Finite Group Databasebeta

← #27195620

Subgroups — #27195620

Order 13184.

304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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×#15693052C211yesmaximal, characteristic
2#20268557C211yesmaximal, characteristic
3#20267807C211yesmaximal, characteristic
4#20267800C211yesmaximal, characteristic, complemented
5#20267563C211yesmaximal, characteristic, complemented
6C103⋊#338C211yesmaximal, characteristic, complemented
7C2×#101×C103C211yesmaximal, characteristic, complemented
8C2×#13110105C2211yescharacteristic
9#15693052—22no—
10#15693052—22no—
11C2×#13110095C412yescomplemented
12C2×#13110092C412yescomplemented
13#15693029—22no—
14#15693027—22no—
15C2×#13110089C2211yescharacteristic
16C2×#13110089C2211yescharacteristic
17M16×D103—22no—
18#15692980C2211yescharacteristic
19#15692947—22no—
20#15692945—22no—
21C22×Q8×C103C2211yescharacteristic
22C2×M16×C103C2211yescharacteristic
23C2×M16×C103C2211yescharacteristic
24#101×C103—22no—
25#13110105—21no—
26#13110105—21no—
27#13110105D412yes—
28#13110105D412yes—
29C2×Dic206C2×C411yescharacteristic
30C2×D412C2×C411yescharacteristic
31C2×C22⋊D103—21no—
32C2×C4×D103—21no—
33#13110095—24no—
34#13110092—24no—
35#13110089—21no—
36#13110089—21no—
37#13110089—21no—
38#13110089—21no—
39#13110088—24no—
40C2×C103⋊C8C2×C412yes—
41C2×C103⋊C8D412yes—
42C8×D103—24no—
43C4⋊Dic103—21no—
44C22⋊Dic103—21no—
45C4×Dic103—21no—
46C2×Q8×C103—21no—
47C2×Q8×C103—21no—
48C2×Q8×C103—21no—
49C2×Q8×C103—21no—
50C2×Q8×C103—21no—
51C2×Q8×C103C2×C412yes—
52C22×C4×C103—21no—
53C22×C4×C103C2311yescharacteristic
54M16×C103—21no—
55M16×C103—21no—
56M16×C103—21no—
57M16×C103D412yes—
58C2×C8×C103—21no—
59C2×C8×C103—21no—
60C23×C103#4111yescharacteristic
61C22×D103—21no—
62Q8×C103—22no—
63Q8×C103—22no—
64Q8×C103—41no—
65Q8×C103—41no—
66C2×C4×C103—22no—
67C2×C4×C103—41no—
68C2×C4×C103—41no—
69C2×C4×C103C22×C411yescharacteristic
70C2×C4×C103C2×D411yescharacteristic
71C2×C4×C103C2×D411yescharacteristic
72C2×C4×C103C2×D411yescharacteristic
73C2×C4×C103C2×D411yescharacteristic
74C2×C4×C103#4111yescharacteristic
75C22⋊D103—22no—
76C22⋊D103—22no—
77C2×Dic103—21no—
78C2×Dic103—41no—
79D412—21no—
80D412C22⋊C412yes—
81C4×D103—22no—
82C4×D103—22no—
83Dic206—21no—
84Dic206C22⋊C412yes—
85C8×C103—22no—
86C8×C103—41no—
87C103⋊C8—22no—
88C103⋊C8—22no—
89C22×C103—41no—
90C22×C103C4×D411yescharacteristic
91C22×C103#12111yescharacteristic
92C22×C103#12311yescharacteristic
93C2×D103—22no—
94C2×D103—81no—
95C4×C103—42no—
96C4×C103C2×C22⋊C411yescharacteristic
97C4×C103C4×D411yescharacteristic
98C4×C103#12011yescharacteristic
99C4×C103#12111yescharacteristic
100Dic103—22no—
101Dic103—81no—
102C2×C103—21no—
103C2×C103—21no—
104C2×C103—21no—
105C2×C103#38611yescharacteristic
106D103—42no—
107#1902—1031nomaximal, Sylow
108C103#190211yescharacteristic, complemented, Sylow
109C2×#137—1031no—
110#568—1031no—
111#421—1031no—
112#419—1031no—
113C2×#101D10311yescharacteristic, complemented
114#344—1031no—
115#338—1031no—
116C2×#41—1031no—
117C22×Q8C2×D10311yescharacteristic
118#137—2062no—
119#137—2062no—
120C2×Q16—1032no—
121C2×SD16—1032no—
122#131—2062no—
123#131—2062no—
124C2×M16—1031no—
125C2×M16—1031no—
126C2×M16—2062no—
127C2×M16C2×D10311yescharacteristic
128C2×M16C2×D10311yescharacteristic
129#117—1031no—
130#104—2062no—
131#103—2062no—
132#101—22no—
133#41—1032no—
134#41—1032no—
135#41—2061no—
136#41—2061no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—1031no—
143C2×Q8C4×D10312yes—
144C2×D4—1031no—
145C2×D4—2061no—
146C22×C4—21no—
147C22×C4—2061no—
148C22×C4C22×D10311yescharacteristic
149Q16—2064no—
150SD16—2064no—
151M16—21no—
152M16—21no—
153M16—21no—
154M16—2064no—
155M16—2061no—
156M16—2061no—
157M16—2061no—
158M16—2061no—
159M16C22⋊D10312yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—1032no—
163C2×C8—1032no—
164C2×C8—2064no—
165C4⋊C4—2061no—
166C22⋊C4—2061no—
167C42—2061no—
168C23—2061no—
169C23#1311010511yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—41no—
173Q8—41no—
174Q8—1032no—
175Q8—2061no—
176D4—1032no—
177D4—2062no—
178D4—2062no—
179D4—2061no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—4121no—
184C2×C4—2061no—
185C2×C4—2062no—
186C2×C4—2062no—
187C2×C4C2×C4×D10311yescharacteristic
188C2×C4D4×D10311yescharacteristic
189C2×C4D4×D10311yescharacteristic
190C2×C4D4×D10311yescharacteristic
191C2×C4C2×C22⋊D10311yescharacteristic
192C2×C4#1311010411yescharacteristic
193C8—22no—
194C8—41no—
195C8—2062no—
196C8—2062no—
197C22—41no—
198C22—8241no—
199C22—2062no—
200C22C4×C22⋊D10311yescharacteristic
201C22#1569299411yescharacteristic
202C22#1569300311yescharacteristic
203C4—42no—
204C4—8241no—
205C4—2062no—
206C4C22⋊C4×D10311yescharacteristic
207C4(C22⋊D103)⋊C411yescharacteristic
208C4#1569298911yescharacteristic
209C4#1569299211yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—4122no—
214C2#2026766711yescharacteristic
subgroupG/H
centerC2#20267667
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×#101×C103C2
socleC2×C103#386
prime radicalC2×#13110105C22
cosocleC22×C4×C103C23
hypercenterC2×#101D103
hypocenterC103#1902
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
4. #20267800C2semidirect
5. #20267563C2semidirect
6. C103⋊#338C2semidirect
7. C2×#101×C103C2semidirect
11. C2×#13110095C4semidirect
12. C2×#13110092C4semidirect
108. C103#1902semidirect
113. C2×#101D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930522
#202685572
#202678072
#202678002
#202675632
C103⋊#3382
C2×#101×C1032
#1902103