Finite Group Databasebeta

← #355×D103 #27196820

Subgroups — #355×D103 #27196820

Order 13184.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D103C211yesmaximal, characteristic
2#101×D103C212yesmaximal, complemented
3#20267588C211yesmaximal, characteristic, complemented
4#20267587C212yesmaximal, complemented
5#355×C103C211yesmaximal, characteristic, complemented
6C2×Q8×D103C2211yescharacteristic
7C2×D4×D103C411yescharacteristic
8M16×D103—22no—
9#15693010C2211yescharacteristic
10#15693009C411yescharacteristic
11#15693008C411yescharacteristic
12#15693007—22no—
13C22⋊C4×D103—22no—
14C42×D103C411yescharacteristic
15#15692940C2212yescomplemented
16#15692939—22no—
17#124×C103C2211yescharacteristic
18#101×C103C2212yescomplemented
19C23×D103—21no—
20C2×Dic206C2×C411yescharacteristic
21C2×Dic206D412yes—
22Q8×D103—41no—
23Q8×D103—41no—
24C2×D412C2×C411yescharacteristic
25C2×C22⋊D103—21no—
26D4×D103—41no—
27D4×D103—41no—
28C2×C4×D103—21no—
29C2×C4×D103C2×C411yescharacteristic
30C2×C4×D103D412yes—
31#13110089—22no—
32#13110088—42no—
33C8×D103—42no—
34C22⋊Dic103—22no—
35(C2×D103)⋊C4—22no—
36(C2×D103)⋊C4—22no—
37C4×Dic103—21no—
38C4×Dic103C2×C411yescharacteristic
39C2×Q8×C103C2311yescharacteristic
40C2×D4×C103C2×C411yescharacteristic
41M16×C103—22no—
42C22⋊C4×C103—22no—
43C42×C103C2×C411yescharacteristic
44C23×C103—21no—
45C22×D103—21no—
46C22×D103—44no—
47C22×D103—41no—
48C22×D103—41no—
49C22×D103C22⋊C411yescharacteristic
50Q8×C103—41no—
51D4×C103—41no—
52C2×C4×C103—21no—
53C2×C4×C103C22×C411yescharacteristic
54C2×C4×C103C2×D412yes—
55C22⋊D103—42no—
56C2×Dic103—21no—
57C2×Dic103C22⋊C411yescharacteristic
58C2×Dic103C22⋊C412yes—
59D412—41no—
60C4×D103—22no—
61C4×D103—22no—
62C4×D103—21no—
63C4×D103—21no—
64C4×D103—42no—
65Dic206—41no—
66Dic206—42no—
67C8×C103—42no—
68C103⋊C8—42no—
69C22×C103—42no—
70C22×C103—41no—
71C22×C103C2×C22⋊C411yescharacteristic
72C2×D103—22no—
73C2×D103—42no—
74C2×D103—41no—
75C2×D103—82no—
76C2×D103—82no—
77C2×D103#9911yescharacteristic
78C2×D103#9911yescharacteristic
79C4×C103—22no—
80C4×C103—21no—
81C4×C103—41no—
82Dic103—22no—
83Dic103—21no—
84Dic103—41no—
85C2×C103—21no—
86C2×C103—81no—
87C2×C103C2×#9911yescharacteristic
88D103—21no—
89D103—81no—
90D103#35512yesdirect product factor
91C2×#355—1031nomaximal, Sylow
92C103C2×#35511yescharacteristic, complemented, Sylow
93C2×#124—1031no—
94C2×#101—1032no—
95#355—1031no—
96#355—1032no—
97#355D10311yescharacteristic, direct product factor
98C22×Q8—1031no—
99C22×D4—1031no—
100C2×M16—2062no—
101#124—1031no—
102#124—1031no—
103#124—1031no—
104#124—2062no—
105#124C2×D10311yescharacteristic
106C2×C22⋊C4—2062no—
107C2×C42—1031no—
108#101—1032no—
109#101—2062no—
110#101C2×D10312yescomplemented
111C24—2061no—
112C2×Q8—1031no—
113C2×Q8—1032no—
114C2×Q8—4121no—
115C2×Q8—4121no—
116C2×Q8C22×D10311yescharacteristic
117C2×D4—1031no—
118C2×D4—4121no—
119C2×D4—4121no—
120C2×D4—2061no—
121C2×D4C4×D10311yescharacteristic
122C22×C4—1031no—
123C22×C4—1032no—
124C22×C4—2061no—
125M16—22no—
126M16—4122no—
127M16—2062no—
128C2×C8—4122no—
129C22⋊C4—22no—
130C22⋊C4—2062no—
131C22⋊C4—2062no—
132C22⋊C4—2062no—
133C42—1031no—
134C42—2061no—
135C42C4×D10311yescharacteristic
136C23—21no—
137C23—1031no—
138C23—4121no—
139C23—4121no—
140C23—4124no—
141C23—2061no—
142Q8—41no—
143Q8—4122no—
144Q8—4121no—
145D4—41no—
146D4—4121no—
147D4—4122no—
148C2×C4—21no—
149C2×C4—1031no—
150C2×C4—1032no—
151C2×C4—4122no—
152C2×C4—2062no—
153C2×C4—2062no—
154C2×C4—2061no—
155C2×C4—2061no—
156C2×C4—2061no—
157C2×C4C2×C4×D10311yescharacteristic
158C2×C4D4×D10312yes—
159C8—42no—
160C8—4122no—
161C22—42no—
162C22—41no—
163C22—8242no—
164C22—8242no—
165C22—1031no—
166C22—1031no—
167C22—4122no—
168C22—4121no—
169C22—2062no—
170C22C22⋊C4×D10311yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—4121no—
175C4—2061no—
176C4—2062no—
177C2—21no—
178C2—81no—
179C2—8241no—
180C2—1032no—
181C2—2061no—
182C2#99×D10311yescharacteristic
subgroupG/H
centerC2#99×D103
commutatorC2×C4×C103C22×C4
FrattiniC2×Q8C22×D103
Fitting#355×C103C2
socleC2×C103C2×#99
prime radicalC2×D4×D103C4
cosocleC2×Q8×C103C23
hypercenter#355D103
hypocenterC103C2×#355
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D103C2semidirect
3. #20267588C2semidirect
4. #20267587C2semidirect
5. #355×C103C2semidirect
15. #15692940C22semidirect
18. #101×C103C22semidirect
90. D103#355direct (N × H)
92. C103C2×#355semidirect
97. #355D103direct (N × H)
110. #101C2×D103semidirect

Maximal subgroups

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

subgroupindex
#124×D1032
#101×D1032
#202675882
#202675872
#355×C1032
C2×#355103