Finite Group Databasebeta

← C4×#11718225 #16789437

Subgroups — C4×#11718225 #16789437

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×#11718225C212yesmaximal
2C4×#88107C212yesmaximal, complemented
3#13129930C212yesmaximal, complemented
4C4×#88128C211yesmaximal, characteristic
5C2×#88128C2211yescharacteristic
6C2×C4×D52—22no—
7C2×C4×D52C411yescharacteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C4×C22⋊#261—22no—
10C2×#88107C2214yes—
11C43×C13C411yescharacteristic, complemented
12#11718600—22no—
13#11718600C411yescharacteristic, complemented
14#11718600C2211yescharacteristic
15#11718596C411yescharacteristic, complemented
16#11718289—22no—
17#11718225C418yesdirect product factor
18C22×D52—22no—
19C22×D52C2×C411yescharacteristic
20C22×D52C2311yescharacteristic
21C22×C4×D13—21no—
22C22×C4×D13D412yes—
23C2×C22⋊#261—24no—
24C2×C4×#261—42no—
25C2×C42×C13—21no—
26C2×C42×C13—21no—
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×#6103—22no—
31C2×#6103—21no—
32C2×#6103—22no—
33C2×#6103D412yes—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37#88128—22no—
38#88128C2×C414yes—
39C4×D52—41no—
40C4×D52—41no—
41C4×D52—48no—
42C4×D52—41no—
43C4×D52—41no—
44(C2×#261)⋊C4—42no—
45#88107—24no—
46#88107C2×C418yescomplemented
47C4×#353—131nomaximal, Sylow
48C23×D13—21no—
49C23×D13C2×D412yes—
50C22×#261—44no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—21no—
57C22×Dic13C22⋊C412yes—
58C2×D52—28no—
59C2×D52—21no—
60C2×D52—41no—
61C2×D52—41no—
62C2×D52—41no—
63C2×D52—41no—
64C2×D52—44no—
65C2×D52—44no—
66C2×D52C4212yescomplemented
67C2×D52C22×C412yes—
68C2×D52#4112yes—
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×C4×D13—44no—
72C2×C4×D13—44no—
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C22⋊#261—28no—
76C22⋊#261—44no—
77C4×#261—84no—
78C42×C13—24no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—41no—
83C42×C13—42no—
84C42×C13C4212yescomplemented
85#6103—42no—
86#6103—44no—
87#6103—44no—
88#6103—42no—
89C4⋊Dic13—41no—
90C4⋊Dic13—44no—
91C4⋊Dic13—41no—
92C4×#127—131no—
93C2×#353—132no—
94C4×#99—132no—
95#1393—132no—
96C23×C13C2×C22⋊C411yescharacteristic
97C22×D13—22no—
98C22×D13—22no—
99C22×D13—22no—
100C22×D13—42no—
101C22×D13—42no—
102C22×D13—42no—
103C22×D13—42no—
104C22×D13—41no—
105C22×D13—41no—
106C22×D13C4×D414yes—
107C2×#261—48no—
108C2×#261—84no—
109C2×#261—84no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—21no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13C2×C4211yescharacteristic
124C2×C4×C13#11711yescharacteristic
125C2×Dic13—22no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—41no—
129D52—42no—
130D52—42no—
131D52—416no—
132D52—42no—
133D52—42no—
134C4×D13—44no—
135C4×D13—82no—
136C4×D13—82no—
137C4×D13—82no—
138C2×#127—131no—
139C2×C4×D4—131no—
140C2×C4×D4—131no—
141C2×C4×D4—262no—
142C2×#99—134no—
143#390—131no—
144#390—131no—
145#390—262no—
146#384—131no—
147C4×C22⋊C4—262no—
148C43#26111yescharacteristic, complemented
149#353—138no—
150#342—262no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13C4×C22⋊C411yescharacteristic
154C22×C13C2×#9911yescharacteristic
155C22×C13#41011yescharacteristic
156C2×D13—24no—
157C2×D13—42no—
158C2×D13—42no—
159C2×D13—44no—
160C2×D13—44no—
161C2×D13—42no—
162C2×D13—82no—
163C2×D13—82no—
164C2×D13—81no—
165C2×D13—81no—
166#261—88no—
167C4×C13—24no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—42no—
172C4×C13—41no—
173C4×C13#35312yescomplemented
174Dic13—42no—
175Dic13—81no—
176C22×D4—131no—
177C22×D4—131no—
178C22×D4—262no—
179C23×C4—132no—
180C23×C4—261no—
181#127—134no—
182#127—262no—
183C4×D4—521no—
184C4×D4—521no—
185C4×D4—528no—
186C4×D4—521no—
187C4×D4—521no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—262no—
191C2×C22⋊C4—132no—
192C2×C22⋊C4—264no—
193C2×C22⋊C4—262no—
194C2×C22⋊C4—262no—
195C2×C22⋊C4—261no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—522no—
199C2×C42C2×#26111yescharacteristic
200C2×C42C2×#26111yescharacteristic
201C2×C42C2×#26111yescharacteristic
202#99—138no—
203#99—264no—
204#95—522no—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13C4×#9911yescharacteristic
208C2×C13C2×#35311yescharacteristic
209C2×C13#212611yescharacteristic
210D13—44no—
211D13—82no—
212C24—132no—
213C24—261no—
214C2×D4—132no—
215C2×D4—132no—
216C2×D4—132no—
217C2×D4—268no—
218C2×D4—261no—
219C2×D4—521no—
220C2×D4—521no—
221C2×D4—521no—
222C2×D4—521no—
223C2×D4—524no—
224C2×D4—524no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—132no—
228C22×C4—262no—
229C22×C4—262no—
230C22×C4—261no—
231C22×C4—524no—
232C22×C4—524no—
233C22×C4—524no—
234C22×C4—521no—
235C22×C4—521no—
236C22×C4C22⋊#26111yescharacteristic
237C22×C4C22⋊#26111yescharacteristic
238C22×C4C22×#26111yescharacteristic
239C4⋊C4—521no—
240C4⋊C4—521no—
241C4⋊C4—524no—
242C22⋊C4—268no—
243C22⋊C4—522no—
244C22⋊C4—524no—
245C22⋊C4—524no—
246C22⋊C4—522no—
247C22⋊C4—524no—
248C42—24no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—41no—
253C42—42no—
254C42—1044no—
255C42C4×#26112yescomplemented
256C13C4×#35311yescharacteristic, complemented, Sylow
257C23—134no—
258C23—262no—
259C23—262no—
260C23—262no—
261C23—522no—
262C23—522no—
263C23—522no—
264C23—522no—
265C23—521no—
266C23—521no—
267C23C2×C22⋊#26111yescharacteristic
268D4—522no—
269D4—522no—
270D4—522no—
271D4—5216no—
272D4—522no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—262no—
285C2×C4—524no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—528no—
289C2×C4—521no—
290C2×C4—1042no—
291C2×C4—1042no—
292C2×C4—1044no—
293C2×C4—1044no—
294C2×C4—1042no—
295C2×C4#8810711yescharacteristic
296C2×C4#8810711yescharacteristic
297C2×C4C2×C4×#26111yescharacteristic
298C2×C4#8823711yescharacteristic
299C22—21no—
300C22—21no—
301C22—264no—
302C22—524no—
303C22—524no—
304C22—522no—
305C22—522no—
306C22—522no—
307C22—1042no—
308C22—1042no—
309C22—1041no—
310C22—1041no—
311C22C2×#8810711yescharacteristic
312C22#1171911611yescharacteristic
313C22C4×C22⋊#26111yescharacteristic
314C4—24no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—42no—
319C4—41no—
320C4—522no—
321C4—1048no—
322C4—1041no—
323C4#1171822512yesdirect product factor
324C2—21no—
325C2—21no—
326C2—524no—
327C2—1042no—
328C2C4×#8810711yescharacteristic
329C2C2×#1171822511yescharacteristic
330C2#1313110911yescharacteristic
subgroupG/H
centerC2×C4#88107
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC43×C13C4
socleC22×C13C2×#99
prime radicalC2×#88128C22
cosocleC22×D52C23
hypercenterC43#261
hypocenterC13C4×#353
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
2. C4×#88107C2semidirect
3. #13129930C2semidirect
7. C2×C4×D52C4semidirect
11. C43×C13C4semidirect
13. #11718600C4semidirect
15. #11718596C4semidirect
17. #11718225C4direct (N × H)
46. #88107C2×C4semidirect
66. C2×D52C42semidirect
84. C42×C13C42semidirect
148. C43#261semidirect
173. C4×C13#353semidirect
255. C42C4×#261semidirect
256. C13C4×#353semidirect
323. C4#11718225direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117182252
C4×#881072
#131299302
C4×#881282
C4×#35313