Finite Group Databasebeta

← #17959846

Subgroups — #17959846

Order 4352.

280 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 60 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#14545153C212yesmaximal, complemented
2#14543789C212yesmaximal, complemented
3#14543786C212yesmaximal, complemented
4#14539184C211yesmaximal, characteristic
5#11763732—22no—
6#11763705—22no—
7#11763701C2214yes—
8C2×#10587556C411yescharacteristic
9#11763177C411yescharacteristic
10#11763177C2211yescharacteristic
11#11763173C411yescharacteristic
12#11763173C2211yescharacteristic
13#11763163—22no—
14#11762810—22no—
15C4×#63223C2211yescharacteristic
16C17×#532C411yescharacteristic
17C2×#41×C17—21no—
18C17×C4⋊Q8C2×C411yescharacteristic
19C17×#127C2×C411yescharacteristic
20C17×#124—21no—
21C17×#121—41no—
22C4×D4×C17—41no—
23C2×C42×C17C2×C411yescharacteristic
24C2×C4⋊Dic17—21no—
25C2×#63225—41no—
26C2×#63223D412yes—
27#10587556—21no—
28#10587556—41no—
29#10587556C2×C411yescharacteristic
30#10587556C2×C411yescharacteristic
31#10587538—24no—
32#10587506—22no—
33#10587506—22no—
34#10587503—22no—
35#10587503—22no—
36#10587474C2×C411yescharacteristic
37#10587474C2311yescharacteristic
38C4×#3622D412yes—
39#41×C17—44no—
40C2×Q8×C17—21no—
41C2×D4×C17—21no—
42C2×D4×C17—41no—
43C2×D4×C17—41no—
44C22×C4×C17—21no—
45C22×C4×C17—41no—
46C22×C4×C17C22⋊C411yescharacteristic
47C22×Dic17—41no—
48C4⋊C4×C17—41no—
49C22⋊C4×C17—42no—
50C42×C17—21no—
51C42×C17C22⋊C411yescharacteristic
52C42×C17C22×C411yescharacteristic
53C4⋊Dic17—21no—
54C4⋊Dic17—21no—
55C4⋊Dic17—41no—
56#63225—42no—
57#63225—41no—
58#63225—41no—
59#63223—42no—
60C2×#3622C22⋊C412yes—
61C2×#3622C2×D412yes—
62#63216—44no—
63#11917—171nomaximal, Sylow
64C23×C17—41no—
65C23×C17#10011yescharacteristic
66Q8×C17—42no—
67D4×C17—42no—
68D4×C17—82no—
69D4×C17—82no—
70C2×C4×C17—22no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—41no—
74C2×C4×C17—82no—
75C2×C4×C17—81no—
76C2×C4×C17#10011yescharacteristic
77C2×C4×C17C2×C22⋊C411yescharacteristic
78C2×Dic17—41no—
79C2×Dic17—41no—
80C2×Dic17—82no—
81#3622—22no—
82#3622—22no—
83#3142—171no—
84#2165—172no—
85#1356—172no—
86#1355—172no—
87C22×C17—21no—
88C22×C17—41no—
89C22×C17—82no—
90C22×C17—81no—
91C22×C17C2×#10011yescharacteristic
92C4×C17—21no—
93C4×C17—41no—
94C4×C17—41no—
95C4×C17—81no—
96C4×C17#42112yes—
97Dic17—81no—
98Dic17—81no—
99#532#59511yescharacteristic
100C2×#125—171no—
101#491—171no—
102#491—171no—
103#490—171no—
104#490—171no—
105#488—342no—
106#417—342no—
107C4×M16—171no—
108#364—342no—
109#349—342no—
110#347—174no—
111C2×C17—21no—
112C2×C17—41no—
113C2×C17—161no—
114C2×C17#153311yescharacteristic
115C2×#41—21no—
116C2×M16—172no—
117C4⋊Q8C2×#59511yescharacteristic
118#127C2×#59511yescharacteristic
119#125—171no—
120#125—171no—
121#125—341no—
122#125—681no—
123#124—21no—
124#121—41no—
125C4×D4—41no—
126C2×C4⋊C4—341no—
127C2×C4⋊C4—681no—
128C2×C42C2×#59511yescharacteristic
129M32—344no—
130#103—342no—
131#103—342no—
132#102—342no—
133#102—342no—
134#97—171no—
135#97—171no—
136C4×C8—172no—
137C17#1191711yescharacteristic, complemented, Sylow
138#41—44no—
139C2×Q8—21no—
140C2×D4—21no—
141C2×D4—41no—
142C2×D4—41no—
143C22×C4—21no—
144C22×C4—41no—
145C22×C4—681no—
146C22×C4C22⋊#59511yescharacteristic
147M16—682no—
148C2×C8—172no—
149C2×C8—172no—
150C4⋊C4—41no—
151C4⋊C4—341no—
152C4⋊C4—341no—
153C4⋊C4—681no—
154C4⋊C4—681no—
155C4⋊C4—682no—
156C4⋊C4—681no—
157C22⋊C4—42no—
158C42—21no—
159C42C22⋊#59511yescharacteristic
160C42C22×#59511yescharacteristic
161C16—684no—
162C23—41no—
163C23#1058755311yescharacteristic
164Q8—42no—
165D4—42no—
166D4—82no—
167D4—82no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—82no—
173C2×C4—81no—
174C2×C4—681no—
175C2×C4—681no—
176C2×C4—1362no—
177C2×C4#1058755311yescharacteristic
178C2×C4C2×C22⋊#59511yescharacteristic
179C8—342no—
180C8—342no—
181C22—21no—
182C22—41no—
183C22—82no—
184C22—81no—
185C22C2×#1058755311yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—81no—
190C4—1361no—
191C4—1361no—
192C4#1176380712yes—
193C2—21no—
194C2—41no—
195C2—161no—
196C2#1454426311yescharacteristic
subgroupG/H
centerC2#14544263
commutatorC42×C17C22×C4
FrattiniC42C22×#595
Fitting, prime radicalC17×#532C4
socleC2×C17#1533
cosocle#10587474C23
hypercenter#532#595
hypocenterC17#11917
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #14545153C2semidirect
2. #14543789C2semidirect
3. #14543786C2semidirect
137. C17#11917semidirect

Maximal subgroups

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

subgroupindex
#145451532
#145437892
#145437862
#145391842
#1191717