Finite Group Databasebeta

← #13118071

Subgroups — #13118071

Order 1664.

696 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 159 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×D4×Dic13C212yesmaximal, complemented
2C2×D4×Dic13C211yesmaximal, characteristic, complemented
3C2×#88131C211yesmaximal, characteristic, complemented
4C13×#392C211yesmaximal, characteristic
5#11718883C211yesmaximal, characteristic, complemented
6#11718883C212yesmaximal, complemented
7#11718614C211yesmaximal, characteristic, complemented
8#11718609C212yesmaximal, complemented
9C22⋊C4×Dic13C212yesmaximal, complemented
10#11718322C211yesmaximal, characteristic, complemented
11#11718310C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×D4×C13C2212yes—
14C23×Dic13C2212yes—
15C23×Dic13C2211yescharacteristic
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×C22⋊Dic13C2212yes—
22C2×C22⋊Dic13C2212yes—
23D4×Dic13—28no—
24D4×Dic13—24no—
25C2×C4⋊Dic13C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2212yes—
30C2×C4×Dic13C2211yescharacteristic
31C2×C4×Dic13C2212yes—
32C2×C4×Dic13C2211yescharacteristic
33#88131—24no—
34C13×#95C2211yescharacteristic
35#88071C2211yescharacteristic
36#88071C2212yes—
37#88071C2212yes—
38C24×C13C2311yescharacteristic
39C24×C13C2312yes—
40C2×D4×C13—24no—
41C2×D4×C13—24no—
42C2×D4×C13—24no—
43C2×D4×C13—22no—
44C2×D4×C13—24no—
45C22×C4×C13C2311yescharacteristic
46C22×C4×C13C2311yescharacteristic
47C22×C4×C13C2312yes—
48C22×Dic13—22no—
49C22×Dic13—22no—
50C22×Dic13—24no—
51C22×Dic13—24no—
52C22×Dic13—24no—
53C22×Dic13D414yescomplemented
54C22×Dic13C2311yescharacteristic
55C22×Dic13C2312yes—
56C22×Dic13C2312yes—
57C22×Dic13C2311yescharacteristic
58C22×Dic13C2311yescharacteristic
59C22×Dic13C2311yescharacteristic
60C13×C22⋊C4—22no—
61C13×C22⋊C4—24no—
62C22⋊Dic13—24no—
63C22⋊Dic13—24no—
64C22⋊Dic13—22no—
65C22⋊Dic13—24no—
66C22⋊Dic13—24no—
67C4⋊Dic13—22no—
68C4⋊Dic13—24no—
69#6101—22no—
70#6101—24no—
71#6101—22no—
72C4×Dic13—22no—
73C4×Dic13—24no—
74C4×Dic13D414yescomplemented
75#2392—131nomaximal, Sylow
76C23×C13—21no—
77C23×C13—22no—
78C23×C13—22no—
79C23×C13—22no—
80C23×C13—21no—
81C23×C13—22no—
82C23×C13—22no—
83C23×C13—22no—
84C23×C13—22no—
85C23×C13—22no—
86C23×C13C2×D412yes—
87C23×C13#4114yes—
88C23×C13C2411yescharacteristic
89D4×C13—28no—
90D4×C13—216no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13C2×D412yes—
97C2×C4×C13#4114yes—
98C2×Dic13—21no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—28no—
102C2×Dic13—21no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—48no—
111C2×Dic13C2×D412yes—
112C2×Dic13C2×D412yes—
113C2×Dic13C2×D412yes—
114C2×Dic13C2×D412yes—
115C2×Dic13#4112yes—
116C2×C4×D4—131no—
117C2×C4×D4—132no—
118C2×#117—131no—
119#398—131no—
120#397—131no—
121#396—132no—
122#394—132no—
123#394—131no—
124#392D1311yescharacteristic
125C4×C4⋊C4—131no—
126C4×C22⋊C4—132no—
127C22×C13—22no—
128C22×C13—24no—
129C22×C13—24no—
130C22×C13—24no—
131C22×C13—24no—
132C22×C13—42no—
133C22×C13—41no—
134C22×C13—42no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13—41no—
138C22×C13—42no—
139C22×C13C22×D411yescharacteristic
140C22×C13C22×D411yescharacteristic
141C22×C13C2×#4112yes—
142C22×C13C2×#4112yes—
143C22×C13C2×#4111yescharacteristic
144C4×C13—22no—
145C4×C13—24no—
146C4×C13—41no—
147Dic13—22no—
148Dic13—22no—
149Dic13—42no—
150Dic13—41no—
151Dic13—42no—
152Dic13#12114yes—
153C22×D4C2×D1311yescharacteristic
154C22×D4C2×D1312yes—
155C23×C4—131no—
156C23×C4—132no—
157C4×D4—264no—
158C4×D4—268no—
159#117—264no—
160C2×C4⋊C4—131no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—132no—
165C2×C22⋊C4—131no—
166C2×C22⋊C4—132no—
167C2×C22⋊C4—132no—
168C2×C22⋊C4—132no—
169C2×C22⋊C4—132no—
170C2×C22⋊C4C2×D1311yescharacteristic
171C2×C22⋊C4C2×D1312yes—
172C2×C42—131no—
173C2×C42—131no—
174C2×C42—132no—
175#95—132no—
176#95—132no—
177#95—131no—
178#95C2×D1311yescharacteristic
179C2×C13—42no—
180C2×C13—44no—
181C2×C13C2×#12111yescharacteristic
182C2×C13#52511yescharacteristic
183C2×C13#52512yes—
184C2×C13#52912yes—
185C2×C13#53211yescharacteristic
186C24C22×D1311yescharacteristic
187C24C22×D1312yes—
188C2×D4—24no—
189C2×D4—24no—
190C2×D4—24no—
191C2×D4—22no—
192C2×D4—24no—
193C22×C4—131no—
194C22×C4—134no—
195C22×C4—131no—
196C22×C4—131no—
197C22×C4—132no—
198C22×C4—131no—
199C22×C4—132no—
200C22×C4—262no—
201C22×C4—262no—
202C22×C4—264no—
203C22×C4—264no—
204C22×C4—264no—
205C22×C4C22×D1311yescharacteristic
206C22×C4C22×D1311yescharacteristic
207C22×C4C22×D1312yes—
208C4⋊C4—262no—
209C4⋊C4—264no—
210C4⋊C4—262no—
211C4⋊C4—262no—
212C4⋊C4—264no—
213C22⋊C4—22no—
214C22⋊C4—24no—
215C22⋊C4—262no—
216C22⋊C4—264no—
217C22⋊C4—264no—
218C22⋊C4—264no—
219C22⋊C4—264no—
220C42—134no—
221C42—262no—
222C42—264no—
223C13#239211yescharacteristic, complemented, Sylow
224C23—21no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—21no—
234C23D4×D1312yes—
235C23#612914yes—
236C23C23×D1311yescharacteristic
237D4—28no—
238D4—216no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—132no—
245C2×C4—132no—
246C2×C4—132no—
247C2×C4—132no—
248C2×C4—132no—
249C2×C4—268no—
250C2×C4—261no—
251C2×C4—262no—
252C2×C4—261no—
253C2×C4—262no—
254C2×C4—261no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—528no—
262C2×C4D4×D1312yes—
263C2×C4#612914yes—
264C22—24no—
265C22—24no—
266C22—24no—
267C22—24no—
268C22—22no—
269C22—41no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—41no—
275C22—42no—
276C22C2×D4×D1311yescharacteristic
277C22C2×D4×D1311yescharacteristic
278C22C2×#612912yes—
279C22C2×#612912yes—
280C22#41×D1311yescharacteristic
281C4—22no—
282C4—24no—
283C4—41no—
284C4—134no—
285C4—262no—
286C4—262no—
287C4—522no—
288C4—521no—
289C4—522no—
290C2—42no—
291C2—44no—
292C2#1171929111yescharacteristic
293C2#1171929112yes—
294C2#1171930512yes—
295C2D13×#12111yescharacteristic
296C2#1171942111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC13×#392C2
hypercenter#392D13
hypocenterC13#2392
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic13C2semidirect
2. C2×D4×Dic13C2semidirect
3. C2×#88131C2semidirect
5. #11718883C2semidirect
6. #11718883C2semidirect
7. #11718614C2semidirect
8. #11718609C2semidirect
9. C22⋊C4×Dic13C2semidirect
10. #11718322C2semidirect
11. #11718310C2semidirect
53. C22×Dic13D4semidirect
74. C4×Dic13D4semidirect
223. C13#2392semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
C2×#881312
C13×#3922
#117188832
#117186142
#117186092
C22⋊C4×Dic132
#117183222
#117183102
#239213