Finite Group Databasebeta

← #16830947

Subgroups — #16830947

Order 3712.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#14271780C212yesmaximal, complemented
2#14271457C212yesmaximal, complemented
3#14271441C212yesmaximal, complemented
4#14271407C212yesmaximal, complemented
5#14271404C211yesmaximal, characteristic, complemented
6#14271384C212yesmaximal, complemented
7#14271376C212yesmaximal, complemented
8#14271189C211yesmaximal, characteristic, complemented
9C29×#466C211yesmaximal, characteristic
10C2×D8×C29C2211yescharacteristic
11C22×C8×C29C2211yescharacteristic
12C29×#121C2212yes—
13#11745298—22no—
14#11745298C2212yes—
15#11745297—22no—
16D4×Dic29C2212yes—
17C2×#90783C2212yes—
18#11745288C2211yescharacteristic
19#11745286C2212yes—
20C2×#90777C2211yescharacteristic
21C2×Dic116C2211yescharacteristic
22#11745250C2212yes—
23#11745249C2212yes—
24#11745241—22no—
25#11745240—22no—
26C29×#107C2211yescharacteristic
27C29×#102C2212yes—
28#11745180C2212yes—
29#11745166C2211yescharacteristic
30#11745164C2212yes—
31#11745162C2212yes—
32#11745162C2212yes—
33#11745158C2212yes—
34#11745155C2212yes—
35C2×D4×C29—22no—
36C2×D4×C29C2312yes—
37C22×C4×C29C2311yescharacteristic
38C22×Dic29—22no—
39C2×Dic58—22no—
40C2×Dic58C2312yes—
41D8×C29—41no—
42C2×C8×C29—41no—
43C2×C8×C29C2311yescharacteristic
44C2×C8×C29C2311yescharacteristic
45C4⋊C4×C29C2312yes—
46C22⋊C4×C29—22no—
47C22⋊Dic29—22no—
48C22⋊Dic29—22no—
49C22⋊Dic29—22no—
50C22⋊Dic29—22no—
51C22⋊Dic29D412yes—
52#90783—42no—
53C4⋊Dic29D411yescharacteristic
54C4⋊Dic29D411yescharacteristic
55C4⋊Dic29C2312yes—
56#90779—22no—
57#90779—22no—
58#90779—22no—
59C4×Dic29—22no—
60C4×Dic29C2312yes—
61#90777—41no—
62C2×#6597C2312yes—
63Dic116—41no—
64C23×C29—22no—
65C23×C29C2×D411yescharacteristic
66D4×C29—22no—
67D4×C29—22no—
68D4×C29—82no—
69C2×C4×C29—21no—
70C2×C4×C29—21no—
71C2×C4×C29—22no—
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2411yescharacteristic
74C2×Dic29—22no—
75C2×Dic29—22no—
76C2×Dic29—82no—
77C2×Dic29C2×D412yes—
78C2×Dic29C2×D412yes—
79Dic58—22no—
80Dic58—22no—
81Dic58—82no—
82C8×C29—21no—
83C8×C29—21no—
84#6597—22no—
85#3262—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—21no—
88C22×C29—21no—
89C22×C29—42no—
90C22×C29—42no—
91C22×C29—42no—
92C22×C29C22×D411yescharacteristic
93C4×C29—21no—
94C4×C29—42no—
95C4×C29H(5,𝔽2)11yescharacteristic
96C4×C292−1+411yescharacteristic
97Dic29—22no—
98Dic29—22no—
99Dic29—42no—
100Dic29—42no—
101#542—292no—
102#477—292no—
103#474—292no—
104#468—292no—
105#467—291no—
106#466D2911yescharacteristic
107#464—292no—
108#463—292no—
109#424—291no—
110C2×C29—41no—
111C2×C29—82no—
112C2×C29#53711yescharacteristic
113C2×C29#57611yescharacteristic
114C2×C29#57811yescharacteristic
115C2×Q16—291no—
116C2×SD16—292no—
117C2×D8C2×D2911yescharacteristic
118C2×M16—291no—
119C22×C8C2×D2911yescharacteristic
120C4⋊Q8—292no—
121#126—582no—
122#124—292no—
123#124—582no—
124#123—582no—
125C22⋊Q8—292no—
126C22⋊Q8—582no—
127#121C2×D2912yes—
128C4×Q8—292no—
129C4×D4—292no—
130#117—291no—
131#107—291no—
132#107—292no—
133#107C2×D2911yescharacteristic
134C4⋊C8—292no—
135C4⋊C8—292no—
136#103—292no—
137#103—292no—
138#102—292no—
139#102C2×D2912yes—
140C29#326211yescharacteristic, complemented, Sylow
141C2×Q8—292no—
142C2×Q8—582no—
143C2×D4—22no—
144C2×D4C22×D2912yes—
145C22×C4—582no—
146C22×C4C22×D2911yescharacteristic
147Q16—1161no—
148SD16—1162no—
149D8—41no—
150M16—1161no—
151C2×C8—41no—
152C2×C8—292no—
153C2×C8C22×D2911yescharacteristic
154C2×C8C22×D2911yescharacteristic
155C4⋊C4—291no—
156C4⋊C4—291no—
157C4⋊C4—292no—
158C4⋊C4—582no—
159C4⋊C4—582no—
160C4⋊C4—582no—
161C4⋊C4C22×D2912yes—
162C22⋊C4—22no—
163C22⋊C4—292no—
164C22⋊C4—582no—
165C22⋊C4—582no—
166C22⋊C4—582no—
167C22⋊C4—582no—
168C42—292no—
169C42—582no—
170C23—22no—
171C23D4×D2911yescharacteristic
172Q8—582no—
173Q8—582no—
174Q8—2322no—
175D4—22no—
176D4—22no—
177D4—82no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—292no—
182C2×C4—292no—
183C2×C4—582no—
184C2×C4—582no—
185C2×C4—2322no—
186C2×C4D4×D2911yescharacteristic
187C2×C4C23×D2911yescharacteristic
188C8—21no—
189C8—21no—
190C8—582no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C2×D4×D2911yescharacteristic
198C4—21no—
199C4—42no—
200C4—582no—
201C4—582no—
202C4—1162no—
203C4—1162no—
204C4#1174535911yescharacteristic
205C4#1174536511yescharacteristic
206C2—41no—
207C2—82no—
208C2#1427174011yescharacteristic
209C2#1427196411yescharacteristic
210C2#1427197711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC29×#466C2
socleC22×C29C22×D4
hypercenter#466D29
hypocenterC29#3262
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #14271780C2semidirect
2. #14271457C2semidirect
3. #14271441C2semidirect
4. #14271407C2semidirect
5. #14271404C2semidirect
6. #14271384C2semidirect
7. #14271376C2semidirect
8. #14271189C2semidirect
140. C29#3262semidirect

Maximal subgroups

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

subgroupindex
#142717802
#142714572
#142714412
#142714072
#142714042
#142713842
#142713762
#142711892
C29×#4662
#326229