Finite Group Databasebeta

← #28372532

Subgroups — #28372532

Order 13952.

526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812725C211yesmaximal, characteristic, complemented
2#20295593C211yesmaximal, characteristic, complemented
3#20295501C211yesmaximal, characteristic, complemented
4#20295239C214yesmaximal, complemented
5#20295219C214yesmaximal, complemented
6#20295052C211yesmaximal, characteristic, complemented
7#20295031C211yesmaximal, characteristic, complemented
8#20295023C211yesmaximal, characteristic, complemented
9C22×D8×C109C211yesmaximal, characteristic, complemented
10C2×#13182029C2211yescharacteristic
11#16812725—24no—
12C2×#13182017C2212yescomplemented
13C2×#13182014C2212yescomplemented
14C2×#13182013C2211yescharacteristic
15#16812695C2212yescomplemented
16#16812686C2212yescomplemented
17#16812670—22no—
18#16812668—22no—
19D4×Dic109—22no—
20D4×Dic109C2214yescomplemented
21#16812658C2211yescharacteristic
22#16812658C2211yescharacteristic
23C2×C22⋊Dic109—22no—
24#16812628C2214yescomplemented
25#16812624C2212yescomplemented
26#16812621C2212yescomplemented
27#16812620C2214yescomplemented
28C22×D4×C109C2211yescharacteristic
29C22×D4×C109C2211yescharacteristic
30C2×D8×C109—24no—
31C2×D8×C109C2214yes—
32C22×C8×C109C2211yescharacteristic
33#13182029—22no—
34#13182029—22no—
35C2×Dic218C2311yescharacteristic
36C2×D436C2311yescharacteristic
37C2×C22⋊D109—21no—
38C2×C22⋊D109—24no—
39C22×Dic109—24no—
40C2×C4×D109—21no—
41#13182017—24no—
42#13182014—24no—
43#13182013—22no—
44C2×#11724784C2312yes—
45C4⋊Dic109D412yes—
46C4⋊Dic109C2312yes—
47C22⋊Dic109—21no—
48C22⋊Dic109—24no—
49C22⋊Dic109—24no—
50C22⋊Dic109D412yes—
51C4×Dic109—21no—
52C4×Dic109C2312yes—
53C24×C109—21no—
54C24×C109—21no—
55C2×D4×C109—21no—
56C2×D4×C109—22no—
57C2×D4×C109—21no—
58C2×D4×C109—22no—
59C2×D4×C109—22no—
60C2×D4×C109D414yescomplemented
61C2×D4×C109C2312yes—
62C2×D4×C109C2312yes—
63C22×C4×C109C2311yescharacteristic
64D8×C109—28no—
65C2×C8×C109—22no—
66C2×C8×C109C2312yes—
67C23×C109—22no—
68C23×C109—24no—
69C23×C109—22no—
70C23×C109—42no—
71C23×C109—82no—
72C23×C109—82no—
73C23×C109C2×D411yescharacteristic
74C22×D109—21no—
75D4×C109—24no—
76D4×C109—22no—
77D4×C109—22no—
78D4×C109—22no—
79D4×C109—42no—
80D4×C109C2×D414yes—
81C2×C4×C109C2×D411yescharacteristic
82C2×C4×C109C2×D412yes—
83C2×C4×C109#4112yes—
84C2×C4×C109C2411yescharacteristic
85C22⋊D109—42no—
86C22⋊D109—84no—
87C2×Dic109—22no—
88C2×Dic109—21no—
89C2×Dic109—84no—
90C2×Dic109C2×D414yes—
91D436—21no—
92D436—21no—
93C4×D109—42no—
94Dic218—21no—
95Dic218—21no—
96C8×C109—22no—
97#11724784—22no—
98C22×C109—22no—
99C22×C109—24no—
100C22×C109—44no—
101C22×C109—42no—
102C22×C109—44no—
103C22×C109—84no—
104C22×C109—84no—
105C22×C109#12112yes—
106C22×C109C22×D411yescharacteristic
107C2×D109—41no—
108C2×D109—42no—
109C4×C109#12112yes—
110C4×C109C22×D411yescharacteristic
111C4×C109C2×#4111yescharacteristic
112Dic109—24no—
113Dic109—41no—
114Dic109—42no—
115C2×C109—22no—
116C2×C109—44no—
117C2×C109—82no—
118C2×C109C2×#12111yescharacteristic
119C2×C109#57612yes—
120D109—81no—
121#3041—1091nomaximal, Sylow
122C109#304111yescharacteristic, complemented, Sylow
123C2×AGL(1,ℤ/8)—1091no—
124C22×D8D10911yescharacteristic, complemented
125#535—1091no—
126#518—1091no—
127#463—1094no—
128#459—1094no—
129#424—1091no—
130#418—1091no—
131#416—1091no—
132C2×#41—1091no—
133C22×D4C2×D10911yescharacteristic
134C22×D4C2×D10911yescharacteristic
135AGL(1,ℤ/8)—2184no—
136C2×SD16—1092no—
137C2×D8—24no—
138C2×D8—1092no—
139C2×D8C2×D10914yes—
140C2×M16—1091no—
141C22×C8C2×D10911yescharacteristic
142#127—1092no—
143#124—1092no—
144#121—2182no—
145#120—2182no—
146C4×D4—1094no—
147C4×D4—2182no—
148#117—1091no—
149#117—1091no—
150C2×C22⋊C4—2182no—
151C4⋊C8—1094no—
152#103—1092no—
153#102—1094no—
154#102—1092no—
155C24—21no—
156C24—21no—
157#41—2182no—
158#41—2182no—
159C2×Q8—1091no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—22no—
165C2×D4—1091no—
166C2×D4—2184no—
167C2×D4—2181no—
168C2×D4C22⋊D10914yescomplemented
169C2×D4C22×D10912yes—
170C2×D4C22×D10912yes—
171C22×C4—2184no—
172C22×C4—2181no—
173C22×C4C22×D10911yescharacteristic
174SD16—2184no—
175D8—28no—
176D8—2184no—
177M16—2182no—
178C2×C8—22no—
179C2×C8—1092no—
180C2×C8C22×D10912yes—
181C4⋊C4—1092no—
182C4⋊C4—1092no—
183C22⋊C4—1092no—
184C22⋊C4—2184no—
185C22⋊C4—2184no—
186C22⋊C4—2181no—
187C42—1092no—
188C42—2181no—
189C23—22no—
190C23—24no—
191C23—22no—
192C23—42no—
193C23—82no—
194C23—82no—
195C23—2181no—
196C23D4×D10911yescharacteristic
197Q8—2181no—
198Q8—2181no—
199D4—24no—
200D4—22no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—8724no—
205D4—4362no—
206D4—2181no—
207D4—2181no—
208D4C2×C22⋊D10914yes—
209C2×C4—8724no—
210C2×C4—1094no—
211C2×C4—4362no—
212C2×C4—2182no—
213C2×C4—2181no—
214C2×C4D4×D10911yescharacteristic
215C2×C4C2×C22⋊D10912yes—
216C2×C4#1318202812yes—
217C2×C4C23×D10911yescharacteristic
218C8—22no—
219C8—2182no—
220C22—22no—
221C22—24no—
222C22—44no—
223C22—42no—
224C22—44no—
225C22—84no—
226C22—84no—
227C22—4361no—
228C22—4362no—
229C22#1681267112yes—
230C22C2×D4×D10911yescharacteristic
231C4—4361no—
232C4—4362no—
233C4—2184no—
234C4#1681267112yes—
235C4C22×C22⋊D10911yescharacteristic
236C4C2×#1318202811yescharacteristic
237C2—22no—
238C2—44no—
239C2—82no—
240C2—8721no—
241C2C2×#1681267111yescharacteristic
242C2#2029582712yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC22×D8×C109C2
socleC22×C109C22×D4
hypercenterC22×D8D109
hypocenterC109#3041
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16812725C2semidirect
2. #20295593C2semidirect
3. #20295501C2semidirect
4. #20295239C2semidirect
5. #20295219C2semidirect
6. #20295052C2semidirect
7. #20295031C2semidirect
8. #20295023C2semidirect
9. C22×D8×C109C2semidirect
12. C2×#13182017C22semidirect
13. C2×#13182014C22semidirect
15. #16812695C22semidirect
16. #16812686C22semidirect
20. D4×Dic109C22semidirect
24. #16812628C22semidirect
25. #16812624C22semidirect
26. #16812621C22semidirect
27. #16812620C22semidirect
60. C2×D4×C109D4semidirect
122. C109#3041semidirect
124. C22×D8D109semidirect
168. C2×D4C22⋊D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168127252
#202955932
#202955012
#202952392
#202952192
#202950522
#202950312
#202950232
C22×D8×C1092
#3041109