Finite Group Databasebeta

← #15875030

Subgroups — #15875030

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718507C211yesmaximal, characteristic
2#13117403C211yesmaximal, characteristic, complemented
3#13117297C211yesmaximal, characteristic
4#13115788C211yesmaximal, characteristic, complemented
5#13115572C212yesmaximal, complemented
6#13115531C212yesmaximal
7#13115462C212yesmaximal
8#13115427C212yesmaximal, complemented
9#13114833C211yesmaximal, characteristic
10#13114691C211yesmaximal, characteristic, complemented
11C13×#1948C211yesmaximal, characteristic, complemented
12C2×#88141—21no—
13C2×C4×D52C2211yescharacteristic
14C2×#88126—21no—
15C2×#88123C2211yescharacteristic
16C2×C13×#106C2212yes—
17C2×C13×C4⋊C8C2211yescharacteristic
18C13×#384C2211yescharacteristic
19C4×C13×C4⋊C4C2211yescharacteristic
20C2×#88061C2212yes—
21C2×#88058C2212yes—
22C2×#88055C2212yes—
23#11718649C2211yescharacteristic
24#11718649C2211yescharacteristic
25C4⋊C4×Dic13—21no—
26C4⋊C4×Dic13C2212yes—
27#11718635—21no—
28#11718634—21no—
29#11718634C2211yescharacteristic
30#11718634C2211yescharacteristic
31#11718634C2212yes—
32C2×#88049C2212yes—
33C4×#6103—21no—
34C42×Dic13C2211yescharacteristic
35C2×C4⋊#1055C2211yescharacteristic
36#11718507C418yescomplemented
37#11718330—21no—
38#11718330—21no—
39C13×#340C2212yes—
40#11718142C2212yes—
41#11718121C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C22×D52C2311yescharacteristic
45C22×C4×D13—21no—
46C22×Dic26—21no—
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—21no—
58C2×#6103—21no—
59C2×#6103—21no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13C2312yes—
62C2×C4⋊Dic13C2311yescharacteristic
63C2×#6101—21no—
64C2×#6101—21no—
65C2×#6101—22no—
66C2×C4×Dic13—22no—
67C2×C4×Dic13D411yescharacteristic
68C2×C4×Dic13D411yescharacteristic
69C2×C4×Dic13D411yescharacteristic
70C2×C4×Dic13D411yescharacteristic
71C2×C4×Dic13C2311yescharacteristic
72C2×C4×Dic13C2311yescharacteristic
73C22×#1055C2312yes—
74#88141—44no—
75C4×D52—22no—
76C4×D52C2×C414yes—
77#88126—44no—
78#88123—22no—
79#88123C2×C414yes—
80C13×#106—42no—
81C13×C4⋊C8C2×C414yes—
82C13×#95—21no—
83#88071—21no—
84#88071—21no—
85#88071—22no—
86#88071—22no—
87#88061C2×C418yes—
88#88058C2×C418yes—
89#88055—42no—
90#88049—42no—
91C4⋊#1055—22no—
92#22116—131nomaximal, Sylow
93C23×D13—21no—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2411yescharacteristic
100C22×Dic13—22no—
101C22×Dic13—21no—
102C22×Dic13C2×D411yescharacteristic
103C22×Dic13C2×D411yescharacteristic
104C22×Dic13C2×D411yescharacteristic
105C22×Dic13C2×D411yescharacteristic
106C2×D52—21no—
107C2×D52—21no—
108C2×D52—21no—
109C2×D52—21no—
110C2×D52—21no—
111C2×D52C22×C412yes—
112C2×C4×D13—24no—
113C2×C4×D13—42no—
114C2×C4×D13—42no—
115C2×Dic26—24no—
116C2×Dic26—42no—
117C2×Dic26—42no—
118C2×C8×C13—22no—
119C2×C8×C13—22no—
120C2×C8×C13C22×C414yes—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—42no—
128C13×C4⋊C4—42no—
129C42×C13—42no—
130C42×C13C22×C412yes—
131C42×C13#4112yes—
132#6103—24no—
133#6103—42no—
134#6103—42no—
135#6103—42no—
136#6103—42no—
137C4⋊Dic13—24no—
138C4⋊Dic13—22no—
139C4⋊Dic13—21no—
140C4⋊Dic13C22×C414yes—
141C4⋊Dic13C22×C412yes—
142#6101—42no—
143#6101—42no—
144#6101—44no—
145C4×Dic13—22no—
146C4×Dic13—22no—
147C4×Dic13—21no—
148C4×Dic13—21no—
149C4×Dic13—21no—
150C4×Dic13—21no—
151C4×Dic13—22no—
152C4×Dic13—41no—
153C4×Dic13—44no—
154C2×#1055—22no—
155C2×#1055—22no—
156C2×#1055—22no—
157C2×#474—131no—
158C4×C4⋊Q8—131no—
159#2293—131no—
160#1988—131no—
161#1948D1311yescharacteristic, complemented
162#1943—132no—
163#1936—132no—
164#1926—132no—
165#1921—132no—
166#1802—131no—
167#1767—131no—
168C23×C13C22×D411yescharacteristic
169C22×D13—22no—
170C22×D13—41no—
171C22×D13—41no—
172C22×D13—41no—
173C22×D13—41no—
174C22×D13—41no—
175C22×D13—41no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—41no—
179C2×C4×C13—42no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—42no—
187C2×C4×C13C4×D412yes—
188C2×C4×C13C4×D412yes—
189C2×C4×C13AGL(1,ℤ/8)12yes—
190C2×C4×C13AGL(1,ℤ/8)12yes—
191C2×C4×C13C23×C411yescharacteristic
192C2×C4×C13C2×#4111yescharacteristic
193C2×C4×C13H(5,𝔽2)11yescharacteristic
194C2×C4×C132−1+411yescharacteristic
195C2×C4×C132−1+411yescharacteristic
196C2×C4×C132−1+411yescharacteristic
197C2×Dic13—21no—
198C2×Dic13—21no—
199C2×Dic13—24no—
200C2×Dic13—22no—
201C2×Dic13—21no—
202C2×Dic13—21no—
203C2×Dic13—21no—
204C2×Dic13—21no—
205C2×Dic13—21no—
206C2×Dic13—21no—
207C2×Dic13—21no—
208C2×Dic13—21no—
209C2×Dic13—21no—
210C2×Dic13—42no—
211C2×Dic13—41no—
212C2×Dic13—42no—
213C2×Dic13—41no—
214C2×Dic13#13712yes—
215D52—22no—
216D52—22no—
217D52—41no—
218D52—41no—
219C4×D13—48no—
220Dic26—48no—
221C8×C13—24no—
222#1055—42no—
223C2×C4⋊Q8—131no—
224C2×C4×Q8—261no—
225C2×C4×D4—131no—
226C2×#117—261no—
227#474—138no—
228C2×#107—132no—
229C2×#106C2×D1312yes—
230C2×C4⋊C8—131no—
231C2×C4⋊C8C2×D1311yescharacteristic
232C2×#102—132no—
233C2×#102—132no—
234C2×#97—132no—
235#391—261no—
236#390—131no—
237#390—131no—
238#389—132no—
239#389—131no—
240#389—131no—
241#389—261no—
242#388—261no—
243#388—261no—
244#384C2×D1311yescharacteristic
245C4×C4⋊C4—132no—
246C4×C4⋊C4—261no—
247C4×C4⋊C4C2×D1311yescharacteristic
248C4×C22⋊C4—261no—
249C43—131no—
250#340—132no—
251#340—132no—
252#340—132no—
253#340C2×D1312yes—
254#336—132no—
255C22×C13C2×C4×D411yescharacteristic
256C22×C13#53611yescharacteristic
257C22×C13#53711yescharacteristic
258C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C13C2×#13711yescharacteristic
261C22×C13#57511yescharacteristic
262C2×D13—42no—
263C2×D13—42no—
264C2×D13—42no—
265C2×D13—81no—
266C2×D13—81no—
267C2×D13—81no—
268C2×D13—81no—
269C4×C13—22no—
270C4×C13—81no—
271C4×C13—82no—
272C4×C13—81no—
273C4×C13#44214yes—
274C4×C13#51911yescharacteristic
275C4×C13#52011yescharacteristic
276C4×C13#54111yescharacteristic
277C4×C13#54211yescharacteristic
278Dic13—22no—
279Dic13—44no—
280Dic13—42no—
281Dic13—41no—
282Dic13—41no—
283Dic13—41no—
284C22×Q8—261no—
285C22×D4—131no—
286C23×C4—261no—
287C22×C8—132no—
288C22×C8C22×D1312yes—
289C4⋊Q8—134no—
290C4⋊Q8—262no—
291C4×Q8—524no—
292C4×D4—134no—
293C4×D4—262no—
294#117—524no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—131no—
298C2×C4⋊C4—132no—
299C2×C4⋊C4—261no—
300C2×C4⋊C4—261no—
301C2×C4⋊C4—261no—
302C2×C4⋊C4—262no—
303C2×C4⋊C4C22×D1311yescharacteristic
304C2×C4⋊C4C22×D1311yescharacteristic
305C2×C4⋊C4C22×D1312yes—
306C2×C22⋊C4—261no—
307C2×C22⋊C4—261no—
308C2×C22⋊C4—261no—
309C2×C22⋊C4—261no—
310C2×C22⋊C4—261no—
311C2×C42—21no—
312C2×C42—131no—
313C2×C42—131no—
314C2×C42—131no—
315C2×C42—131no—
316C2×C42—131no—
317C2×C42—131no—
318C2×C42—262no—
319C2×C42C22×D1311yescharacteristic
320#107—138no—
321#106—42no—
322C4⋊C8—262no—
323C4⋊C8C4×D1314yes—
324#102—138no—
325#102—522no—
326#97—522no—
327#95—21no—
328#95—261no—
329#95—261no—
330#95—262no—
331#95—262no—
332C2×C13#232311yescharacteristic
333C2×C13C2×#44211yescharacteristic
334C2×C13C4×#13711yescharacteristic
335C2×C13#323511yescharacteristic
336C2×C13#323911yescharacteristic
337C2×C13#325111yescharacteristic
338C2×C13#325411yescharacteristic
339D13—82no—
340C24—261no—
341C2×Q8—264no—
342C2×Q8—522no—
343C2×Q8—522no—
344C2×D4—132no—
345C2×D4—261no—
346C2×D4—261no—
347C2×D4—261no—
348C2×D4—261no—
349C2×D4—261no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—131no—
354C22×C4—131no—
355C22×C4—131no—
356C22×C4—131no—
357C22×C4—262no—
358C22×C4—261no—
359C22×C4—264no—
360C22×C4—522no—
361C22×C4—522no—
362C22×C4D4×D1311yescharacteristic
363C22×C4D4×D1311yescharacteristic
364C22×C4C23×D1311yescharacteristic
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—262no—
368C2×C8—262no—
369C2×C8—262no—
370C2×C8C2×C4×D1314yes—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—42no—
378C4⋊C4—42no—
379C4⋊C4—134no—
380C4⋊C4—132no—
381C4⋊C4—264no—
382C4⋊C4—261no—
383C4⋊C4—262no—
384C4⋊C4—522no—
385C4⋊C4—522no—
386C4⋊C4—524no—
387C22⋊C4—264no—
388C22⋊C4—522no—
389C22⋊C4—522no—
390C22⋊C4—522no—
391C22⋊C4—522no—
392C42—42no—
393C42—262no—
394C42—262no—
395C42—262no—
396C42—261no—
397C42—261no—
398C42—261no—
399C42—261no—
400C42—521no—
401C42—524no—
402C42C2×C4×D1312yes—
403C42#613112yes—
404C13#2211611yescharacteristic, complemented, Sylow
405C23—262no—
406C23—521no—
407C23—521no—
408C23—521no—
409C23—521no—
410C23—521no—
411C23—521no—
412C23C2×D4×D1311yescharacteristic
413Q8—528no—
414D4—262no—
415D4—262no—
416D4—521no—
417D4—521no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—132no—
430C2×C4—261no—
431C2×C4—261no—
432C2×C4—262no—
433C2×C4—264no—
434C2×C4—261no—
435C2×C4—261no—
436C2×C4—261no—
437C2×C4—261no—
438C2×C4—261no—
439C2×C4—261no—
440C2×C4—261no—
441C2×C4—261no—
442C2×C4—261no—
443C2×C4—522no—
444C2×C4—521no—
445C2×C4—521no—
446C2×C4—522no—
447C2×C4—528no—
448C2×C4#8814712yes—
449C2×C4#8814712yes—
450C2×C4#8816812yes—
451C2×C4#8816812yes—
452C2×C4C22×C4×D1311yescharacteristic
453C2×C4#8825111yescharacteristic
454C2×C4C2×#613111yescharacteristic
455C2×C4#8825411yescharacteristic
456C2×C4#8825711yescharacteristic
457C2×C4#8825711yescharacteristic
458C8—24no—
459C8—522no—
460C22—522no—
461C22—522no—
462C22—522no—
463C22—1041no—
464C22—1041no—
465C22—1041no—
466C22—1041no—
467C22C2×#8814711yescharacteristic
468C22#1171931311yescharacteristic
469C22#1171933311yescharacteristic
470C22C2×#8816811yescharacteristic
471C22C2×#8816811yescharacteristic
472C22#1171947811yescharacteristic
473C22D13×#13711yescharacteristic
474C4—22no—
475C4—82no—
476C4—81no—
477C4—81no—
478C4—262no—
479C4—522no—
480C4—524no—
481C4—521no—
482C4—521no—
483C4—521no—
484C4#1171853014yes—
485C4#1171925111yescharacteristic
486C4#1171927711yescharacteristic
487C4#1171940211yescharacteristic
488C4#1171943811yescharacteristic
489C2—1042no—
490C2#1311751611yescharacteristic
491C2C2×#1171853011yescharacteristic
492C2#1312365411yescharacteristic
493C2#1312603211yescharacteristic
494C2#1312607011yescharacteristic
495C2#1312619611yescharacteristic
496C2#1312622011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1948C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1948D13
hypocenterC13#22116
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
2. #13117403C2semidirect
4. #13115788C2semidirect
5. #13115572C2semidirect
8. #13115427C2semidirect
10. #13114691C2semidirect
11. C13×#1948C2semidirect
36. #11718507C4semidirect
161. #1948D13semidirect
404. C13#22116semidirect

Maximal subgroups

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

subgroupindex
C2×#117185072
#131174032
#131172972
#131157882
#131155722
#131155312
#131154622
#131154272
#131148332
#131146912
C13×#19482
#2211613