Finite Group Databasebeta

← #16790029

Subgroups — #16790029

Order 3328.

480 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 86 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×#11718295C212yesmaximal
2#13130702C212yesmaximal, complemented
3#13129934C212yesmaximal, complemented
4#13117548C211yesmaximal, characteristic
5C2×C4×D4×C13C411yescharacteristic
6C2×#88190C2211yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C2×#88113C2214yes—
9#11719129—22no—
10#11718882C411yescharacteristic
11#11718871—22no—
12#11718637C411yescharacteristic
13#11718635C2211yescharacteristic
14#11718605—22no—
15#11718593C411yescharacteristic
16#11718295—24no—
17#11718291—22no—
18C22×D4×C13C2×C411yescharacteristic
19C23×C4×C13—21no—
20C22×Dic26C2311yescharacteristic
21C2×#6122—24no—
22C4×D4×C13—42no—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C13×C22⋊C4—21no—
25C2×C42×C13C2×C411yescharacteristic
26C2×C22⋊Dic13—22no—
27C2×C22⋊Dic13—22no—
28#88190—22no—
29#88190D412yes—
30#88190Q812yes—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—22no—
33C2×#6101D412yes—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13D412yes—
37C4×Dic26—42no—
38#88113—24no—
39#88113—24no—
40#88112—42no—
41C4⋊#1057—42no—
42#88071—21no—
43#88071—21no—
44#88071—22no—
45#12803—131nomaximal, Sylow
46C24×C13—21no—
47C2×D4×C13—21no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13C4⋊C412yes—
51C22×C4×C13—21no—
52C22×C4×C13—42no—
53C22×C4×C13—82no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×Dic13—21no—
58C22×Dic13—21no—
59C22×Dic13C22⋊C412yes—
60C22×Dic13C2×D412yes—
61C2×Dic26—41no—
62C2×Dic26—41no—
63C2×Dic26C2×D411yescharacteristic
64C2×Dic26C2×Q811yescharacteristic
65C2×Dic26#4112yes—
66#6122—44no—
67#6122—44no—
68C2×#1057—44no—
69C13×C4⋊C4—41no—
70C13×C22⋊C4—42no—
71C42×C13—22no—
72C22⋊Dic13—24no—
73C22⋊Dic13—24no—
74C22⋊Dic13—82no—
75C4⋊Dic13—41no—
76#6101—42no—
77#6101—82no—
78C4×Dic13—22no—
79C4×Dic13—22no—
80C4×Dic13—21no—
81C4×Dic13—41no—
82C4×Dic13C4⋊C412yes—
83#2326—131no—
84C2×#355—132no—
85#1801—132no—
86#1394—132no—
87C23×C13—22no—
88C23×C13—42no—
89C23×C13—42no—
90C23×C13—41no—
91C23×C13—41no—
92C23×C13C2×C22⋊C411yescharacteristic
93D4×C13—42no—
94D4×C13—42no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×C4×C13—84no—
103C2×C4×C13#9912yes—
104C2×C4×C13C2×C4⋊C411yescharacteristic
105C2×C4×C13#11711yescharacteristic
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—41no—
111C2×Dic13—41no—
112C2×Dic13—42no—
113C2×Dic13—41no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13#12112yes—
117C2×Dic13C22⋊Q812yes—
118Dic26—41no—
119Dic26—41no—
120Dic26—42no—
121#1057—84no—
122C2×#124—131no—
123C2×C4×Q8—131no—
124C2×C4×D4#26111yescharacteristic
125#423—262no—
126C2×#101—134no—
127#391—131no—
128#390—131no—
129#388—262no—
130#385—262no—
131#384—131no—
132#376—131no—
133#355—264no—
134#343—262no—
135C22×C13—21no—
136C22×C13—21no—
137C22×C13—44no—
138C22×C13—42no—
139C22×C13—82no—
140C22×C13—81no—
141C22×C13—81no—
142C22×C13#38011yescharacteristic
143C22×C13C2×#9911yescharacteristic
144C22×C13#41011yescharacteristic
145C4×C13—21no—
146C4×C13—21no—
147C4×C13—22no—
148C4×C13—41no—
149C4×C13—81no—
150Dic13—22no—
151Dic13—22no—
152Dic13—42no—
153Dic13—42no—
154Dic13—81no—
155C22×Q8—131no—
156C22×D4C2×#26111yescharacteristic
157C23×C4—21no—
158C2×M16—264no—
159#124—132no—
160#124—132no—
161#124—262no—
162C4×Q8—522no—
163C4×D4—42no—
164C2×C4⋊C4—132no—
165C2×C4⋊C4—131no—
166C2×C4⋊C4—262no—
167C2×C4⋊C4C2×#26111yescharacteristic
168C2×C22⋊C4—21no—
169C2×C22⋊C4—262no—
170C2×C22⋊C4—262no—
171C2×C42—131no—
172C2×C42—132no—
173C2×C42—131no—
174C2×C42C2×#26111yescharacteristic
175C4⋊C8—522no—
176C4⋊C8—522no—
177#101—264no—
178#101—264no—
179#95—262no—
180#95—261no—
181#95—261no—
182C2×C13—21no—
183C2×C13—21no—
184C2×C13—82no—
185C2×C13#179911yescharacteristic
186C2×C13#213311yescharacteristic
187C2×C13#213411yescharacteristic
188C24—21no—
189C2×Q8—131no—
190C2×Q8—131no—
191C2×Q8—132no—
192C2×Q8—521no—
193C2×Q8—521no—
194C2×D4—21no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4C4⋊#26112yes—
198C22×C4—21no—
199C22×C4—42no—
200C22×C4—82no—
201C22×C4—132no—
202C22×C4—132no—
203C22×C4—261no—
204C22×C4—261no—
205C22×C4C22⋊#26111yescharacteristic
206C22×C4C22⋊#26111yescharacteristic
207C22×C4C22×#26111yescharacteristic
208M16—524no—
209M16—524no—
210C2×C8—524no—
211C4⋊C4—41no—
212C4⋊C4—522no—
213C4⋊C4—521no—
214C4⋊C4—1042no—
215C22⋊C4—42no—
216C22⋊C4—264no—
217C22⋊C4—264no—
218C22⋊C4—1042no—
219C42—22no—
220C42—132no—
221C42—262no—
222C42—262no—
223C42—261no—
224C42—521no—
225C13#1280311yescharacteristic, complemented, Sylow
226C23—22no—
227C23—42no—
228C23—42no—
229C23—41no—
230C23—41no—
231C23C2×C22⋊#26111yescharacteristic
232Q8—521no—
233Q8—521no—
234Q8—522no—
235D4—42no—
236D4—42no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—84no—
245C2×C4—132no—
246C2×C4—132no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4—522no—
254C2×C4—521no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4#8811912yes—
258C2×C4C2×C4⋊#26111yescharacteristic
259C2×C4#8823711yescharacteristic
260C8—1044no—
261C22—21no—
262C22—21no—
263C22—44no—
264C22—42no—
265C22—82no—
266C22—81no—
267C22—81no—
268C22#1171911611yescharacteristic
269C22#1171913611yescharacteristic
270C22C2×#8811911yescharacteristic
271C4—22no—
272C4—21no—
273C4—21no—
274C4—41no—
275C4—81no—
276C4—262no—
277C4—262no—
278C4—522no—
279C4—522no—
280C4—1041no—
281C2—21no—
282C2—21no—
283C2—82no—
284C2#1313069611yescharacteristic
285C2#1313113111yescharacteristic
286C2#1313113511yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC22×Dic26C23
hypercenterC2×C4×D4#261
hypocenterC13#12803
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #13130702C2semidirect
3. #13129934C2semidirect
225. C13#12803semidirect

Maximal subgroups

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

subgroupindex
C2×#117182952
#131307022
#131299342
#131175482
#1280313