Finite Group Databasebeta

← #16834910

Subgroups — #16834910

Order 3712.

286 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 58 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#14272135C211yesmaximal, characteristic, complemented
2#14272105C211yesmaximal, characteristic, complemented
3#14272017C212yesmaximal, complemented
4#14272015C212yesmaximal, complemented
5#14271676C211yesmaximal, characteristic
6C2×#90809C411yescharacteristic, complemented
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181—21no—
9C2×#90800—21no—
10C2×C4⋊#1181—21no—
11C29×C22⋊Q8C411yescharacteristic, complemented
12#11745308C2211yescharacteristic
13#11745292C411yescharacteristic, complemented
14#11745257C2211yescharacteristic
15#11745256—21no—
16#11745255—21no—
17#11745254C411yescharacteristic, complemented
18#11745244—21no—
19#11745243—21no—
20(C2×#1181)⋊C4C2212yes—
21#11745219—21no—
22#11745219C2212yes—
23C23×D29D411yescharacteristic
24C22×#1181—22no—
25C2×Q8×C29C2×C411yescharacteristic
26C22×C4×C29C2×C411yescharacteristic
27C2×C22⋊D29—21no—
28C22×Dic29D411yescharacteristic
29#90809—42no—
30C2×D116—21no—
31C2×D116—21no—
32C2×D116C2×C411yescharacteristic
33C2×C4×D29—21no—
34C2×C4×D29—42no—
35C2×C4×D29C2×C411yescharacteristic
36C2×C4×D29D411yescharacteristic
37C2×C4×D29D411yescharacteristic
38C2×C4×D29C2311yescharacteristic
39C22⋊#1181—42no—
40#90800—42no—
41C2×#6599—22no—
42C4⋊#1181—42no—
43C4⋊C4×C29—21no—
44C4⋊C4×C29C2×C411yescharacteristic
45C22⋊C4×C29—21no—
46#90781—21no—
47#90781—21no—
48#90781—21no—
49#90781—21no—
50C4⋊Dic29C2×C411yescharacteristic
51#90779—21no—
52C4×Dic29—21no—
53C23×C29C22⋊C411yescharacteristic
54C22×D29—21no—
55C22×D29—21no—
56C22×D29—21no—
57C22×D29—41no—
58C22×D29—41no—
59C22×D29C22⋊C411yescharacteristic
60C22×D29C2×D411yescharacteristic
61C2×#1181—42no—
62C2×#1181—42no—
63C2×#1181—42no—
64Q8×C29—41no—
65C2×C4×C29—21no—
66C2×C4×C29—21no—
67C2×C4×C29—41no—
68C2×C4×C29C22⋊C411yescharacteristic
69C2×C4×C29C22×C411yescharacteristic
70C22⋊D29—42no—
71C2×Dic29—22no—
72C2×Dic29—21no—
73C2×Dic29C22⋊C411yescharacteristic
74C2×Dic29C2×D411yescharacteristic
75D116—41no—
76D116—42no—
77D116—41no—
78D116—41no—
79C4×D29—22no—
80C4×D29—22no—
81C4×D29—41no—
82C4×D29—41no—
83C4×D29—42no—
84#6599—42no—
85#1513—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—21no—
88C22×C29—21no—
89C22×C29C2×C22⋊C411yescharacteristic
90C2×D29—21no—
91C2×D29—21no—
92C2×D29—21no—
93C2×D29—21no—
94C2×D29—21no—
95C2×D29—42no—
96C2×D29—42no—
97C2×D29—41no—
98C2×D29—41no—
99C2×D29—41no—
100C2×D29AGL(1,ℤ/8)11yescharacteristic
101C2×D29#13711yescharacteristic
102#1181—82no—
103C4×C29—21no—
104C4×C29—21no—
105C4×C29—41no—
106C4×C29—41no—
107Dic29—21no—
108Dic29—41no—
109Dic29#9912yes—
110#525—291no—
111#407—291no—
112#380—291no—
113#328—292no—
114#327—292no—
115C2×C29—41no—
116C2×C29C2×#9911yescharacteristic
117C2×C29#41711yescharacteristic
118C2×C29#42111yescharacteristic
119D29—21no—
120D29—21no—
121D29—41no—
122D29—81no—
123C2×#41—291no—
124C23×C4—291no—
125C2×M16—581no—
126#123—581no—
127C22⋊Q8—291no—
128C22⋊Q8#118111yescharacteristic, complemented
129#121—291no—
130#121—291no—
131#120—581no—
132C4×D4—581no—
133C4×D4—581no—
134#117—291no—
135C2×C4⋊C4—581no—
136C2×C22⋊C4—581no—
137C22⋊C8—292no—
138C22⋊C8—581no—
139#95—292no—
140C29#151311yescharacteristic, complemented, Sylow
141C24—291no—
142#41—1162no—
143C2×Q8C2×#118111yescharacteristic
144C2×D4—291no—
145C2×D4—581no—
146C2×D4—581no—
147C2×D4—581no—
148C22×C4—291no—
149C22×C4—291no—
150C22×C4—291no—
151C22×C4—291no—
152C22×C4—291no—
153C22×C4—581no—
154C22×C4—582no—
155C22×C4—1162no—
156C22×C4C2×#118111yescharacteristic
157M16—1162no—
158C2×C8—582no—
159C4⋊C4—21no—
160C4⋊C4—291no—
161C4⋊C4—581no—
162C4⋊C4—1162no—
163C4⋊C4C2×#118111yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—581no—
168C22⋊C4—581no—
169C22⋊C4—1162no—
170C42—581no—
171C23—291no—
172C23—291no—
173C23—581no—
174C23—581no—
175C23—581no—
176C23—1161no—
177C23—1161no—
178C23C22⋊#118111yescharacteristic
179Q8—41no—
180D4—1161no—
181D4—1161no—
182D4—1161no—
183D4—1162no—
184D4—1162no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—291no—
189C2×C4—291no—
190C2×C4—582no—
191C2×C4—582no—
192C2×C4—582no—
193C2×C4—581no—
194C2×C4—1161no—
195C2×C4—1161no—
196C2×C4—1162no—
197C2×C4—1162no—
198C2×C4—1162no—
199C2×C4—1162no—
200C2×C4C22⋊#118111yescharacteristic
201C2×C4C22×#118111yescharacteristic
202C8—1162no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—291no—
207C22—291no—
208C22—581no—
209C22—581no—
210C22—581no—
211C22—581no—
212C22—581no—
213C22—1162no—
214C22—1162no—
215C22—1161no—
216C22—1161no—
217C22—1161no—
218C22C2×C22⋊#118111yescharacteristic
219C4—21no—
220C4—21no—
221C4—41no—
222C4—41no—
223C4—292no—
224C4—581no—
225C4—1161no—
226C4—2322no—
227C2—41no—
228C2—581no—
229C2—581no—
230C2—1161no—
231C2—2321no—
232C2D29⋊#9911yescharacteristic
233C2#1427215411yescharacteristic
234C2#1427216211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×C22⋊Q8C4
socleC22×C29C2×C22⋊C4
prime radical#14271676C2
cosocleC2×C4×D29C23
hypercenterC22⋊Q8#1181
hypocenterC29#1513
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #14272135C2semidirect
2. #14272105C2semidirect
3. #14272017C2semidirect
4. #14272015C2semidirect
6. C2×#90809C4semidirect
11. C29×C22⋊Q8C4semidirect
13. #11745292C4semidirect
17. #11745254C4semidirect
128. C22⋊Q8#1181semidirect
140. C29#1513semidirect

Maximal subgroups

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

subgroupindex
#142721352
#142721052
#142720172
#142720152
#142716762
#151329