Finite Group Databasebeta

← #17959983

Subgroups — #17959983

Order 4352.

284 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 76 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#14545147C211yesmaximal, characteristic
2#14544347C211yesmaximal, characteristic
3#14543801C214yesmaximal, complemented
4#14539295C211yesmaximal, characteristic
5#11763831—21no—
6#11763730C2212yes—
7#11763704—21no—
8#11763697—21no—
9#11763673—21no—
10#11763671C2212yes—
11#11763364—21no—
12#11763214C411yescharacteristic
13#11763210—21no—
14#11763210C2212yes—
15#11763205—21no—
16#11762846—21no—
17#11762846C412yes—
18C4×C8×D17C2211yescharacteristic
19C17×#500C411yescharacteristic
20C17×C4⋊Q8—21no—
21#10587632—41no—
22Q8×Dic17—41no—
23C2×C8×D17C2×C411yescharacteristic
24C2×C8×D17D411yescharacteristic
25#10587583—41no—
26#10587578—22no—
27#10587576—22no—
28#10587573—41no—
29C42×D17D411yescharacteristic
30#10587555—21no—
31#10587543—41no—
32#10587542—41no—
33C4⋊#3624—22no—
34C2×#63216—22no—
35C17×#107—21no—
36C17×#107C2×C412yes—
37C4×C8×C17C2×C411yescharacteristic
38#10587489—21no—
39#10587489C2×C412yes—
40C8×Dic17D411yescharacteristic
41C8×Dic17C2311yescharacteristic
42#10587479—22no—
43#10587479—22no—
44C4×#3622D411yescharacteristic
45C2×Q8×C17—41no—
46C2×C4×D17C22⋊C411yescharacteristic
47C2×C4×D17D811yescharacteristic
48C2×C4×D17SD1611yescharacteristic
49C2×Dic34—41no—
50C2×#3624—42no—
51C2×C8×C17C22⋊C411yescharacteristic
52C2×C8×C17C22×C411yescharacteristic
53C4⋊C4×C17—22no—
54C4⋊C4×C17—41no—
55C42×C17C22⋊C411yescharacteristic
56#63227—42no—
57C4⋊Dic17—22no—
58C4⋊Dic17—41no—
59C4⋊Dic17—42no—
60#63225—42no—
61C4×Dic17—42no—
62C4×Dic17D811yescharacteristic
63C4×Dic17SD1611yescharacteristic
64C4×Dic17C2×D411yescharacteristic
65C2×#3622C22⋊C411yescharacteristic
66C2×#3622C2×D411yescharacteristic
67C8×D17—22no—
68C8×D17—22no—
69#63216—42no—
70#11970—171nomaximal, Sylow
71C22×D17#10211yescharacteristic
72Q8×C17—82no—
73C2×C4×C17—42no—
74C2×C4×C17#10211yescharacteristic
75C2×C4×C17#10211yescharacteristic
76C2×C4×C17C2×C22⋊C411yescharacteristic
77C2×Dic17—42no—
78C2×Dic17#10211yescharacteristic
79C2×Dic17C2×D811yescharacteristic
80C2×Dic17C2×SD1611yescharacteristic
81C4×D17—21no—
82C4×D17—21no—
83C4×D17—41no—
84C4×D17—41no—
85Dic34—82no—
86#3624—82no—
87C8×C17—21no—
88C8×C17—21no—
89#3622#10112yes—
90#3622#13712yes—
91#3160—171no—
92#2163—171no—
93#1568—171no—
94#1363—174no—
95C22×C17C2×#10211yescharacteristic
96C2×D17—21no—
97C2×D17—21no—
98C2×D17—21no—
99C4×C17—21no—
100C4×C17—21no—
101C4×C17—82no—
102C4×C17C2×#10111yescharacteristic
103C4×C17#41911yescharacteristic
104Dic17—21no—
105Dic17—21no—
106Dic17—21no—
107Dic17—82no—
108#533—341no—
109#500—171no—
110#500#59511yescharacteristic
111#499—172no—
112#499—341no—
113#498—341no—
114#432—341no—
115#427—172no—
116#427—341no—
117C2×C4×C8—171no—
118C4⋊C16—172no—
119C22⋊C16—341no—
120#346—341no—
121#335—341no—
122#334—172no—
123C2×C17#154611yescharacteristic
124C2×C17#214311yescharacteristic
125C2×C17#214511yescharacteristic
126D17—41no—
127C22×C8—171no—
128C22×C8—171no—
129C4⋊Q8—21no—
130C4⋊Q8—341no—
131#125—342no—
132C22⋊Q8—681no—
133C22⋊Q8—681no—
134C4×Q8—681no—
135C4×Q8—681no—
136#117—342no—
137C2×C42—171no—
138C2×C16—342no—
139#107—21no—
140#107—172no—
141#107—341no—
142#107C2×#59512yes—
143#106—342no—
144#106—342no—
145C4⋊C8—342no—
146C22⋊C8—681no—
147#97—681no—
148C4×C8—171no—
149C4×C8—171no—
150C4×C8—171no—
151C4×C8C2×#59511yescharacteristic
152C17#1197011yescharacteristic, complemented, Sylow
153C2×Q8—41no—
154C2×Q8—681no—
155C22×C4—171no—
156C22×C4—171no—
157C22×C4—171no—
158C2×C8—171no—
159C2×C8—171no—
160C2×C8—342no—
161C2×C8—342no—
162C2×C8—682no—
163C2×C8C22⋊#59511yescharacteristic
164C2×C8C22×#59511yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—41no—
167C4⋊C4—342no—
168C4⋊C4—682no—
169C4⋊C4—682no—
170C4⋊C4—681no—
171C22⋊C4—682no—
172C42—171no—
173C42—171no—
174C42—171no—
175C42—682no—
176C42C22⋊#59511yescharacteristic
177C16—682no—
178C23—171no—
179Q8—82no—
180Q8—1362no—
181C2×C4—42no—
182C2×C4—171no—
183C2×C4—171no—
184C2×C4—171no—
185C2×C4—341no—
186C2×C4—341no—
187C2×C4—681no—
188C2×C4—681no—
189C2×C4—682no—
190C2×C4#1058754711yescharacteristic
191C2×C4#1058754711yescharacteristic
192C2×C4C2×C22⋊#59511yescharacteristic
193C8—21no—
194C8—21no—
195C8—172no—
196C8—172no—
197C8—1362no—
198C22—341no—
199C22—341no—
200C22—341no—
201C22C2×#1058754711yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—341no—
206C4—341no—
207C4—341no—
208C4—1362no—
209C4D17⋊#10111yescharacteristic
210C4#1176380211yescharacteristic
211C2—681no—
212C2#1454429411yescharacteristic
213C2#1454510011yescharacteristic
214C2#1454510511yescharacteristic
subgroupG/H
centerC22C2×#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC17×#500C4
socleC22×C17C2×#102
prime radicalC22×D17#102
cosocleC8×Dic17C23
hypercenter#500#595
hypocenterC17#11970
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #14543801C2semidirect
152. C17#11970semidirect

Maximal subgroups

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

subgroupindex
#145451472
#145443472
#145438012
#145392952
#1197017