Finite Group Databasebeta

← #17959847

Subgroups — #17959847

Order 4352.

280 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 58 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#14545155C212yesmaximal, complemented
2#14543791C211yesmaximal, characteristic, complemented
3#14543790C211yesmaximal, characteristic, complemented
4#14543786C212yesmaximal, complemented
5#14539183C211yesmaximal, characteristic
6#11763731—22no—
7#11763706—22no—
8#11763701C2212yes—
9#11763701C2212yes—
10#11763357C411yescharacteristic
11#125×D17C411yescharacteristic
12#11763179C2211yescharacteristic
13#11763178C411yescharacteristic
14#11763173C2211yescharacteristic
15#11763162—22no—
16#11762807—22no—
17#11762761C2211yescharacteristic
18C17×#490C411yescharacteristic
19C2×#63254—21no—
20C17×#127C2×C411yescharacteristic
21C17×#125C2×C411yescharacteristic
22#10587624—41no—
23#10587622—21no—
24D4×Dic17—41no—
25C2×#63218D412yes—
26C4⋊C4×D17—21no—
27C4⋊C4×D17—41no—
28#10587576—21no—
29#10587575—41no—
30C42×D17C2×C411yescharacteristic
31#10587556C2×C411yescharacteristic
32#10587555C2×C411yescharacteristic
33#10587538—22no—
34#10587538—22no—
35C17×#102—22no—
36C17×#97C2×C411yescharacteristic
37#10587503—22no—
38#10587487—22no—
39C8×Dic17D412yes—
40#10587481—22no—
41#10587474C2311yescharacteristic
42C2×D4×C17—21no—
43C2×D4×C17—41no—
44C2×C22⋊D17—41no—
45C22×Dic17—41no—
46#63254—44no—
47C2×C4×D17—21no—
48C2×C4×D17—41no—
49C2×C4×D17C22⋊C411yescharacteristic
50C2×Dic34—21no—
51C2×C8×C17C22⋊C412yes—
52C4⋊C4×C17—21no—
53C4⋊C4×C17—41no—
54C42×C17C22×C411yescharacteristic
55C22⋊Dic17—42no—
56C4⋊Dic17—21no—
57C4⋊Dic17—41no—
58C4⋊Dic17—41no—
59#63225—41no—
60#63225—41no—
61#63225—41no—
62C4×Dic17—21no—
63C4×Dic17C22⋊C411yescharacteristic
64C2×#3622C2×D412yes—
65#63218—42no—
66#63216—42no—
67#63216—42no—
68#11917—171nomaximal, Sylow
69C23×C17—41no—
70C22×D17#10011yescharacteristic
71D4×C17—42no—
72D4×C17—82no—
73C2×C4×C17—21no—
74C2×C4×C17—41no—
75C2×C4×C17C2×C22⋊C411yescharacteristic
76C22⋊D17—82no—
77C2×Dic17—21no—
78C2×Dic17—41no—
79C2×Dic17—41no—
80C2×Dic17—82no—
81C2×Dic17#10011yescharacteristic
82C4×D17—22no—
83C4×D17—81no—
84C4×D17—82no—
85Dic34—42no—
86C8×C17—22no—
87#3622—22no—
88#3142—171no—
89#2165—172no—
90#1356—171no—
91#1356—171no—
92#1355—172no—
93C22×C17—82no—
94C22×C17—81no—
95C22×C17C2×#10011yescharacteristic
96C2×D17—21no—
97C2×D17—41no—
98C4×C17—41no—
99C4×C17—81no—
100C4×C17#42112yes—
101Dic17—21no—
102Dic17—41no—
103Dic17—81no—
104Dic17—81no—
105#532—171no—
106C2×#125—171no—
107#491—171no—
108#491—171no—
109#490—171no—
110#490#59511yescharacteristic
111#488—342no—
112#417—342no—
113C4×M16—171no—
114#364—342no—
115#349—342no—
116#347—172no—
117#347—172no—
118C2×C17—21no—
119C2×C17—161no—
120C2×C17#153311yescharacteristic
121D17—41no—
122C2×#41—341no—
123C2×M16—172no—
124C4⋊Q8—171no—
125#127C2×#59511yescharacteristic
126#125—171no—
127#125—341no—
128#125—681no—
129#125C2×#59511yescharacteristic
130#124—341no—
131#121—681no—
132C4×D4—681no—
133C2×C4⋊C4—341no—
134C2×C4⋊C4—681no—
135C2×C42—171no—
136M32—342no—
137M32—342no—
138#103—342no—
139#103—342no—
140#102—22no—
141#102—342no—
142#97—171no—
143#97C2×#59511yescharacteristic
144C4×C8—172no—
145C17#1191711yescharacteristic, complemented, Sylow
146#41—684no—
147C2×Q8—341no—
148C2×D4—21no—
149C2×D4—41no—
150C2×D4—681no—
151C22×C4—171no—
152C22×C4—341no—
153C22×C4—681no—
154C22×C4—681no—
155M16—682no—
156C2×C8—172no—
157C2×C8C22⋊#59512yes—
158C4⋊C4—21no—
159C4⋊C4—41no—
160C4⋊C4—341no—
161C4⋊C4—681no—
162C4⋊C4—681no—
163C4⋊C4—681no—
164C4⋊C4—681no—
165C4⋊C4—681no—
166C22⋊C4—682no—
167C42—171no—
168C42—341no—
169C42C22×#59511yescharacteristic
170C16—682no—
171C16—682no—
172C23—41no—
173C23—171no—
174Q8—682no—
175D4—42no—
176D4—82no—
177D4—1362no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—171no—
181C2×C4—342no—
182C2×C4—341no—
183C2×C4—681no—
184C2×C4—681no—
185C2×C4—1361no—
186C2×C4—1362no—
187C2×C4—1362no—
188C2×C4C2×C22⋊#59511yescharacteristic
189C8—22no—
190C8—342no—
191C22—82no—
192C22—81no—
193C22—341no—
194C22—681no—
195C22D17⋊#10011yescharacteristic
196C4—41no—
197C4—81no—
198C4—341no—
199C4—681no—
200C4—1361no—
201C4—1361no—
202C4#1176380612yes—
203C2—21no—
204C2—161no—
205C2—681no—
206C2#1454426411yescharacteristic
subgroupG/H
centerC2#14544264
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC17×#490C4
socleC2×C17#1533
prime radical#11763357C4
cosocle#10587474C23
hypercenter#490#595
hypocenterC17#11917
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14545155C2semidirect
2. #14543791C2semidirect
3. #14543790C2semidirect
4. #14543786C2semidirect
145. C17#11917semidirect

Maximal subgroups

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

subgroupindex
#145451552
#145437912
#145437902
#145437862
#145391832
#1191717