Finite Group Databasebeta

← #15773658

Subgroups — #15773658

Order 3328.

586 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 87 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×#11718640C211yesmaximal, characteristic
2#13114916C211yesmaximal, characteristic
3#13112867C214yesmaximal, complemented
4C13×#1463C211yesmaximal, characteristic
5C23×Dic26C411yescharacteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×#6101—21no—
8C13×#407—21no—
9C2×#88071—21no—
10C2×#88071C411yescharacteristic
11#11718868—21no—
12#11718640—21no—
13#11718640—21no—
14#11718640C412yes—
15#11718640C2212yes—
16C13×#324—21no—
17C13×#324C2212yes—
18#11718122—21no—
19#11718122C2212yes—
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C22×Dic26—21no—
26C22×Dic26—41no—
27C22×Dic26—41no—
28C22×Dic26—44no—
29C22×Dic26C2×C412yes—
30C2×C13×M16—41no—
31C2×C13×C4⋊C4—41no—
32C2×C13×C4⋊C4—41no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4C2311yescharacteristic
37C2×#6101—22no—
38C2×#6101—22no—
39C2×#6101—44no—
40C2×#6099—22no—
41C13×C22⋊C8—22no—
42C13×C22⋊C8—41no—
43#88071—22no—
44#88071—21no—
45#88071—22no—
46#88071C2×C412yes—
47C22⋊#1055—41no—
48C22⋊#1055—41no—
49#11815—131nomaximal, Sylow
50C24×C13C22⋊C411yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—41no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×Dic13—24no—
68C22×Dic13—24no—
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—42no—
72C22×Dic13—42no—
73C22×Dic13—42no—
74C22×Dic13—41no—
75C22×Dic13—41no—
76C2×Dic26—44no—
77C2×Dic26—42no—
78C2×Dic26—44no—
79C2×Dic26—48no—
80C2×Dic26—42no—
81C2×Dic26—44no—
82C2×Dic26—44no—
83C13×M16—82no—
84C2×C8×C13—42no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89#6101—44no—
90#6101—44no—
91#6099—42no—
92#6099—42no—
93C2×#1055—42no—
94C2×#395—131no—
95#1821—131no—
96#1463D1311yescharacteristic
97#1354—134no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13#9911yescharacteristic
103C23×C13#9911yescharacteristic
104C23×C13C2×C22⋊C411yescharacteristic
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—81no—
124C2×C4×C13#13712yes—
125C2×Dic13—24no—
126C2×Dic13—24no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—44no—
130C2×Dic13—48no—
131C2×Dic13—44no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134Dic26—48no—
135Dic26—44no—
136Dic26—44no—
137C8×C13—82no—
138#1055—82no—
139C23×Q8—131no—
140C22×C4⋊C4—261no—
141C22×C4⋊C4C2×D1311yescharacteristic
142#407—21no—
143#407—261no—
144#395—132no—
145#395—132no—
146#395—261no—
147#395—261no—
148C2×#95—131no—
149C2×#95—261no—
150#343—132no—
151#343—261no—
152#324—21no—
153#324C2×D1312yes—
154C22×C13—24no—
155C22×C13—24no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13AΣL(1,𝔽16)12yes—
163C22×C13#35612yes—
164C22×C13C2×#9911yescharacteristic
165C22×C13#41911yescharacteristic
166C22×C13#42111yescharacteristic
167C4×C13—22no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173Dic13—44no—
174Dic13—44no—
175C22×Q8—132no—
176C22×Q8—261no—
177C22×Q8—521no—
178C22×Q8—521no—
179C22×Q8—524no—
180C23×C4—261no—
181C23×C4—261no—
182C23×C4C4×D1311yescharacteristic
183C23×C4D5211yescharacteristic
184C23×C4C22⋊D1311yescharacteristic
185C2×M16—41no—
186C2×M16—262no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—262no—
190C2×C4⋊C4—262no—
191C2×C4⋊C4—524no—
192C2×C4⋊C4C4×D1311yescharacteristic
193C2×C4⋊C4D5211yescharacteristic
194C2×C4⋊C4C22⋊D1311yescharacteristic
195C2×C4⋊C4C22×D1311yescharacteristic
196C22⋊C8—22no—
197C22⋊C8—41no—
198C22⋊C8—521no—
199C22⋊C8—521no—
200#95—132no—
201#95—261no—
202#95—262no—
203#95—262no—
204C2×C13—21no—
205C2×C13—22no—
206C2×C13—22no—
207C2×C13—21no—
208C2×C13#151111yescharacteristic
209C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
210C2×C13C2×#35611yescharacteristic
211C24#610311yescharacteristic
212C2×Q8—522no—
213C2×Q8—522no—
214C2×Q8—524no—
215C2×Q8—524no—
216C2×Q8—528no—
217C2×Q8—524no—
218C2×Q8—524no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—264no—
230C22×C4—264no—
231C22×C4—262no—
232C22×C4—262no—
233C22×C4—522no—
234C22×C4—522no—
235C22×C4—522no—
236C22×C4—521no—
237C22×C4—521no—
238C22×C4#610311yescharacteristic
239C22×C4#610311yescharacteristic
240C22×C4#610311yescharacteristic
241C22×C4C2×C4×D1311yescharacteristic
242C22×C4C2×D5211yescharacteristic
243C22×C4C2×C22⋊D1311yescharacteristic
244M16—82no—
245M16—522no—
246M16—522no—
247C2×C8—42no—
248C2×C8—522no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—524no—
254C4⋊C4—524no—
255C13#1181511yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—22no—
259C23—22no—
260C23#8804611yescharacteristic
261C23#8804611yescharacteristic
262C23C2×#610311yescharacteristic
263Q8—524no—
264Q8—528no—
265Q8—524no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—264no—
286C2×C4—264no—
287C2×C4—522no—
288C2×C4—528no—
289C2×C4—522no—
290C2×C4—524no—
291C2×C4—522no—
292C2×C4—524no—
293C2×C4—522no—
294C2×C4#8816312yes—
295C8—82no—
296C8—1042no—
297C22—24no—
298C22—24no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22#1171806312yes—
306C22#1171807012yes—
307C22C2×#8804611yescharacteristic
308C22#1171878111yescharacteristic
309C22#1171880011yescharacteristic
310C4—22no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—524no—
317C4—524no—
318C2—21no—
319C2—21no—
320C2—22no—
321C2—22no—
322C2#1311337011yescharacteristic
323C2C2×#1171806311yescharacteristic
324C2C2×#1171807011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1463C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1463D13
hypocenterC13#11815
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #13112867C2semidirect
255. C13#11815semidirect

Maximal subgroups

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

subgroupindex
C2×#117186402
#131149162
#131128672
C13×#14632
#1181513