Finite Group Databasebeta

← #15773513

Subgroups — #15773513

Order 3328.

414 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#13119821C211yesmaximal, characteristic
2#13113180C211yesmaximal, characteristic
3#13112841C214yesmaximal
4C4×C13×#101C211yesmaximal, characteristic
5C2×C4×Q8×C13C2211yescharacteristic
6C2×#88198—21no—
7C2×#88123C411yescharacteristic
8C2×C13×#101—21no—
9C4×C13×M16—21no—
10#11718644C412yes—
11#11718644C2212yes—
12#11718635—21no—
13C4×C4⋊Dic13C411yescharacteristic
14#11718589—21no—
15#11718589—21no—
16#11718587—21no—
17C13×#343C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C22×Q8×C13D411yescharacteristic
21C22×Dic26—21no—
22C2×C13×M16—22no—
23C4×Q8×C13—41no—
24C4×Q8×C13—41no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C4⋊C4C2311yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31#88198—44no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C412yes—
35C2×#6101—22no—
36C2×#6101—22no—
37C2×C4×Dic13—21no—
38#88123—41no—
39#88123—41no—
40C13×#101—24no—
41C13×#97—41no—
42C4×C8×C13—41no—
43#88071—22no—
44#88071—22no—
45#88071C2×C412yes—
46C22⋊#1055—22no—
47C4⋊#1055—41no—
48#88043—41no—
49#11782—131nomaximal, Sylow
50C2×Q8×C13—22no—
51C2×Q8×C13—22no—
52C2×Q8×C13—41no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—22no—
61C22×Dic13—22no—
62C2×Dic26—42no—
63C2×Dic26—42no—
64C2×Dic26—42no—
65C13×M16—24no—
66C13×M16—42no—
67C2×C8×C13—42no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C4⋊Dic13—24no—
78C4⋊Dic13—41no—
79C4⋊Dic13—41no—
80C4⋊Dic13—42no—
81#6101—44no—
82#6101—44no—
83C4×Dic13—42no—
84C2×#1055—42no—
85#2546—131no—
86C4×#101D1311yescharacteristic
87#1467—131no—
88#1346—134no—
89C23×C13C2×C22⋊C411yescharacteristic
90Q8×C13—44no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13#9911yescharacteristic
106C2×C4×C13#9911yescharacteristic
107C2×C4×C13#10412yes—
108C2×C4×C13AGL(1,ℤ/8)12yes—
109C2×Dic13—24no—
110C2×Dic13—42no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115Dic26—84no—
116C8×C13—44no—
117#1055—82no—
118C2×C4⋊Q8—131no—
119C2×C4⋊Q8—261no—
120C2×C4×Q8C2×D1311yescharacteristic
121#432—261no—
122C2×#101—21no—
123C4×M16—21no—
124#398—132no—
125#398—132no—
126#391—261no—
127#389—261no—
128#389—261no—
129C4×C4⋊C4—131no—
130#343C2×D1312yes—
131#324—132no—
132#324—261no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13C2×#9911yescharacteristic
136C22×C13#41811yescharacteristic
137C22×C13C2×#10411yescharacteristic
138C4×C13—21no—
139C4×C13—22no—
140C4×C13—22no—
141C4×C13—41no—
142C4×C13—41no—
143C4×C13—41no—
144C4×C13—41no—
145C4×C13#35612yes—
146Dic13—44no—
147Dic13—82no—
148C22×Q8—261no—
149C22×Q8C22⋊D1311yescharacteristic
150C2×M16—22no—
151C4⋊Q8—521no—
152C4⋊Q8—521no—
153C4⋊Q8—524no—
154C4×Q8—41no—
155C4×Q8—41no—
156C2×C4⋊C4—132no—
157C2×C4⋊C4—261no—
158C2×C4⋊C4—262no—
159C2×C4⋊C4—261no—
160C2×C4⋊C4—262no—
161C2×C4⋊C4C4×D1311yescharacteristic
162C2×C4⋊C4D5211yescharacteristic
163C2×C4⋊C4C22×D1311yescharacteristic
164C2×C42—261no—
165C2×C42C4×D1311yescharacteristic
166C2×C42D5211yescharacteristic
167C2×C42C22⋊D1311yescharacteristic
168C4⋊C8—521no—
169#101—24no—
170C22⋊C8—262no—
171#97—41no—
172#97—521no—
173C4×C8—41no—
174#95—132no—
175#95—262no—
176#95—262no—
177C2×C13—21no—
178C2×C13—21no—
179C2×C13#150711yescharacteristic
180C2×C13#212311yescharacteristic
181C2×C13C2×#35611yescharacteristic
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—41no—
185C2×Q8—522no—
186C2×Q8—522no—
187C2×Q8—522no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4#610311yescharacteristic
191C22×C4#610311yescharacteristic
192C22×C4#610311yescharacteristic
193C22×C4#610311yescharacteristic
194C22×C4C2×C4×D1311yescharacteristic
195C22×C4C2×D5211yescharacteristic
196C22×C4C2×C22⋊D1311yescharacteristic
197M16—24no—
198M16—42no—
199C2×C8—42no—
200C2×C8—522no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—264no—
205C4⋊C4—522no—
206C4⋊C4—524no—
207C4⋊C4—524no—
208C4⋊C4—521no—
209C4⋊C4—521no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—522no—
217C13#1178211yescharacteristic, complemented, Sylow
218C23C2×#610311yescharacteristic
219Q8—44no—
220Q8—1044no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—264no—
236C2×C4—522no—
237C2×C4—522no—
238C2×C4—522no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4#8804512yes—
242C2×C4#8804611yescharacteristic
243C2×C4#8804611yescharacteristic
244C2×C4#8820312yes—
245C8—44no—
246C8—1042no—
247C22—21no—
248C22—21no—
249C22C2×#8804511yescharacteristic
250C22C2×#8804611yescharacteristic
251C22#1171866211yescharacteristic
252C4—22no—
253C4—22no—
254C4—21no—
255C4—41no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—524no—
260C4—1042no—
261C4#1171807012yes—
262C2—21no—
263C2—21no—
264C2#1311335111yescharacteristic
265C2#1311649111yescharacteristic
266C2C2×#1171807011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC4×C13×#101C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenterC4×#101D13
hypocenterC13#11782
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
217. C13#11782semidirect

Maximal subgroups

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

subgroupindex
#131198212
#131131802
#131128412
C4×C13×#1012
#1178213