Finite Group Databasebeta

← #13120778

Subgroups — #13120778

Order 1664.

584 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 133 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×#88194C211yesmaximal, characteristic
2C2×#88143C211yesmaximal, characteristic, complemented
3C13×#394C211yesmaximal, characteristic, complemented
4#11718883C211yesmaximal, characteristic, complemented
5#11718652C211yesmaximal, characteristic, complemented
6#11718622C212yesmaximal, complemented
7#11718620C212yesmaximal, complemented
8#11718618C212yesmaximal, complemented
9#11718618C212yesmaximal, complemented
10#11718333C211yesmaximal, characteristic, complemented
11#11718309C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13C2212yes—
14C22×C22⋊D13C2212yes—
15C22×D52C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2212yes—
18C2×C13×C22⋊C4C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21#88194—24no—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×C4×Dic13C2212yes—
32C2×C4×Dic13C2211yescharacteristic
33#88143—24no—
34C13×#95C2211yescharacteristic
35#88071C2212yes—
36#88071C2211yescharacteristic
37C24×C13C2312yes—
38C23×D13C2312yes—
39C2×D4×C13—22no—
40C2×D4×C13—42no—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—24no—
46C2×C22⋊D13—24no—
47C2×C22⋊D13—24no—
48C2×C22⋊D13—24no—
49C2×C22⋊D13—42no—
50C2×C22⋊D13—42no—
51C22×Dic13C2312yes—
52C22×Dic13C2311yescharacteristic
53C22×Dic13C2311yescharacteristic
54C22×Dic13C2311yescharacteristic
55C22×Dic13C2311yescharacteristic
56C2×D52—22no—
57C2×D52—42no—
58C13×C4⋊C4—22no—
59C13×C22⋊C4—42no—
60C13×C22⋊C4—42no—
61C22⋊Dic13—42no—
62C22⋊Dic13—42no—
63#6103—42no—
64#6103—42no—
65#6103—42no—
66#6103—42no—
67C4⋊Dic13—22no—
68#6101—22no—
69#6101—22no—
70#6101—22no—
71#6101—22no—
72C4×Dic13—24no—
73C4×Dic13D414yes—
74#2641—131nomaximal, Sylow
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—22no—
79C23×C13—22no—
80C23×C13—22no—
81C23×C13—22no—
82C23×C13C2411yescharacteristic
83C22×D13—22no—
84C22×D13—22no—
85C22×D13—22no—
86C22×D13—22no—
87C22×D13—22no—
88C22×D13—22no—
89C22×D13—22no—
90D4×C13—44no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13C2×D412yes—
101C22⋊D13—48no—
102C22⋊D13—48no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—21no—
113C2×Dic13C2×D412yes—
114C2×Dic13C2×D412yes—
115C2×Dic13#4114yes—
116D52—44no—
117C2×#127—131no—
118C2×#125—131no—
119#394—131no—
120#394—131no—
121#394—132no—
122#394—132no—
123#394—131no—
124#394D1311yescharacteristic, complemented
125#390—132no—
126#390—132no—
127#376—131no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13C22×D411yescharacteristic
136C22×C13C2×#4112yes—
137C22×C13H(5,𝔽2)12yes—
138C22×C13H(5,𝔽2)11yescharacteristic
139C22×C13H(5,𝔽2)11yescharacteristic
140C2×D13—42no—
141C2×D13—42no—
142C2×D13—42no—
143C2×D13—42no—
144C2×D13—42no—
145C2×D13—42no—
146C2×D13—42no—
147C4×C13—22no—
148C4×C13—41no—
149C4×C13—41no—
150C4×C13—42no—
151Dic13—22no—
152Dic13—41no—
153Dic13—41no—
154Dic13—42no—
155Dic13#12414yes—
156C22×D4—132no—
157C22×D4—132no—
158C22×D4—131no—
159C22×D4C2×D1311yescharacteristic
160#127—264no—
161#125—264no—
162C2×C4⋊C4—131no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—131no—
165C2×C4⋊C4—131no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4C2×D1311yescharacteristic
168C2×C22⋊C4—132no—
169C2×C22⋊C4—132no—
170C2×C22⋊C4—132no—
171C2×C22⋊C4—132no—
172C2×C22⋊C4—132no—
173C2×C22⋊C4—132no—
174C2×C22⋊C4C2×D1312yes—
175C2×C22⋊C4C2×D1312yes—
176C2×C42—131no—
177C2×C42—132no—
178#95—132no—
179#95—131no—
180#95C2×D1311yescharacteristic
181C2×C13—82no—
182C2×C13C2×#12411yescharacteristic
183C2×C13#53511yescharacteristic
184C2×C13#53511yescharacteristic
185C2×C13#54012yes—
186C2×C13#54012yes—
187D13—82no—
188C24—132no—
189C24C22×D1312yes—
190C2×D4—22no—
191C2×D4—42no—
192C2×D4—264no—
193C2×D4—264no—
194C2×D4—264no—
195C2×D4—264no—
196C2×D4—262no—
197C2×D4—522no—
198C2×D4—522no—
199C2×D4—522no—
200C22×C4—131no—
201C22×C4—131no—
202C22×C4—132no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4C22×D1312yes—
206C22×C4C22×D1311yescharacteristic
207C22×C4C22×D1311yescharacteristic
208C22×C4C22×D1311yescharacteristic
209C4⋊C4—22no—
210C4⋊C4—262no—
211C4⋊C4—262no—
212C4⋊C4—262no—
213C4⋊C4—262no—
214C4⋊C4—262no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C22⋊C4—522no—
218C22⋊C4—522no—
219C22⋊C4—522no—
220C22⋊C4—522no—
221C22⋊C4—522no—
222C22⋊C4—522no—
223C42—134no—
224C42—264no—
225C13#264111yescharacteristic, complemented, Sylow
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—262no—
234C23—262no—
235C23—262no—
236C23—262no—
237C23—262no—
238C23—262no—
239C23—262no—
240C23C23×D1311yescharacteristic
241D4—44no—
242D4—524no—
243D4—528no—
244D4—528no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—132no—
255C2×C4—134no—
256C2×C4—132no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—261no—
260C2×C4—261no—
261C2×C4—262no—
262C2×C4—261no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—261no—
266C2×C4—262no—
267C2×C4D4×D1312yes—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—522no—
276C22—522no—
277C22—522no—
278C22—522no—
279C22—522no—
280C22—522no—
281C22—522no—
282C22C2×D4×D1311yescharacteristic
283C22#8825112yes—
284C22#8825111yescharacteristic
285C22#41×D1312yes—
286C22#8825611yescharacteristic
287C4—22no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—134no—
292C4—262no—
293C4—521no—
294C4—521no—
295C4—522no—
296C2—82no—
297C2—1042no—
298C2#1171929711yescharacteristic
299C2#1171931211yescharacteristic
300C2#1171932012yes—
301C2#1171936812yes—
302C2D13×#12411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC2×#88194C2
hypercenter#394D13
hypocenterC13#2641
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88143C2semidirect
3. C13×#394C2semidirect
4. #11718883C2semidirect
5. #11718652C2semidirect
6. #11718622C2semidirect
7. #11718620C2semidirect
8. #11718618C2semidirect
9. #11718618C2semidirect
10. #11718333C2semidirect
11. #11718309C2semidirect
124. #394D13semidirect
225. C13#2641semidirect

Maximal subgroups

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

subgroupindex
C2×#881942
C2×#881432
C13×#3942
#117188832
#117186522
#117186222
#117186202
#117186182
#117183332
#117183092
#264113