Finite Group Databasebeta

← #34057833

Subgroups — #34057833

Order 19072.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#23750438C211yesmaximal, characteristic, complemented
2#23750426C211yesmaximal, characteristic, complemented
3#23750066C211yesmaximal, characteristic, complemented
4#23750064C212yesmaximal, complemented
5#23750062C212yesmaximal, complemented
6#23750061C211yesmaximal, characteristic, complemented
7#23750057C211yesmaximal, characteristic, complemented
8#23750056C212yesmaximal, complemented
9SD32×D149C212yesmaximal, complemented
10#23750041C211yesmaximal, characteristic, complemented
11C2×SD32×C149C211yesmaximal, characteristic, complemented
12#18011959—21no—
13#18011956—21no—
14#18011943—22no—
15#18011942—21no—
16#18011937—21no—
17#18011935—22no—
18#18011934C2212yescomplemented
19#18011933C2211yescharacteristic
20#18011933C2211yescharacteristic, complemented
21#18011930C2212yes—
22Q16×D149C2212yescomplemented
23D8×D149C2212yes—
24#18011917C2211yescharacteristic
25Dic1192C2211yescharacteristic, complemented
26#18011857C2212yescomplemented
27#18011856C2211yescharacteristic, complemented
28#18011856C2211yescharacteristic, complemented
29#18011855C2212yescomplemented
30#18011854C2212yescomplemented
31D2384C2211yescharacteristic, complemented
32#18011852C2212yescomplemented
33#18011851C2211yescharacteristic, complemented
34#18011850C2212yescomplemented
35C16×D149C2212yescomplemented
36C2×Q16×C149C2211yescharacteristic, complemented
37C2×D8×C149C2211yescharacteristic
38SD32×C149C2212yescomplemented
39SD32×C149C2212yescomplemented
40C2×C16×C149C2211yescharacteristic, complemented
41#14558737—22no—
42#14558737—41no—
43#14558736—21no—
44#14558736—21no—
45#14558736—42no—
46#14558736D411yescharacteristic
47#14558735—22no—
48#14558735—41no—
49Q8×D149—22no—
50Q8×D149—41no—
51C2×C22⋊D149—42no—
52D4×D149—22no—
53D4×D149—41no—
54Dic596C2311yescharacteristic
55Dic596C2311yescharacteristic
56#14558726—22no—
57#14558725—21no—
58#14558725—21no—
59#14558724—22no—
60#14558723—22no—
61D1192C2311yescharacteristic
62D1192C2311yescharacteristic
63#14558721—22no—
64#14558720D411yescharacteristic
65#14558719D412yes—
66C8×D149C2312yes—
67#14558711C2312yes—
68C2×Q8×C149—21no—
69C2×D4×C149—21no—
70Q16×C149—21no—
71Q16×C149C2312yes—
72D8×C149—21no—
73D8×C149C2312yes—
74C2×C8×C149C2311yescharacteristic
75C16×C149C2311yescharacteristic
76C16×C149C2311yescharacteristic
77C22×D149—42no—
78Dic298—21no—
79Dic298—21no—
80Dic298—42no—
81Dic298D811yescharacteristic
82D596—21no—
83D596—21no—
84D596—42no—
85D596D811yescharacteristic
86C22⋊D149—41no—
87C22⋊D149—41no—
88C22⋊D149—42no—
89C22⋊D149—42no—
90C22⋊D149D812yes—
91C2×Dic149—42no—
92C4×D149—42no—
93C4×D149—41no—
94C4×D149—41no—
95C4×D149—42no—
96C4×D149C2×D412yes—
97#11924746C2×D412yes—
98C23×C149—41no—
99Q8×C149—22no—
100Q8×C149—41no—
101D4×C149—22no—
102D4×C149—41no—
103C2×C4×C149—41no—
104C2×C4×C149C2×D411yescharacteristic
105C8×C149C2×D411yescharacteristic
106C8×C149C2411yescharacteristic
107C22×C149—42no—
108C22×C149—161no—
109C22×C149C2×D811yescharacteristic
110C2×D149—41no—
111C2×D149—41no—
112C2×D149—162no—
113C2×D149C2×D812yes—
114C4×C149—42no—
115C4×C149C2×D811yescharacteristic
116C4×C149C22×D411yescharacteristic
117Dic149—41no—
118Dic149—41no—
119Dic149C2×D812yes—
120C2×C149—21no—
121C2×C149—82no—
122C2×C149C22×D811yescharacteristic
123D149—22no—
124D149—81no—
125D149—81no—
126C149#341611yescharacteristic, complemented, Sylow
127#3416—1491nomaximal, Sylow
128#578—1491no—
129#576—1491no—
130#510—1491no—
131#510—1492no—
132#509—1491no—
133#509—1492no—
134#508—1492no—
135#508—1491no—
136C2×SD32—1492no—
137C2×SD32D14911yescharacteristic, complemented
138#504—1491no—
1392−1+4—2981no—
140H(5,𝔽2)—2981no—
141#137—2982no—
142#137—2981no—
143AGL(1,ℤ/8)—2982no—
144AGL(1,ℤ/8)—2981no—
145#135—1492no—
146#135—1492no—
147#135—1491no—
148#135—1491no—
149C2×Q16—1492no—
150C2×Q16C2×D14911yescharacteristic, complemented
151C2×D8—1492no—
152C2×D8C2×D14911yescharacteristic
153#131—1491no—
154Q32—1492no—
155Q32—1491no—
156SD32—1492no—
157SD32—1492no—
158SD32—1491no—
159SD32—1491no—
160SD32C2×D14912yescomplemented
161SD32C2×D14912yescomplemented
162D16—1492no—
163D16—1491no—
164M32—1491no—
165M32—1492no—
166C2×C16—1492no—
167C2×C16C2×D14911yescharacteristic, complemented
168#41—2982no—
169#41—2982no—
170#41—2981no—
171#41—2981no—
172#41—5962no—
173#41—5961no—
174#41—5961no—
175#41—1491no—
176C2×Q8—21no—
177C2×Q8—2982no—
178C2×Q8—5961no—
179C2×D4—21no—
180C2×D4—2982no—
181C2×D4—5961no—
182C2×D4—5962no—
183Q16—21no—
184Q16—2982no—
185Q16—1491no—
186Q16—1491no—
187Q16C22×D14912yes—
188SD16—2982no—
189SD16—2982no—
190SD16—2981no—
191SD16—2981no—
192D8—21no—
193D8—2982no—
194D8—1491no—
195D8—1491no—
196D8C22×D14912yes—
197M16—1491no—
198M16—1492no—
199C2×C8—1492no—
200C2×C8C22×D14911yescharacteristic
201C16—1492no—
202C16C22×D14911yescharacteristic
203C16C22×D14911yescharacteristic
204C23—41no—
205C23—5962no—
206Q8—22no—
207Q8—41no—
208Q8—2981no—
209Q8—2981no—
210Q8—5962no—
211Q8—1491no—
212D4—22no—
213D4—41no—
214D4—2981no—
215D4—2981no—
216D4—5962no—
217D4—5962no—
218D4—5961no—
219D4—5961no—
220D4—5962no—
221D4—1492no—
222D4—1491no—
223C2×C4—41no—
224C2×C4—5962no—
225C2×C4—5962no—
226C2×C4—5962no—
227C2×C4—5961no—
228C2×C4—5961no—
229C2×C4—1492no—
230C2×C4D4×D14911yescharacteristic
231C8—1492no—
232C8D4×D14911yescharacteristic
233C8C23×D14911yescharacteristic
234C22—42no—
235C22—161no—
236C22—23842no—
237C22—5961no—
238C22—5961no—
239C22—1492no—
240C22D8×D14911yescharacteristic
241C4—42no—
242C4—5961no—
243C4—5961no—
244C4—1492no—
245C4D8×D14911yescharacteristic
246C4C2×D4×D14911yescharacteristic
247C2—21no—
248C2—82no—
249C2—2982no—
250C2—11921no—
251C2—11921no—
252C2C2×D8×D14911yescharacteristic
subgroupG/H
centerC2C2×D8×D149
commutator, cosocleC8×C149C24
FrattiniC8C23×D149
FittingC2×SD32×C149C2
socleC2×C149C22×D8
hypercenterC2×SD32D149
hypocenterC149#3416
LCSG ▷ C8×C149 ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #23750438C2semidirect
2. #23750426C2semidirect
3. #23750066C2semidirect
4. #23750064C2semidirect
5. #23750062C2semidirect
6. #23750061C2semidirect
7. #23750057C2semidirect
8. #23750056C2semidirect
9. SD32×D149C2semidirect
10. #23750041C2semidirect
11. C2×SD32×C149C2semidirect
18. #18011934C22semidirect
20. #18011933C22semidirect
22. Q16×D149C22semidirect
25. Dic1192C22semidirect
26. #18011857C22semidirect
27. #18011856C22semidirect
28. #18011856C22semidirect
29. #18011855C22semidirect
30. #18011854C22semidirect
31. D2384C22semidirect
32. #18011852C22semidirect
33. #18011851C22semidirect
34. #18011850C22semidirect
35. C16×D149C22semidirect
36. C2×Q16×C149C22semidirect
38. SD32×C149C22semidirect
39. SD32×C149C22semidirect
40. C2×C16×C149C22semidirect
126. C149#3416semidirect
137. C2×SD32D149semidirect
150. C2×Q16C2×D149semidirect
160. SD32C2×D149semidirect
161. SD32C2×D149semidirect
167. C2×C16C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504382
#237504262
#237500662
#237500642
#237500622
#237500612
#237500572
#237500562
SD32×D1492
#237500412
C2×SD32×C1492
#3416149