Finite Group Databasebeta

← #16818727

Subgroups — #16818727

Order 3712.

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

normal subgroups only

This group has 240 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#14271566C211yesmaximal, characteristic, complemented
2#14271443C211yesmaximal, characteristic, complemented
3#14271368C211yesmaximal, characteristic, complemented
4#14270909C211yesmaximal, characteristic, complemented
5D4⋊#6597C211yesmaximal, characteristic, complemented
6D4⋊#6597C211yesmaximal, characteristic, complemented
7C29×#547C211yesmaximal, characteristic
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×#90783—21no—
17#11745231C2211yescharacteristic
18#11745180—21no—
19#11745158—21no—
20#11745155—22no—
21#11745155—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×Dic58—21no—
35C4⋊C4×C29—22no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29D411yescharacteristic
38C4⋊C4×C29D411yescharacteristic
39C4⋊C4×C29D412yes—
40C22⋊C4×C29—22no—
41C22⋊C4×C29—21no—
42C22⋊C4×C29—21no—
43C42×C29C2311yescharacteristic
44#90783—42no—
45C4⋊Dic29—21no—
46C4⋊Dic29—21no—
47C2×#6597—21no—
48C2×#6597—21no—
49C2×#6597—21no—
50C23×C29—21no—
51C23×C29—21no—
52Q8×C29—41no—
53Q8×C29—41no—
54D4×C29—21no—
55D4×C29—21no—
56D4×C29—21no—
57D4×C29—44no—
58D4×C29D812yes—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—22no—
62C2×C4×C29—44no—
63C2×C4×C29—41no—
64C2×C4×C29—41no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29C2×D411yescharacteristic
68C2×C4×C29C2×D411yescharacteristic
69C2×C4×C29C2×D411yescharacteristic
70C2×Dic29—41no—
71Dic58—41no—
72Dic58—41no—
73#6597—22no—
74#6597—41no—
75#6597—41no—
76#1647—291nomaximal, Sylow
77C22×C29—22no—
78C22×C29—41no—
79C22×C29—41no—
80C22×C29—41no—
81C22×C29—41no—
82C22×C29—41no—
83C22×C29#12011yescharacteristic
84C4×C29—21no—
85C4×C29—41no—
86C4×C29—42no—
87C4×C29—41no—
88C4×C29C2×D811yescharacteristic
89C4×C29#13511yescharacteristic
90C4×C29AGL(1,ℤ/8)11yescharacteristic
91C4×C29#13711yescharacteristic
92Dic29—81no—
93#547D2911yescharacteristic
94#500—291no—
95#474—291no—
96#461—291no—
97#332—291no—
98D4⋊C8—291no—
99D4⋊C8—291no—
100C2×C29—42no—
101C2×C29—81no—
102C2×C29#44711yescharacteristic
103C2×C29#45211yescharacteristic
104C2×C29#45611yescharacteristic
105C2×#41—21no—
106C2×SD16—581no—
107C4⋊Q8—291no—
108C4⋊Q8C2×D2911yescharacteristic
109#123—22no—
110C22⋊Q8—21no—
111#121—21no—
112C4×D4C2×D2911yescharacteristic
113C4×D4C2×D2911yescharacteristic
114C2×C4⋊C4—21no—
115#107—581no—
116#107—582no—
117C4⋊C8—291no—
118C4⋊C8—291no—
119#103—581no—
120#102—581no—
121C4×C8—291no—
122C29#164711yescharacteristic, complemented, Sylow
123#41—42no—
124#41—42no—
125C2×Q8—21no—
126C2×Q8—581no—
127C2×D4—22no—
128C2×D4C22⋊D2911yescharacteristic
129C2×D4C22⋊D2911yescharacteristic
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133SD16—1162no—
134C2×C8—581no—
135C2×C8—581no—
136C2×C8—581no—
137C4⋊C4—22no—
138C4⋊C4—21no—
139C4⋊C4—581no—
140C4⋊C4—581no—
141C4⋊C4C22⋊D2911yescharacteristic
142C4⋊C4C22⋊D2911yescharacteristic
143C4⋊C4C22⋊D2912yes—
144C22⋊C4—22no—
145C22⋊C4—21no—
146C22⋊C4—21no—
147C42C22×D2911yescharacteristic
148C23—21no—
149C23—21no—
150Q8—41no—
151Q8—41no—
152Q8—1161no—
153Q8—1161no—
154D4—21no—
155D4—21no—
156D4—21no—
157D4—44no—
158D4#9078212yes—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—44no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—1161no—
168C2×C4C2×C22⋊D2911yescharacteristic
169C2×C4C2×C22⋊D2911yescharacteristic
170C2×C4C2×C22⋊D2911yescharacteristic
171C8—582no—
172C8—1161no—
173C8—1161no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22#1174531511yescharacteristic
181C4—21no—
182C4—41no—
183C4—42no—
184C4—41no—
185C4—2321no—
186C4C2×#9078211yescharacteristic
187C4#1174529411yescharacteristic
188C4#1174531211yescharacteristic
189C4#1174531311yescharacteristic
190C2—42no—
191C2—81no—
192C2#1427129711yescharacteristic
193C2#1427132511yescharacteristic
194C2#1427134611yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
Fitting, prime radicalC29×#547C2
socleC22×C29#120
hypercenter#547D29
hypocenterC29#1647
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. #14271566C2semidirect
2. #14271443C2semidirect
3. #14271368C2semidirect
4. #14270909C2semidirect
5. D4⋊#6597C2semidirect
6. D4⋊#6597C2semidirect
122. C29#1647semidirect

Maximal subgroups

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

subgroupindex
#142715662
#142714432
#142713682
#142709092
D4⋊#65972
C29×#5472
#164729