Finite Group Databasebeta

← D17⋊#354 #14545053

Subgroups — D17⋊#354 #14545053

Order 2176.

284 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D17⋊#99C212yesmaximal
2#11763716C212yesmaximal, complemented
3#11763715C212yesmaximal, complemented
4#124×D17C211yesmaximal, characteristic
5C2×Q8×D17C411yescharacteristic, complemented
6C2×D4×D17C2211yescharacteristic
7C2×C22⋊#595—22no—
8C17×#124C411yescharacteristic, complemented
9#10587633C2211yescharacteristic
10#10587622C411yescharacteristic, complemented
11#10587571—22no—
12C22⋊C4×D17—22no—
13#10587561C2211yescharacteristic
14C42×D17C411yescharacteristic, complemented
15#10587551—22no—
16#10587539C2214yes—
17C23×D17D412yes—
18C22×#595—42no—
19C2×Q8×C17C2×C411yescharacteristic, complemented
20C2×D4×C17C2×C411yescharacteristic
21C2×C22⋊D17D412yes—
22Q8×D17—41no—
23Q8×D17—41no—
24D4×D17—41no—
25D4×D17—41no—
26C2×D68C2311yescharacteristic
27C2×C4×D17—21no—
28C2×C4×D17—21no—
29C2×C4×D17C2×C411yescharacteristic
30C2×Dic34—21no—
31C2×Dic34C2×C411yescharacteristic, complemented
32C22⋊#595—24no—
33C22⋊#595—42no—
34C22⋊C4×C17—22no—
35C42×C17C2×C411yescharacteristic, complemented
36C22⋊Dic17—22no—
37#63227—22no—
38#63227—22no—
39C4×Dic17—21no—
40C4×Dic17C2×C411yescharacteristic, complemented
41C23×C17C22⋊C412yes—
42C22×D17—22no—
43C22×D17—22no—
44C22×D17—44no—
45C22×D17C22⋊C411yescharacteristic
46C22×D17C2×D412yes—
47C2×#595—44no—
48C2×#595—84no—
49Q8×C17—41no—
50D4×C17—41no—
51C2×C4×C17—21no—
52C2×C4×C17—21no—
53C2×C4×C17C22×C411yescharacteristic
54C22⋊D17—42no—
55C2×Dic17—21no—
56C2×Dic17—21no—
57C2×Dic17C22⋊C411yescharacteristic
58D68—41no—
59C4×D17—21no—
60C4×D17—21no—
61C4×D17—42no—
62C4×D17—41no—
63C4×D17—41no—
64Dic34—42no—
65Dic34—41no—
66C2×#354—171nomaximal, Sylow
67C22×C17—22no—
68C22×C17—42no—
69C22×C17C2×C22⋊C411yescharacteristic
70C2×D17—22no—
71C2×D17—22no—
72C2×D17—44no—
73C2×D17—42no—
74C2×D17—82no—
75C2×D17#9911yescharacteristic
76C2×D17#9911yescharacteristic
77#595—84no—
78C4×C17—21no—
79C4×C17—41no—
80C4×C17—41no—
81Dic17—21no—
82Dic17—41no—
83Dic17—41no—
84C2×#124—171no—
85C2×#99—172no—
86#354—172no—
87#354—172no—
88C2×C17—21no—
89C2×C17—42no—
90C2×C17C2×#9911yescharacteristic
91D17—21no—
92D17—42no—
93D17#35412yescomplemented
94C22×Q8—171no—
95C22×D4—171no—
96#124—171no—
97#124—171no—
98#124—171no—
99#124—342no—
100#124#59511yescharacteristic, complemented
101C2×C22⋊C4—342no—
102C2×C22⋊C4—342no—
103C2×C42—171no—
104#99—174no—
105#99—342no—
106C17C2×#35411yescharacteristic, complemented, Sylow
107C24—172no—
108C2×Q8—171no—
109C2×Q8—341no—
110C2×Q8—681no—
111C2×Q8—681no—
112C2×Q8C2×#59511yescharacteristic, complemented
113C2×D4—172no—
114C2×D4—171no—
115C2×D4—681no—
116C2×D4—681no—
117C2×D4C2×#59511yescharacteristic
118C22×C4—171no—
119C22×C4—341no—
120C22×C4—341no—
121C22×C4—682no—
122C22⋊C4—22no—
123C22⋊C4—342no—
124C22⋊C4—342no—
125C22⋊C4—342no—
126C22⋊C4—344no—
127C22⋊C4—682no—
128C42—171no—
129C42—341no—
130C42C2×#59511yescharacteristic, complemented
131C23—171no—
132C23—172no—
133C23—342no—
134C23—342no—
135C23—684no—
136C23C22⋊#59512yes—
137Q8—41no—
138Q8—681no—
139Q8—682no—
140D4—41no—
141D4—681no—
142D4—682no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—171no—
146C2×C4—341no—
147C2×C4—341no—
148C2×C4—341no—
149C2×C4—341no—
150C2×C4—681no—
151C2×C4—681no—
152C2×C4—682no—
153C2×C4—684no—
154C2×C4—1364no—
155C2×C4C22×#59511yescharacteristic
156C22—22no—
157C22—42no—
158C22—171no—
159C22—171no—
160C22—342no—
161C22—342no—
162C22—682no—
163C22—684no—
164C22—1362no—
165C22C2×C22⋊#59511yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—341no—
170C4—681no—
171C4—681no—
172C4—1364no—
173C2—21no—
174C2—42no—
175C2—172no—
176C2—341no—
177C2—682no—
178C2D17⋊#9911yescharacteristic
subgroupG/H
centerC2D17⋊#99
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC17×#124C4
socleC2×C17C2×#99
prime radicalC2×D4×D17C22
cosocleC2×D68C23
hypercenter#124#595
hypocenterC17C2×#354
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11763716C2semidirect
3. #11763715C2semidirect
5. C2×Q8×D17C4semidirect
8. C17×#124C4semidirect
10. #10587622C4semidirect
14. C42×D17C4semidirect
19. C2×Q8×C17C2×C4semidirect
31. C2×Dic34C2×C4semidirect
35. C42×C17C2×C4semidirect
40. C4×Dic17C2×C4semidirect
93. D17#354semidirect
100. #124#595semidirect
106. C17C2×#354semidirect
112. C2×Q8C2×#595semidirect
130. C42C2×#595semidirect

Maximal subgroups

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

subgroupindex
D17⋊#992
#117637162
#117637152
#124×D172
C2×#35417