Finite Group Databasebeta

← #16778484

Subgroups — #16778484

Order 3328.

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

normal subgroups only

This group has 434 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#13130621C211yesmaximal, characteristic
2#13130553C211yesmaximal, characteristic
3#13129656C212yesmaximal
4#13129654C212yesmaximal
5#13117314C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×#88112—21no—
8C2×#88110—21no—
9C2×#88110—21no—
10#11718891C411yescharacteristic
11#11718891C2211yescharacteristic
12#11718646C411yescharacteristic
13#11718646C2211yescharacteristic
14#11718642—21no—
15#11718642—21no—
16C4×C4⋊Dic13—21no—
17C4×C4⋊Dic13C411yescharacteristic
18#11718593—21no—
19C42×Dic13C2211yescharacteristic
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C4×Q8×C13—22no—
27C4×Q8×C13—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C42×C13—21no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4×Dic13—21no—
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13C2311yescharacteristic
43#88112—24no—
44#88110—24no—
45#88110—42no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#7630—131nomaximal, Sylow
54C2×Q8×C13—21no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13M1612yes—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C2×D411yescharacteristic
68C22×Dic13C2×D411yescharacteristic
69C2×#1057—24no—
70C2×#1057—24no—
71C2×#1057—42no—
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C13×C4⋊C4—24no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4M1612yes—
78C42×C13—24no—
79C42×C13—21no—
80C42×C13—21no—
81C4⋊Dic13—42no—
82C4⋊Dic13—41no—
83C4⋊Dic13—41no—
84C4⋊Dic13—41no—
85C4⋊Dic13—41no—
86C4×Dic13—22no—
87C4×Dic13—22no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C4×Dic13—22no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93C4×Dic13—42no—
94#2295—131no—
95#1767—131no—
96#1745—131no—
97#1272—132no—
98#1271—132no—
99C23×C13C2×C22⋊C411yescharacteristic
100Q8×C13—42no—
101Q8×C13—42no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13#10412yes—
116C2×C4×C13C2×M1611yescharacteristic
117C2×C4×C13C2×M1611yescharacteristic
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13#10412yes—
134C2×Dic13AGL(1,ℤ/8)11yescharacteristic
135C2×Dic13#13711yescharacteristic
136C2×Dic13#13712yes—
137#1057—44no—
138#1057—44no—
139C2×C4×Q8#26111yescharacteristic
140C2×C4⋊C8—261no—
141C2×#97—261no—
142C2×#97—261no—
143#391—131no—
144#391—131no—
145#389—131no—
146#389—131no—
147#387—261no—
148#387—261no—
149C4×C4⋊C4—131no—
150C4×C4⋊C4—261no—
151#376—261no—
152C43—131no—
153#336—132no—
154#336—132no—
155#336—261no—
156C22×C13#40711yescharacteristic
157C22×C13#41011yescharacteristic
158C22×C13#41311yescharacteristic
159C22×C13#41711yescharacteristic
160C22×C13#41911yescharacteristic
161C22×C13C2×#10411yescharacteristic
162C22×C13C2×#10411yescharacteristic
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—22no—
166C4×C13—42no—
167C4×C13—41no—
168C4×C13—42no—
169Dic13—22no—
170Dic13—21no—
171Dic13—21no—
172Dic13—22no—
173Dic13—41no—
174Dic13—81no—
175Dic13—81no—
176C22×Q8C2×#26111yescharacteristic
177C22×C8—262no—
178C22×C8—262no—
179C4×Q8—22no—
180C4×Q8—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4C2×#26111yescharacteristic
187C2×C42—21no—
188C2×C42—131no—
189C2×C42—131no—
190C2×C42—131no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—261no—
195C2×C42C2×#26111yescharacteristic
196C4⋊C8—264no—
197#97—264no—
198#97—522no—
199#95—261no—
200#95—261no—
201#95—261no—
202#95—261no—
203#95—261no—
204#95—261no—
205#95—261no—
206C2×C13#146411yescharacteristic
207C2×C13#148911yescharacteristic
208C2×C13#149111yescharacteristic
209C2×C13#150611yescharacteristic
210C2×C13#150911yescharacteristic
211C2×C13#152411yescharacteristic
212C2×C13#155911yescharacteristic
213C2×Q8—21no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8#612212yes—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—131no—
223C22×C4—261no—
224C22×C4—261no—
225C22×C4C22⋊#26111yescharacteristic
226C22×C4C22⋊#26111yescharacteristic
227C22×C4C22×#26111yescharacteristic
228C2×C8—264no—
229C2×C8—264no—
230C2×C8—522no—
231C2×C8—522no—
232C2×C8—522no—
233C2×C8—522no—
234C4⋊C4—24no—
235C4⋊C4—21no—
236C4⋊C4—521no—
237C4⋊C4—521no—
238C4⋊C4—522no—
239C4⋊C4—521no—
240C4⋊C4—521no—
241C4⋊C4#612212yes—
242C42—24no—
243C42—21no—
244C42—21no—
245C42—262no—
246C42—261no—
247C42—262no—
248C42—261no—
249C42—262no—
250C42—521no—
251C42—521no—
252C42—522no—
253C13#763011yescharacteristic, complemented, Sylow
254C23C2×C22⋊#26111yescharacteristic
255Q8—42no—
256Q8—42no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—132no—
271C2×C4—132no—
272C2×C4—131no—
273C2×C4—131no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4#8811812yes—
290C2×C4C2×#612211yescharacteristic
291C2×C4C2×#612211yescharacteristic
292C8—524no—
293C8—524no—
294C22#1171911611yescharacteristic
295C22#1171913211yescharacteristic
296C22#1171915311yescharacteristic
297C22C2×#8811811yescharacteristic
298C22D13⋊#10411yescharacteristic
299C22#1171916411yescharacteristic
300C22#1171916911yescharacteristic
301C4—21no—
302C4—21no—
303C4—22no—
304C4—42no—
305C4—41no—
306C4—42no—
307C4—261no—
308C4—261no—
309C4—262no—
310C4—262no—
311C4—521no—
312C4—1041no—
313C4—1041no—
314C2#1313008711yescharacteristic
315C2#1313017111yescharacteristic
316C2#1313017811yescharacteristic
317C2#1313022911yescharacteristic
318C2#1313024011yescharacteristic
319C2#1313028811yescharacteristic
320C2#1313037111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×Q8#261
hypocenterC13#7630
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
253. C13#7630semidirect

Maximal subgroups

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

subgroupindex
#131306212
#131305532
#131296562
#131296542
#131173142
#763013