Finite Group Databasebeta

← #14539028

Subgroups — #14539028

Order 2176.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#11763414C211yesmaximal, characteristic, complemented
2#11763283C211yesmaximal, characteristic, complemented
3#11763134C212yesmaximal, complemented
4#11763110C212yesmaximal, complemented
5#11763005C212yesmaximal, complemented
6#11762945C212yesmaximal, complemented
7#11762922C212yesmaximal, complemented
8C4×D136C212yesmaximal, complemented
9C17×#433C211yesmaximal, characteristic, complemented
10C22×D68C2211yescharacteristic
11C17×#117C2211yescharacteristic
12#10587616C2212yes—
13#10587612C2211yescharacteristic
14C2×D136C2212yes—
15C2×D136C2212yes—
16#10587580—22no—
17#10587579—22no—
18#10587570—22no—
19C22⋊C4×D17—22no—
20#10587560C2211yescharacteristic, complemented
21C4×D68C2212yes—
22C4×D68C2212yes—
23C4×D68C2212yescomplemented
24#10587556C2211yescharacteristic, complemented
25C17×C4⋊C8C2212yescomplemented
26C17×C22⋊C8C2212yes—
27C17×#97C2211yescharacteristic, complemented
28C4×C8×C17C2211yescharacteristic, complemented
29#10587492C2212yes—
30#10587492C2212yes—
31#10587492C2212yescomplemented
32#10587492C2212yescomplemented
33#10587489C2212yescomplemented
34#10587488C2212yescomplemented
35C23×D17—21no—
36C22×C4×C17C2311yescharacteristic
37C2×C22⋊D17—22no—
38C2×D68—21no—
39C2×D68—24no—
40C2×D68—22no—
41C2×D68C2312yes—
42C2×D68C2312yes—
43C2×C4×D17—22no—
44C2×C4×D17—22no—
45C2×C4×D17—22no—
46C2×C8×C17C2312yes—
47C2×C8×C17C2312yes—
48C4⋊C4×C17D412yes—
49C22⋊C4×C17D412yes—
50C42×C17C2311yescharacteristic
51C42×C17C2311yescharacteristic
52C22⋊Dic17—21no—
53#63227—22no—
54#63227—22no—
55#63227—22no—
56#63227—22no—
57C4⋊Dic17C2312yes—
58C4⋊Dic17C2312yes—
59#63225—22no—
60C4×Dic17—21no—
61D136—24no—
62D136—24no—
63C23×C17C2×D411yescharacteristic
64C22×D17—22no—
65C22×D17—24no—
66C22×D17—22no—
67C22×D17—82no—
68C2×C4×C17—22no—
69C2×C4×C17C2×D412yes—
70C2×C4×C17C2×D412yes—
71C2×C4×C17C2×D411yescharacteristic
72C2×C4×C17C2411yescharacteristic
73C22⋊D17—82no—
74C2×Dic17—22no—
75C2×Dic17—22no—
76D68—24no—
77D68—22no—
78D68—22no—
79D68—22no—
80D68—82no—
81D68#4114yes—
82C4×D17—82no—
83C4×D17—82no—
84C4×D17—82no—
85C8×C17—22no—
86C8×C17—22no—
87#3122—171nomaximal, Sylow
88C22×C17—21no—
89C22×C17—22no—
90C22×C17C22×D411yescharacteristic
91C2×D17—24no—
92C2×D17—42no—
93C2×D17—42no—
94C2×D17—42no—
95C2×D17—42no—
96C2×D17—42no—
97C2×D17—84no—
98C4×C17—21no—
99C4×C17—22no—
100C4×C17—22no—
101C4×C17C2×#4112yes—
102Dic17—42no—
103Dic17—42no—
104#540—171no—
105#518—171no—
106#482—172no—
107#478—172no—
108#459—172no—
109#447—172no—
110#442—172no—
111C4×D8—172no—
112#433D1711yescharacteristic, complemented
113C2×C17—41no—
114C2×C17#52511yescharacteristic
115C2×C17#57612yes—
116D17—44no—
117D17—82no—
118C22×D4—171no—
119C2×D8—172no—
120C2×D8—172no—
121#127—171no—
122#125—171no—
123#123—342no—
124#121—172no—
125#121—342no—
126C4×D4—172no—
127C4×D4—172no—
128C4×D4—172no—
129C4×D4—342no—
130#117—171no—
131#117C2×D1711yescharacteristic
132C2×C22⋊C4—342no—
133#107—172no—
134#106—172no—
135C4⋊C8C2×D1712yescomplemented
136#102—172no—
137#102—172no—
138#102—172no—
139#102—172no—
140C22⋊C8C2×D1712yes—
141#97C2×D1711yescharacteristic, complemented
142C4×C8C2×D1711yescharacteristic, complemented
143C17#312211yescharacteristic, complemented, Sylow
144C24—341no—
145C2×D4—172no—
146C2×D4—172no—
147C2×D4—344no—
148C2×D4—342no—
149C2×D4—341no—
150C2×D4—342no—
151C22×C4—342no—
152C22×C4—342no—
153C22×C4—342no—
154C22×C4C22×D1711yescharacteristic
155D8—344no—
156D8—344no—
157C2×C8C22×D1712yes—
158C2×C8C22×D1712yes—
159C4⋊C4—172no—
160C4⋊C4—172no—
161C4⋊C4—342no—
162C4⋊C4D6812yes—
163C22⋊C4—341no—
164C22⋊C4—342no—
165C22⋊C4—342no—
166C22⋊C4—342no—
167C22⋊C4—342no—
168C22⋊C4D6812yes—
169C42—341no—
170C42C22×D1711yescharacteristic
171C42C22×D1711yescharacteristic
172C23—344no—
173C23—342no—
174C23—342no—
175C23—1362no—
176C23C2×D6811yescharacteristic
177D4—174no—
178D4—344no—
179D4—342no—
180D4—342no—
181D4—342no—
182D4—1362no—
183D4—1362no—
184C2×C4—22no—
185C2×C4—342no—
186C2×C4—342no—
187C2×C4—1362no—
188C2×C4—1362no—
189C2×C4—1362no—
190C2×C4C2×D6811yescharacteristic
191C2×C4C2×D6812yes—
192C2×C4C2×D6812yes—
193C2×C4C23×D1711yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—344no—
199C22—682no—
200C22—682no—
201C22—682no—
202C22—682no—
203C22—682no—
204C22—1364no—
205C22C22×D6811yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—682no—
210C4—682no—
211C4#41×D1712yes—
212C2—41no—
213C2—684no—
214C2—1362no—
215C2#1176332111yescharacteristic
216C2#1176361412yes—
subgroupG/H
centerC22C22×D68
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#433C2
socleC22×C17C22×D4
hypercenter#433D17
hypocenterC17#3122
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #11763414C2semidirect
2. #11763283C2semidirect
3. #11763134C2semidirect
4. #11763110C2semidirect
5. #11763005C2semidirect
6. #11762945C2semidirect
7. #11762922C2semidirect
8. C4×D136C2semidirect
9. C17×#433C2semidirect
20. #10587560C22semidirect
23. C4×D68C22semidirect
24. #10587556C22semidirect
25. C17×C4⋊C8C22semidirect
27. C17×#97C22semidirect
28. C4×C8×C17C22semidirect
31. #10587492C22semidirect
32. #10587492C22semidirect
33. #10587489C22semidirect
34. #10587488C22semidirect
112. #433D17semidirect
135. C4⋊C8C2×D17semidirect
141. #97C2×D17semidirect
142. C4×C8C2×D17semidirect
143. C17#3122semidirect

Maximal subgroups

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

subgroupindex
#117634142
#117632832
#117631342
#117631102
#117630052
#117629452
#117629222
C4×D1362
C17×#4332
#312217