Finite Group Databasebeta

← #14530127

Subgroups — #14530127

Order 2176.

246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 73 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#11763437C211yesmaximal, characteristic
2#11762849C211yesmaximal, characteristic
3#11762678C211yesmaximal, characteristic
4#11762577C211yesmaximal, characteristic
5#11762570C211yesmaximal, characteristic
6#11762568C211yesmaximal, characteristic
7C17×#428C211yesmaximal, characteristic
8C2×M16×C17C2211yescharacteristic
9C17×#117C2211yescharacteristic
10C2×C4⋊C4×C17C2211yescharacteristic
11#10587612C2211yescharacteristic
12C2×C4⋊Dic17C2211yescharacteristic
13C2×#63225—22no—
14C2×C4×Dic17C2211yescharacteristic
15C2×#63223C2211yescharacteristic
16#10587576—21no—
17#10587574—21no—
18#10587564—22no—
19#10587556—21no—
20#10587555—21no—
21C17×#107—21no—
22C17×#106—21no—
23#10587479—21no—
24#10587478—21no—
25C22×C4×C17—21no—
26C22×C4×C17C2311yescharacteristic
27C22×Dic17—21no—
28C22×Dic17D412yes—
29C2×Dic34—22no—
30M16×C17—21no—
31M16×C17Q812yescomplemented
32C2×C8×C17—21no—
33C4⋊C4×C17—21no—
34C4⋊C4×C17—21no—
35C4⋊C4×C17D411yescharacteristic
36C4⋊C4×C17D411yescharacteristic
37C22⋊C4×C17—21no—
38C42×C17—21no—
39C22⋊Dic17—21no—
40C4⋊Dic17—22no—
41C4⋊Dic17—21no—
42C4⋊Dic17—21no—
43C4⋊Dic17D411yescharacteristic
44C4⋊Dic17D411yescharacteristic
45#63225—22no—
46#63225—22no—
47#63225—44no—
48C4×Dic17—21no—
49C4×Dic17—21no—
50C4×Dic17Q812yescomplemented
51#63223—21no—
52#63223Q812yescomplemented
53C2×#3622—21no—
54C23×C17C2×D411yescharacteristic
55C2×C4×C17—21no—
56C2×C4×C17—21no—
57C2×C4×C17—42no—
58C2×C4×C17—41no—
59C2×C4×C17C2×D411yescharacteristic
60C2×C4×C17C2×D411yescharacteristic
61C2×C4×C17C2×Q811yescharacteristic
62C2×C4×C17C2×Q811yescharacteristic
63C2×C4×C17C2×Q811yescharacteristic
64C2×C4×C17#4111yescharacteristic
65C2×Dic17—22no—
66C2×Dic17—22no—
67C2×Dic17—22no—
68C2×Dic17—21no—
69C2×Dic17—21no—
70C2×Dic17—22no—
71C2×Dic17—42no—
72Dic34—82no—
73C8×C17—22no—
74#3622—22no—
75#2060—171nomaximal, Sylow
76C22×C17—21no—
77C22×C17—21no—
78C22×C17#12011yescharacteristic
79C22×C17C22⋊Q811yescharacteristic
80C22×C17C4⋊Q811yescharacteristic
81C4×C17—41no—
82C4×C17—41no—
83C4×C17—81no—
84C4×C17C22⋊Q811yescharacteristic
85C4×C17C22⋊Q811yescharacteristic
86C4×C17C4⋊Q811yescharacteristic
87C4×C17C4⋊Q811yescharacteristic
88Dic17—24no—
89Dic17—41no—
90Dic17—42no—
91Dic17—41no—
92#544—171no—
93#428—171no—
94#428D1711yescharacteristic
95#384—171no—
96#343—171no—
97#339—171no—
98#339—171no—
99C2×C17—21no—
100C2×C17—21no—
101C2×C17#39511yescharacteristic
102C2×C17#45311yescharacteristic
103C2×C17#45611yescharacteristic
104C2×M16—171no—
105C2×M16C2×D1711yescharacteristic
106C4⋊Q8—341no—
107C4⋊Q8—341no—
108#125—341no—
109#125—341no—
110C22⋊Q8—342no—
111#117—171no—
112#117C2×D1711yescharacteristic
113C2×C4⋊C4—171no—
114C2×C4⋊C4—342no—
115C2×C4⋊C4C2×D1711yescharacteristic
116C2×C42—171no—
117#107—21no—
118#107—341no—
119#106—21no—
120#106—341no—
121C17#206011yescharacteristic, complemented, Sylow
122C2×Q8—342no—
123C22×C4—21no—
124C22×C4—172no—
125C22×C4—341no—
126C22×C4C22×D1711yescharacteristic
127M16—21no—
128M16—172no—
129M16—341no—
130M16Dic3412yescomplemented
131C2×C8—21no—
132C2×C8—341no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—171no—
136C4⋊C4—171no—
137C4⋊C4—342no—
138C4⋊C4—342no—
139C4⋊C4—342no—
140C4⋊C4—341no—
141C4⋊C4—341no—
142C4⋊C4—684no—
143C4⋊C4C22⋊D1711yescharacteristic
144C4⋊C4C22⋊D1711yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—341no—
147C42—21no—
148C42—172no—
149C42—341no—
150C42—341no—
151C23D4×D1711yescharacteristic
152Q8—1362no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—342no—
158C2×C4—342no—
159C2×C4—342no—
160C2×C4—341no—
161C2×C4—341no—
162C2×C4—342no—
163C2×C4—682no—
164C2×C4C2×Dic3411yescharacteristic
165C2×C4#6325211yescharacteristic
166C2×C4D4×D1711yescharacteristic
167C2×C4Q8×D1711yescharacteristic
168C2×C4Q8×D1711yescharacteristic
169C2×C4C2×C22⋊D1711yescharacteristic
170C8—22no—
171C8—342no—
172C22—21no—
173C22—21no—
174C22#1058757411yescharacteristic
175C22#1058758211yescharacteristic
176C22#1058762311yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—344no—
181C4—682no—
182C4—681no—
183C4—681no—
184C4#1058757411yescharacteristic
185C4#1058758211yescharacteristic
186C4#1058761011yescharacteristic
187C4#1058763011yescharacteristic
188C2—21no—
189C2—21no—
190C2#1176272911yescharacteristic
191C2#1176297511yescharacteristic
192C2#1176299011yescharacteristic
subgroupG/H
centerC22#10587623
commutator, cosocleC22×C4×C17C23
FrattiniC22×C4C22×D17
FittingC17×#428C2
socleC22×C17#120
prime radicalC23×C17C2×D4
hypercenter#428D17
hypocenterC17#2060
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
31. M16×C17Q8semidirect
50. C4×Dic17Q8semidirect
52. #63223Q8semidirect
121. C17#2060semidirect
130. M16Dic34semidirect

Maximal subgroups

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

subgroupindex
#117634372
#117628492
#117626782
#117625772
#117625702
#117625682
C17×#4282
#206017