Finite Group Databasebeta

← #27196186

Subgroups — #27196186

Order 13184.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#15693046C212yesmaximal, complemented
2C2×#15692948C212yesmaximal, complemented
3#20267692C211yesmaximal, characteristic, complemented
4#20267560C211yesmaximal, characteristic, complemented
5#537×C103C211yesmaximal, characteristic, complemented
6C22×D412C2211yescharacteristic
7#15693046—24no—
8#15693046—24no—
9C2×#13110092—22no—
10C2×#13110090—22no—
11C2×#13110089C2212yes—
12C2×(C2×D103)⋊C4—22no—
13C2×C4×Dic103C2211yescharacteristic
14#15692948—24no—
15C2×#41×C103C2212yes—
16C22⋊Q8×C103—22no—
17#121×C103—22no—
18#121×C103—22no—
19C2×C4⋊C4×C103C2211yescharacteristic
20C23×D103—21no—
21C2×D412—22no—
22C2×D412—22no—
23C2×D412—21no—
24C2×D412D412yescomplemented
25C22×Dic103—21no—
26#13110092—28no—
27#13110090—28no—
28#13110089—22no—
29#13110089D414yescomplemented
30C2×C103⋊C8—22no—
31(C2×D103)⋊C4—44no—
32C4×Dic103—22no—
33#41×C103—22no—
34#41×C103—22no—
35#41×C103—22no—
36#41×C103—22no—
37C2×Q8×C103D412yes—
38C2×D4×C103—22no—
39C2×D4×C103—22no—
40C2×D4×C103D412yes—
41C22×C4×C103—22no—
42C22×C4×C103D412yes—
43C22×C4×C103C2311yescharacteristic
44C4⋊C4×C103—22no—
45C4⋊C4×C103—22no—
46C22⋊C4×C103—24no—
47C23×C103—22no—
48C23×C103C2×D411yescharacteristic
49C22×D103—22no—
50C22×D103—42no—
51C22×D103—42no—
52C22×D103—41no—
53C22×D103—41no—
54Q8×C103—22no—
55Q8×C103—22no—
56D4×C103—22no—
57D4×C103—22no—
58D4×C103—42no—
59D4×C103—42no—
60D4×C103—82no—
61C2×C4×C103—22no—
62C2×C4×C103—22no—
63C2×C4×C103—42no—
64C2×C4×C103—42no—
65C2×C4×C103—42no—
66C2×C4×C103C2×D411yescharacteristic
67C2×C4×C103C2×D412yes—
68C2×C4×C103C2×D412yes—
69C2×C4×C103#4111yescharacteristic
70C2×Dic103—22no—
71C2×Dic103—41no—
72C2×Dic103—41no—
73D412—24no—
74D412—42no—
75C103⋊C8—24no—
76C22×C103—21no—
77C22×C103—21no—
78C22×C103—42no—
79C22×C103—42no—
80C22×C103—42no—
81C22×C103#12011yescharacteristic
82C22×C103#12111yescharacteristic
83C22×C103#12711yescharacteristic
84C2×D103—44no—
85C2×D103—42no—
86C2×D103—82no—
87C2×D103—81no—
88C2×D103—81no—
89C4×C103—42no—
90C4×C103—42no—
91C4×C103#12012yes—
92C4×C103#12112yes—
93Dic103—42no—
94C2×C103—21no—
95C2×C103—21no—
96C2×C103—82no—
97C2×C103#39211yescharacteristic
98C2×C103#45311yescharacteristic
99C2×C103#45411yescharacteristic
100D103—82no—
101#2006—1031nomaximal, Sylow
102C103#200611yescharacteristic, complemented, Sylow
103C2×AGL(1,ℤ/8)—1032no—
104#537D10311yescharacteristic, complemented
105C2×#104—1032no—
106#390—1031no—
107#343—1031no—
108C2×#41C2×D10312yes—
109C22×D4—1031no—
110AGL(1,ℤ/8)—2064no—
111AGL(1,ℤ/8)—2064no—
112C2×SD16—2062no—
113C2×D8—2062no—
114C2×M16—1032no—
115C22⋊Q8—22no—
116#121—22no—
117#121—22no—
118C2×C4⋊C4C2×D10311yescharacteristic
119C2×C22⋊C4—2062no—
120C2×C42—1031no—
121#104—2064no—
122C24—2061no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D10312yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—1032no—
131C2×D4—2062no—
132C2×D4—2062no—
133C2×D4—2061no—
134C2×D4C22⋊D10312yes—
135C22×C4—22no—
136C22×C4—2061no—
137C22×C4C22⋊D10312yes—
138C22×C4C22×D10311yescharacteristic
139SD16—2068no—
140D8—2068no—
141M16—1034no—
142M16—2062no—
143C2×C8—2062no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—4124no—
148C42—2062no—
149C23—22no—
150C23—4122no—
151C23—4122no—
152C23—4121no—
153C23—4121no—
154C23—2062no—
155C23C2×C22⋊D10311yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—4122no—
164D4—2064no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—4121no—
171C2×C4—4121no—
172C2×C4—2062no—
173C2×C4D4×D10311yescharacteristic
174C2×C4D4×D10312yes—
175C2×C4C2×C22⋊D10312yes—
176C2×C4#1311010411yescharacteristic
177C8—2064no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—8242no—
184C22—8241no—
185C22—8241no—
186C22—4124no—
187C22—4122no—
188C22#1569299011yescharacteristic
189C22#1569299211yescharacteristic
190C22#1569301711yescharacteristic
191C4—42no—
192C4—42no—
193C4—4122no—
194C4#1569298912yes—
195C4#1569299312yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—8242no—
200C2#2026769911yescharacteristic
201C2#2026795911yescharacteristic
202C2#2026796411yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#537×C103C2
socleC22×C103#120
hypercenter#537D103
hypocenterC103#2006
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#15693046C2semidirect
2. C2×#15692948C2semidirect
3. #20267692C2semidirect
4. #20267560C2semidirect
5. #537×C103C2semidirect
24. C2×D412D4semidirect
29. #13110089D4semidirect
102. C103#2006semidirect
104. #537D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930462
C2×#156929482
#202676922
#202675602
#537×C1032
#2006103