Finite Group Databasebeta

← #13118460

Subgroups — #13118460

Order 1664.

836 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 185 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
1C22×C13×#41C211yesmaximal, characteristic
2C2×#88198C211yesmaximal, characteristic, complemented
3C2×#88190C211yesmaximal, characteristic, complemented
4C2×#88178C211yesmaximal, characteristic, complemented
5#11718891C211yesmaximal, characteristic, complemented
6#11718883C214yesmaximal, complemented
7#11718882C211yesmaximal, characteristic, complemented
8#11718871C214yesmaximal, complemented
9C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
10C2×C13×#41—24no—
11C2×C13×#41—24no—
12C2×C13×#41—24no—
13C22×Q8×C13C2211yescharacteristic
14C22×D4×C13C2212yes—
15C22×D4×C13C2211yescharacteristic
16C23×C4×C13C2212yes—
17C23×C4×C13C2211yescharacteristic
18C22×Dic26C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2214yes—
21C2×C22⋊Dic13C2212yes—
22C2×C22⋊Dic13C2214yes—
23#88198—24no—
24#88190—24no—
25C2×C4⋊Dic13C2211yescharacteristic
26#88178—24no—
27C2×#6101C2212yes—
28C2×#6101C2214yes—
29C2×C4×Dic13C2211yescharacteristic
30C2×C4×Dic13C2211yescharacteristic
31#88071C2212yes—
32#88071C2214yes—
33C24×C13C2312yes—
34C24×C13C2311yescharacteristic
35C13×#41—232no—
36C2×Q8×C13—22no—
37C2×Q8×C13—22no—
38C2×Q8×C13D414yes—
39C2×D4×C13—24no—
40C2×D4×C13—24no—
41C2×D4×C13—24no—
42C2×D4×C13—22no—
43C2×D4×C13—22no—
44C2×D4×C13D414yes—
45C22×C4×C13—24no—
46C22×C4×C13—24no—
47C22×C4×C13—24no—
48C22×C4×C13—22no—
49C22×C4×C13—22no—
50C22×C4×C13D414yes—
51C22×C4×C13C2311yescharacteristic
52C22×C4×C13C2312yes—
53C22×C4×C13C2311yescharacteristic
54C22×Dic13C2312yes—
55C22×Dic13C2312yes—
56C22×Dic13C2312yes—
57C22×Dic13C2312yes—
58C2×Dic26—22no—
59C2×Dic26—22no—
60C2×Dic26—22no—
61C22⋊Dic13—24no—
62C22⋊Dic13—28no—
63C22⋊Dic13—24no—
64C22⋊Dic13—28no—
65C4⋊Dic13—22no—
66#6101—24no—
67#6101—28no—
68C4×Dic13—22no—
69C4×Dic13—22no—
70#2432—131nomaximal, Sylow
71C23×C13—22no—
72C23×C13—21no—
73C23×C13—22no—
74C23×C13—21no—
75C23×C13—22no—
76C23×C13—24no—
77C23×C13—22no—
78C23×C13—24no—
79C23×C13C2×D414yes—
80C23×C13C2×D412yes—
81C23×C13C2411yescharacteristic
82Q8×C13—28no—
83D4×C13—216no—
84D4×C13—28no—
85C2×C4×C13—216no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—28no—
91C2×C4×C13C2×D412yes—
92C2×C4×C13C2×D414yes—
93C2×C4×C13C2×D412yes—
94C2×C4×C13C2×D412yes—
95C2×C4×C13C2×D412yes—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—24no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13#4114yescomplemented
107Dic26—44no—
108C22×#41D1311yescharacteristic
109C2×C4⋊Q8—131no—
110C2×#124—131no—
111C2×C22⋊Q8—131no—
112#394—134no—
113#391—131no—
114#390—131no—
115#385—134no—
116C4×C22⋊C4—131no—
117C22×C13—24no—
118C22×C13—22no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—28no—
122C22×C13—42no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—44no—
127C22×C13C22×D411yescharacteristic
128C22×C13C22×D411yescharacteristic
129C22×C13C22×D411yescharacteristic
130C22×C13C2×#4112yes—
131C22×C132−1+412yes—
132C4×C13—22no—
133C4×C13—24no—
134C4×C13#12014yes—
135Dic13—24no—
136Dic13—42no—
137Dic13—42no—
138Dic13—42no—
139C2×#41—24no—
140C2×#41—24no—
141C2×#41—24no—
142C22×Q8—131no—
143C22×Q8C2×D1311yescharacteristic
144C22×D4C2×D1312yes—
145C22×D4C2×D1311yescharacteristic
146C23×C4C2×D1312yes—
147C23×C4C2×D1311yescharacteristic
148C4⋊Q8—264no—
149#124—264no—
150C22⋊Q8—264no—
151C2×C4⋊C4—132no—
152C2×C4⋊C4—131no—
153C2×C4⋊C4—134no—
154C2×C22⋊C4—132no—
155C2×C22⋊C4—134no—
156C2×C22⋊C4—132no—
157C2×C22⋊C4—134no—
158C2×C42—131no—
159C2×C42—131no—
160#95—132no—
161#95—134no—
162C2×C13—42no—
163C2×C13—44no—
164C2×C13C2×#12011yescharacteristic
165C2×C13#53211yescharacteristic
166C2×C13#53611yescharacteristic
167C2×C13#54712yes—
168C2×C13#54812yes—
169C24C22×D1312yes—
170C24C22×D1311yescharacteristic
171#41—232no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—262no—
175C2×Q8—262no—
176C2×Q8—262no—
177C2×Q8C22⋊D1314yes—
178C2×D4—24no—
179C2×D4—24no—
180C2×D4—24no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4C22⋊D1314yes—
184C22×C4—24no—
185C22×C4—24no—
186C22×C4—24no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—132no—
190C22×C4—132no—
191C22×C4—132no—
192C22×C4—132no—
193C22×C4C22⋊D1314yes—
194C22×C4C22×D1311yescharacteristic
195C22×C4C22×D1312yes—
196C22×C4C22×D1311yescharacteristic
197C4⋊C4—264no—
198C4⋊C4—262no—
199C4⋊C4—268no—
200C22⋊C4—264no—
201C22⋊C4—268no—
202C22⋊C4—264no—
203C22⋊C4—268no—
204C42—262no—
205C42—262no—
206C13#243211yescharacteristic, complemented, Sylow
207C23—24no—
208C23—22no—
209C23—24no—
210C23—22no—
211C23—21no—
212C23—22no—
213C23—22no—
214C23—21no—
215C23C2×C22⋊D1314yes—
216C23C2×C22⋊D1312yes—
217C23C23×D1311yescharacteristic
218Q8—28no—
219Q8—524no—
220D4—216no—
221D4—28no—
222C2×C4—216no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—28no—
228C2×C4—134no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—264no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4C2×C22⋊D1312yes—
240C2×C4C2×C22⋊D1314yes—
241C2×C4C2×C22⋊D1312yes—
242C2×C4C2×C22⋊D1312yes—
243C2×C4C2×C22⋊D1312yes—
244C22—28no—
245C22—22no—
246C22—22no—
247C22—24no—
248C22—22no—
249C22—42no—
250C22—42no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22#41×D1312yes—
255C22#8825712yes—
256C22C22×C22⋊D1311yescharacteristic
257C22C22×C22⋊D1311yescharacteristic
258C22C22×C22⋊D1311yescharacteristic
259C4—22no—
260C4—24no—
261C4—264no—
262C4—522no—
263C4—522no—
264C4—522no—
265C4#8820714yes—
266C2—44no—
267C2—42no—
268C2#1171952912yes—
269C2#1171953011yescharacteristic
270C2#1171953612yes—
271C2#1171953711yescharacteristic
272C2C2×#8820711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC22×C13×#41C2
hypercenterC22×#41D13
hypocenterC13#2432
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
2. C2×#88198C2semidirect
3. C2×#88190C2semidirect
4. C2×#88178C2semidirect
5. #11718891C2semidirect
6. #11718883C2semidirect
7. #11718882C2semidirect
8. #11718871C2semidirect
9. C4×C22⋊Dic13C2semidirect
106. C2×Dic13#41semidirect
206. C13#2432semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#412
C2×#881982
C2×#881902
C2×#881782
#117188912
#117188832
#117188822
#117188712
C4×C22⋊Dic132
#243213