Finite Group Databasebeta

← #27206036

Subgroups — #27206036

Order 13184.

378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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#20268364C212yesmaximal
2#20268135C212yesmaximal, complemented
3#20268130C212yesmaximal, complemented
4#20268049C211yesmaximal, characteristic, complemented
5#20268030C212yesmaximal, complemented
6#20267948C212yesmaximal, complemented
7#20267945C212yesmaximal, complemented
8#20267759C211yesmaximal, characteristic
9#470×C103C211yesmaximal, characteristic, complemented
10C2×#13110105C2211yescharacteristic
11C2×Q8×D103C2212yes—
12C2×Dic412C2211yescharacteristic
13C2×#13110095C2212yes—
14C22×C103⋊C8C2211yescharacteristic
15#15693020—22no—
16#15693007—22no—
17#15693006—22no—
18#15693003—22no—
19#15693001C2212yes—
20#15693000C2212yes—
21#15692997C2212yes—
22#15692979C2212yes—
23#15692954C2212yes—
24#15692953C2211yescharacteristic
25#15692946C2212yes—
26#15692945C2212yes—
27#15692944C2212yes—
28(C2×D103)⋊C8C2212yes—
29(C2×D103)⋊C8C2212yes—
30C2×Q16×C103C2211yescharacteristic
31C2×M16×C103C2211yescharacteristic
32C22⋊Q8×C103C2212yes—
33#106×C103C2211yescharacteristic
34#103×C103C2212yes—
35#13110105—41no—
36#13110105—41no—
37C2×Dic206—22no—
38C2×Dic206D411yescharacteristic
39C2×Dic206C2312yes—
40Q8×D103—42no—
41Q8×D103—42no—
42C2×D412D411yescharacteristic
43C2×C22⋊D103D412yes—
44C2×C4×D103—22no—
45C2×C4×D103C2312yes—
46Dic412—41no—
47#13110095—42no—
48C2×C103⋊C8—41no—
49C2×C103⋊C8C2312yes—
50C4⋊Dic103—22no—
51C4⋊Dic103C2312yes—
52Dic103⋊C4—22no—
53Dic103⋊C4—22no—
54C22⋊Dic103—22no—
55(C2×D103)⋊C4—22no—
56(C2×D103)⋊C4—22no—
57(C2×D103)⋊C4—22no—
58C4×Dic103—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×D103C2×D412yes—
70Q8×C103—22no—
71Q8×C103—22no—
72C2×C4×C103—21no—
73C2×C4×C103—21no—
74C2×C4×C103—22no—
75C2×C4×C103—22no—
76C2×C4×C103C2×D411yescharacteristic
77C2×C4×C103C2411yescharacteristic
78C22⋊D103—42no—
79C2×Dic103—22no—
80C2×Dic103—22no—
81C2×Dic103C2×D412yes—
82D412—41no—
83C4×D103—22no—
84C4×D103—22no—
85C4×D103—44no—
86Dic206—22no—
87Dic206—22no—
88Dic206—41no—
89Dic206—44no—
90C8×C103—21no—
91C8×C103—21no—
92C103⋊C8—22no—
93C22×C103—21no—
94C22×C103—22no—
95C22×C103C22×D411yescharacteristic
96C2×D103—22no—
97C2×D103—24no—
98C4×C103—21no—
99C4×C103—42no—
100C4×C103—42no—
101C4×C103H(5,𝔽2)11yescharacteristic
102C4×C103H(5,𝔽2)11yescharacteristic
103Dic103—22no—
104Dic103—42no—
105Dic103—42no—
106C2×C103—41no—
107C2×C103#53411yescharacteristic
108C2×C103#57812yes—
109D103—42no—
110#3202—1031nomaximal, Sylow
111C103#320211yescharacteristic, complemented, Sylow
112#536—1032no—
113#485—1032no—
114#485—1032no—
115#470—1031no—
116#470D10311yescharacteristic, complemented
117#467—1032no—
118#451—1032no—
119#451—1032no—
120#408—1031no—
121C2×#41—1031no—
122C22×Q8—1032no—
123C2×Q16—1032no—
124C2×Q16—1031no—
125C2×Q16C2×D10311yescharacteristic
126C2×M16C2×D10311yescharacteristic
127C22×C8—1031no—
128C4⋊Q8—2062no—
129#124—2062no—
130#123—2062no—
131#123—2062no—
132C22⋊Q8—1032no—
133C22⋊Q8—1032no—
134C22⋊Q8—1032no—
135C22⋊Q8C2×D10312yes—
136#117—1032no—
137#107—1032no—
138#106—1031no—
139#106C2×D10311yescharacteristic
140#103—1032no—
141#103—1032no—
142#103—1032no—
143#103C2×D10312yes—
144C22⋊C8—1032no—
145C22⋊C8—1032no—
146#41—4121no—
147#41—4121no—
148C2×Q8—1031no—
149C2×Q8—1032no—
150C2×Q8—4122no—
151C2×Q8—4122no—
152C2×Q8—2062no—
153C2×Q8C22×D10312yes—
154C2×D4—1032no—
155C2×D4—1031no—
156C22×C4—1032no—
157C22×C4—2062no—
158C22×C4C22×D10311yescharacteristic
159Q16—41no—
160Q16—4121no—
161Q16—4122no—
162M16—41no—
163C2×C8—1032no—
164C2×C8—4121no—
165C2×C8C22×D10311yescharacteristic
166C2×C8C22×D10311yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—1032no—
169C4⋊C4—2062no—
170C4⋊C4—2062no—
171C4⋊C4—2062no—
172C4⋊C4C22×D10312yes—
173C22⋊C4—22no—
174C22⋊C4—2062no—
175C22⋊C4—2062no—
176C22⋊C4—2062no—
177C22⋊C4—2062no—
178C42—2062no—
179C23—1032no—
180C23D4×D10311yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—4121no—
184Q8—4124no—
185Q8—2062no—
186Q8—2062no—
187D4—4121no—
188D4—4122no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—1032no—
194C2×C4—4124no—
195C2×C4—2062no—
196C2×C4—2062no—
197C2×C4—2062no—
198C2×C4—2062no—
199C2×C4D4×D10311yescharacteristic
200C2×C4C23×D10311yescharacteristic
201C8—21no—
202C8—21no—
203C8—2062no—
204C22—21no—
205C22—22no—
206C22—2062no—
207C22—2064no—
208C22C2×D4×D10311yescharacteristic
209C4—21no—
210C4—42no—
211C4—42no—
212C4—4122no—
213C4—4122no—
214C4—2062no—
215C4#1569306611yescharacteristic
216C4#1569306711yescharacteristic
217C2—41no—
218C2—4122no—
219C2#2026834911yescharacteristic
220C2#2026860712yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#470×C103C2
socleC22×C103C22×D4
prime radicalC2×#13110105C22
hypercenter#470D103
hypocenterC103#3202
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. #20268135C2semidirect
3. #20268130C2semidirect
4. #20268049C2semidirect
5. #20268030C2semidirect
6. #20267948C2semidirect
7. #20267945C2semidirect
9. #470×C103C2semidirect
111. C103#3202semidirect
116. #470D103semidirect

Maximal subgroups

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

subgroupindex
#202683642
#202681352
#202681302
#202680492
#202680302
#202679482
#202679452
#202677592
#470×C1032
#3202103