Finite Group Databasebeta

← #13120312

Subgroups — #13120312

Order 1664.

596 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 139 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×#88149C211yesmaximal, characteristic
2C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
3C13×#400C211yesmaximal, characteristic, complemented
4#11718652C211yesmaximal, characteristic, complemented
5#11718643C211yesmaximal, characteristic, complemented
6#11718333C211yesmaximal, characteristic, complemented
7#11718331C212yesmaximal, complemented
8#11718330C212yesmaximal, complemented
9#11718327C211yesmaximal, characteristic, complemented
10#11718326C212yesmaximal, complemented
11#11718326C212yesmaximal, complemented
12C22×D52C2212yes—
13C22×D52C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C22×C4×D13C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×C4⋊Dic13C2211yescharacteristic
26C2×#6101C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×C4×Dic13C2212yes—
29#88149—24no—
30C4⋊C4×D13—24no—
31C13×#95C2212yes—
32C13×#95C2212yes—
33C13×#95C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2211yescharacteristic
37C23×D13C2312yes—
38C23×D13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C2×D52—24no—
49C2×D52—24no—
50C2×D52—24no—
51C2×D52—22no—
52C2×D52—42no—
53C2×C4×D13—22no—
54C2×C4×D13—22no—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—42no—
58C2×C4×D13—42no—
59C2×C4×D13D414yes—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—22no—
62#6103—24no—
63#6103—24no—
64#6103—24no—
65#6103—24no—
66#6103—42no—
67#6103—42no—
68C4⋊Dic13—22no—
69#6101—22no—
70#6101—22no—
71C4×Dic13—42no—
72#2591—131nomaximal, Sylow
73C23×C13C2411yescharacteristic
74C22×D13—21no—
75C22×D13—21no—
76C22×D13—22no—
77C22×D13—22no—
78C22×D13—22no—
79C22×D13—22no—
80C22×D13—22no—
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—22no—
84C22×D13C2×D412yes—
85C22×D13#4114yes—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13C2×D412yes—
98C2×C4×C13#4112yes—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—22no—
102C2×Dic13—21no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13C2×D412yes—
108C2×Dic13#4112yes—
109D52—44no—
110D52—48no—
111C4×D13—28no—
112C4×D13—44no—
113C4×D13—44no—
114C2×#121—131no—
115C22×C4⋊C4—131no—
116#400—131no—
117#400D1311yescharacteristic, complemented
118#394—131no—
119#394—131no—
120#388—132no—
121#388—132no—
122#386—132no—
123#386—132no—
124C4×C22⋊C4—131no—
125C22×C13C22×D411yescharacteristic
126C22×C13C2×#4111yescharacteristic
127C22×C13C2×#4111yescharacteristic
128C22×C13C2×#4112yes—
129C22×C13H(5,𝔽2)12yes—
130C2×D13—22no—
131C2×D13—22no—
132C2×D13—24no—
133C2×D13—24no—
134C2×D13—42no—
135C2×D13—42no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—42no—
139C2×D13—42no—
140C2×D13—42no—
141C2×D13#12414yes—
142C4×C13—22no—
143C4×C13—22no—
144C4×C13—42no—
145C4×C13—41no—
146C4×C13—42no—
147Dic13—22no—
148Dic13—22no—
149Dic13—41no—
150Dic13—42no—
151C22×D4—132no—
152C22×D4—131no—
153C23×C4—131no—
154C23×C4—131no—
155C23×C4—131no—
156#121—264no—
157C2×C4⋊C4—131no—
158C2×C4⋊C4—131no—
159C2×C4⋊C4—131no—
160C2×C4⋊C4—264no—
161C2×C4⋊C4C2×D1311yescharacteristic
162C2×C4⋊C4C2×D1311yescharacteristic
163C2×C22⋊C4—132no—
164C2×C22⋊C4—132no—
165C2×C22⋊C4—132no—
166C2×C22⋊C4—132no—
167C2×C22⋊C4—132no—
168C2×C22⋊C4—132no—
169C2×C42—132no—
170#95—131no—
171#95—132no—
172#95—132no—
173#95C2×D1311yescharacteristic
174#95C2×D1312yes—
175#95C2×D1312yes—
176C2×C13#52511yescharacteristic
177C2×C13C2×#12411yescharacteristic
178C2×C13#53411yescharacteristic
179C2×C13#55312yes—
180C2×C13#55312yes—
181D13—24no—
182D13—82no—
183C24—131no—
184C24—132no—
185C2×D4—264no—
186C2×D4—264no—
187C2×D4—264no—
188C2×D4—262no—
189C2×D4—522no—
190C22×C4—131no—
191C22×C4—131no—
192C22×C4—134no—
193C22×C4—132no—
194C22×C4—131no—
195C22×C4—262no—
196C22×C4—262no—
197C22×C4—262no—
198C22×C4—262no—
199C22×C4—522no—
200C22×C4—522no—
201C22×C4C22×D1312yes—
202C22×C4C22×D1312yes—
203C22×C4C22×D1311yescharacteristic
204C22×C4C22×D1311yescharacteristic
205C22×C4C22×D1311yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—262no—
209C4⋊C4—262no—
210C4⋊C4—262no—
211C22⋊C4—264no—
212C22⋊C4—264no—
213C22⋊C4—264no—
214C22⋊C4—264no—
215C22⋊C4—522no—
216C22⋊C4—522no—
217C42—522no—
218C13#259111yescharacteristic, complemented, Sylow
219C23—132no—
220C23—134no—
221C23—261no—
222C23—261no—
223C23—262no—
224C23—262no—
225C23—262no—
226C23—262no—
227C23—262no—
228C23—262no—
229C23—262no—
230C23—262no—
231C23C23×D1311yescharacteristic
232D4—524no—
233D4—528no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—132no—
246C2×C4—132no—
247C2×C4—268no—
248C2×C4—261no—
249C2×C4—261no—
250C2×C4—262no—
251C2×C4—261no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—262no—
256C2×C4—524no—
257C2×C4—524no—
258C2×C4D4×D1312yes—
259C2×C4#613112yes—
260C22—134no—
261C22—262no—
262C22—262no—
263C22—264no—
264C22—264no—
265C22—522no—
266C22—522no—
267C22—522no—
268C22—522no—
269C22—522no—
270C22—522no—
271C22—522no—
272C22C2×D4×D1311yescharacteristic
273C22C2×#613111yescharacteristic
274C22#41×D1311yescharacteristic
275C22#41×D1312yes—
276C22#8825612yes—
277C4—22no—
278C4—22no—
279C4—41no—
280C4—42no—
281C4—42no—
282C4—262no—
283C4—262no—
284C4—521no—
285C4—522no—
286C2—264no—
287C2—1042no—
288C2#1171933211yescharacteristic
289C2#1171935811yescharacteristic
290C2D13×#12411yescharacteristic
291C2#1171940012yes—
292C2#1171941412yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#400C2
prime radicalC2×#88149C2
hypercenter#400D13
hypocenterC13#2591
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D13C2semidirect
3. C13×#400C2semidirect
4. #11718652C2semidirect
5. #11718643C2semidirect
6. #11718333C2semidirect
7. #11718331C2semidirect
8. #11718330C2semidirect
9. #11718327C2semidirect
10. #11718326C2semidirect
11. #11718326C2semidirect
117. #400D13semidirect
218. C13#2591semidirect

Maximal subgroups

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

subgroupindex
C2×#881492
C2×C4⋊C4×D132
C13×#4002
#117186522
#117186432
#117183332
#117183312
#117183302
#117183272
#117183262
#259113