Finite Group Databasebeta

← #14544946

Subgroups — #14544946

Order 2176.

276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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⋊#108C211yesmaximal, characteristic
2#11763802C212yesmaximal
3D17⋊#101C212yesmaximal
4#11763772C211yesmaximal, characteristic
5C2×Q16×D17C211yesmaximal, characteristic
6C2×Q8×D17C2212yes—
7#10587677C2211yescharacteristic
8D17⋊M16C2212yes—
9D17⋊M16C2211yescharacteristic
10C2×Q16×C17C411yescharacteristic, complemented
11C2×#63231C412yescomplemented
12Q16×D17—21no—
13Q16×D17—21no—
14Q16×D17—21no—
15Q16×D17—21no—
16C2×Dic68C411yescharacteristic, complemented
17C2×C8×D17C2211yescharacteristic
18#10587549—24no—
19#10587545—24no—
20#10587536—21no—
21#10587535—21no—
22#10587532—21no—
23C8×#595—21no—
24C2×Q8×C17C2×C412yes—
25Q8×D17—22no—
26Q8×D17—22no—
27Q8×D17—22no—
28Q8×D17—22no—
29C2×C4×D17—22no—
30C2×C4×D17C2311yescharacteristic
31C2×Dic34—22no—
32C2×Dic34C2×C412yes—
33C22⋊#595—21no—
34#63247—22no—
35#63247D412yes—
36C4⋊#595D412yes—
37C4×#595—21no—
38#63243—21no—
39#63243—22no—
40#63242—21no—
41#63242—22no—
42Q16×C17—21no—
43Q16×C17—21no—
44C2×C8×C17C2×C411yescharacteristic
45#63231—22no—
46#63231—22no—
47C2×#3622C2×C411yescharacteristic
48Dic68—21no—
49Dic68—21no—
50C8×D17D411yescharacteristic
51C8×D17D411yescharacteristic
52C8×D17D411yescharacteristic
53C8×D17D411yescharacteristic
54C22×D17#4111yescharacteristic
55C2×#595—22no—
56Q8×C17—22no—
57Q8×C17—22no—
58C2×C4×C17—22no—
59C2×C4×C17C22×C411yescharacteristic
60C2×Dic17—22no—
61C2×Dic17C2×D411yescharacteristic
62C4×D17—42no—
63C4×D17—42no—
64C4×D17C2×D411yescharacteristic
65C4×D17C2×D411yescharacteristic
66C4×D17C2×D411yescharacteristic
67C4×D17#4111yescharacteristic
68Dic34—22no—
69Dic34—22no—
70Dic34—42no—
71Dic34—42no—
72#3624—22no—
73#3624—42no—
74C8×C17C22⋊C411yescharacteristic
75C8×C17C22⋊C411yescharacteristic
76#3622C22⋊C411yescharacteristic
77#3622C22⋊C411yescharacteristic
78#1979—171nomaximal, Sylow
79C22×C17C4×D411yescharacteristic
80C2×D17—22no—
81C2×D17#12111yescharacteristic
82C2×D17#12411yescharacteristic
83#595—42no—
84C4×C17—42no—
85C4×C17C2×C22⋊C411yescharacteristic
86C4×C17C4×D411yescharacteristic
87Dic17—42no—
88Dic17#12111yescharacteristic
89Dic17#12711yescharacteristic
90C22×Q16—171no—
91C2×#108—171no—
92#419—172no—
93C2×#101—172no—
94#405—171no—
95C2×C17—21no—
96C2×C17#39011yescharacteristic
97D17—21no—
98D17#47312yes—
99C22×Q8—172no—
100C2×Q16—172no—
101C2×Q16—171no—
102C2×Q16—341no—
103C2×Q16—341no—
104C2×Q16—341no—
105C2×Q16—341no—
106C2×Q16#59511yescharacteristic, complemented
107C2×M16—171no—
108C2×M16—172no—
109C22×C8—171no—
110#117—171no—
111#108—341no—
112#108—341no—
113#103—344no—
114#101—344no—
115#97—341no—
116C4×C8—341no—
117C17#197911yescharacteristic, complemented, Sylow
118C2×Q8—172no—
119C2×Q8—342no—
120C2×Q8—342no—
121C2×Q8—342no—
122C2×Q8—342no—
123C2×Q8—342no—
124C2×Q8C2×#59512yes—
125C22×C4—171no—
126C22×C4—342no—
127Q16—21no—
128Q16—21no—
129Q16—342no—
130Q16—342no—
131Q16—341no—
132Q16—341no—
133M16—172no—
134M16—341no—
135M16—342no—
136M16—342no—
137C2×C8—171no—
138C2×C8—171no—
139C2×C8—171no—
140C2×C8—171no—
141C2×C8—171no—
142C2×C8—341no—
143C2×C8—342no—
144C2×C8C2×#59511yescharacteristic
145C4⋊C4—172no—
146C22⋊C4—341no—
147C42—341no—
148C23—171no—
149Q8—22no—
150Q8—22no—
151Q8—342no—
152Q8—342no—
153Q8—682no—
154Q8—682no—
155C2×C4—22no—
156C2×C4—171no—
157C2×C4—171no—
158C2×C4—171no—
159C2×C4—171no—
160C2×C4—171no—
161C2×C4—342no—
162C2×C4—342no—
163C2×C4—682no—
164C2×C4—682no—
165C2×C4C22×#59511yescharacteristic
166C8—171no—
167C8—171no—
168C8—342no—
169C8—682no—
170C8C22⋊#59511yescharacteristic
171C8C22⋊#59511yescharacteristic
172C22—171no—
173C22—171no—
174C22—342no—
175C22D4×#59511yescharacteristic
176C4—42no—
177C4—171no—
178C4—171no—
179C4—682no—
180C4—682no—
181C4D4×#59511yescharacteristic
182C4C2×C22⋊#59511yescharacteristic
183C2—21no—
184C2—172no—
185C2—341no—
186C2#1176376111yescharacteristic
subgroupG/H
centerC2#11763761
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC2×Q16×C17C4
socleC2×C17#390
prime radicalC22×D17#41
cosocleC2×C4×D17C23
hypercenterC2×Q16#595
hypocenterC17#1979
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
10. C2×Q16×C17C4semidirect
11. C2×#63231C4semidirect
16. C2×Dic68C4semidirect
106. C2×Q16#595semidirect
117. C17#1979semidirect

Maximal subgroups

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

subgroupindex
D17⋊#1082
#117638022
D17⋊#1012
#117637722
C2×Q16×D172
#197917