Finite Group Databasebeta

← #16818581

Subgroups — #16818581

Order 3712.

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

normal subgroups only

This group has 256 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#14271511C211yesmaximal, characteristic, complemented
2#14271358C211yesmaximal, characteristic, complemented
3#14271358C211yesmaximal, characteristic, complemented
4#14270909C211yesmaximal, characteristic, complemented
5D4⋊#6597C211yesmaximal, characteristic, complemented
6D4⋊#6597C211yesmaximal, characteristic, complemented
7C29×#547C211yesmaximal, characteristic, complemented
8C2×#41×C29—21no—
9C29×C4⋊Q8C2211yescharacteristic
10C29×#123—22no—
11C29×C22⋊Q8—21no—
12C29×#121—21no—
13C4×D4×C29C2211yescharacteristic
14C4×D4×C29C2211yescharacteristic
15C2×C4⋊C4×C29—21no—
16C2×#90782—21no—
17C2×#90782—21no—
18#11745236C2211yescharacteristic
19#11745157—22no—
20#11745157—21no—
21#11745157—21no—
22C4⋊#6597C2211yescharacteristic
23C4⋊#6597C2211yescharacteristic
24C4×#6597C2211yescharacteristic
25#41×C29—42no—
26#41×C29—42no—
27C2×Q8×C29—21no—
28C2×D4×C29—22no—
29C2×D4×C29D411yescharacteristic
30C2×D4×C29D411yescharacteristic
31C22×C4×C29—22no—
32C22×C4×C29—21no—
33C22×C4×C29—21no—
34C2×D116—21no—
35C2×D116—21no—
36C2×D116—21no—
37C4⋊C4×C29—22no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29D411yescharacteristic
40C4⋊C4×C29D411yescharacteristic
41C4⋊C4×C29D412yes—
42C22⋊C4×C29—22no—
43C22⋊C4×C29—21no—
44C22⋊C4×C29—21no—
45C42×C29C2311yescharacteristic
46#90782—42no—
47#90782—42no—
48C2×#6597—21no—
49C2×#6597—21no—
50C2×#6597—21no—
51C23×C29—21no—
52C23×C29—21no—
53C22×D29—41no—
54Q8×C29—41no—
55Q8×C29—41no—
56D4×C29—21no—
57D4×C29—21no—
58D4×C29—21no—
59D4×C29—44no—
60D4×C29D812yescomplemented
61C2×C4×C29—21no—
62C2×C4×C29—21no—
63C2×C4×C29—22no—
64C2×C4×C29—44no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29C2×D411yescharacteristic
71C2×C4×C29C2×D411yescharacteristic
72D116—42no—
73D116—41no—
74D116—41no—
75D116—41no—
76D116—41no—
77#6597—41no—
78#6597—41no—
79#6597—41no—
80#1625—291nomaximal, Sylow
81C22×C29—22no—
82C22×C29—41no—
83C22×C29—41no—
84C22×C29—41no—
85C22×C29—41no—
86C22×C29—41no—
87C22×C29#12011yescharacteristic
88C2×D29—81no—
89C2×D29—81no—
90C2×D29—81no—
91C4×C29—21no—
92C4×C29—41no—
93C4×C29—42no—
94C4×C29—41no—
95C4×C29C2×D811yescharacteristic
96C4×C29#13511yescharacteristic
97C4×C29AGL(1,ℤ/8)11yescharacteristic
98C4×C29AGL(1,ℤ/8)11yescharacteristic
99#547D2911yescharacteristic, complemented
100#486—291no—
101#459—291no—
102#459—291no—
103#332—291no—
104D4⋊C8—291no—
105D4⋊C8—291no—
106C2×C29—42no—
107C2×C29—81no—
108C2×C29#44711yescharacteristic
109C2×C29#44911yescharacteristic
110C2×C29#45411yescharacteristic
111D29—161no—
112C2×#41—21no—
113C2×D8—581no—
114C2×D8—581no—
115C4⋊Q8C2×D2911yescharacteristic
116#127—291no—
117#123—22no—
118C22⋊Q8—21no—
119#121—21no—
120C4×D4C2×D2911yescharacteristic
121C4×D4C2×D2911yescharacteristic
122C2×C4⋊C4—21no—
123C4⋊C8—291no—
124C4⋊C8—291no—
125#102—581no—
126#102—581no—
127#102—582no—
128C4×C8—291no—
129C29#162511yescharacteristic, complemented, Sylow
130#41—42no—
131#41—42no—
132C2×Q8—21no—
133C2×D4—22no—
134C2×D4—581no—
135C2×D4—581no—
136C2×D4—581no—
137C2×D4C22⋊D2911yescharacteristic
138C2×D4C22⋊D2911yescharacteristic
139C22×C4—22no—
140C22×C4—21no—
141C22×C4—21no—
142D8—1162no—
143D8—1162no—
144C2×C8—581no—
145C2×C8—581no—
146C2×C8—581no—
147C4⋊C4—22no—
148C4⋊C4—21no—
149C4⋊C4C22⋊D2911yescharacteristic
150C4⋊C4C22⋊D2911yescharacteristic
151C4⋊C4C22⋊D2912yes—
152C22⋊C4—22no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C42C22×D2911yescharacteristic
156C23—21no—
157C23—21no—
158C23—1161no—
159Q8—41no—
160Q8—41no—
161D4—21no—
162D4—21no—
163D4—21no—
164D4—44no—
165D4—1162no—
166D4—1161no—
167D4—1161no—
168D4—1161no—
169D4—1161no—
170D4#9078212yescomplemented
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—44no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4C2×C22⋊D2911yescharacteristic
180C2×C4C2×C22⋊D2911yescharacteristic
181C2×C4C2×C22⋊D2911yescharacteristic
182C8—1161no—
183C8—1161no—
184C8—1161no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—2321no—
192C22—2321no—
193C22—2321no—
194C22#1174531511yescharacteristic
195C4—21no—
196C4—41no—
197C4—42no—
198C4—41no—
199C4C2×#9078211yescharacteristic
200C4#1174529411yescharacteristic
201C4#1174531111yescharacteristic
202C4#1174531211yescharacteristic
203C2—42no—
204C2—81no—
205C2—4641no—
206C2#1427129711yescharacteristic
207C2#1427130811yescharacteristic
208C2#1427133611yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#547C2
socleC22×C29#120
hypercenter#547D29
hypocenterC29#1625
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14271511C2semidirect
2. #14271358C2semidirect
3. #14271358C2semidirect
4. #14270909C2semidirect
5. D4⋊#6597C2semidirect
6. D4⋊#6597C2semidirect
7. C29×#547C2semidirect
60. D4×C29D8semidirect
99. #547D29semidirect
129. C29#1625semidirect
170. D4#90782semidirect

Maximal subgroups

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

subgroupindex
#142715112
#142713582
#142709092
D4⋊#65972
C29×#5472
#162529