Finite Group Databasebeta

← C2×#14543929 #17962723

Subgroups — C2×#14543929 #17962723

Order 4352.

340 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 64 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×#11763718C211yesmaximal, characteristic
2C2×#11763716C211yesmaximal, characteristic
3#14543929C214yesmaximal, direct product factor
4C2×#11763166C211yesmaximal, characteristic
5C2×#10587545—21no—
6C2×#10587539—21no—
7#11763718—21no—
8#11763718C2212yes—
9#11763716—21no—
10#11763716C2212yes—
11C2×#10587561C2211yescharacteristic
12#11763166—21no—
13#11763166—21no—
14#11763166C412yescomplemented
15#11763166C2212yes—
16C2×#10587481—21no—
17C2×#10587480—21no—
18C2×C4×#3622C411yescharacteristic, complemented
19C2×C17×#125C411yescharacteristic, complemented
20C22×D68D411yescharacteristic
21C22×Dic34D411yescharacteristic
22C2×C22⋊#595—41no—
23C2×#63247—41no—
24C17×#125—21no—
25C17×#125—41no—
26C17×#125C2×C412yescomplemented
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—41no—
29C2×C42×C17C2×C411yescharacteristic
30C2×#63227—41no—
31C22×#3622—21no—
32#10587561—41no—
33#10587561C2×C411yescharacteristic
34#10587561D411yescharacteristic
35#10587561D411yescharacteristic
36#10587561C2311yescharacteristic
37#10587545—22no—
38#10587545—41no—
39#10587539—22no—
40#10587539—41no—
41#10587481—22no—
42#10587481—22no—
43#10587480—22no—
44#10587480—22no—
45C4×#3622—21no—
46C4×#3622C2×C412yescomplemented
47C23×D17—21no—
48C22×#595—81no—
49C22×C4×C17—21no—
50C22×C4×C17—41no—
51C22×C4×C17C22⋊C411yescharacteristic
52C22×Dic17—21no—
53C2×D68—21no—
54C2×D68—41no—
55C2×D68—41no—
56C2×D68C22⋊C411yescharacteristic
57C2×D68C2×D411yescharacteristic
58C2×Dic34—21no—
59C2×Dic34—41no—
60C2×Dic34—41no—
61C2×Dic34C22⋊C411yescharacteristic
62C2×Dic34C2×D411yescharacteristic
63C22⋊#595—42no—
64C22⋊#595—81no—
65#63247—42no—
66#63247—81no—
67C2×#3624—81no—
68C4⋊C4×C17—22no—
69C4⋊C4×C17—42no—
70C4⋊C4×C17—42no—
71C4⋊C4×C17—41no—
72C42×C17—21no—
73C42×C17C22⋊C411yescharacteristic
74C42×C17C22×C411yescharacteristic
75#63227—41no—
76#63227—41no—
77#63227—41no—
78#63227—41no—
79C2×#3622—22no—
80C2×#3622—41no—
81C2×#3622—41no—
82C2×#1414—171nomaximal, Sylow
83C23×C17#9911yescharacteristic
84C22×D17—21no—
85C22×D17—21no—
86C22×D17—41no—
87C22×D17—41no—
88C22×D17—82no—
89C2×#595—82no—
90C2×#595—162no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—42no—
96C2×C4×C17—42no—
97C2×C4×C17—82no—
98C2×C4×C17#9911yescharacteristic
99C2×C4×C17C2×C22⋊C411yescharacteristic
100C2×Dic17—21no—
101C2×Dic17—21no—
102C2×Dic17—41no—
103C2×Dic17—41no—
104D68—41no—
105D68—41no—
106D68—81no—
107Dic34—41no—
108Dic34—41no—
109Dic34—81no—
110#3624—82no—
111#3622—42no—
112C2×#488—171no—
113C2×#355—171no—
114C2×#354—171no—
115#1414—174no—
116C22×C17—22no—
117C22×C17#35411yescharacteristic
118C22×C17#35411yescharacteristic
119C22×C17C2×#9911yescharacteristic
120C2×D17—41no—
121C2×D17—41no—
122C2×D17—82no—
123C2×D17—81no—
124C2×D17—81no—
125C2×D17—161no—
126#595—162no—
127C4×C17—21no—
128C4×C17—21no—
129C4×C17—41no—
130C4×C17—41no—
131C4×C17—82no—
132Dic17—41no—
133Dic17—41no—
134C2×#125#59511yescharacteristic, complemented
135C2×#124—171no—
136#488—172no—
137#488—172no—
138#488—341no—
139#488—341no—
140C2×#103—341no—
141C2×#102—341no—
142C2×#101—341no—
143C2×#99—341no—
144C2×C4×C8—171no—
145#355—172no—
146#355—341no—
147#354—172no—
148#354—341no—
149C2×C17—21no—
150C2×C17—21no—
151C2×C17#141412yescomplemented
152C2×C17C2×#35411yescharacteristic
153D17—81no—
154D17—81no—
155C22×Q8—171no—
156C22×D4—171no—
157C2×M16—681no—
158C22×C8—341no—
159#125—21no—
160#125—41no—
161#125C2×#59512yescomplemented
162#124—171no—
163#124—171no—
164#124—171no—
165#124—171no—
166#124—681no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—41no—
169C2×C22⋊C4—681no—
170C2×C22⋊C4—681no—
171C2×C42C2×#59511yescharacteristic
172#103—342no—
173#103—342no—
174#102—342no—
175#102—342no—
176#101—342no—
177#101—681no—
178#99—342no—
179#99—681no—
180C4×C8—172no—
181C4×C8—341no—
182C17C2×#141411yescharacteristic, complemented, Sylow
183C24—341no—
184C2×Q8—171no—
185C2×Q8—171no—
186C2×Q8—341no—
187C2×Q8—681no—
188C2×Q8—681no—
189C2×D4—171no—
190C2×D4—171no—
191C2×D4—341no—
192C2×D4—681no—
193C2×D4—681no—
194C22×C4—21no—
195C22×C4—41no—
196C22×C4—341no—
197C22×C4—1361no—
198C22×C4C22⋊#59511yescharacteristic
199M16—682no—
200M16—1361no—
201C2×C8—342no—
202C2×C8—681no—
203C2×C8—681no—
204C2×C8—1361no—
205C4⋊C4—22no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C22⋊C4—681no—
210C22⋊C4—681no—
211C22⋊C4—681no—
212C22⋊C4—681no—
213C22⋊C4—682no—
214C22⋊C4—1361no—
215C42—21no—
216C42C22⋊#59511yescharacteristic
217C42C22×#59511yescharacteristic
218C23—341no—
219C23—341no—
220C23—681no—
221C23—681no—
222C23—1362no—
223C23#1058755111yescharacteristic
224Q8—681no—
225Q8—681no—
226Q8—1361no—
227D4—681no—
228D4—681no—
229D4—1361no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—82no—
237C2×C4—2722no—
238C2×C4—341no—
239C2×C4—341no—
240C2×C4—681no—
241C2×C4—681no—
242C2×C4—1362no—
243C2×C4#1058755111yescharacteristic
244C2×C4C2×C22⋊#59511yescharacteristic
245C8—682no—
246C8—1362no—
247C22—22no—
248C22—2721no—
249C22—681no—
250C22—681no—
251C22—1361no—
252C22—1361no—
253C22—1362no—
254C22#1176371511yescharacteristic
255C22#1176371511yescharacteristic
256C22C2×#1058755111yescharacteristic
257C4—21no—
258C4—21no—
259C4—41no—
260C4—41no—
261C4—82no—
262C4—2722no—
263C4—681no—
264C4—681no—
265C2—21no—
266C2—21no—
267C2—1361no—
268C2—1361no—
269C2#1454392912yesdirect product factor
270C2C2×#1176371511yescharacteristic
subgroupG/H
centerC22#11763715
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC2×C17×#125C4
socleC22×C17#354
prime radicalC22×D68D4
cosocle#10587561C23
hypercenterC2×#125#595
hypocenterC17C2×#1414
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #14543929C2direct (N × H)
14. #11763166C4semidirect
18. C2×C4×#3622C4semidirect
19. C2×C17×#125C4semidirect
26. C17×#125C2×C4semidirect
46. C4×#3622C2×C4semidirect
134. C2×#125#595semidirect
151. C2×C17#1414semidirect
161. #125C2×#595semidirect
182. C17C2×#1414semidirect
269. C2#14543929direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637182
C2×#117637162
#145439292
C2×#117631662
C2×#141417