Finite Group Databasebeta

← #16818558

Subgroups — #16818558

Order 3712.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#14271833C211yesmaximal, characteristic, complemented
2#14271539C211yesmaximal, characteristic, complemented
3#14271364C211yesmaximal, characteristic, complemented
4#14271359C211yesmaximal, characteristic, complemented
5#14270893C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×#331C211yesmaximal, characteristic, complemented
8C2×#90807—21no—
9C29×#127C2211yescharacteristic
10#11745302—21no—
11#11745301—22no—
12#11745300—21no—
13D4×Dic29—21no—
14C2×#90782—22no—
15C2×D232—21no—
16C2×#90773—21no—
17#11745236C2211yescharacteristic
18C4×D116C2211yescharacteristic
19C4×Dic58C2211yescharacteristic
20C29×C4⋊C8C2211yescharacteristic
21C29×C4⋊C8C2211yescharacteristic
22#11745169—21no—
23#11745169—21no—
24C4×#6597C2211yescharacteristic
25C2×D4×C29—21no—
26C2×D4×C29—21no—
27C2×D4×C29D412yes—
28C2×C22⋊D29—22no—
29C2×C22⋊D29—22no—
30C22×Dic29—22no—
31#90807—42no—
32#90807—42no—
33C2×D116—21no—
34C2×D116—21no—
35C2×D116—21no—
36C2×D116D411yescharacteristic
37C2×C4×D29—21no—
38C2×Dic58D411yescharacteristic
39C2×C8×C29—21no—
40C2×C8×C29—21no—
41C42×C29C2311yescharacteristic
42C22⋊Dic29—22no—
43#90782—44no—
44#90781—21no—
45C4⋊Dic29D411yescharacteristic
46C4⋊Dic29D411yescharacteristic
47#90779—21no—
48C4×Dic29—21no—
49C2×#6597—21no—
50D232—42no—
51#90773—42no—
52C23×C29—22no—
53C22×D29—21no—
54C22×D29—41no—
55D4×C29—42no—
56D4×C29—41no—
57D4×C29—41no—
58D4×C29—41no—
59D4×C29—41no—
60C2×C4×C29C2×D411yescharacteristic
61C2×C4×C29C2×D411yescharacteristic
62C2×C4×C29C2×D411yescharacteristic
63C22⋊D29—44no—
64C22⋊D29—82no—
65C2×Dic29—21no—
66C2×Dic29—21no—
67C2×Dic29—21no—
68C2×Dic29—44no—
69D116—21no—
70D116—21no—
71D116—42no—
72D116—41no—
73D116—41no—
74D116—41no—
75D116—41no—
76C4×D29—41no—
77C4×D29—41no—
78Dic58—21no—
79Dic58D812yescomplemented
80C8×C29—41no—
81C8×C29—41no—
82#6597—22no—
83#1621—291nomaximal, Sylow
84C22×C29—42no—
85C22×C29—42no—
86C22×C29—42no—
87C22×C29#12011yescharacteristic
88C2×D29—41no—
89C2×D29—41no—
90C2×D29—41no—
91C2×D29—81no—
92C2×D29—81no—
93C2×D29—81no—
94C4×C29—21no—
95C4×C29C2×D811yescharacteristic
96C4×C29#13511yescharacteristic
97C4×C29AGL(1,ℤ/8)11yescharacteristic
98C4×C29AGL(1,ℤ/8)11yescharacteristic
99Dic29—22no—
100Dic29—41no—
101Dic29—41no—
102#550—291no—
103#493—291no—
104#460—291no—
105#459—291no—
106#331D2911yescharacteristic, complemented
107Q8⋊C8—291no—
108D4⋊C8—291no—
109C2×C29—82no—
110C2×C29#44711yescharacteristic
111C2×C29#44911yescharacteristic
112C2×C29#45311yescharacteristic
113D29—81no—
114D29—161no—
115C2×#41—581no—
116C2×SD16—581no—
117C2×D8—581no—
118C2×D8—582no—
119#127—291no—
120#127—581no—
121#127C2×D2911yescharacteristic
122#121—581no—
123#121—582no—
124C4×Q8—291no—
125C4×D4—291no—
126C4×D4—581no—
127C4⋊C8C2×D2911yescharacteristic
128C4⋊C8C2×D2911yescharacteristic
129#102—581no—
130#102—581no—
131C4×C8—291no—
132C29#162111yescharacteristic, complemented, Sylow
133#41—1162no—
134#41—1162no—
135C2×Q8—291no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—291no—
139C2×D4—582no—
140C2×D4—582no—
141C2×D4—581no—
142C2×D4—581no—
143C2×D4—581no—
144C2×D4D11612yes—
145C22×C4—582no—
146C22×C4—581no—
147SD16—1162no—
148D8—1162no—
149D8—1164no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—581no—
153C4⋊C4—291no—
154C4⋊C4—291no—
155C4⋊C4—581no—
156C22⋊C4—582no—
157C22⋊C4—581no—
158C42—581no—
159C42C22×D2911yescharacteristic
160C23—22no—
161C23—581no—
162C23—1161no—
163Q8—292no—
164Q8—581no—
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—581no—
171D4—581no—
172D4—1162no—
173D4—1164no—
174D4—1161no—
175D4—1161no—
176D4—1161no—
177D4—1161no—
178D4—2322no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—581no—
182C2×C4—1164no—
183C2×C4—1161no—
184C2×C4—1161no—
185C2×C4C2×D11611yescharacteristic
186C2×C4D4×D2911yescharacteristic
187C2×C4D4×D2911yescharacteristic
188C8—41no—
189C8—41no—
190C8—582no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—1161no—
195C22—1161no—
196C22—1161no—
197C22—2321no—
198C22—2321no—
199C22—2321no—
200C22#1174524411yescharacteristic
201C4—21no—
202C4—582no—
203C4—1161no—
204C4—1161no—
205C4D8×D2911yescharacteristic
206C4#1174527311yescharacteristic
207C4#1174527611yescharacteristic
208C4#1174527811yescharacteristic
209C2—82no—
210C2—4641no—
211C2—2321no—
212C2#1427129811yescharacteristic
213C2#1427130911yescharacteristic
214C2#1427133311yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#331C2
socleC22×C29#120
hypercenter#331D29
hypocenterC29#1621
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #14271833C2semidirect
2. #14271539C2semidirect
3. #14271364C2semidirect
4. #14271359C2semidirect
5. #14270893C2semidirect
6. #14270890C2semidirect
7. C29×#331C2semidirect
79. Dic58D8semidirect
106. #331D29semidirect
132. C29#1621semidirect

Maximal subgroups

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

subgroupindex
#142718332
#142715392
#142713642
#142713592
#142708932
#142708902
C29×#3312
#162129