Finite Group Databasebeta

← #27203625

Subgroups — #27203625

Order 13184.

704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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×#15693068C211yesmaximal, characteristic
2#20268557C212yesmaximal, complemented
3#20267775C211yesmaximal, characteristic, complemented
4#20267772C214yesmaximal, complemented
5C2×#15692939C212yesmaximal, complemented
6#101×D103C214yesmaximal, complemented
7#413×C103C211yesmaximal, characteristic, complemented
8#15693068—24no—
9#15693068—24no—
10C2×#13110105C412yes—
11C2×#13110105C2211yescharacteristic
12C2×#13110104C414yes—
13C2×#13110104C2212yes—
14C22×Dic206C412yes—
15C22×Dic206C2211yescharacteristic
16C2×Q8×D103C2212yes—
17#15693029—24no—
18#15693027—24no—
19C2×#13110089C2212yes—
20M16×D103C2218yes—
21#15692940C2212yes—
22#15692939C2218yes—
23#15692938C2212yes—
24C2×#41×C103C2211yescharacteristic
25C2×M16×C103C2212yes—
26#101×C103C2212yes—
27#100×C103C2212yes—
28#13110105—24no—
29#13110105—24no—
30#13110105D414yes—
31#13110105D414yes—
32#13110104—216no—
33#13110104—28no—
34C2×Dic206—22no—
35C2×Dic206—22no—
36C2×Dic206—24no—
37C2×Dic206—24no—
38C2×Dic206C2×C414yes—
39C2×Dic206C2×C412yes—
40C2×Dic206C2×C411yescharacteristic
41C2×Dic206C2312yes—
42Q8×D103—28no—
43C2×D412C2×C411yescharacteristic
44C2×C22⋊D103C2×C414yes—
45C2×C22⋊D103C2×C412yes—
46C22×Dic103C2×C414yes—
47C22×Dic103C2×C412yes—
48C2×C4×D103C2×C414yes—
49C2×C4×D103C2312yes—
50#13110089—22no—
51#13110089C2314yes—
52#13110088—28no—
53C2×C103⋊C8—22no—
54C8×D103—28no—
55#41×C103—22no—
56#41×C103—22no—
57C2×Q8×C103C2311yescharacteristic
58C2×D4×C103C2×C412yes—
59C2×D4×C103C2311yescharacteristic
60C22×C4×C103C2×C412yes—
61C22×C4×C103C2311yescharacteristic
62M16×C103—22no—
63M16×C103C2314yes—
64C2×C8×C103—22no—
65C23×C103C22×C412yes—
66C23×C103C22×C411yescharacteristic
67C22×D103C22×C412yes—
68Q8×C103—22no—
69D4×C103—24no—
70D4×C103—22no—
71C2×C4×C103—22no—
72C2×C4×C103—22no—
73C2×C4×C103C22×C412yes—
74C2×C4×C103C22×C411yescharacteristic
75C2×C4×C103C2×D412yes—
76C2×C4×C103C2×D412yes—
77C2×C4×C103C2411yescharacteristic
78C22⋊D103—28no—
79C22⋊D103C22⋊C418yes—
80C2×Dic103—24no—
81C2×Dic103—28no—
82C2×Dic103C22×C414yes—
83C2×Dic103C22×C412yes—
84D412C22⋊C412yes—
85D412C22⋊C412yes—
86C4×D103—28no—
87C4×D103C2×D418yes—
88Dic206—22no—
89Dic206—22no—
90Dic206—24no—
91Dic206—28no—
92Dic206C22⋊C412yes—
93Dic206C22⋊C412yes—
94C8×C103—24no—
95C103⋊C8—24no—
96C22×C103—22no—
97C22×C103—41no—
98C22×C103—42no—
99C22×C103C2×C22⋊C412yes—
100C22×C103C23×C411yescharacteristic
101C2×D103—42no—
102C2×D103C2×C22⋊C414yes—
103C4×C103—22no—
104C4×C103C2×C22⋊C411yescharacteristic
105C4×C103C2×C22⋊C411yescharacteristic
106C4×C103C22×D412yes—
107Dic103—24no—
108Dic103C2×C22⋊C414yes—
109C2×C103—21no—
110C2×C103—22no—
111C2×C103—42no—
112C2×C103C22×C22⋊C411yescharacteristic
113D103—24no—
114#2889—1031nomaximal, Sylow
115C103#288911yescharacteristic, complemented, Sylow
116C2×2−1+4—1031no—
117#568—1032no—
118#413—1031no—
119#413—1034no—
120#413D10311yescharacteristic, complemented
121C2×#101—1032no—
122C2×#101—1034no—
1232−1+4—2064no—
1242−1+4—2064no—
125C2×#41—1034no—
126C2×#41—1032no—
127C2×#41—1032no—
128C2×#41—1031no—
129C2×#41C2×D10311yescharacteristic
130C22×Q8—1032no—
131C22×Q8—1032no—
132C22×Q8—1031no—
133#131—2064no—
134#131—2064no—
135C2×M16—1032no—
136C2×M16—1038no—
137C2×M16C2×D10312yes—
138#101—1032no—
139#101—1038no—
140#101C2×D10312yes—
141#100—1032no—
142#100C2×D10312yes—
143#41—22no—
144#41—22no—
145#41—1034no—
146#41—1034no—
147#41—2064no—
148#41—2064no—
149#41—2068no—
150#41—20616no—
151C2×Q8—1031no—
152C2×Q8—1034no—
153C2×Q8—1032no—
154C2×Q8—1032no—
155C2×Q8—2064no—
156C2×Q8—2064no—
157C2×Q8—2068no—
158C2×Q8—2062no—
159C2×Q8—2062no—
160C2×Q8C22×D10311yescharacteristic
161C2×D4—1032no—
162C2×D4—1034no—
163C2×D4—1031no—
164C2×D4C4×D10312yes—
165C2×D4C22×D10311yescharacteristic
166C22×C4—1032no—
167C22×C4—1034no—
168C22×C4—1032no—
169C22×C4—1034no—
170C22×C4C4×D10312yes—
171C22×C4C22×D10311yescharacteristic
172M16—22no—
173M16—1034no—
174M16—2068no—
175M16—2062no—
176M16C22×D10314yes—
177C2×C8—22no—
178C2×C8—2068no—
179C2×C8—2062no—
180C23—1032no—
181C23C2×C4×D10312yes—
182C23C2×C4×D10311yescharacteristic
183Q8—22no—
184Q8—1032no—
185Q8—1032no—
186Q8—2068no—
187Q8—2064no—
188Q8—2062no—
189Q8—2062no—
190D4—24no—
191D4—22no—
192D4—1038no—
193D4—1032no—
194D4—1032no—
195D4—2068no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—1032no—
199C2×C4—1038no—
200C2×C4—1034no—
201C2×C4—2068no—
202C2×C4—2068no—
203C2×C4—2064no—
204C2×C4C2×C4×D10312yes—
205C2×C4C2×C4×D10311yescharacteristic
206C2×C4D4×D10312yes—
207C2×C4D4×D10312yes—
208C2×C4C23×D10311yescharacteristic
209C8—24no—
210C8—2064no—
211C22—22no—
212C22—41no—
213C22—42no—
214C22—1034no—
215C22—4122no—
216C22C22⋊C4×D10312yes—
217C22C22×C4×D10311yescharacteristic
218C4—22no—
219C4—1034no—
220C4—2064no—
221C4C22⋊C4×D10311yescharacteristic
222C4C22⋊C4×D10311yescharacteristic
223C4C2×D4×D10312yes—
224C2—21no—
225C2—22no—
226C2—42no—
227C2—2064no—
228C2C2×C22⋊C4×D10311yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D103
commutatorC22×C103C23×C4
FrattiniC2×C4C23×D103
Fitting#413×C103C2
socleC2×C103C22×C22⋊C4
prime radicalC2×#15693068C2
cosocleC2×C4×C103C24
hypercenter#413D103
hypocenterC103#2889
LCSG ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #20268557C2semidirect
3. #20267775C2semidirect
4. #20267772C2semidirect
5. C2×#15692939C2semidirect
6. #101×D103C2semidirect
7. #413×C103C2semidirect
115. C103#2889semidirect
120. #413D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930682
#202685572
#202677752
#202677722
C2×#156929392
#101×D1032
#413×C1032
#2889103