Finite Group Databasebeta

← #34079070

Subgroups — #34079070

Order 19328.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#23752781C211yesmaximal, characteristic
2#23752693C211yesmaximal, characteristic, complemented
3#23752539C212yesmaximal, complemented
4#23752538C212yesmaximal, complemented
5#23752532C212yesmaximal, complemented
6#23752527C212yesmaximal, complemented
7#23752248C211yesmaximal, characteristic, complemented
8#23752218C211yesmaximal, characteristic, complemented
9C2×#18012659C211yesmaximal, characteristic, complemented
10#23752180C211yesmaximal, characteristic, complemented
11#428×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×D604C2211yescharacteristic
14C22×C151⋊C8C2211yescharacteristic
15#18012736—21no—
16#18012727—21no—
17#18012714C2212yes—
18#18012714C2212yes—
19#18012709—22no—
20#18012704—21no—
21#18012701—21no—
22C4×C22⋊D151—22no—
23#18012698C2211yescharacteristic
24#18012697C2212yescomplemented
25C4⋊C4×D151C2212yescomplemented
26#18012672C2211yescharacteristic, complemented
27#18012672C2211yescharacteristic, complemented
28#18012670C2211yescharacteristic, complemented
29#18012670C2211yescharacteristic, complemented
30#18012661C2212yes—
31#18012661C2212yes—
32#18012659C2212yes—
33#18012659C2212yes—
34(C2×D151)⋊C8C2212yescomplemented
35(C2×D151)⋊C8C2212yescomplemented
36C2×M16×C151C2211yescharacteristic
37#117×C151C2211yescharacteristic
38C2×C4⋊C4×C151C2211yescharacteristic
39#107×C151C2212yescomplemented
40#106×C151C2212yescomplemented
41C23×D151—21no—
42#14559004—22no—
43#14559004—22no—
44C2×Dic302D411yescharacteristic
45C2×D604—22no—
46C2×D604—22no—
47C2×D604—21no—
48C2×D604—22no—
49C2×D604—22no—
50C2×D604D411yescharacteristic
51C2×D604C2312yes—
52C2×C22⋊D151D412yes—
53C2×C4×D151—22no—
54C2×C4×D151C2312yes—
55C2×C151⋊C8—22no—
56C2×C151⋊C8C2311yescharacteristic
57C2×C151⋊C8C2311yescharacteristic
58C4⋊Dic151C2311yescharacteristic
59C4⋊Dic151C2311yescharacteristic
60Dic151⋊C4—22no—
61C22⋊Dic151—21no—
62(C2×D151)⋊C4—22no—
63(C2×D151)⋊C4—22no—
64(C2×D151)⋊C4—22no—
65C4×Dic151—22no—
66C4×Dic151—21no—
67C22×C4×C151—21no—
68C22×C4×C151C2311yescharacteristic
69M16×C151—22no—
70C2×C8×C151C2312yes—
71C4⋊C4×C151—21no—
72C4⋊C4×C151C2311yescharacteristic
73C4⋊C4×C151C2311yescharacteristic
74C4⋊C4×C151C2312yes—
75C22⋊C4×C151—21no—
76C42×C151—21no—
77C22×D151—22no—
78C22×D151—42no—
79C22×D151—81no—
80C22×D151—81no—
81C22×D151C2×D412yes—
82Dic302—22no—
83D604—22no—
84D604—22no—
85D604—22no—
86D604—42no—
87D604—82no—
88D604—82no—
89C22⋊D151—24no—
90C2×Dic151—21no—
91C2×Dic151—21no—
92C2×Dic151C2×D412yes—
93C4×D151—22no—
94C4×D151—22no—
95C4×D151—82no—
96C151⋊C8—21no—
97C151⋊C8—21no—
98C23×C151C2×D411yescharacteristic
99C2×C4×C151—22no—
100C2×C4×C151—21no—
101C2×C4×C151—21no—
102C2×C4×C151—81no—
103C2×C4×C151C2×D411yescharacteristic
104C2×C4×C151#4112yes—
105C2×C4×C151#4112yes—
106C2×C4×C151C2411yescharacteristic
107C8×C151—22no—
108C22×C151—21no—
109C22×C151—21no—
110C22×C151#12312yes—
111C22×C151C22×D411yescharacteristic
112C2×D151—22no—
113C2×D151—22no—
114C2×D151—22no—
115C2×D151—42no—
116C2×D151—42no—
117C2×D151—42no—
118C2×D151—84no—
119C4×C151—42no—
120C4×C151—41no—
121C4×C151—41no—
122C4×C151#12312yes—
123C4×C151C2×#4111yescharacteristic
124C4×C151C2×#4111yescharacteristic
125Dic151—22no—
126Dic151—41no—
127Dic151—41no—
128C2×C151—22no—
129C2×C151C2×#12311yescharacteristic
130C2×C151#57611yescharacteristic
131C2×C151#57711yescharacteristic
132D151—42no—
133D151—82no—
134C151#309611yescharacteristic, complemented, Sylow
135#3096—1511nomaximal, Sylow
136#535—1511no—
137#520—1511no—
138#482—1512no—
139#482—1512no—
140#481—1512no—
141#480—1512no—
142#428D15111yescharacteristic, complemented
143#427—1511no—
144#418—1511no—
145C2×#102—1511no—
146#408—1511no—
147C2×#41—1511no—
148C22×D4—1511no—
149C2×M16C2×D15111yescharacteristic
150C22×C8—1511no—
151#127—3021no—
152#124—3021no—
153#121—1512no—
154#121—1512no—
155#120—3022no—
156C4×Q8—3021no—
157C4×D4—3021no—
158C4×D4—3022no—
159#117—1511no—
160#117—1512no—
161#117C2×D15111yescharacteristic
162C2×C4⋊C4—1512no—
163C2×C4⋊C4C2×D15111yescharacteristic
164#107—1511no—
165#107—1511no—
166#107C2×D15112yescomplemented
167#106—1511no—
168#106—1511no—
169#106C2×D15112yescomplemented
170#102—1512no—
171#102—1512no—
172#102—1512no—
173#102—1512no—
174C22⋊C8—1512no—
175C22⋊C8—1512no—
176C24—3021no—
177#41—3022no—
178#41—3022no—
179C2×Q8—1511no—
180C2×D4—3022no—
181C2×D4—3022no—
182C2×D4—3021no—
183C2×D4—3022no—
184C2×D4—3022no—
185C2×D4—1512no—
186C2×D4—1511no—
187C2×D4—1512no—
188C22×C4—21no—
189C22×C4—3022no—
190C22×C4—1512no—
191C22×C4C22×D15111yescharacteristic
192M16—22no—
193C2×C8—3022no—
194C2×C8—1511no—
195C2×C8—1511no—
196C2×C8C22×D15112yes—
197C4⋊C4—21no—
198C4⋊C4—3022no—
199C4⋊C4—1511no—
200C4⋊C4—1511no—
201C4⋊C4C22×D15112yes—
202C4⋊C4C22×D15111yescharacteristic
203C4⋊C4C22×D15111yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—3022no—
206C22⋊C4—3022no—
207C22⋊C4—3022no—
208C22⋊C4—3021no—
209C42—21no—
210C42—3022no—
211C42—3021no—
212C23—3022no—
213C23—6042no—
214C23—1512no—
215C23—12081no—
216C23—12081no—
217C23D4×D15111yescharacteristic
218Q8—3022no—
219D4—3024no—
220D4—3022no—
221D4—3022no—
222D4—3022no—
223D4—6042no—
224D4—12082no—
225D4—12082no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—81no—
230C2×C4—3022no—
231C2×C4—3022no—
232C2×C4—3021no—
233C2×C4—3021no—
234C2×C4—1512no—
235C2×C4—12082no—
236C2×C4D4×D15111yescharacteristic
237C2×C4#1455900412yes—
238C2×C4#1455900512yes—
239C2×C4C23×D15111yescharacteristic
240C8—22no—
241C8—3021no—
242C8—3021no—
243C22—21no—
244C22—21no—
245C22—3022no—
246C22—3022no—
247C22—3022no—
248C22—6042no—
249C22—6042no—
250C22—6042no—
251C22—12084no—
252C22#1801272412yes—
253C22C2×D4×D15111yescharacteristic
254C4—42no—
255C4—41no—
256C4—41no—
257C4—3022no—
258C4—6041no—
259C4—6041no—
260C4#1801272412yes—
261C4C2×#1455900411yescharacteristic
262C4C2×#1455900511yescharacteristic
263C2—22no—
264C2—6042no—
265C2—12082no—
266C2C2×#1801272411yescharacteristic
267C2#2375301611yescharacteristic
268C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#428×C151C2
socleC22×C151C22×D4
prime radical#23752781C2
hypercenter#428D151
hypocenterC151#3096
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #23752693C2semidirect
3. #23752539C2semidirect
4. #23752538C2semidirect
5. #23752532C2semidirect
6. #23752527C2semidirect
7. #23752248C2semidirect
8. #23752218C2semidirect
9. C2×#18012659C2semidirect
10. #23752180C2semidirect
11. #428×C151C2semidirect
24. #18012697C22semidirect
25. C4⋊C4×D151C22semidirect
26. #18012672C22semidirect
27. #18012672C22semidirect
28. #18012670C22semidirect
29. #18012670C22semidirect
34. (C2×D151)⋊C8C22semidirect
35. (C2×D151)⋊C8C22semidirect
39. #107×C151C22semidirect
40. #106×C151C22semidirect
134. C151#3096semidirect
142. #428D151semidirect
166. #107C2×D151semidirect
169. #106C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527812
#237526932
#237525392
#237525382
#237525322
#237525272
#237522482
#237522182
C2×#180126592
#237521802
#428×C1512
#3096151