Finite Group Databasebeta

← #16830933

Subgroups — #16830933

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#14271768C211yesmaximal, characteristic
2#14271470C212yesmaximal, complemented
3#14271460C212yesmaximal, complemented
4#14271411C212yesmaximal, complemented
5#14271394C212yesmaximal, complemented
6#14271365C212yesmaximal, complemented
7#14271363C212yesmaximal, complemented
8#14271190C211yesmaximal, characteristic, complemented
9C29×#541C211yesmaximal, characteristic, complemented
10C29×C4⋊Q8C2211yescharacteristic
11C29×#126—22no—
12C29×#125—22no—
13C29×#125C2211yescharacteristic
14C29×C22⋊Q8C2212yes—
15C4×Q8×C29C2212yes—
16C29×#117C2211yescharacteristic
17C2×#90784C2212yes—
18C2×#90784C2212yes—
19#11745292C2212yes—
20C2×#90777C2211yescharacteristic
21C22×#6597C2211yescharacteristic
22#11745256—22no—
23#11745246—22no—
24#11745236C2211yescharacteristic
25C4×D116C2212yes—
26#11745232C2211yescharacteristic
27#11745183C2212yes—
28#11745183C2212yes—
29#11745157C2212yes—
30#11745157C2212yes—
31#11745156C2212yes—
32#11745155C2212yes—
33C4⋊#6597C2212yes—
34C4⋊#6597C2212yes—
35C2×Q8×C29C2312yes—
36C22×C4×C29C2311yescharacteristic
37C2×C22⋊D29—22no—
38C2×D116—22no—
39C2×D116C2312yes—
40C2×C4×D29—22no—
41C4⋊C4×C29—22no—
42C4⋊C4×C29—22no—
43C4⋊C4×C29—22no—
44C4⋊C4×C29—22no—
45C4⋊C4×C29D412yes—
46C4⋊C4×C29C2312yes—
47C22⋊C4×C29—22no—
48C22⋊C4×C29D412yes—
49C42×C29—22no—
50C42×C29C2311yescharacteristic
51C42×C29C2311yescharacteristic
52#90784—42no—
53#90784—42no—
54#90781—22no—
55#90781—22no—
56C4⋊Dic29C2312yes—
57#90779—22no—
58#90777—41no—
59C2×#6597—41no—
60C2×#6597C2312yes—
61C2×#6597C2312yes—
62C23×C29C2×D411yescharacteristic
63C22×D29—22no—
64Q8×C29—22no—
65Q8×C29—22no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—22no—
69C2×C4×C29—22no—
70C2×C4×C29C2×D412yes—
71C2×C4×C29C2×D411yescharacteristic
72C2×C4×C29C2×D412yes—
73C2×C4×C29C2411yescharacteristic
74C22⋊D29—82no—
75C2×Dic29—22no—
76D116—22no—
77D116—22no—
78D116—82no—
79C4×D29—82no—
80#6597—22no—
81#6597—22no—
82#3260—291nomaximal, Sylow
83C22×C29—21no—
84C22×C29—22no—
85C22×C29C22×D411yescharacteristic
86C2×D29—42no—
87C2×D29—42no—
88C2×D29—42no—
89C4×C29—21no—
90C4×C29—22no—
91C4×C29—22no—
92C4×C29—42no—
93C4×C29—42no—
94C4×C29H(5,𝔽2)11yescharacteristic
95C4×C292−1+411yescharacteristic
96Dic29—42no—
97#541D2911yescharacteristic, complemented
98#540—291no—
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#53711yescharacteristic
108C2×C29#57712yes—
109D29—82no—
110C2×SD16—292no—
111C2×SD16—292no—
112C2×M16—291no—
113C22×C8—291no—
114C4⋊Q8C2×D2911yescharacteristic
115#127—291no—
116#126—22no—
117#125—22no—
118#125—291no—
119#125C2×D2911yescharacteristic
120#123—582no—
121C22⋊Q8C2×D2912yes—
122#121—292no—
123#121—582no—
124C4×Q8C2×D2912yes—
125C4×D4—292no—
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×Q8C22×D2912yes—
137C2×D4—292no—
138C2×D4—582no—
139C2×D4—582no—
140C22×C4—582no—
141C22×C4C22×D2911yescharacteristic
142SD16—1162no—
143SD16—1162no—
144M16—1161no—
145C2×C8—292no—
146C2×C8—292no—
147C2×C8—1161no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—292no—
153C4⋊C4—582no—
154C4⋊C4C22⋊D2912yes—
155C4⋊C4C22×D2912yes—
156C22⋊C4—22no—
157C22⋊C4—582no—
158C22⋊C4—582no—
159C22⋊C4C22⋊D2912yes—
160C42—22no—
161C42C22×D2911yescharacteristic
162C42C22×D2911yescharacteristic
163C23—582no—
164C23C2×C22⋊D2911yescharacteristic
165Q8—22no—
166Q8—22no—
167D4—582no—
168D4—582no—
169D4—2322no—
170D4—2322no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—582no—
176C2×C4—2322no—
177C2×C4C2×C22⋊D2912yes—
178C2×C4C2×C22⋊D2912yes—
179C2×C4C2×C22⋊D2911yescharacteristic
180C2×C4C23×D2911yescharacteristic
181C8—582no—
182C8—582no—
183C22—22no—
184C22—21no—
185C22—1162no—
186C22—1162no—
187C22—1162no—
188C22C22×C22⋊D2911yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—42no—
193C4—42no—
194C4—1162no—
195C4#1174536411yescharacteristic
196C4#1174536511yescharacteristic
197C2—41no—
198C2—2322no—
199C2#1427174111yescharacteristic
200C2#1427197112yes—
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#541C2
socleC22×C29C22×D4
prime radical#14271768C2
hypercenter#541D29
hypocenterC29#3260
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #14271470C2semidirect
3. #14271460C2semidirect
4. #14271411C2semidirect
5. #14271394C2semidirect
6. #14271365C2semidirect
7. #14271363C2semidirect
8. #14271190C2semidirect
9. C29×#541C2semidirect
97. #541D29semidirect
135. C29#3260semidirect

Maximal subgroups

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

subgroupindex
#142717682
#142714702
#142714602
#142714112
#142713942
#142713652
#142713632
#142711902
C29×#5412
#326029