Finite Group Databasebeta

← #16818557

Subgroups — #16818557

Order 3712.

278 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 61 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#14271539C211yesmaximal, characteristic, complemented
2#14271363C211yesmaximal, characteristic, complemented
3#14271358C211yesmaximal, characteristic, complemented
4#14270907C211yesmaximal, characteristic, complemented
5Q8⋊#6597C211yesmaximal, characteristic, complemented
6D4⋊#6597C211yesmaximal, characteristic, complemented
7C29×#550C211yesmaximal, characteristic, complemented
8C2×#41×C29—21no—
9C29×#127—21no—
10C29×#127C2211yescharacteristic
11C29×#121—22no—
12C29×#121—21no—
13C4×Q8×C29C2211yescharacteristic
14C4×D4×C29—21no—
15C4×D4×C29C2211yescharacteristic
16C2×#90784—21no—
17C2×#90782—22no—
18C2×#90782—21no—
19#11745236C2211yescharacteristic
20#11745157—21no—
21#11745157—21no—
22C4⋊#6597C2211yescharacteristic
23C4⋊#6597C2211yescharacteristic
24C4×#6597C2211yescharacteristic
25#41×C29—42no—
26#41×C29—42no—
27C2×Q8×C29D411yescharacteristic
28C2×D4×C29—22no—
29C2×D4×C29—22no—
30C2×D4×C29—21no—
31C2×D4×C29—21no—
32C2×D4×C29D411yescharacteristic
33C2×D4×C29D412yes—
34C22×C4×C29—22no—
35C22×C4×C29—21no—
36C2×D116—21no—
37C2×D116—21no—
38C2×D116—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29D411yescharacteristic
41C4⋊C4×C29D411yescharacteristic
42C22⋊C4×C29—22no—
43C22⋊C4×C29—21no—
44C42×C29—21no—
45C42×C29C2311yescharacteristic
46#90784—42no—
47#90782—44no—
48#90782—42no—
49C2×#6597—21no—
50C2×#6597—21no—
51C2×#6597—21no—
52C23×C29—21no—
53C23×C29—22no—
54C22×D29—41no—
55Q8×C29—21no—
56Q8×C29D812yescomplemented
57D4×C29—21no—
58D4×C29—21no—
59D4×C29—42no—
60D4×C29—44no—
61D4×C29—41no—
62D4×C29—41no—
63D4×C29—41no—
64D4×C29—41no—
65D4×C29—82no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—21no—
69C2×C4×C29—44no—
70C2×C4×C29—41no—
71C2×C4×C29—41no—
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2×D411yescharacteristic
74C2×C4×C29C2×D411yescharacteristic
75D116—42no—
76D116—41no—
77D116—41no—
78D116—41no—
79D116—41no—
80#6597—22no—
81#6597—41no—
82#6597—41no—
83#1621—291nomaximal, Sylow
84C22×C29—42no—
85C22×C29—41no—
86C22×C29—41no—
87C22×C29—42no—
88C22×C29—42no—
89C22×C29—41no—
90C22×C29#12011yescharacteristic
91C2×D29—81no—
92C2×D29—81no—
93C2×D29—81no—
94C4×C29—22no—
95C4×C29—21no—
96C4×C29—41no—
97C4×C29—41no—
98C4×C29C2×D811yescharacteristic
99C4×C29#13511yescharacteristic
100C4×C29AGL(1,ℤ/8)11yescharacteristic
101C4×C29AGL(1,ℤ/8)11yescharacteristic
102#550D2911yescharacteristic, complemented
103#493—291no—
104#460—291no—
105#459—291no—
106#331—291no—
107Q8⋊C8—291no—
108D4⋊C8—291no—
109C2×C29—81no—
110C2×C29—82no—
111C2×C29#44711yescharacteristic
112C2×C29#44911yescharacteristic
113C2×C29#45311yescharacteristic
114D29—161no—
115C2×#41—21no—
116C2×SD16—581no—
117C2×D8—581no—
118C2×D8—582no—
119#127—21no—
120#127—291no—
121#127C2×D2911yescharacteristic
122#121—22no—
123#121—21no—
124C4×Q8C2×D2911yescharacteristic
125C4×D4—21no—
126C4×D4C2×D2911yescharacteristic
127C4⋊C8—291no—
128C4⋊C8—291no—
129#102—581no—
130#102—581no—
131C4×C8—291no—
132C29#162111yescharacteristic, complemented, Sylow
133#41—42no—
134#41—42no—
135C2×Q8C22⋊D2911yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—581no—
141C2×D4—581no—
142C2×D4—581no—
143C2×D4C22⋊D2911yescharacteristic
144C2×D4C22⋊D2912yes—
145C22×C4—22no—
146C22×C4—21no—
147SD16—1162no—
148D8—1164no—
149D8—1162no—
150C2×C8—581no—
151C2×C8—581no—
152C2×C8—581no—
153C4⋊C4—21no—
154C4⋊C4C22⋊D2911yescharacteristic
155C4⋊C4C22⋊D2911yescharacteristic
156C22⋊C4—22no—
157C22⋊C4—21no—
158C42—21no—
159C42C22×D2911yescharacteristic
160C23—21no—
161C23—22no—
162C23—1161no—
163Q8—21no—
164Q8#9078212yescomplemented
165D4—21no—
166D4—21no—
167D4—42no—
168D4—44no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—82no—
174D4—1162no—
175D4—1161no—
176D4—1161no—
177D4—1161no—
178D4—1161no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—44no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4C2×C22⋊D2911yescharacteristic
186C2×C4C2×C22⋊D2911yescharacteristic
187C2×C4C2×C22⋊D2911yescharacteristic
188C8—582no—
189C8—1161no—
190C8—1161no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22—42no—
195C22—42no—
196C22—41no—
197C22—2321no—
198C22—2321no—
199C22—2321no—
200C22#1174531511yescharacteristic
201C4—22no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4C2×#9078211yescharacteristic
206C4#1174529411yescharacteristic
207C4#1174531111yescharacteristic
208C4#1174531211yescharacteristic
209C2—81no—
210C2—82no—
211C2—4641no—
212C2#1427129711yescharacteristic
213C2#1427130811yescharacteristic
214C2#1427133111yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#550C2
socleC22×C29#120
hypercenter#550D29
hypocenterC29#1621
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #14271539C2semidirect
2. #14271363C2semidirect
3. #14271358C2semidirect
4. #14270907C2semidirect
5. Q8⋊#6597C2semidirect
6. D4⋊#6597C2semidirect
7. C29×#550C2semidirect
56. Q8×C29D8semidirect
102. #550D29semidirect
132. C29#1621semidirect
164. Q8#90782semidirect

Maximal subgroups

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

subgroupindex
#142715392
#142713632
#142713582
#142709072
Q8⋊#65972
D4⋊#65972
C29×#5502
#162129