Finite Group Databasebeta

← #15765228

Subgroups — #15765228

Order 3328.

676 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718688C212yesmaximal
2#13115641C211yesmaximal, characteristic
3C2×Q8⋊#1055C212yesmaximal, complemented
4#13112719C211yesmaximal, characteristic, complemented
5C13×#2582C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2212yes—
7C22×#6106—22no—
8C2×#88128C2211yescharacteristic
9C13×#398—22no—
10C13×#391—22no—
11C13×#389—22no—
12C13×#384C2211yescharacteristic
13#11718688—24no—
14#11718688—24no—
15C2×#88049—22no—
16C2×#88049—22no—
17C2×C4⋊#1055C2212yes—
18C2×C4×#1055C2211yescharacteristic
19Q8⋊#1055—24no—
20C22×Q8×C13D412yes—
21C22×D52—22no—
22C22×D52—21no—
23C4×Q8×C13—22no—
24C4×Q8×C13—22no—
25C4×Q8×C13—22no—
26C4×Q8×C13—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4D412yes—
31C2×C13×C4⋊C4D412yes—
32C2×C42×C13—22no—
33C2×C42×C13C2311yescharacteristic
34C2×#6106—28no—
35C2×#6106—44no—
36C2×#6106—44no—
37C22×#1055—22no—
38C22×#1055—21no—
39#88128—22no—
40#88128—21no—
41#88128D412yes—
42C13×#95—24no—
43C13×#95—22no—
44#88049—28no—
45#88049—44no—
46C4⋊#1055—22no—
47C4⋊#1055D414yes—
48C4×#1055—22no—
49#10230—131nomaximal, Sylow
50C23×D13—41no—
51C2×Q8×C13—22no—
52C2×Q8×C13—22no—
53C2×Q8×C13—22no—
54C2×Q8×C13—22no—
55C2×Q8×C13—22no—
56C2×Q8×C13SD1614yescomplemented
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D412yes—
62C2×D52—24no—
63C2×D52—22no—
64C2×D52—42no—
65C2×D52—42no—
66C2×D52—42no—
67C2×D52—42no—
68C2×D52—42no—
69C2×D52—42no—
70C2×D52—42no—
71C2×D52—41no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—82no—
80C42×C13—42no—
81C42×C13—42no—
82C42×C13C2×D411yescharacteristic
83C42×C13C2×D412yes—
84C42×C13#4111yescharacteristic
85#6106—416no—
86C2×#1055—22no—
87C2×#1055—24no—
88C2×#1055—41no—
89C2×#1055—41no—
90C2×#1055—42no—
91C2×#1055—42no—
92C2×#460—132no—
93#2582D1311yescharacteristic, complemented
94#1957—131no—
95C2×Q8⋊C8—132no—
96#1296—131no—
97C23×C13#12011yescharacteristic
98C22×D13—42no—
99C22×D13—82no—
100C22×D13—82no—
101C22×D13—81no—
102C22×D13—81no—
103Q8×C13—24no—
104Q8×C13—24no—
105Q8×C13—42no—
106Q8×C13—42no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—24no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—44no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13#12012yes—
118C2×C4×C13#12111yescharacteristic
119C2×C4×C13#12112yes—
120C2×C4×C13#12711yescharacteristic
121C2×C4×C13C2×SD1612yes—
122C2×C4×C13#13512yes—
123C2×C4×C13AGL(1,ℤ/8)12yes—
124C2×C4×C13#13712yes—
125D52—44no—
126D52—44no—
127D52—44no—
128D52—82no—
129D52—82no—
130D52—82no—
131#1055—42no—
132#1055—44no—
133C22×SD16—262no—
134C2×#127—131no—
135C2×C4×Q8C2×D1312yes—
136#460—264no—
137#460—264no—
138C2×C4⋊C8—132no—
139C2×#102—262no—
140C2×#102—262no—
141C2×C4×C8—131no—
142#398—22no—
143#391—22no—
144#389—22no—
145#384C2×D1311yescharacteristic
146Q8⋊C8—264no—
147C22×C13#39211yescharacteristic
148C22×C13#44812yes—
149C22×C13#44912yes—
150C22×C13#45311yescharacteristic
151C22×C13#45411yescharacteristic
152C2×D13—84no—
153C2×D13—82no—
154C2×D13—161no—
155C2×D13—161no—
156C2×D13—162no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—44no—
160C4×C13—82no—
161C4×C13—82no—
162C4×C13#45012yes—
163C4×C13#45212yes—
164C4×C13#46512yes—
165C4×C13#46812yes—
166C22×Q8C22⋊D1312yes—
167C22×D4—262no—
168C22×D4—261no—
169C2×SD16—268no—
170C2×SD16—524no—
171C2×SD16—524no—
172C22×C8—262no—
173C22×C8—261no—
174#127—132no—
175#127—262no—
176#127—261no—
177C4×Q8—22no—
178C4×Q8—22no—
179C4×Q8—22no—
180C4×Q8—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4C22⋊D1312yes—
185C2×C4⋊C4C22⋊D1312yes—
186C2×C42—22no—
187C2×C42C22×D1311yescharacteristic
188C4⋊C8—134no—
189C4⋊C8—262no—
190#102—268no—
191#102—524no—
192C4×C8—262no—
193#95—24no—
194#95—22no—
195C2×C13#162011yescharacteristic
196C2×C13#162311yescharacteristic
197C2×C13#162612yes—
198C2×C13#200012yes—
199C2×C13#200611yescharacteristic
200D13—162no—
201C24—521no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8#610614yescomplemented
208C2×D4—264no—
209C2×D4—262no—
210C2×D4—522no—
211C2×D4—522no—
212C2×D4—522no—
213C2×D4—521no—
214C2×D4—522no—
215C2×D4—522no—
216C2×D4—522no—
217C2×D4—522no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4C2×C22⋊D1311yescharacteristic
222C22×C4C2×C22⋊D1312yes—
223SD16—5216no—
224C2×C8—262no—
225C2×C8—264no—
226C2×C8—521no—
227C2×C8—521no—
228C2×C8—522no—
229C2×C8—522no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—82no—
238C42—42no—
239C42—42no—
240C42D4×D1311yescharacteristic
241C42D4×D1312yes—
242C42#612911yescharacteristic
243C13#1023011yescharacteristic, complemented, Sylow
244C23—522no—
245C23—1042no—
246C23—1042no—
247C23—1041no—
248C23—1041no—
249C23#8820711yescharacteristic
250Q8—24no—
251Q8—24no—
252Q8—42no—
253Q8—42no—
254D4—524no—
255D4—524no—
256D4—524no—
257D4—1042no—
258D4—1042no—
259D4—1042no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—24no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—44no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4#8819112yes—
271C2×C4#8819211yescharacteristic
272C2×C4#8819312yes—
273C2×C4#8819411yescharacteristic
274C2×C4C2×#610612yes—
275C2×C4#8819612yes—
276C2×C4#8820312yes—
277C2×C4#8820412yes—
278C8—522no—
279C8—524no—
280C22—1044no—
281C22—1042no—
282C22—2081no—
283C22—2081no—
284C22—2082no—
285C22#1171888411yescharacteristic
286C22#1171888812yes—
287C22#1171889912yes—
288C22#1171890211yescharacteristic
289C22#1171890611yescharacteristic
290C4—21no—
291C4—21no—
292C4—44no—
293C4—82no—
294C4—82no—
295C4#1171870712yes—
296C4#1171870812yes—
297C4#1171870912yes—
298C4#1171871012yes—
299C2—2082no—
300C2#1311389511yescharacteristic
301C2#1311391411yescharacteristic
302C2#1311393212yes—
303C2#1311583712yes—
304C2#1311587811yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2582C2
socleC23×C13#120
prime radicalC2×#88128C22
hypercenter#2582D13
hypocenterC13#10230
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2582

Complements

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

NH ≅ G/Ntype
3. C2×Q8⋊#1055C2semidirect
4. #13112719C2semidirect
5. C13×#2582C2semidirect
56. C2×Q8×C13SD16semidirect
93. #2582D13semidirect
207. C2×Q8#6106semidirect
243. C13#10230semidirect

Maximal subgroups

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

subgroupindex
C2×#117186882
#131156412
C2×Q8⋊#10552
#131127192
C13×#25822
#1023013