Finite Group Databasebeta

← #13122867

Subgroups — #13122867

Order 1664.

528 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 125 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×#88192C211yesmaximal, characteristic
2C2×#88150C211yesmaximal, characteristic, complemented
3C13×#394C211yesmaximal, characteristic, complemented
4#11718883C211yesmaximal, characteristic, complemented
5#11718644C211yesmaximal, characteristic, complemented
6#11718622C212yesmaximal, complemented
7#11718620C212yesmaximal, complemented
8#11718610C212yesmaximal, complemented
9#11718608C212yesmaximal, complemented
10#11718325C211yesmaximal, characteristic, complemented
11#11718322C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13C2212yes—
14C22×C4×D13C2211yescharacteristic
15C22×Dic26C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2212yes—
18C2×C13×C22⋊C4C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×C22⋊Dic13C2212yes—
22#88192—24no—
23C2×#6103C2211yescharacteristic
24C2×#6103C2211yescharacteristic
25C2×#6103C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2212yes—
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2212yes—
31#88150—24no—
32C13×#95C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C24×C13C2312yes—
38C23×D13C2311yescharacteristic
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—42no—
47C2×C22⋊D13—42no—
48C22×Dic13C2312yes—
49C22×Dic13C2312yes—
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2311yescharacteristic
53C2×C4×D13—42no—
54C2×C4×D13D414yes—
55C2×Dic26—22no—
56C2×Dic26—42no—
57C13×C4⋊C4—22no—
58C13×C22⋊C4—42no—
59C13×C22⋊C4—42no—
60C22⋊Dic13—24no—
61C22⋊Dic13—42no—
62C22⋊Dic13—42no—
63#6103—22no—
64#6103—22no—
65#6103—42no—
66C4⋊Dic13—22no—
67C4⋊Dic13—42no—
68#6101—22no—
69#6101—22no—
70#6101—42no—
71#2816—131nomaximal, Sylow
72C23×C13—22no—
73C23×C13—22no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—22no—
79C23×C13C2411yescharacteristic
80C22×D13—22no—
81C22×D13—21no—
82C22×D13—21no—
83C22×D13—22no—
84C22×D13C2×D412yes—
85D4×C13—44no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13C2×D412yes—
96C22⋊D13—48no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—21no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13C2×D412yes—
110C4×D13—44no—
111Dic26—44no—
112C2×C22⋊Q8—131no—
113C2×#121—131no—
114#399—132no—
115#398—131no—
116#398—131no—
117#394—131no—
118#394—132no—
119#394—132no—
120#394D1311yescharacteristic, complemented
121#393—132no—
122#381—131no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13C22×D411yescharacteristic
131C22×C13H(5,𝔽2)12yes—
132C22×C13H(5,𝔽2)11yescharacteristic
133C22×C13H(5,𝔽2)11yescharacteristic
134C22×C132−1+412yes—
135C2×D13—22no—
136C2×D13—22no—
137C2×D13—22no—
138C2×D13—42no—
139C2×D13—42no—
140C4×C13—22no—
141C4×C13—41no—
142C4×C13—41no—
143C4×C13—42no—
144Dic13—22no—
145Dic13—41no—
146Dic13—41no—
147Dic13—42no—
148Dic13—42no—
149C22×Q8—131no—
150C22×D4—132no—
151C22×D4C2×D1311yescharacteristic
152C23×C4—131no—
153C22⋊Q8—264no—
154#121—264no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—131no—
157C2×C4⋊C4—131no—
158C2×C4⋊C4—132no—
159C2×C4⋊C4—132no—
160C2×C4⋊C4C2×D1311yescharacteristic
161C2×C22⋊C4—132no—
162C2×C22⋊C4—131no—
163C2×C22⋊C4—131no—
164C2×C22⋊C4—132no—
165C2×C22⋊C4—132no—
166C2×C22⋊C4—132no—
167C2×C22⋊C4C2×D1312yes—
168C2×C22⋊C4C2×D1312yes—
169#95—132no—
170#95—131no—
171#95—132no—
172#95—132no—
173#95C2×D1311yescharacteristic
174C2×C13—82no—
175C2×C13#53411yescharacteristic
176C2×C13#53511yescharacteristic
177C2×C13#53611yescharacteristic
178C2×C13#56212yes—
179C2×C13#56212yes—
180D13—42no—
181C24—131no—
182C24C22×D1312yes—
183C2×Q8—262no—
184C2×Q8—522no—
185C2×D4—22no—
186C2×D4—42no—
187C2×D4—264no—
188C2×D4—522no—
189C2×D4—522no—
190C22×C4—131no—
191C22×C4—134no—
192C22×C4—132no—
193C22×C4—131no—
194C22×C4—132no—
195C22×C4—131no—
196C22×C4—522no—
197C22×C4C22×D1312yes—
198C22×C4C22×D1311yescharacteristic
199C22×C4C22×D1311yescharacteristic
200C22×C4C22×D1311yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—262no—
203C4⋊C4—262no—
204C4⋊C4—262no—
205C4⋊C4—522no—
206C4⋊C4—522no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C22⋊C4—262no—
210C22⋊C4—262no—
211C22⋊C4—264no—
212C22⋊C4—522no—
213C22⋊C4—522no—
214C22⋊C4—522no—
215C13#281611yescharacteristic, complemented, Sylow
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—132no—
224C23—262no—
225C23—261no—
226C23—261no—
227C23—262no—
228C23C23×D1311yescharacteristic
229Q8—524no—
230D4—44no—
231D4—528no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—132no—
242C2×C4—262no—
243C2×C4—261no—
244C2×C4—262no—
245C2×C4—261no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—261no—
249C2×C4—262no—
250C2×C4—261no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—524no—
255C2×C4D4×D1312yes—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—262no—
264C22—262no—
265C22—262no—
266C22—522no—
267C22—522no—
268C22C2×D4×D1311yescharacteristic
269C22#8825112yes—
270C22#8825111yescharacteristic
271C22#8825611yescharacteristic
272C22#8825712yes—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—42no—
277C4—262no—
278C4—521no—
279C4—521no—
280C4—522no—
281C4—522no—
282C2—82no—
283C2—522no—
284C2#1171929411yescharacteristic
285C2#1171931211yescharacteristic
286C2#1171932612yes—
287C2#1171937212yes—
288C2#1171938011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC2×#88192C2
hypercenter#394D13
hypocenterC13#2816
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88150C2semidirect
3. C13×#394C2semidirect
4. #11718883C2semidirect
5. #11718644C2semidirect
6. #11718622C2semidirect
7. #11718620C2semidirect
8. #11718610C2semidirect
9. #11718608C2semidirect
10. #11718325C2semidirect
11. #11718322C2semidirect
120. #394D13semidirect
215. C13#2816semidirect

Maximal subgroups

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

subgroupindex
C2×#881922
C2×#881502
C13×#3942
#117188832
#117186442
#117186222
#117186202
#117186102
#117186082
#117183252
#117183222
#281613