Finite Group Databasebeta

← #16789226

Subgroups — #16789226

Order 3328.

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

normal subgroups only

This group has 746 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
1C22×#88113C212yesmaximal
2#13129934C214yesmaximal, complemented
3#13117420C211yesmaximal, characteristic
4C23×Dic26C2211yescharacteristic
5C22×#6122—22no—
6C2×C13×#117C411yescharacteristic
7C2×#88180C411yescharacteristic
8C2×#88113—22no—
9C2×#88113—24no—
10C2×#88113C418yescomplemented
11C2×#88113C2214yes—
12#11718635C412yes—
13#11718635C2212yes—
14#11718604—22no—
15#11718590—22no—
16C23×C4×C13C2×C411yescharacteristic
17C23×Dic13D412yes—
18C22×Dic26—42no—
19C22×Dic26—42no—
20C22×Dic26C2×C411yescharacteristic
21C22×Dic26C2×C414yes—
22C22×Dic26D412yes—
23C22×Dic26D412yes—
24C22×Dic26Q812yes—
25C22×Dic26C2311yescharacteristic
26C2×#6122—28no—
27C2×#6122—24no—
28C2×#6122—44no—
29C2×#6122—42no—
30C22×#1057—42no—
31C13×#117—42no—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C22⋊C4—21no—
34C2×C42×C13—21no—
35C2×C22⋊Dic13—21no—
36#88180—42no—
37C2×C4⋊Dic13—21no—
38C2×C4×Dic13C2×C412yes—
39#88113—28no—
40#88113—24no—
41#88113C2×C418yes—
42#88071—24no—
43#88071—24no—
44#12586—131nomaximal, Sylow
45C24×C13C22⋊C411yescharacteristic
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—22no—
49C22×C4×C13C4212yes—
50C22×C4×C13C22⋊C411yescharacteristic
51C22×C4×C13C4⋊C412yes—
52C22×C4×C13C22×C411yescharacteristic
53C22×Dic13—22no—
54C22×Dic13—24no—
55C22×Dic13—22no—
56C22×Dic13—22no—
57C22×Dic13C22⋊C412yes—
58C22×Dic13C22⋊C414yes—
59C22×Dic13C4⋊C414yes—
60C22×Dic13C2×D412yes—
61C2×Dic26—41no—
62C2×Dic26—41no—
63C2×Dic26—44no—
64C2×Dic26—44no—
65C2×Dic26—42no—
66C2×Dic26—42no—
67C2×Dic26—44no—
68C2×Dic26—44no—
69C2×Dic26—41no—
70C2×Dic26—41no—
71C2×Dic26C4212yes—
72C2×Dic26C22⋊C414yes—
73C2×Dic26C4⋊C412yes—
74C2×Dic26C4⋊C414yes—
75C2×Dic26C22×C412yes—
76C2×Dic26C2×D411yescharacteristic
77C2×Dic26C2×Q811yescharacteristic
78#6122—28no—
79#6122—48no—
80#6122—44no—
81C2×#1057—48no—
82C2×#1057—44no—
83C13×C4⋊C4—42no—
84C13×C22⋊C4—42no—
85C42×C13—42no—
86C22⋊Dic13—42no—
87C4⋊Dic13—42no—
88C4×Dic13—42no—
89C22×#101—132no—
90#2310—131no—
91#1394—134no—
92C23×C13—42no—
93C23×C13#9512yes—
94C23×C13#9912yes—
95C23×C13#9912yes—
96C23×C13C2×C22⋊C411yescharacteristic
97C2×C4×C13—24no—
98C2×C4×C13—24no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—44no—
104C2×C4×C13—42no—
105C2×C4×C13#9512yes—
106C2×C4×C13C2×C4211yescharacteristic
107C2×C4×C13C2×C4⋊C411yescharacteristic
108C2×Dic13—24no—
109C2×Dic13—24no—
110C2×Dic13—24no—
111C2×Dic13—24no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—22no—
116C2×Dic13—44no—
117C2×Dic13—42no—
118C2×Dic13#9514yes—
119C2×Dic13C2×C22⋊C412yes—
120C2×Dic13C2×C4⋊C412yes—
121Dic26—42no—
122Dic26—44no—
123Dic26—42no—
124Dic26—44no—
125Dic26—42no—
126Dic26—41no—
127Dic26—41no—
128#1057—48no—
129C23×Q8—131no—
130C22×M16—262no—
131C2×#117—131no—
132C2×#117#26111yescharacteristic
133C2×#101—134no—
134C2×#101—138no—
135C2×#101—264no—
136C2×#101—262no—
137#391—132no—
138#391—132no—
139#391—262no—
140#381—262no—
141C22×C13—22no—
142C22×C13—24no—
143C22×C13—42no—
144C22×C13—42no—
145C22×C13#34214yes—
146C22×C13C2×#9511yescharacteristic
147C22×C13C2×#9911yescharacteristic
148C22×C13C2×#9911yescharacteristic
149C4×C13—22no—
150C4×C13—21no—
151C4×C13—21no—
152C4×C13—82no—
153Dic13—22no—
154Dic13—24no—
155Dic13—22no—
156Dic13—82no—
157C22×Q8—134no—
158C22×Q8—132no—
159C22×Q8—132no—
160C22×Q8—132no—
161C22×Q8—131no—
162C22×Q8—131no—
163C22×Q8—522no—
164C22×Q8—522no—
165C23×C4—132no—
166C23×C4C2×#26111yescharacteristic
167C2×M16—268no—
168C2×M16—264no—
169C2×M16—524no—
170C2×M16—522no—
171C22×C8—522no—
172#117—42no—
173#117—522no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4C2×#26112yes—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—261no—
178C2×C42—21no—
179C2×C42—132no—
180#101—138no—
181#101—268no—
182#101—264no—
183#95—264no—
184#95—264no—
185C2×C13—21no—
186C2×C13—24no—
187C2×C13—21no—
188C2×C13C2×#34211yescharacteristic
189C2×C13#213312yes—
190C24C22⋊#26111yescharacteristic
191C2×Q8—134no—
192C2×Q8—134no—
193C2×Q8—132no—
194C2×Q8—132no—
195C2×Q8—131no—
196C2×Q8—132no—
197C2×Q8—131no—
198C2×Q8—524no—
199C2×Q8—524no—
200C2×Q8—524no—
201C2×Q8—524no—
202C2×Q8—521no—
203C2×Q8—521no—
204C2×Q8—522no—
205C2×Q8—522no—
206C2×Q8—521no—
207C2×Q8—521no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—134no—
212C22×C4—134no—
213C22×C4—132no—
214C22×C4—132no—
215C22×C4—264no—
216C22×C4—262no—
217C22×C4—262no—
218C22×C4—262no—
219C22×C4C4×#26112yes—
220C22×C4C4⋊#26112yes—
221C22×C4C22⋊#26111yescharacteristic
222C22×C4C22×#26111yescharacteristic
223M16—268no—
224M16—528no—
225M16—524no—
226C2×C8—528no—
227C2×C8—524no—
228C4⋊C4—42no—
229C4⋊C4—522no—
230C22⋊C4—42no—
231C22⋊C4—522no—
232C42—42no—
233C42—522no—
234C13#1258611yescharacteristic, complemented, Sylow
235C23—42no—
236C23#8810712yes—
237C23(C2×#261)⋊C412yes—
238C23#8811912yes—
239C23C2×C22⋊#26111yescharacteristic
240Q8—524no—
241Q8—524no—
242Q8—522no—
243Q8—522no—
244Q8—521no—
245Q8—522no—
246Q8—521no—
247C2×C4—24no—
248C2×C4—24no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—44no—
254C2×C4—42no—
255C2×C4—132no—
256C2×C4—134no—
257C2×C4—132no—
258C2×C4—264no—
259C2×C4—264no—
260C2×C4—264no—
261C2×C4—264no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—524no—
267C2×C4—522no—
268C2×C4(C2×#261)⋊C412yes—
269C2×C4C2×C4×#26111yescharacteristic
270C2×C4C2×C4⋊#26111yescharacteristic
271C8—528no—
272C22—22no—
273C22—24no—
274C22—42no—
275C22—42no—
276C22#1171828914yes—
277C22C2×#8810711yescharacteristic
278C22C2×(C2×#261)⋊C411yescharacteristic
279C22C2×#8811911yescharacteristic
280C4—22no—
281C4—21no—
282C4—21no—
283C4—82no—
284C4—262no—
285C4—264no—
286C4—262no—
287C4—1042no—
288C2—21no—
289C2—24no—
290C2—21no—
291C2C2×#1171828911yescharacteristic
292C2#1313113112yes—
subgroupG/H
centerC22C2×#88119
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC22×Dic26C23
hypercenterC2×#117#261
hypocenterC13#12586
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129934C2semidirect
10. C2×#88113C4semidirect
234. C13#12586semidirect

Maximal subgroups

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

subgroupindex
C22×#881132
#131299342
#131174202
#1258613