Finite Group Databasebeta

← #27205964

Subgroups — #27205964

Order 13184.

410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C22⋊Q8×D103C212yesmaximal
2#20268123C212yesmaximal, complemented
3#20268120C212yesmaximal, complemented
4#20268049C211yesmaximal, characteristic, complemented
5#20268047C212yesmaximal, complemented
6#20267948C212yesmaximal, complemented
7#20267945C212yesmaximal, complemented
8#20267754C211yesmaximal, characteristic
9#470×C103C211yesmaximal, characteristic, complemented
10C2×Q8×D103C2212yes—
11C22×C4×D103C2211yescharacteristic
12C2×Dic412C2211yescharacteristic, complemented
13C2×#13110095C2212yescomplemented
14C2×#13110089C2211yescharacteristic
15#15693001C2212yes—
16#15693000C2212yes—
17#15692999—22no—
18#15692998—22no—
19#15692997C2212yes—
20C4⋊C4×D103—22no—
21C4⋊C4×D103C2212yes—
22C22⋊C4×D103—22no—
23#15692953C2211yescharacteristic, complemented
24#15692952C2212yescomplemented
25#15692946C2212yescomplemented
26#15692945C2212yescomplemented
27#15692944C2212yescomplemented
28(C2×D103)⋊C8C2212yes—
29(C2×D103)⋊C8C2212yes—
30C2×Q16×C103C2211yescharacteristic, complemented
31C2×M16×C103C2211yescharacteristic
32C22⋊Q8×C103C2212yes—
33#106×C103C2211yescharacteristic, complemented
34#103×C103C2212yescomplemented
35C23×D103D411yescharacteristic
36C2×Dic206—22no—
37C2×Dic206C2312yes—
38Q8×D103—42no—
39Q8×D103—42no—
40C22×Dic103D411yescharacteristic
41C2×C4×D103—22no—
42C2×C4×D103—22no—
43C2×C4×D103—41no—
44C2×C4×D103—41no—
45C2×C4×D103D412yes—
46C2×C4×D103C2312yes—
47Dic412—41no—
48#13110095—42no—
49#13110089—41no—
50C2×C103⋊C8C2312yes—
51C4⋊Dic103—22no—
52C4⋊Dic103C2312yes—
53Dic103⋊C4—22no—
54Dic103⋊C4—22no—
55Dic103⋊C4—22no—
56C22⋊Dic103—22no—
57(C2×D103)⋊C4—22no—
58(C2×D103)⋊C4—22no—
59C2×Q8×C103C2312yes—
60C22×C4×C103C2311yescharacteristic
61Q16×C103—41no—
62M16×C103—41no—
63C2×C8×C103C2311yescharacteristic
64C2×C8×C103C2311yescharacteristic
65C4⋊C4×C103—22no—
66C4⋊C4×C103C2312yes—
67C22⋊C4×C103—22no—
68C23×C103C2×D411yescharacteristic
69C22×D103—24no—
70C22×D103—41no—
71C22×D103C2×D412yes—
72Q8×C103—22no—
73Q8×C103—22no—
74C2×C4×C103—21no—
75C2×C4×C103—21no—
76C2×C4×C103—22no—
77C2×C4×C103—22no—
78C2×C4×C103C2×D411yescharacteristic
79C2×C4×C103C2411yescharacteristic
80C2×Dic103—22no—
81C2×Dic103—22no—
82C2×Dic103—41no—
83C2×Dic103C2×D412yes—
84C4×D103—22no—
85C4×D103—22no—
86C4×D103—42no—
87C4×D103—44no—
88C4×D103—44no—
89Dic206—22no—
90Dic206—22no—
91Dic206—44no—
92C8×C103—21no—
93C8×C103—21no—
94C103⋊C8—22no—
95C22×C103—21no—
96C22×C103—22no—
97C22×C103C22×D411yescharacteristic
98C2×D103—22no—
99C2×D103—22no—
100C2×D103—44no—
101C2×D103#13714yes—
102C4×C103—21no—
103C4×C103—42no—
104C4×C103—42no—
105C4×C103H(5,𝔽2)11yescharacteristic
106C4×C103H(5,𝔽2)11yescharacteristic
107Dic103—22no—
108Dic103—42no—
109Dic103—42no—
110C2×C103—41no—
111C2×C103#53411yescharacteristic
112C2×C103C2×#13712yes—
113D103—24no—
114#3195—1031nomaximal, Sylow
115C103#319511yescharacteristic, complemented, Sylow
116C2×C22⋊Q8—1032no—
117#483—1032no—
118#483—1032no—
119#470—1031no—
120#470—1032no—
121#470D10311yescharacteristic, complemented
122#451—1032no—
123#451—1032no—
124#407—1031no—
125C22×Q8—1032no—
126C23×C4—1031no—
127C2×Q16—1032no—
128C2×Q16—1031no—
129C2×Q16C2×D10311yescharacteristic, complemented
130C2×M16—1031no—
131C2×M16C2×D10311yescharacteristic
132C22⋊Q8—1032no—
133C22⋊Q8—1032no—
134C22⋊Q8—1032no—
135C22⋊Q8—2062no—
136C22⋊Q8—2062no—
137C22⋊Q8C2×D10312yes—
138C2×C4⋊C4—1032no—
139C2×C4⋊C4—2062no—
140C2×C22⋊C4—2062no—
141#106—1031no—
142#106—1032no—
143#106C2×D10311yescharacteristic, complemented
144#103—1032no—
145#103—1032no—
146#103—1032no—
147#103C2×D10312yescomplemented
148C22⋊C8—1032no—
149C22⋊C8—1032no—
150C24—1031no—
151C2×Q8—1032no—
152C2×Q8—4122no—
153C2×Q8—4122no—
154C2×Q8—2062no—
155C2×Q8C22×D10312yes—
156C22×C4—1031no—
157C22×C4—1032no—
158C22×C4—1032no—
159C22×C4—4121no—
160C22×C4—4121no—
161C22×C4—2062no—
162C22×C4—2062no—
163C22×C4C22×D10311yescharacteristic
164Q16—41no—
165Q16—4121no—
166Q16—4122no—
167M16—41no—
168M16—4121no—
169C2×C8—1032no—
170C2×C8C22×D10311yescharacteristic
171C2×C8C22×D10311yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—1032no—
174C4⋊C4—2062no—
175C4⋊C4—2062no—
176C4⋊C4—2062no—
177C4⋊C4—2062no—
178C4⋊C4C22×D10312yes—
179C22⋊C4—22no—
180C22⋊C4—2062no—
181C22⋊C4—2062no—
182C22⋊C4—2062no—
183C23—1032no—
184C23—4121no—
185C23—2064no—
186C23D4×D10311yescharacteristic
187Q8—22no—
188Q8—22no—
189Q8—4124no—
190Q8—2062no—
191Q8—2062no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—1032no—
197C2×C4—4122no—
198C2×C4—4124no—
199C2×C4—4124no—
200C2×C4—4121no—
201C2×C4—2062no—
202C2×C4—2062no—
203C2×C4—2062no—
204C2×C4—2062no—
205C2×C4D4×D10311yescharacteristic
206C2×C4C23×D10311yescharacteristic
207C8—21no—
208C8—21no—
209C8—2062no—
210C22—22no—
211C22—21no—
212C22—1034no—
213C22—4124no—
214C22—2062no—
215C22—2062no—
216C22C2×D4×D10311yescharacteristic
217C4—21no—
218C4—42no—
219C4—42no—
220C4—4122no—
221C4—4122no—
222C4—2062no—
223C4#1569306611yescharacteristic
224C4#1569306711yescharacteristic
225C2—41no—
226C2—2064no—
227C2#2026834911yescharacteristic
228C2#137×D10312yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#470×C103C2
socleC22×C103C22×D4
prime radicalC23×D103D4
hypercenter#470D103
hypocenterC103#3195
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #20268123C2semidirect
3. #20268120C2semidirect
4. #20268049C2semidirect
5. #20268047C2semidirect
6. #20267948C2semidirect
7. #20267945C2semidirect
9. #470×C103C2semidirect
12. C2×Dic412C22semidirect
13. C2×#13110095C22semidirect
23. #15692953C22semidirect
24. #15692952C22semidirect
25. #15692946C22semidirect
26. #15692945C22semidirect
27. #15692944C22semidirect
30. C2×Q16×C103C22semidirect
33. #106×C103C22semidirect
34. #103×C103C22semidirect
115. C103#3195semidirect
121. #470D103semidirect
129. C2×Q16C2×D103semidirect
143. #106C2×D103semidirect
147. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1032
#202681232
#202681202
#202680492
#202680472
#202679482
#202679452
#202677542
#470×C1032
#3195103