Finite Group Databasebeta

← C2×#14543917 #17962658

Subgroups — C2×#14543917 #17962658

Order 4352.

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

normal subgroups only

This group has 474 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×#11763714C212yesmaximal
2#14543917C214yesmaximal, direct product factor
3C2×#11763183C211yesmaximal, characteristic
4C2×#10587539—22no—
5#11763714—22no—
6#11763714C2214yes—
7C22×#63230—22no—
8C2×#10587560C2211yescharacteristic
9#11763183—22no—
10#11763183C412yescomplemented
11#11763183C2212yes—
12C2×C4×#3622C411yescharacteristic, complemented
13C2×C17×C4⋊Q8C411yescharacteristic, complemented
14C22×Q8×C17—21no—
15C22×D68—41no—
16C22×D68D412yes—
17C2×C22⋊#595—42no—
18C17×C4⋊Q8—21no—
19C17×C4⋊Q8—41no—
20C17×C4⋊Q8C2×C412yescomplemented
21C2×C4⋊C4×C17—41no—
22C2×C42×C17C2×C411yescharacteristic
23C2×#63230—24no—
24C2×#63230—24no—
25C2×#63230—44no—
26C2×#63230—44no—
27C22×#3622—21no—
28#10587560—41no—
29#10587560C2×C411yescharacteristic
30#10587560D412yes—
31#10587560C2311yescharacteristic
32#10587539—24no—
33#10587539—42no—
34C4×#3622—21no—
35C4×#3622C2×C412yescomplemented
36C23×D17—22no—
37C22×#595—82no—
38C2×Q8×C17—22no—
39C2×Q8×C17—42no—
40C2×Q8×C17—42no—
41C2×Q8×C17—41no—
42C22×C4×C17—21no—
43C22×C4×C17—41no—
44C22×C4×C17C22⋊C411yescharacteristic
45C2×D68—22no—
46C2×D68—42no—
47C2×D68—42no—
48C2×D68—41no—
49C2×D68—42no—
50C2×D68—41no—
51C2×D68—84no—
52C2×D68C22⋊C412yes—
53C2×D68C2×D412yes—
54C22⋊#595—44no—
55C22⋊#595—82no—
56C4⋊C4×C17—42no—
57C4⋊C4×C17—42no—
58C42×C17—21no—
59C42×C17C22⋊C411yescharacteristic
60C42×C17C22×C411yescharacteristic
61#63230—48no—
62#63230—48no—
63C2×#3622—22no—
64C2×#3622—22no—
65C2×#3622—22no—
66C2×#1409—171nomaximal, Sylow
67C23×C17#9911yescharacteristic
68C22×D17—22no—
69C22×D17—22no—
70C22×D17—42no—
71C22×D17—42no—
72C22×D17—84no—
73C2×#595—84no—
74C2×#595—164no—
75Q8×C17—44no—
76Q8×C17—82no—
77C2×C4×C17—24no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—42no—
83C2×C4×C17—81no—
84C2×C4×C17—81no—
85C2×C4×C17#9911yescharacteristic
86C2×C4×C17C2×C22⋊C411yescharacteristic
87D68—42no—
88D68—42no—
89D68—82no—
90D68—82no—
91D68—84no—
92D68—82no—
93#3622—24no—
94C2×#492—171no—
95C2×#353—172no—
96#1409—174no—
97C22×C17—22no—
98C22×C17#35311yescharacteristic
99C22×C17#35311yescharacteristic
100C22×C17C2×#9911yescharacteristic
101C2×D17—42no—
102C2×D17—42no—
103C2×D17—84no—
104C2×D17—82no—
105C2×D17—82no—
106C2×D17—162no—
107#595—164no—
108C4×C17—22no—
109C4×C17—22no—
110C4×C17—21no—
111C4×C17—21no—
112C4×C17—82no—
113C22×SD16—342no—
114C2×C4⋊Q8#59511yescharacteristic, complemented
115C2×#127—171no—
116#492—172no—
117#492—172no—
118#492—342no—
119C2×#99—342no—
120C2×C4×C8—171no—
121#353—174no—
122#353—342no—
123C2×C17—21no—
124C2×C17—21no—
125C2×C17#140912yescomplemented
126C2×C17C2×#35311yescharacteristic
127D17—82no—
128D17—82no—
129C22×Q8—21no—
130C22×D4—172no—
131C22×D4—681no—
132C2×SD16—344no—
133C2×SD16—344no—
134C2×SD16—684no—
135C2×SD16—684no—
136C22×C8—341no—
137C4⋊Q8—21no—
138C4⋊Q8—41no—
139C4⋊Q8C2×#59512yescomplemented
140#127—172no—
141#127—171no—
142#127—171no—
143#127—681no—
144C2×C4⋊C4—41no—
145C2×C22⋊C4—682no—
146C2×C42C2×#59511yescharacteristic
147#99—344no—
148#99—682no—
149C4×C8—172no—
150C4×C8—341no—
151C17C2×#140911yescharacteristic, complemented, Sylow
152C24—342no—
153C2×Q8—22no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8—41no—
157C2×D4—172no—
158C2×D4—172no—
159C2×D4—342no—
160C2×D4—682no—
161C2×D4—682no—
162C2×D4—682no—
163C2×D4—681no—
164C2×D4—681no—
165C2×D4—1364no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—1362no—
169C22×C4C22⋊#59511yescharacteristic
170SD16—688no—
171SD16—688no—
172C2×C8—342no—
173C2×C8—342no—
174C2×C8—342no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C22⋊C4—684no—
178C22⋊C4—1362no—
179C42—21no—
180C42C22⋊#59511yescharacteristic
181C42C22×#59511yescharacteristic
182C23—342no—
183C23—342no—
184C23—682no—
185C23—682no—
186C23—1364no—
187C23#1058755111yescharacteristic
188Q8—44no—
189Q8—82no—
190D4—682no—
191D4—682no—
192D4—1362no—
193D4—1364no—
194D4—1362no—
195D4—1362no—
196C2×C4—24no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—2724no—
205C2×C4—1364no—
206C2×C4#1058755111yescharacteristic
207C2×C4C2×C22⋊#59511yescharacteristic
208C8—344no—
209C22—22no—
210C22—2722no—
211C22—682no—
212C22—682no—
213C22—1362no—
214C22—1362no—
215C22—1364no—
216C22#1176371311yescharacteristic
217C22#1176371311yescharacteristic
218C22C2×#1058755111yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—2724no—
225C2—21no—
226C2—21no—
227C2—1362no—
228C2—1362no—
229C2#1454391712yesdirect product factor
230C2C2×#1176371311yescharacteristic
subgroupG/H
centerC22#11763713
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17#353
prime radicalC2×#10587560C22
cosocle#10587560C23
hypercenterC2×C4⋊Q8#595
hypocenterC17C2×#1409
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #14543917C2direct (N × H)
10. #11763183C4semidirect
12. C2×C4×#3622C4semidirect
13. C2×C17×C4⋊Q8C4semidirect
20. C17×C4⋊Q8C2×C4semidirect
35. C4×#3622C2×C4semidirect
114. C2×C4⋊Q8#595semidirect
125. C2×C17#1409semidirect
139. C4⋊Q8C2×#595semidirect
151. C17C2×#1409semidirect
229. C2#14543917direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637142
#145439172
C2×#117631832
C2×#140917