Finite Group Databasebeta

← C4×#11763717 #17960860

Subgroups — C4×#11763717 #17960860

Order 4352.

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×#11763717C212yesmaximal
2C4×#10587545C212yesmaximal, complemented
3#14543882C212yesmaximal, complemented
4C4×#10587622C211yesmaximal, characteristic
5C2×#10587545C2214yes—
6C4×#63247—22no—
7#11763717C418yesdirect product factor
8#11763689—22no—
9C2×#10587622C2211yescharacteristic
10C2×C4×Dic34C2211yescharacteristic
11#11762714C2211yescharacteristic
12#11762712C411yescharacteristic
13#11762703—22no—
14#11762674C411yescharacteristic
15C4×C22⋊Dic17—22no—
16C42×Dic17C411yescharacteristic
17C2×C4×D4×C17C411yescharacteristic
18C22×D4×C17C2×C411yescharacteristic
19C23×C4×C17—21no—
20C22×Dic34C2311yescharacteristic
21C2×#63247—24no—
22C4×D4×C17—41no—
23C4×D4×C17—41no—
24C2×C4⋊C4×C17C2×C411yescharacteristic
25C2×C22⋊C4×C17—21no—
26C2×C42×C17C2×C411yescharacteristic
27C2×C22⋊Dic17—22no—
28C2×C22⋊Dic17—22no—
29#10587622—22no—
30#10587622C2×C414yes—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×#63225D412yes—
33C2×C4×Dic17—21no—
34C2×C4×Dic17—21no—
35C2×C4×Dic17C2×C411yescharacteristic
36C2×C4×Dic17C2×C411yescharacteristic
37C2×C4×Dic17D412yes—
38C4×Dic34—41no—
39C4×Dic34—41no—
40#10587545—24no—
41#10587545C2×C418yescomplemented
42#10587542—42no—
43C4×#3624—42no—
44#10587502—22no—
45#10587502—22no—
46C24×C17—21no—
47C2×D4×C17—21no—
48C2×D4×C17—41no—
49C2×D4×C17—41no—
50C2×D4×C17C4212yes—
51C22×C4×C17—21no—
52C22×C4×C17—44no—
53C22×C4×C17—41no—
54C22×C4×C17—41no—
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22×C411yescharacteristic
58C22×Dic17—21no—
59C22×Dic17—21no—
60C22×Dic17C22⋊C412yes—
61C22×Dic17C2×D412yes—
62C2×Dic34—41no—
63C2×Dic34—41no—
64C2×Dic34C22×C412yes—
65C2×Dic34#4112yes—
66#63247—28no—
67#63247—44no—
68C2×#3624—44no—
69C4⋊C4×C17—41no—
70C22⋊C4×C17—42no—
71C42×C17—21no—
72C42×C17—21no—
73C22⋊Dic17—28no—
74C22⋊Dic17—44no—
75C4⋊Dic17—41no—
76#63225—42no—
77C4×Dic17—22no—
78C4×Dic17—22no—
79C4×Dic17—21no—
80C4×Dic17—42no—
81C4×Dic17—42no—
82C4×Dic17—41no—
83C4×Dic17C4212yes—
84C4×#355—171nomaximal, Sylow
85C23×C17—22no—
86C23×C17—42no—
87C23×C17—42no—
88C23×C17—41no—
89C23×C17—41no—
90C23×C17C2×C22⋊C411yescharacteristic
91D4×C17—42no—
92D4×C17—42no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—22no—
96C2×C4×C17—21no—
97C2×C4×C17—41no—
98C2×C4×C17—42no—
99C2×C4×C17—41no—
100C2×C4×C17—82no—
101C2×C4×C17—82no—
102C2×C4×C17#9911yescharacteristic
103C2×C4×C17#9911yescharacteristic
104C2×C4×C17C2×C4211yescharacteristic
105C2×C4×C17#11711yescharacteristic
106C2×Dic17—22no—
107C2×Dic17—22no—
108C2×Dic17—22no—
109C2×Dic17—22no—
110C2×Dic17—22no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17—41no—
115C2×Dic17—42no—
116C2×Dic17C4×D414yes—
117Dic34—42no—
118Dic34—42no—
119#3624—48no—
120C4×#124—171no—
121C2×#355—172no—
122C4×#101—172no—
123#1394—172no—
124C22×C17—21no—
125C22×C17—21no—
126C22×C17—44no—
127C22×C17—42no—
128C22×C17—82no—
129C22×C17—81no—
130C22×C17—81no—
131C22×C17C4×C22⋊C411yescharacteristic
132C22×C17C2×#9911yescharacteristic
133C22×C17#41011yescharacteristic
134C4×C17—21no—
135C4×C17—21no—
136C4×C17—21no—
137C4×C17—41no—
138C4×C17—81no—
139C4×C17#35512yescomplemented
140Dic17—24no—
141Dic17—42no—
142Dic17—42no—
143Dic17—42no—
144C2×#124—171no—
145C2×C4×Q8—171no—
146C2×C4×D4#59511yescharacteristic
147C2×#101—174no—
148C4×M16—342no—
149#391—171no—
150#390—171no—
151#388—342no—
152#382—171no—
153C4×C22⋊C4—342no—
154C43—171no—
155#355—178no—
156#343—342no—
157C2×C17—21no—
158C2×C17—21no—
159C2×C17—82no—
160C2×C17C4×#9911yescharacteristic
161C2×C17C2×#35511yescharacteristic
162C2×C17#213211yescharacteristic
163C22×Q8—171no—
164C22×D4C2×#59511yescharacteristic
165C23×C4—21no—
166C2×M16—344no—
167#124—174no—
168#124—342no—
169C4×Q8—681no—
170C4×Q8—681no—
171C4×D4—41no—
172C4×D4—41no—
173C2×C4⋊C4—172no—
174C2×C4⋊C4—171no—
175C2×C4⋊C4C2×#59511yescharacteristic
176C2×C22⋊C4—21no—
177C2×C22⋊C4—342no—
178C2×C22⋊C4—342no—
179C2×C42—171no—
180C2×C42—172no—
181C2×C42—171no—
182C2×C42—341no—
183C2×C42—341no—
184C2×C42C2×#59511yescharacteristic
185#101—178no—
186#101—344no—
187#97—682no—
188C4×C8—682no—
189#95—342no—
190#95—342no—
191C17C4×#35511yescharacteristic, complemented, Sylow
192C24—21no—
193C2×Q8—172no—
194C2×Q8—172no—
195C2×Q8—681no—
196C2×Q8—681no—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4C4×#59512yes—
201C22×C4—21no—
202C22×C4—44no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—172no—
206C22×C4—172no—
207C22×C4—341no—
208C22×C4—341no—
209C22×C4C22⋊#59511yescharacteristic
210C22×C4C22⋊#59511yescharacteristic
211C22×C4C22×#59511yescharacteristic
212M16—348no—
213M16—684no—
214C2×C8—684no—
215C4⋊C4—41no—
216C4⋊C4—682no—
217C4⋊C4—681no—
218C22⋊C4—42no—
219C22⋊C4—348no—
220C22⋊C4—684no—
221C42—21no—
222C42—21no—
223C42—172no—
224C42—341no—
225C42—342no—
226C42—342no—
227C42—681no—
228C42—682no—
229C42—682no—
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23C2×C22⋊#59511yescharacteristic
236Q8—682no—
237Q8—682no—
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—174no—
250C2×C4—342no—
251C2×C4—342no—
252C2×C4—342no—
253C2×C4—342no—
254C2×C4—342no—
255C2×C4—681no—
256C2×C4—681no—
257C2×C4—681no—
258C2×C4—681no—
259C2×C4—682no—
260C2×C4#1058755111yescharacteristic
261C2×C4#1058755111yescharacteristic
262C2×C4C2×C4×#59511yescharacteristic
263C2×C4#1058767711yescharacteristic
264C8—688no—
265C22—21no—
266C22—21no—
267C22—44no—
268C22—42no—
269C22—82no—
270C22—81no—
271C22—81no—
272C22C4×C22⋊#59511yescharacteristic
273C22C2×#1058755111yescharacteristic
274C22#1176378811yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—41no—
279C4—81no—
280C4—344no—
281C4—682no—
282C4—682no—
283C4—682no—
284C4#1176371712yesdirect product factor
285C2—21no—
286C2—21no—
287C2—82no—
288C2C4×#1058755111yescharacteristic
289C2C2×#1176371711yescharacteristic
290C2#1454507511yescharacteristic
subgroupG/H
centerC2×C4#10587551
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC2×C4×D4×C17C4
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC22×Dic34C23
hypercenterC2×C4×D4#595
hypocenterC17C4×#355
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
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×#10587545C2semidirect
3. #14543882C2semidirect
7. #11763717C4direct (N × H)
41. #10587545C2×C4semidirect
139. C4×C17#355semidirect
191. C17C4×#355semidirect
284. C4#11763717direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637172
C4×#105875452
#145438822
C4×#105876222
C4×#35517