Finite Group Databasebeta

← #34056621

Subgroups — #34056621

Order 19072.

398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750340C211yesmaximal, characteristic, complemented
2#23750279C211yesmaximal, characteristic, complemented
3#23749976C211yesmaximal, characteristic, complemented
4#23749968C212yesmaximal, complemented
5#23749915C211yesmaximal, characteristic, complemented
6#23749853C212yesmaximal, complemented
7#23749830C211yesmaximal, characteristic, complemented
8#23749767C212yesmaximal, complemented
9C8×D596C211yesmaximal, characteristic, complemented
10#23749618C212yesmaximal, complemented
11C4×D8×C149C211yesmaximal, characteristic, complemented
12C2×#14558735C2212yes—
13C2×#14558724C2212yes—
14C2×C8×D149C2212yes—
15#18011911C2211yescharacteristic
16#18011911C2211yescharacteristic
17#18011897—22no—
18#18011895—22no—
19#18011891C2212yes—
20#18011885—21no—
21#18011885—21no—
22#18011882C2212yes—
23C4×D596C2211yescharacteristic
24#18011870—21no—
25#18011869C2212yes—
26C2×C4⋊Dic149—21no—
27#18011842C2212yes—
28C4⋊#11924746C2211yescharacteristic
29#18011836C2212yes—
30#18011836C2212yes—
31#18011834C2212yes—
32#18011832C2212yes—
33#18011823C2212yes—
34C2×D8×C149C2211yescharacteristic
35C4×D4×C149C2211yescharacteristic
36C4×D4×C149C2211yescharacteristic
37#107×C149C2211yescharacteristic
38#102×C149C2211yescharacteristic
39#102×C149C2211yescharacteristic
40C4×C8×C149C2211yescharacteristic
41#14558735—24no—
42#14558735—42no—
43C2×Dic298—21no—
44C2×Dic298C2312yes—
45C2×D596D411yescharacteristic
46C2×C22⋊D149—22no—
47C2×C22⋊D149—22no—
48C22×Dic149—22no—
49C2×C4×D149C2312yes—
50#14558724—42no—
51C2×#11924746C2312yes—
52C8×D149—42no—
53C4⋊Dic149—22no—
54C4⋊Dic149—21no—
55C4⋊Dic149—21no—
56C4⋊Dic149—21no—
57C4⋊Dic149D411yescharacteristic
58C4⋊Dic149C2312yes—
59C22⋊Dic149—22no—
60#14558713—22no—
61#14558713—22no—
62#14558713D412yes—
63C4×Dic149—22no—
64C2×D4×C149C2311yescharacteristic
65C2×D4×C149C2311yescharacteristic
66C22×C4×C149—21no—
67C22×C4×C149—21no—
68D8×C149—22no—
69C2×C8×C149C2311yescharacteristic
70C2×C8×C149C2311yescharacteristic
71C4⋊C4×C149C2311yescharacteristic
72C4⋊C4×C149C2311yescharacteristic
73C22⋊C4×C149—21no—
74C22⋊C4×C149—21no—
75C42×C149C2311yescharacteristic
76C22×D149C2×D412yes—
77Dic298—22no—
78Dic298—22no—
79Dic298—81no—
80D596—22no—
81C22⋊D149—44no—
82C22⋊D149—82no—
83C2×Dic149—22no—
84C2×Dic149—22no—
85C2×Dic149—44no—
86C2×Dic149C2×D412yes—
87C4×D149—22no—
88C4×D149—22no—
89#11924746—22no—
90C23×C149—21no—
91C23×C149—21no—
92D4×C149—21no—
93D4×C149—21no—
94D4×C149—21no—
95D4×C149#4112yes—
96C2×C4×C149—21no—
97C2×C4×C149—21no—
98C2×C4×C149—42no—
99C2×C4×C149—42no—
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2411yescharacteristic
103C8×C149—21no—
104C8×C149—21no—
105C22×C149—22no—
106C22×C149—41no—
107C22×C149—41no—
108C22×C149—41no—
109C22×C149—41no—
110C22×C149—41no—
111C22×C149C22×D411yescharacteristic
112C2×D149—22no—
113C2×D149—22no—
114C2×D149—22no—
115C4×C149—21no—
116C4×C149—41no—
117C4×C149—41no—
118C4×C149#13512yes—
119C4×C149C2×#4111yescharacteristic
120C4×C149H(5,𝔽2)11yescharacteristic
121Dic149—22no—
122Dic149—42no—
123Dic149—42no—
124C2×C149—42no—
125C2×C149—81no—
126C2×C149#54611yescharacteristic
127C2×C149C2×#13511yescharacteristic
128C2×C149#57711yescharacteristic
129D149—42no—
130C149#330311yescharacteristic, complemented, Sylow
131#3303—1491nomaximal, Sylow
132#555—1491no—
133#547—1491no—
134#487—1491no—
135#485—1492no—
136#476—1491no—
137#465—1492no—
138#461—1491no—
139#449—1492no—
140C4×D8D14911yescharacteristic, complemented
141C8×D4—1491no—
142#416—1492no—
143C2×#41—1492no—
144C2×SD16—1492no—
145C2×D8C2×D14911yescharacteristic
146C22×C8—1492no—
147C4⋊Q8—1491no—
148C4⋊Q8—1491no—
149#124—2982no—
150#123—2982no—
151C22⋊Q8—1492no—
152#121—2981no—
153#121—2981no—
154#121—1492no—
155C4×D4—1491no—
156C4×D4C2×D14911yescharacteristic
157C4×D4C2×D14911yescharacteristic
158#117—2981no—
159#117—1492no—
160C2×C4⋊C4—2981no—
161#107C2×D14911yescharacteristic
162#106—1492no—
163C4⋊C8—1491no—
164#103—1492no—
165#103—1492no—
166#103—1492no—
167#102—1492no—
168#102C2×D14911yescharacteristic
169#102C2×D14911yescharacteristic
170C22⋊C8—1492no—
171C4×C8C2×D14911yescharacteristic
172#41—2984no—
173#41—5962no—
174C2×Q8—2981no—
175C2×Q8—1492no—
176C2×D4—2982no—
177C2×D4—2982no—
178C2×D4—1491no—
179C2×D4C22×D14911yescharacteristic
180C2×D4C22×D14911yescharacteristic
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—2982no—
184C22×C4—1492no—
185SD16—5962no—
186D8—22no—
187C2×C8—5962no—
188C2×C8—1492no—
189C2×C8C22×D14911yescharacteristic
190C2×C8C22×D14911yescharacteristic
191C4⋊C4—2982no—
192C4⋊C4—2981no—
193C4⋊C4—2981no—
194C4⋊C4—2981no—
195C4⋊C4—1492no—
196C4⋊C4—1491no—
197C4⋊C4C22×D14911yescharacteristic
198C4⋊C4C22×D14911yescharacteristic
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—2982no—
202C22⋊C4—2982no—
203C22⋊C4—2982no—
204C22⋊C4—1492no—
205C42—2982no—
206C42C22×D14911yescharacteristic
207C23—21no—
208C23—21no—
209C23—1492no—
210Q8—2982no—
211Q8—2982no—
212Q8—11921no—
213D4—21no—
214D4—21no—
215D4—21no—
216D4—2982no—
217D4—5964no—
218D4—11922no—
219D4#1455873612yes—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—2982no—
225C2×C4—2982no—
226C2×C4—2982no—
227C2×C4—2982no—
228C2×C4—5964no—
229C2×C4—1492no—
230C2×C4D4×D14911yescharacteristic
231C2×C4D4×D14911yescharacteristic
232C2×C4C23×D14911yescharacteristic
233C8—21no—
234C8—21no—
235C8—2982no—
236C22—22no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—2982no—
243C22—2982no—
244C22—2982no—
245C22C2×D4×D14911yescharacteristic
246C4—21no—
247C4—41no—
248C4—41no—
249C4—2982no—
250C4—5962no—
251C4—5962no—
252C4#1801193012yes—
253C4C2×#1455873611yescharacteristic
254C4#1801195711yescharacteristic
255C2—42no—
256C2—81no—
257C2—5962no—
258C2#2375027111yescharacteristic
259C2C2×#1801193011yescharacteristic
260C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×D8×C149C2
socleC22×C149C22×D4
hypercenterC4×D8D149
hypocenterC149#3303
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23750340C2semidirect
2. #23750279C2semidirect
3. #23749976C2semidirect
4. #23749968C2semidirect
5. #23749915C2semidirect
6. #23749853C2semidirect
7. #23749830C2semidirect
8. #23749767C2semidirect
9. C8×D596C2semidirect
10. #23749618C2semidirect
11. C4×D8×C149C2semidirect
130. C149#3303semidirect
140. C4×D8D149semidirect

Maximal subgroups

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

subgroupindex
#237503402
#237502792
#237499762
#237499682
#237499152
#237498532
#237498302
#237497672
C8×D5962
#237496182
C4×D8×C1492
#3303149