Finite Group Databasebeta

← #15873500

Subgroups — #15873500

Order 3328.

786 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718366C211yesmaximal, characteristic
2#13117241C211yesmaximal, characteristic
3#13117229C211yesmaximal, characteristic
4#13115607C212yesmaximal, complemented
5#13115603C212yesmaximal, complemented
6#13115038C212yesmaximal
7#13115036C212yesmaximal
8#13115004C211yesmaximal, characteristic, complemented
9#13115002C211yesmaximal, characteristic, complemented
10#13114969C211yesmaximal, characteristic, complemented
11C13×#1836C211yesmaximal, characteristic, complemented
12C2×#88146C2212yes—
13C2×C42×D13C2211yescharacteristic
14C2×C13×#97C2211yescharacteristic
15C13×#384C2211yescharacteristic
16C13×#382C2211yescharacteristic
17C2×#88060C2212yes—
18C2×#88058C2212yes—
19C2×#88057C2212yes—
20C2×#88054C2212yes—
21#11718648—21no—
22#11718648—21no—
23#11718648C2211yescharacteristic
24#11718648C2211yescharacteristic
25#11718638C2212yes—
26C4⋊C4×Dic13—21no—
27C4⋊C4×Dic13—21no—
28C4⋊C4×Dic13C2211yescharacteristic
29C4⋊C4×Dic13C2211yescharacteristic
30C2×#88048C2212yes—
31C2×#88047C2212yes—
32#11718597C2211yescharacteristic
33#11718596C2211yescharacteristic
34C2×#88043C2211yescharacteristic
35#11718366C418yescomplemented
36#11718327—21no—
37#11718325—21no—
38#11718312—21no—
39#11718309—21no—
40C13×#340C2212yes—
41C13×#340C2212yes—
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×C13C2311yescharacteristic
54C2×#6103—22no—
55C2×#6103—21no—
56C2×#6103—21no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13C2312yes—
60C2×C4⋊Dic13C2311yescharacteristic
61C2×C4⋊Dic13C2311yescharacteristic
62C2×C4×Dic13—22no—
63C2×C4×Dic13—21no—
64C2×C4×Dic13—21no—
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13C2311yescharacteristic
68C22×#1055C2312yes—
69#88146—42no—
70#88146—42no—
71C42×D13C2×C414yes—
72C42×D13Q814yes—
73C13×#97C2×C414yes—
74C13×#95—21no—
75C13×#95—21no—
76#88071—21no—
77#88071—21no—
78#88071—21no—
79#88071—21no—
80#88071—21no—
81#88071—21no—
82#88071—22no—
83#88071—22no—
84#88060C2×C418yes—
85#88058—42no—
86#88057—42no—
87#88054C2×C418yes—
88#88048—42no—
89#88047—42no—
90#88043C2×C414yes—
91#21989—131nomaximal, Sylow
92C23×D13C2×D411yescharacteristic
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—22no—
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2411yescharacteristic
99C22×Dic13—21no—
100C22×Dic13—21no—
101C22×Dic13—22no—
102C22×Dic13C2×D411yescharacteristic
103C22×Dic13C2×D411yescharacteristic
104C22×Dic13C2×D411yescharacteristic
105C2×C4×D13—22no—
106C2×C4×D13—22no—
107C2×C4×D13—41no—
108C2×C4×D13—41no—
109C2×C4×D13—41no—
110C2×C4×D13—41no—
111C2×C4×D13C4⋊C414yes—
112C2×C4×D13C4⋊C414yes—
113C2×C4×D13C22×C412yes—
114C2×C4×D13C2×Q812yes—
115C2×C8×C13—22no—
116C2×C8×C13—22no—
117C2×C8×C13C22×C414yes—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—22no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—42no—
123C13×C4⋊C4—42no—
124C42×C13C22×C412yes—
125C42×C13C2×Q812yes—
126#6103—44no—
127#6103—42no—
128#6103—42no—
129C4⋊Dic13—22no—
130C4⋊Dic13—22no—
131C4⋊Dic13—22no—
132C4⋊Dic13—22no—
133C4⋊Dic13—42no—
134C4⋊Dic13—42no—
135C4×Dic13—44no—
136C4×Dic13—42no—
137C4×Dic13—42no—
138C4×Dic13C4⋊C414yes—
139C4×Dic13C4⋊C414yes—
140C4×Dic13C22×C412yes—
141C4×Dic13C2×Q812yes—
142C2×#1055—22no—
143C2×#1055—22no—
144C2×#1055C22×C414yes—
145C2×#432—131no—
146#2285—131no—
147#2283—131no—
148#1949—132no—
149#1949—132no—
150#1854—132no—
151#1854—132no—
152#1847—131no—
153#1847—131no—
154#1836—131no—
155#1836D1311yescharacteristic, complemented
156C23×C13C22×D411yescharacteristic
157C22×D13—21no—
158C22×D13—21no—
159C22×D13—21no—
160C22×D13—21no—
161C22×D13—21no—
162C22×D13—21no—
163C22×D13C2×C4⋊C412yes—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—42no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13C2×C4⋊C412yes—
178C2×C4×C13C2×C4⋊C412yes—
179C2×C4×C13C23×C411yescharacteristic
180C2×C4×C13C22×Q811yescharacteristic
181C2×C4×C13H(5,𝔽2)12yes—
182C2×C4×C132−1+412yes—
183C2×Dic13—21no—
184C2×Dic13—21no—
185C2×Dic13—21no—
186C2×Dic13—21no—
187C2×Dic13—21no—
188C2×Dic13—21no—
189C2×Dic13—42no—
190C2×Dic13—41no—
191C2×Dic13—41no—
192C2×Dic13—41no—
193C2×Dic13—41no—
194C2×Dic13—42no—
195C2×Dic13—42no—
196C2×Dic13—41no—
197C2×Dic13—41no—
198C2×Dic13C2×C4⋊C412yes—
199C2×Dic13C2×C4⋊C412yes—
200C2×Dic13C2×C4⋊C412yes—
201C4×D13—24no—
202C4×D13—24no—
203C4×D13—44no—
204C4×D13—44no—
205C8×C13—24no—
206#1055—24no—
207C2×#117—132no—
208C22×C42—131no—
209#432—138no—
210C2×#107—132no—
211C2×#107—132no—
212C2×#106—132no—
213C2×#106—132no—
214C2×C4⋊C8—132no—
215C2×C22⋊C8—132no—
216C2×#97—131no—
217C2×#97C2×D1311yescharacteristic
218#384—131no—
219#384C2×D1311yescharacteristic
220#383—261no—
221#382—132no—
222#382—131no—
223#382C2×D1311yescharacteristic
224#381—261no—
225#380—131no—
226#380—131no—
227#380—261no—
228#380—261no—
229C4×C4⋊C4—131no—
230C4×C4⋊C4—131no—
231C4×C4⋊C4—261no—
232C4×C4⋊C4—261no—
233C4×C22⋊C4—261no—
234#376—261no—
235#340—132no—
236#340—132no—
237#340C2×D1312yes—
238#340C2×D1312yes—
239C22×C13C22×C4⋊C411yescharacteristic
240C22×C13#53511yescharacteristic
241C22×C13#53611yescharacteristic
242C22×C13#57511yescharacteristic
243C22×C13#57511yescharacteristic
244C22×C13#57511yescharacteristic
245C22×C13#57511yescharacteristic
246C2×D13—22no—
247C2×D13—22no—
248C2×D13—22no—
249C2×D13—41no—
250C2×D13—41no—
251C2×D13—41no—
252C2×D13—41no—
253C4×C13—22no—
254C4×C13—22no—
255C4×C13—82no—
256C4×C13—81no—
257C4×C13—81no—
258C4×C13#52012yes—
259C4×C13#54412yes—
260Dic13—22no—
261Dic13—22no—
262Dic13—22no—
263Dic13—81no—
264Dic13—82no—
265Dic13—81no—
266C23×C4—131no—
267C23×C4—131no—
268C23×C4—131no—
269C22×C8—132no—
270C22×C8C22×D1312yes—
271#117—522no—
272#117—522no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—132no—
276C2×C4⋊C4—131no—
277C2×C4⋊C4—131no—
278C2×C4⋊C4—261no—
279C2×C4⋊C4—261no—
280C2×C4⋊C4C22×D1312yes—
281C2×C4⋊C4C22×D1311yescharacteristic
282C2×C4⋊C4C22×D1311yescharacteristic
283C2×C22⋊C4—262no—
284C2×C22⋊C4—261no—
285C2×C22⋊C4—261no—
286C2×C42—131no—
287C2×C42—131no—
288C2×C42—131no—
289C2×C42—134no—
290C2×C42—134no—
291C2×C42—262no—
292C2×C42—261no—
293C2×C42—261no—
294C2×C42C22×D1311yescharacteristic
295#107—522no—
296#107—522no—
297#106—522no—
298#106—522no—
299C4⋊C8—138no—
300C22⋊C8—138no—
301#97—134no—
302#97C4×D1314yes—
303#95—21no—
304#95—21no—
305#95—261no—
306#95—261no—
307#95—261no—
308#95—261no—
309#95—262no—
310#95—262no—
311#95—261no—
312#95—261no—
313C2×C13#231711yescharacteristic
314C2×C13#291111yescharacteristic
315C2×C13#291111yescharacteristic
316C2×C13#321911yescharacteristic
317C2×C13#321911yescharacteristic
318C2×C13#324011yescharacteristic
319C2×C13#324011yescharacteristic
320D13—42no—
321C24—131no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—131no—
326C22×C4—131no—
327C22×C4—131no—
328C22×C4—132no—
329C22×C4—132no—
330C22×C4—134no—
331C22×C4—134no—
332C22×C4—262no—
333C22×C4—262no—
334C22×C4—261no—
335C22×C4—261no—
336C22×C4—262no—
337C22×C4—521no—
338C22×C4—521no—
339C22×C4—521no—
340C22×C4—521no—
341C22×C4D4×D1311yescharacteristic
342C22×C4D4×D1311yescharacteristic
343C22×C4C23×D1311yescharacteristic
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—134no—
347C2×C8—262no—
348C2×C8—262no—
349C2×C8C2×C4×D1314yes—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—42no—
355C4⋊C4—42no—
356C4⋊C4—262no—
357C4⋊C4—262no—
358C4⋊C4—262no—
359C4⋊C4—262no—
360C4⋊C4—522no—
361C4⋊C4—522no—
362C22⋊C4—524no—
363C22⋊C4—522no—
364C22⋊C4—522no—
365C42—134no—
366C42—134no—
367C42—132no—
368C42—132no—
369C42—524no—
370C42—522no—
371C42—522no—
372C42C2×C4×D1312yes—
373C42Q8×D1312yes—
374C13#2198911yescharacteristic, complemented, Sylow
375C23—132no—
376C23—261no—
377C23—261no—
378C23—261no—
379C23—261no—
380C23—261no—
381C23—261no—
382C23C2×D4×D1311yescharacteristic
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—132no—
397C2×C4—132no—
398C2×C4—132no—
399C2×C4—261no—
400C2×C4—261no—
401C2×C4—261no—
402C2×C4—261no—
403C2×C4—261no—
404C2×C4—261no—
405C2×C4—264no—
406C2×C4—264no—
407C2×C4—524no—
408C2×C4—524no—
409C2×C4—521no—
410C2×C4—521no—
411C2×C4—521no—
412C2×C4—521no—
413C2×C4—522no—
414C2×C4—522no—
415C2×C4—522no—
416C2×C4—521no—
417C2×C4—521no—
418C2×C4C4⋊C4×D1312yes—
419C2×C4C4⋊C4×D1312yes—
420C2×C4C22×C4×D1311yescharacteristic
421C2×C4C2×Q8×D1311yescharacteristic
422C2×C4#8825612yes—
423C2×C4#8825712yes—
424C8—24no—
425C8—264no—
426C22—262no—
427C22—262no—
428C22—262no—
429C22—521no—
430C22—521no—
431C22—521no—
432C22—521no—
433C22C2×C4⋊C4×D1311yescharacteristic
434C22#1171937911yescharacteristic
435C22#1171938011yescharacteristic
436C22#1171947811yescharacteristic
437C22#1171947811yescharacteristic
438C22#1171948211yescharacteristic
439C22#1171948211yescharacteristic
440C4—22no—
441C4—22no—
442C4—81no—
443C4—81no—
444C4—82no—
445C4—262no—
446C4—262no—
447C4—262no—
448C4—1041no—
449C4—1041no—
450C4—1042no—
451C4#1171922812yes—
452C4#1171939412yes—
453C2—522no—
454C2#1311746111yescharacteristic
455C2#1312342311yescharacteristic
456C2#1312342311yescharacteristic
457C2#1312587411yescharacteristic
458C2#1312587611yescharacteristic
459C2#1312607111yescharacteristic
460C2#1312607311yescharacteristic
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#21989
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. #13115004C2semidirect
9. #13115002C2semidirect
10. #13114969C2semidirect
11. C13×#1836C2semidirect
35. #11718366C4semidirect
155. #1836D13semidirect
374. C13#21989semidirect

Maximal subgroups

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

subgroupindex
C2×#117183662
#131172412
#131172292
#131156072
#131156032
#131150382
#131150362
#131150042
#131150022
#131149692
C13×#18362
#2198913