Finite Group Databasebeta

← #16818809

Subgroups — #16818809

Order 3712.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#14271573C211yesmaximal, characteristic, complemented
2#14271558C211yesmaximal, characteristic, complemented
3#14271522C211yesmaximal, characteristic, complemented
4#14270905C211yesmaximal, characteristic, complemented
5#14270903C211yesmaximal, characteristic, complemented
6#14270903C211yesmaximal, characteristic, complemented
7C29×#562C211yesmaximal, characteristic
8C29×#125C2211yescharacteristic
9C29×#124C2211yescharacteristic
10C29×#124C2211yescharacteristic
11C29×#123—21no—
12C29×#123—21no—
13C29×C22⋊Q8—21no—
14C29×C22⋊Q8—21no—
15C29×#121—21no—
16C29×#121—21no—
17C2×#90785—21no—
18C2×#90783—21no—
19#11745231C2211yescharacteristic
20#11745183—21no—
21#11745180—21no—
22#11745156—21no—
23#11745155—21no—
24#11745151C2211yescharacteristic
25#11745151C2211yescharacteristic
26#11745151C2211yescharacteristic
27C2×Q8×C29D411yescharacteristic
28C2×Q8×C29D411yescharacteristic
29C2×D4×C29—21no—
30C2×D4×C29—21no—
31C2×D4×C29D411yescharacteristic
32C2×D4×C29D411yescharacteristic
33C22×C4×C29—21no—
34C22×C4×C29—21no—
35C2×Dic58—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29D411yescharacteristic
41C4⋊C4×C29D411yescharacteristic
42C22⋊C4×C29—21no—
43C22⋊C4×C29—21no—
44C22⋊C4×C29—21no—
45C22⋊C4×C29—21no—
46C22⋊C4×C29—21no—
47C22⋊C4×C29—21no—
48C42×C29C2311yescharacteristic
49#90785—42no—
50#90783—42no—
51C4⋊Dic29—21no—
52C4⋊Dic29—21no—
53C2×#6597—21no—
54C2×#6597—21no—
55C2×#6597—21no—
56C23×C29—21no—
57C23×C29—21no—
58Q8×C29—41no—
59Q8×C29—41no—
60D4×C29—41no—
61D4×C29—41no—
62D4×C29—81no—
63D4×C29—81no—
64C2×C4×C29—21no—
65C2×C4×C29—21no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—81no—
69C2×C4×C29—81no—
70C2×C4×C29C2×D411yescharacteristic
71C2×C4×C29C2×D411yescharacteristic
72C2×C4×C29C2×D411yescharacteristic
73C2×Dic29—41no—
74Dic58—41no—
75Dic58—41no—
76#6597—22no—
77#6597—22no—
78#6597—41no—
79#1661—291nomaximal, Sylow
80C22×C29—41no—
81C22×C29—41no—
82C22×C29—41no—
83C22×C29—41no—
84C22×C29—41no—
85C22×C29—41no—
86C22×C29#12011yescharacteristic
87C4×C29—21no—
88C4×C29—21no—
89C4×C29—21no—
90C4×C29—41no—
91C4×C29—41no—
92C4×C29—41no—
93C4×C29—41no—
94Dic29—81no—
95#562D2911yescharacteristic
96#501—291no—
97#497—291no—
98#489—291no—
99#330—291no—
100#329—291no—
101#329—291no—
102C2×C29—81no—
103C2×C29—81no—
104C2×C29#45311yescharacteristic
105C2×C29#45511yescharacteristic
106C2×C29#45611yescharacteristic
107C2×Q16—581no—
108C2×SD16—581no—
109C4⋊Q8—291no—
110#125C2×D2911yescharacteristic
111#124C2×D2911yescharacteristic
112#124C2×D2911yescharacteristic
113#123—21no—
114#123—21no—
115C22⋊Q8—21no—
116C22⋊Q8—21no—
117#121—21no—
118#121—21no—
119#107—581no—
120#106—581no—
121#103—581no—
122#102—581no—
123#97—291no—
124#97—291no—
125#97—291no—
126C29#166111yescharacteristic, complemented, Sylow
127C2×Q8—581no—
128C2×Q8C22⋊D2911yescharacteristic
129C2×Q8C22⋊D2911yescharacteristic
130C2×D4—21no—
131C2×D4—21no—
132C2×D4C22⋊D2911yescharacteristic
133C2×D4C22⋊D2911yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136Q16—1162no—
137SD16—1162no—
138C2×C8—581no—
139C2×C8—581no—
140C2×C8—581no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—581no—
146C4⋊C4—581no—
147C4⋊C4C22⋊D2911yescharacteristic
148C4⋊C4C22⋊D2911yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C42C22×D2911yescharacteristic
156C23—21no—
157C23—21no—
158Q8—41no—
159Q8—41no—
160Q8—1161no—
161Q8—1161no—
162D4—41no—
163D4—41no—
164D4—81no—
165D4—81no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4—1161no—
173C2×C4C2×C22⋊D2911yescharacteristic
174C2×C4C2×C22⋊D2911yescharacteristic
175C2×C4C2×C22⋊D2911yescharacteristic
176C8—582no—
177C8—582no—
178C8—1161no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22#1174531511yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—41no—
192C4—41no—
193C4—2321no—
194C2—81no—
195C2—81no—
196C2#1427133111yescharacteristic
197C2#1427134111yescharacteristic
198C2#1427134611yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
Fitting, prime radicalC29×#562C2
socleC22×C29#120
hypercenter#562D29
hypocenterC29#1661
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #14271573C2semidirect
2. #14271558C2semidirect
3. #14271522C2semidirect
4. #14270905C2semidirect
5. #14270903C2semidirect
6. #14270903C2semidirect
126. C29#1661semidirect

Maximal subgroups

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

subgroupindex
#142715732
#142715582
#142715222
#142709052
#142709032
C29×#5622
#166129