Finite Group Databasebeta

← #34054829

Subgroups — #34054829

Order 19072.

450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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#23750159C211yesmaximal, characteristic, complemented
2#23749955C211yesmaximal, characteristic, complemented
3#23749938C211yesmaximal, characteristic, complemented
4#23749925C212yesmaximal, complemented
5#23749840C212yesmaximal, complemented
6#23749776C211yesmaximal, characteristic, complemented
7#23749759C211yesmaximal, characteristic
8#23749735C212yesmaximal, complemented
9#23749725C212yesmaximal, complemented
10#23749682C211yesmaximal, characteristic, complemented
11C2×C4×D4×C149C211yesmaximal, characteristic, complemented
12C2×#14558724C2212yes—
13C2×#14558721C2212yes—
14#18011905—21no—
15#18011903C2211yescharacteristic, complemented
16#18011899C2211yescharacteristic, complemented
17#18011894—21no—
18#18011890C2211yescharacteristic
19#18011885C2211yescharacteristic
20C4×Dic298C2211yescharacteristic, complemented
21C4×D596C2211yescharacteristic, complemented
22C4×C22⋊D149—21no—
23#18011868—21no—
24#18011844C2212yescomplemented
25#18011842C2212yescomplemented
26C4⋊#11924746C2212yescomplemented
27#18011834C2212yescomplemented
28#18011832C2212yes—
29#18011832C2212yes—
30#18011831C2212yescomplemented
31C22⋊#11924746C2211yescharacteristic
32C22⋊#11924746C2211yescharacteristic
33#18011822C2212yescomplemented
34C22×D4×C149C2211yescharacteristic
35C23×C4×C149—21no—
36C4×D4×C149—21no—
37C4×D4×C149—21no—
38C4×D4×C149C2212yes—
39C4×D4×C149C2212yes—
40C2×C4⋊C4×C149C2211yescharacteristic
41C2×C22⋊C4×C149—21no—
42C2×C42×C149C2211yescharacteristic
43C2×Dic298C2311yescharacteristic
44C2×D596C2311yescharacteristic
45C2×C22⋊D149—21no—
46C2×C4×D149—21no—
47#14558724—24no—
48#14558721—24no—
49C2×#11924746C2312yes—
50C2×#11924746C2312yes—
51C4⋊Dic149C2311yescharacteristic
52C4⋊Dic149C2311yescharacteristic
53#14558715—21no—
54#14558715—21no—
55#14558715—21no—
56#14558715—21no—
57C22⋊Dic149—21no—
58#14558713—21no—
59#14558713—21no—
60#14558713—21no—
61#14558713—21no—
62C4×Dic149—21no—
63C24×C149—21no—
64C2×D4×C149—24no—
65C2×D4×C149—21no—
66C2×D4×C149C2312yes—
67C22×C4×C149—21no—
68C22×C4×C149—22no—
69C22×C4×C149—22no—
70C22×C4×C149—44no—
71C22×C4×C149D411yescharacteristic
72C22×C4×C149D411yescharacteristic
73C22×C4×C149C2311yescharacteristic
74C4⋊C4×C149—21no—
75C4⋊C4×C149C2312yes—
76C22⋊C4×C149—22no—
77C22⋊C4×C149—22no—
78C42×C149D411yescharacteristic
79C42×C149D411yescharacteristic
80C42×C149C2311yescharacteristic
81C42×C149C2311yescharacteristic
82C22×D149—21no—
83Dic298—22no—
84D596—22no—
85C22⋊D149—42no—
86C2×Dic149—21no—
87C2×Dic149—21no—
88C2×Dic149—21no—
89C4×D149—42no—
90#11924746—22no—
91#11924746—22no—
92C23×C149—24no—
93C23×C149—22no—
94C23×C149—42no—
95C23×C149—42no—
96C23×C149C2×D411yescharacteristic
97D4×C149—24no—
98D4×C149—22no—
99D4×C149#4114yes—
100C2×C4×C149—22no—
101C2×C4×C149—22no—
102C2×C4×C149—22no—
103C2×C4×C149—41no—
104C2×C4×C149—44no—
105C2×C4×C149—44no—
106C2×C4×C149—42no—
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2×D411yescharacteristic
112C2×C4×C149C2411yescharacteristic
113C22×C149—21no—
114C22×C149—21no—
115C22×C149—24no—
116C22×C149—48no—
117C22×C149—42no—
118C22×C149—42no—
119C22×C149AGL(1,ℤ/8)12yes—
120C22×C149C22×D411yescharacteristic
121C2×D149—41no—
122C2×D149—41no—
123C2×D149—41no—
124C4×C149—21no—
125C4×C149—21no—
126C4×C149—21no—
127C4×C149—21no—
128C4×C149—21no—
129C4×C149—42no—
130C4×C149C2×#4112yes—
131Dic149—41no—
132Dic149—41no—
133Dic149—41no—
134C2×C149—22no—
135C2×C149—44no—
136C2×C149#52511yescharacteristic
137C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C149#57511yescharacteristic
139D149—81no—
140C149#311411yescharacteristic, complemented, Sylow
141#3114—1491nomaximal, Sylow
142#529—1491no—
143C2×C4×D4D14911yescharacteristic, complemented
144#483—1491no—
145#480—1491no—
146#478—1492no—
147#463—1492no—
148#450—1491no—
149#447—1491no—
150#442—1492no—
151#440—1492no—
152#432—1491no—
153C22×D4C2×D14911yescharacteristic
154C23×C4—21no—
155C2×SD16—1492no—
156C2×D8—1492no—
157#126—2981no—
158#125—1491no—
159#124—1491no—
160#123—2981no—
161C22⋊Q8—1491no—
162#121—1491no—
163C4×Q8—1491no—
164C4×D4—21no—
165C4×D4—21no—
166C4×D4—2981no—
167C4×D4—1491no—
168C4×D4C2×D14912yes—
169C4×D4C2×D14912yes—
170#117—2981no—
171C2×C4⋊C4C2×D14911yescharacteristic
172C2×C22⋊C4—21no—
173C2×C42C2×D14911yescharacteristic
174#107—1492no—
175#106—1492no—
176C4⋊C8—1492no—
177#103—1492no—
178#102—1492no—
179#102—1492no—
180#102—1492no—
181C22⋊C8—1491no—
182C22⋊C8—1491no—
183#97—1492no—
184C24—21no—
185C2×Q8—1491no—
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—2981no—
189C2×D4—1491no—
190C2×D4C22×D14912yes—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4—2981no—
196C22×C4C22⋊D14911yescharacteristic
197C22×C4C22⋊D14911yescharacteristic
198C22×C4C22×D14911yescharacteristic
199SD16—2984no—
200D8—2984no—
201C2×C8—1492no—
202C2×C8—1492no—
203C4⋊C4—21no—
204C4⋊C4—2981no—
205C4⋊C4—2981no—
206C4⋊C4—2981no—
207C4⋊C4—2981no—
208C4⋊C4—1491no—
209C4⋊C4—1491no—
210C4⋊C4C22×D14912yes—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—2981no—
214C22⋊C4—2981no—
215C22⋊C4—2981no—
216C22⋊C4—2981no—
217C22⋊C4—2981no—
218C42—2981no—
219C42C22⋊D14911yescharacteristic
220C42C22⋊D14911yescharacteristic
221C42C22×D14911yescharacteristic
222C42C22×D14911yescharacteristic
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—2981no—
228C23C2×C22⋊D14911yescharacteristic
229Q8—2982no—
230D4—24no—
231D4—22no—
232D4—2982no—
233D4—5962no—
234D4#1455873614yes—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—2981no—
243C2×C4—2981no—
244C2×C4—2981no—
245C2×C4—5962no—
246C2×C4C2×C22⋊D14911yescharacteristic
247C2×C4C2×C22⋊D14911yescharacteristic
248C2×C4C2×C22⋊D14911yescharacteristic
249C2×C4C2×C22⋊D14911yescharacteristic
250C2×C4C2×C22⋊D14911yescharacteristic
251C2×C4C23×D14911yescharacteristic
252C8—2982no—
253C8—2982no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—5961no—
261C22—5961no—
262C22—5961no—
263C22#1801193712yes—
264C22C22×C22⋊D14911yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—5961no—
272C4—5961no—
273C4—5961no—
274C4C2×#1455873612yes—
275C2—22no—
276C2—44no—
277C2—11921no—
278C2#2375013611yescharacteristic
279C2C2×#1801193711yescharacteristic
280C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×C4×D4×C149C2
socleC22×C149C22×D4
prime radical#23749759C2
hypercenterC2×C4×D4D149
hypocenterC149#3114
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #23750159C2semidirect
2. #23749955C2semidirect
3. #23749938C2semidirect
4. #23749925C2semidirect
5. #23749840C2semidirect
6. #23749776C2semidirect
8. #23749735C2semidirect
9. #23749725C2semidirect
10. #23749682C2semidirect
11. C2×C4×D4×C149C2semidirect
15. #18011903C22semidirect
16. #18011899C22semidirect
20. C4×Dic298C22semidirect
21. C4×D596C22semidirect
24. #18011844C22semidirect
25. #18011842C22semidirect
26. C4⋊#11924746C22semidirect
27. #18011834C22semidirect
30. #18011831C22semidirect
33. #18011822C22semidirect
140. C149#3114semidirect
143. C2×C4×D4D149semidirect

Maximal subgroups

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

subgroupindex
#237501592
#237499552
#237499382
#237499252
#237498402
#237497762
#237497592
#237497352
#237497252
#237496822
C2×C4×D4×C1492
#3114149