Finite Group Databasebeta

← #16818442

Subgroups — #16818442

Order 3712.

308 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 51 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#14271721C211yesmaximal, characteristic
2#14271302C211yesmaximal, characteristic, complemented
3#14271074C211yesmaximal, characteristic, complemented
4#14270898C211yesmaximal, characteristic, complemented
5#14270897C211yesmaximal, characteristic, complemented
6#14270886C211yesmaximal, characteristic, complemented
7C29×#448C211yesmaximal, characteristic, complemented
8C22×Q8×C29C2211yescharacteristic, complemented
9C2×D4×D29—21no—
10C2×SD16×C29—21no—
11C29×#121C2211yescharacteristic
12C2×#90784—21no—
13#11745301—21no—
14#11745299—21no—
15#11745292C2211yescharacteristic
16C2×#90781—21no—
17C2×#90781C2211yescharacteristic
18#11745256—21no—
19#11745245—21no—
20#11745244—21no—
21C29×#103—21no—
22C29×C22⋊C8C2211yescharacteristic, complemented
23#11745183—21no—
24#11745179—21no—
25#11745179C2211yescharacteristic, complemented
26C22⋊#6597C2211yescharacteristic, complemented
27C23×D29—21no—
28C23×D29D411yescharacteristic
29C2×Q8×C29—21no—
30C2×Q8×C29—21no—
31C2×Q8×C29—42no—
32C2×D4×C29—21no—
33C2×D4×C29D411yescharacteristic
34C22×C4×C29—21no—
35C22×C4×C29C2311yescharacteristic
36C2×C22⋊D29—21no—
37C2×C22⋊D29—21no—
38C2×C22⋊D29—21no—
39C22×Dic29—21no—
40C22×Dic29D411yescharacteristic
41D4×D29—42no—
42D4×D29—42no—
43C2×D116—21no—
44C2×D116D411yescharacteristic
45C2×C4×D29—21no—
46SD16×C29—42no—
47C2×C8×C29—21no—
48C4⋊C4×C29D411yescharacteristic
49C22⋊C4×C29—21no—
50C22⋊Dic29—21no—
51#90784—42no—
52#90781—21no—
53#90781—21no—
54#90781—21no—
55#90781—21no—
56#90781—42no—
57C4⋊Dic29D411yescharacteristic
58#90779—21no—
59C2×#6597—21no—
60C23×C29—21no—
61C23×C29C2×D411yescharacteristic
62C22×D29—21no—
63C22×D29—21no—
64C22×D29—21no—
65C22×D29—42no—
66C22×D29—41no—
67C22×D29—41no—
68C22×D29—81no—
69C22×D29—81no—
70C22×D29SD1612yescomplemented
71Q8×C29—22no—
72Q8×C29—22no—
73Q8×C29—41no—
74Q8×C29—41no—
75D4×C29—41no—
76D4×C29—41no—
77D4×C29—41no—
78C2×C4×C29—22no—
79C2×C4×C29—21no—
80C2×C4×C29—41no—
81C2×C4×C29—41no—
82C2×C4×C29—41no—
83C2×C4×C29C2×D411yescharacteristic
84C2×C4×C29C2×D411yescharacteristic
85C22⋊D29—42no—
86C22⋊D29—41no—
87C22⋊D29—41no—
88C22⋊D29—81no—
89C2×Dic29—21no—
90C2×Dic29—21no—
91C2×Dic29—41no—
92C2×Dic29—41no—
93C2×Dic29—41no—
94C2×Dic29—41no—
95D116—41no—
96D116—42no—
97C4×D29—42no—
98C8×C29—41no—
99#6597—41no—
100#1601—291nomaximal, Sylow
101C22×C29—21no—
102C22×C29—21no—
103C22×C29—41no—
104C22×C29—41no—
105C22×C29—41no—
106C22×C29#12011yescharacteristic
107C22×C29C2×SD1611yescharacteristic
108C22×C29AGL(1,ℤ/8)11yescharacteristic
109C2×D29—22no—
110C2×D29—41no—
111C2×D29—41no—
112C2×D29—42no—
113C2×D29—41no—
114C2×D29—41no—
115C2×D29—41no—
116C2×D29—81no—
117C2×D29—84no—
118C4×C29—21no—
119C4×C29—21no—
120C4×C29—41no—
121C4×C29—42no—
122Dic29—41no—
123Dic29—41no—
124Dic29—81no—
125#534—291no—
126#448—291no—
127#448D2911yescharacteristic, complemented
128#393—291no—
129#327—291no—
130#327—291no—
131#323—291no—
132C2×C29—21no—
133C2×C29—21no—
134C2×C29—81no—
135C2×C29#45011yescharacteristic
136C2×C29#45511yescharacteristic
137C2×C29B(4,𝔽2)11yescharacteristic
138D29—42no—
139D29—81no—
140C22×Q8C2×D2911yescharacteristic, complemented
141C22×D4—581no—
142C2×SD16—21no—
143C2×SD16—581no—
144#123—581no—
145#123—581no—
146#121—291no—
147#121—581no—
148#121C2×D2911yescharacteristic
149#120—581no—
150#120—581no—
151C2×C22⋊C4—291no—
152C2×C22⋊C4—581no—
153#103—21no—
154#103—581no—
155C22⋊C8—291no—
156C22⋊C8C2×D2911yescharacteristic, complemented
157#95—291no—
158#95—581no—
159C29#160111yescharacteristic, complemented, Sylow
160C24—291no—
161C24—581no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—42no—
165C2×D4—21no—
166C2×D4—291no—
167C2×D4—581no—
168C2×D4—581no—
169C2×D4—581no—
170C2×D4—581no—
171C2×D4—1162no—
172C2×D4—1162no—
173C2×D4C22⋊D2911yescharacteristic
174C22×C4—21no—
175C22×C4—291no—
176C22×C4—581no—
177C22×C4—581no—
178C22×C4C22×D2911yescharacteristic
179SD16—42no—
180SD16—1162no—
181C2×C8—21no—
182C2×C8—581no—
183C4⋊C4—291no—
184C4⋊C4—581no—
185C4⋊C4C22⋊D2911yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—581no—
188C22⋊C4—581no—
189C22⋊C4—581no—
190C22⋊C4—581no—
191C22⋊C4—581no—
192C22⋊C4—1162no—
193C23—21no—
194C23—292no—
195C23—581no—
196C23—581no—
197C23—581no—
198C23—1161no—
199C23—1161no—
200C23—1162no—
201C23—2321no—
202C23—2321no—
203C23D4×D2911yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—41no—
207Q8—41no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—1161no—
212D4—1162no—
213D4—1162no—
214D4—1161no—
215D4—1161no—
216D4—2321no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—581no—
223C2×C4—581no—
224C2×C4—1162no—
225C2×C4—1161no—
226C2×C4—1161no—
227C2×C4—1161no—
228C2×C4—1161no—
229C2×C4D4×D2911yescharacteristic
230C2×C4C2×C22⋊D2911yescharacteristic
231C8—41no—
232C8—1161no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—582no—
239C22—1162no—
240C22—1161no—
241C22—1161no—
242C22—1161no—
243C22—1161no—
244C22—1161no—
245C22—2321no—
246C22—2324no—
247C22SD16×D2911yescharacteristic
248C22#1174527611yescharacteristic
249C22#1174529911yescharacteristic
250C4—21no—
251C4—21no—
252C4—41no—
253C4—42no—
254C4—1161no—
255C4—1161no—
256C4—2321no—
257C2—21no—
258C2—21no—
259C2—81no—
260C2—1162no—
261C2—2321no—
262C2#1427131211yescharacteristic
263C2#1427133911yescharacteristic
264C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#448C2
socleC22×C29#120
prime radical#14271721C2
hypercenter#448D29
hypocenterC29#1601
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #14271302C2semidirect
3. #14271074C2semidirect
4. #14270898C2semidirect
5. #14270897C2semidirect
6. #14270886C2semidirect
7. C29×#448C2semidirect
8. C22×Q8×C29C22semidirect
22. C29×C22⋊C8C22semidirect
25. #11745179C22semidirect
26. C22⋊#6597C22semidirect
70. C22×D29SD16semidirect
127. #448D29semidirect
140. C22×Q8C2×D29semidirect
156. C22⋊C8C2×D29semidirect
159. C29#1601semidirect

Maximal subgroups

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

subgroupindex
#142717212
#142713022
#142710742
#142708982
#142708972
#142708862
C29×#4482
#160129