Finite Group Databasebeta

← #16781158

Subgroups — #16781158

Order 3328.

1030 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 152 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#13130693C212yesmaximal
2C2×#11718303C214yesmaximal, complemented
3C2×D13×C4⋊Q8C211yesmaximal, characteristic
4C22×Q8×D13C412yes—
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×#88198C2212yes—
7D13×C4⋊Q8—28no—
8C2×C4⋊C4×D13—22no—
9C2×#88142—22no—
10C2×C42×D13C2211yescharacteristic
11C2×#88123C411yescharacteristic
12C2×#88112C2214yes—
13C2×#88111—22no—
14#11718303—28no—
15#11718290—22no—
16C22×Q8×C13C2×C412yes—
17C2×Q8×D13—24no—
18C2×Q8×D13—24no—
19C2×Q8×D13—44no—
20C2×Q8×D13—44no—
21C22×C4×D13—22no—
22C22×C4×D13C2×C411yescharacteristic
23C22×C4×D13D412yes—
24C22×Dic26—22no—
25C22×Dic26C2×C412yes—
26C22×#1057—24no—
27C13×C4⋊Q8—24no—
28C2×C13×C4⋊C4—22no—
29C2×C42×C13C2×C411yescharacteristic
30#88198—24no—
31#88198D418yes—
32C2×C4⋊Dic13—22no—
33C2×#6101—24no—
34C2×C4×Dic13D412yes—
35C2×C4×Dic13C2311yescharacteristic
36C4⋊C4×D13—216no—
37#88142—216no—
38C42×D13—24no—
39#88123—24no—
40#88112—28no—
41#88111—44no—
42#8342—131nomaximal, Sylow
43C23×D13C22⋊C411yescharacteristic
44C2×Q8×C13—22no—
45C2×Q8×C13—42no—
46C2×Q8×C13—42no—
47C2×Q8×C13C22⋊C414yes—
48C22×C4×C13—22no—
49C22×C4×C13C22⋊C412yes—
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13C22⋊C411yescharacteristic
53C22×Dic13C2×D412yes—
54Q8×D13—416no—
55Q8×D13—416no—
56C2×C4×D13—22no—
57C2×C4×D13—22no—
58C2×C4×D13—22no—
59C2×C4×D13—24no—
60C2×C4×D13—24no—
61C2×C4×D13—28no—
62C2×C4×D13—44no—
63C2×C4×D13—44no—
64C2×C4×D13SD1614yes—
65C2×C4×D13Q1614yes—
66C2×Dic26—28no—
67C2×Dic26—22no—
68C2×Dic26—44no—
69C2×Dic26—44no—
70C2×Dic26—42no—
71C2×Dic26—42no—
72C2×Dic26C22⋊C414yes—
73C2×#1057—44no—
74C2×#1057—44no—
75C2×#1057—44no—
76C13×C4⋊C4—28no—
77C42×C13—22no—
78C4⋊Dic13—28no—
79#6101—216no—
80C4×Dic13—24no—
81C4×Dic13C2×D414yes—
82C22×C4⋊Q8—131no—
83#1797—132no—
84C2×#333—134no—
85C23×C13C2×C22⋊C411yescharacteristic
86C22×D13—21no—
87C22×D13—21no—
88C22×D13—22no—
89C22×D13#10012yes—
90C22×D13#10314yes—
91Q8×C13—44no—
92Q8×C13—44no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—24no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13#10314yes—
101C2×C4×C13C2×C22⋊C412yes—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—24no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13#10012yes—
108C2×Dic13#12014yes—
109C2×Dic13C2×SD1612yes—
110C2×Dic13C2×Q1612yes—
111C2×Dic13#13714yes—
112C4×D13—28no—
113C4×D13—28no—
114C4×D13—28no—
115C4×D13—416no—
116Dic26—416no—
117Dic26—44no—
118Dic26—44no—
119#1057—84no—
120C23×Q8—132no—
121C2×C4⋊Q8—132no—
122C2×C4⋊Q8—131no—
123C2×C4⋊Q8—262no—
124C2×C4⋊Q8—268no—
125C2×C4⋊Q8#26111yescharacteristic
126C22×C4⋊C4—262no—
127C22×C42—131no—
128C2×C4⋊C8—134no—
129C2×C22⋊C8—262no—
130#336—262no—
131#333—268no—
132C22×C13#37911yescharacteristic
133C22×C13C2×#10011yescharacteristic
134C22×C13C2×#10011yescharacteristic
135C22×C13C2×#10312yes—
136C22×C13#41912yes—
137C2×D13—24no—
138C2×D13—22no—
139C2×D13—22no—
140C2×D13—24no—
141C2×D13#33314yescomplemented
142C4×C13—22no—
143C4×C13—24no—
144C4×C13—44no—
145Dic13—22no—
146Dic13—44no—
147Dic13#44814yes—
148Dic13#45114yes—
149C22×Q8—132no—
150C22×Q8—262no—
151C22×Q8—264no—
152C22×Q8—264no—
153C22×Q8—524no—
154C22×Q8—524no—
155C22×Q8C2×#26112yes—
156C23×C4—132no—
157C23×C4—131no—
158C23×C4—262no—
159C22×C8—264no—
160C4⋊Q8—24no—
161C4⋊Q8—138no—
162C4⋊Q8—264no—
163C4⋊Q8—264no—
164C4⋊Q8—2616no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—2616no—
167C2×C4⋊C4—264no—
168C2×C4⋊C4—262no—
169C2×C42—131no—
170C2×C42—132no—
171C2×C42—264no—
172C2×C42C2×#26111yescharacteristic
173C4⋊C8—268no—
174C22⋊C8—524no—
175C2×C13C2×#33311yescharacteristic
176C2×C13#154812yes—
177C2×C13#155811yescharacteristic
178C2×C13#178311yescharacteristic
179C2×C13#178712yes—
180D13—24no—
181C24—131no—
182C2×Q8—22no—
183C2×Q8—42no—
184C2×Q8—42no—
185C2×Q8—134no—
186C2×Q8—268no—
187C2×Q8—262no—
188C2×Q8—522no—
189C2×Q8—522no—
190C2×Q8—524no—
191C2×Q8—524no—
192C2×Q8—5216no—
193C2×Q8—5216no—
194C2×Q8C22⋊#26114yes—
195C22×C4—22no—
196C22×C4—132no—
197C22×C4—131no—
198C22×C4—134no—
199C22×C4—134no—
200C22×C4—264no—
201C22×C4—262no—
202C22×C4—264no—
203C22×C4—262no—
204C22×C4—268no—
205C22×C4—262no—
206C22×C4—262no—
207C22×C4—524no—
208C22×C4—524no—
209C22×C4C22⋊#26112yes—
210C22×C4C22×#26111yescharacteristic
211C2×C8—524no—
212C2×C8—524no—
213C2×C8—524no—
214C4⋊C4—28no—
215C4⋊C4—2616no—
216C4⋊C4—268no—
217C42—22no—
218C42—134no—
219C42—264no—
220C13#834211yescharacteristic, complemented, Sylow
221C23—132no—
222C23—134no—
223C23—261no—
224C23—261no—
225C23—262no—
226C23C2×C22⋊#26111yescharacteristic
227Q8—44no—
228Q8—44no—
229Q8—524no—
230Q8—524no—
231Q8—5216no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—24no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—134no—
240C2×C4—132no—
241C2×C4—132no—
242C2×C4—134no—
243C2×C4—132no—
244C2×C4—268no—
245C2×C4—268no—
246C2×C4—268no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—264no—
250C2×C4—5216no—
251C2×C4—522no—
252C2×C4—522no—
253C2×C4#8811714yes—
254C2×C4C2×C22⋊#26112yes—
255C8—1044no—
256C22—134no—
257C22—264no—
258C22—262no—
259C22—262no—
260C22—264no—
261C22D13⋊#10011yescharacteristic
262C22D13⋊#10011yescharacteristic
263C22C2×#8811712yes—
264C22#1171915312yes—
265C22#1171917111yescharacteristic
266C4—22no—
267C4—24no—
268C4—44no—
269C4—134no—
270C4—134no—
271C4—262no—
272C4—524no—
273C2—264no—
274C2D13⋊#33311yescharacteristic
275C2#1313035012yes—
276C2#1313037011yescharacteristic
277C2#1313066911yescharacteristic
278C2#1313067512yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#8342
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11718303C2semidirect
141. C2×D13#333semidirect
220. C13#8342semidirect

Maximal subgroups

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

subgroupindex
#131306932
C2×#117183032
C2×D13×C4⋊Q82
#834213