
245C22×C13C22×C4⋊C411yescharacteristic
246C22×C13#53511yescharacteristic
247C22×C13#53611yescharacteristic
248C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
249C22×C13C2×#13711yescharacteristic
250C22×C13#57511yescharacteristic
251C22×C13#57511yescharacteristic
252C2×D13—22no—
253C2×D13—22no—
254C2×D13—22no—
255C2×D13—22no—
256C2×D13—22no—
257C2×D13—22no—
258C2×D13#42814yes—
259C4×C13—22no—
260C4×C13—22no—
261C4×C13—81no—
262C4×C13—81no—
263C4×C13—82no—
264C4×C13#52012yes—
265C4×C13#54412yes—
266Dic13—22no—
267Dic13—22no—
268Dic13—22no—
269Dic13—81no—
270Dic13—82no—
271Dic13—81no—
272C23×C4—131no—
273C23×C4—131no—
274C23×C4—131no—
275C23×C4—261no—
276C23×C4—261no—
277C22×C8—132no—
278C22×C8C22×D1312yes—
279#117—524no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—131no—
283C2×C4⋊C4—131no—
284C2×C4⋊C4—132no—
285C2×C4⋊C4—261no—
286C2×C4⋊C4—261no—
287C2×C4⋊C4—261no—
288C2×C4⋊C4—261no—
289C2×C4⋊C4—522no—
290C2×C4⋊C4—522no—
291C2×C4⋊C4C22×D1311yescharacteristic
292C2×C4⋊C4C22×D1311yescharacteristic
293C2×C4⋊C4C22×D1312yes—
294C2×C22⋊C4—262no—
295C2×C42—131no—
296C2×C42—131no—
297C2×C42—131no—
298C2×C42—134no—
299C2×C42—134no—
300C2×C42—262no—
301C2×C42C22×D1311yescharacteristic
302#107—522no—
303#107—522no—
304#106—522no—
305#106—522no—
306C4⋊C8—138no—
307C22⋊C8—138no—
308#97—134no—
309#97C4×D1314yescomplemented
310#95—21no—
311#95—21no—
312#95—261no—
313#95—261no—
314#95—261no—
315#95—261no—
316#95—262no—
317#95—262no—
318#95—261no—
319#95—261no—
320C2×C13#231711yescharacteristic
321C2×C13C2×#42811yescharacteristic
322C2×C13#291111yescharacteristic
323C2×C13#321311yescharacteristic
324C2×C13#321511yescharacteristic
325C2×C13#323411yescharacteristic
326C2×C13#323611yescharacteristic
327D13—24no—
328C24—131no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—131no—
333C22×C4—131no—
334C22×C4—131no—
335C22×C4—134no—
336C22×C4—132no—
337C22×C4—132no—
338C22×C4—134no—
339C22×C4—262no—
340C22×C4—262no—
341C22×C4—262no—
342C22×C4—262no—
343C22×C4—261no—
344C22×C4—261no—
345C22×C4—262no—
346C22×C4—521no—
347C22×C4—521no—
348C22×C4—522no—
349C22×C4—522no—
350C22×C4—522no—
351C22×C4—522no—
352C22×C4—522no—
353C22×C4—522no—
354C22×C4D4×D1311yescharacteristic
355C22×C4D4×D1311yescharacteristic
356C22×C4C23×D1311yescharacteristic
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—134no—
360C2×C8—262no—
361C2×C8—262no—
362C2×C8C2×C4×D1314yes—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—24no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—262no—
369C4⋊C4—262no—
370C4⋊C4—262no—
371C4⋊C4—262no—
372C4⋊C4—522no—
373C4⋊C4—522no—
374C4⋊C4—522no—
375C4⋊C4—522no—
376C22⋊C4—524no—
377C42—134no—
378C42—134no—
379C42—132no—
380C42—132no—
381C42—524no—
382C42C2×C4×D1312yes—
383C42Q8×D1312yes—
384C13#2198611yescharacteristic, complemented, Sylow
385C23—132no—
386C23—132no—
387C23—132no—
388C23—261no—
389C23—261no—
390C23—261no—
391C23—261no—
392C23C2×D4×D1311yescharacteristic
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—132no—
407C2×C4—132no—
408C2×C4—132no—
409C2×C4—268no—
410C2×C4—261no—
411C2×C4—261no—
412C2×C4—261no—
413C2×C4—261no—
414C2×C4—261no—
415C2×C4—261no—
416C2×C4—264no—
417C2×C4—264no—
418C2×C4—524no—
419C2×C4—522no—
420C2×C4—521no—
421C2×C4—521no—
422C2×C4—521no—
423C2×C4—522no—
424C2×C4—521no—
425C2×C4—521no—
426C2×C4—521no—
427C2×C4—522no—
428C2×C4—1044no—
429C2×C4—1044no—
430C2×C4C4⋊C4×D1312yes—
431C2×C4C4⋊C4×D1312yes—
432C2×C4C22×C4×D1311yescharacteristic
433C2×C4C2×Q8×D1311yescharacteristic
434C2×C4#8825612yes—
435C2×C4#8825712yes—
436C8—24no—
437C8—264no—
438C22—134no—
439C22—262no—
440C22—262no—
441C22—262no—
442C22—262no—
443C22—262no—
444C22—262no—
445C22C2×C4⋊C4×D1311yescharacteristic
446C22#1171937911yescharacteristic
447C22#1171938011yescharacteristic
448C22D13×AGL(1,ℤ/8)11yescharacteristic
449C22#1171947811yescharacteristic
450C22D13×#13711yescharacteristic
451C22#1171948211yescharacteristic
452C4—22no—
453C4—22no—
454C4—82no—
455C4—81no—
456C4—81no—
457C4—262no—
458C4—262no—
459C4—262no—
460C4—1042no—
461C4—1041no—
462C4—1041no—
463C4#1171922812yes—
464C4#1171939412yes—
465C2—264no—
466C2#1311746111yescharacteristic
467C2D13×#42811yescharacteristic
468C2#1312342311yescharacteristic
469C2#1312582411yescharacteristic
470C2#1312584011yescharacteristic
471C2#1312602111yescharacteristic
472C2#1312603711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1836C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1836D13
hypocenterC13#21986
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
4. #13115607C2semidirect
5. #13115603C2semidirect
8. #13115005C2semidirect
9. #13115004C2semidirect
10. #13114971C2semidirect
11. C13×#1836C2semidirect
35. #11718366C4semidirect
74. C13×#97C2×C4semidirect
88. #88054C2×C4semidirect
91. #88043C2×C4semidirect
159. #1836D13semidirect
309. #97C4×D13semidirect
384. C13#21986semidirect

Maximal subgroups

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

subgroupindex
C2×#117183662
#131172412
D13×#3822
#131156072
#131156032
#131150302
#131150252
#131150052
#131150042
#131149712
C13×#18362
#2198613