Finite Group Databasebeta

← #14540137

Subgroups — #14540137

Order 2176.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#11763345C212yesmaximal, complemented
2#11763118C212yesmaximal, complemented
3#11763112C212yesmaximal, complemented
4#11763045C211yesmaximal, characteristic
5#11763040C212yesmaximal, complemented
6#11763033C212yesmaximal, complemented
7#11763027C212yesmaximal, complemented
8C2×#10587485C211yesmaximal, characteristic, complemented
9C17×#467C211yesmaximal, characteristic, complemented
10C2×Q16×C17C2211yescharacteristic
11C22×C8×C17C2211yescharacteristic
12C17×C22⋊Q8C2212yes—
13#10587633C2212yes—
14Q8×Dic17C2212yes—
15C2×#63230C2212yes—
16#10587616C2212yes—
17C2×C4×Dic17C2211yescharacteristic
18C22×#3622C2211yescharacteristic
19C2×D136C2211yescharacteristic
20#10587584—22no—
21#10587579C2212yes—
22#10587578—22no—
23#10587576C2212yes—
24#10587572—22no—
25#10587567—22no—
26C17×#107C2211yescharacteristic
27C17×#103C2212yes—
28#10587506C2212yes—
29#10587492C2212yes—
30#10587489C2211yescharacteristic
31#10587485C2212yes—
32#10587485C2212yes—
33#10587480C2212yes—
34#10587479C2212yes—
35C2×Q8×C17C2312yes—
36C22×C4×C17C2311yescharacteristic
37C2×C22⋊D17—22no—
38C22×Dic17D411yescharacteristic
39C22×Dic17D411yescharacteristic
40C2×D68C2312yes—
41C2×C4×D17—22no—
42Q16×C17—41no—
43C2×C8×C17—41no—
44C2×C8×C17C2311yescharacteristic
45C2×C8×C17C2311yescharacteristic
46C4⋊C4×C17—22no—
47C4⋊C4×C17C2312yes—
48C22⋊C4×C17—22no—
49#63230—42no—
50#63227—22no—
51#63227—22no—
52#63227—22no—
53#63227—22no—
54C4⋊Dic17—22no—
55C4⋊Dic17—22no—
56C4⋊Dic17C2312yes—
57#63225—22no—
58C4×Dic17—22no—
59C4×Dic17D412yes—
60C4×Dic17C2312yes—
61C2×#3622—41no—
62C2×#3622C2312yes—
63D136—41no—
64C23×C17C2×D411yescharacteristic
65C22×D17—22no—
66Q8×C17—22no—
67Q8×C17—22no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—22no—
71C2×C4×C17—22no—
72C2×C4×C17C2×D411yescharacteristic
73C2×C4×C17C2411yescharacteristic
74C22⋊D17—44no—
75C2×Dic17—22no—
76C2×Dic17—22no—
77C2×Dic17—41no—
78C2×Dic17C2×D412yes—
79C2×Dic17C2×D412yes—
80D68—22no—
81D68—22no—
82C4×D17—44no—
83C8×C17—21no—
84C8×C17—21no—
85#3622—22no—
86#3250—171nomaximal, Sylow
87C22×C17—21no—
88C22×C17—21no—
89C22×C17#13512yes—
90C22×C17C22×D411yescharacteristic
91C2×D17—42no—
92C2×D17—42no—
93C2×D17—42no—
94C4×C17—21no—
95C4×C17—42no—
96C4×C17—42no—
97C4×C17H(5,𝔽2)11yescharacteristic
98C4×C172−1+411yescharacteristic
99Dic17—22no—
100Dic17—22no—
101Dic17—42no—
102#529—172no—
103#479—172no—
104#478—172no—
105#467D1711yescharacteristic, complemented
106#466—171no—
107#465—172no—
108#464—172no—
109#463—172no—
110C2×C4⋊C8—171no—
111C2×C17—22no—
112C2×C17#53711yescharacteristic
113C2×C17C2×#13511yescharacteristic
114C2×C17#57511yescharacteristic
115D17—82no—
116C2×Q16C2×D1711yescharacteristic
117C2×SD16—172no—
118C2×D8—171no—
119C22×C8—171no—
120C22×C8C2×D1711yescharacteristic
121#126—342no—
122#125—172no—
123#124—172no—
124#123—342no—
125C22⋊Q8C2×D1712yes—
126#121—172no—
127C4×Q8—172no—
128C4×D4—172no—
129C4×D4—342no—
130#117—342no—
131C2×C42—171no—
132#107—171no—
133#107C2×D1711yescharacteristic
134#106—172no—
135C4⋊C8—172no—
136C4⋊C8—172no—
137#103—172no—
138#103C2×D1712yes—
139#102—172no—
140#102—172no—
141C17#325011yescharacteristic, complemented, Sylow
142C2×Q8C22×D1712yes—
143C2×D4—172no—
144C2×D4—342no—
145C22×C4—171no—
146C22×C4—171no—
147C22×C4—342no—
148C22×C4C22×D1711yescharacteristic
149Q16—41no—
150SD16—682no—
151D8—681no—
152C2×C8—41no—
153C2×C8—172no—
154C2×C8—681no—
155C2×C8C22×D1711yescharacteristic
156C2×C8C22×D1711yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—172no—
159C4⋊C4—342no—
160C4⋊C4—342no—
161C4⋊C4—342no—
162C4⋊C4C22×D1712yes—
163C22⋊C4—22no—
164C22⋊C4—342no—
165C22⋊C4—342no—
166C22⋊C4—342no—
167C22⋊C4—342no—
168C42—172no—
169C42—172no—
170C42—342no—
171C23—342no—
172C23D4×D1711yescharacteristic
173Q8—22no—
174Q8—22no—
175D4—342no—
176D4—342no—
177D4—684no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—172no—
183C2×C4—172no—
184C2×C4—342no—
185C2×C4—342no—
186C2×C4—684no—
187C2×C4—681no—
188C2×C4D4×D1711yescharacteristic
189C2×C4C23×D1711yescharacteristic
190C8—21no—
191C8—21no—
192C8—342no—
193C22—21no—
194C22—21no—
195C22—682no—
196C22—682no—
197C22—682no—
198C22#1058760512yes—
199C22C2×D4×D1711yescharacteristic
200C4—21no—
201C4—42no—
202C4—42no—
203C4—342no—
204C4—342no—
205C4—682no—
206C4#1058769111yescharacteristic
207C4#1058769711yescharacteristic
208C2—22no—
209C2—1362no—
210C2#1176338611yescharacteristic
211C2C2×#1058760511yescharacteristic
212C2#1176360611yescharacteristic
subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#467C2
socleC22×C17C22×D4
prime radical#11763045C2
hypercenter#467D17
hypocenterC17#3250
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #11763345C2semidirect
2. #11763118C2semidirect
3. #11763112C2semidirect
5. #11763040C2semidirect
6. #11763033C2semidirect
7. #11763027C2semidirect
8. C2×#10587485C2semidirect
9. C17×#467C2semidirect
105. #467D17semidirect
141. C17#3250semidirect

Maximal subgroups

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

subgroupindex
#117633452
#117631182
#117631122
#117630452
#117630402
#117630332
#117630272
C2×#105874852
C17×#4672
#325017