Finite Group Databasebeta

← #34055610

Subgroups — #34055610

Order 19072.

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

normal subgroups only

This group has 532 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#23750176C211yesmaximal, characteristic, complemented
2#127×D149C211yesmaximal, characteristic, complemented
3#23750002C211yesmaximal, characteristic, complemented
4#23750001C211yesmaximal, characteristic, complemented
5#23749973C211yesmaximal, characteristic, complemented
6#23749819C214yesmaximal, complemented
7#23749760C214yesmaximal, complemented
8#23749676C211yesmaximal, characteristic, complemented
9#486×C149C211yesmaximal, characteristic, complemented
10C2×#14558737—21no—
11C2×D4×D149—21no—
12C2×D4×D149—21no—
13C2×D4×D149C2212yes—
14C2×D1192C2214yescomplemented
15C2×#14558721C2214yescomplemented
16#18011908C2211yescharacteristic
17#18011908C2211yescharacteristic, complemented
18#18011907—21no—
19#18011907—21no—
20#18011907C2212yes—
21#18011900—21no—
22#18011886—21no—
23#18011886C2212yes—
24#18011873—21no—
25#18011873C2212yescomplemented
26C42×D149C2211yescharacteristic
27#18011840C2212yescomplemented
28#18011831C2214yescomplemented
29#18011823C2212yes—
30C4×#11924746C2211yescharacteristic, complemented
31C4⋊Q8×C149C2211yescharacteristic, complemented
32#127×C149C2211yescharacteristic
33#102×C149C2214yescomplemented
34C4×C8×C149C2211yescharacteristic, complemented
35C23×D149—22no—
36#14558737—44no—
37C2×D596—22no—
38C2×D596—21no—
39C2×D596—21no—
40C2×D596—21no—
41C2×D596—21no—
42C2×D596C2312yes—
43C2×D596C2312yes—
44C2×C22⋊D149—22no—
45C2×C22⋊D149—22no—
46C2×C22⋊D149—22no—
47D4×D149—44no—
48D4×D149—44no—
49D4×D149—44no—
50C2×C4×D149—22no—
51C2×C4×D149D411yescharacteristic
52C2×C4×D149D411yescharacteristic
53C2×C4×D149C2311yescharacteristic
54D1192—44no—
55#14558721—44no—
56C2×#11924746C2312yes—
57#14558713—22no—
58#14558713—22no—
59C4×Dic149D411yescharacteristic
60C4×Dic149D411yescharacteristic
61C4×Dic149C2311yescharacteristic
62C2×Q8×C149—21no—
63C2×D4×C149—21no—
64C2×D4×C149—21no—
65C2×D4×C149C2312yes—
66C2×C8×C149C2312yes—
67C4⋊C4×C149—21no—
68C4⋊C4×C149C2312yes—
69C42×C149C2311yescharacteristic
70C22×D149—22no—
71C22×D149—22no—
72C22×D149—44no—
73C22×D149—44no—
74C22×D149—44no—
75C22×D149C2×D411yescharacteristic
76D596—24no—
77D596—24no—
78D596—44no—
79D596—42no—
80D596—42no—
81D596—42no—
82D596—42no—
83C22⋊D149—44no—
84C22⋊D149—44no—
85C22⋊D149—44no—
86C2×Dic149C2×D411yescharacteristic
87C2×Dic149C2×D411yescharacteristic
88C2×Dic149C2×D411yescharacteristic
89C4×D149—22no—
90C4×D149—22no—
91C4×D149—44no—
92C4×D149D814yescomplemented
93#11924746—22no—
94C23×C149—22no—
95Q8×C149—42no—
96D4×C149—24no—
97D4×C149—42no—
98D4×C149—42no—
99C2×C4×C149—22no—
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2411yescharacteristic
103C8×C149—22no—
104C22×C149—42no—
105C22×C149—42no—
106C22×C149—42no—
107C22×C149C22×D411yescharacteristic
108C2×D149—21no—
109C2×D149—21no—
110C2×D149—42no—
111C2×D149—42no—
112C2×D149—42no—
113C2×D149—42no—
114C2×D149—42no—
115C2×D149—42no—
116C2×D149—88no—
117C2×D149C2×D812yes—
118C4×C149—42no—
119C4×C149C2×D812yes—
120C4×C149AGL(1,ℤ/8)12yes—
121C4×C149H(5,𝔽2)12yes—
122Dic149—21no—
123Dic149—21no—
124Dic149C2×D812yes—
125C2×C149—82no—
126C2×C149#53511yescharacteristic
127C2×C149C22×D811yescharacteristic
128C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
129D149—22no—
130D149—82no—
131D149—82no—
132C149#320511yescharacteristic, complemented, Sylow
133#3205—1491nomaximal, Sylow
134#532—1491no—
135C2×#127—1491no—
136#493—1491no—
137#493—1491no—
138#486—1491no—
139#486D14911yescharacteristic, complemented
140#459—1494no—
141#447—1494no—
142#431—1491no—
143C2×#41—2981no—
144C22×D4—2981no—
145C22×D4—2981no—
146C22×D4—1492no—
147C2×D8—1494no—
148C2×D8—1494no—
149C4⋊Q8C2×D14911yescharacteristic, complemented
150#127—2981no—
151#127—2981no—
152#127—1492no—
153#127—1491no—
154#127—1491no—
155#127C2×D14911yescharacteristic
156#124—2981no—
157#121—2981no—
158#121—1492no—
159C4×D4—2981no—
160C4×D4—1492no—
161C2×C42—1491no—
162C4⋊C8—1492no—
163#102—1494no—
164#102C2×D14914yescomplemented
165C22⋊C8—1492no—
166C4×C8—1491no—
167C4×C8C2×D14911yescharacteristic, complemented
168C24—2982no—
169#41—5964no—
170C2×Q8—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—2982no—
174C2×D4—2982no—
175C2×D4—2982no—
176C2×D4—2982no—
177C2×D4—2981no—
178C2×D4—2981no—
179C2×D4—2981no—
180C2×D4—2981no—
181C2×D4—5964no—
182C2×D4—5964no—
183C2×D4—5964no—
184C2×D4—1492no—
185C2×D4—1492no—
186C2×D4C22×D14912yes—
187C22×C4—2982no—
188C22×C4—1491no—
189C22×C4—1491no—
190C22×C4—1491no—
191D8—5964no—
192D8—5964no—
193C2×C8—1492no—
194C2×C8C22×D14912yes—
195C4⋊C4—21no—
196C4⋊C4C22×D14912yes—
197C22⋊C4—2982no—
198C22⋊C4—2982no—
199C42—1491no—
200C42—1491no—
201C42—1491no—
202C42C22×D14911yescharacteristic
203C23—22no—
204C23—2982no—
205C23—2982no—
206C23—5964no—
207C23—5964no—
208C23—5964no—
209C23—1491no—
210Q8—42no—
211D4—24no—
212D4—42no—
213D4—42no—
214D4—2984no—
215D4—2984no—
216D4—5964no—
217D4—5964no—
218D4—5964no—
219D4—5964no—
220D4—5962no—
221D4—5962no—
222D4—5962no—
223D4—5962no—
224C2×C4—22no—
225C2×C4—2982no—
226C2×C4—2982no—
227C2×C4—5964no—
228C2×C4—1491no—
229C2×C4—1491no—
230C2×C4—1491no—
231C2×C4—1494no—
232C2×C4D4×D14911yescharacteristic
233C2×C4D4×D14911yescharacteristic
234C2×C4C23×D14911yescharacteristic
235C8—22no—
236C8—2982no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—2981no—
241C22—2981no—
242C22—5962no—
243C22—5962no—
244C22—5962no—
245C22—5962no—
246C22—5962no—
247C22—5962no—
248C22—1492no—
249C22—11928no—
250C22C2×D4×D14911yescharacteristic
251C4—42no—
252C4—2981no—
253C4—2981no—
254C4—1492no—
255C4D8×D14912yes—
256C4#1801193812yes—
257C4#1801195712yes—
258C2—82no—
259C2—2982no—
260C2—11922no—
261C2—11922no—
262C2#2375019311yescharacteristic
263C2C2×D8×D14911yescharacteristic
264C2C2×#1801193811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#486×C149C2
socleC22×C149C22×D4
hypercenter#486D149
hypocenterC149#3205
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #23750176C2semidirect
2. #127×D149C2semidirect
3. #23750002C2semidirect
4. #23750001C2semidirect
5. #23749973C2semidirect
6. #23749819C2semidirect
7. #23749760C2semidirect
8. #23749676C2semidirect
9. #486×C149C2semidirect
14. C2×D1192C22semidirect
15. C2×#14558721C22semidirect
17. #18011908C22semidirect
25. #18011873C22semidirect
27. #18011840C22semidirect
28. #18011831C22semidirect
30. C4×#11924746C22semidirect
31. C4⋊Q8×C149C22semidirect
33. #102×C149C22semidirect
34. C4×C8×C149C22semidirect
92. C4×D149D8semidirect
132. C149#3205semidirect
139. #486D149semidirect
149. C4⋊Q8C2×D149semidirect
164. #102C2×D149semidirect
167. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501762
#127×D1492
#237500022
#237500012
#237499732
#237498192
#237497602
#237496762
#486×C1492
#3205149