Finite Group Databasebeta

← #16818445

Subgroups — #16818445

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#14271304C211yesmaximal, characteristic, complemented
3#14271301C211yesmaximal, characteristic, complemented
4#14271076C211yesmaximal, characteristic, complemented
5#14270896C211yesmaximal, characteristic, complemented
6#14270886C211yesmaximal, characteristic, complemented
7C29×#327C211yesmaximal, characteristic, complemented
8C2×D4×D29—21no—
9C22×Dic58C2211yescharacteristic, complemented
10C29×#121C2211yescharacteristic
11#11745301—21no—
12#11745299—21no—
13C2×#90783—21no—
14#11745292C2211yescharacteristic
15C2×#90781—21no—
16C2×#90781C2211yescharacteristic
17C2×#90773—21no—
18#11745256—21no—
19#11745245—21no—
20#11745244—21no—
21C29×C22⋊C8C2211yescharacteristic, complemented
22C29×#95C2211yescharacteristic, complemented
23#11745179—21no—
24C22⋊#6597C2211yescharacteristic, complemented
25#11745164—21no—
26#11745158—21no—
27C23×D29—21no—
28C23×D29D411yescharacteristic
29C2×D4×C29—21no—
30C2×D4×C29D411yescharacteristic
31C22×C4×C29—21no—
32C22×C4×C29C2311yescharacteristic
33C2×C22⋊D29—21no—
34C2×C22⋊D29—21no—
35C2×C22⋊D29—21no—
36C22×Dic29—21no—
37C22×Dic29D411yescharacteristic
38D4×D29—42no—
39D4×D29—42no—
40C2×D116—21no—
41C2×D116D411yescharacteristic
42C2×C4×D29—21no—
43C2×Dic58—21no—
44C2×Dic58—21no—
45C2×Dic58—42no—
46C2×C8×C29—21no—
47C4⋊C4×C29D411yescharacteristic
48C22⋊C4×C29—21no—
49C22⋊Dic29—21no—
50#90783—42no—
51#90781—21no—
52#90781—21no—
53#90781—21no—
54#90781—21no—
55#90781—42no—
56C4⋊Dic29D411yescharacteristic
57#90779—21no—
58C2×#6597—21no—
59#90773—42no—
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
71D4×C29—41no—
72D4×C29—41no—
73D4×C29—41no—
74C2×C4×C29—21no—
75C2×C4×C29—41no—
76C2×C4×C29—41no—
77C2×C4×C29—41no—
78C2×C4×C29—41no—
79C2×C4×C29C2×D411yescharacteristic
80C2×C4×C29C2×D411yescharacteristic
81C22⋊D29—42no—
82C22⋊D29—41no—
83C22⋊D29—41no—
84C22⋊D29—81no—
85C2×Dic29—22no—
86C2×Dic29—21no—
87C2×Dic29—21no—
88C2×Dic29—41no—
89C2×Dic29—41no—
90C2×Dic29—41no—
91D116—41no—
92D116—42no—
93C4×D29—42no—
94Dic58—22no—
95Dic58—22no—
96Dic58—41no—
97Dic58—41no—
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—81no—
122Dic29—41no—
123Dic29—41no—
124Dic29—42no—
125#534—291no—
126#448—291no—
127#448—291no—
128#393—291no—
129#327—291no—
130#327D2911yescharacteristic, complemented
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×Q8—291no—
141C22×D4—581no—
142C2×SD16—581no—
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—581no—
154#103—581no—
155C22⋊C8—291no—
156C22⋊C8C2×D2911yescharacteristic, complemented
157#95—581no—
158#95C2×D2911yescharacteristic, complemented
159C29#160111yescharacteristic, complemented, Sylow
160C24—291no—
161C24—581no—
162C2×Q8—581no—
163C2×Q8—581no—
164C2×Q8—1162no—
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×D4D11611yescharacteristic
174C22×C4—21no—
175C22×C4—291no—
176C22×C4—581no—
177C22×C4—581no—
178C22×C4C22×D2911yescharacteristic
179SD16—1162no—
180SD16—1162no—
181C2×C8—21no—
182C2×C8—581no—
183C4⋊C4—291no—
184C4⋊C4—581no—
185C4⋊C4D11611yescharacteristic
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—582no—
205Q8—582no—
206Q8—1161no—
207Q8—1161no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—1161no—
212D4—1162no—
213D4—1162no—
214D4—1161no—
215D4—1161no—
216D4—2321no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—582no—
223C2×C4—581no—
224C2×C4—581no—
225C2×C4—1162no—
226C2×C4—1161no—
227C2×C4—1161no—
228C2×C4—1161no—
229C2×C4C2×D11611yescharacteristic
230C2×C4D4×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—
247C22#1174524411yescharacteristic
248C22#1174527311yescharacteristic
249C22SD16×D2911yescharacteristic
250C4—21no—
251C4—21no—
252C4—41no—
253C4—81no—
254C4—1161no—
255C4—1161no—
256C4—1162no—
257C2—21no—
258C2—21no—
259C2—81no—
260C2—1162no—
261C2—2321no—
262C2#1427131511yescharacteristic
263C2#1427134211yescharacteristic
264C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#327C2
socleC22×C29#120
prime radical#14271721C2
hypercenter#327D29
hypocenterC29#1601
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14271304C2semidirect
3. #14271301C2semidirect
4. #14271076C2semidirect
5. #14270896C2semidirect
6. #14270886C2semidirect
7. C29×#327C2semidirect
9. C22×Dic58C22semidirect
21. C29×C22⋊C8C22semidirect
22. C29×#95C22semidirect
24. C22⋊#6597C22semidirect
70. C22×D29SD16semidirect
130. #327D29semidirect
156. C22⋊C8C2×D29semidirect
158. #95C2×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
#142713042
#142713012
#142710762
#142708962
#142708862
C29×#3272
#160129