Finite Group Databasebeta

← #15873316

Subgroups — #15873316

Order 3328.

874 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718498C211yesmaximal, characteristic
2#13117241C211yesmaximal, characteristic
3#13117240C211yesmaximal, characteristic
4#13115597C211yesmaximal, characteristic, complemented
5#13115596C212yesmaximal, complemented
6#13115595C211yesmaximal, characteristic, complemented
7#13115594C211yesmaximal, characteristic, complemented
8#13115593C212yesmaximal, complemented
9#13114868C212yesmaximal
10#13114866C212yesmaximal
11C13×#1948C211yesmaximal, characteristic, complemented
12C22×#6094C2212yes—
13C2×#88146—21no—
14C2×#88126—21no—
15C2×C42×D13C2211yescharacteristic
16C2×C13×#106C2212yes—
17C2×C13×C4⋊C8C2211yescharacteristic
18C13×#384C2211yescharacteristic
19C4×C13×C4⋊C4C2211yescharacteristic
20C2×#88058C2212yes—
21C2×#88054C2212yes—
22#11718648—21no—
23#11718648C2211yescharacteristic
24#11718648C2211yescharacteristic
25#11718648C2212yes—
26#11718638—21no—
27#11718637C2211yescharacteristic
28#11718637C2211yescharacteristic
29C4⋊C4×Dic13—21no—
30C4⋊C4×Dic13C2212yes—
31C2×#88048C2212yes—
32C2×#88047C2212yes—
33#11718596C2211yescharacteristic
34C4×C4⋊Dic13C2211yescharacteristic
35C4×#6101—21no—
36C2×C4⋊#1055C2211yescharacteristic
37#11718498C418yescomplemented
38#11718328—21no—
39#11718311—21no—
40C13×#340C2212yes—
41#11718143C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C22×C4×D13D411yescharacteristic
45C22×C4×D13D411yescharacteristic
46C22×C4×D13C2311yescharacteristic
47C22×C8×C13C2312yes—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4C2311yescharacteristic
51C2×C13×C4⋊C4C2311yescharacteristic
52C2×C13×C4⋊C4C2312yes—
53C2×C42×C13—21no—
54C2×C42×C13C2311yescharacteristic
55C2×#6103—21no—
56C2×#6103—21no—
57C2×#6103—22no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13C2311yescharacteristic
61C2×C4⋊Dic13C2312yes—
62C2×C4⋊Dic13C2311yescharacteristic
63C2×#6101—21no—
64C2×#6101—21no—
65C2×#6101—21no—
66C2×#6101—21no—
67C2×C4×Dic13—21no—
68C2×C4×Dic13—22no—
69C2×C4×Dic13D411yescharacteristic
70C2×C4×Dic13D411yescharacteristic
71C2×C4×Dic13C2311yescharacteristic
72C22×#1055C2312yes—
73C2×#6094—42no—
74C2×#6094—42no—
75C2×#6094C2×C418yes—
76#88146—44no—
77#88126—44no—
78C42×D13C2×C414yes—
79C42×D13Q814yes—
80C13×#106—42no—
81C13×C4⋊C8C2×C414yes—
82C13×#95—21no—
83#88071—21no—
84#88071—21no—
85#88071—21no—
86#88071—22no—
87#88071—22no—
88#88058—42no—
89#88054C2×C418yes—
90#88048—42no—
91#88047—42no—
92C4⋊#1055C2×C414yes—
93#21964—131nomaximal, Sylow
94C23×D13C2×D411yescharacteristic
95C22×C4×C13—22no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2411yescharacteristic
101C22×Dic13—21no—
102C22×Dic13—21no—
103C22×Dic13—22no—
104C22×Dic13C2×D411yescharacteristic
105C22×Dic13C2×D411yescharacteristic
106C22×Dic13C2×D411yescharacteristic
107C2×C4×D13—22no—
108C2×C4×D13—22no—
109C2×C4×D13—21no—
110C2×C4×D13—21no—
111C2×C4×D13—21no—
112C2×C4×D13—21no—
113C2×C4×D13—22no—
114C2×C4×D13—22no—
115C2×C4×D13C4⋊C414yes—
116C2×C4×D13C4⋊C414yes—
117C2×C4×D13C22×C412yes—
118C2×C4×D13C2×Q812yes—
119C2×C8×C13—22no—
120C2×C8×C13—22no—
121C2×C8×C13C22×C414yes—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—22no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—42no—
129C13×C4⋊C4—42no—
130C42×C13—42no—
131C42×C13C22×C412yes—
132C42×C13C2×Q812yes—
133#6103—42no—
134#6103—42no—
135#6103—44no—
136C4⋊Dic13—22no—
137C4⋊Dic13—21no—
138C4⋊Dic13—21no—
139C4⋊Dic13—21no—
140C4⋊Dic13—22no—
141C4⋊Dic13—21no—
142C4⋊Dic13—42no—
143C4⋊Dic13—42no—
144#6101—42no—
145#6101—42no—
146#6101—42no—
147#6101—42no—
148C4×Dic13—42no—
149C4×Dic13—44no—
150C4×Dic13C4⋊C414yes—
151C4×Dic13C4⋊C414yes—
152C4×Dic13C22×C412yes—
153C4×Dic13C2×Q812yes—
154C2×#1055—22no—
155C2×#1055—22no—
156C2×#1055C22×C414yes—
157#6094—48no—
158C2×#423—131no—
159#2285—131no—
160#2285—131no—
161#1948—132no—
162#1948—131no—
163#1948D1311yescharacteristic, complemented
164#1947—131no—
165#1947—131no—
166#1947—132no—
167#1809—132no—
168#1809—132no—
169C23×C13C22×D411yescharacteristic
170C22×D13—21no—
171C22×D13—21no—
172C22×D13—21no—
173C22×D13—21no—
174C22×D13—21no—
175C22×D13—21no—
176C22×D13C2×C4⋊C412yes—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—42no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—42no—
188C2×C4×C13C2×C4⋊C412yes—
189C2×C4×C13C2×C4⋊C412yes—
190C2×C4×C13AGL(1,ℤ/8)12yes—
191C2×C4×C13#13712yes—
192C2×C4×C13C23×C411yescharacteristic
193C2×C4×C13C22×Q811yescharacteristic
194C2×C4×C13H(5,𝔽2)11yescharacteristic
195C2×C4×C13H(5,𝔽2)11yescharacteristic
196C2×C4×C132−1+411yescharacteristic
197C2×C4×C132−1+411yescharacteristic
198C2×Dic13—21no—
199C2×Dic13—21no—
200C2×Dic13—21no—
201C2×Dic13—21no—
202C2×Dic13—42no—
203C2×Dic13—41no—
204C2×Dic13—41no—
205C2×Dic13—41no—
206C2×Dic13—41no—
207C2×Dic13—42no—
208C2×Dic13—41no—
209C2×Dic13—42no—
210C2×Dic13—41no—
211C2×Dic13C2×C4⋊C412yes—
212C2×Dic13C2×C4⋊C412yes—
213C2×Dic13C2×C4⋊C412yes—
214C2×Dic13AGL(1,ℤ/8)12yes—
215C2×Dic13#13712yes—
216C4×D13—22no—
217C4×D13—22no—
218C4×D13—22no—
219C4×D13—22no—
220C4×D13—28no—
221C4×D13—28no—
222C8×C13—24no—
223#1055—24no—
224C22×M16—132no—
225C2×#117—261no—
226C2×#117—261no—
227C22×C42—131no—
228C2×#107—132no—
229C2×#107—132no—
230C2×#106—132no—
231C2×#106C2×D1312yes—
232#423—138no—
233C2×C4⋊C8—132no—
234C2×C4⋊C8—131no—
235C2×C4⋊C8C2×D1311yescharacteristic
236#384—131no—
237#384—131no—
238#384—131no—
239#384C2×D1311yescharacteristic
240#382—261no—
241#382—261no—
242#380—131no—
243#380—131no—
244#380—132no—
245#380—261no—
246#380—261no—
247C4×C4⋊C4—132no—
248C4×C4⋊C4—131no—
249C4×C4⋊C4—261no—
250C4×C4⋊C4—261no—
251C4×C4⋊C4C2×D1311yescharacteristic
252#340—132no—
253#340—132no—
254#340—132no—
255#340C2×D1312yes—
256C22×C13C22×C4⋊C411yescharacteristic
257C22×C13#53711yescharacteristic
258C22×C13#53711yescharacteristic
259C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C13C2×#13711yescharacteristic
262C22×C13C2×#13711yescharacteristic
263C2×D13—22no—
264C2×D13—22no—
265C2×D13—22no—
266C2×D13—41no—
267C2×D13—41no—
268C2×D13—41no—
269C2×D13—41no—
270C4×C13—22no—
271C4×C13—81no—
272C4×C13—81no—
273C4×C13—82no—
274C4×C13#42814yes—
275C4×C13#51811yescharacteristic
276C4×C13#51911yescharacteristic
277C4×C13#54411yescharacteristic
278C4×C13#54411yescharacteristic
279Dic13—22no—
280Dic13—22no—
281Dic13—81no—
282Dic13—82no—
283Dic13—81no—
284Dic13#42814yes—
285C23×C4—131no—
286C23×C4—131no—
287C23×C4—131no—
288C2×M16—138no—
289C2×M16—522no—
290C2×M16—522no—
291C22×C8—132no—
292C22×C8C22×D1312yes—
293#117—524no—
294#117—524no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—131no—
298C2×C4⋊C4—132no—
299C2×C4⋊C4—131no—
300C2×C4⋊C4—261no—
301C2×C4⋊C4—261no—
302C2×C4⋊C4—261no—
303C2×C4⋊C4—261no—
304C2×C4⋊C4—261no—
305C2×C4⋊C4—261no—
306C2×C4⋊C4C22×D1311yescharacteristic
307C2×C4⋊C4C22×D1312yes—
308C2×C4⋊C4C22×D1311yescharacteristic
309C2×C22⋊C4—261no—
310C2×C22⋊C4—261no—
311C2×C22⋊C4—262no—
312C2×C42—21no—
313C2×C42—131no—
314C2×C42—131no—
315C2×C42—131no—
316C2×C42—134no—
317C2×C42—134no—
318C2×C42—262no—
319C2×C42—261no—
320C2×C42C22×D1311yescharacteristic
321#107—522no—
322#107—522no—
323#106—42no—
324#106—522no—
325C4⋊C8—138no—
326C4⋊C8—134no—
327C4⋊C8C4×D1314yes—
328#95—21no—
329#95—262no—
330#95—261no—
331#95—261no—
332#95—262no—
333#95—261no—
334C2×C13#231611yescharacteristic
335C2×C13C2×#42811yescharacteristic
336C2×C13C2×#42811yescharacteristic
337C2×C13#325311yescharacteristic
338C2×C13#325411yescharacteristic
339C2×C13#325411yescharacteristic
340C2×C13#325511yescharacteristic
341D13—42no—
342C24—131no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—131no—
347C22×C4—131no—
348C22×C4—131no—
349C22×C4—134no—
350C22×C4—134no—
351C22×C4—132no—
352C22×C4—132no—
353C22×C4—262no—
354C22×C4—262no—
355C22×C4—262no—
356C22×C4—262no—
357C22×C4—261no—
358C22×C4—261no—
359C22×C4—261no—
360C22×C4—261no—
361C22×C4—261no—
362C22×C4—261no—
363C22×C4—262no—
364C22×C4D4×D1311yescharacteristic
365C22×C4D4×D1311yescharacteristic
366C22×C4C23×D1311yescharacteristic
367M16—528no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—134no—
371C2×C8—262no—
372C2×C8—262no—
373C2×C8C2×C4×D1314yes—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—261no—
383C4⋊C4—262no—
384C4⋊C4—261no—
385C4⋊C4—262no—
386C4⋊C4—261no—
387C4⋊C4—261no—
388C4⋊C4—522no—
389C4⋊C4—522no—
390C4⋊C4—522no—
391C4⋊C4—522no—
392C4⋊C4—522no—
393C4⋊C4—522no—
394C22⋊C4—522no—
395C22⋊C4—522no—
396C22⋊C4—524no—
397C42—42no—
398C42—134no—
399C42—134no—
400C42—132no—
401C42—132no—
402C42—524no—
403C42—522no—
404C42C2×C4×D1312yes—
405C42Q8×D1312yes—
406C13#2196411yescharacteristic, complemented, Sylow
407C23—132no—
408C23—261no—
409C23—261no—
410C23—261no—
411C23—261no—
412C23—261no—
413C23—261no—
414C23C2×D4×D1311yescharacteristic
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—132no—
427C2×C4—132no—
428C2×C4—132no—
429C2×C4—132no—
430C2×C4—132no—
431C2×C4—268no—
432C2×C4—261no—
433C2×C4—261no—
434C2×C4—261no—
435C2×C4—261no—
436C2×C4—262no—
437C2×C4—262no—
438C2×C4—262no—
439C2×C4—268no—
440C2×C4—262no—
441C2×C4—521no—
442C2×C4—521no—
443C2×C4—522no—
444C2×C4—522no—
445C2×C4—521no—
446C2×C4—521no—
447C2×C4—521no—
448C2×C4—521no—
449C2×C4—522no—
450C2×C4C4⋊C4×D1312yes—
451C2×C4C4⋊C4×D1312yes—
452C2×C4#8816812yes—
453C2×C4#8816912yes—
454C2×C4C22×C4×D1311yescharacteristic
455C2×C4#8825111yescharacteristic
456C2×C4C2×Q8×D1311yescharacteristic
457C2×C4#8825411yescharacteristic
458C2×C4#8825611yescharacteristic
459C2×C4#8825711yescharacteristic
460C8—24no—
461C8—264no—
462C22—262no—
463C22—262no—
464C22—262no—
465C22—521no—
466C22—521no—
467C22—521no—
468C22—521no—
469C22C2×C4⋊C4×D1311yescharacteristic
470C22#1171931311yescharacteristic
471C22#1171933411yescharacteristic
472C22C2×#8816811yescharacteristic
473C22C2×#8816911yescharacteristic
474C22D13×AGL(1,ℤ/8)11yescharacteristic
475C22D13×#13711yescharacteristic
476C4—22no—
477C4—81no—
478C4—81no—
479C4—82no—
480C4—134no—
481C4—262no—
482C4—262no—
483C4—1041no—
484C4—1042no—
485C4—1041no—
486C4#1171852214yes—
487C4#1171925011yescharacteristic
488C4#1171927711yescharacteristic
489C4#1171939411yescharacteristic
490C4#1171943411yescharacteristic
491C2—522no—
492C2#1311745111yescharacteristic
493C2D13×#42811yescharacteristic
494C2C2×#1171852211yescharacteristic
495C2#1312621611yescharacteristic
496C2#1312622011yescharacteristic
497C2#1312622111yescharacteristic
498C2#1312622911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1948C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1948D13
hypocenterC13#21964
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
4. #13115597C2semidirect
5. #13115596C2semidirect
6. #13115595C2semidirect
7. #13115594C2semidirect
8. #13115593C2semidirect
11. C13×#1948C2semidirect
37. #11718498C4semidirect
163. #1948D13semidirect
406. C13#21964semidirect

Maximal subgroups

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

subgroupindex
C2×#117184982
#131172412
#131172402
#131155972
#131155962
#131155952
#131155942
#131155932
#131148682
#131148662
C13×#19482
#2196413