Finite Group Databasebeta

← #28372534

Subgroups — #28372534

Order 13952.

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

normal subgroups only

This group has 526 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×#16812727C211yesmaximal, characteristic, complemented
2C22×#13182014C211yesmaximal, characteristic, complemented
3#20295593C211yesmaximal, characteristic, complemented
4#20295500C211yesmaximal, characteristic, complemented
5#20295240C214yesmaximal, complemented
6#20295220C214yesmaximal, complemented
7#20295054C211yesmaximal, characteristic, complemented
8#20295020C211yesmaximal, characteristic, complemented
9#418×C109C211yesmaximal, characteristic, complemented
10C2×#13182029C2211yescharacteristic
11C22×D436C2211yescharacteristic
12#16812727—24no—
13C2×#13182018C2212yescomplemented
14C2×D872C2212yescomplemented
15C2×#13182014—24no—
16C2×#13182014C2214yes—
17C22×#11724784C2211yescharacteristic
18#16812695C2212yescomplemented
19#16812686C2212yescomplemented
20#16812670—22no—
21#16812668—22no—
22C4×D436—22no—
23#16812661C2214yescomplemented
24#16812658C2211yescharacteristic
25C22⋊C4×D109—22no—
26#16812628C2214yescomplemented
27#16812622C2212yescomplemented
28#16812619C2212yescomplemented
29C22×D4×C109C2211yescharacteristic
30C2×M16×C109C2211yescharacteristic
31#117×C109C2211yescharacteristic
32#102×C109C2214yescomplemented
33C23×D109—21no—
34#13182029—22no—
35#13182029—22no—
36C2×Dic218C2311yescharacteristic
37C2×D436—21no—
38C2×D436—22no—
39C2×D436D414yescomplemented
40C2×D436C2311yescharacteristic
41C2×D436C2312yes—
42C2×C22⋊D109—21no—
43C2×C22⋊D109—24no—
44C2×C4×D109—21no—
45C2×C4×D109—24no—
46#13182018—24no—
47D872—24no—
48#13182014—28no—
49C2×#11724784—22no—
50C2×#11724784C2312yes—
51C4⋊Dic109D412yes—
52C22⋊Dic109—24no—
53C22⋊Dic109D412yes—
54#13182006—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—22no—
72C22×D109—24no—
73C22×D109—21no—
74C22×D109—82no—
75D4×C109—22no—
76D4×C109—22no—
77D4×C109—42no—
78C2×C4×C109—22no—
79C2×C4×C109C2×D411yescharacteristic
80C2×C4×C109C2×D412yes—
81C2×C4×C109#4112yes—
82C2×C4×C109C2411yescharacteristic
83C22⋊D109—42no—
84C22⋊D109—84no—
85C2×Dic109—21no—
86C2×Dic109C2×D414yes—
87D436—24no—
88D436—21no—
89D436—22no—
90D436—21no—
91D436C2×D414yes—
92C4×D109—42no—
93C4×D109—84no—
94Dic218—21no—
95Dic218—21no—
96C8×C109—22no—
97#11724784—22no—
98C22×C109—22no—
99C22×C109—42no—
100C22×C109—44no—
101C22×C109—84no—
102C22×C109#12112yes—
103C22×C109C22×D411yescharacteristic
104C2×D109—24no—
105C2×D109—44no—
106C2×D109—41no—
107C2×D109—42no—
108C2×D109—84no—
109C4×C109—42no—
110C4×C109#12112yes—
111C4×C109C22×D411yescharacteristic
112C4×C109C2×#4111yescharacteristic
113Dic109—24no—
114Dic109—41no—
115C2×C109—22no—
116C2×C109—82no—
117C2×C109C2×#12111yescharacteristic
118C2×C109#57612yes—
119D109—44no—
120D109—81no—
121#3041—1091nomaximal, Sylow
122C109#304111yescharacteristic, complemented, Sylow
123C2×AGL(1,ℤ/8)—1091no—
124C22×D8—1091no—
125#535—1091no—
126#518—1091no—
127#463—1094no—
128#459—1094no—
129#424—1091no—
130#418D10911yescharacteristic, complemented
131#416—1091no—
132C2×#41—1091no—
133C22×D4—1091no—
134C22×D4C2×D10911yescharacteristic
135AGL(1,ℤ/8)—2184no—
136C2×SD16—1092no—
137C2×D8—1094no—
138C2×D8—1092no—
139C2×D8—2184no—
140C2×M16C2×D10911yescharacteristic
141C22×C8—1091no—
142#127—1092no—
143#124—1092no—
144#121—2182no—
145#120—2182no—
146C4×D4—1094no—
147C4×D4—2182no—
148#117—1091no—
149#117C2×D10911yescharacteristic
150C2×C22⋊C4—2182no—
151C4⋊C8—1094no—
152#103—1092no—
153#102—1092no—
154#102C2×D10914yescomplemented
155C24—21no—
156C24—2181no—
157#41—2182no—
158#41—2182no—
159C2×Q8—1091no—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—1094no—
164C2×D4—1092no—
165C2×D4—1091no—
166C2×D4—2184no—
167C2×D4—2181no—
168C2×D4—2181no—
169C2×D4—2182no—
170C2×D4C22×D10912yes—
171C22×C4—2184no—
172C22×C4—2181no—
173C22×C4C22×D10911yescharacteristic
174SD16—2184no—
175D8—2184no—
176D8—2188no—
177M16—22no—
178C2×C8—1092no—
179C2×C8—2182no—
180C2×C8C22×D10912yes—
181C4⋊C4—1092no—
182C4⋊C4C22×D10912yes—
183C22⋊C4—21no—
184C22⋊C4—1092no—
185C22⋊C4—2184no—
186C22⋊C4—2184no—
187C42—21no—
188C42—1092no—
189C23—22no—
190C23—42no—
191C23—82no—
192C23—8722no—
193C23—2184no—
194C23—2181no—
195C23—2182no—
196C23D4×D10911yescharacteristic
197Q8—2181no—
198Q8—2181no—
199D4—22no—
200D4—22no—
201D4—42no—
202D4—8724no—
203D4—1094no—
204D4—4362no—
205D4—2184no—
206D4—2181no—
207D4—2181no—
208D4—2182no—
209C2×C4—22no—
210C2×C4—8724no—
211C2×C4—1094no—
212C2×C4—4362no—
213C2×C4—2181no—
214C2×C4D4×D10911yescharacteristic
215C2×C4D4×D10912yes—
216C2×C4#1318202912yes—
217C2×C4C23×D10911yescharacteristic
218C8—22no—
219C8—2182no—
220C22—22no—
221C22—42no—
222C22—44no—
223C22—84no—
224C22—8724no—
225C22—4361no—
226C22—4362no—
227C22—4364no—
228C22—2184no—
229C22#1681267212yes—
230C22C2×D4×D10911yescharacteristic
231C4—42no—
232C4—4361no—
233C4—2184no—
234C4#1681267212yes—
235C4C2×D4×D10911yescharacteristic
236C4C2×#1318202911yescharacteristic
237C2—22no—
238C2—82no—
239C2—8721no—
240C2—4364no—
241C2C2×#1681267211yescharacteristic
242C2#2029583012yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#418×C109C2
socleC22×C109C22×D4
hypercenter#418D109
hypocenterC109#3041
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×#16812727C2semidirect
2. C22×#13182014C2semidirect
3. #20295593C2semidirect
4. #20295500C2semidirect
5. #20295240C2semidirect
6. #20295220C2semidirect
7. #20295054C2semidirect
8. #20295020C2semidirect
9. #418×C109C2semidirect
13. C2×#13182018C22semidirect
14. C2×D872C22semidirect
18. #16812695C22semidirect
19. #16812686C22semidirect
23. #16812661C22semidirect
26. #16812628C22semidirect
27. #16812622C22semidirect
28. #16812619C22semidirect
32. #102×C109C22semidirect
39. C2×D436D4semidirect
122. C109#3041semidirect
130. #418D109semidirect
154. #102C2×D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168127272
C22×#131820142
#202955932
#202955002
#202952402
#202952202
#202950542
#202950202
#418×C1092
#3041109