Finite Group Databasebeta

← C2×#14543715 #17958146

Subgroups — C2×#14543715 #17958146

Order 4352.

618 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 120 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×#11763654C212yesmaximal
2#14543715C214yesmaximal, direct product factor
3C2×#11762715C211yesmaximal, characteristic
4C2×C22⋊#3624—22no—
5#11763654—22no—
6#11763654C2214yes—
7C23×Dic34C411yescharacteristic
8C22×C4⋊Dic17C2211yescharacteristic
9#11762715—22no—
10#11762715C412yes—
11#11762715C2212yes—
12C2×#10587502—22no—
13C22×C42×C17C411yescharacteristic
14C23×C4×C17—21no—
15C23×C4×C17C2×C411yescharacteristic
16C23×Dic17—21no—
17C23×Dic17D412yes—
18C22×Dic34—21no—
19C22×Dic34—22no—
20C22×Dic34—41no—
21C22×Dic34—41no—
22C22×Dic34—42no—
23C22×Dic34C814yescomplemented
24C22×Dic34C2×C412yes—
25C22×#3624—42no—
26C2×C42×C17—21no—
27C2×C42×C17—42no—
28C2×C42×C17C2×C412yes—
29C2×C4⋊Dic17—41no—
30C2×C4⋊Dic17—41no—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×C4⋊Dic17D412yes—
33C2×C4⋊Dic17C2311yescharacteristic
34C22⋊#3624—24no—
35C22⋊#3624—42no—
36#10587502—24no—
37#10587502—24no—
38C24×C17C22⋊C411yescharacteristic
39C22×C4×C17—21no—
40C22×C4×C17—21no—
41C22×C4×C17—22no—
42C22×C4×C17—24no—
43C22×C4×C17—22no—
44C22×C4×C17—42no—
45C22×C4×C17—42no—
46C22×C4×C17C22⋊C411yescharacteristic
47C22×C4×C17C2×C812yes—
48C22×C4×C17M1612yes—
49C22×C4×C17C22×C411yescharacteristic
50C22×Dic17—24no—
51C22×Dic17—22no—
52C22×Dic17—22no—
53C22×Dic17—22no—
54C22×Dic17—41no—
55C22×Dic17—41no—
56C22×Dic17—42no—
57C22×Dic17—44no—
58C22×Dic17C22⋊C412yes—
59C22×Dic17C2×D412yes—
60C2×Dic34—24no—
61C2×Dic34—22no—
62C2×Dic34—44no—
63C2×Dic34—44no—
64C2×Dic34—42no—
65C2×Dic34—42no—
66C2×Dic34—44no—
67C2×Dic34—44no—
68C2×Dic34—42no—
69C2×Dic34—42no—
70C2×Dic34C2×C814yescomplemented
71C2×#3624—44no—
72C2×#3624—84no—
73C42×C17—42no—
74C42×C17—42no—
75C4⋊Dic17—41no—
76C4⋊Dic17—42no—
77C4⋊Dic17—41no—
78C2×#1319—171nomaximal, Sylow
79C23×C17—22no—
80C23×C17—22no—
81C23×C17C22⋊C812yes—
82C23×C17#9911yescharacteristic
83C23×C17#9911yescharacteristic
84C23×C17#10012yes—
85C23×C17C2×C22⋊C411yescharacteristic
86C2×C4×C17—22no—
87C2×C4×C17—22no—
88C2×C4×C17—22no—
89C2×C4×C17—22no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—24no—
95C2×C4×C17—48no—
96C2×C4×C17—42no—
97C2×C4×C17—42no—
98C2×C4×C17C22⋊C812yes—
99C2×C4×C17C22×C811yescharacteristic
100C2×C4×C17C2×M1611yescharacteristic
101C2×Dic17—24no—
102C2×Dic17—22no—
103C2×Dic17—22no—
104C2×Dic17—44no—
105C2×Dic17—44no—
106C2×Dic17—44no—
107C2×Dic17—42no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—42no—
111C2×Dic17—82no—
112Dic34—48no—
113Dic34—44no—
114Dic34—44no—
115#3624—84no—
116C2×#391—171no—
117C2×#324—172no—
118#1319—174no—
119C22×C17—24no—
120C22×C17—24no—
121C22×C17—21no—
122C22×C17—21no—
123C22×C17—21no—
124C22×C17—21no—
125C22×C17#32312yes—
126C22×C17#32312yes—
127C22×C17#35412yes—
128C22×C17#35612yes—
129C22×C17C2×C22⋊C811yescharacteristic
130C22×C17C2×#9911yescharacteristic
131C22×C17C2×#10011yescharacteristic
132C4×C17—22no—
133C4×C17—21no—
134C4×C17—21no—
135C4×C17—44no—
136Dic17—42no—
137Dic17—42no—
138Dic17—44no—
139C23×Q8—171no—
140C22×C4⋊C4—171no—
141C22×C42#59511yescharacteristic
142C2×C22⋊C8—342no—
143#391—172no—
144#391—172no—
145#391—342no—
146C2×#95—342no—
147#324—174no—
148#324—342no—
149C2×C17—21no—
150C2×C17—22no—
151C2×C17—21no—
152C2×C17#131914yescomplemented
153C2×C17C2×#32311yescharacteristic
154C2×C17C2×#35411yescharacteristic
155C2×C17C2×#35611yescharacteristic
156C22×Q8—174no—
157C22×Q8—172no—
158C22×Q8—342no—
159C22×Q8—341no—
160C22×Q8—681no—
161C22×Q8—681no—
162C22×Q8—682no—
163C23×C4—21no—
164C23×C4—172no—
165C23×C4—341no—
166C23×C4C2×#59511yescharacteristic
167C22×C8—682no—
168C2×C4⋊C4—172no—
169C2×C4⋊C4—171no—
170C2×C4⋊C4—171no—
171C2×C4⋊C4—681no—
172C2×C4⋊C4—681no—
173C2×C42—21no—
174C2×C42—42no—
175C2×C42C2×#59512yes—
176C22⋊C8—344no—
177C22⋊C8—682no—
178#95—344no—
179#95—344no—
180C17C2×#131911yescharacteristic, complemented, Sylow
181C24C22⋊#59511yescharacteristic
182C2×Q8—174no—
183C2×Q8—342no—
184C2×Q8—344no—
185C2×Q8—682no—
186C2×Q8—682no—
187C2×Q8—684no—
188C2×Q8—684no—
189C2×Q8—682no—
190C2×Q8—682no—
191C2×Q8—684no—
192C2×Q8—684no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—24no—
197C22×C4—22no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—172no—
201C22×C4—172no—
202C22×C4—342no—
203C22×C4—342no—
204C22×C4—344no—
205C22×C4—342no—
206C22×C4—681no—
207C22×C4—681no—
208C22×C4—682no—
209C22×C4—684no—
210C22×C4#6324212yes—
211C22×C4#6324312yes—
212C22×C4C22⋊#59511yescharacteristic
213C22×C4C22×#59511yescharacteristic
214C2×C8—684no—
215C2×C8—1364no—
216C4⋊C4—682no—
217C4⋊C4—681no—
218C4⋊C4—681no—
219C42—42no—
220C42—42no—
221C23—22no—
222C23—22no—
223C23#1058753911yescharacteristic
224C23#1058753911yescharacteristic
225C23#1058754312yes—
226C23#1058755312yes—
227C23C2×C22⋊#59511yescharacteristic
228Q8—684no—
229Q8—684no—
230Q8—688no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—48no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—344no—
244C2×C4—342no—
245C2×C4—342no—
246C2×C4—684no—
247C2×C4—682no—
248C2×C4—682no—
249C2×C4—684no—
250C2×C4—684no—
251C2×C4—682no—
252C2×C4—682no—
253C2×C4—1362no—
254C2×C4#1058754312yes—
255C2×C4C2×#6324211yescharacteristic
256C2×C4C2×#6324311yescharacteristic
257C8—1364no—
258C22—24no—
259C22—24no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22#1176365312yes—
265C22#1176365312yes—
266C22#1176371612yes—
267C22#1176372012yes—
268C22C2×#1058754311yescharacteristic
269C22C2×#1058753911yescharacteristic
270C22C2×#1058755311yescharacteristic
271C4—21no—
272C4—21no—
273C4—22no—
274C4—44no—
275C4—684no—
276C4—682no—
277C4—682no—
278C2—21no—
279C2—21no—
280C2—22no—
281C2#1454371514yesdirect product factor
282C2C2×#1176365311yescharacteristic
283C2C2×#1176371611yescharacteristic
284C2C2×#1176372011yescharacteristic
subgroupG/H
centerC23#10587539
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC23×C17#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC22×C42#595
hypocenterC17C2×#1319
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #14543715C2direct (N × H)
23. C22×Dic34C8semidirect
70. C2×Dic34C2×C8semidirect
152. C2×C17#1319semidirect
180. C17C2×#1319semidirect
281. C2#14543715direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117636542
#145437152
C2×#117627152
C2×#131917