Finite Group Databasebeta

← #28373275

Subgroups — #28373275

Order 13952.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#20295631C211yesmaximal, characteristic, complemented
2#20295350C212yesmaximal, complemented
3#20295326C212yesmaximal, complemented
4#20295221C212yesmaximal, complemented
5#20295160C212yesmaximal, complemented
6#20295136C212yesmaximal, complemented
7C4×#13182014C212yesmaximal, complemented
8#20295087C211yesmaximal, characteristic, complemented
9#518×C109C211yesmaximal, characteristic, complemented
10C2×#13182014C2212yes—
11C2×#13182014C2212yes—
12#16812696C2211yescharacteristic, complemented
13#16812691C2211yescharacteristic, complemented
14#16812684—22no—
15#16812673C2212yes—
16#16812672—22no—
17C4×D436C2212yescomplemented
18#16812632C2212yescomplemented
19#16812630C2212yescomplemented
20C4⋊#11724784C2212yescomplemented
21#16812620C2212yes—
22#16812620C2212yes—
23#16812619C2212yescomplemented
24#16812619C2212yescomplemented
25C22⋊#11724784C2212yes—
26#16812610C2211yescharacteristic, complemented
27C4×#11724784C2211yescharacteristic, complemented
28C22×D4×C109C2211yescharacteristic
29C4×D4×C109—22no—
30C4×D4×C109C2212yes—
31C4×D4×C109C2212yes—
32#117×C109C2211yescharacteristic
33#117×C109C2211yescharacteristic
34C2×C22⋊C4×C109—22no—
35C2×D436—22no—
36C2×D436C2312yes—
37C2×C22⋊D109—22no—
38C2×C4×D109—22no—
39#13182014—24no—
40#13182014—24no—
41C2×#11724784C2312yes—
42C2×#11724784C2312yes—
43C4⋊Dic109C2312yes—
44#13182008—22no—
45#13182006—22no—
46#13182006—22no—
47C24×C109—21no—
48C2×D4×C109—24no—
49C2×D4×C109—21no—
50C2×D4×C109C2312yes—
51C22×C4×C109—22no—
52C22×C4×C109—22no—
53C22×C4×C109C2311yescharacteristic
54C4⋊C4×C109D412yes—
55C4⋊C4×C109C2312yes—
56C22⋊C4×C109—21no—
57C22⋊C4×C109—22no—
58C22⋊C4×C109—22no—
59C22⋊C4×C109D412yes—
60C42×C109—21no—
61C42×C109C2311yescharacteristic
62C42×C109C2311yescharacteristic
63C23×C109—24no—
64C23×C109—22no—
65C23×C109—82no—
66C23×C109C2×D411yescharacteristic
67C22×D109—22no—
68D4×C109—24no—
69D4×C109—22no—
70D4×C109#4114yes—
71C2×C4×C109—22no—
72C2×C4×C109—22no—
73C2×C4×C109—82no—
74C2×C4×C109—82no—
75C2×C4×C109C2×D411yescharacteristic
76C2×C4×C109C2×D412yes—
77C2×C4×C109C2×D412yes—
78C2×C4×C109C2411yescharacteristic
79C22⋊D109—82no—
80C2×Dic109—22no—
81D436—22no—
82D436—22no—
83D436—82no—
84C4×D109—82no—
85#11724784—22no—
86#11724784—22no—
87C22×C109—21no—
88C22×C109—24no—
89C22×C109—22no—
90C22×C109—42no—
91C22×C109—42no—
92C22×C109—84no—
93C22×C109C22×D411yescharacteristic
94C2×D109—42no—
95C2×D109—42no—
96C2×D109—42no—
97C4×C109—21no—
98C4×C109—22no—
99C4×C109—22no—
100C4×C109—42no—
101C4×C109C2×#4112yes—
102Dic109—42no—
103C2×C109—41no—
104C2×C109—44no—
105C2×C109#52511yescharacteristic
106C2×C109#57612yes—
107D109—82no—
108#3122—1091nomaximal, Sylow
109C109#312211yescharacteristic, complemented, Sylow
110#540—1091no—
111#518D10911yescharacteristic, complemented
112#482—1092no—
113#478—1092no—
114#459—1092no—
115#447—1092no—
116#442—1092no—
117C4×D8—1092no—
118#433—1091no—
119C22×D4C2×D10911yescharacteristic
120C2×D8—1092no—
121C2×D8—1092no—
122#127—1091no—
123#125—1091no—
124#123—2182no—
125#121—1092no—
126#121—2182no—
127C4×D4—22no—
128C4×D4—1092no—
129C4×D4C2×D10912yes—
130C4×D4C2×D10912yes—
131#117C2×D10911yescharacteristic
132#117C2×D10911yescharacteristic
133C2×C22⋊C4—22no—
134#107—1092no—
135#106—1092no—
136C4⋊C8—1092no—
137#102—1092no—
138#102—1092no—
139#102—1092no—
140#102—1092no—
141C22⋊C8—1092no—
142#97—1091no—
143C4×C8—1091no—
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—1092no—
148C2×D4—2182no—
149C2×D4—2182no—
150C2×D4C22×D10912yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—2182no—
154C22×C4C22×D10911yescharacteristic
155D8—2184no—
156D8—2184no—
157C2×C8—1092no—
158C2×C8—1092no—
159C4⋊C4—1092no—
160C4⋊C4—2182no—
161C4⋊C4C22⋊D10912yes—
162C4⋊C4C22×D10912yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—2182no—
167C22⋊C4—2182no—
168C22⋊C4C22⋊D10912yes—
169C42—21no—
170C42C22×D10911yescharacteristic
171C42C22×D10911yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—2182no—
176C23C2×C22⋊D10911yescharacteristic
177D4—24no—
178D4—22no—
179D4—8722no—
180D4—8722no—
181D4—2182no—
182D4—2182no—
183D4#1318202914yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—8722no—
189C2×C4—2182no—
190C2×C4C2×C22⋊D10911yescharacteristic
191C2×C4C2×C22⋊D10912yes—
192C2×C4C2×C22⋊D10912yes—
193C2×C4C23×D10911yescharacteristic
194C8—2182no—
195C8—2182no—
196C22—21no—
197C22—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—4362no—
203C22—4362no—
204C22—4362no—
205C22C22×C22⋊D10911yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—4362no—
211C4C2×#1318202912yes—
212C2—41no—
213C2—44no—
214C2—8722no—
215C2#2029553711yescharacteristic
216C2#2029582912yes—
subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#518×C109C2
socleC22×C109C22×D4
hypercenter#518D109
hypocenterC109#3122
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #20295631C2semidirect
2. #20295350C2semidirect
3. #20295326C2semidirect
4. #20295221C2semidirect
5. #20295160C2semidirect
6. #20295136C2semidirect
7. C4×#13182014C2semidirect
8. #20295087C2semidirect
9. #518×C109C2semidirect
12. #16812696C22semidirect
13. #16812691C22semidirect
17. C4×D436C22semidirect
18. #16812632C22semidirect
19. #16812630C22semidirect
20. C4⋊#11724784C22semidirect
23. #16812619C22semidirect
24. #16812619C22semidirect
26. #16812610C22semidirect
27. C4×#11724784C22semidirect
109. C109#3122semidirect
111. #518D109semidirect

Maximal subgroups

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

subgroupindex
#202956312
#202953502
#202953262
#202952212
#202951602
#202951362
C4×#131820142
#202950872
#518×C1092
#3122109