Finite Group Databasebeta

← #16818559

Subgroups — #16818559

Order 3712.

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

normal subgroups only

This group has 278 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#14271835C211yesmaximal, characteristic, complemented
2#14271540C211yesmaximal, characteristic, complemented
3#14271363C211yesmaximal, characteristic, complemented
4#14271359C211yesmaximal, characteristic, complemented
5#14270906C211yesmaximal, characteristic, complemented
6#14270892C211yesmaximal, characteristic, complemented
7C29×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#90809—21no—
9C4×Q8×C29C2211yescharacteristic
10C2×#90784—21no—
11C2×D232—22no—
12C2×D232—21no—
13#11745257—22no—
14#11745257—21no—
15#11745236—21no—
16#11745236C2211yescharacteristic
17#11745236C2211yescharacteristic
18C4×D116—21no—
19C4×D116C2211yescharacteristic
20C29×C4⋊C8C2211yescharacteristic
21C4×C8×C29C2211yescharacteristic
22#11745169—21no—
23#11745157—21no—
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29D411yescharacteristic
26#90809—42no—
27#90809—42no—
28C2×D116—22no—
29C2×D116—21no—
30C2×D116—21no—
31C2×D116—21no—
32C2×D116—21no—
33C2×D116—21no—
34C2×D116—22no—
35C2×D116D411yescharacteristic
36C2×D116D412yes—
37C2×C4×D29—22no—
38C2×C4×D29—21no—
39C2×C8×C29—21no—
40C2×C8×C29—21no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29D411yescharacteristic
43C42×C29—21no—
44C42×C29C2311yescharacteristic
45#90784—42no—
46#90781—22no—
47#90781—21no—
48C4⋊Dic29D411yescharacteristic
49C2×#6597—21no—
50D232—44no—
51D232—42no—
52C22×D29—21no—
53C22×D29—22no—
54C22×D29—41no—
55Q8×C29—21no—
56Q8×C29D812yescomplemented
57C2×C4×C29—21no—
58C2×C4×C29—21no—
59C2×C4×C29C2×D411yescharacteristic
60C2×C4×C29C2×D411yescharacteristic
61C2×C4×C29C2×D411yescharacteristic
62C2×Dic29—21no—
63D116—21no—
64D116—21no—
65D116—42no—
66D116—44no—
67D116—42no—
68D116—41no—
69D116—41no—
70D116—41no—
71D116—41no—
72D116—41no—
73D116—41no—
74D116—41no—
75D116—41no—
76D116—82no—
77C4×D29—44no—
78C4×D29—41no—
79C4×D29—41no—
80C8×C29—22no—
81C8×C29—41no—
82#6597—41no—
83#1621—291nomaximal, Sylow
84C22×C29#12011yescharacteristic
85C2×D29—42no—
86C2×D29—41no—
87C2×D29—41no—
88C2×D29—42no—
89C2×D29—42no—
90C2×D29—41no—
91C2×D29—81no—
92C2×D29—81no—
93C2×D29—81no—
94C4×C29—22no—
95C4×C29—21no—
96C4×C29—41no—
97C4×C29C2×D811yescharacteristic
98C4×C29#13511yescharacteristic
99C4×C29AGL(1,ℤ/8)11yescharacteristic
100C4×C29AGL(1,ℤ/8)11yescharacteristic
101Dic29—41no—
102#550—291no—
103#493—291no—
104#460—291no—
105#459—291no—
106#331—291no—
107Q8⋊C8D2911yescharacteristic, complemented
108D4⋊C8—291no—
109C2×C29#44711yescharacteristic
110C2×C29#44911yescharacteristic
111C2×C29#45311yescharacteristic
112D29—81no—
113D29—82no—
114D29—161no—
115C2×#41—581no—
116C2×SD16—581no—
117C2×D8—581no—
118C2×D8—582no—
119#127—291no—
120#127—291no—
121#127—581no—
122#121—582no—
123#121—581no—
124C4×Q8C2×D2911yescharacteristic
125C4×D4—291no—
126C4×D4—581no—
127C4⋊C8—291no—
128C4⋊C8C2×D2911yescharacteristic
129#102—581no—
130#102—581no—
131C4×C8C2×D2911yescharacteristic
132C29#162111yescharacteristic, complemented, Sylow
133#41—1162no—
134#41—1162no—
135C2×Q8D11611yescharacteristic
136C2×D4—291no—
137C2×D4—292no—
138C2×D4—582no—
139C2×D4—582no—
140C2×D4—581no—
141C2×D4—581no—
142C2×D4—581no—
143C2×D4—581no—
144C2×D4—581no—
145C22×C4—582no—
146C22×C4—581no—
147SD16—1162no—
148D8—1164no—
149D8—1162no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—581no—
153C4⋊C4—21no—
154C4⋊C4—291no—
155C4⋊C4D11611yescharacteristic
156C22⋊C4—582no—
157C22⋊C4—581no—
158C42—21no—
159C42C22×D2911yescharacteristic
160C23—581no—
161C23—582no—
162C23—1161no—
163Q8—21no—
164Q8D23212yescomplemented
165D4—581no—
166D4—581no—
167D4—1162no—
168D4—1164no—
169D4—1162no—
170D4—1161no—
171D4—1161no—
172D4—1161no—
173D4—1161no—
174D4—1161no—
175D4—1161no—
176D4—1161no—
177D4—1161no—
178D4—2322no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—581no—
182C2×C4—1164no—
183C2×C4—1161no—
184C2×C4—1161no—
185C2×C4C2×D11611yescharacteristic
186C2×C4D4×D2911yescharacteristic
187C2×C4D4×D2911yescharacteristic
188C8—22no—
189C8—41no—
190C8—1161no—
191C22—1162no—
192C22—1161no—
193C22—1161no—
194C22—1162no—
195C22—1162no—
196C22—1161no—
197C22—2321no—
198C22—2321no—
199C22—2321no—
200C22#1174524411yescharacteristic
201C4—22no—
202C4—21no—
203C4—41no—
204C4—1161no—
205C4C2×D23211yescharacteristic
206C4#1174527011yescharacteristic
207C4#1174527611yescharacteristic
208C4#1174528111yescharacteristic
209C2—4641no—
210C2—2321no—
211C2—2322no—
212C2#1427129911yescharacteristic
213C2#1427131111yescharacteristic
214C2#1427133211yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×Q8⋊C8C2
socleC22×C29#120
hypercenterQ8⋊C8D29
hypocenterC29#1621
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #14271835C2semidirect
2. #14271540C2semidirect
3. #14271363C2semidirect
4. #14271359C2semidirect
5. #14270906C2semidirect
6. #14270892C2semidirect
7. C29×Q8⋊C8C2semidirect
56. Q8×C29D8semidirect
107. Q8⋊C8D29semidirect
132. C29#1621semidirect
164. Q8D232semidirect

Maximal subgroups

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

subgroupindex
#142718352
#142715402
#142713632
#142713592
#142709062
#142708922
C29×Q8⋊C82
#162129