Finite Group Databasebeta

← C4×#11718294 #16789435

Subgroups — C4×#11718294 #16789435

Order 3328.

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

normal subgroups only

This group has 720 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×#11718294C212yesmaximal
2C4×#88107C212yesmaximal, complemented
3#13129931C212yesmaximal, complemented
4C4×#88194C211yesmaximal, characteristic
5C2×C4×D4×C13C411yescharacteristic, complemented
6C2×#88194C2211yescharacteristic
7C2×C4×C22⋊D13—22no—
8C2×C4×D52C2211yescharacteristic
9C4×C22⋊#261—22no—
10C2×#88107C2214yes—
11#11718882C411yescharacteristic, complemented
12#11718649C2211yescharacteristic
13#11718637C411yescharacteristic, complemented
14#11718618—22no—
15C42×Dic13C411yescharacteristic, complemented
16#11718294C418yesdirect product factor
17#11718289—22no—
18C22×D4×C13C2×C411yescharacteristic
19C23×C4×C13—21no—
20C22×C22⋊D13—22no—
21C22×D52C2311yescharacteristic
22C22×C4×D13D412yes—
23C2×C22⋊#261—24no—
24C2×C4×#261—42no—
25C4×D4×C13—41no—
26C4×D4×C13—41no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C22⋊C4—21no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C22⋊Dic13—22no—
31#88194—22no—
32#88194C2×C414yes—
33C4×C22⋊D13—48no—
34C2×#6103—22no—
35C2×#6103D412yes—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—22no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C4×D52—41no—
43C4×D52—41no—
44(C2×#261)⋊C4—42no—
45#88107—24no—
46#88107C2×C418yescomplemented
47C4×#353—131nomaximal, Sylow
48C24×C13—21no—
49C23×D13C2×D412yes—
50C22×#261—44no—
51C2×D4×C13—21no—
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C2×D4×C13C4212yescomplemented
55C22×C4×C13—21no—
56C22×C4×C13—44no—
57C22×C4×C13—41no—
58C22×C4×C13—41no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C2×C22⋊D13—28no—
63C2×C22⋊D13—44no—
64C2×C22⋊D13—44no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13C22⋊C412yes—
68C2×D52—41no—
69C2×D52—41no—
70C2×D52C22×C412yes—
71C2×D52#4112yes—
72C2×C4×D13—22no—
73C2×C4×D13—22no—
74C2×C4×D13—44no—
75C22⋊#261—28no—
76C22⋊#261—44no—
77C4×#261—84no—
78C13×C4⋊C4—41no—
79C13×C22⋊C4—42no—
80C42×C13—21no—
81C42×C13—21no—
82C22⋊Dic13—44no—
83#6103—42no—
84#6103—44no—
85C4⋊Dic13—41no—
86#6101—44no—
87C4×Dic13—24no—
88C4×Dic13—21no—
89C4×Dic13—42no—
90C4×Dic13—41no—
91C4×Dic13C4212yescomplemented
92C4×#127—131no—
93C2×#353—132no—
94C4×#99—132no—
95#1393—132no—
96C23×C13—22no—
97C23×C13—42no—
98C23×C13—42no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13C2×C22⋊C411yescharacteristic
102C22×D13—22no—
103C22×D13—22no—
104C22×D13—42no—
105C22×D13—42no—
106C22×D13C4×D414yes—
107C2×#261—48no—
108C2×#261—84no—
109C2×#261—84no—
110D4×C13—42no—
111D4×C13—42no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—82no—
120C2×C4×C13—82no—
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13C2×C4211yescharacteristic
124C2×C4×C13#11711yescharacteristic
125C22⋊D13—416no—
126C2×Dic13—22no—
127C2×Dic13—22no—
128C2×Dic13—22no—
129C2×Dic13—22no—
130C2×Dic13—22no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—42no—
134D52—42no—
135D52—42no—
136C4×D13—44no—
137C4×D13—82no—
138C2×#127—131no—
139C2×C4×D4—131no—
140C2×C4×D4—262no—
141C2×C4×D4#26111yescharacteristic, complemented
142C2×#99—134no—
143#390—131no—
144#390—131no—
145#390—262no—
146#384—131no—
147C4×C22⋊C4—262no—
148C43—131no—
149#353—138no—
150#342—262no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—44no—
154C22×C13—42no—
155C22×C13—82no—
156C22×C13—81no—
157C22×C13—81no—
158C22×C13C4×C22⋊C411yescharacteristic
159C22×C13C2×#9911yescharacteristic
160C22×C13#41011yescharacteristic
161C2×D13—24no—
162C2×D13—42no—
163C2×D13—42no—
164C2×D13—44no—
165C2×D13—82no—
166#261—88no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—81no—
172C4×C13#35312yescomplemented
173Dic13—24no—
174Dic13—42no—
175Dic13—42no—
176C22×D4—131no—
177C22×D4—262no—
178C22×D4C2×#26111yescharacteristic
179C23×C4—21no—
180C23×C4—132no—
181#127—134no—
182#127—262no—
183C4×D4—41no—
184C4×D4—41no—
185C4×D4—521no—
186C4×D4—521no—
187C4×D4—528no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—262no—
190C2×C4⋊C4C2×#26111yescharacteristic
191C2×C22⋊C4—21no—
192C2×C22⋊C4—132no—
193C2×C22⋊C4—264no—
194C2×C22⋊C4—262no—
195C2×C22⋊C4—262no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—261no—
199C2×C42—261no—
200C2×C42—522no—
201C2×C42C2×#26111yescharacteristic
202#99—138no—
203#99—264no—
204#95—522no—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13—82no—
208C2×C13C4×#9911yescharacteristic
209C2×C13C2×#35311yescharacteristic
210C2×C13#212611yescharacteristic
211D13—44no—
212C24—21no—
213C24—132no—
214C2×D4—21no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—132no—
218C2×D4—132no—
219C2×D4—268no—
220C2×D4—521no—
221C2×D4—521no—
222C2×D4—524no—
223C2×D4—524no—
224C2×D4C4×#26112yescomplemented
225C22×C4—21no—
226C22×C4—44no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—132no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4—262no—
233C22×C4—262no—
234C22×C4—524no—
235C22×C4—524no—
236C22×C4C22⋊#26111yescharacteristic
237C22×C4C22⋊#26111yescharacteristic
238C22×C4C22×#26111yescharacteristic
239C4⋊C4—41no—
240C4⋊C4—521no—
241C4⋊C4—524no—
242C22⋊C4—42no—
243C22⋊C4—268no—
244C22⋊C4—522no—
245C22⋊C4—524no—
246C22⋊C4—524no—
247C22⋊C4—524no—
248C42—21no—
249C42—21no—
250C42—132no—
251C42—264no—
252C42—261no—
253C42—521no—
254C42—522no—
255C42—1044no—
256C13C4×#35311yescharacteristic, complemented, Sylow
257C23—22no—
258C23—42no—
259C23—42no—
260C23—41no—
261C23—41no—
262C23—134no—
263C23—262no—
264C23—262no—
265C23—522no—
266C23—522no—
267C23C2×C22⋊#26111yescharacteristic
268D4—42no—
269D4—42no—
270D4—522no—
271D4—522no—
272D4—5216no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—262no—
283C2×C4—262no—
284C2×C4—262no—
285C2×C4—262no—
286C2×C4—262no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—524no—
290C2×C4—522no—
291C2×C4—528no—
292C2×C4—1042no—
293C2×C4—1044no—
294C2×C4—1044no—
295C2×C4#8811911yescharacteristic
296C2×C4#8811911yescharacteristic
297C2×C4C2×C4×#26111yescharacteristic
298C2×C4#8823711yescharacteristic
299C22—21no—
300C22—21no—
301C22—44no—
302C22—42no—
303C22—82no—
304C22—81no—
305C22—81no—
306C22—264no—
307C22—524no—
308C22—522no—
309C22—522no—
310C22—1042no—
311C22#1171911611yescharacteristic
312C22C4×C22⋊#26111yescharacteristic
313C22C2×#8811911yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—81no—
319C4—264no—
320C4—522no—
321C4—522no—
322C4—1048no—
323C4#1171829412yesdirect product factor
324C2—21no—
325C2—21no—
326C2—82no—
327C2—524no—
328C2C4×#8811911yescharacteristic
329C2C2×#1171829411yescharacteristic
330C2#1313110711yescharacteristic
subgroupG/H
centerC2×C4#88119
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC22×C13C2×#99
prime radicalC2×#88194C22
cosocleC22×D52C23
hypercenterC2×C4×D4#261
hypocenterC13C4×#353
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×#88107C2semidirect
3. #13129931C2semidirect
5. C2×C4×D4×C13C4semidirect
11. #11718882C4semidirect
13. #11718637C4semidirect
15. C42×Dic13C4semidirect
16. #11718294C4direct (N × H)
46. #88107C2×C4semidirect
54. C2×D4×C13C42semidirect
91. C4×Dic13C42semidirect
141. C2×C4×D4#261semidirect
172. C4×C13#353semidirect
224. C2×D4C4×#261semidirect
256. C13C4×#353semidirect
323. C4#11718294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117182942
C4×#881072
#131299312
C4×#881942
C4×#35313