Finite Group Databasebeta

← #17959838

Subgroups — #17959838

Order 4352.

272 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 62 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#14545159C211yesmaximal, characteristic
2#14545006C211yesmaximal, characteristic
3#14543789C214yesmaximal, complemented
4#14539440C211yesmaximal, characteristic
5#11763865—21no—
6#11763731—21no—
7#11763706—21no—
8#11763702—21no—
9#11763701C2212yes—
10#11763701C2212yes—
11#11763420C412yes—
12#11763211C411yescharacteristic
13#11763177C2212yes—
14#11763064—21no—
15#11763047—21no—
16#11762916—21no—
17Q16×Dic17—21no—
18#11762763C2211yescharacteristic
19C17×#494C411yescharacteristic
20C2×Q16×C17—21no—
21C2×Q16×C17—21no—
22C17×C4⋊Q8C2×C412yes—
23#10587632—22no—
24Q8×Dic17—22no—
25C2×#63218D411yescharacteristic
26C2×C8×D17D411yescharacteristic
27#10587584—42no—
28#10587575—42no—
29#10587558C2×C411yescharacteristic
30#10587556C2×C412yes—
31#10587538—22no—
32#10587538—22no—
33#10587530—22no—
34#10587529—22no—
35C4×C8×C17C2×C411yescharacteristic
36#10587506—22no—
37#10587506—22no—
38#10587489—21no—
39#10587488—21no—
40#10587486D411yescharacteristic
41C8×Dic17D411yescharacteristic
42#10587474C2311yescharacteristic
43C2×Q8×C17—22no—
44C2×C4×D17C22⋊C411yescharacteristic
45Q16×C17—42no—
46Q16×C17—41no—
47Q16×C17—41no—
48C2×C8×C17C22⋊C411yescharacteristic
49C2×C8×C17C22⋊C411yescharacteristic
50C4⋊C4×C17—42no—
51C42×C17C22×C411yescharacteristic
52#63227—21no—
53#63227—42no—
54C4⋊Dic17—22no—
55C4⋊Dic17—42no—
56#63225—21no—
57#63225—42no—
58#63225—42no—
59C4×Dic17—42no—
60C4×Dic17C22⋊C411yescharacteristic
61C2×#3622C2×D411yescharacteristic
62C2×#3622C2×D411yescharacteristic
63#63218—41no—
64C8×D17—21no—
65C8×D17—21no—
66#63216—24no—
67#63216—42no—
68#11914—171nomaximal, Sylow
69C22×D17#10011yescharacteristic
70Q8×C17—42no—
71Q8×C17—42no—
72C2×C4×C17—21no—
73C2×C4×C17—42no—
74C2×C4×C17C2×C22⋊C411yescharacteristic
75C2×Dic17—21no—
76C2×Dic17—42no—
77C2×Dic17#10011yescharacteristic
78C4×D17—21no—
79C4×D17—21no—
80C8×C17—21no—
81C8×C17#10411yescharacteristic
82C8×C17#10411yescharacteristic
83#3622—21no—
84#3622—21no—
85#3177—171no—
86#2166—171no—
87#2110—171no—
88#1356—174no—
89C22×C17C2×#10011yescharacteristic
90C2×D17—21no—
91C2×D17—41no—
92C4×C17—41no—
93C4×C17—82no—
94C4×C17C2×#10411yescharacteristic
95C4×C17#42111yescharacteristic
96Dic17—21no—
97Dic17—41no—
98Dic17—82no—
99#541—172no—
100C2×M32—341no—
101#499—171no—
102#494#59511yescharacteristic
103#491—172no—
104#470—341no—
105#467—341no—
106#441—341no—
107C4×Q16—341no—
108#405—171no—
109#364—341no—
110#349—341no—
111#347—172no—
112#347—172no—
113#347—341no—
114C2×C17—21no—
115C2×C17#153011yescharacteristic
116D17—41no—
117C2×Q16—21no—
118C2×Q16—21no—
119C2×M16—171no—
120C22×C8—171no—
121C4⋊Q8C2×#59512yes—
122#126—682no—
123#125—172no—
124#125—682no—
125C22⋊Q8—342no—
126C4×Q8—342no—
127#117—171no—
128M32—342no—
129M32—342no—
130M32—342no—
131C2×C16—342no—
132#107—341no—
133#106—341no—
134#103—342no—
135#103—342no—
136#97—171no—
137#97—171no—
138C4×C8—171no—
139C4×C8C2×#59511yescharacteristic
140C17#1191411yescharacteristic, complemented, Sylow
141C2×Q8—22no—
142C22×C4—171no—
143Q16—42no—
144Q16—41no—
145Q16—41no—
146M16—681no—
147C2×C8—171no—
148C2×C8—171no—
149C2×C8—341no—
150C2×C8—341no—
151C2×C8C22⋊#59511yescharacteristic
152C2×C8C22⋊#59511yescharacteristic
153C4⋊C4—42no—
154C4⋊C4—341no—
155C4⋊C4—342no—
156C4⋊C4—682no—
157C4⋊C4—682no—
158C4⋊C4—682no—
159C22⋊C4—341no—
160C22⋊C4—682no—
161C42—171no—
162C42—682no—
163C42C22×#59511yescharacteristic
164C16—344no—
165C16—682no—
166C23—171no—
167Q8—42no—
168Q8—42no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—171no—
172C2×C4—341no—
173C2×C4—341no—
174C2×C4—341no—
175C2×C4—682no—
176C2×C4C2×C22⋊#59511yescharacteristic
177C8—21no—
178C8—341no—
179C8—341no—
180C8#1058754811yescharacteristic
181C8#1058754811yescharacteristic
182C22—341no—
183C22—681no—
184C22D17⋊#10011yescharacteristic
185C4—41no—
186C4—82no—
187C4—341no—
188C4—681no—
189C4—1362no—
190C4C2×#1058754811yescharacteristic
191C4#1176380711yescharacteristic
192C2—21no—
193C2—681no—
194C2#1454425411yescharacteristic
subgroupG/H
centerC2#14544254
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC17×#494C4
socleC2×C17#1530
prime radicalC22×D17#100
cosocle#10587474C23
hypercenter#494#595
hypocenterC17#11914
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #14543789C2semidirect
140. C17#11914semidirect

Maximal subgroups

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

subgroupindex
#145451592
#145450062
#145437892
#145394402
#1191417