Finite Group Databasebeta

← #28372552

Subgroups — #28372552

Order 13952.

490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#16812732C211yesmaximal, characteristic, complemented
2C22×#13182017C211yesmaximal, characteristic, complemented
3#20295593C211yesmaximal, characteristic
4#20295503C211yesmaximal, characteristic, complemented
5#20295247C214yesmaximal, complemented
6#20295225C214yesmaximal, complemented
7#20295054C211yesmaximal, characteristic, complemented
8#20295020C211yesmaximal, characteristic, complemented
9#418×C109C211yesmaximal, characteristic, complemented
10C2×#13182029C2211yescharacteristic
11C22×Dic218C2211yescharacteristic
12#16812732—24no—
13C2×Dic436C2212yescomplemented
14C2×#13182018C2212yescomplemented
15C2×#13182017—24no—
16C2×#13182017C2214yes—
17C22×#11724784C2211yescharacteristic
18#16812695C2212yes—
19#16812686C2212yes—
20#16812670—22no—
21#16812668—22no—
22C4×Dic218—22no—
23#16812664C2214yescomplemented
24#16812658C2211yescharacteristic
25#16812655—22no—
26#16812628C2214yescomplemented
27#16812622C2212yescomplemented
28#16812619C2212yescomplemented
29C22×D4×C109C2211yescharacteristic
30C2×M16×C109C2211yescharacteristic
31#117×C109C2211yescharacteristic
32#102×C109C2214yes—
33#13182029—22no—
34#13182029—22no—
35C2×Dic218—21no—
36C2×Dic218—22no—
37C2×Dic218D414yescomplemented
38C2×Dic218C2311yescharacteristic
39C2×Dic218C2312yes—
40C2×D436C2311yescharacteristic
41C2×C22⋊D109—21no—
42C2×C22⋊D109—24no—
43C22×Dic109—21no—
44C2×C4×D109—21no—
45Dic436—24no—
46#13182018—24no—
47#13182017—28no—
48C2×#11724784—22no—
49C2×#11724784C2312yes—
50C4⋊Dic109D412yes—
51#13182008—24no—
52C22⋊Dic109—24no—
53C22⋊Dic109D412yes—
54C4×Dic109—24no—
55C4×Dic109C2312yes—
56C24×C109—21no—
57C2×D4×C109—22no—
58C2×D4×C109—21no—
59C2×D4×C109—22no—
60C2×D4×C109C2312yes—
61C22×C4×C109C2311yescharacteristic
62M16×C109—22no—
63C2×C8×C109C2312yes—
64C4⋊C4×C109C2312yes—
65C22⋊C4×C109—21no—
66C42×C109—21no—
67C23×C109—22no—
68C23×C109—42no—
69C23×C109—82no—
70C23×C109C2×D411yescharacteristic
71C22×D109—21no—
72D4×C109—22no—
73D4×C109—22no—
74D4×C109—42no—
75C2×C4×C109—22no—
76C2×C4×C109C2×D411yescharacteristic
77C2×C4×C109C2×D412yes—
78C2×C4×C109#4112yes—
79C2×C4×C109C2411yescharacteristic
80C22⋊D109—42no—
81C22⋊D109—84no—
82C2×Dic109—24no—
83C2×Dic109—22no—
84C2×Dic109—21no—
85C2×Dic109C2×D414yes—
86D436—21no—
87D436—21no—
88C4×D109—42no—
89Dic218—24no—
90Dic218—22no—
91Dic218—21no—
92Dic218—21no—
93Dic218C2×D414yes—
94C8×C109—22no—
95#11724784—22no—
96C22×C109—22no—
97C22×C109—42no—
98C22×C109—44no—
99C22×C109—84no—
100C22×C109#12112yes—
101C22×C109C22×D411yescharacteristic
102C2×D109—41no—
103C2×D109—42no—
104C4×C109—42no—
105C4×C109#12112yes—
106C4×C109C22×D411yescharacteristic
107C4×C109C2×#4111yescharacteristic
108Dic109—24no—
109Dic109—24no—
110Dic109—41no—
111C2×C109—22no—
112C2×C109—82no—
113C2×C109C2×#12111yescharacteristic
114C2×C109#57712yes—
115D109—81no—
116#3043—1091nomaximal, Sylow
117C109#304311yescharacteristic, complemented, Sylow
118C2×#137—1091no—
119C22×SD16—1091no—
120#535—1091no—
121#519—1091no—
122#464—1094no—
123#460—1094no—
124#424—1091no—
125#418D10911yescharacteristic, complemented
126#416—1091no—
127C2×#41—1091no—
128C22×Q8—1091no—
129C22×D4C2×D10911yescharacteristic
130#137—2184no—
131C2×Q16—1092no—
132C2×SD16—1094no—
133C2×SD16—1092no—
134C2×SD16—2184no—
135C2×M16C2×D10911yescharacteristic
136C22×C8—1091no—
137#127—1092no—
138#124—1092no—
139#121—2182no—
140#120—2182no—
141C4×Q8—1094no—
142C4×Q8—2182no—
143#117—1091no—
144#117—2182no—
145#117C2×D10911yescharacteristic
146C4⋊C8—1094no—
147#103—1092no—
148#102—1092no—
149#102C2×D10914yes—
150C24—21no—
151#41—2182no—
152#41—2182no—
153C2×Q8—1094no—
154C2×Q8—1092no—
155C2×Q8—1091no—
156C2×Q8—2181no—
157C2×Q8—2182no—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—22no—
161C2×D4—1091no—
162C2×D4—2184no—
163C2×D4—2181no—
164C2×D4C22×D10912yes—
165C22×C4—2181no—
166C22×C4—2181no—
167C22×C4C22×D10911yescharacteristic
168Q16—2184no—
169SD16—2184no—
170SD16—2188no—
171M16—22no—
172C2×C8—1092no—
173C2×C8—2182no—
174C2×C8C22×D10912yes—
175C4⋊C4—1092no—
176C4⋊C4—2184no—
177C4⋊C4C22×D10912yes—
178C22⋊C4—21no—
179C22⋊C4—1092no—
180C22⋊C4—2184no—
181C42—21no—
182C42—1092no—
183C42—2184no—
184C23—22no—
185C23—42no—
186C23—82no—
187C23—2181no—
188C23D4×D10911yescharacteristic
189Q8—1094no—
190Q8—2181no—
191Q8—2181no—
192Q8—2184no—
193Q8—2182no—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—8724no—
198D4—4362no—
199D4—2181no—
200D4—2181no—
201C2×C4—22no—
202C2×C4—1094no—
203C2×C4—4362no—
204C2×C4—2181no—
205C2×C4—2184no—
206C2×C4—2182no—
207C2×C4D4×D10911yescharacteristic
208C2×C4D4×D10912yes—
209C2×C4#1318202912yes—
210C2×C4C23×D10911yescharacteristic
211C8—22no—
212C8—2182no—
213C22—22no—
214C22—42no—
215C22—44no—
216C22—84no—
217C22—4361no—
218C22—4362no—
219C22#1681267212yes—
220C22C2×D4×D10911yescharacteristic
221C4—42no—
222C4—4361no—
223C4—2184no—
224C4—2184no—
225C4#1681267212yes—
226C4C2×D4×D10911yescharacteristic
227C4C2×#1318202911yescharacteristic
228C2—22no—
229C2—82no—
230C2—8721no—
231C2C2×#1681267211yescharacteristic
232C2#2029583612yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#418×C109C2
socleC22×C109C22×D4
prime radical#20295593C2
hypercenter#418D109
hypocenterC109#3043
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#16812732C2semidirect
2. C22×#13182017C2semidirect
4. #20295503C2semidirect
5. #20295247C2semidirect
6. #20295225C2semidirect
7. #20295054C2semidirect
8. #20295020C2semidirect
9. #418×C109C2semidirect
13. C2×Dic436C22semidirect
14. C2×#13182018C22semidirect
23. #16812664C22semidirect
26. #16812628C22semidirect
27. #16812622C22semidirect
28. #16812619C22semidirect
37. C2×Dic218D4semidirect
117. C109#3043semidirect
125. #418D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168127322
C22×#131820172
#202955932
#202955032
#202952472
#202952252
#202950542
#202950202
#418×C1092
#3043109