Finite Group Databasebeta

← #16817902

Subgroups — #16817902

Order 3712.

234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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#14271695C211yesmaximal, characteristic
2C4⋊C8×D29C211yesmaximal, characteristic, complemented
3C4×#90772C211yesmaximal, characteristic, complemented
4#14270895C211yesmaximal, characteristic, complemented
5#14270893C211yesmaximal, characteristic, complemented
6D4⋊#6597C211yesmaximal, characteristic, complemented
7C29×D4⋊C8C211yesmaximal, characteristic, complemented
8C4×D4×C29C2211yescharacteristic
9#11745300C411yescharacteristic
10#11745298C411yescharacteristic
11C4×C22⋊D29—21no—
12#11745288—21no—
13C2×#90772—21no—
14C2×C8×D29—21no—
15#11745259C411yescharacteristic
16#11745252C411yescharacteristic
17#11745245—21no—
18#11745241—21no—
19C42×D29C2211yescharacteristic
20C4×Dic58C2211yescharacteristic
21C29×C4⋊C8C2211yescharacteristic
22C4×C8×C29C2211yescharacteristic
23#11745163—21no—
24#11745162—21no—
25C4⋊#6597C2211yescharacteristic
26C4×#6597C2211yescharacteristic
27C2×D4×C29C2×C411yescharacteristic
28C22×C4×C29—21no—
29C2×C22⋊D29—21no—
30C2×C4×D29C2×C411yescharacteristic
31C2×C4×D29D411yescharacteristic
32C2×C4×D29D411yescharacteristic
33C2×Dic58C2×C411yescharacteristic
34C2×C8×C29—21no—
35C2×C8×C29—21no—
36C4⋊C4×C29C2×C411yescharacteristic
37C22⋊C4×C29—21no—
38C42×C29C2311yescharacteristic
39C22⋊Dic29—21no—
40C22⋊Dic29—21no—
41C22⋊Dic29—21no—
42#90781—21no—
43C4⋊Dic29—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29C2×C411yescharacteristic
46#90779—21no—
47#90779—21no—
48C4×Dic29—21no—
49C4×Dic29C2×C411yescharacteristic
50C4×Dic29D411yescharacteristic
51C4×Dic29D411yescharacteristic
52C2×#6597—21no—
53C2×#6597—21no—
54#90772—24no—
55C8×D29—42no—
56C23×C29—21no—
57C22×D29C22⋊C411yescharacteristic
58D4×C29—21no—
59D4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29C22×C411yescharacteristic
64C2×C4×C29C2×D411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C22⋊D29—42no—
67C2×Dic29—21no—
68C2×Dic29—21no—
69C2×Dic29C22⋊C411yescharacteristic
70C2×Dic29C22⋊C411yescharacteristic
71C2×Dic29C22⋊C411yescharacteristic
72C4×D29—22no—
73C4×D29—21no—
74C4×D29—21no—
75C4×D29—21no—
76C4×D29—21no—
77Dic58—21no—
78Dic58—21no—
79C8×C29—22no—
80C8×C29—41no—
81#6597—22no—
82#6597—41no—
83#1483—291nomaximal, Sylow
84C22×C29—41no—
85C22×C29—41no—
86C22×C29—41no—
87C22×C29C2×C22⋊C411yescharacteristic
88C2×D29—21no—
89C2×D29—21no—
90C2×D29#10412yes—
91C4×C29—21no—
92C4×C29—41no—
93C4×C29#13111yescharacteristic
94C4×C29#13111yescharacteristic
95C4×C29AGL(1,ℤ/8)11yescharacteristic
96C4×C29#13711yescharacteristic
97Dic29—21no—
98Dic29—21no—
99Dic29—21no—
100Dic29—41no—
101Dic29—41no—
102#529—291no—
103C2×C4⋊C8—291no—
104C4×M16—291no—
105Q8⋊C8—291no—
106Q8⋊C8—291no—
107D4⋊C8—291no—
108D4⋊C8D2911yescharacteristic, complemented
109C2×C29—81no—
110C2×C29#40811yescharacteristic
111C2×C29#41711yescharacteristic
112C2×C29C2×#10411yescharacteristic
113D29—22no—
114C2×M16—581no—
115C22×C8—581no—
116#126—581no—
117#125—291no—
118#124—291no—
119#123—581no—
120C22⋊Q8—291no—
121#121—291no—
122C4×Q8—291no—
123C4×D4—581no—
124C4×D4C2×D2911yescharacteristic
125#117—581no—
126C2×C42—291no—
127C4⋊C8—291no—
128C4⋊C8—581no—
129C4⋊C8C2×D2911yescharacteristic
130#97—581no—
131C4×C8—291no—
132C4×C8C2×D2911yescharacteristic
133C29#148311yescharacteristic, complemented, Sylow
134C2×Q8—291no—
135C2×D4—581no—
136C2×D4C4×D2911yescharacteristic
137C22×C4—21no—
138C22×C4—291no—
139C22×C4—291no—
140C22×C4—291no—
141M16—584no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—581no—
145C2×C8—581no—
146C2×C8—1162no—
147C4⋊C4—291no—
148C4⋊C4—581no—
149C4⋊C4—581no—
150C4⋊C4—581no—
151C4⋊C4—581no—
152C4⋊C4C4×D2911yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—581no—
155C22⋊C4—581no—
156C22⋊C4—581no—
157C22⋊C4—581no—
158C42—291no—
159C42—291no—
160C42—291no—
161C42—581no—
162C42C22×D2911yescharacteristic
163C23—21no—
164C23—291no—
165Q8—581no—
166Q8—581no—
167D4—21no—
168D4—21no—
169D4—1162no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—291no—
174C2×C4—291no—
175C2×C4—291no—
176C2×C4—582no—
177C2×C4—581no—
178C2×C4—581no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—581no—
182C2×C4—581no—
183C2×C4C2×C4×D2911yescharacteristic
184C2×C4D4×D2911yescharacteristic
185C2×C4D4×D2911yescharacteristic
186C8—22no—
187C8—41no—
188C8—582no—
189C8—1161no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—292no—
194C22—581no—
195C22—581no—
196C22C22⋊C4×D2911yescharacteristic
197C4—21no—
198C4—41no—
199C4—581no—
200C4—581no—
201C4—581no—
202C4—1161no—
203C4—1161no—
204C4#1174526311yescharacteristic
205C4#1174526911yescharacteristic
206C4#1174527311yescharacteristic
207C4#1174527711yescharacteristic
208C2—81no—
209C2—582no—
210C2#1427112811yescharacteristic
211C2#1427116111yescharacteristic
212C2#104×D2911yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC42C22×D29
FittingC29×D4⋊C8C2
socleC22×C29C2×C22⋊C4
prime radical#11745300C4
cosocleC42×C29C23
hypercenterD4⋊C8D29
hypocenterC29#1483
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×D29C2semidirect
3. C4×#90772C2semidirect
4. #14270895C2semidirect
5. #14270893C2semidirect
6. D4⋊#6597C2semidirect
7. C29×D4⋊C8C2semidirect
108. D4⋊C8D29semidirect
133. C29#1483semidirect

Maximal subgroups

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

subgroupindex
#142716952
C4⋊C8×D292
C4×#907722
#142708952
#142708932
D4⋊#65972
C29×D4⋊C82
#148329