Finite Group Databasebeta

← #16829411

Subgroups — #16829411

Order 3712.

458 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 123 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#14271673C211yesmaximal, characteristic
2C2×C4⋊C4×D29C211yesmaximal, characteristic, complemented
3#14271500C212yesmaximal, complemented
4#14271494C211yesmaximal, characteristic, complemented
5#14271493C211yesmaximal, characteristic, complemented
6#14271480C212yesmaximal, complemented
7#14271474C211yesmaximal, characteristic, complemented
8#14271204C212yesmaximal, complemented
9#14271161C212yesmaximal, complemented
10#14271125C211yesmaximal, characteristic, complemented
11C29×#480C211yesmaximal, characteristic, complemented
12C2×#90807C2211yescharacteristic
13C22×C4×D29—21no—
14C22×C4×D29C2211yescharacteristic
15C29×#121C2211yescharacteristic
16C2×C4⋊C4×C29C2211yescharacteristic
17#11745300C2211yescharacteristic
18#11745299—21no—
19D4×Dic29—21no—
20C2×C4⋊Dic29C2211yescharacteristic
21#11745286C2211yescharacteristic
22C2×#90779—21no—
23C2×#90772C2212yes—
24#11745259C2211yescharacteristic
25#11745254C2211yescharacteristic
26C4⋊C4×D29—21no—
27C4⋊C4×D29—21no—
28C4⋊C4×D29C2212yes—
29C4⋊C4×D29C2212yes—
30#11745245—21no—
31#11745243—21no—
32C29×#107C2212yescomplemented
33C29×#102C2212yescomplemented
34C29×C22⋊C8C2211yescharacteristic
35#11745180C2212yescomplemented
36C22⋊#6597C2211yescharacteristic
37#11745168C2212yes—
38#11745165C2212yescomplemented
39#11745164C2212yescomplemented
40#11745158C2212yescomplemented
41#11745156C2212yescomplemented
42#11745155C2212yescomplemented
43C23×D29D411yescharacteristic
44C2×D4×C29—21no—
45C2×D4×C29C2311yescharacteristic
46C22×C4×C29—21no—
47C22×C4×C29C2311yescharacteristic
48C2×C22⋊D29—21no—
49C2×C22⋊D29—21no—
50C22×Dic29—21no—
51C22×Dic29—21no—
52C22×Dic29D411yescharacteristic
53#90807—24no—
54C2×C4×D29—24no—
55C2×C4×D29—22no—
56C2×C4×D29—22no—
57C2×C4×D29—44no—
58C2×C4×D29D411yescharacteristic
59C2×C4×D29D411yescharacteristic
60C2×C4×D29C2311yescharacteristic
61C2×C4×D29C2311yescharacteristic
62C2×Dic58C2311yescharacteristic
63C2×C8×C29C2312yes—
64C4⋊C4×C29—21no—
65C4⋊C4×C29C2312yes—
66C4⋊C4×C29C2311yescharacteristic
67C22⋊C4×C29—21no—
68C22⋊Dic29—21no—
69C22⋊Dic29—21no—
70#90781—21no—
71#90781—21no—
72C4⋊Dic29—21no—
73C4⋊Dic29—21no—
74C4⋊Dic29C2311yescharacteristic
75C4⋊Dic29C2312yes—
76#90779—21no—
77#90779—22no—
78#90779—22no—
79C4×Dic29—21no—
80C2×#6597C2312yes—
81#90772—24no—
82C23×C29—21no—
83C23×C29C2×D411yescharacteristic
84C22×D29—22no—
85C22×D29—22no—
86C22×D29—22no—
87C22×D29C2×D411yescharacteristic
88C22×D29C2×D411yescharacteristic
89D4×C29—22no—
90D4×C29—42no—
91C2×C4×C29—22no—
92C2×C4×C29—21no—
93C2×C4×C29—22no—
94C2×C4×C29—42no—
95C2×C4×C29C2×D411yescharacteristic
96C2×C4×C29C2411yescharacteristic
97C22⋊D29—42no—
98C22⋊D29—42no—
99C2×Dic29—22no—
100C2×Dic29—21no—
101C2×Dic29—22no—
102C2×Dic29—21no—
103C2×Dic29—42no—
104C2×Dic29—42no—
105C2×Dic29C2×D411yescharacteristic
106C2×Dic29C2×D411yescharacteristic
107C4×D29—22no—
108C4×D29—22no—
109C4×D29—22no—
110C4×D29—44no—
111C4×D29—44no—
112C4×D29#4114yes—
113Dic58—22no—
114C8×C29—22no—
115#6597—22no—
116#3092—291nomaximal, Sylow
117C22×C29—21no—
118C22×C29—21no—
119C22×C29—41no—
120C22×C29—41no—
121C22×C29—41no—
122C22×C29AGL(1,ℤ/8)12yes—
123C22×C29C22×D411yescharacteristic
124C2×D29—28no—
125C2×D29—21no—
126C2×D29—21no—
127C2×D29—21no—
128C2×D29—21no—
129C2×D29#12312yes—
130C2×D29#13712yes—
131C4×C29—21no—
132C4×C29—42no—
133C4×C29—41no—
134C4×C29C2×#4112yes—
135Dic29—21no—
136Dic29—41no—
137Dic29—42no—
138Dic29—41no—
139Dic29#12312yes—
140#525—291no—
141C22×C4⋊C4—291no—
142#484—292no—
143#483—291no—
144#483—291no—
145#481—292no—
146#480—291no—
147#480D2911yescharacteristic, complemented
148#428—292no—
149#417—292no—
150#407—291no—
151C2×C29—22no—
152C2×C29—81no—
153C2×C29C2×#12311yescharacteristic
154C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
155C2×C29C2×#13711yescharacteristic
156D29—22no—
157D29—22no—
158C2×#41—291no—
159C23×C4—291no—
160C23×C4—581no—
161C2×M16—292no—
162#123—581no—
163C22⋊Q8—291no—
164C22⋊Q8—291no—
165#121—291no—
166#121C2×D2911yescharacteristic
167#120—581no—
168C4×D4—581no—
169C4×D4—581no—
170#117—291no—
171C2×C4⋊C4—291no—
172C2×C4⋊C4—292no—
173C2×C4⋊C4—292no—
174C2×C4⋊C4—581no—
175C2×C4⋊C4—581no—
176C2×C4⋊C4—581no—
177C2×C4⋊C4C2×D2911yescharacteristic
178#107—292no—
179#107C2×D2912yescomplemented
180#106—292no—
181#106—292no—
182#103—292no—
183#103—292no—
184#102—292no—
185#102C2×D2912yescomplemented
186C22⋊C8—291no—
187C22⋊C8—292no—
188C22⋊C8C2×D2911yescharacteristic
189C29#309211yescharacteristic, complemented, Sylow
190C24—291no—
191#41—584no—
192C2×Q8—291no—
193C2×D4—21no—
194C2×D4—581no—
195C2×D4—581no—
196C2×D4C22×D2911yescharacteristic
197C22×C4—21no—
198C22×C4—291no—
199C22×C4—291no—
200C22×C4—291no—
201C22×C4—291no—
202C22×C4—291no—
203C22×C4—584no—
204C22×C4—582no—
205C22×C4—582no—
206C22×C4—581no—
207C22×C4—581no—
208C22×C4—1164no—
209C22×C4C22×D2911yescharacteristic
210M16—584no—
211C2×C8—292no—
212C2×C8C22×D2912yes—
213C4⋊C4—21no—
214C4⋊C4—292no—
215C4⋊C4—291no—
216C4⋊C4—582no—
217C4⋊C4—582no—
218C4⋊C4—581no—
219C4⋊C4—581no—
220C4⋊C4—581no—
221C4⋊C4C22×D2912yes—
222C4⋊C4C22×D2911yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—581no—
225C22⋊C4—581no—
226C22⋊C4—581no—
227C22⋊C4—581no—
228C42—581no—
229C23—21no—
230C23—291no—
231C23—291no—
232C23—582no—
233C23—582no—
234C23—582no—
235C23D4×D2911yescharacteristic
236Q8—582no—
237D4—22no—
238D4—42no—
239D4—1162no—
240D4—1162no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—291no—
246C2×C4—294no—
247C2×C4—291no—
248C2×C4—582no—
249C2×C4—582no—
250C2×C4—582no—
251C2×C4—582no—
252C2×C4—581no—
253C2×C4—581no—
254C2×C4—582no—
255C2×C4—1164no—
256C2×C4—1164no—
257C2×C4—1162no—
258C2×C4—1162no—
259C2×C4D4×D2911yescharacteristic
260C2×C4C23×D2911yescharacteristic
261C8—22no—
262C8—582no—
263C22—21no—
264C22—21no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—292no—
269C22—292no—
270C22—588no—
271C22—581no—
272C22—581no—
273C22—581no—
274C22—581no—
275C22#1174527312yes—
276C22C2×D4×D2911yescharacteristic
277C4—21no—
278C4—42no—
279C4—41no—
280C4—292no—
281C4—581no—
282C4—1161no—
283C4—1162no—
284C4—1161no—
285C4#41×D2912yes—
286C2—22no—
287C2—81no—
288C2—582no—
289C2—582no—
290C2#123×D2911yescharacteristic
291C2C2×#1174527311yescharacteristic
292C2#137×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#480C2
socleC22×C29C22×D4
prime radical#14271673C2
hypercenter#480D29
hypocenterC29#3092
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D29C2semidirect
3. #14271500C2semidirect
4. #14271494C2semidirect
5. #14271493C2semidirect
6. #14271480C2semidirect
7. #14271474C2semidirect
8. #14271204C2semidirect
9. #14271161C2semidirect
10. #14271125C2semidirect
11. C29×#480C2semidirect
32. C29×#107C22semidirect
33. C29×#102C22semidirect
35. #11745180C22semidirect
38. #11745165C22semidirect
39. #11745164C22semidirect
40. #11745158C22semidirect
41. #11745156C22semidirect
42. #11745155C22semidirect
147. #480D29semidirect
179. #107C2×D29semidirect
185. #102C2×D29semidirect
189. C29#3092semidirect

Maximal subgroups

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

subgroupindex
#142716732
C2×C4⋊C4×D292
#142715002
#142714942
#142714932
#142714802
#142714742
#142712042
#142711612
#142711252
C29×#4802
#309229