Finite Group Databasebeta

← #36352803

Subgroups — #36352803

Order 22144.

194 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 55 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#26012219C211yesmaximal, characteristic
2#26011894C211yesmaximal, characteristic
3#26011773C211yesmaximal, characteristic
4#26011238C211yesmaximal, characteristic
5Q8⋊#13063436C211yesmaximal, characteristic
6#26011221C211yesmaximal, characteristic
7#462×C173C211yesmaximal, characteristic
8#19149679C2211yescharacteristic
9#19149677—21no—
10#19149671—21no—
11#19149669—22no—
12C4×Dic346—21no—
13C4×Dic346C2211yescharacteristic
14#19149644—21no—
15#19149612—22no—
16#19149610—21no—
17C4⋊#13063436C2211yescharacteristic
18#19149602—21no—
19C4×#13063436C2211yescharacteristic
20C2×Q16×C173—21no—
21C4⋊Q8×C173C2211yescharacteristic
22C4×Q8×C173C2211yescharacteristic
23C4⋊C8×C173C2211yescharacteristic
24#103×C173—21no—
25C2×Dic346—21no—
26C2×Dic346D411yescharacteristic
27C2×#13063436—21no—
28C2×#13063436—21no—
29C4⋊Dic173—21no—
30C4⋊Dic173D411yescharacteristic
31C4⋊Dic173D412yes—
32#14583805—22no—
33#14583805—22no—
34#14583805—22no—
35#14583805—21no—
36C4×Dic173—22no—
37C4×Dic173—21no—
38C2×Q8×C173—21no—
39C2×Q8×C173D411yescharacteristic
40Q16×C173—42no—
41C2×C8×C173—21no—
42C4⋊C4×C173—21no—
43C4⋊C4×C173—21no—
44C4⋊C4×C173—21no—
45C4⋊C4×C173D411yescharacteristic
46C42×C173—21no—
47C42×C173C2311yescharacteristic
48Dic346—21no—
49Dic346—41no—
50Dic346—41no—
51Dic346Q1612yescomplemented
52C2×Dic173—21no—
53C2×Dic173—22no—
54C2×Dic173—21no—
55#13063436—22no—
56#13063436—41no—
57Q8×C173—21no—
58Q8×C173—21no—
59Q8×C173—41no—
60Q8×C173—41no—
61C2×C4×C173—21no—
62C2×C4×C173—21no—
63C2×C4×C173—41no—
64C2×C4×C173C2×D411yescharacteristic
65C2×C4×C173C2×D411yescharacteristic
66C2×C4×C173C2×D411yescharacteristic
67C8×C173—41no—
68C22×C173#12011yescharacteristic
69C4×C173—21no—
70C4×C173—41no—
71C4×C173—41no—
72C4×C173—81no—
73C4×C173C2×Q1611yescharacteristic
74C4×C173#13511yescharacteristic
75C4×C173AGL(1,ℤ/8)11yescharacteristic
76C4×C173#13711yescharacteristic
77Dic173—22no—
78Dic173—42no—
79Dic173—41no—
80C2×C173#44911yescharacteristic
81C2×C173#45111yescharacteristic
82C2×C173#45611yescharacteristic
83C173#164811yescharacteristic, complemented, Sylow
84#1648—1731nomaximal, Sylow
85#557—1731no—
86#500—1731no—
87#475—1731no—
88#462D17311yescharacteristic
89#332—1731no—
90Q8⋊C8—1731no—
91Q8⋊C8—1731no—
92C2×Q16—21no—
93C4⋊Q8—3461no—
94C4⋊Q8—1731no—
95C4⋊Q8C2×D17311yescharacteristic
96#125—3461no—
97#125—3462no—
98C4×Q8—3461no—
99C4×Q8—3461no—
100C4×Q8—1731no—
101C4×Q8C2×D17311yescharacteristic
102#107—3462no—
103#106—3461no—
104C4⋊C8—1731no—
105C4⋊C8C2×D17311yescharacteristic
106#103—21no—
107#103—3461no—
108C4×C8—1731no—
109C2×Q8—21no—
110C2×Q8—3461no—
111C2×Q8—1731no—
112C2×Q8C22⋊D17311yescharacteristic
113Q16—42no—
114C2×C8—21no—
115C2×C8—3461no—
116C2×C8—3461no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—3462no—
121C4⋊C4—3462no—
122C4⋊C4—3462no—
123C4⋊C4—3461no—
124C4⋊C4—3461no—
125C4⋊C4—1731no—
126C4⋊C4—1732no—
127C4⋊C4C22⋊D17311yescharacteristic
128C42—21no—
129C42—3462no—
130C42—3461no—
131C42C22×D17311yescharacteristic
132Q8—21no—
133Q8—21no—
134Q8—41no—
135Q8—41no—
136Q8—3461no—
137Q8—1732no—
138Q8—6921no—
139Q8—6921no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—3461no—
144C2×C4—3461no—
145C2×C4—3462no—
146C2×C4D4×D17311yescharacteristic
147C2×C4D4×D17311yescharacteristic
148C2×C4C2×C22⋊D17311yescharacteristic
149C8—41no—
150C8—3462no—
151C8—6921no—
152C22#1914964711yescharacteristic
153C4—21no—
154C4—41no—
155C4—41no—
156C4—81no—
157C4—3462no—
158C4—6921no—
159C4—6922no—
160C4Q16×D17311yescharacteristic
161C4#1914969911yescharacteristic
162C4#1914970511yescharacteristic
163C4#1914971111yescharacteristic
164C2#2601163411yescharacteristic
165C2#2601164511yescharacteristic
166C2#2601167211yescharacteristic
subgroupG/H
centerC22#19149647
commutator, cosocleC42×C173C23
FrattiniC42C22×D173
Fitting#462×C173C2
socle, prime radicalC22×C173#120
hypercenter#462D173
hypocenterC173#1648
LCSG ▷ C42×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
51. Dic346Q16semidirect
83. C173#1648semidirect

Maximal subgroups

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

subgroupindex
#260122192
#260118942
#260117732
#260112382
Q8⋊#130634362
#260112212
#462×C1732
#1648173