Finite Group Databasebeta

← #27203624

Subgroups — #27203624

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×#15693069C211yesmaximal, characteristic
2#20268557C212yesmaximal, complemented
3#20267774C214yesmaximal, complemented
4#20267773C212yesmaximal, complemented
5C2×#15692940C211yesmaximal, characteristic, complemented
6#101×D103C214yesmaximal, complemented
7C2×#101×C103C211yesmaximal, characteristic, complemented
8#15693069—24no—
9#15693069—24no—
10C2×#13110106C412yes—
11C2×#13110106C2212yes—
12C2×#13110105C414yes—
13C2×#13110105C2211yescharacteristic
14C2×#13110105C2211yescharacteristic
15C2×Q8×D103C412yes—
16C2×Q8×D103C2212yes—
17#15693029—24no—
18#15693027—24no—
19C2×#13110089C2212yes—
20M16×D103C2218yes—
21#15692940C2214yes—
22#15692939C2214yes—
23#15692937C2214yes—
24C22×Q8×C103C2211yescharacteristic
25C2×M16×C103C2212yes—
26#101×C103C2214yes—
27#13110106—28no—
28#13110106—28no—
29#13110105—22no—
30#13110105—22no—
31#13110105—28no—
32#13110105—28no—
33#13110105D414yes—
34#13110105D414yes—
35C2×Dic206C2×C414yes—
36C2×Dic206C2×C411yescharacteristic
37C2×Dic206C2311yescharacteristic
38Q8×D103—28no—
39Q8×D103—28no—
40C2×D412C2×C414yes—
41C2×D412C2×C411yescharacteristic
42C2×D412C2311yescharacteristic
43C2×C22⋊D103C2×C412yes—
44C2×C22⋊D103C2×C412yes—
45C2×C4×D103C2×C414yes—
46C2×C4×D103C2×C412yes—
47C2×C4×D103C2×C414yes—
48C2×C4×D103C2312yes—
49#13110089—22no—
50#13110089C2314yes—
51#13110088—28no—
52C2×C103⋊C8—22no—
53C8×D103—28no—
54C2×Q8×C103—22no—
55C2×Q8×C103—22no—
56C2×Q8×C103C2×C412yes—
57C2×Q8×C103C2312yes—
58C22×C4×C103C2×C412yes—
59C22×C4×C103C2311yescharacteristic
60M16×C103—22no—
61M16×C103C2314yes—
62C2×C8×C103—22no—
63C23×C103C22×C411yescharacteristic
64C22×D103C22×C412yes—
65C22×D103C22×C412yes—
66Q8×C103—24no—
67Q8×C103—24no—
68C2×C4×C103—22no—
69C2×C4×C103—22no—
70C2×C4×C103C22×C414yes—
71C2×C4×C103C22×C411yescharacteristic
72C2×C4×C103C2×D412yes—
73C2×C4×C103C2×D412yes—
74C2×C4×C103C2411yescharacteristic
75C22⋊D103—22no—
76C22⋊D103—22no—
77C22⋊D103C22⋊C414yes—
78C22⋊D103C22⋊C414yes—
79C2×Dic103C22×C412yes—
80C2×Dic103C22×C412yes—
81D412—28no—
82D412—22no—
83D412C22⋊C414yes—
84C4×D103—28no—
85C4×D103—24no—
86C4×D103—28no—
87C4×D103C2×D418yes—
88Dic206—22no—
89Dic206—28no—
90Dic206C22⋊C414yes—
91C8×C103—24no—
92C103⋊C8—24no—
93C22×C103—41no—
94C22×C103C2×C22⋊C411yescharacteristic
95C22×C103C2×C22⋊C411yescharacteristic
96C22×C103C23×C411yescharacteristic
97C2×D103—22no—
98C2×D103—42no—
99C2×D103—42no—
100C2×D103C2×C22⋊C414yes—
101C4×C103—24no—
102C4×C103C2×C22⋊C412yes—
103C4×C103C22×D412yes—
104Dic103—22no—
105Dic103C2×C22⋊C414yes—
106C2×C103—21no—
107C2×C103—21no—
108C2×C103—21no—
109C2×C103C22×C22⋊C411yescharacteristic
110D103—24no—
111D103—42no—
112#2889—1031nomaximal, Sylow
113C103#288911yescharacteristic, complemented, Sylow
114C2×2−1+4—1031no—
115#568—1032no—
116#413—1032no—
117#413—1034no—
118C2×#101—1031no—
119C2×#101—1034no—
120C2×#101D10311yescharacteristic, complemented
1212−1+4—2064no—
1222−1+4—2064no—
123C2×#41—1032no—
124C2×#41—1032no—
125C2×#41—1034no—
126C2×#41—1031no—
127C2×#41—1031no—
128C22×Q8—1032no—
129C22×Q8—1032no—
130C22×Q8C2×D10311yescharacteristic
131#131—2064no—
132#131—2064no—
133C2×M16—1032no—
134C2×M16—1038no—
135C2×M16C2×D10312yes—
136#101—1034no—
137#101—1034no—
138#101C2×D10314yes—
139#100—1034no—
140#41—1034no—
141#41—1034no—
142#41—2068no—
143#41—2068no—
144#41—2068no—
145#41—2068no—
146#41—2062no—
147#41—2062no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—1031no—
151C2×Q8—1034no—
152C2×Q8—1031no—
153C2×Q8—2068no—
154C2×Q8—2068no—
155C2×Q8C4×D10312yes—
156C2×Q8C22×D10312yes—
157C2×D4—1032no—
158C2×D4—1032no—
159C2×D4—1031no—
160C2×D4—1034no—
161C2×D4—1031no—
162C22×C4—1032no—
163C22×C4—1034no—
164C22×C4—1034no—
165C22×C4—1032no—
166C22×C4C4×D10312yes—
167C22×C4C22×D10311yescharacteristic
168M16—22no—
169M16—1034no—
170M16—2068no—
171M16—2062no—
172M16C22×D10314yes—
173C2×C8—22no—
174C2×C8—2068no—
175C2×C8—2062no—
176C23—1032no—
177C23—1032no—
178C23C2×C4×D10311yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—1034no—
182Q8—2068no—
183Q8—2062no—
184D4—1034no—
185D4—1034no—
186D4—1034no—
187D4—2068no—
188D4—2062no—
189D4—2062no—
190D4—2062no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—1032no—
194C2×C4—1038no—
195C2×C4—1032no—
196C2×C4—2068no—
197C2×C4—2068no—
198C2×C4—2064no—
199C2×C4C2×C4×D10314yes—
200C2×C4C2×C4×D10311yescharacteristic
201C2×C4D4×D10312yes—
202C2×C4D4×D10312yes—
203C2×C4C23×D10311yescharacteristic
204C8—24no—
205C8—2064no—
206C22—41no—
207C22—1034no—
208C22—4122no—
209C22—4122no—
210C22—2062no—
211C22C22⋊C4×D10311yescharacteristic
212C22C22⋊C4×D10311yescharacteristic
213C22C22×C4×D10311yescharacteristic
214C4—24no—
215C4—1034no—
216C4—2062no—
217C4C22⋊C4×D10312yes—
218C4C2×D4×D10312yes—
219C2—21no—
220C2—21no—
221C2—21no—
222C2—4122no—
223C2—2064no—
224C2C2×C22⋊C4×D10311yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D103
commutatorC22×C103C23×C4
FrattiniC2×C4C23×D103
FittingC2×#101×C103C2
socleC2×C103C22×C22⋊C4
prime radicalC2×#15693069C2
cosocleC2×C4×C103C24
hypercenterC2×#101D103
hypocenterC103#2889
LCSG ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #20268557C2semidirect
3. #20267774C2semidirect
4. #20267773C2semidirect
5. C2×#15692940C2semidirect
6. #101×D103C2semidirect
7. C2×#101×C103C2semidirect
113. C103#2889semidirect
120. C2×#101D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930692
#202685572
#202677742
#202677732
C2×#156929402
#101×D1032
C2×#101×C1032
#2889103