Finite Group Databasebeta

← #16830938

Subgroups — #16830938

Order 3712.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#14271775C211yesmaximal, characteristic, complemented
2#14271467C212yesmaximal, complemented
3#14271463C212yesmaximal, complemented
4#14271407C212yesmaximal, complemented
5#14271390C212yesmaximal, complemented
6#14271368C212yesmaximal, complemented
7#14271360C212yesmaximal, complemented
8#14271190C211yesmaximal, characteristic, complemented
9C29×#540C211yesmaximal, characteristic
10C29×#127C2211yescharacteristic
11C29×#125C2211yescharacteristic
12C29×#123—22no—
13C29×#121—22no—
14C29×#121C2212yes—
15C4×D4×C29C2212yes—
16C29×#117C2211yescharacteristic
17C2×#90783C2212yes—
18C2×#90783C2212yes—
19#11745286C2212yes—
20C2×#90777C2211yescharacteristic
21C22×#6597C2211yescharacteristic
22#11745251—22no—
23#11745241—22no—
24#11745232C2211yescharacteristic
25#11745231C2211yescharacteristic
26C4×Dic58C2212yes—
27#11745180C2212yes—
28#11745180C2212yes—
29#11745158C2212yes—
30#11745158C2212yes—
31#11745156C2212yes—
32#11745155C2212yes—
33C4⋊#6597C2212yes—
34C4⋊#6597C2212yes—
35C2×D4×C29—22no—
36C2×D4×C29—22no—
37C2×D4×C29C2312yes—
38C22×C4×C29—22no—
39C22×C4×C29C2311yescharacteristic
40C2×Dic58C2312yes—
41C4⋊C4×C29—22no—
42C4⋊C4×C29D412yes—
43C4⋊C4×C29C2312yes—
44C22⋊C4×C29—22no—
45C22⋊C4×C29—22no—
46C22⋊C4×C29D412yes—
47C42×C29C2311yescharacteristic
48C42×C29C2311yescharacteristic
49C22⋊Dic29—22no—
50#90783—42no—
51#90783—42no—
52C4⋊Dic29—22no—
53C4⋊Dic29C2312yes—
54#90779—22no—
55#90779—22no—
56#90779—22no—
57C4×Dic29—22no—
58#90777—41no—
59C2×#6597—41no—
60C2×#6597C2312yes—
61C2×#6597C2312yes—
62C23×C29—22no—
63C23×C29C2×D411yescharacteristic
64D4×C29—22no—
65D4×C29—22no—
66D4×C29—82no—
67D4×C29—82no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29—22no—
71C2×C4×C29—82no—
72C2×C4×C29C2×D412yes—
73C2×C4×C29C2×D411yescharacteristic
74C2×C4×C29C2×D412yes—
75C2×C4×C29C2411yescharacteristic
76C2×Dic29—22no—
77C2×Dic29—22no—
78Dic58—22no—
79Dic58—22no—
80#6597—22no—
81#6597—22no—
82#3260—291nomaximal, Sylow
83C22×C29—21no—
84C22×C29—22no—
85C22×C29—42no—
86C22×C29—42no—
87C22×C29—42no—
88C22×C29C22×D411yescharacteristic
89C4×C29—21no—
90C4×C29—22no—
91C4×C29—22no—
92C4×C29—42no—
93C4×C29H(5,𝔽2)11yescharacteristic
94C4×C292−1+411yescharacteristic
95Dic29—42no—
96Dic29—42no—
97#541—291no—
98#540D2911yescharacteristic
99#479—292no—
100#478—292no—
101#468—292no—
102#465—292no—
103#461—292no—
104#460—292no—
105#424—291no—
106C2×C29—41no—
107C2×C29—82no—
108C2×C29#53711yescharacteristic
109C2×C29#57712yes—
110C2×SD16—292no—
111C2×SD16—292no—
112C2×M16—291no—
113C22×C8—291no—
114C4⋊Q8—291no—
115#127C2×D2911yescharacteristic
116#126—582no—
117#125—291no—
118#125—582no—
119#125C2×D2911yescharacteristic
120#123—22no—
121C22⋊Q8—292no—
122#121—22no—
123#121C2×D2912yes—
124C4×Q8—292no—
125C4×D4C2×D2912yes—
126#117C2×D2911yescharacteristic
127#107—292no—
128#106—292no—
129C4⋊C8—292no—
130C4⋊C8—292no—
131#103—292no—
132#103—292no—
133#102—292no—
134#102—292no—
135C29#326011yescharacteristic, complemented, Sylow
136C2×Q8—292no—
137C2×D4—22no—
138C2×D4—22no—
139C2×D4C22×D2912yes—
140C22×C4—22no—
141C22×C4C22×D2911yescharacteristic
142SD16—1162no—
143SD16—1162no—
144M16—1161no—
145C2×C8—292no—
146C2×C8—292no—
147C2×C8—1161no—
148C4⋊C4—22no—
149C4⋊C4—292no—
150C4⋊C4—582no—
151C4⋊C4—582no—
152C4⋊C4—582no—
153C4⋊C4—582no—
154C4⋊C4C22⋊D2912yes—
155C4⋊C4C22×D2912yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—582no—
159C22⋊C4C22⋊D2912yes—
160C42—582no—
161C42C22×D2911yescharacteristic
162C42C22×D2911yescharacteristic
163C23—22no—
164C23C2×C22⋊D2911yescharacteristic
165Q8—582no—
166Q8—582no—
167D4—22no—
168D4—22no—
169D4—82no—
170D4—82no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—82no—
175C2×C4—582no—
176C2×C4—582no—
177C2×C4C2×C22⋊D2912yes—
178C2×C4C2×C22⋊D2912yes—
179C2×C4C2×C22⋊D2911yescharacteristic
180C2×C4C23×D2911yescharacteristic
181C8—582no—
182C8—582no—
183C22—22no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22C22×C22⋊D2911yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—42no—
193C4—1162no—
194C4—1162no—
195C4#1174536411yescharacteristic
196C4#1174536511yescharacteristic
197C2—41no—
198C2—82no—
199C2#1427174111yescharacteristic
200C2#1427197412yes—
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC29×#540C2
socleC22×C29C22×D4
hypercenter#540D29
hypocenterC29#3260
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #14271775C2semidirect
2. #14271467C2semidirect
3. #14271463C2semidirect
4. #14271407C2semidirect
5. #14271390C2semidirect
6. #14271368C2semidirect
7. #14271360C2semidirect
8. #14271190C2semidirect
135. C29#3260semidirect

Maximal subgroups

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

subgroupindex
#142717752
#142714672
#142714632
#142714072
#142713902
#142713682
#142713602
#142711902
C29×#5402
#326029