Finite Group Databasebeta

← D17×#353 #14530440

Subgroups — D17×#353 #14530440

Order 2176.

368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 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
1#127×D17C211yesmaximal, characteristic
2#99×D17C212yesmaximal, complemented
3#11762602C211yesmaximal, characteristic, complemented
4#11762601C212yesmaximal, complemented
5C17×#353C211yesmaximal, characteristic, complemented
6C2×D4×D17—22no—
7C2×D4×D17C411yescharacteristic, complemented
8C2×D4×D17C2211yescharacteristic
9C17×#127C2211yescharacteristic
10#10587626—22no—
11#10587626C411yescharacteristic, complemented
12#10587626C2211yescharacteristic
13C22⋊C4×D17—22no—
14#10587560C411yescharacteristic, complemented
15C42×D17C411yescharacteristic, complemented
16C17×#99C2212yescomplemented
17#10587505C2212yescomplemented
18#10587477—22no—
19C23×D17—21no—
20C23×D17D412yes—
21C2×D4×C17—22no—
22C2×D4×C17C2×C411yescharacteristic, complemented
23C2×D4×C17C2311yescharacteristic
24C2×C22⋊D17—22no—
25C2×C22⋊D17—22no—
26C2×C22⋊D17—21no—
27C2×C22⋊D17D412yes—
28D4×D17—41no—
29D4×D17—41no—
30D4×D17—41no—
31D4×D17—41no—
32D4×D17—48no—
33C2×D68—22no—
34C2×D68C2×C411yescharacteristic
35C2×D68C2×C411yescharacteristic, complemented
36C2×C4×D17—21no—
37C2×C4×D17—42no—
38C2×C4×D17C2×C411yescharacteristic
39C22⋊C4×C17—22no—
40C42×C17C2×C411yescharacteristic, complemented
41C22⋊Dic17—22no—
42#63227—42no—
43C4×Dic17—21no—
44C4×Dic17C2×C411yescharacteristic, complemented
45C23×C17—21no—
46C23×C17C2×D412yes—
47C22×D17—22no—
48C22×D17—22no—
49C22×D17—21no—
50C22×D17—44no—
51C22×D17—44no—
52C22×D17—41no—
53C22×D17—41no—
54C22×D17C22⋊C411yescharacteristic
55C22×D17C22⋊C412yes—
56D4×C17—41no—
57D4×C17—41no—
58D4×C17—44no—
59C2×C4×C17—21no—
60C2×C4×C17—42no—
61C2×C4×C17C22×C411yescharacteristic
62C22⋊D17—42no—
63C22⋊D17—44no—
64C22⋊D17—44no—
65C22⋊D17—42no—
66C2×Dic17—21no—
67C2×Dic17—42no—
68C2×Dic17C22⋊C411yescharacteristic
69D68—41no—
70D68—41no—
71D68—44no—
72C4×D17—24no—
73C4×D17—21no—
74C4×D17—21no—
75C4×D17—84no—
76C2×#353—171nomaximal, Sylow
77C22×C17—22no—
78C22×C17—42no—
79C22×C17—42no—
80C22×C17—41no—
81C22×C17C2×C22⋊C411yescharacteristic
82C2×D17—22no—
83C2×D17—22no—
84C2×D17—44no—
85C2×D17—42no—
86C2×D17—42no—
87C2×D17—41no—
88C2×D17—82no—
89C2×D17—82no—
90C2×D17—82no—
91C2×D17#9911yescharacteristic
92C2×D17#9911yescharacteristic
93C4×C17—22no—
94C4×C17—21no—
95C4×C17—82no—
96Dic17—22no—
97Dic17—21no—
98Dic17—82no—
99C2×#127—171no—
100C2×#99—172no—
101#353—171no—
102#353—172no—
103#353D1711yescharacteristic, direct product factor
104C2×C17—21no—
105C2×C17—42no—
106C2×C17—81no—
107C2×C17C2×#9911yescharacteristic
108D17—21no—
109D17—42no—
110D17—81no—
111D17#35312yesdirect product factor
112C22×D4—171no—
113C22×D4—171no—
114C22×D4—342no—
115#127—171no—
116#127—171no—
117#127—171no—
118#127—342no—
119#127C2×D1711yescharacteristic
120C2×C22⋊C4—342no—
121C2×C42—171no—
122#99—172no—
123#99—342no—
124#99C2×D1712yescomplemented
125C17C2×#35311yescharacteristic, complemented, Sylow
126C24—172no—
127C24—341no—
128C2×D4—22no—
129C2×D4—172no—
130C2×D4—171no—
131C2×D4—171no—
132C2×D4—342no—
133C2×D4—341no—
134C2×D4—342no—
135C2×D4—342no—
136C2×D4—681no—
137C2×D4—681no—
138C2×D4—681no—
139C2×D4—681no—
140C2×D4—688no—
141C2×D4C4×D1711yescharacteristic, complemented
142C2×D4C22×D1711yescharacteristic
143C22×C4—171no—
144C22×C4—341no—
145C22×C4—682no—
146C22⋊C4—22no—
147C22⋊C4—342no—
148C22⋊C4—682no—
149C42—171no—
150C42—341no—
151C42C4×D1711yescharacteristic, complemented
152C23—21no—
153C23—171no—
154C23—172no—
155C23—342no—
156C23—342no—
157C23—341no—
158C23—681no—
159C23—681no—
160C23—684no—
161C23—684no—
162C23D4×D1712yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—681no—
167D4—681no—
168D4—684no—
169D4—682no—
170D4—684no—
171D4—684no—
172D4—682no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—171no—
176C2×C4—341no—
177C2×C4—341no—
178C2×C4—344no—
179C2×C4—341no—
180C2×C4—682no—
181C2×C4—1364no—
182C2×C4C2×C4×D1711yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—171no—
188C22—171no—
189C22—342no—
190C22—342no—
191C22—682no—
192C22—682no—
193C22—684no—
194C22—681no—
195C22—1362no—
196C22—1362no—
197C22—1362no—
198C22C22⋊C4×D1711yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—342no—
203C4—341no—
204C4—1362no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—172no—
209C2—341no—
210C2—682no—
211C2—1361no—
212C2#99×D1711yescharacteristic
subgroupG/H
centerC2#99×D17
commutatorC2×C4×C17C22×C4
FrattiniC2×D4C22×D17
FittingC17×#353C2
socleC2×C17C2×#99
prime radical#127×D17C2
cosocleC2×D4×C17C23
hypercenter#353D17
hypocenterC17C2×#353
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D17C2semidirect
3. #11762602C2semidirect
4. #11762601C2semidirect
5. C17×#353C2semidirect
7. C2×D4×D17C4semidirect
11. #10587626C4semidirect
14. #10587560C4semidirect
15. C42×D17C4semidirect
16. C17×#99C22semidirect
17. #10587505C22semidirect
22. C2×D4×C17C2×C4semidirect
35. C2×D68C2×C4semidirect
40. C42×C17C2×C4semidirect
44. C4×Dic17C2×C4semidirect
103. #353D17direct (N × H)
111. D17#353direct (N × H)
124. #99C2×D17semidirect
125. C17C2×#353semidirect
141. C2×D4C4×D17semidirect
151. C42C4×D17semidirect

Maximal subgroups

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

subgroupindex
#127×D172
#99×D172
#117626022
#117626012
C17×#3532
C2×#35317