Finite Group Databasebeta

← #34078470

Subgroups — #34078470

Order 19328.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#18012784C211yesmaximal, characteristic, complemented
2#23753012C212yesmaximal, complemented
3#23752779C211yesmaximal, characteristic, complemented
4#23752392C214yesmaximal, complemented
5#23752382C214yesmaximal, complemented
6#23752228C212yesmaximal, complemented
7C2×#100×C151C211yesmaximal, characteristic, complemented
8#18012784—22no—
9#18012784—24no—
10#18012784C2214yes—
11C2×#14559004C2212yes—
12C2×#14559004C2211yescharacteristic, complemented
13C2×#14559003—22no—
14C22×C22⋊D151—22no—
15C2×D4×D151—22no—
16#18012772—22no—
17#18012772C2214yescomplemented
18#18012767—22no—
19#18012767C2214yescomplemented
20#18012761—24no—
21#18012735C2212yescomplemented
22#18012726C2212yescomplemented
23#18012710—22no—
24#18012708—22no—
25#18012698C2211yescharacteristic, complemented
26#18012665C2218yescomplemented
27C22×D4×C151C2211yescharacteristic
28C2×M16×C151C2212yescomplemented
29#100×C151C2214yescomplemented
30C23×D151—22no—
31#14559004—22no—
32#14559004—22no—
33#14559004—22no—
34#14559004—22no—
35#14559004D414yescomplemented
36#14559004C2314yes—
37#14559003—28no—
38#14559003—28no—
39C2×Dic302D412yescomplemented
40C2×Dic302C2311yescharacteristic, complemented
41C2×D604D412yescomplemented
42C2×D604C2311yescharacteristic, complemented
43C2×C22⋊D151—24no—
44C2×C22⋊D151—28no—
45C2×C22⋊D151—22no—
46C2×C22⋊D151—28no—
47C2×C22⋊D151—21no—
48C2×C22⋊D151—24no—
49D4×D151—28no—
50D4×D151—28no—
51C22×Dic151—22no—
52C2×C4×D151—22no—
53C2×C4×D151—21no—
54Dic604—24no—
55#14558993—24no—
56#14558993—24no—
57D1208—24no—
58C4⋊Dic151—21no—
59C22⋊Dic151—21no—
60C22⋊Dic151—24no—
61C4×Dic151C2312yescomplemented
62C24×C151D412yes—
63C2×D4×C151—22no—
64C2×D4×C151—22no—
65C2×D4×C151D412yes—
66C2×D4×C151C2312yes—
67C22×C4×C151C2311yescharacteristic
68M16×C151—22no—
69M16×C151C2314yescomplemented
70C2×C8×C151—22no—
71C22×D151—22no—
72C22×D151—28no—
73C22×D151—21no—
74C22×D151—84no—
75Dic302—22no—
76Dic302—22no—
77Dic302C2×D414yes—
78D604—22no—
79D604—22no—
80D604C2×D414yes—
81C22⋊D151—216no—
82C22⋊D151—24no—
83C22⋊D151—24no—
84C22⋊D151—41no—
85C22⋊D151—41no—
86C22⋊D151—84no—
87C2×Dic151—28no—
88C2×Dic151—22no—
89C2×Dic151—22no—
90C2×Dic151—21no—
91C4×D151—24no—
92C4×D151—24no—
93C4×D151—42no—
94C23×C151—22no—
95C23×C151—22no—
96C23×C151—82no—
97C23×C151C2×D414yes—
98C23×C151C2×D411yescharacteristic
99D4×C151—24no—
100D4×C151—24no—
101C2×C4×C151C2×D412yes—
102C2×C4×C151C2×D412yes—
103C2×C4×C151C2×D411yescharacteristic
104C2×C4×C151C2411yescharacteristic
105C8×C151—24no—
106C22×C151—24no—
107C22×C151—41no—
108C22×C151—44no—
109C22×C151—44no—
110C22×C151—82no—
111C22×C151#12011yescharacteristic
112C22×C151#12011yescharacteristic
113C22×C151C22×D411yescharacteristic
114C2×D151—24no—
115C2×D151—44no—
116C2×D151—42no—
117C2×D151—41no—
118C2×D151—88no—
119C4×C151#12012yes—
120C4×C151C22×D412yes—
121Dic151—24no—
122Dic151—42no—
123Dic151—41no—
124C2×C151—21no—
125C2×C151—21no—
126C2×C151—21no—
127C2×C151—44no—
128C2×C151C2×#12011yescharacteristic
129D151—44no—
130D151—81no—
131C151#301911yescharacteristic, complemented, Sylow
132#3019—1511nomaximal, Sylow
133C2×H(5,𝔽2)—1511no—
134#575—1512no—
135#535—1511no—
136#455—1514no—
137#453—1514no—
138#421—1512no—
139C2×#100D15111yescharacteristic, complemented
140H(5,𝔽2)—3024no—
141H(5,𝔽2)—3022no—
142H(5,𝔽2)—1514no—
143C2×#41—3022no—
144C2×#41—1511no—
145C2×#41—1512no—
146C22×D4—3022no—
147C22×D4—3022no—
148C22×D4C2×D15111yescharacteristic
149#137—3022no—
150#137—1514no—
151AGL(1,ℤ/8)—3022no—
152AGL(1,ℤ/8)—1514no—
153#135—3024no—
154C2×M16C2×D15112yescomplemented
155#127—1512no—
156#124—1512no—
157#121—3022no—
158#120—3022no—
159#117—1511no—
160#104—1518no—
161#100C2×D15114yescomplemented
162C24—3022no—
163C24D60412yes—
164#41—3028no—
165#41—3028no—
166#41—3022no—
167#41—3022no—
168#41—3022no—
169#41—3022no—
170#41—1514no—
171#41—1514no—
172C2×Q8—1512no—
173C2×Q8—1511no—
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—3028no—
177C2×D4—3028no—
178C2×D4—3024no—
179C2×D4—3028no—
180C2×D4—3022no—
181C2×D4—3028no—
182C2×D4—3021no—
183C2×D4—3024no—
184C2×D4—1512no—
185C2×D4—1511no—
186C2×D4D60412yes—
187C2×D4C22×D15112yes—
188C22×C4—3022no—
189C22×C4—3022no—
190C22×C4—3021no—
191C22×C4C22×D15111yescharacteristic
192Q16—3024no—
193SD16—3024no—
194SD16—3024no—
195D8—3024no—
196M16—22no—
197M16C22×D15114yescomplemented
198C2×C8—22no—
199C4⋊C4—3021no—
200C22⋊C4—3021no—
201C22⋊C4—3024no—
202C42—1512no—
203C23—22no—
204C23—22no—
205C23—82no—
206C23—3028no—
207C23—3022no—
208C23—3021no—
209C23—12084no—
210C23C2×D60414yes—
211C23C2×D60411yescharacteristic
212Q8—3022no—
213Q8—3022no—
214Q8—1514no—
215D4—24no—
216D4—24no—
217D4—30216no—
218D4—3024no—
219D4—3024no—
220D4—3022no—
221D4—3022no—
222D4—6041no—
223D4—6041no—
224D4—1514no—
225D4—12084no—
226C2×C4—3028no—
227C2×C4—3022no—
228C2×C4—3024no—
229C2×C4—3024no—
230C2×C4—3022no—
231C2×C4—3021no—
232C2×C4—6042no—
233C2×C4D4×D15112yes—
234C2×C4D4×D15112yes—
235C2×C4C2×D60411yescharacteristic
236C2×C4C23×D15111yescharacteristic
237C8—24no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—82no—
243C22—3024no—
244C22—6044no—
245C22—6042no—
246C22—6041no—
247C22—12088no—
248C22#1801270911yescharacteristic
249C22#1801270911yescharacteristic
250C22C22×D60411yescharacteristic
251C4—3024no—
252C4—6042no—
253C4—6041no—
254C4#1801270912yes—
255C4C2×D4×D15112yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—6044no—
261C2—12081no—
262C2C2×#1801270911yescharacteristic
subgroupG/H
centerC2C2×#18012709
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#100×C151C2
socleC2×C151C2×#120
hypercenterC2×#100D151
hypocenterC151#3019
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#18012784C2semidirect
2. #23753012C2semidirect
3. #23752779C2semidirect
4. #23752392C2semidirect
5. #23752382C2semidirect
6. #23752228C2semidirect
7. C2×#100×C151C2semidirect
12. C2×#14559004C22semidirect
17. #18012772C22semidirect
19. #18012767C22semidirect
21. #18012735C22semidirect
22. #18012726C22semidirect
25. #18012698C22semidirect
26. #18012665C22semidirect
28. C2×M16×C151C22semidirect
29. #100×C151C22semidirect
35. #14559004D4semidirect
39. C2×Dic302D4semidirect
40. C2×Dic302C23semidirect
41. C2×D604D4semidirect
42. C2×D604C23semidirect
61. C4×Dic151C23semidirect
69. M16×C151C23semidirect
131. C151#3019semidirect
139. C2×#100D151semidirect
154. C2×M16C2×D151semidirect
161. #100C2×D151semidirect
197. M16C22×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127842
#237530122
#237527792
#237523922
#237523822
#237522282
C2×#100×C1512
#3019151