Finite Group Databasebeta

← #16818411

Subgroups — #16818411

Order 3712.

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

normal subgroups only

This group has 368 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, complemented
2#14271299C211yesmaximal, characteristic, complemented
3#14271296C211yesmaximal, characteristic, complemented
4#14271073C211yesmaximal, characteristic, complemented
5#14270896C211yesmaximal, characteristic, complemented
6#14270886C211yesmaximal, characteristic, complemented
7C29×#327C211yesmaximal, characteristic, complemented
8C2×D4×D29—21no—
9C22×D116—21no—
10C22×D116C2211yescharacteristic, complemented
11C29×#121C2211yescharacteristic
12#11745301—21no—
13#11745299—21no—
14C2×#90782—21no—
15#11745292C2211yescharacteristic
16C2×#90781—21no—
17C2×#90781C2211yescharacteristic
18C2×D232—21no—
19#11745256—21no—
20#11745245—21no—
21#11745244—21no—
22C29×C22⋊C8C2211yescharacteristic, complemented
23C29×#95C2211yescharacteristic, complemented
24C22⋊#6597C2211yescharacteristic, complemented
25#11745169—21no—
26#11745157—21no—
27C23×D29—21no—
28C23×D29—21no—
29C23×D29D411yescharacteristic
30C2×D4×C29—21no—
31C2×D4×C29D411yescharacteristic, complemented
32C22×C4×C29—21no—
33C22×C4×C29C2311yescharacteristic
34C2×C22⋊D29—21no—
35C2×C22⋊D29—21no—
36C2×C22⋊D29—21no—
37C22×Dic29D411yescharacteristic
38D4×D29—42no—
39D4×D29—42no—
40C2×D116—21no—
41C2×D116—21no—
42C2×D116—21no—
43C2×D116—42no—
44C2×D116—42no—
45C2×D116—42no—
46C2×D116—42no—
47C2×D116D411yescharacteristic, complemented
48C2×C4×D29—21no—
49C2×C8×C29—21no—
50C4⋊C4×C29D411yescharacteristic, complemented
51C22⋊C4×C29—21no—
52C22⋊Dic29—21no—
53#90782—42no—
54#90781—21no—
55#90781—21no—
56#90781—21no—
57#90781—21no—
58#90781—42no—
59C4⋊Dic29D411yescharacteristic, complemented
60#90779—21no—
61C2×#6597—21no—
62D232—42no—
63C23×C29—21no—
64C23×C29C2×D411yescharacteristic
65C22×D29—21no—
66C22×D29—21no—
67C22×D29—22no—
68C22×D29—21no—
69C22×D29—42no—
70C22×D29—41no—
71C22×D29—41no—
72C22×D29—41no—
73C22×D29—41no—
74C22×D29—41no—
75C22×D29—41no—
76C22×D29—41no—
77C22×D29—41no—
78C22×D29—81no—
79C22×D29—81no—
80C22×D29D812yescomplemented
81D4×C29—41no—
82D4×C29—41no—
83D4×C29—41no—
84C2×C4×C29—22no—
85C2×C4×C29—21no—
86C2×C4×C29—41no—
87C2×C4×C29—41no—
88C2×C4×C29—41no—
89C2×C4×C29C2×D411yescharacteristic
90C2×C4×C29C2×D411yescharacteristic
91C22⋊D29—42no—
92C22⋊D29—41no—
93C22⋊D29—41no—
94C22⋊D29—81no—
95C2×Dic29—21no—
96C2×Dic29—21no—
97C2×Dic29—41no—
98D116—22no—
99D116—22no—
100D116—41no—
101D116—41no—
102D116—41no—
103D116—42no—
104D116—48no—
105C4×D29—42no—
106C8×C29—41no—
107#6597—41no—
108#1595—291nomaximal, Sylow
109C22×C29—21no—
110C22×C29—21no—
111C22×C29—41no—
112C22×C29—41no—
113C22×C29—41no—
114C22×C29#12011yescharacteristic
115C22×C29C2×D811yescharacteristic
116C22×C29AGL(1,ℤ/8)11yescharacteristic
117C2×D29—22no—
118C2×D29—41no—
119C2×D29—41no—
120C2×D29—42no—
121C2×D29—42no—
122C2×D29—42no—
123C2×D29—41no—
124C2×D29—41no—
125C2×D29—42no—
126C2×D29—41no—
127C2×D29—81no—
128C2×D29—84no—
129C2×D29—81no—
130C2×D29—81no—
131C2×D29—81no—
132C2×D29—81no—
133C4×C29—21no—
134C4×C29—21no—
135C4×C29—42no—
136C4×C29—41no—
137Dic29—41no—
138Dic29—41no—
139#534—291no—
140#447—291no—
141#447—291no—
142#392—291no—
143#327—291no—
144#327D2911yescharacteristic, complemented
145#323—291no—
146C2×C29—21no—
147C2×C29—21no—
148C2×C29—81no—
149C2×C29#44711yescharacteristic
150C2×C29#45311yescharacteristic
151C2×C29B(4,𝔽2)11yescharacteristic
152D29—42no—
153D29—82no—
154D29—81no—
155C22×D4—291no—
156C22×D4—581no—
157C22×D4—581no—
158C2×D8—581no—
159C2×D8—581no—
160#123—581no—
161#123—581no—
162#121—291no—
163#121—581no—
164#121C2×D2911yescharacteristic
165#120—581no—
166#120—581no—
167C2×C22⋊C4—291no—
168C2×C22⋊C4—581no—
169#102—581no—
170#102—581no—
171C22⋊C8—291no—
172C22⋊C8C2×D2911yescharacteristic, complemented
173#95C2×D2911yescharacteristic, complemented
174C29#159511yescharacteristic, complemented, Sylow
175C24—291no—
176C24—581no—
177C24—581no—
178C2×D4—21no—
179C2×D4—291no—
180C2×D4—581no—
181C2×D4—581no—
182C2×D4—581no—
183C2×D4—581no—
184C2×D4—581no—
185C2×D4—581no—
186C2×D4—1162no—
187C2×D4—1162no—
188C2×D4—1162no—
189C2×D4—1162no—
190C2×D4—1162no—
191C2×D4—1162no—
192C2×D4D11611yescharacteristic, complemented
193C22×C4—21no—
194C22×C4—291no—
195C22×C4—581no—
196C22×C4C22×D2911yescharacteristic
197D8—1162no—
198D8—1162no—
199C2×C8—21no—
200C2×C8—581no—
201C4⋊C4—291no—
202C4⋊C4—581no—
203C4⋊C4D11611yescharacteristic, complemented
204C22⋊C4—21no—
205C22⋊C4—581no—
206C22⋊C4—581no—
207C22⋊C4—581no—
208C22⋊C4—581no—
209C22⋊C4—581no—
210C22⋊C4—1162no—
211C23—21no—
212C23—292no—
213C23—582no—
214C23—581no—
215C23—581no—
216C23—581no—
217C23—1161no—
218C23—1161no—
219C23—1161no—
220C23—1161no—
221C23—1161no—
222C23—1162no—
223C23—1161no—
224C23—1161no—
225C23—1161no—
226C23—2321no—
227C23—2321no—
228C23D4×D2911yescharacteristic
229D4—41no—
230D4—41no—
231D4—41no—
232D4—582no—
233D4—582no—
234D4—1161no—
235D4—1161no—
236D4—1161no—
237D4—1162no—
238D4—1168no—
239D4—1162no—
240D4—1161no—
241D4—1161no—
242D4—2321no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—581no—
249C2×C4—581no—
250C2×C4—1162no—
251C2×C4—1161no—
252C2×C4C2×D11611yescharacteristic
253C2×C4D4×D2911yescharacteristic
254C8—41no—
255C8—1161no—
256C22—21no—
257C22—21no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—582no—
262C22—1162no—
263C22—1162no—
264C22—1162no—
265C22—1161no—
266C22—1161no—
267C22—1161no—
268C22—1161no—
269C22—1162no—
270C22—1161no—
271C22—2321no—
272C22—2321no—
273C22—2321no—
274C22—2324no—
275C22—2321no—
276C22—2321no—
277C22#1174524411yescharacteristic
278C22D8×D2911yescharacteristic
279C22#1174527611yescharacteristic
280C4—21no—
281C4—21no—
282C4—42no—
283C4—41no—
284C4—1161no—
285C4—1161no—
286C2—21no—
287C2—21no—
288C2—81no—
289C2—1162no—
290C2—2322no—
291C2—2321no—
292C2#1427129811yescharacteristic
293C2#1427133211yescharacteristic
294C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#327C2
socleC22×C29#120
hypercenter#327D29
hypocenterC29#1595
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
1. #14271721C2semidirect
2. #14271299C2semidirect
3. #14271296C2semidirect
4. #14271073C2semidirect
5. #14270896C2semidirect
6. #14270886C2semidirect
7. C29×#327C2semidirect
10. C22×D116C22semidirect
22. C29×C22⋊C8C22semidirect
23. C29×#95C22semidirect
24. C22⋊#6597C22semidirect
31. C2×D4×C29D4semidirect
47. C2×D116D4semidirect
50. C4⋊C4×C29D4semidirect
59. C4⋊Dic29D4semidirect
80. C22×D29D8semidirect
144. #327D29semidirect
172. C22⋊C8C2×D29semidirect
173. #95C2×D29semidirect
174. C29#1595semidirect
192. C2×D4D116semidirect
203. C4⋊C4D116semidirect

Maximal subgroups

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

subgroupindex
#142717212
#142712992
#142712962
#142710732
#142708962
#142708862
C29×#3272
#159529