Finite Group Databasebeta

← #15873521

Subgroups — #15873521

Order 3328.

762 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718351C211yesmaximal, characteristic
2#13117461C211yesmaximal, characteristic
3#13117446C211yesmaximal, characteristic
4#13115607C212yesmaximal, complemented
5#13115593C212yesmaximal, complemented
6#13115038C212yesmaximal
7#13115025C212yesmaximal
8#13115005C211yesmaximal, characteristic, complemented
9#13114996C211yesmaximal, characteristic, complemented
10#13114969C211yesmaximal, characteristic, complemented
11C13×#1835C211yesmaximal, characteristic, complemented
12C2×#88146C2211yescharacteristic
13C2×C4⋊C4×D13C2211yescharacteristic
14C2×#88126C2211yescharacteristic
15C2×C4×C8×C13C2211yescharacteristic
16C13×#382C2211yescharacteristic
17C13×#382C2211yescharacteristic
18C2×#88060C2212yes—
19C2×#88058C2212yes—
20C2×#88058C2212yes—
21C2×#88054C2212yes—
22#11718648C2212yes—
23#11718638C2211yescharacteristic
24#11718637C2211yescharacteristic
25C4⋊C4×Dic13C2212yes—
26C2×#88048C2212yes—
27C2×#88047C2212yes—
28#11718596C2211yescharacteristic
29#11718596C2211yescharacteristic
30C2×#88043C2211yescharacteristic
31#11718351C418yescomplemented
32#11718331—22no—
33#11718329—22no—
34#11718316—22no—
35#11718308—22no—
36C13×#340C2212yes—
37C13×#340C2212yes—
38#11718121C2212yes—
39#11718121C2212yes—
40C22×C4×D13—21no—
41C22×C4×D13C2311yescharacteristic
42C22×C8×C13C2312yes—
43C2×C13×C4⋊C4C2311yescharacteristic
44C2×C13×C4⋊C4C2311yescharacteristic
45C2×C13×C4⋊C4C2312yes—
46C2×C42×C13C2311yescharacteristic
47C2×#6103—21no—
48C2×#6103—22no—
49C2×#6103D412yes—
50C2×C4⋊Dic13—22no—
51C2×C4⋊Dic13—22no—
52C2×C4⋊Dic13C2311yescharacteristic
53C2×C4⋊Dic13C2311yescharacteristic
54C2×C4⋊Dic13C2312yes—
55C2×#6101—21no—
56C2×#6101—22no—
57C2×#6101D412yes—
58C2×C4×Dic13—21no—
59C2×C4×Dic13—22no—
60C2×C4×Dic13C2311yescharacteristic
61C22×#1055C2312yes—
62#88146—42no—
63C4⋊C4×D13—42no—
64#88126C2×C414yes—
65#88126Q814yes—
66C4×C8×C13C2×C414yescomplemented
67C13×#95—22no—
68C13×#95—22no—
69#88071—22no—
70#88071—22no—
71#88071—22no—
72#88060C2×C418yes—
73#88058—42no—
74#88058—42no—
75#88054C2×C418yescomplemented
76#88048—42no—
77#88047—42no—
78#88043C2×C414yescomplemented
79#21991—131nomaximal, Sylow
80C23×D13C2×D411yescharacteristic
81C22×C4×C13—21no—
82C22×C4×C13—22no—
83C22×C4×C13—21no—
84C22×C4×C13C2×D412yes—
85C22×C4×C13C2411yescharacteristic
86C22×Dic13—22no—
87C22×Dic13—21no—
88C22×Dic13—21no—
89C22×Dic13C2×D412yes—
90C22×Dic13C2×D411yescharacteristic
91C2×C4×D13—22no—
92C2×C4×D13—22no—
93C2×C4×D13—42no—
94C2×C4×D13—82no—
95C2×C4×D13C22×C412yes—
96C2×C4×D13C2×Q812yes—
97C2×C8×C13—22no—
98C2×C8×C13—22no—
99C2×C8×C13C22×C414yes—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—24no—
103C42×C13C22×C412yes—
104C42×C13C2×Q812yes—
105#6103—42no—
106#6103—82no—
107#6103C4⋊C418yes—
108C4⋊Dic13—22no—
109C4⋊Dic13—22no—
110C4⋊Dic13—22no—
111C4⋊Dic13—22no—
112C4⋊Dic13—82no—
113C4⋊Dic13—82no—
114#6101—42no—
115#6101—82no—
116#6101C4⋊C418yes—
117C4×Dic13—42no—
118C4×Dic13—82no—
119C4×Dic13C22×C412yes—
120C4×Dic13C2×Q812yes—
121C2×#1055—22no—
122C2×#1055—22no—
123C2×#1055C22×C414yes—
124C2×#433—131no—
125#2317—131no—
126#2314—131no—
127#1949—132no—
128#1947—132no—
129#1854—132no—
130#1852—132no—
131#1847—131no—
132#1845—131no—
133#1836—131no—
134#1835D1311yescharacteristic, complemented
135C23×C13C22×D411yescharacteristic
136C22×D13—21no—
137C22×D13—21no—
138C22×D13—22no—
139C22×D13—22no—
140C22×D13C2×C4⋊C412yes—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13C2×C4⋊C414yes—
151C2×C4×C13C23×C411yescharacteristic
152C2×C4×C13C22×Q811yescharacteristic
153C2×C4×C13H(5,𝔽2)12yes—
154C2×C4×C132−1+412yes—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—22no—
158C2×Dic13—22no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13—42no—
166C2×Dic13C2×C4⋊C414yes—
167C2×Dic13C2×C4⋊C412yes—
168C4×D13—24no—
169C4×D13—24no—
170C4×D13—84no—
171C8×C13—24no—
172#1055—24no—
173C2×#117—131no—
174C2×#117—131no—
175C22×C4⋊C4—131no—
176#433—138no—
177C2×#107—132no—
178C2×#107—132no—
179C2×#107—132no—
180C2×#106—132no—
181C2×C4⋊C8—132no—
182C2×C22⋊C8—132no—
183C2×#97—131no—
184C2×C4×C8C2×D1311yescharacteristic
185#389—262no—
186#388—262no—
187#387—262no—
188#385—262no—
189#384—131no—
190#384—131no—
191#384—131no—
192#382—131no—
193#382C2×D1311yescharacteristic
194#382C2×D1311yescharacteristic
195#380—132no—
196C4×C4⋊C4—132no—
197#340—132no—
198#340—132no—
199#340C2×D1312yes—
200#340C2×D1312yes—
201C22×C13C22×C4⋊C411yescharacteristic
202C22×C13#53511yescharacteristic
203C22×C13#53611yescharacteristic
204C22×C13#57612yes—
205C22×C13#57812yes—
206C2×D13—22no—
207C2×D13—24no—
208C2×D13—41no—
209C2×D13—41no—
210C2×D13—42no—
211C4×C13—24no—
212C4×C13—81no—
213C4×C13—81no—
214C4×C13—82no—
215C4×C13#52012yes—
216C4×C13#54412yes—
217Dic13—22no—
218Dic13—24no—
219Dic13—81no—
220Dic13—81no—
221Dic13—82no—
222C23×C4—131no—
223C23×C4—261no—
224C22×C8—132no—
225C22×C8C22×D1312yes—
226#117—134no—
227#117—134no—
228#117—522no—
229C2×C4⋊C4—132no—
230C2×C4⋊C4—131no—
231C2×C4⋊C4—131no—
232C2×C4⋊C4—132no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4—262no—
235C2×C4⋊C4—262no—
236C2×C4⋊C4—262no—
237C2×C4⋊C4—522no—
238C2×C4⋊C4C22×D1311yescharacteristic
239C2×C4⋊C4C22×D1311yescharacteristic
240C2×C4⋊C4C22×D1312yes—
241C2×C22⋊C4—132no—
242C2×C22⋊C4—261no—
243C2×C22⋊C4—262no—
244C2×C42—131no—
245C2×C42—261no—
246C2×C42—262no—
247C2×C42C22×D1311yescharacteristic
248#107—522no—
249#107—522no—
250#107—522no—
251#106—522no—
252C4⋊C8—138no—
253C22⋊C8—138no—
254#97—134no—
255C4×C8C4×D1314yescomplemented
256#95—22no—
257#95—22no—
258#95—262no—
259#95—262no—
260#95—262no—
261C2×C13#231711yescharacteristic
262C2×C13#291312yes—
263C2×C13#322011yescharacteristic
264C2×C13#322311yescharacteristic
265C2×C13#324312yes—
266D13—42no—
267C24—131no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—132no—
272C22×C4—131no—
273C22×C4—132no—
274C22×C4—132no—
275C22×C4—262no—
276C22×C4—262no—
277C22×C4—262no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—522no—
281C22×C4—1042no—
282C22×C4D4×D1312yes—
283C22×C4C23×D1311yescharacteristic
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—134no—
287C2×C8—262no—
288C2×C8—262no—
289C2×C8C2×C4×D1314yes—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—24no—
293C4⋊C4—138no—
294C4⋊C4—262no—
295C4⋊C4—262no—
296C4⋊C4—262no—
297C4⋊C4—262no—
298C4⋊C4—522no—
299C4⋊C4—1042no—
300C4⋊C4—1042no—
301C4⋊C4—1042no—
302C22⋊C4—138no—
303C22⋊C4—522no—
304C22⋊C4—1042no—
305C42—132no—
306C42—132no—
307C42—522no—
308C42—1042no—
309C42C2×C4×D1312yes—
310C42Q8×D1312yes—
311C13#2199111yescharacteristic, complemented, Sylow
312C23—132no—
313C23—262no—
314C23—262no—
315C23—261no—
316C23—261no—
317C23C2×D4×D1311yescharacteristic
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—134no—
328C2×C4—132no—
329C2×C4—262no—
330C2×C4—262no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—264no—
334C2×C4—264no—
335C2×C4—522no—
336C2×C4—522no—
337C2×C4—522no—
338C2×C4—522no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—522no—
342C2×C4—1044no—
343C2×C4C4⋊C4×D1314yes—
344C2×C4C22×C4×D1311yescharacteristic
345C2×C4C2×Q8×D1311yescharacteristic
346C2×C4#8825612yes—
347C2×C4#8825712yes—
348C8—24no—
349C8—264no—
350C22—262no—
351C22—264no—
352C22—521no—
353C22—521no—
354C22—522no—
355C22C2×C4⋊C4×D1311yescharacteristic
356C22#1171937911yescharacteristic
357C22#1171938011yescharacteristic
358C22#1171947412yes—
359C22#1171947612yes—
360C4—24no—
361C4—81no—
362C4—81no—
363C4—82no—
364C4—262no—
365C4—264no—
366C4—1042no—
367C4—1041no—
368C4—1041no—
369C4#1171922812yes—
370C4#1171939412yes—
371C2—522no—
372C2#1311746111yescharacteristic
373C2#1312343312yes—
374C2#1312588911yescharacteristic
375C2#1312592211yescharacteristic
376C2#1312611212yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1835C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1835D13
hypocenterC13#21991
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1835

Complements

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

NH ≅ G/Ntype
4. #13115607C2semidirect
5. #13115593C2semidirect
8. #13115005C2semidirect
9. #13114996C2semidirect
10. #13114969C2semidirect
11. C13×#1835C2semidirect
31. #11718351C4semidirect
66. C4×C8×C13C2×C4semidirect
75. #88054C2×C4semidirect
78. #88043C2×C4semidirect
134. #1835D13semidirect
255. C4×C8C4×D13semidirect
311. C13#21991semidirect

Maximal subgroups

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

subgroupindex
C2×#117183512
#131174612
#131174462
#131156072
#131155932
#131150382
#131150252
#131150052
#131149962
#131149692
C13×#18352
#2199113