Finite Group Databasebeta

← #16778513

Subgroups — #16778513

Order 3328.

468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 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
1#13130553C211yesmaximal, characteristic
2#13130553C211yesmaximal, characteristic
3#13129655C212yesmaximal
4#13129654C212yesmaximal
5C4×#88142C211yesmaximal, characteristic
6C2×#88142C411yescharacteristic
7C2×C4×Dic26—21no—
8C2×#88110—21no—
9C2×#88110—21no—
10C4×C13×C4⋊C4C411yescharacteristic
11#11718646C2211yescharacteristic
12#11718637C411yescharacteristic
13#11718634C2211yescharacteristic
14C4×C4⋊Dic13C411yescharacteristic
15C4×#6101—21no—
16C42×Dic13C2211yescharacteristic
17#11718308—21no—
18#11718307—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×Dic26—21no—
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C42×C13—21no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×#6101—21no—
34C2×#6101—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44#88142—22no—
45#88142—22no—
46C4×Dic26—44no—
47#88110—24no—
48#88110—24no—
49C13×#95—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#7638—131nomaximal, Sylow
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×Dic13—21no—
60C22×Dic13—21no—
61C22×Dic13C22⋊C411yescharacteristic
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C2×D411yescharacteristic
64C22×Dic13C2×D411yescharacteristic
65C2×Dic26—24no—
66C2×Dic26—42no—
67C2×Dic26—42no—
68C2×#1057—24no—
69C2×#1057—24no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C2×#1057—42no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4M1612yes—
77C42×C13—22no—
78C42×C13—42no—
79C4⋊Dic13—21no—
80C4⋊Dic13—42no—
81C4⋊Dic13—41no—
82C4⋊Dic13M1612yes—
83#6101—24no—
84#6101—42no—
85#6101—42no—
86#6101—42no—
87C4×Dic13—21no—
88C4×Dic13—21no—
89C4×Dic13—22no—
90C4×Dic13—22no—
91C4×Dic13—22no—
92C4×Dic13—22no—
93C4×Dic13—41no—
94C4×Dic13—42no—
95C4×C4⋊Q8—131no—
96#1745—131no—
97#1745—131no—
98#1271—132no—
99#1271—132no—
100C23×C13C2×C22⋊C411yescharacteristic
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—22no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13#10112yes—
115C2×C4×C13C2×M1611yescharacteristic
116C2×C4×C13C2×M1611yescharacteristic
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—22no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13#10412yes—
132C2×Dic13#10412yes—
133C2×Dic13AGL(1,ℤ/8)12yes—
134C2×Dic13#13712yes—
135Dic26—48no—
136#1057—44no—
137#1057—44no—
138C2×C4⋊Q8—131no—
139C2×C4×Q8—261no—
140C2×#97—261no—
141C2×#97—261no—
142#391—261no—
143#389—131no—
144#389—131no—
145#389—261no—
146#384—131no—
147C4×C4⋊C4—131no—
148C4×C4⋊C4—261no—
149C4×C4⋊C4#26111yescharacteristic
150C43—131no—
151#336—132no—
152#336—132no—
153#336—261no—
154#336—261no—
155C22×C13#40711yescharacteristic
156C22×C13#41011yescharacteristic
157C22×C13C2×#10111yescharacteristic
158C22×C13#41811yescharacteristic
159C22×C13#41911yescharacteristic
160C22×C13C2×#10411yescharacteristic
161C22×C13C2×#10411yescharacteristic
162C4×C13—22no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—42no—
166C4×C13—41no—
167C4×C13—81no—
168Dic13—22no—
169Dic13—22no—
170Dic13—22no—
171Dic13—22no—
172Dic13—42no—
173Dic13—81no—
174C22×Q8—261no—
175C22×C8—262no—
176C22×C8—262no—
177C4⋊Q8—262no—
178C4⋊Q8—262no—
179C4×Q8—524no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4C2×#26111yescharacteristic
188C2×C4⋊C4C2×#26111yescharacteristic
189C2×C42—21no—
190C2×C42—131no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—261no—
197C2×C42C2×#26111yescharacteristic
198#97—264no—
199#97—264no—
200#95—21no—
201#95—261no—
202#95—261no—
203#95—261no—
204C2×C13#146711yescharacteristic
205C2×C13#149011yescharacteristic
206C2×C13#149111yescharacteristic
207C2×C13#150511yescharacteristic
208C2×C13#150611yescharacteristic
209C2×C13#152611yescharacteristic
210C2×C13#155611yescharacteristic
211C2×Q8—264no—
212C2×Q8—522no—
213C2×Q8—522no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—131no—
220C22×C4—261no—
221C22×C4—261no—
222C22×C4C22⋊#26111yescharacteristic
223C22×C4C22⋊#26111yescharacteristic
224C22×C4C22×#26111yescharacteristic
225C2×C8—264no—
226C2×C8—264no—
227C2×C8—522no—
228C2×C8—522no—
229C2×C8—522no—
230C2×C8—522no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—132no—
234C4⋊C4—264no—
235C4⋊C4—261no—
236C4⋊C4—521no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C4⋊C4—522no—
240C4⋊C4—522no—
241C4⋊C4#611812yes—
242C42—22no—
243C42—42no—
244C42—262no—
245C42—262no—
246C42—262no—
247C42—262no—
248C42—261no—
249C42—261no—
250C42—521no—
251C42—522no—
252C13#763811yescharacteristic, complemented, Sylow
253C23C2×C22⋊#26111yescharacteristic
254Q8—528no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—132no—
269C2×C4—132no—
270C2×C4—132no—
271C2×C4—132no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—262no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4#8811312yes—
287C2×C4C2×#611811yescharacteristic
288C2×C4D13⋊M1611yescharacteristic
289C8—524no—
290C8—524no—
291C22#1171911611yescharacteristic
292C22#1171912711yescharacteristic
293C22C2×#8811311yescharacteristic
294C22#1171913811yescharacteristic
295C22#1171915311yescharacteristic
296C22D13⋊#10411yescharacteristic
297C22D13⋊#10411yescharacteristic
298C4—21no—
299C4—21no—
300C4—22no—
301C4—41no—
302C4—42no—
303C4—81no—
304C4—262no—
305C4—262no—
306C4—262no—
307C4—262no—
308C4—522no—
309C4—1041no—
310C2#1313009811yescharacteristic
311C2#1313017611yescharacteristic
312C2#1313017911yescharacteristic
313C2#1313022611yescharacteristic
314C2#1313022911yescharacteristic
315C2#1313029311yescharacteristic
316C2#1313036511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#7638
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
252. C13#7638semidirect

Maximal subgroups

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

subgroupindex
#131305532
#131296552
#131296542
C4×#881422
#763813