Finite Group Databasebeta

← C4×#11718295 #16789455

Subgroups — C4×#11718295 #16789455

Order 3328.

532 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 106 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
2C4×#88113C212yesmaximal, complemented
3#13129934C212yesmaximal, complemented
4C4×#88190C211yesmaximal, characteristic
5C2×C4×D4×C13C411yescharacteristic
6C2×#88190C2211yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C2×#88113C2214yes—
9C4×#6122—22no—
10#11718882C411yescharacteristic
11C4×C22⋊Dic13—22no—
12#11718638C411yescharacteristic
13#11718635C2211yescharacteristic
14#11718606—22no—
15C42×Dic13C411yescharacteristic
16#11718295C418yesdirect product factor
17#11718291—22no—
18C22×D4×C13C2×C411yescharacteristic
19C23×C4×C13—21no—
20C22×Dic26C2311yescharacteristic
21C2×#6122—24no—
22C4×D4×C13—41no—
23C4×D4×C13—41no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C22⋊C4—21no—
26C2×C42×C13C2×C411yescharacteristic
27C2×C22⋊Dic13—22no—
28C2×C22⋊Dic13—22no—
29#88190—22no—
30#88190C2×C414yes—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101D412yes—
33C2×C4×Dic13—21no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D412yes—
38C4×Dic26—41no—
39C4×Dic26—41no—
40#88113—24no—
41#88113C2×C418yescomplemented
42#88110—42no—
43C4×#1057—42no—
44#88071—22no—
45#88071—22no—
46C4×#355—131nomaximal, Sylow
47C24×C13—21no—
48C2×D4×C13—21no—
49C2×D4×C13—41no—
50C2×D4×C13—41no—
51C2×D4×C13C4212yes—
52C22×C4×C13—21no—
53C22×C4×C13—44no—
54C22×C4×C13—41no—
55C22×C4×C13—41no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×Dic13—21no—
60C22×Dic13—21no—
61C22×Dic13C22⋊C412yes—
62C22×Dic13C2×D412yes—
63C2×Dic26—41no—
64C2×Dic26—41no—
65C2×Dic26C22×C412yes—
66C2×Dic26#4112yes—
67#6122—28no—
68#6122—44no—
69C2×#1057—44no—
70C13×C4⋊C4—41no—
71C13×C22⋊C4—42no—
72C42×C13—21no—
73C42×C13—21no—
74C22⋊Dic13—28no—
75C22⋊Dic13—44no—
76C4⋊Dic13—41no—
77#6101—42no—
78C4×Dic13—22no—
79C4×Dic13—22no—
80C4×Dic13—21no—
81C4×Dic13—42no—
82C4×Dic13—42no—
83C4×Dic13—41no—
84C4×Dic13C4212yes—
85C4×#124—131no—
86C2×#355—132no—
87C4×#101—132no—
88#1394—132no—
89C23×C13—22no—
90C23×C13—42no—
91C23×C13—42no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13C2×C22⋊C411yescharacteristic
95D4×C13—42no—
96D4×C13—42no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—21no—
101C2×C4×C13—41no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—82no—
105C2×C4×C13—82no—
106C2×C4×C13#9911yescharacteristic
107C2×C4×C13#9911yescharacteristic
108C2×C4×C13C2×C4211yescharacteristic
109C2×C4×C13#11711yescharacteristic
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—42no—
120C2×Dic13C4×D414yes—
121Dic26—42no—
122Dic26—42no—
123#1057—48no—
124C2×#124—131no—
125C2×C4×Q8—131no—
126C2×C4×D4#26111yescharacteristic
127C2×#101—134no—
128C4×M16—262no—
129#391—131no—
130#390—131no—
131#388—262no—
132#382—131no—
133C4×C22⋊C4—262no—
134C43—131no—
135#355—138no—
136#343—262no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—44no—
140C22×C13—42no—
141C22×C13—82no—
142C22×C13—81no—
143C22×C13—81no—
144C22×C13C4×C22⋊C411yescharacteristic
145C22×C13C2×#9911yescharacteristic
146C22×C13#41011yescharacteristic
147C4×C13—21no—
148C4×C13—21no—
149C4×C13—21no—
150C4×C13—41no—
151C4×C13—81no—
152C4×C13#35512yescomplemented
153Dic13—24no—
154Dic13—42no—
155Dic13—42no—
156Dic13—42no—
157C22×Q8—131no—
158C22×D4C2×#26111yescharacteristic
159C23×C4—21no—
160C2×M16—264no—
161#124—134no—
162#124—262no—
163C4×Q8—521no—
164C4×Q8—521no—
165C4×D4—41no—
166C4×D4—41no—
167C2×C4⋊C4—132no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4C2×#26111yescharacteristic
170C2×C22⋊C4—21no—
171C2×C22⋊C4—262no—
172C2×C22⋊C4—262no—
173C2×C42—131no—
174C2×C42—132no—
175C2×C42—131no—
176C2×C42—261no—
177C2×C42—261no—
178C2×C42C2×#26111yescharacteristic
179#101—138no—
180#101—264no—
181#97—522no—
182C4×C8—522no—
183#95—262no—
184#95—262no—
185C2×C13—21no—
186C2×C13—21no—
187C2×C13—82no—
188C2×C13C4×#9911yescharacteristic
189C2×C13C2×#35511yescharacteristic
190C2×C13#213211yescharacteristic
191C24—21no—
192C2×Q8—132no—
193C2×Q8—132no—
194C2×Q8—521no—
195C2×Q8—521no—
196C2×D4—21no—
197C2×D4—41no—
198C2×D4—41no—
199C2×D4C4×#26112yes—
200C22×C4—21no—
201C22×C4—44no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—132no—
205C22×C4—132no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4C22⋊#26111yescharacteristic
209C22×C4C22⋊#26111yescharacteristic
210C22×C4C22×#26111yescharacteristic
211M16—268no—
212M16—524no—
213C2×C8—524no—
214C4⋊C4—41no—
215C4⋊C4—522no—
216C4⋊C4—521no—
217C22⋊C4—42no—
218C22⋊C4—268no—
219C22⋊C4—524no—
220C42—21no—
221C42—21no—
222C42—132no—
223C42—262no—
224C42—262no—
225C42—261no—
226C42—521no—
227C42—522no—
228C42—522no—
229C13C4×#35511yescharacteristic, complemented, Sylow
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23C2×C22⋊#26111yescharacteristic
236Q8—522no—
237Q8—522no—
238D4—42no—
239D4—42no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4—134no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4—521no—
259C2×C4—522no—
260C2×C4#8811911yescharacteristic
261C2×C4#8811911yescharacteristic
262C2×C4C2×C4×#26111yescharacteristic
263C2×C4#8823711yescharacteristic
264C8—528no—
265C22—21no—
266C22—21no—
267C22—44no—
268C22—42no—
269C22—82no—
270C22—81no—
271C22—81no—
272C22#1171911611yescharacteristic
273C22C4×C22⋊#26111yescharacteristic
274C22C2×#8811911yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—41no—
279C4—81no—
280C4—264no—
281C4—522no—
282C4—522no—
283C4—522no—
284C4#1171829512yesdirect product factor
285C2—21no—
286C2—21no—
287C2—82no—
288C2C4×#8811911yescharacteristic
289C2C2×#1171829511yescharacteristic
290C2#1313112711yescharacteristic
subgroupG/H
centerC2×C4#88119
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC22×Dic26C23
hypercenterC2×C4×D4#261
hypocenterC13C4×#355
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×#88113C2semidirect
3. #13129934C2semidirect
16. #11718295C4direct (N × H)
41. #88113C2×C4semidirect
152. C4×C13#355semidirect
229. C13C4×#355semidirect
284. C4#11718295direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117182952
C4×#881132
#131299342
C4×#881902
C4×#35513